From 39242c0884b0305935b3907e3f234ace755c1137 Mon Sep 17 00:00:00 2001 From: johntiger1 Date: Mon, 19 Mar 2018 23:26:54 -0400 Subject: [PATCH 01/17] remove idea settings from version control --- .idea/markdown-navigator.xml | 72 -- .../markdown-navigator/profiles_settings.xml | 3 - .idea/modules.xml | 8 - .idea/rucs-uoft.github.io.iml | 8 - .idea/vcs.xml | 6 - .idea/workspace.xml | 1027 ----------------- 6 files changed, 1124 deletions(-) delete mode 100644 .idea/markdown-navigator.xml delete mode 100644 .idea/markdown-navigator/profiles_settings.xml delete mode 100644 .idea/modules.xml delete mode 100644 .idea/rucs-uoft.github.io.iml delete mode 100644 .idea/vcs.xml delete mode 100644 .idea/workspace.xml diff --git a/.idea/markdown-navigator.xml b/.idea/markdown-navigator.xml deleted file mode 100644 index e41dd85..0000000 --- a/.idea/markdown-navigator.xml +++ /dev/null @@ -1,72 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - \ No newline at end of file diff --git a/.idea/markdown-navigator/profiles_settings.xml b/.idea/markdown-navigator/profiles_settings.xml deleted file mode 100644 index 9c51dfe..0000000 --- a/.idea/markdown-navigator/profiles_settings.xml +++ /dev/null @@ -1,3 +0,0 @@ - - - \ No newline at end of file diff --git a/.idea/modules.xml b/.idea/modules.xml deleted file mode 100644 index 141f5d4..0000000 --- a/.idea/modules.xml +++ /dev/null @@ -1,8 +0,0 @@ - - - - - - - - \ No newline at end of file diff --git a/.idea/rucs-uoft.github.io.iml b/.idea/rucs-uoft.github.io.iml deleted file mode 100644 index c956989..0000000 --- a/.idea/rucs-uoft.github.io.iml +++ /dev/null @@ -1,8 +0,0 @@ - - - - - - - - \ No newline at end of file diff --git a/.idea/vcs.xml b/.idea/vcs.xml deleted file mode 100644 index 94a25f7..0000000 --- a/.idea/vcs.xml +++ /dev/null @@ -1,6 +0,0 @@ - - - - - - \ No newline at end of file diff --git a/.idea/workspace.xml b/.idea/workspace.xml deleted file mode 100644 index d7a2a12..0000000 --- a/.idea/workspace.xml +++ /dev/null @@ -1,1027 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - true - DEFINITION_ORDER - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - project - - - - - - - - - - - - - - - - project - - - true - - bdd - - DIRECTORY - - false - - - - - - - - - - - - 1501553913910 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - \ No newline at end of file From cd3944c900a4cd729a523e35a68625b689e0266e Mon Sep 17 00:00:00 2001 From: johntiger1 Date: Mon, 19 Mar 2018 23:41:54 -0400 Subject: [PATCH 02/17] width fix for appeal/style --- _includes/table_of_contents.html | 2 +- css/style.css | 5 +++++ 2 files changed, 6 insertions(+), 1 deletion(-) diff --git a/_includes/table_of_contents.html b/_includes/table_of_contents.html index df06eaf..e209df1 100644 --- a/_includes/table_of_contents.html +++ b/_includes/table_of_contents.html @@ -12,7 +12,7 @@ {% assign chapter_titles = goodCats | sort %}
-
+
diff --git a/css/style.css b/css/style.css index bc294ba..303674d 100644 --- a/css/style.css +++ b/css/style.css @@ -8711,4 +8711,9 @@ figcaption { /*# sourceMappingURL=style.css.map */ #submit-button { padding-bottom: 100px; +} + +.row-center-fix { + + width: 80%; } \ No newline at end of file From 18c5af079f5b8a5655f1b48d0cf8d02ca31776c7 Mon Sep 17 00:00:00 2001 From: johntiger1 Date: Tue, 20 Mar 2018 23:27:28 -0400 Subject: [PATCH 03/17] remove submit button --- _includes/news.html | 4 +--- 1 file changed, 1 insertion(+), 3 deletions(-) diff --git a/_includes/news.html b/_includes/news.html index 2b7e1c7..7e55219 100644 --- a/_includes/news.html +++ b/_includes/news.html @@ -14,6 +14,4 @@

- + From 25bcd410d41e20a6f4e22b6c5b8e7e56eaea7285 Mon Sep 17 00:00:00 2001 From: johntiger1 Date: Tue, 20 Mar 2018 23:32:45 -0400 Subject: [PATCH 04/17] add submissions tab --- _includes/table_of_contents.html | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) diff --git a/_includes/table_of_contents.html b/_includes/table_of_contents.html index e209df1..b56d268 100644 --- a/_includes/table_of_contents.html +++ b/_includes/table_of_contents.html @@ -28,6 +28,10 @@
Our Team
+ +
Submissions
+
+
@@ -51,6 +55,10 @@ {% include meet-the-team.html %}
+
+ {% include submissions.html %} +
+
@@ -87,6 +95,14 @@ +
  • +
    Submissions
    +
    + + {% include submissions.html %} +
    +
  • + {% assign i = 1 %} From be22ce2bf439f1d65213d7702c7ed4f7418b504b Mon Sep 17 00:00:00 2001 From: johntiger1 Date: Tue, 20 Mar 2018 23:35:42 -0400 Subject: [PATCH 05/17] add submissions partial --- _includes/submissions.html | 1 + 1 file changed, 1 insertion(+) create mode 100644 _includes/submissions.html diff --git a/_includes/submissions.html b/_includes/submissions.html new file mode 100644 index 0000000..b6da5fb --- /dev/null +++ b/_includes/submissions.html @@ -0,0 +1 @@ +

    This is a placeholder for the submissions page

    \ No newline at end of file From a34b7140edff9e7394b55125aa5836f2e1507cd8 Mon Sep 17 00:00:00 2001 From: johntiger1 Date: Tue, 20 Mar 2018 23:39:04 -0400 Subject: [PATCH 06/17] add word wrap --- css/style.css | 1 + 1 file changed, 1 insertion(+) diff --git a/css/style.css b/css/style.css index 303674d..c179c35 100644 --- a/css/style.css +++ b/css/style.css @@ -8607,6 +8607,7 @@ figcaption { color: #8c333d; text-transform: none; font-weight: bold; + word-wrap: break-word; } .toc-enum { From 32c654d77d146b1662006d14a6ef0e6b37a4f038 Mon Sep 17 00:00:00 2001 From: Tyler Pham Date: Thu, 22 Mar 2018 19:34:22 -0400 Subject: [PATCH 07/17] 2017 background loads on all pages; added prototype for submission page --- _includes/meet-the-team.html | 2 - _includes/submissions.html | 10 +- _includes/table_of_contents.html | 1 - _posts/2017/2017-03-24-Andrew-Jemin-Choi.md | 113 ++++++++++++ _sass/style.css | 10 +- _sass/style.scss | 2 +- assets/2017/A.Choi/ac_example.pdf | Bin 0 -> 15725 bytes assets/2017/A.Choi/ac_example.png | Bin 0 -> 15635 bytes assets/2017/A.Choi/alg1.png | Bin 0 -> 717759 bytes assets/2017/A.Choi/alg2.png | Bin 0 -> 835311 bytes .../feedforward_circuits_andrewchoi.tex | 167 ++++++++++++++++++ assets/2017/A.Choi/feedforward_example.pdf | Bin 0 -> 21567 bytes assets/2017/A.Choi/feedforward_example.png | Bin 0 -> 21715 bytes css/masthead.css | 4 +- css/page/masthead.css | 10 +- css/post.css | 10 +- css/style.css | 2 +- 17 files changed, 308 insertions(+), 23 deletions(-) create mode 100644 _posts/2017/2017-03-24-Andrew-Jemin-Choi.md create mode 100644 assets/2017/A.Choi/ac_example.pdf create mode 100644 assets/2017/A.Choi/ac_example.png create mode 100644 assets/2017/A.Choi/alg1.png create mode 100644 assets/2017/A.Choi/alg2.png create mode 100644 assets/2017/A.Choi/feedforward_circuits_andrewchoi.tex create mode 100644 assets/2017/A.Choi/feedforward_example.pdf create mode 100644 assets/2017/A.Choi/feedforward_example.png diff --git a/_includes/meet-the-team.html b/_includes/meet-the-team.html index d5b51a1..105fd33 100644 --- a/_includes/meet-the-team.html +++ b/_includes/meet-the-team.html @@ -3,9 +3,7 @@

    Meet the RUCS team

    - -
    diff --git a/_includes/submissions.html b/_includes/submissions.html index b6da5fb..1baceca 100644 --- a/_includes/submissions.html +++ b/_includes/submissions.html @@ -1 +1,9 @@ -

    This is a placeholder for the submissions page

    \ No newline at end of file +
    +

    Papers

    + {% for post in site.posts %} + {% capture year %}{{post.date | date: "%Y"}}{% endcapture %} + {% if post.year == "2017" %} +

    {{post.author}} in {{post.category}} : {{post.title}}

    + {% endif %} + {% endfor %} +
    diff --git a/_includes/table_of_contents.html b/_includes/table_of_contents.html index b56d268..5dbda80 100644 --- a/_includes/table_of_contents.html +++ b/_includes/table_of_contents.html @@ -104,7 +104,6 @@ - {% assign i = 1 %} {% for chapter in chapter_titles %} {% if chapter[0] == 'profiles and interviews' %} diff --git a/_posts/2017/2017-03-24-Andrew-Jemin-Choi.md b/_posts/2017/2017-03-24-Andrew-Jemin-Choi.md new file mode 100644 index 0000000..ebeb4b6 --- /dev/null +++ b/_posts/2017/2017-03-24-Andrew-Jemin-Choi.md @@ -0,0 +1,113 @@ +--- +layout: post +title: "A Feed-Forward Algorithm for Arithmetic Circuits" +author: "Andrew Jemin Choi" +supervisors: "Professor Guy Van den Broeck" +category: "Category 1" +permalink: /a-feed-forward-algorithm-for-arithmetic-circuits +year: "2017" + +--- + +Introduction +============ + +Probabilistic queries are a foundation to many machine learning problems. We often query probabilistic models, such as Bayesian networks, to gain information about the variables in a system and make inferences about them. However, even the simplest queries in these networks, such as finding marginal probabilities of the input, come at an exponential cost. In fact, the problem of exact inference and making such queries in these probabilistic models is NP-hard [1]. + +An effective approach for making exact inferences in networks is to construct an Arithmetic Circuit (AC) from the network polynomial. The network polynomial is a linear function that outputs the probability of an event given the input parameters of the network. Although building the AC from a network takes exponential time and space, queries can be executed linearly, i.e. O(n), where n is the size of the circuit [2]. Therefore, compiling or learning ACs from networks provides an efficient alternative to making exact inferences [3]. + +The state-of-the-art method uses a software algorithm to backpropagate the marginal probabilities of the network using bit-encoding[4]. We propose a new algorithm that will calculate marginal probabilities by using feed-forward ACs. The advantage of using strictly feed-forward ACs is that the entire circuit can be built in hardware, which can drastically reduce inference time and consume significantly less power compared to software implementations. + +Background +========== + +An arithmetic circuit is a directed acyclic graph (DAG) with leaves that are variables or constants and interior nodes that are addition or multiplication operations. An arithmetic circuit can calculate the output value of a polynomial in linear size, where size is defined as the number of edges in the circuit. + + +

    + +

    + +

    Figure 1: A binary arithmetic circuit that expresses the linear polynomial: $f = (y) + (0.5(x) + 1$)

    + +By using ACs, we can calculate the partial derivatives and find the marginal +probabilities in linear size, i.e. $O(n)$ edges [2]. This process is called backpropagation +because we start calculating derivatives from the root (output) node and work our +way backwards to the leaf (input) nodes to find the partial derivatives. The state-of- +the-art uses bit-encoding backpropagation and a series of divisions in order to find +partial derivatives in one pass. We began this project in hopes of finding a way to +calculate the partial derivatives in a feed-forward network, in linear size. + +Approach +======== + +We can fundamentally calculate partial derivatives by calculating the products of +all sibling nodes of a child node, where the derivative of a child node is defined as: + +$dr(c) = dr(p) \times \pi_{c \neq c\prime} vr(c\prime) [4]$ + +This “naive” method requires $O(n^2)$ number of edges in the circuit. + +Our approach to finding marginal probabilities involves only using product nodes +in a feed-forward circuit. We achieve this by applying memoization to cache previously +computed products. By caching the products into a register to calculate partial +derivatives, backpropagation can be done in $O(n)$ edges. +This cache-based algorithm has two apparent advantages: + +1. The partial derivatives can be calculated linearly, i.e. $O(n)$ edges, regardless of +the DAG structure. The algorithm works correctly for non-alternating trees, +which is a feature absent from bit-encoded backpropagation. +2. The algorithm can be implemented into a feed-forward arithmetic circuit using +hardware. + +Figure 2 and 3 below outlines the forward pass and backward pass of the algorithm, respectively. In the forward pass, the number of child node accesses is bound by a constant (number of parent nodes). Similarly, in the backward pass, the edges needed to evaluate the derivative of a multiplication node is bounded by a constant number of operations (two products and one sum). Since every node operation is bound by a constant, we can see that the algorithm is $O(n)$. + + +

    + +

    + +

    Figure 2:Algorithm for computing circuit output and initializing the product caches

    + + +

    + +

    + +

    Figure 3:Feed-forward algorithm to calculate marginals

    + + +Analysis +======== + +We compared the performance of three algorithms, written in C, on three different data sets. For the cache-based algorithm, we generated a feed-forward arithmetic circuit and compiled the circuit into C code. Then, we measured the CPU time needed to find the marginal probability of one variable from the initialized circuit structures. + + +Test Set (nodes) | Bit-encoded (s) | Compiled-Cache (s) | Naive (s) | +|:---------------:|:--------:|:--------:|:--------:|:--------:| +**Verysimple.ac** (20) | 0.01994 | **0.00504** | 0.01921 | +**Voting.ac** (12468) [5] | 2.29930 | **0.34500** | 6.85860 +**Movie.ac** (21714) [5] | 0.84004 | **0.18353** | 1.31189 + +Table 1: CPU times (in seconds) of 10000 iterations of bit-encoded, cache, and naive algorithms. The values were averaged from 3 trials. + +The CPU times show that the compiled cache-based method is 4 to 5 times faster on simple circuit structures (verysimple.ac and movie.ac) and about 8 times faster for more complex structures (voting.ac) compared to bit-encoded backpropagation. We can attribute the improvement in performance to the simpler output circuit structure of the compiled code, and better performance in the forward pass compared to backpropagation. The cache-based algorithm was found to give correct results even for non-alternating circuits, which makes this algorithm suitable for a wider range of applications. In addition, it can be used into a hardware circuit, leading to faster and energy efficient inferences. We hope to compare the differences between a software and hardware implementation in future work. + +Conclusion +========== + +We proposed a new algorithm to find the marginal probabilities in an arithmetic circuit in linear size using a cache-based feed-forward algorithm. We found that finding the marginal probabilities by compiling the feed-forward circuit significantly reduces inference time. The algorithm can also be used for a wider range of circuits, and it can be implemented in hardware, potentially using much less resources. + + +### Acknowledgement + +I would like to thank Prof. Guy Van den Broeck for his brilliant insight and mentorship during this project. I am also grateful to his students in the StarAI Lab for their enlightening discussions during my stay at UCLA. + +### References + +1. Cooper, G. F., 1990. The computational complexity of probabilistic inference using Bayesian belief networks. Artif. Intell. 42, pp. 393-405. +2. Darwiche, A., 2003. A Differential Approach to Inference in Bayesian Networks. J. ACM 50, pp. 280-305. +3. Chavira, M. and Darwiche, A., 2005. Compiling Bayesian networks with local structure. In Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI), pp. 13061312. +4. Darwiche, A., 2009. Modeling and Reasoning with Bayesian Networks. Cambridge University Press, Chapter 12. +5. Bekker, J., Davis, J., Choi, A., Darwiche, A., and Van den Broeck, G., 2015. Tractable Learning for Complex Probability Queries. Advances in Neural Information Processing Systems 28 (NIPS). + diff --git a/_sass/style.css b/_sass/style.css index c79c39c..b6c2f98 100644 --- a/_sass/style.css +++ b/_sass/style.css @@ -8397,7 +8397,7 @@ figcaption { border-left: 4px solid #67373f !important; } .header-background { - background: url("../resources/backgroundweb2016.svg"); + background: url("../resources/backgroundweb2017.png"); background-position: center; } .review-subtitle { @@ -8409,7 +8409,7 @@ figcaption { padding: 0 !important; } .page-footer { - background: url("../resources/backgroundweb2016.svg"); + background: url("../resources/backgroundweb2017.png"); margin: 0px !important; min-height: 100px; padding: 30px 0 30px 0 !important; } @@ -8430,7 +8430,7 @@ figcaption { .background { height: 100vh; - background: url("../resources/backgroundweb2016.svg"); + background: url("../resources/backgroundweb2017.png"); background-size: cover; width: 100vw; } @@ -8449,7 +8449,7 @@ figcaption { @media only screen and (min-width: 651px) and (max-width: 992px) { .background { height: 100vh; - background: url("../resources/backgroundweb2016.svg"); + background: url("../resources/backgroundweb2017.png"); background-size: cover; width: 100%; } @@ -8508,7 +8508,7 @@ figcaption { @media only screen and (max-width: 650px) { .background { height: 100vh; - background: url("../resources/backgroundweb2016.svg"); + background: url("../resources/backgroundweb2017.png"); background-size: cover; } .collapsible-toc { diff --git a/_sass/style.scss b/_sass/style.scss index bbaa799..2d32790 100644 --- a/_sass/style.scss +++ b/_sass/style.scss @@ -44,7 +44,7 @@ $web-title: "Code Pro Demo"; $post-title-font: "Calibri"; $post-font: "CMU Serif"; -$background: url("../resources/backgroundweb2016.svg"); +$background: url("../resources/backgroundweb2017.svg"); $toc-height: 570px; $toc-width: 896px; diff --git a/assets/2017/A.Choi/ac_example.pdf b/assets/2017/A.Choi/ac_example.pdf new file mode 100644 index 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+%\usepackage{graphics} +\usepackage{natbib} +\usepackage[colorlinks=true, urlcolor=blue, linkcolor=black, citecolor=black]{hyperref} +\usepackage{color} +\usepackage{natbib} +\usepackage{sectsty} +\setcounter{MaxMatrixCols}{10} + + +\sectionfont{\fontsize{12}{15}\selectfont} + +\renewcommand{\thefootnote}{} +\setlength{\oddsidemargin}{1pt} \setlength{\evensidemargin}{1pt} +\setlength{\hoffset}{-1in} \addtolength{\hoffset}{25mm} +\setlength{\textwidth}{140mm} +\setlength{\marginparsep}{0pt} \setlength{\marginparwidth}{0pt} +\setlength{\topmargin}{0pt} +\setlength{\voffset}{-2in} \addtolength{\voffset}{20mm} +\setlength{\textheight}{300mm} +\setlength{\headsep}{20mm} +\setlength{\footskip}{15mm} +\pagestyle{fancy} +\fancyhead{} \fancyfoot{} + + + +% Theorem environments +\newtheorem{thm}{Theorem}[section] +\newtheorem{algorithm}[thm]{Algorithm} +\newtheorem{axiom}[thm]{Axiom} +\newtheorem{lem}[thm]{Lemma} +\newtheorem{example}[thm]{Example} +\newtheorem{exercise}[thm]{Exercise} +\newtheorem{notation}[thm]{Notation} +\newtheorem{problem}[thm]{Problem} +\theoremstyle{proposition} +\newtheorem{prop}{Proposition}[section] +\newtheorem{case}[thm]{Case} +\newtheorem{claim}[thm]{Claim} +\newtheorem{conclusion}[thm]{Conclusion} +\newtheorem{condition}[thm]{Condition} +\newtheorem{conjecture}[thm]{Conjecture} +\newtheorem{cor}[thm]{Corollary} +\newtheorem{criterion}[thm]{Criterion} +\theoremstyle{definition} +\newtheorem{defn}{Definition}[section] +\theoremstyle{remark} +\newtheorem{rem}{Remark}[section] +\newtheorem{solution}[thm]{Solution} +\newtheorem{summary}[thm]{Summary} +\numberwithin{equation}{section} +\pagenumbering{arabic} % 1, 2, 3, 4, ... + +\begin{document} +\hyphenpenalty=100000 + +\begin{center} +{\Large \textbf{\\A Feed-Forward Algorithm for Arithmetic Circuits}}\\[5mm] +{\large \textbf{Andrew Jemin Choi}\\[1mm]} +{\normalsize \emph{Under the supervision of Professor Guy Van den Broeck}\\[1mm]} +\end{center} + +% Introduction +\section{Introduction}\label{I1} +Probabilistic queries are a foundation to many machine learning problems. We often query probabilistic models, such as Bayesian networks, to gain information about the variables in a system and make inferences about them. However, even the simplest queries in these networks, such as finding marginal probabilities of the input, come at an exponential cost. In fact, the problem of exact inference and making such queries in these probabilistic models is NP-hard. [1, 2] + +An effective approach for making exact inferences in networks is to construct an Arithmetic Circuit (AC) from the network. [3] The state-of-the-art method uses a software algorithm to backpropagate the marginal probabilities of the AC. [4] We propose a new algorithm for calculating marginal probabilities by using feed-forward ACs, which can potentially reduce inference time and power comsumption. + +% Background +\section{Background}\label{I2} +A network polynomial is a linear function that outputs the probability of an event given the input parameters of the network. An example of one such polynomial is: \newline \centerline{$f=0.4\times(\theta_{f}) + 0.6\times(\theta_{\overline{f}})$} \newline +Evaluating the network polynomial is important in making inferences in our network. However, the number of terms in the polynomial is exponential with respect to the number of inputs. One compact way of representing these exponential terms is to express the polynomial using an arithmetic circuit. [2] + +An arithmetic circuit is a directed acyclic graph (DAG) whose leaves are variables or constants and whose interior nodes are addition or multiplication operations. The size of an arithmetic circuit is defined as the number of edges within the circuit. The size of the circuit also grows linearly with respect to the number of terms in the polynomial. + +% Diagram here +\begin{figure}[h] + \caption{A binary arithmetic circuit that expresses the linear polynomial: $f=0.4\times(\theta_{f}) + 0.6\times(\theta_{\overline{f}})$} + \centering + \includegraphics[width=9cm]{ac_example.pdf} +\end{figure} +\newpage +% End Diagram + +By traversing the AC from the leaves, we can calculate the output of the polynomial at the root. Furthermore, if we start from the root, we can calculate the marginal probabilities by evaluating the partial derivatives for interior nodes, similar to how backpropation is used to update weights in a neural network. Both of these processes are linear in time with respect to the circuit size [2]. Similarly, the state-of-the-art uses a software implementation of bit-encoding backpropagation, where the original AC is traversed twice in order to find the marginal probabilities. One limitation to using bit-encoding is that it only works for alternating circuits, where every level of interior nodes alternate between addition and multiplication nodes. + +% Approach +\section{Approach}\label{I3} +We propose a feed-forward approach to finding marginal probabilities. This approach would produce two arithmetic circuits, where the first circuit outputs the result of the polynomial and the second circuit outputs the marginal probability of a variable. By creating an additional circuit, we can perform additional optimizations and construct it in hardware to perform more efficient inferences. + +% Diagram here +\begin{figure}[h] + \caption{A high-level model of the proposed feed-forward AC} + \centering + \includegraphics[width=10cm]{feedforward_example.pdf} +\end{figure} +\newpage +% End Diagram + +Since partial derivatives of addition nodes are generally equal to the partial derivatives of the child nodes, we can calculate the partial derivatives by calculating the products of all sibling nodes of a child node, as follows: \newline\centerline{dr(c) = dr(p)$\times$ $\prod\limits_{c \neq c'}^{} vr(c')$ [4]}\newline where dr(c) is the derivative of the child node, dr(p) is the derivative of the parent node, and vr(c') is the value of a sibling node. This naive method requires many more edges than our original AC. As a result, the new AC will be quadratic in size with respect to our original AC using a naive approach. + +Like the naive approach, our approach to finding marginal probabilities involves using only the product nodes; however, we do so i in a more efficient manner. We can do this by caching previously computed products and accessing them in future calculations, which is also a memoization technique. By caching the products into a register to calculate partial derivatives, the calculation can be done in linear size with respect to our original AC. + +This cache-based algorithm has two significant advantages compared to the bit-encoding algorithm: +\begin{enumerate} +\item The partial derivatives can be calculated in linear size, irrespective of the circuit structure. The feed-forward algorithm works correctly for non-alternating circuits, which is a feature absent from bit-encoded backpropagation. +\item The algorithm can be used to create an external circuit that we can construct in hardware, which will allow us to perform additional optimizations to reduce inference time. +\end{enumerate} + +% Analysis +\section{Analysis}\label{I4} + +We compared the performance of three algorithms, written in C, on three different data sets. For the feed-forward algorithm, we generated a feed-forward arithmetic circuit from the original circuit, and then compiled the circuit back into C code. Then, we measured the CPU time needed to find the marginal probability of one variable from the initialized circuit structures. + + + \begin{table}[h!] + \centering + \begin{tabular}{||c c c c ||} + \hline + \textbf{Test Set} (nodes) & Bit-Encoded (s) & \textbf{Feed-Forward} (s) & Naive (s)\\ %[0.5ex] + \hline\hline + \textbf{Verysimple.ac} (20) & 0.01994 & \textbf{0.00504} & 0.01921\\ + \hline + \textbf{Voting.ac} (12468) [5] & 2.29930 & \textbf{0.34500} & 6.85860\\ + \hline + \textbf{Movie.ac} (21714) [5] & 0.84004 & \textbf{0.18353} & 1.31189\\ %[1ex] + \hline +\end{tabular} +\caption{CPU times (in seconds) of 10000 iterations of bit-encoded, feed-forward, and naive algorithms. The values were averaged from 3 trials. } +\end{table} + +The CPU times show that the feed-forward approach is 4 to 5 times faster on simple circuit structures (verysimple.ac and movie.ac) and about 8 times faster for more complex structures (voting.ac) compared to bit-encoded backpropagation. We can attribute the improvement in performance to the simpler output circuit structure of the compiled code, and better performance in the forward passes compared to the backward pass. The feed-forward algorithm was found to give correct results even for non-alternating circuits, which makes this algorithm suitable for a wider range of applications. In addition, it can be represented by a hardware circuit, leading to more energy efficient and faster inferences. We hope to compare the differences between a software and hardware implementation in future work. +\newpage + +% Conclusion +\section{Conclusion} +We proposed a new algorithm to find the marginal probabilities in an arithmetic circuit in linear size using a cache-based feed-forward algorithm. We found that calculating the marginal probabilities by compiling the feed-forward circuit significantly reduces inference time. The algorithm can also be used for a wider range of circuits, and it can be implemented in a hardware circuit, potentially using fewer resources. + +\mbox{}\\ + +% Acknowledgements +\noindent \Large\textbf{Acknowledgements}\\[1mm] +\normalsize \noindent I would like to thank Prof. Guy Van den Broeck for his brilliant insight and mentorship during this project. I am also grateful to his students in the StarAI Lab for their enlightening discussions during my stay at UCLA. \\[3mm] + +\newpage + +% References and Citations +\noindent \Large\textbf{References}\\[1mm] +\normalsize \noindent +[1] Cooper, G. F., 1990. The computational complexity of probabilistic inference using Bayesian belief networks. Artif. Intell. 42, pp. 393-405. \newline \newline +[2] Darwiche, A., 2003. A Differential Approach to Inference in Bayesian Networks. J. ACM 50, pp. 280-305. \newline \newline +[3] Chavira, M. and Darwiche, A., 2005. Compiling Bayesian networks with local structure. In Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI), pp. 1306–1312. \newline \newline +[4] Darwiche, A., 2009. Modeling and Reasoning with Bayesian Networks. Cambridge University Press, Chapter 12.\newline \newline +[5] Bekker, J., Davis, J., Choi, A., Darwiche, A., and Van den Broeck, G., 2015. Tractable Learning for Complex Probability Queries. 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Date: Fri, 23 Mar 2018 19:18:06 -0400 Subject: [PATCH 08/17] updated a.choi to reflect danya's edited version --- _posts/2017/2017-03-24-Andrew-Jemin-Choi.md | 28 ++++++--------------- 1 file changed, 7 insertions(+), 21 deletions(-) diff --git a/_posts/2017/2017-03-24-Andrew-Jemin-Choi.md b/_posts/2017/2017-03-24-Andrew-Jemin-Choi.md index ebeb4b6..b0a8016 100644 --- a/_posts/2017/2017-03-24-Andrew-Jemin-Choi.md +++ b/_posts/2017/2017-03-24-Andrew-Jemin-Choi.md @@ -3,7 +3,7 @@ layout: post title: "A Feed-Forward Algorithm for Arithmetic Circuits" author: "Andrew Jemin Choi" supervisors: "Professor Guy Van den Broeck" -category: "Category 1" +category: "Artificial Intelligence" permalink: /a-feed-forward-algorithm-for-arithmetic-circuits year: "2017" @@ -13,9 +13,7 @@ Introduction ============ Probabilistic queries are a foundation to many machine learning problems. We often query probabilistic models, such as Bayesian networks, to gain information about the variables in a system and make inferences about them. However, even the simplest queries in these networks, such as finding marginal probabilities of the input, come at an exponential cost. In fact, the problem of exact inference and making such queries in these probabilistic models is NP-hard [1]. - -An effective approach for making exact inferences in networks is to construct an Arithmetic Circuit (AC) from the network polynomial. The network polynomial is a linear function that outputs the probability of an event given the input parameters of the network. Although building the AC from a network takes exponential time and space, queries can be executed linearly, i.e. O(n), where n is the size of the circuit [2]. Therefore, compiling or learning ACs from networks provides an efficient alternative to making exact inferences [3]. - +An effective approach for making exact inferences in networks is to construct an Arithmetic Circuit (AC) from the network polynomial. The network polynomial is a linear function that outputs the probability of an event given the input parameters of the network. Although building the AC from a network takes exponential time and space, queries can be executed linearly, i.e. $O(n)$, where n is the size of the circuit [2]. Therefore, compiling or learning ACs from networks provides an efficient alternative to making exact inferences [3]. The state-of-the-art method uses a software algorithm to backpropagate the marginal probabilities of the network using bit-encoding[4]. We propose a new algorithm that will calculate marginal probabilities by using feed-forward ACs. The advantage of using strictly feed-forward ACs is that the entire circuit can be built in hardware, which can drastically reduce inference time and consume significantly less power compared to software implementations. Background @@ -23,20 +21,13 @@ Background An arithmetic circuit is a directed acyclic graph (DAG) with leaves that are variables or constants and interior nodes that are addition or multiplication operations. An arithmetic circuit can calculate the output value of a polynomial in linear size, where size is defined as the number of edges in the circuit. -

    Figure 1: A binary arithmetic circuit that expresses the linear polynomial: $f = (y) + (0.5(x) + 1$)

    -By using ACs, we can calculate the partial derivatives and find the marginal -probabilities in linear size, i.e. $O(n)$ edges [2]. This process is called backpropagation -because we start calculating derivatives from the root (output) node and work our -way backwards to the leaf (input) nodes to find the partial derivatives. The state-of- -the-art uses bit-encoding backpropagation and a series of divisions in order to find -partial derivatives in one pass. We began this project in hopes of finding a way to -calculate the partial derivatives in a feed-forward network, in linear size. +By using ACs, we can calculate the partial derivatives and find the marginal probabilities in linear size, i.e. $O(n)$ edges [2]. This process is called backpropagation because we start calculating derivatives from the root (output) node and work our way backwards to the leaf (input) nodes to find the partial derivatives. The state-of- the-art uses bit-encoding backpropagation and a series of divisions in order to find partial derivatives in one pass. We began this project in hopes of finding a way to calculate the partial derivatives in a feed-forward network, in linear size. Approach ======== @@ -48,21 +39,17 @@ $dr(c) = dr(p) \times \pi_{c \neq c\prime} vr(c\prime) [4]$ This “naive” method requires $O(n^2)$ number of edges in the circuit. -Our approach to finding marginal probabilities involves only using product nodes -in a feed-forward circuit. We achieve this by applying memoization to cache previously -computed products. By caching the products into a register to calculate partial -derivatives, backpropagation can be done in $O(n)$ edges. +Our approach to finding marginal probabilities involves only using product nodes in a feed-forward circuit. We achieve this by applying memoization to cache previously computed products. By caching the products into a register to calculate partial derivatives, backpropagation can be done in $O(n)$ edges. + This cache-based algorithm has two apparent advantages: -1. The partial derivatives can be calculated linearly, i.e. $O(n)$ edges, regardless of -the DAG structure. The algorithm works correctly for non-alternating trees, -which is a feature absent from bit-encoded backpropagation. +1. The partial derivatives can be calculated linearly, i.e. $O(n)$ edges, regardless of the DAG structure. The algorithm works correctly for non-alternating trees, which is a feature absent from bit-encoded backpropagation. + 2. The algorithm can be implemented into a feed-forward arithmetic circuit using hardware. Figure 2 and 3 below outlines the forward pass and backward pass of the algorithm, respectively. In the forward pass, the number of child node accesses is bound by a constant (number of parent nodes). Similarly, in the backward pass, the edges needed to evaluate the derivative of a multiplication node is bounded by a constant number of operations (two products and one sum). Since every node operation is bound by a constant, we can see that the algorithm is $O(n)$. -

    @@ -98,7 +85,6 @@ Conclusion We proposed a new algorithm to find the marginal probabilities in an arithmetic circuit in linear size using a cache-based feed-forward algorithm. We found that finding the marginal probabilities by compiling the feed-forward circuit significantly reduces inference time. The algorithm can also be used for a wider range of circuits, and it can be implemented in hardware, potentially using much less resources. - ### Acknowledgement I would like to thank Prof. Guy Van den Broeck for his brilliant insight and mentorship during this project. I am also grateful to his students in the StarAI Lab for their enlightening discussions during my stay at UCLA. 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assets/2017/D.Moore/smallRadius.png diff --git a/_posts/2017/2017-03-24-Andrew-Jemin-Choi.md b/_posts/2017/2017-03-24-A-Choi.md similarity index 95% rename from _posts/2017/2017-03-24-Andrew-Jemin-Choi.md rename to _posts/2017/2017-03-24-A-Choi.md index b0a8016..c668c6f 100644 --- a/_posts/2017/2017-03-24-Andrew-Jemin-Choi.md +++ b/_posts/2017/2017-03-24-A-Choi.md @@ -12,7 +12,7 @@ year: "2017" Introduction ============ -Probabilistic queries are a foundation to many machine learning problems. We often query probabilistic models, such as Bayesian networks, to gain information about the variables in a system and make inferences about them. However, even the simplest queries in these networks, such as finding marginal probabilities of the input, come at an exponential cost. In fact, the problem of exact inference and making such queries in these probabilistic models is NP-hard [1]. +Probabilistic queries are a foundation to many machine learning problems. We often query probabilistic models, such as Bayesian networks, to gain information about the variables in a system and make an Indians, Canadians, Brazilians, etc. Foreign students pay the full ride, so yes they are often upper middinferences about them. However, even the simplest queries in these networks, such as finding marginal probabilities of the input, come at an exponential cost. In fact, the problem of exact inference and making such queries in these probabilistic models is NP-hard [1]. An effective approach for making exact inferences in networks is to construct an Arithmetic Circuit (AC) from the network polynomial. The network polynomial is a linear function that outputs the probability of an event given the input parameters of the network. Although building the AC from a network takes exponential time and space, queries can be executed linearly, i.e. $O(n)$, where n is the size of the circuit [2]. Therefore, compiling or learning ACs from networks provides an efficient alternative to making exact inferences [3]. The state-of-the-art method uses a software algorithm to backpropagate the marginal probabilities of the network using bit-encoding[4]. We propose a new algorithm that will calculate marginal probabilities by using feed-forward ACs. The advantage of using strictly feed-forward ACs is that the entire circuit can be built in hardware, which can drastically reduce inference time and consume significantly less power compared to software implementations. diff --git a/_posts/2017/2017-03-28-A-Yasodhara.md b/_posts/2017/2017-03-28-A-Yasodhara.md new file mode 100644 index 0000000..4f2b1da --- /dev/null +++ b/_posts/2017/2017-03-28-A-Yasodhara.md @@ -0,0 +1,98 @@ +--- +layout: post +title: "Uncovering predisposition to COPD with predicted gene expression" +author: "Angeline Yasodhara" +supervisors: "Aziz Mezlini and Anna Goldenberg" +category: "Computational Biology" +permalink: /uncovering-predisposition-to-copd-with-predicted-gene-expression +year: "2017" + +--- + +Introduction +=== + +Chronic Obstructive Pulmonary Disease (COPD) is a term used to describe various lung diseases characterized by airflow limitation, including emphysema, chronic bronchitis, refractory (non-reversible) asthma, and certain forms of bronchiectasis. COPD is one of the leading causes of death worldwide, causing an estimate of 3 million deaths in 2015, and is hypothesized to be associated with heritable genetic factors as well as environmental exposures (e.g., smoking). + +One of the conventional ways to uncover genes associated with diseases is through a genome-wide association study (GWAS). This method examines the whole genome to find positions (loci) where patients suffering from COPD (cases) and those who do not (controls) differ significantly in nucleotides proportion, suggesting that it may influence the risk of the disease. + +Through GWAS, 836 loci have been discovered to be associated with COPD [1],[2]. However, these discovered loci do not provide information on how these loci affect lung function; for example, these loci may regulate the expression of the closest gene, or it could be distantly affecting other genes. For more insight, we can examine transcriptome data, which provides information on levels of messenger RNA that were transcribed from genes. The challenge with this approach is that there is a smaller number of individuals with observed transcriptome data than genotype data. To overcome these challenges, this project seeks to identify COPD-associated genes by looking at the predicted gene expression that was calculated from the larger genotype dataset. + +In this project, we explored different association tests to find genes associated with COPD. We used a novel statistical test, developed by Aziz Mezlini, one of the co-authors of this paper. + +Approach +=== + +We were provided with transcriptome and genotype datasets from populations of two ethnicities: African-American and Non-Hispanic White. + + + +The core of the approach was to apply machine learning methodologies to predict the genetically-regulated component of the gene expression; this was achieved by incorporating regions of the genome which have been known to influence the expression level of one or more genes, regions known as expression quantitative trait loci (eQTL). These eQTL regions serve as our predictor variables in the predictive model. There have been two new tools that attempt to predict gene expression using eQTL, namely PrediXcan [3] and fQTL [4]. These two tools approach the problem from a slightly different angle; while PrediXcan adopts an elastic net model, training on different tissue type datasets separately, fQTL takes a multi-tissue, multivariate approach, in which the eQTL effects are decomposed into tissue-specific and loci-specific components. For this project, we predicted gene expression using PrediXcan and fQTL for whole-blood and lung tissues. + + + +After predicting gene expression using PrediXcan and fQTL, we performed association tests through different hypothesis-driven approaches, integrating transcriptome information with predicted expression. + +We used the following statistical tests during association analysis: +1. T-test +2. Logistic regression of gene expression values on case/control status +3. Logistic regression of gene expression values on case/control status and smoking duration +4. Mezlini’s test + +Mezlini’s test is a new statistical test developed by Aziz Mezlini to analyze if two populations are different by looking for enrichment close to the end of a distribution, as depicted by Figure 3. + + + + +We identified 15 statistically-significant genes, 2 of which were previously discovered by GWAS. These genes genetically interacted and are located in the vicinity of previously GWAS-discovered loci. + + + + + + + + +Through this project, we have shown that Mezlini’s test is able to detect associations overlooked by other statistical tests, as shown in Fig. 5. Notably,, we have also found different genes associated with COPD in African-American and Non-Hispanic White datasets. This may be due partly to the difference in the numbers of individuals (AA:NHW = 2801 :5982). Additionally, it suggests that genes have varying degrees of predisposition (to COPD) among ethnicities. + +This project also shows that GWAS is insufficient in providing insight on the genetics behind COPD; inspecting predicted expression provides such insight on how these genes influence certain traits. + +Acknowledgements +=== +Thank you to Dr. Anna Goldenberg and Aziz Mezlini for the continuous guidance and support! Special thanks to our collaborators from Brigham and Women’s Hospital, Harvard Medical School who have provided us with the COPD datasets: Michael Cho and Craig Hersh. + +Shoutout to all the lab members for all the help, discussions, and brainstorming sessions: Ben, Lauren, Daniel H., Ladislav, Shems, Mingjie, Kingsley, Daniel C., Lebo, Jaryd, Mohamed, and Walter. + +Citations +=== + +1. K. Probert et al., “Developmental genetics of the COPD lung,” COPD Research and Practice, vol. 1, no. 1, pp. 10, Nov. 2015. doi: 10.1186/s40749-015-0014-x +2. T. Burdett et al. (2017, August 14). The NHGRI-EBI Catalog of published genome-wide association studies [Online]. Available: http://www.ebi.ac.uk/gwas +3. E. Gamazon et al., “A gene-based association method for mapping traits using reference transcriptome data,” Nat. Gen., vol. 47, no. 9, pp. 1091-1098, Sep. 2015. doi: 10.1038/ng.3367 +4. Y. Park et al., “Multi-tissue polygenic models for transcriptome-wide association studies,” bioRxiv, 2017. doi: 10.1101/107623 diff --git a/_posts/2017/2017-03-28-C-Herng-Yi.md b/_posts/2017/2017-03-28-C-Herng-Yi.md new file mode 100644 index 0000000..560d2ba --- /dev/null +++ b/_posts/2017/2017-03-28-C-Herng-Yi.md @@ -0,0 +1,119 @@ +--- +layout: post +title: "Solving PDEs on Deconstructed Domains for Geometry Processing" +author: "Herng Yi Cheng, Mitchell Dembowski, Silvia González Sellán and Christine Ma" +supervisors: "Professor Alec Jacobson" +category: "Scientific Computer/Numerical Analysis" +permalink: /solving-pdes-on-deconstructed-domains-for-geometry-processing +year: "2017" + +--- + +Introduction +=== + +The Laplace equation and Possion equation are partial differential equations (PDEs) which arise naturally from analyzing heat flow, Maxwell's equations of electromagnetism, and shape recognition in computer graphics [?]. We studied a new way to solve these equations on overlapping triangular mesh domains, in order to smoothen the computer animation of objects that are represented using those meshes. We designed several variants of a divide-and-conquer solution method, and tested them against each other for accuracy. + +Background +=== + +The Laplace equation models the steady-state distribution of heat on a domain $A \subset \mathbb{R}^2$ with each point $(p_1,p_2)$ on its boundary $\partial A$ held at a fixed temperature $g(p_1,p_2)$. The steady-state temperature distribution $u(x,y) : A \to \mathbb{R}$ must satisfy + +
    +$\Delta u(x, y) = 0$ for all $(x, y) \in A \backslash \partial \mathbb{A}, (2.1) $
    +$ u(p_1, p_2) = g(p_1, p_2) $ for all $(p_1, p_2) \in \partial \mathbb{A}, (2.2) $ +
    + +where (2.1) is the Laplace equation, $ \Delta = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2}$ is the Laplace operator and (2.2) is the boundary condition. (2.1) can be generalized to the Poisson equation. + +\begin{equation} +\Delta u = h \text{ for constant } h \in \mathbb{R}. (2.3) +\end{equation} + +The usual method for solving these PDEs numerically, known as finite element discretization, consists in approximating $A$ using a triangle mesh with vertices $v_1,\dotsc,v_n$ and substituting every function $f$ defined on $A$ by the vector of its finite evaluations $f_i=f(v_i)$. From this discrete perspective, solving either of the equations above becomes an optimization problem over a finite number of variables. The solutions to these optimization problems approximate the smooth solutions of the original PDE. + +In the case of the Laplace and Poisson equations, this optimization problem amounts to minimizing the discrete Dirichlet energy function, which has the form + +\begin{equation}\label{Eq:DirichletEnergy} +E(u) = \frac{1}{2}{u^T}_A Qu_A + {c^T}u_A \text{, where } u_A = + (2.4) +\end{equation} + +for some constant vector $c \in \mathbb{R}^n$. The $n \times n$ cotangent matrix $Q$ is ubiquitous in geometry processing and serves as the discrete equivalent of the continuous Laplace operator seen above; its derivation can be found in [?. ]. This energy is to be minimized over all $u_A \in \mathbb{R}^n$, subject to the boundary condition that fixes the entries of $u_A$ that correspond to vertices on $\partial A$. Expanding the matrix products in (2.4) shows that the right-hand-side is quadratic in the entries of $u_A$, therefore standard techniques of quadratic programming that minimize quadratic functions subject to constraints yield the energy minimizer, or the vector $u_A$ that minimizes (2.4). However, the precise method by which these optimization problems are solved will not be a concern throughout the paper. + +Domain Decomposition +=== + +How well the energy minimizers approximate solutions to the smooth PDEs depends on the quality of the mesh. Two important parameters of a mesh that determine its quality are its coarseness, as measured by the average lengths of edges (segments connecting vertices), and its regularity, as measured by the aspect ratios of its triangles. Very regular meshes have triangles that are roughly equilateral, while long and thin triangles make an irregular mesh. As mesh quality improves, the energy minimizers should converge to solutions to the PDEs. + +Generating quality meshes that represent complex shapes is an active field of research. In 3D, it is often much easier to decompose complex 3D shapes into the union of simpler domains, and then generate quality meshes for those domains. Thus, we study a divide-and-conquer approach to minimize the Dirichlet energy over the union of many domains by minimizing parts of that energy over each individual domain, while demanding that the minimizers agree wherever the domains overlap, to ensure a compatible combined minimizer. We will refer to this as the consistency requirement (formalized below). We implemented this approach to handle general pairs of overlapping 2D domains $A$ and $B$, with corresponding meshes. + +However, functions over $A$ and $B$ cannot be compared because they are represented, respectively, by vectors $u_A$ and $u_B$, whose entries are values on different sets of vertices. In order to formulate that consistency requirement, we linearly interpolate from $u_A$ over the triangles of $A$'s mesh to reconstruct a function $u_A : A \to \mathbb{R}$; this is to say, we take $u_A$ to be the only function which is linear on every triangle of $A$'s mesh while taking the values of $u_A$ at its vertices. +Similarly, we reconstruct $u_B : B \to \mathbb{R}$. This reconstruction can be plotted out, as in Figure 1. Our contribution is to analyze the following two formulations of the consistency requirement as the linear constraints of quadratic programs, in the hopes that they can be generalized to 3D. + +**_Overlap sampling constraint (OSC)_** $u_A$ and $u_B$ must agree at the combined vertices of both meshes. + +**_Dirichlet sampling constraint (DSC)_** $u_A$ and $u_B$ must agree at the vertices of both meshes that lie on $\partial(A \cap B)$ (a small subset of the overlap sampling constraint). + +
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    Figure 1: Energy minimizers for the OSC (left) and the DSC (right), subject to the same boundary condition $g(x,y) = (x+0.3)^2y^2$. Note how the two generate virtually identical solutions, even though the second one is only enforcing equality on a much smaller number of vertices.

    + +Experiments and results +=== + +From each constraint we derived a quadratic program to solve the Laplace or Poisson equation over $A \cup B$, subject to a boundary condition $g : \partial(A \cup B) \to \mathbb{R}$. Namely, we minimized a weighted combination of $E(u_A)$ and $E(u_B)$, such that $u_A$ and $u_B$ satisfy that constraint, and take values on vertices in $\partial(A \cup B)$ as dictated by $g$. We subjected each type of quadratic program to a convergence test over two annular domains with annular union (see figure 1), and measured the maximum of the distance of the approximations provided by each method to the known analytical solution. We repeated this test for $\Delta u=0$, $\Delta u=1$ and for different levels of mesh regularity. $\Delta u = 1$ was chosen for a simple nonzero right-hand side; using any other nonzero constant would have simply scaled $u$. + + +We concurrently tested the "ideal" method: combining the meshes of $A$ and $B$ into a combined mesh for $A \cup B$, and treating the minimizer of the Dirichlet energy over that combined mesh as a ground truth (GT) proxy to the analytic solution, when the latter is unknown. This ground truth would be unavailable in 3D where combining meshes is far more difficult, but it serves as a useful benchmark of our quadratic programs in 2D. + + +

    + +

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    Figure 2: A pair of annular domains, in blue and red.

    + +Our results, presented in Figure 3, show the Dirichlet sampling constraint to be clearly superior. While the overlap constraint appears to be accurate when solving $\Delta u=0$ on regular meshes, it fails and does not even converge to the analytical solution for $\Delta u = 1$, or when the meshes become increasingly irregular. As expected, the ground truth deviates the least from the analytic solution and converges to it the fastest. + +We performed similar tests on different domain shapes, which can be seen in Figure 4. Since no analytical solution is available for these pairs of meshes, we simply measured the error between our methods and the co-refined ground truth (yellow line in figure 3), safely assuming that this last one will surely converge to the smooth solution of the PDE. The results obtained from these experiments agreed completely with those observed for the pair of annular domains. + + + +

    + +

    + +

    Figure 3: Convergence of our methods for annular domains. The top row shows the results for regular meshes, while the bottom one shows the results for irregular meshes. The left column contains results for the equation $\Delta u=0$, while the right one does so for $\Delta u=1$.

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    Figure 4: Examples of pairs of meshes over which we have tested convergences

    + +Conclusion +=== + +The overlap sampling constraint performed inconsistently between $\Delta u = 0$ and $\Delta u = 1$, as well as between regular and irregular meshes, although it was surprisingly accurate when solving the Laplace equation on regular meshes. + +The Dirichlet sampling constraint converged in every one of our experiments for both the Laplace and Poisson equations, regardless of regularity and shape of the meshes. While converging slower than the ground truth, its rate of convergence appears to be at least linear. It is the best candidate for future research to generalize to 3D, progressing toward our goal of solving PDEs over the union of multiple domains when computing a common mesh is infeasible. + +Acknowledgement +=== +The authors would like to thank Prof. Alec Jacobson for his patient and dedicated mentorship, as well as the Fields Institute for bringing our research group together, and supporting our research with a stipend, through the Fields Undergraduate Summer Research Program. The third author would also like to express deep gratitude to the María Cristina Masavéu Peterson Foundation for its financial support of her studies. diff --git a/_posts/2017/2017-03-29-D-Moore.md b/_posts/2017/2017-03-29-D-Moore.md new file mode 100644 index 0000000..d40a955 --- /dev/null +++ b/_posts/2017/2017-03-29-D-Moore.md @@ -0,0 +1,130 @@ +--- +layout: post +title: "Geodesicness for Meshfree Simulation Methods" +author: "Darren Moore" +supervisors: "Professor David I.W. Levin and Professor Alec Jacobson" +category: "Computer Graphics" +permalink: /geodesicness-for-meshfree-simulation-methods +year: "2017" + +--- + +Introduction +=== + +Elasticity simulation can be used to animate the clothes that CGI characters wear or calculate how much weight structures will hold before they collapse [?] [?]. In general it lets us model how objects deform when forces are applied to them. The numerical methods used to do this require the object we're simulating to be discretized into finite pieces. The technique by which we discretize the object gives rise to two classes of numerical methods. One class, called Finite Element Methods, uses a polygon mesh discretization (Figure 1a), but mesh generation requires a lot of user tuning and can fail if the object has complicated geometry. The other class is Meshfree Methods, which uses a point cloud discretization (Figure 1b) rather than a mesh to perform the simulation. + + +
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    a) A triangle mesh for the finite element method.

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    b) Two discretizations of an object that can be used for simulation.

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    Figure 1: Two discretizations of an object that can be used for simulation.

    + + +An important distinction between point cloud and polygon mesh representations is the point cloud's lack of connectivity information. Elasticity requires a notion of connectivity to determine how applying a force to one point affects the points connected to it. Most meshfree methods simply take the set of all points in a certain radius $h$ around a given point to be connected to it (Figure 2). [?] + +This radial approach is problematic if two points are close to each other in space but have a large geodesic distance. Geodesic distance is the shortest distance between two points when taking paths that stay on the object (Figure 3). An incorrect interpretation of the topology will result in "invisible connections" that incorrectly constrain the movement of the object (Figure 4). The goal of our paper is to enhance the interpretation of the topology using point cloud geodesics. If you think of the point cloud as approximating a 2D shape, then a point cloud geodesic between two points is the geodesic distance between the points lying that 2D shape. + +
    +
    + +
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    (a) All points in a radius $h$ are connected.

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    (b) A case where the radial approach connects across a gap.

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    Figure 2: The radial approach in meshfree methods

    + +
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    (a) Euclidean distance cuts through space.

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    (b) Geodesic distance stays on the object.

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    Figure 3: The Euclidean distance vs. geodesic distance distance between two points on a circle.

    + +Approach +=== + +We combine meshfree methods with point cloud geodesics to more accurately simulate point cloud data. The core of our approach is to use shortest-path graph searches to compute point cloud geodesic distances, then simulating the particles using those geodesic distances rather than standard Euclidean distances. + +To compute these point cloud geodesic distances, we represent the point cloud as a weighted graph with edge weights equal to the Euclidean distance between points (Figure 5). By exponentiating the weights we penalize large jumps. With sufficiently large exponent, the shortest-path graph distance approximates the geodesic distance. + +We define our graph as follows: given points $x_i$ and $x_j$, $(x_i, x_j)$ is an edge if and only if $\|x_i - x_j\| \leq h$, where $\|\cdot\|$ is the Euclidean norm. While our methods work if the graph is complete, we only connect points in a small radius to increase efficiency. Denote the edge weights by $w(x_i,x_j)$. + +We define a parameter, the $geodesicness$, which represents the extent to which our method avoids large jumps while searching for a geodesic path between points. Let $\gamma \geq 1.0$ denote the geodesicness. Different point clouds may require different values of $\gamma$ since there will be different sized jumps in the data. This parameter is tuned by the user. + +
    +
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    Figure 4: Due to an "invisible connection" in (a) the movement of the object is incorrectly constrained in (b). We expect the elastic lower bar to bend downwards.

    + +

    + +

    + +

    Figure 5: A graph defined over a point cloud. Two points are connected by an edge when their Euclidean distance is less than or equal to $h$. Edge weights are not represented in this figure

    + + +Our geodesic approach uses $w(x_i, x_j) = \|x_i - x_j\|^\gamma$. As a result, large jumps in the data are expensive for the shortest-path graph search. With a sufficiently large $\gamma$, the path will walk around gaps and take a point cloud geodesic path (Figure 7). It can be seen that letting $\gamma = 1.0$ is equivalent to the traditional approach. The geodesicness required to get an improved simulation result depends on the size of the gaps in the data, the number of points along the geodesic paths, and the distance between each point along the geodesic paths. + +Results +=== + +We demonstrate our method's effectiveness by applying it to several point cloud data sets. Our simulations were done using a linear elastic material model, although our method works independently of the material model. + +Figure 8 uses a point cloud of two bars connected only on the left. We fix the top bar in place and leave the bottom bar free to deform under gravity. With the traditional radial approach, the bottom bar does not deform, since it is incorrectly connected to the fixed top bar. With our geodesic approach, the bottom bar is free to bend downwards. + +Figure 9 demonstrates our approach in the case of a user interacting with a pair of point cloud pants. We begin by fixing the top of the pants in place and allow the legs to deform freely. Next, a user attempts to pull the right leg to the right. With the traditional radial approach, the legs are incorrectly connected together and both pant legs deform. With our geodesic approach, the legs can move independently of each other as expected. + +Figure 10 demonstrates an application of our approach to character animation. We begin by fixing the head of the octopus in place and allow the arms to deform freely. With the traditional approach, the animator can't wiggle the arms around as they are stuck together. With our geodesic approach, the arms can move independently, allowing the octopus to wave hello. + +Limitations +=== + +Unfortunately, the quality of a simulation produced using this method does not gracefully degrade as the geodesicness decreases. If the geodesicness falls below a certain threshold, the close points that are far geodesically will immediately connect and the simulation will behave as in the traditional radial approach. + + + +Conlusion +=== + +Since point clouds have no connectivity information it's easy to incorrectly interpret the topology when simulating elasticity. We introduced a method which combines meshfree methods with point cloud geodesics to help interpret the topology in cases where points are close in space but far geodesically. Future work includes generalizing to three dimensions and investigating a gracefully degrading point cloud geodesic distance. + +Acknowledgement +=== +I would like to acknowledge David Levin and Alec Jacobson, my supervisors, and Tim Jeruzalski, my mentor, for their support and ideas throughout this project. + + + + \ No newline at end of file diff --git a/assets/2017/C.Herng Yi/2017-03-24-C-Herng-Yi.md b/assets/2017/C.Herng Yi/2017-03-24-C-Herng-Yi.md new file mode 100644 index 0000000..a32538a --- /dev/null +++ b/assets/2017/C.Herng Yi/2017-03-24-C-Herng-Yi.md @@ -0,0 +1,15 @@ +--- +layout: post +title: "Solving PDEs on Deconstructed Domains for Geometry Processing" +author: "Herng Yi Cheng, Mitchell Dembowski, {Silvia Gonz\'alez Sell\'an} and Christine Ma" +supervisors: "Professor Alec Jacobson" +category: "Scientific Computer/Numerical Analysis" +permalink: /solving-pdes-on-deconstructed-domains-for-geometry-processing +year: "2017" + +--- + +Introduction +=== + +The Laplace equation and Possion equation are partial differential equations (PDEs) which arise naturally from analyzing heat flow, Maxwell's equations of electromagnetism, and shape recognition in computer graphics \cite{ShapeRepresentation}. We studied a new way to solve these equations on overlapping triangular mesh domains, in order to smoothen the computer animation of objects that are represented using those meshes. We designed several variants of a divide-and-conquer solution method, and tested them against each other for accuracy. diff --git a/assets/2017/C.Herng Yi/Bibliography.bib b/assets/2017/C.Herng Yi/Bibliography.bib new file mode 100644 index 0000000..4b6e6dd --- /dev/null +++ b/assets/2017/C.Herng Yi/Bibliography.bib @@ -0,0 +1,165 @@ +@Inbook{Cai2003, +author="Cai, X.", +editor="Langtangen, Hans Petter +and Tveito, Aslak", +title="Overlapping Domain Decomposition Methods", +bookTitle="Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming", +year="2003", +publisher="Springer Berlin Heidelberg", +address="Berlin, Heidelberg", +pages="57--95", +abstract="Overlapping domain decomposition methods are efficient and flexible. It is also important that such methods are inherently suitable for parallel computing. In this chapter, we will first explain the mathematical formulation and algorithmic composition of the overlapping domain decomposition methods. Afterwards, we will focus on a generic implementation framework and its applications within Diffpack.", +isbn="978-3-642-18237-2", +doi="10.1007/978-3-642-18237-2_2", +url="http://dx.doi.org/10.1007/978-3-642-18237-2_2" +} + +@book{nocedal2006numerical, + title={Numerical Optimization}, + author={Nocedal, J. and Wright, S.}, + isbn={9780387303031}, + lccn={99013263}, + series={Springer Series in Operations Research and Financial Engineering}, + url={https://books.google.es/books?id=eNlPAAAAMAAJ}, + year={2006}, + publisher={Springer New York} +} + + +@article{MinRough, +title = "Minimal roughness property of the Delaunay triangulation", +journal = "Computer Aided Geometric Design", +volume = "7", +number = "6", +pages = "489 - 497", +year = "1990", +note = "", +issn = "0167-8396", +doi = "http://dx.doi.org/10.1016/0167-8396(90)90011-F", +url = "http://www.sciencedirect.com/science/article/pii/016783969090011F", +author = "Samuel Rippa", +keywords = "Triangulations", +keywords = "Delaunay triangulation." +} + + + +@article{RelaxLapHeat, + author={Robert J Low}, + title={Relaxation: from Laplace's equation to the heat equation and discretely back again}, + journal={European Journal of Physics}, + volume={36}, + number={3}, + pages={035010}, + url={http://stacks.iop.org/0143-0807/36/i=3/a=035010}, + year={2015}, + abstract={We see how the relaxation method for Laplace's equation is related to a numerical solution of the heat equation, which is in turn motivated by thinking of the Hamiltonian as the the time evolution operator in quantum mechanics. This gives some physical insight into what the relaxation method is doing. We also use this to suggest investigative work for a student learning about computational methods in physics.} +} + +@book {RandomWalkHeat, + AUTHOR = {Lawler, Gregory F.}, + TITLE = {Random walk and the heat equation}, + SERIES = {Student Mathematical Library}, + VOLUME = {55}, + PUBLISHER = {American Mathematical Society, Providence, RI}, + YEAR = {2010}, + PAGES = {x+156}, + ISBN = {978-0-8218-4829-6}, + MRCLASS = {60-01 (28A80 35R60 60G42 60G50 60J65)}, + MRNUMBER = {2732325}, +MRREVIEWER = {Peter M\"orters}, + DOI = {10.1090/stml/055}, + URL = {http://dx.doi.org/10.1090/stml/055}, +} + +@book {MarkovStewart, + AUTHOR = {Stewart, William J.}, + TITLE = {Probability, {M}arkov chains, queues, and simulation}, + NOTE = {The mathematical basis of performance modeling}, + PUBLISHER = {Princeton University Press, Princeton, NJ}, + YEAR = {2009}, + PAGES = {xviii+758}, + ISBN = {978-0-691-14062-9}, + MRCLASS = {60-01 (60J10 60K25 65C05 65C10 65C40)}, + MRNUMBER = {2518195}, +} + + +@book{DomainDecomp, +title = "Domain decomposition : parallel multilevel methods for elliptic partial differential equations", +author = "Smith, {Barry F.} and Bjørstad, {Petter E.} and Gropp, {William D.}", +year = "1996", +publisher = "Cambridge University Press", +} + +@inproceedings{NoFreeLunch, + author = {Wardetzky, Max and Mathur, Saurabh and K\"{a}lberer, Felix and Grinspun, Eitan}, + title = {Discrete Laplace Operators: No Free Lunch}, + booktitle = {Proceedings of the Fifth Eurographics Symposium on Geometry Processing}, + series = {SGP '07}, + year = {2007}, + isbn = {978-3-905673-46-3}, + location = {Barcelona, Spain}, + pages = {33--37}, + numpages = {5}, + url = {http://dl.acm.org/citation.cfm?id=1281991.1281995}, + acmid = {1281995}, + publisher = {Eurographics Association}, + address = {Aire-la-Ville, Switzerland, Switzerland}, +} + +@phdthesis{AlecThesis, + title = {Algorithms and Interfaces for Real-Time Deformation of 2{D} and 3{D} Shapes}, + school = {ETH Zurich}, + author = {Jacobson, Alec}, + year = {2013}, +} + +@book{evans1998partial, + title={Partial Differential Equations}, + author={Evans, L.C.}, + isbn={9780821807729}, + lccn={97041033}, + series={Graduate studies in mathematics}, + url={https://books.google.ca/books?id=5Pv4LVB\_m8AC}, + year={1998}, + publisher={American Mathematical Society} +} + +@book{courant2005dirichlet, + title={Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces}, + author={Courant, R.}, + isbn={9780486445526}, + lccn={2005049736}, + series={Dover books on mathematics}, + url={https://books.google.ca/books?id=FLr5JDljqY4C}, + year={2005}, + publisher={Dover Publications} +} + +@article{IntroFEM, + title={A gentle introduction to the Finite Element Method}, + author={Sayas, Francisco-Javier}, + journal={University of Delaware}, + year={2008} +} + +@article{ShapeRepresentation, + author = {Gorelick, Lena and Galun, Meirav and Sharon, Eitan and Basri, Ronen and Brandt, Achi}, + title = {Shape Representation and Classification Using the Poisson Equation}, + journal = {IEEE Trans. Pattern Anal. Mach. Intell.}, + issue_date = {December 2006}, + volume = {28}, + number = {12}, + month = dec, + year = {2006}, + issn = {0162-8828}, + pages = {1991--2005}, + numpages = {15}, + url = {http://dx.doi.org/10.1109/TPAMI.2006.253}, + doi = {10.1109/TPAMI.2006.253}, + acmid = {1176239}, + publisher = {IEEE Computer Society}, + address = {Washington, DC, USA}, + keywords = {Computer vision, Computer vision, shape, Poisson equation, silhouette classification., Poisson equation, shape, silhouette classification.}, +} diff --git a/assets/2017/C.Herng Yi/Dirichlet_Sampling_Constraint.jpg b/assets/2017/C.Herng Yi/Dirichlet_Sampling_Constraint.jpg new file mode 100644 index 0000000000000000000000000000000000000000..41e869e8026a55938ffd3c5ca4ed5a59b9a87166 GIT binary patch literal 71321 zcmbTe1za4>cXxM(;O_438XSTI2(H219fG?CcXxM!hBsvAoW0Ne?!E7Q zujg0YHPh8qwN@?tclW$5ylw!HrNkt~03aYB0Da&G@VbfCDe7)v3IIq-QURa=001}u z00IsG0oJ-efz>~CO<)}r1nl?kZ|4|6KmnM*BOkCR1Bwh=5Wq>dM8WIu;5&{|u3JL}W8WtWM 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100644 index 0000000..b9c2c64 --- /dev/null +++ b/assets/2017/C.Herng Yi/IEEEtranS.bst @@ -0,0 +1,2607 @@ +%% +%% IEEEtranS.bst +%% BibTeX Bibliography Style file +%% Sorting version of IEEEtran.bst +%% *** Not for normal IEEE work *** +%% Version 1.14 (2015/08/26) +%% +%% Copyright (c) 2003-2015 Michael Shell +%% +%% Original starting code base and algorithms obtained from the output of +%% Patrick W. Daly's makebst package as well as from prior versions of +%% IEEE BibTeX styles: +%% +%% 1. Howard Trickey and Oren Patashnik's ieeetr.bst (1985/1988) +%% 2. Silvano Balemi and Richard H. Roy's IEEEbib.bst (1993) +%% +%% Added sorting code is from plain.bst. +%% +%% Support sites: +%% http://www.michaelshell.org/tex/ieeetran/ +%% http://www.ctan.org/pkg/ieeetran +%% and/or +%% http://www.ieee.org/ +%% +%% For use with BibTeX version 0.99a or later +%% +%% This is a numerical citation style. +%% +%%************************************************************************* +%% Legal Notice: +%% This code is offered as-is without any warranty either expressed or +%% implied; without even the implied warranty of MERCHANTABILITY or +%% FITNESS FOR A PARTICULAR PURPOSE! +%% User assumes all risk. +%% In no event shall the IEEE or any contributor to this code be liable for +%% any damages or losses, including, but not limited to, incidental, +%% consequential, or any other damages, resulting from the use or misuse +%% of any information contained here. +%% +%% All comments are the opinions of their respective authors and are not +%% necessarily endorsed by the IEEE. +%% +%% This work is distributed under the LaTeX Project Public License (LPPL) +%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used, +%% distributed and modified. A copy of the LPPL, version 1.3, is included +%% in the base LaTeX documentation of all distributions of LaTeX released +%% 2003/12/01 or later. +%% Retain all contribution notices and credits. +%% ** Modified files should be clearly indicated as such, including ** +%% ** renaming them and changing author support contact information. ** +%%************************************************************************* + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% DEFAULTS FOR THE CONTROLS OF THE BST STYLE %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% These are the defaults for the user adjustable controls. The values used +% here can be overridden by the user via IEEEtranBSTCTL entry type. + +% NOTE: The recommended LaTeX command to invoke a control entry type is: +% +%\makeatletter +%\def\bstctlcite{\@ifnextchar[{\@bstctlcite}{\@bstctlcite[@auxout]}} +%\def\@bstctlcite[#1]#2{\@bsphack +% \@for\@citeb:=#2\do{% +% \edef\@citeb{\expandafter\@firstofone\@citeb}% +% \if@filesw\immediate\write\csname #1\endcsname{\string\citation{\@citeb}}\fi}% +% \@esphack} +%\makeatother +% +% It is called at the start of the document, before the first \cite, like: +% \bstctlcite{IEEEexample:BSTcontrol} +% +% IEEEtran.cls V1.6 and later does provide this command. + + + +% #0 turns off the display of the number for articles. +% #1 enables +FUNCTION {default.is.use.number.for.article} { #1 } + + +% #0 turns off the display of the paper and type fields in @inproceedings. +% #1 enables +FUNCTION {default.is.use.paper} { #1 } + + +% #0 turns off the display of urls +% #1 enables +FUNCTION {default.is.use.url} { #1 } + + +% #0 turns off the forced use of "et al." +% #1 enables +FUNCTION {default.is.forced.et.al} { #0 } + + +% The maximum number of names that can be present beyond which an "et al." +% usage is forced. Be sure that num.names.shown.with.forced.et.al (below) +% is not greater than this value! +% Note: There are many instances of references in IEEE journals which have +% a very large number of authors as well as instances in which "et al." is +% used profusely. +FUNCTION {default.max.num.names.before.forced.et.al} { #10 } + + +% The number of names that will be shown with a forced "et al.". +% Must be less than or equal to max.num.names.before.forced.et.al +FUNCTION {default.num.names.shown.with.forced.et.al} { #1 } + + +% #0 turns off the alternate interword spacing for entries with URLs. +% #1 enables +FUNCTION {default.is.use.alt.interword.spacing} { #1 } + + +% If alternate interword spacing for entries with URLs is enabled, this is +% the interword spacing stretch factor that will be used. For example, the +% default "4" here means that the interword spacing in entries with URLs can +% stretch to four times normal. Does not have to be an integer. Note that +% the value specified here can be overridden by the user in their LaTeX +% code via a command such as: +% "\providecommand\BIBentryALTinterwordstretchfactor{1.5}" in addition to +% that via the IEEEtranBSTCTL entry type. +FUNCTION {default.ALTinterwordstretchfactor} { "4" } + + +% #0 turns off the "dashification" of repeated (i.e., identical to those +% of the previous entry) names. The IEEE normally does this. +% #1 enables +FUNCTION {default.is.dash.repeated.names} { #1 } + + +% The default name format control string. +FUNCTION {default.name.format.string}{ "{f.~}{vv~}{ll}{, jj}" } + + +% The default LaTeX font command for the names. +FUNCTION {default.name.latex.cmd}{ "" } + + +% The default URL prefix. +FUNCTION {default.name.url.prefix}{ "[Online]. Available:" } + + +% Other controls that cannot be accessed via IEEEtranBSTCTL entry type. + +% #0 turns off the terminal startup banner/completed message so as to +% operate more quietly. +% #1 enables +FUNCTION {is.print.banners.to.terminal} { #1 } + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FILE VERSION AND BANNER %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +FUNCTION{bst.file.version} { "1.14" } +FUNCTION{bst.file.date} { "2015/08/26" } +FUNCTION{bst.file.website} { "http://www.michaelshell.org/tex/ieeetran/bibtex/" } + +FUNCTION {banner.message} +{ is.print.banners.to.terminal + { "-- IEEEtranS.bst version" " " * bst.file.version * + " (" * bst.file.date * ") " * "by Michael Shell." * + top$ + "-- " bst.file.website * + top$ + "-- See the " quote$ * "IEEEtran_bst_HOWTO.pdf" * quote$ * " manual for usage information." * + top$ + "** Sorting version - not for normal IEEE work." + top$ + } + { skip$ } + if$ +} + +FUNCTION {completed.message} +{ is.print.banners.to.terminal + { "" + top$ + "Done." + top$ + } + { skip$ } + if$ +} + + + + +%%%%%%%%%%%%%%%%%%%%%% +%% STRING CONSTANTS %% +%%%%%%%%%%%%%%%%%%%%%% +FUNCTION {bbl.a}{ "A" } +FUNCTION {bbl.an}{ "An" } +FUNCTION {bbl.and}{ "and" } +FUNCTION {bbl.etal}{ "et~al." } +FUNCTION {bbl.editors}{ "eds." } +FUNCTION {bbl.editor}{ "ed." } +FUNCTION {bbl.edition}{ "ed." } +FUNCTION {bbl.volume}{ "vol." } +FUNCTION {bbl.of}{ "of" } +FUNCTION {bbl.number}{ "no." } +FUNCTION {bbl.in}{ "in" } +FUNCTION {bbl.pages}{ "pp." } +FUNCTION {bbl.page}{ "p." } +FUNCTION {bbl.chapter}{ "ch." } +FUNCTION {bbl.paper}{ "paper" } +FUNCTION {bbl.part}{ "pt." } +FUNCTION {bbl.patent}{ "Patent" } +FUNCTION {bbl.patentUS}{ "U.S." } +FUNCTION {bbl.revision}{ "Rev." } +FUNCTION {bbl.series}{ "ser." } +FUNCTION {bbl.standard}{ "Std." } +FUNCTION {bbl.techrep}{ "Tech. Rep." } +FUNCTION {bbl.the}{ "The" } +FUNCTION {bbl.mthesis}{ "Master's thesis" } +FUNCTION {bbl.phdthesis}{ "Ph.D. dissertation" } +FUNCTION {bbl.st}{ "st" } +FUNCTION {bbl.nd}{ "nd" } +FUNCTION {bbl.rd}{ "rd" } +FUNCTION {bbl.th}{ "th" } + + +% This is the LaTeX spacer that is used when a larger than normal space +% is called for (such as just before the address:publisher). +FUNCTION {large.space} { "\hskip 1em plus 0.5em minus 0.4em\relax " } + +% The LaTeX code for dashes that are used to represent repeated names. +% Note: Some older IEEE journals used something like +% "\rule{0.275in}{0.5pt}\," which is fairly thick and runs right along +% the baseline. However, the IEEE now uses a thinner, above baseline, +% six dash long sequence. +FUNCTION {repeated.name.dashes} { "------" } + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% PREDEFINED STRING MACROS %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +MACRO {jan} {"Jan."} +MACRO {feb} {"Feb."} +MACRO {mar} {"Mar."} +MACRO {apr} {"Apr."} +MACRO {may} {"May"} +MACRO {jun} {"Jun."} +MACRO {jul} {"Jul."} +MACRO {aug} {"Aug."} +MACRO {sep} {"Sep."} +MACRO {oct} {"Oct."} +MACRO {nov} {"Nov."} +MACRO {dec} {"Dec."} + + + +%%%%%%%%%%%%%%%%%% +%% ENTRY FIELDS %% +%%%%%%%%%%%%%%%%%% + +ENTRY + { address + assignee + author + booktitle + chapter + day + dayfiled + edition + editor + howpublished + institution + intype + journal + key + language + month + monthfiled + nationality + note + number + organization + pages + paper + publisher + school + series + revision + title + type + url + volume + year + yearfiled + CTLuse_article_number + CTLuse_paper + CTLuse_url + CTLuse_forced_etal + CTLmax_names_forced_etal + CTLnames_show_etal + CTLuse_alt_spacing + CTLalt_stretch_factor + CTLdash_repeated_names + CTLname_format_string + CTLname_latex_cmd + CTLname_url_prefix + } + {} + { label } + + + + +%%%%%%%%%%%%%%%%%%%%%%% +%% INTEGER VARIABLES %% +%%%%%%%%%%%%%%%%%%%%%%% + +INTEGERS { prev.status.punct this.status.punct punct.std + punct.no punct.comma punct.period + prev.status.space this.status.space space.std + space.no space.normal space.large + prev.status.quote this.status.quote quote.std + quote.no quote.close + prev.status.nline this.status.nline nline.std + nline.no nline.newblock + status.cap cap.std + cap.no cap.yes} + +INTEGERS { longest.label.width multiresult nameptr namesleft number.label numnames } + +INTEGERS { is.use.number.for.article + is.use.paper + is.use.url + is.forced.et.al + max.num.names.before.forced.et.al + num.names.shown.with.forced.et.al + is.use.alt.interword.spacing + is.dash.repeated.names} + + +%%%%%%%%%%%%%%%%%%%%%% +%% STRING VARIABLES %% +%%%%%%%%%%%%%%%%%%%%%% + +STRINGS { bibinfo + longest.label + oldname + s + t + ALTinterwordstretchfactor + name.format.string + name.latex.cmd + name.url.prefix} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%% +%% LOW LEVEL FUNCTIONS %% +%%%%%%%%%%%%%%%%%%%%%%%%% + +FUNCTION {initialize.controls} +{ default.is.use.number.for.article 'is.use.number.for.article := + default.is.use.paper 'is.use.paper := + default.is.use.url 'is.use.url := + default.is.forced.et.al 'is.forced.et.al := + default.max.num.names.before.forced.et.al 'max.num.names.before.forced.et.al := + default.num.names.shown.with.forced.et.al 'num.names.shown.with.forced.et.al := + default.is.use.alt.interword.spacing 'is.use.alt.interword.spacing := + default.is.dash.repeated.names 'is.dash.repeated.names := + default.ALTinterwordstretchfactor 'ALTinterwordstretchfactor := + default.name.format.string 'name.format.string := + default.name.latex.cmd 'name.latex.cmd := + default.name.url.prefix 'name.url.prefix := +} + + +% This IEEEtran.bst features a very powerful and flexible mechanism for +% controlling the capitalization, punctuation, spacing, quotation, and +% newlines of the formatted entry fields. (Note: IEEEtran.bst does not need +% or use the newline/newblock feature, but it has been implemented for +% possible future use.) The output states of IEEEtran.bst consist of +% multiple independent attributes and, as such, can be thought of as being +% vectors, rather than the simple scalar values ("before.all", +% "mid.sentence", etc.) used in most other .bst files. +% +% The more flexible and complex design used here was motivated in part by +% the IEEE's rather unusual bibliography style. For example, the IEEE ends the +% previous field item with a period and large space prior to the publisher +% address; the @electronic entry types use periods as inter-item punctuation +% rather than the commas used by the other entry types; and URLs are never +% followed by periods even though they are the last item in the entry. +% Although it is possible to accommodate these features with the conventional +% output state system, the seemingly endless exceptions make for convoluted, +% unreliable and difficult to maintain code. +% +% IEEEtran.bst's output state system can be easily understood via a simple +% illustration of two most recently formatted entry fields (on the stack): +% +% CURRENT_ITEM +% "PREVIOUS_ITEM +% +% which, in this example, is to eventually appear in the bibliography as: +% +% "PREVIOUS_ITEM," CURRENT_ITEM +% +% It is the job of the output routine to take the previous item off of the +% stack (while leaving the current item at the top of the stack), apply its +% trailing punctuation (including closing quote marks) and spacing, and then +% to write the result to BibTeX's output buffer: +% +% "PREVIOUS_ITEM," +% +% Punctuation (and spacing) between items is often determined by both of the +% items rather than just the first one. The presence of quotation marks +% further complicates the situation because, in standard English, trailing +% punctuation marks are supposed to be contained within the quotes. +% +% IEEEtran.bst maintains two output state (aka "status") vectors which +% correspond to the previous and current (aka "this") items. Each vector +% consists of several independent attributes which track punctuation, +% spacing, quotation, and newlines. Capitalization status is handled by a +% separate scalar because the format routines, not the output routine, +% handle capitalization and, therefore, there is no need to maintain the +% capitalization attribute for both the "previous" and "this" items. +% +% When a format routine adds a new item, it copies the current output status +% vector to the previous output status vector and (usually) resets the +% current (this) output status vector to a "standard status" vector. Using a +% "standard status" vector in this way allows us to redefine what we mean by +% "standard status" at the start of each entry handler and reuse the same +% format routines under the various inter-item separation schemes. For +% example, the standard status vector for the @book entry type may use +% commas for item separators, while the @electronic type may use periods, +% yet both entry handlers exploit many of the exact same format routines. +% +% Because format routines have write access to the output status vector of +% the previous item, they can override the punctuation choices of the +% previous format routine! Therefore, it becomes trivial to implement rules +% such as "Always use a period and a large space before the publisher." By +% pushing the generation of the closing quote mark to the output routine, we +% avoid all the problems caused by having to close a quote before having all +% the information required to determine what the punctuation should be. +% +% The IEEEtran.bst output state system can easily be expanded if needed. +% For instance, it is easy to add a "space.tie" attribute value if the +% bibliography rules mandate that two items have to be joined with an +% unbreakable space. + +FUNCTION {initialize.status.constants} +{ #0 'punct.no := + #1 'punct.comma := + #2 'punct.period := + #0 'space.no := + #1 'space.normal := + #2 'space.large := + #0 'quote.no := + #1 'quote.close := + #0 'cap.no := + #1 'cap.yes := + #0 'nline.no := + #1 'nline.newblock := +} + +FUNCTION {std.status.using.comma} +{ punct.comma 'punct.std := + space.normal 'space.std := + quote.no 'quote.std := + nline.no 'nline.std := + cap.no 'cap.std := +} + +FUNCTION {std.status.using.period} +{ punct.period 'punct.std := + space.normal 'space.std := + quote.no 'quote.std := + nline.no 'nline.std := + cap.yes 'cap.std := +} + +FUNCTION {initialize.prev.this.status} +{ punct.no 'prev.status.punct := + space.no 'prev.status.space := + quote.no 'prev.status.quote := + nline.no 'prev.status.nline := + punct.no 'this.status.punct := + space.no 'this.status.space := + quote.no 'this.status.quote := + nline.no 'this.status.nline := + cap.yes 'status.cap := +} + +FUNCTION {this.status.std} +{ punct.std 'this.status.punct := + space.std 'this.status.space := + quote.std 'this.status.quote := + nline.std 'this.status.nline := +} + +FUNCTION {cap.status.std}{ cap.std 'status.cap := } + +FUNCTION {this.to.prev.status} +{ this.status.punct 'prev.status.punct := + this.status.space 'prev.status.space := + this.status.quote 'prev.status.quote := + this.status.nline 'prev.status.nline := +} + + +FUNCTION {not} +{ { #0 } + { #1 } + if$ +} + +FUNCTION {and} +{ { skip$ } + { pop$ #0 } + if$ +} + +FUNCTION {or} +{ { pop$ #1 } + { skip$ } + if$ +} + + +% convert the strings "yes" or "no" to #1 or #0 respectively +FUNCTION {yes.no.to.int} +{ "l" change.case$ duplicate$ + "yes" = + { pop$ #1 } + { duplicate$ "no" = + { pop$ #0 } + { "unknown boolean " quote$ * swap$ * quote$ * + " in " * cite$ * warning$ + #0 + } + if$ + } + if$ +} + + +% pushes true if the single char string on the stack is in the +% range of "0" to "9" +FUNCTION {is.num} +{ chr.to.int$ + duplicate$ "0" chr.to.int$ < not + swap$ "9" chr.to.int$ > not and +} + +% multiplies the integer on the stack by a factor of 10 +FUNCTION {bump.int.mag} +{ #0 'multiresult := + { duplicate$ #0 > } + { #1 - + multiresult #10 + + 'multiresult := + } + while$ +pop$ +multiresult +} + +% converts a single character string on the stack to an integer +FUNCTION {char.to.integer} +{ duplicate$ + is.num + { chr.to.int$ "0" chr.to.int$ - } + {"noninteger character " quote$ * swap$ * quote$ * + " in integer field of " * cite$ * warning$ + #0 + } + if$ +} + +% converts a string on the stack to an integer +FUNCTION {string.to.integer} +{ duplicate$ text.length$ 'namesleft := + #1 'nameptr := + #0 'numnames := + { nameptr namesleft > not } + { duplicate$ nameptr #1 substring$ + char.to.integer numnames bump.int.mag + + 'numnames := + nameptr #1 + + 'nameptr := + } + while$ +pop$ +numnames +} + + + + +% The output routines write out the *next* to the top (previous) item on the +% stack, adding punctuation and such as needed. Since IEEEtran.bst maintains +% the output status for the top two items on the stack, these output +% routines have to consider the previous output status (which corresponds to +% the item that is being output). Full independent control of punctuation, +% closing quote marks, spacing, and newblock is provided. +% +% "output.nonnull" does not check for the presence of a previous empty +% item. +% +% "output" does check for the presence of a previous empty item and will +% remove an empty item rather than outputing it. +% +% "output.warn" is like "output", but will issue a warning if it detects +% an empty item. + +FUNCTION {output.nonnull} +{ swap$ + prev.status.punct punct.comma = + { "," * } + { skip$ } + if$ + prev.status.punct punct.period = + { add.period$ } + { skip$ } + if$ + prev.status.quote quote.close = + { "''" * } + { skip$ } + if$ + prev.status.space space.normal = + { " " * } + { skip$ } + if$ + prev.status.space space.large = + { large.space * } + { skip$ } + if$ + write$ + prev.status.nline nline.newblock = + { newline$ "\newblock " write$ } + { skip$ } + if$ +} + +FUNCTION {output} +{ duplicate$ empty$ + 'pop$ + 'output.nonnull + if$ +} + +FUNCTION {output.warn} +{ 't := + duplicate$ empty$ + { pop$ "empty " t * " in " * cite$ * warning$ } + 'output.nonnull + if$ +} + +% "fin.entry" is the output routine that handles the last item of the entry +% (which will be on the top of the stack when "fin.entry" is called). + +FUNCTION {fin.entry} +{ this.status.punct punct.no = + { skip$ } + { add.period$ } + if$ + this.status.quote quote.close = + { "''" * } + { skip$ } + if$ +write$ +newline$ +} + + +FUNCTION {is.last.char.not.punct} +{ duplicate$ + "}" * add.period$ + #-1 #1 substring$ "." = +} + +FUNCTION {is.multiple.pages} +{ 't := + #0 'multiresult := + { multiresult not + t empty$ not + and + } + { t #1 #1 substring$ + duplicate$ "-" = + swap$ duplicate$ "," = + swap$ "+" = + or or + { #1 'multiresult := } + { t #2 global.max$ substring$ 't := } + if$ + } + while$ + multiresult +} + +FUNCTION {capitalize}{ "u" change.case$ "t" change.case$ } + +FUNCTION {emphasize} +{ duplicate$ empty$ + { pop$ "" } + { "\emph{" swap$ * "}" * } + if$ +} + +FUNCTION {do.name.latex.cmd} +{ name.latex.cmd + empty$ + { skip$ } + { name.latex.cmd "{" * swap$ * "}" * } + if$ +} + +% IEEEtran.bst uses its own \BIBforeignlanguage command which directly +% invokes the TeX hyphenation patterns without the need of the Babel +% package. Babel does a lot more than switch hyphenation patterns and +% its loading can cause unintended effects in many class files (such as +% IEEEtran.cls). +FUNCTION {select.language} +{ duplicate$ empty$ 'pop$ + { language empty$ 'skip$ + { "\BIBforeignlanguage{" language * "}{" * swap$ * "}" * } + if$ + } + if$ +} + +FUNCTION {tie.or.space.prefix} +{ duplicate$ text.length$ #3 < + { "~" } + { " " } + if$ + swap$ +} + +FUNCTION {get.bbl.editor} +{ editor num.names$ #1 > 'bbl.editors 'bbl.editor if$ } + +FUNCTION {space.word}{ " " swap$ * " " * } + + +% Field Conditioners, Converters, Checkers and External Interfaces + +FUNCTION {empty.field.to.null.string} +{ duplicate$ empty$ + { pop$ "" } + { skip$ } + if$ +} + +FUNCTION {either.or.check} +{ empty$ + { pop$ } + { "can't use both " swap$ * " fields in " * cite$ * warning$ } + if$ +} + +FUNCTION {empty.entry.warn} +{ author empty$ title empty$ howpublished empty$ + month empty$ year empty$ note empty$ url empty$ + and and and and and and + { "all relevant fields are empty in " cite$ * warning$ } + 'skip$ + if$ +} + + +% The bibinfo system provides a way for the electronic parsing/acquisition +% of a bibliography's contents as is done by ReVTeX. For example, a field +% could be entered into the bibliography as: +% \bibinfo{volume}{2} +% Only the "2" would show up in the document, but the LaTeX \bibinfo command +% could do additional things with the information. IEEEtran.bst does provide +% a \bibinfo command via "\providecommand{\bibinfo}[2]{#2}". However, it is +% currently not used as the bogus bibinfo functions defined here output the +% entry values directly without the \bibinfo wrapper. The bibinfo functions +% themselves (and the calls to them) are retained for possible future use. +% +% bibinfo.check avoids acting on missing fields while bibinfo.warn will +% issue a warning message if a missing field is detected. Prior to calling +% the bibinfo functions, the user should push the field value and then its +% name string, in that order. + +FUNCTION {bibinfo.check} +{ swap$ duplicate$ missing$ + { pop$ pop$ "" } + { duplicate$ empty$ + { swap$ pop$ } + { swap$ pop$ } + if$ + } + if$ +} + +FUNCTION {bibinfo.warn} +{ swap$ duplicate$ missing$ + { swap$ "missing " swap$ * " in " * cite$ * warning$ pop$ "" } + { duplicate$ empty$ + { swap$ "empty " swap$ * " in " * cite$ * warning$ } + { swap$ pop$ } + if$ + } + if$ +} + + +% The IEEE separates large numbers with more than 4 digits into groups of +% three. The IEEE uses a small space to separate these number groups. +% Typical applications include patent and page numbers. + +% number of consecutive digits required to trigger the group separation. +FUNCTION {large.number.trigger}{ #5 } + +% For numbers longer than the trigger, this is the blocksize of the groups. +% The blocksize must be less than the trigger threshold, and 2 * blocksize +% must be greater than the trigger threshold (can't do more than one +% separation on the initial trigger). +FUNCTION {large.number.blocksize}{ #3 } + +% What is actually inserted between the number groups. +FUNCTION {large.number.separator}{ "\," } + +% So as to save on integer variables by reusing existing ones, numnames +% holds the current number of consecutive digits read and nameptr holds +% the number that will trigger an inserted space. +FUNCTION {large.number.separate} +{ 't := + "" + #0 'numnames := + large.number.trigger 'nameptr := + { t empty$ not } + { t #-1 #1 substring$ is.num + { numnames #1 + 'numnames := } + { #0 'numnames := + large.number.trigger 'nameptr := + } + if$ + t #-1 #1 substring$ swap$ * + t #-2 global.max$ substring$ 't := + numnames nameptr = + { duplicate$ #1 nameptr large.number.blocksize - substring$ swap$ + nameptr large.number.blocksize - #1 + global.max$ substring$ + large.number.separator swap$ * * + nameptr large.number.blocksize - 'numnames := + large.number.blocksize #1 + 'nameptr := + } + { skip$ } + if$ + } + while$ +} + +% Converts all single dashes "-" to double dashes "--". +FUNCTION {n.dashify} +{ large.number.separate + 't := + "" + { t empty$ not } + { t #1 #1 substring$ "-" = + { t #1 #2 substring$ "--" = not + { "--" * + t #2 global.max$ substring$ 't := + } + { { t #1 #1 substring$ "-" = } + { "-" * + t #2 global.max$ substring$ 't := + } + while$ + } + if$ + } + { t #1 #1 substring$ * + t #2 global.max$ substring$ 't := + } + if$ + } + while$ +} + + +% This function detects entries with names that are identical to that of +% the previous entry and replaces the repeated names with dashes (if the +% "is.dash.repeated.names" user control is nonzero). +FUNCTION {name.or.dash} +{ 's := + oldname empty$ + { s 'oldname := s } + { s oldname = + { is.dash.repeated.names + { repeated.name.dashes } + { s 'oldname := s } + if$ + } + { s 'oldname := s } + if$ + } + if$ +} + +% Converts the number string on the top of the stack to +% "numerical ordinal form" (e.g., "7" to "7th"). There is +% no artificial limit to the upper bound of the numbers as the +% two least significant digits determine the ordinal form. +FUNCTION {num.to.ordinal} +{ duplicate$ #-2 #1 substring$ "1" = + { bbl.th * } + { duplicate$ #-1 #1 substring$ "1" = + { bbl.st * } + { duplicate$ #-1 #1 substring$ "2" = + { bbl.nd * } + { duplicate$ #-1 #1 substring$ "3" = + { bbl.rd * } + { bbl.th * } + if$ + } + if$ + } + if$ + } + if$ +} + +% If the string on the top of the stack begins with a number, +% (e.g., 11th) then replace the string with the leading number +% it contains. Otherwise retain the string as-is. s holds the +% extracted number, t holds the part of the string that remains +% to be scanned. +FUNCTION {extract.num} +{ duplicate$ 't := + "" 's := + { t empty$ not } + { t #1 #1 substring$ + t #2 global.max$ substring$ 't := + duplicate$ is.num + { s swap$ * 's := } + { pop$ "" 't := } + if$ + } + while$ + s empty$ + 'skip$ + { pop$ s } + if$ +} + +% Converts the word number string on the top of the stack to +% Arabic string form. Will be successful up to "tenth". +FUNCTION {word.to.num} +{ duplicate$ "l" change.case$ 's := + s "first" = + { pop$ "1" } + { skip$ } + if$ + s "second" = + { pop$ "2" } + { skip$ } + if$ + s "third" = + { pop$ "3" } + { skip$ } + if$ + s "fourth" = + { pop$ "4" } + { skip$ } + if$ + s "fifth" = + { pop$ "5" } + { skip$ } + if$ + s "sixth" = + { pop$ "6" } + { skip$ } + if$ + s "seventh" = + { pop$ "7" } + { skip$ } + if$ + s "eighth" = + { pop$ "8" } + { skip$ } + if$ + s "ninth" = + { pop$ "9" } + { skip$ } + if$ + s "tenth" = + { pop$ "10" } + { skip$ } + if$ +} + + +% Converts the string on the top of the stack to numerical +% ordinal (e.g., "11th") form. +FUNCTION {convert.edition} +{ duplicate$ empty$ 'skip$ + { duplicate$ #1 #1 substring$ is.num + { extract.num + num.to.ordinal + } + { word.to.num + duplicate$ #1 #1 substring$ is.num + { num.to.ordinal } + { "edition ordinal word " quote$ * edition * quote$ * + " may be too high (or improper) for conversion" * " in " * cite$ * warning$ + } + if$ + } + if$ + } + if$ +} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% LATEX BIBLIOGRAPHY CODE %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +FUNCTION {start.entry} +{ newline$ + "\bibitem{" write$ + cite$ write$ + "}" write$ + newline$ + "" + initialize.prev.this.status +} + +% Here we write out all the LaTeX code that we will need. The most involved +% code sequences are those that control the alternate interword spacing and +% foreign language hyphenation patterns. The heavy use of \providecommand +% gives users a way to override the defaults. Special thanks to Javier Bezos, +% Johannes Braams, Robin Fairbairns, Heiko Oberdiek, Donald Arseneau and all +% the other gurus on comp.text.tex for their help and advice on the topic of +% \selectlanguage, Babel and BibTeX. +FUNCTION {begin.bib} +{ "% Generated by IEEEtranS.bst, version: " bst.file.version * " (" * bst.file.date * ")" * + write$ newline$ + preamble$ empty$ 'skip$ + { preamble$ write$ newline$ } + if$ + "\begin{thebibliography}{" longest.label * "}" * + write$ newline$ + "\providecommand{\url}[1]{#1}" + write$ newline$ + "\csname url@samestyle\endcsname" + write$ newline$ + "\providecommand{\newblock}{\relax}" + write$ newline$ + "\providecommand{\bibinfo}[2]{#2}" + write$ newline$ + "\providecommand{\BIBentrySTDinterwordspacing}{\spaceskip=0pt\relax}" + write$ newline$ + "\providecommand{\BIBentryALTinterwordstretchfactor}{" + ALTinterwordstretchfactor * "}" * + write$ newline$ + "\providecommand{\BIBentryALTinterwordspacing}{\spaceskip=\fontdimen2\font plus " + write$ newline$ + "\BIBentryALTinterwordstretchfactor\fontdimen3\font minus \fontdimen4\font\relax}" + write$ newline$ + "\providecommand{\BIBforeignlanguage}[2]{{%" + write$ newline$ + "\expandafter\ifx\csname l@#1\endcsname\relax" + write$ newline$ + "\typeout{** WARNING: IEEEtranS.bst: No hyphenation pattern has been}%" + write$ newline$ + "\typeout{** loaded for the language `#1'. Using the pattern for}%" + write$ newline$ + "\typeout{** the default language instead.}%" + write$ newline$ + "\else" + write$ newline$ + "\language=\csname l@#1\endcsname" + write$ newline$ + "\fi" + write$ newline$ + "#2}}" + write$ newline$ + "\providecommand{\BIBdecl}{\relax}" + write$ newline$ + "\BIBdecl" + write$ newline$ +} + +FUNCTION {end.bib} +{ newline$ "\end{thebibliography}" write$ newline$ } + +FUNCTION {if.url.alt.interword.spacing} +{ is.use.alt.interword.spacing + { is.use.url + { url empty$ 'skip$ {"\BIBentryALTinterwordspacing" write$ newline$} if$ } + { skip$ } + if$ + } + { skip$ } + if$ +} + +FUNCTION {if.url.std.interword.spacing} +{ is.use.alt.interword.spacing + { is.use.url + { url empty$ 'skip$ {"\BIBentrySTDinterwordspacing" write$ newline$} if$ } + { skip$ } + if$ + } + { skip$ } + if$ +} + + + + +%%%%%%%%%%%%%%%%%%%%%%%% +%% LONGEST LABEL PASS %% +%%%%%%%%%%%%%%%%%%%%%%%% + +FUNCTION {initialize.longest.label} +{ "" 'longest.label := + #1 'number.label := + #0 'longest.label.width := +} + +FUNCTION {longest.label.pass} +{ type$ "ieeetranbstctl" = + { skip$ } + { number.label int.to.str$ 'label := + number.label #1 + 'number.label := + label width$ longest.label.width > + { label 'longest.label := + label width$ 'longest.label.width := + } + { skip$ } + if$ + } + if$ +} + + + + +%%%%%%%%%%%%%%%%%%%%% +%% FORMAT HANDLERS %% +%%%%%%%%%%%%%%%%%%%%% + +%% Lower Level Formats (used by higher level formats) + +FUNCTION {format.address.org.or.pub.date} +{ 't := + "" + year empty$ + { "empty year in " cite$ * warning$ } + { skip$ } + if$ + address empty$ t empty$ and + year empty$ and month empty$ and + { skip$ } + { this.to.prev.status + this.status.std + cap.status.std + address "address" bibinfo.check * + t empty$ + { skip$ } + { punct.period 'prev.status.punct := + space.large 'prev.status.space := + address empty$ + { skip$ } + { ": " * } + if$ + t * + } + if$ + year empty$ month empty$ and + { skip$ } + { t empty$ address empty$ and + { skip$ } + { ", " * } + if$ + month empty$ + { year empty$ + { skip$ } + { year "year" bibinfo.check * } + if$ + } + { month "month" bibinfo.check * + year empty$ + { skip$ } + { " " * year "year" bibinfo.check * } + if$ + } + if$ + } + if$ + } + if$ +} + + +FUNCTION {format.names} +{ 'bibinfo := + duplicate$ empty$ 'skip$ { + this.to.prev.status + this.status.std + 's := + "" 't := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + name.format.string + format.name$ + bibinfo bibinfo.check + 't := + nameptr #1 > + { nameptr num.names.shown.with.forced.et.al #1 + = + numnames max.num.names.before.forced.et.al > + is.forced.et.al and and + { "others" 't := + #1 'namesleft := + } + { skip$ } + if$ + namesleft #1 > + { ", " * t do.name.latex.cmd * } + { s nameptr "{ll}" format.name$ duplicate$ "others" = + { 't := } + { pop$ } + if$ + t "others" = + { " " * bbl.etal emphasize * } + { numnames #2 > + { "," * } + { skip$ } + if$ + bbl.and + space.word * t do.name.latex.cmd * + } + if$ + } + if$ + } + { t do.name.latex.cmd } + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ + cap.status.std + } if$ +} + + + + +%% Higher Level Formats + +%% addresses/locations + +FUNCTION {format.address} +{ address duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + } + if$ +} + + + +%% author/editor names + +FUNCTION {format.authors}{ author "author" format.names } + +FUNCTION {format.editors} +{ editor "editor" format.names duplicate$ empty$ 'skip$ + { ", " * + get.bbl.editor + capitalize + * + } + if$ +} + + + +%% date + +FUNCTION {format.date} +{ + month "month" bibinfo.check duplicate$ empty$ + year "year" bibinfo.check duplicate$ empty$ + { swap$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + "there's a month but no year in " cite$ * warning$ } + if$ + * + } + { this.to.prev.status + this.status.std + cap.status.std + swap$ 'skip$ + { + swap$ + " " * swap$ + } + if$ + * + } + if$ +} + +FUNCTION {format.date.electronic} +{ month "month" bibinfo.check duplicate$ empty$ + year "year" bibinfo.check duplicate$ empty$ + { swap$ + { pop$ } + { "there's a month but no year in " cite$ * warning$ + pop$ ")" * "(" swap$ * + this.to.prev.status + punct.no 'this.status.punct := + space.normal 'this.status.space := + quote.no 'this.status.quote := + cap.yes 'status.cap := + } + if$ + } + { swap$ + { swap$ pop$ ")" * "(" swap$ * } + { "(" swap$ * ", " * swap$ * ")" * } + if$ + this.to.prev.status + punct.no 'this.status.punct := + space.normal 'this.status.space := + quote.no 'this.status.quote := + cap.yes 'status.cap := + } + if$ +} + + + +%% edition/title + +% Note: The IEEE considers the edition to be closely associated with +% the title of a book. So, in IEEEtran.bst the edition is normally handled +% within the formatting of the title. The format.edition function is +% retained here for possible future use. +FUNCTION {format.edition} +{ edition duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + convert.edition + status.cap + { "t" } + { "l" } + if$ change.case$ + "edition" bibinfo.check + "~" * bbl.edition * + cap.status.std + } + if$ +} + +% This is used to format the booktitle of a conference proceedings. +% Here we use the "intype" field to provide the user a way to +% override the word "in" (e.g., with things like "presented at") +% Use of intype stops the emphasis of the booktitle to indicate that +% we no longer mean the written conference proceedings, but the +% conference itself. +FUNCTION {format.in.booktitle} +{ booktitle "booktitle" bibinfo.check duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + select.language + intype missing$ + { emphasize + bbl.in " " * + } + { intype " " * } + if$ + swap$ * + cap.status.std + } + if$ +} + +% This is used to format the booktitle of collection. +% Here the "intype" field is not supported, but "edition" is. +FUNCTION {format.in.booktitle.edition} +{ booktitle "booktitle" bibinfo.check duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + select.language + emphasize + edition empty$ 'skip$ + { ", " * + edition + convert.edition + "l" change.case$ + * "~" * bbl.edition * + } + if$ + bbl.in " " * swap$ * + cap.status.std + } + if$ +} + +FUNCTION {format.article.title} +{ title duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + "t" change.case$ + } + if$ + "title" bibinfo.check + duplicate$ empty$ 'skip$ + { quote.close 'this.status.quote := + is.last.char.not.punct + { punct.std 'this.status.punct := } + { punct.no 'this.status.punct := } + if$ + select.language + "``" swap$ * + cap.status.std + } + if$ +} + +FUNCTION {format.article.title.electronic} +{ title duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + "t" change.case$ + } + if$ + "title" bibinfo.check + duplicate$ empty$ + { skip$ } + { select.language } + if$ +} + +FUNCTION {format.book.title.edition} +{ title "title" bibinfo.check + duplicate$ empty$ + { "empty title in " cite$ * warning$ } + { this.to.prev.status + this.status.std + select.language + emphasize + edition empty$ 'skip$ + { ", " * + edition + convert.edition + status.cap + { "t" } + { "l" } + if$ + change.case$ + * "~" * bbl.edition * + } + if$ + cap.status.std + } + if$ +} + +FUNCTION {format.book.title} +{ title "title" bibinfo.check + duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + select.language + emphasize + } + if$ +} + + + +%% journal + +FUNCTION {format.journal} +{ journal duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + select.language + emphasize + } + if$ +} + + + +%% how published + +FUNCTION {format.howpublished} +{ howpublished duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + } + if$ +} + + + +%% institutions/organization/publishers/school + +FUNCTION {format.institution} +{ institution duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + } + if$ +} + +FUNCTION {format.organization} +{ organization duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + } + if$ +} + +FUNCTION {format.address.publisher.date} +{ publisher "publisher" bibinfo.warn format.address.org.or.pub.date } + +FUNCTION {format.address.publisher.date.nowarn} +{ publisher "publisher" bibinfo.check format.address.org.or.pub.date } + +FUNCTION {format.address.organization.date} +{ organization "organization" bibinfo.check format.address.org.or.pub.date } + +FUNCTION {format.school} +{ school duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + cap.status.std + } + if$ +} + + + +%% volume/number/series/chapter/pages + +FUNCTION {format.volume} +{ volume empty.field.to.null.string + duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + bbl.volume + status.cap + { capitalize } + { skip$ } + if$ + swap$ tie.or.space.prefix + "volume" bibinfo.check + * * + cap.status.std + } + if$ +} + +FUNCTION {format.number} +{ number empty.field.to.null.string + duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + status.cap + { bbl.number capitalize } + { bbl.number } + if$ + swap$ tie.or.space.prefix + "number" bibinfo.check + * * + cap.status.std + } + if$ +} + +FUNCTION {format.number.if.use.for.article} +{ is.use.number.for.article + { format.number } + { "" } + if$ +} + +% The IEEE does not seem to tie the series so closely with the volume +% and number as is done in other bibliography styles. Instead the +% series is treated somewhat like an extension of the title. +FUNCTION {format.series} +{ series empty$ + { "" } + { this.to.prev.status + this.status.std + bbl.series " " * + series "series" bibinfo.check * + cap.status.std + } + if$ +} + + +FUNCTION {format.chapter} +{ chapter empty$ + { "" } + { this.to.prev.status + this.status.std + type empty$ + { bbl.chapter } + { type "l" change.case$ + "type" bibinfo.check + } + if$ + chapter tie.or.space.prefix + "chapter" bibinfo.check + * * + cap.status.std + } + if$ +} + + +% The intended use of format.paper is for paper numbers of inproceedings. +% The paper type can be overridden via the type field. +% We allow the type to be displayed even if the paper number is absent +% for things like "postdeadline paper" +FUNCTION {format.paper} +{ is.use.paper + { paper empty$ + { type empty$ + { "" } + { this.to.prev.status + this.status.std + type "type" bibinfo.check + cap.status.std + } + if$ + } + { this.to.prev.status + this.status.std + type empty$ + { bbl.paper } + { type "type" bibinfo.check } + if$ + " " * paper + "paper" bibinfo.check + * + cap.status.std + } + if$ + } + { "" } + if$ +} + + +FUNCTION {format.pages} +{ pages duplicate$ empty$ 'skip$ + { this.to.prev.status + this.status.std + duplicate$ is.multiple.pages + { + bbl.pages swap$ + n.dashify + } + { + bbl.page swap$ + } + if$ + tie.or.space.prefix + "pages" bibinfo.check + * * + cap.status.std + } + if$ +} + + + +%% technical report number + +FUNCTION {format.tech.report.number} +{ number "number" bibinfo.check + this.to.prev.status + this.status.std + cap.status.std + type duplicate$ empty$ + { pop$ + bbl.techrep + } + { skip$ } + if$ + "type" bibinfo.check + swap$ duplicate$ empty$ + { pop$ } + { tie.or.space.prefix * * } + if$ +} + + + +%% note + +FUNCTION {format.note} +{ note empty$ + { "" } + { this.to.prev.status + this.status.std + punct.period 'this.status.punct := + note #1 #1 substring$ + duplicate$ "{" = + { skip$ } + { status.cap + { "u" } + { "l" } + if$ + change.case$ + } + if$ + note #2 global.max$ substring$ * "note" bibinfo.check + cap.yes 'status.cap := + } + if$ +} + + + +%% patent + +FUNCTION {format.patent.date} +{ this.to.prev.status + this.status.std + year empty$ + { monthfiled duplicate$ empty$ + { "monthfiled" bibinfo.check pop$ "" } + { "monthfiled" bibinfo.check } + if$ + dayfiled duplicate$ empty$ + { "dayfiled" bibinfo.check pop$ "" * } + { "dayfiled" bibinfo.check + monthfiled empty$ + { "dayfiled without a monthfiled in " cite$ * warning$ + * + } + { " " swap$ * * } + if$ + } + if$ + yearfiled empty$ + { "no year or yearfiled in " cite$ * warning$ } + { yearfiled "yearfiled" bibinfo.check + swap$ + duplicate$ empty$ + { pop$ } + { ", " * swap$ * } + if$ + } + if$ + } + { month duplicate$ empty$ + { "month" bibinfo.check pop$ "" } + { "month" bibinfo.check } + if$ + day duplicate$ empty$ + { "day" bibinfo.check pop$ "" * } + { "day" bibinfo.check + month empty$ + { "day without a month in " cite$ * warning$ + * + } + { " " swap$ * * } + if$ + } + if$ + year "year" bibinfo.check + swap$ + duplicate$ empty$ + { pop$ } + { ", " * swap$ * } + if$ + } + if$ + cap.status.std +} + +FUNCTION {format.patent.nationality.type.number} +{ this.to.prev.status + this.status.std + nationality duplicate$ empty$ + { "nationality" bibinfo.warn pop$ "" } + { "nationality" bibinfo.check + duplicate$ "l" change.case$ "united states" = + { pop$ bbl.patentUS } + { skip$ } + if$ + " " * + } + if$ + type empty$ + { bbl.patent "type" bibinfo.check } + { type "type" bibinfo.check } + if$ + * + number duplicate$ empty$ + { "number" bibinfo.warn pop$ } + { "number" bibinfo.check + large.number.separate + swap$ " " * swap$ * + } + if$ + cap.status.std +} + + + +%% standard + +FUNCTION {format.organization.institution.standard.type.number} +{ this.to.prev.status + this.status.std + organization duplicate$ empty$ + { pop$ + institution duplicate$ empty$ + { "institution" bibinfo.warn } + { "institution" bibinfo.warn " " * } + if$ + } + { "organization" bibinfo.warn " " * } + if$ + type empty$ + { bbl.standard "type" bibinfo.check } + { type "type" bibinfo.check } + if$ + * + number duplicate$ empty$ + { "number" bibinfo.check pop$ } + { "number" bibinfo.check + large.number.separate + swap$ " " * swap$ * + } + if$ + cap.status.std +} + +FUNCTION {format.revision} +{ revision empty$ + { "" } + { this.to.prev.status + this.status.std + bbl.revision + revision tie.or.space.prefix + "revision" bibinfo.check + * * + cap.status.std + } + if$ +} + + +%% thesis + +FUNCTION {format.master.thesis.type} +{ this.to.prev.status + this.status.std + type empty$ + { + bbl.mthesis + } + { + type "type" bibinfo.check + } + if$ +cap.status.std +} + +FUNCTION {format.phd.thesis.type} +{ this.to.prev.status + this.status.std + type empty$ + { + bbl.phdthesis + } + { + type "type" bibinfo.check + } + if$ +cap.status.std +} + + + +%% URL +%% +FUNCTION {format.url} +{ is.use.url + { url empty$ + { "" } + { this.to.prev.status + this.status.std + cap.yes 'status.cap := + name.url.prefix " " * + "\url{" * url * "}" * + punct.no 'this.status.punct := + punct.period 'prev.status.punct := + space.normal 'this.status.space := + space.normal 'prev.status.space := + quote.no 'this.status.quote := + } + if$ + } + { "" } + if$ +} + + + + +%%%%%%%%%%%%%%%%%%%% +%% ENTRY HANDLERS %% +%%%%%%%%%%%%%%%%%%%% + + +% Note: In many journals, the IEEE (or the authors) tend not to show the number +% for articles, so the display of the number is controlled here by the +% switch "is.use.number.for.article" +FUNCTION {article} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors "author" output.warn + name.or.dash + format.article.title "title" output.warn + format.journal "journal" bibinfo.check "journal" output.warn + format.volume output + format.number.if.use.for.article output + format.pages output + format.date "year" output.warn + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {book} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + author empty$ + { format.editors "author and editor" output.warn } + { format.authors output.nonnull } + if$ + name.or.dash + format.book.title.edition output + format.series output + author empty$ + { skip$ } + { format.editors output } + if$ + format.address.publisher.date output + format.volume output + format.number output + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {booklet} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors output + name.or.dash + format.article.title "title" output.warn + format.howpublished "howpublished" bibinfo.check output + format.organization "organization" bibinfo.check output + format.address "address" bibinfo.check output + format.date output + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {electronic} +{ std.status.using.period + start.entry + if.url.alt.interword.spacing + format.authors output + name.or.dash + format.date.electronic output + format.article.title.electronic output + format.howpublished "howpublished" bibinfo.check output + format.organization "organization" bibinfo.check output + format.address "address" bibinfo.check output + format.note output + format.url output + fin.entry + empty.entry.warn + if.url.std.interword.spacing +} + +FUNCTION {inbook} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + author empty$ + { format.editors "author and editor" output.warn } + { format.authors output.nonnull } + if$ + name.or.dash + format.book.title.edition output + format.series output + format.address.publisher.date output + format.volume output + format.number output + format.chapter output + format.pages output + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {incollection} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors "author" output.warn + name.or.dash + format.article.title "title" output.warn + format.in.booktitle.edition "booktitle" output.warn + format.series output + format.editors output + format.address.publisher.date.nowarn output + format.volume output + format.number output + format.chapter output + format.pages output + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {inproceedings} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors "author" output.warn + name.or.dash + format.article.title "title" output.warn + format.in.booktitle "booktitle" output.warn + format.series output + format.editors output + format.volume output + format.number output + publisher empty$ + { format.address.organization.date output } + { format.organization "organization" bibinfo.check output + format.address.publisher.date output + } + if$ + format.paper output + format.pages output + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {manual} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors output + name.or.dash + format.book.title.edition "title" output.warn + format.howpublished "howpublished" bibinfo.check output + format.organization "organization" bibinfo.check output + format.address "address" bibinfo.check output + format.date output + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {mastersthesis} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors "author" output.warn + name.or.dash + format.article.title "title" output.warn + format.master.thesis.type output.nonnull + format.school "school" bibinfo.warn output + format.address "address" bibinfo.check output + format.date "year" output.warn + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {misc} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors output + name.or.dash + format.article.title output + format.howpublished "howpublished" bibinfo.check output + format.organization "organization" bibinfo.check output + format.address "address" bibinfo.check output + format.pages output + format.date output + format.note output + format.url output + fin.entry + empty.entry.warn + if.url.std.interword.spacing +} + +FUNCTION {patent} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors output + name.or.dash + format.article.title output + format.patent.nationality.type.number output + format.patent.date output + format.note output + format.url output + fin.entry + empty.entry.warn + if.url.std.interword.spacing +} + +FUNCTION {periodical} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.editors output + name.or.dash + format.book.title "title" output.warn + format.series output + format.volume output + format.number output + format.organization "organization" bibinfo.check output + format.date "year" output.warn + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {phdthesis} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors "author" output.warn + name.or.dash + format.article.title "title" output.warn + format.phd.thesis.type output.nonnull + format.school "school" bibinfo.warn output + format.address "address" bibinfo.check output + format.date "year" output.warn + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {proceedings} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.editors output + name.or.dash + format.book.title "title" output.warn + format.series output + format.volume output + format.number output + publisher empty$ + { format.address.organization.date output } + { format.organization "organization" bibinfo.check output + format.address.publisher.date output + } + if$ + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {standard} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors output + name.or.dash + format.book.title "title" output.warn + format.howpublished "howpublished" bibinfo.check output + format.organization.institution.standard.type.number output + format.revision output + format.date output + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {techreport} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors "author" output.warn + name.or.dash + format.article.title "title" output.warn + format.howpublished "howpublished" bibinfo.check output + format.institution "institution" bibinfo.warn output + format.address "address" bibinfo.check output + format.tech.report.number output.nonnull + format.date "year" output.warn + format.note output + format.url output + fin.entry + if.url.std.interword.spacing +} + +FUNCTION {unpublished} +{ std.status.using.comma + start.entry + if.url.alt.interword.spacing + format.authors "author" output.warn + name.or.dash + format.article.title "title" output.warn + format.date output + format.note "note" output.warn + format.url output + fin.entry + if.url.std.interword.spacing +} + + +% The special entry type which provides the user interface to the +% BST controls +FUNCTION {IEEEtranBSTCTL} +{ is.print.banners.to.terminal + { "** IEEEtran BST control entry " quote$ * cite$ * quote$ * " detected." * + top$ + } + { skip$ } + if$ + CTLuse_article_number + empty$ + { skip$ } + { CTLuse_article_number + yes.no.to.int + 'is.use.number.for.article := + } + if$ + CTLuse_paper + empty$ + { skip$ } + { CTLuse_paper + yes.no.to.int + 'is.use.paper := + } + if$ + CTLuse_url + empty$ + { skip$ } + { CTLuse_url + yes.no.to.int + 'is.use.url := + } + if$ + CTLuse_forced_etal + empty$ + { skip$ } + { CTLuse_forced_etal + yes.no.to.int + 'is.forced.et.al := + } + if$ + CTLmax_names_forced_etal + empty$ + { skip$ } + { CTLmax_names_forced_etal + string.to.integer + 'max.num.names.before.forced.et.al := + } + if$ + CTLnames_show_etal + empty$ + { skip$ } + { CTLnames_show_etal + string.to.integer + 'num.names.shown.with.forced.et.al := + } + if$ + CTLuse_alt_spacing + empty$ + { skip$ } + { CTLuse_alt_spacing + yes.no.to.int + 'is.use.alt.interword.spacing := + } + if$ + CTLalt_stretch_factor + empty$ + { skip$ } + { CTLalt_stretch_factor + 'ALTinterwordstretchfactor := + "\renewcommand{\BIBentryALTinterwordstretchfactor}{" + ALTinterwordstretchfactor * "}" * + write$ newline$ + } + if$ + CTLdash_repeated_names + empty$ + { skip$ } + { CTLdash_repeated_names + yes.no.to.int + 'is.dash.repeated.names := + } + if$ + CTLname_format_string + empty$ + { skip$ } + { CTLname_format_string + 'name.format.string := + } + if$ + CTLname_latex_cmd + empty$ + { skip$ } + { CTLname_latex_cmd + 'name.latex.cmd := + } + if$ + CTLname_url_prefix + missing$ + { skip$ } + { CTLname_url_prefix + 'name.url.prefix := + } + if$ + + + num.names.shown.with.forced.et.al max.num.names.before.forced.et.al > + { "CTLnames_show_etal cannot be greater than CTLmax_names_forced_etal in " cite$ * warning$ + max.num.names.before.forced.et.al 'num.names.shown.with.forced.et.al := + } + { skip$ } + if$ +} + + +%%%%%%%%%%%%%%%%%%% +%% ENTRY ALIASES %% +%%%%%%%%%%%%%%%%%%% +FUNCTION {conference}{inproceedings} +FUNCTION {online}{electronic} +FUNCTION {internet}{electronic} +FUNCTION {webpage}{electronic} +FUNCTION {www}{electronic} +FUNCTION {default.type}{misc} + + + +%%%%%%%%%%%%%%%%%% +%% MAIN PROGRAM %% +%%%%%%%%%%%%%%%%%% + +READ + +EXECUTE {initialize.controls} +EXECUTE {initialize.status.constants} +EXECUTE {banner.message} + + + +% BEGIN sort code based on that of plain.bst + +FUNCTION {sortify} +{ purify$ + "l" change.case$ +} + +INTEGERS { len } + +FUNCTION {chop.word} +{ 's := + 'len := + s #1 len substring$ = + { s len #1 + global.max$ substring$ } + { s } + if$ +} + +FUNCTION {sort.format.names} +{ 's := + #1 'nameptr := + "" + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { nameptr #1 > + { " " * } + { skip$ } + if$ + s nameptr "{vv{ } }{ll{ }}{ ff{ }}{ jj{ }}" format.name$ 't := + nameptr numnames = t "others" = and + { "et al" * } + { t sortify * } + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {sort.format.title} +{ 't := + bbl.a " " * #2 + bbl.an " " * #3 + bbl.the " " * #4 t chop.word + chop.word + chop.word + sortify + #1 global.max$ substring$ +} + +FUNCTION {author.sort} +{ author empty$ + { key empty$ + { "to sort, need author or key in " cite$ * warning$ "" } + { key sortify } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {author.editor.sort} +{ author empty$ + { editor empty$ + { key empty$ + { "to sort, need author, editor, or key in " cite$ * warning$ "" } + { key sortify } + if$ + } + { editor sort.format.names } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {author.organization.sort} +{ author empty$ + { organization empty$ + { key empty$ + { "to sort, need author, organization, or key in " cite$ * warning$ "" } + { key sortify } + if$ + } + { bbl.the " " * #4 organization chop.word sortify } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {editor.organization.sort} +{ editor empty$ + { organization empty$ + { key empty$ + { "to sort, need editor, organization, or key in " cite$ * warning$ "" } + { key sortify } + if$ + } + { bbl.the " " * #4 organization chop.word sortify } + if$ + } + { editor sort.format.names } + if$ +} + +FUNCTION {author.organization.institution.sort} +{ author empty$ + { organization empty$ + { institution empty$ + { key empty$ + { "to sort, need author, organization, institution or key in " cite$ * warning$ "" } + { key sortify } + if$ + } + { bbl.the " " * #4 institution chop.word sortify } + if$ + } + { bbl.the " " * #4 organization chop.word sortify } + if$ + } + { author sort.format.names } + if$ +} + + +FUNCTION {presort} +{ type$ "ieeetranbstctl" = + { key empty$ + { "_" } + { key sortify } + if$ + } + { type$ "book" = + type$ "inbook" = + or + { author.editor.sort } + { type$ "proceedings" = + type$ "periodical" = + or + { editor.organization.sort } + { type$ "manual" = + type$ "electronic" = + type$ "misc" = + or or + { author.organization.sort } + { type$ "standard" = + { author.organization.institution.sort } + { author.sort } + if$ + } + if$ + } + if$ + } + if$ + " " + * + type$ "patent" = + { year empty$ + { yearfiled } + { year } + if$ + } + { year } + if$ + empty.field.to.null.string sortify + * + " " + * + title 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We studied a new way to solve these equations on overlapping triangular mesh domains, in order to smoothen the computer animation of objects that are represented using those meshes. We designed several variants of a divide-and-conquer solution method, and tested them against each other for accuracy. + +\section{Background}\label{I1} + +%We studied a new way to solve some partial differential equations (PDEs) using a divide-and-conquer method. In particular, we studied +The Laplace equation models the steady-state distribution of heat on a domain $A \subset \R^2$ with each point $(p_1,p_2)$ on its boundary $\partial A$ held at a fixed temperature $g(p_1,p_2)$. The steady-state temperature distribution $u(x,y) : A \to \R$ must satisfy +\begin{align} +\lap u (x,y) &= 0 &\text{ for all } &(x,y) \in A\setminus\partial A,\label{Eq:LaplaceEquation}\\ +u(p_1,p_2) &= g(p_1,p_2) &\text{ for all } &(p_1,p_2) \in \partial A\label{Eq:BoundaryCondition}, +\end{align} +where \eqref{Eq:LaplaceEquation} is the Laplace equation, $\lap = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2}$ is the Laplace operator and \eqref{Eq:BoundaryCondition} is the boundary condition. \eqref{Eq:LaplaceEquation} can be generalized to the Poisson equation +\begin{equation} +\lap u = h \text{ for constant } h \in \R. +\end{equation} + +The usual method for solving these PDEs numerically, known as finite element discretization, consists in approximating $A$ using a triangle mesh with vertices $v_1,\dotsc,v_n$ and substituting every function $f$ defined on $A$ by the vector of its finite evaluations $f_i=f(v_i)$. From this discrete perspective, solving either of the equations above becomes an optimization problem over a finite number of variables. The solutions to these optimization problems approximate the smooth solutions of the original PDE. + +%To solve these PDEs numerically, these equations that involve ``smooth'' differentiation over a continuous space are often ``discretized'' by approximating $A$ using a triangle mesh with vertices $v_1,\dotsc,v_n$, and formulating a ``dual optimization problem'' to the PDE over a finite number of variables. The solutions of these optimization problems approximate smooth solutions of the original PDEs. + +In the case of the Laplace and Poisson equations, this optimization problem amounts to minimizing the discrete Dirichlet energy function, which has the form +%The optimization problem consists in minimizing the Dirichlet energy function, which has the form +\begin{equation}\label{Eq:DirichletEnergy} +E(u) = \frac12\m{u}_A\tp\m{Q}\m{u}_A + \m{c}\tp\m{u}_A \text{, where } \m{u}_A = \begin{bmatrix} +u(v_1) \\ \vdots \\ u(v_n) +\end{bmatrix}, +\end{equation} +for some constant vector $\m{c} \in \R^n$. The $n \times n$ cotangent matrix $\m{Q}$ is ubiquitous in geometry processing and serves as the discrete equivalent of the continuous Laplace operator seen above; its derivation can be found in \cite{AlecThesis}. This energy is to be minimized over all $\m{u}_A \in \R^n$, subject to the boundary condition that fixes the entries of $\m{u}_A$ that correspond to vertices on $\partial A$. Expanding the matrix products in \eqref{Eq:DirichletEnergy} shows that the right-hand-side is quadratic in the entries of $\m{u}_A$, therefore standard techniques of quadratic programming that minimize quadratic functions subject to constraints yield the energy minimizer, or the vector $\m{u}_A$ that minimizes \eqref{Eq:DirichletEnergy}. However, the precise method by which these optimization problems are solved will not be a concern throughout the paper. + + +%\section{Introduction} + + +\newpage +\section{Domain Decomposition} + +How well the energy minimizers approximate solutions to the smooth PDEs depends on the quality of the mesh. Two important parameters of a mesh that determine its quality are its coarseness, as measured by the average lengths of edges (segments connecting vertices), and its regularity, as measured by the aspect ratios of its triangles. Very regular meshes have triangles that are roughly equilateral, while long and thin triangles make an irregular mesh. As mesh quality improves, the energy minimizers should converge to solutions to the PDEs. + +Generating quality meshes that represent complex shapes is an active field of research. In 3D, it is often much easier to decompose complex 3D shapes into the union of simpler domains, and then generate quality meshes for those domains. Thus, we study a divide-and-conquer approach to minimize the Dirichlet energy over the union of many domains by minimizing parts of that energy over each individual domain, while demanding that the minimizers agree wherever the domains overlap, to ensure a compatible combined minimizer. We will refer to this as the consistency requirement (formalized below). We implemented this approach to handle general pairs of overlapping 2D domains $A$ and $B$, with corresponding meshes. + +However, functions over $A$ and $B$ cannot be compared because they are represented, respectively, by vectors $\m{u}_A$ and $\m{u}_B$, whose entries are values on different sets of vertices. In order to formulate that consistency requirement, we linearly interpolate from $\m{u}_A$ over the triangles of $A$'s mesh to reconstruct a function $u_A : A \to \R$; this is to say, we take $u_A$ to be the only function which is linear on every triangle of $A$'s mesh while taking the values of $\m{u}_A$ at its vertices. +Similarly, we reconstruct $u_B : B \to \R$. This reconstruction can be plotted out, as in Figure~\ref{Fig:VisualizingConstraints}. Our contribution is to analyze the following two formulations of the consistency requirement as the linear constraints of quadratic programs, in the hopes that they can be generalized to 3D. +\begin{description} + \item[Overlap sampling constraint (OSC)] $u_A$ and $u_B$ must agree at the combined vertices of both meshes. + \item[Dirichlet sampling constraint (DSC)] $u_A$ and $u_B$ must agree at the vertices of both meshes that lie on $\partial(A \cap B)$ (a small subset of the overlap sampling constraint). +\end{description} + +\begin{figure}[h]\centering +\begin{tabular}{ccc}\\ +\includegraphics[height=5cm]{Overlap_sampling_constraint} & \quad & +\includegraphics[height=5cm]{Dirichlet_Sampling_Constraint} +\end{tabular} +\caption{Energy minimizers for the OSC (left) and the DSC (right), subject to the same boundary condition $g(x,y) = (x+0.3)^2y^2$. Note how the two generate virtually identical solutions, even though the second one is only enforcing equality on a much smaller number of vertices. +} +%The Dirichlet sampling constraint yields two barely-distinguishable layers over $A \cap B$, where equality is not enforced.} +\label{Fig:VisualizingConstraints} +\end{figure} + +\newpage +\section{Experiments and results}\label{I2} + +From each constraint we derived a quadratic program to solve the Laplace or Poisson equation over $A \cup B$, subject to a boundary condition $g : \partial(A \cup B) \to \R$. Namely, we minimized a weighted combination of $E(u_A)$ and $E(u_B)$, such that $u_A$ and $u_B$ satisfy that constraint, and take values on vertices in $\partial(A \cup B)$ as dictated by $g$. We subjected each type of quadratic program to a convergence test over two annular domains with annular union (see figure \ref{Fig:AnnulusShape}), and measured the maximum of the distance of the approximations provided by each method to the known analytical solution. We repeated this test for $\lap u=0$, $\lap u=1$ and for different levels of mesh regularity. $\lap u = 1$ was chosen for a simple nonzero right-hand side; using any other nonzero constant would have simply scaled $u$. + +We concurrently tested the ``ideal'' method: combining the meshes of $A$ and $B$ into a combined mesh for $A \cup B$, and treating the minimizer of the Dirichlet energy over that combined mesh as a ground truth (GT) proxy to the analytic solution, when the latter is unknown. This ground truth would be unavailable in 3D where combining meshes is far more difficult, but it serves as a useful benchmark of our quadratic programs in 2D. + +\begin{figure}[h] +\begin{center} +\includegraphics[width=0.6\textwidth]{annulusshape.png} + \caption{A pair of annular domains, in blue and red.} +\label{Fig:AnnulusShape} +\end{center} +\end{figure} + +Our results, presented in Figure \ref{Fig:AnnulusResults}, show the Dirichlet sampling constraint to be clearly superior. While the overlap constraint appears to be accurate when solving $\lap u=0$ on regular meshes, it fails and does not even converge to the analytical solution for $\lap u = 1$, or when the meshes become increasingly irregular. As expected, the ground truth deviates the least from the analytic solution and converges to it the fastest. + +We performed similar tests on different domain shapes, which can be seen in Figure~\ref{Fig:ExamplesShape}. Since no analytical solution is available for these pairs of meshes, we simply measured the error between our methods and the co-refined ground truth (yellow line in figure~\ref{Fig:AnnulusResults}), safely assuming that this last one will surely converge to the smooth solution of the PDE. The results obtained from these experiments agreed completely with those observed for the pair of annular domains. + +\newpage + +\begin{figure}[h] +\begin{center} +\includegraphics[width=.95\textwidth]{allfigs2.jpg} +\caption{Convergence of our methods for annular domains. The top row shows the results for regular meshes, while the bottom one shows the results for irregular meshes. The left column contains results for the equation $\lap u=0$, while the right one does so for $\lap u=1$.} +\label{Fig:AnnulusResults} +\end{center} +\end{figure} + + + +\begin{figure}[h] +\begin{center} +\includegraphics[width=0.3\textwidth]{pres1.jpg} \quad +\includegraphics[width=0.3\textwidth]{pres2.jpg} \quad +\includegraphics[width=0.3\textwidth]{pres3.jpg} \\ +\includegraphics[width=0.3\textwidth]{pres5.jpg} \quad +\includegraphics[width=0.3\textwidth]{pres6.jpg} \quad +\includegraphics[width=0.3\textwidth]{pres7.jpg} +\caption{Examples of pairs of meshes over which we have tested convergence.} +\label{Fig:ExamplesShape} +\end{center} +\end{figure} + +\newpage +\section{Conclusion} + +The overlap sampling constraint performed inconsistently between $\lap u = 0$ and $\lap u = 1$, as well as between regular and irregular meshes, although it was surprisingly accurate when solving the Laplace equation on regular meshes. + +The Dirichlet sampling constraint converged in every one of our experiments for both the Laplace and Poisson equations, regardless of regularity and shape of the meshes. While converging slower than the ground truth, its rate of convergence appears to be at least linear. It is the best candidate for future research to generalize to 3D, progressing toward our goal of solving PDEs over the union of multiple domains when computing a common mesh is infeasible. + +\mbox{}\\ + +\noindent {\Large\textbf{Acknowledgement}\\[1mm] } + +The authors would like to thank Prof. Alec Jacobson for his patient and dedicated mentorship, as well as the Fields Institute for bringing our research group together, and supporting our research with a stipend, through the Fields Undergraduate Summer Research Program. The third author would also like to express deep gratitude to the Mar\'ia Cristina Masav\'eu Peterson Foundation for its financial support of her studies. + +\bibliography{Bibliography} +\bibliographystyle{plain} + +\end{document} + diff --git a/assets/2017/C.Herng Yi/poisson_irregular.png b/assets/2017/C.Herng Yi/poisson_irregular.png new file mode 100644 index 0000000000000000000000000000000000000000..e2f8c47cf8a54752115182da5b2f7f7a4765dfcf GIT binary patch literal 27090 zcmeFZby$_%*DkuSz(5g25v2rFQt3{mB}9-Cus}jW=|;ssM5IJgBot6US{7-d0wM^4 zq)2xuNbmc>U;T5wbM`)eoa=mhuj_pk7f;MN=9nYyagQ0Gt*K1CiD46oM50zzIi^D* ztvf>^tyQ5~gKsE>wsPaIjSeb?jwI6N9mM|>r07_B;&)D}8j6%%RQtAzQx>?=$l@z@ zCq)CNllB%)u4k{9lQiUYkIO6Yu;^NvvuK=kvedV~V&lleqH1@ZPs*U3c*K6<`lDCO z&pKJz+p*|c*_x9C#CYYMFY*c;;TL7$7nBedl{g|An;MRbSxBnKp3r1 zP9Bc&W67bS;<`qans#+BU-ILqZx=#;WF~1?^d2hmH-7jqx;ON}sU-2FUhSZ0n^K1ojTc}B)~Tan{PGe7Iw_F`A{b;-)XOuS}gi}SyS6>evrujD$JNOMpt zzOCH1oaWrbk5_7q+UuS3E|KImo<2uO8lq)j;IfSsyZo~y--cX#k6D&4g^l&?m&Zq` 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  • - - {% assign i = 1 %} - {% for chapter in chapter_titles %} - {% if chapter[0] == 'profiles and interviews' %} - {% assign i = i | minus: 1 %} - {% else %} -
  • -
    {{ chapter[0] }}
    - {% for abstracts in chapter %} - {% if forloop.first == false %} - {% for abstract in abstracts %} -
    - {% include marginless_card_panel.html %} -
    - {% endfor %} - {% endif %} - {% endfor %} -
  • - {% endif %} - {% assign i = i | plus: i %} - {% endfor %} - -
    -
    - diff --git a/_posts/2017/2017-03-28-C-Herng-Yi.md b/_posts/2017/2017-03-28-C-Herng-Yi.md index 2bdbfec..093509b 100644 --- a/_posts/2017/2017-03-28-C-Herng-Yi.md +++ b/_posts/2017/2017-03-28-C-Herng-Yi.md @@ -3,7 +3,7 @@ layout: post title: "Solving PDEs on Deconstructed Domains for Geometry Processing" author: "Herng Yi Cheng, Mitchell Dembowski, Silvia González Sellán and Christine Ma" supervisors: "Professor Alec Jacobson" -category: "Scientific Computer/Numerical Analysis" +category: "Scientific Computing/Numerical Analysis" permalink: /solving-pdes-on-deconstructed-domains-for-geometry-processing year: "2017" diff --git a/_posts/2017/2017-03-30-R-An.md b/_posts/2017/2017-03-30-R-An.md index 6002883..a0a6a34 100644 --- a/_posts/2017/2017-03-30-R-An.md +++ b/_posts/2017/2017-03-30-R-An.md @@ -3,7 +3,7 @@ layout: post title: "Parallel approach to single-source shortest path problem on large complete graphs" author: "Ruijian An" supervisors: "" -category: "Computer Systems / Software Engineering" +category: "Computer Systems/Software Engineering" permalink: /parallel-approach-to-single-source-shortest-path-problem-on-large-complete-graphs year: "2017" diff --git a/_posts/2017/2017-04-08-A-Mishkin.md b/_posts/2017/2017-04-08-A-Mishkin.md index e8645a9..0ae78be 100644 --- a/_posts/2017/2017-04-08-A-Mishkin.md +++ b/_posts/2017/2017-04-08-A-Mishkin.md @@ -3,7 +3,7 @@ layout: post title: "Web ValueCharts: Analyzing Individual and Group Preferences with Interactive, Web-based Visualizations" author: "Aaron Mishkin" supervisors: "Professor Poole and Professor Giuseppe Carenini" -category: "Scientific Computing/Numerical Analysis" +category: "HCI" permalink: /web-valuecharts-analyzing-individual-and-group-preferences-with-interactive-web-based-visualizations year: "2017" From f811256a925b4873da660d3f26812363edf41dda Mon Sep 17 00:00:00 2001 From: Tyler Pham Date: Sat, 14 Apr 2018 00:49:33 -0400 Subject: [PATCH 16/17] fixed header redirecting to non existent URL --- _includes/header.html | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/_includes/header.html b/_includes/header.html index 64ea735..56b3fbf 100644 --- a/_includes/header.html +++ b/_includes/header.html @@ -5,7 +5,8 @@