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Articles 1 - 11 of 11
Full-Text Articles in Mathematics
Ranked List Fusion And Re-Ranking With Pre-Trained Transformers For Arqmath Lab, Shaurya Rohatgi, Jian Wu, C. Lee Giles
Ranked List Fusion And Re-Ranking With Pre-Trained Transformers For Arqmath Lab, Shaurya Rohatgi, Jian Wu, C. Lee Giles
Computer Science Faculty Publications
This paper elaborates on our submission to the ARQMath track at CLEF 2021. For our submission this year we use a collection of methods to retrieve and re-rank the answers in Math Stack Exchange in addition to our two-stage model which was comparable to the best model last year in terms of NDCG’. We also provide a detailed analysis of what the transformers are learning and why is it hard to train a math language model using transformers. This year’s submission to Task-1 includes summarizing long question-answer pairs to augment and index documents, using byte-pair encoding to tokenize formula and …
Psu At Clef-2020 Arqmath Track: Unsupervised Re-Ranking Using Pretraining, Shaurya Rohatgi, Jian Wu, C. Lee Giles
Psu At Clef-2020 Arqmath Track: Unsupervised Re-Ranking Using Pretraining, Shaurya Rohatgi, Jian Wu, C. Lee Giles
Computer Science Faculty Publications
This paper elaborates on our submission to the ARQMath track at CLEF 2020. Our primary run for the main Task-1: Question Answering uses a two-stage retrieval technique in which the first stage is a fusion of traditional BM25 scoring and tf-idf with cosine similarity-based retrieval while the second stage is a finer re-ranking technique using contextualized embeddings. For the re-ranking we use a pre-trained robertabase model (110 million parameters) to make the language model more math-aware. Our approach achieves a higher NDCG0 score than the baseline, while our MAP and P@10 scores are competitive, performing better than the best submission …
Convergence Analysis Of Markov Chain Monte Carlo Linear Solvers Using Ulam--Von Neumann Algorithm, Hao Ji, Michael Mascagni, Yaohang Li
Convergence Analysis Of Markov Chain Monte Carlo Linear Solvers Using Ulam--Von Neumann Algorithm, Hao Ji, Michael Mascagni, Yaohang Li
Computer Science Faculty Publications
The convergence of Markov chain--based Monte Carlo linear solvers using the Ulam--von Neumann algorithm for a linear system of the form x = Hx + b is investigated in this paper. We analyze the convergence of the Monte Carlo solver based on the original Ulam--von Neumann algorithm under the conditions that ||H|| < 1 as well as ρ(H) < 1, where ρ(H) is the spectral radius of H. We find that although the Monte Carlo solver is based on sampling the Neumann series, the convergence of Neumann series is not a sufficient condition for the convergence of the Monte Carlo solver. Actually, properties of H are not the only factors determining the convergence of the Monte Carlo solver; the underlying transition probability matrix plays an important role. An improper selection of the transition matrix may result in divergence even though the condition ||H|| <1 holds. However, if the condition ||H|| < 1 is satisfied, we show that there always exist certain transition matrices that guarantee convergence of the Monte Carlo solver. On the other hand, if ρ(H) <1 but ||H|| ≥ 1, the Monte Carlo linear solver may or may not converge. In particular, if the row sum ∑ n/j= 1|Hij > 1 for every row in H or, more generally, ρ(H+) >1, where H+ is the nonnegative matrix where H+ij = |Hij|, we show that transition matrices leading to convergence of the Monte Carlo solver do not exist. Finally, given …
Intensity-Based Skeletonization Of Cryoem Gray-Scale Images Using A True Segmentation-Free Algorithm, Kamal Al Nasr, Chunmei Liu, Mugizi Rwebangira, Legand Burge, Jing He
Intensity-Based Skeletonization Of Cryoem Gray-Scale Images Using A True Segmentation-Free Algorithm, Kamal Al Nasr, Chunmei Liu, Mugizi Rwebangira, Legand Burge, Jing He
Computer Science Faculty Publications
Cryo-electron microscopy is an experimental technique that is able to produce 3D gray-scale images of protein molecules. In contrast to other experimental techniques, cryo-electron microscopy is capable of visualizing large molecular complexes such as viruses and ribosomes. At medium resolution, the positions of the atoms are not visible and the process cannot proceed. The medium-resolution images produced by cryo-electron microscopy are used to derive the atomic structure of the proteins in de novo modeling. The skeletons of the 3D gray-scale images are used to interpret important information that is helpful in de novo modeling. Unfortunately, not all features of the …
Applications Of Hidden Markov Models In Microarray Gene Expression Data, Huimin Geng, Xutao Deng, Hesham Ali
Applications Of Hidden Markov Models In Microarray Gene Expression Data, Huimin Geng, Xutao Deng, Hesham Ali
Computer Science Faculty Publications
Hidden Markov models (HMMs) are well developed statistical models to capture hidden information from observable sequential symbols. They were first used in speech recognition in 1970s and have been successfully applied to the analysis of biological sequences since late 1980s as in finding protein secondary structure, CpG islands and families of related DNA or protein sequences [1]. In a HMM, the system being modeled is assumed to be a Markov process with unknown parameters, and the challenge is to determine the hidden parameters from the observable parameters. In this chapter, we described two applications using HMMs to predict gene functions …
From Isotropic To Anisotropic Side Chain Representations: Comparison Of Three Models For Residue Contact Estimation, Weitao Sun, Jing He
From Isotropic To Anisotropic Side Chain Representations: Comparison Of Three Models For Residue Contact Estimation, Weitao Sun, Jing He
Computer Science Faculty Publications
The criterion to determine residue contact is a fundamental problem in deriving knowledge-based mean-force potential energy calculations for protein structures. A frequently used criterion is to require the side chain center-to-center distance or the C-alpha-to-C-alpha atom distance to be within a pre-determined cutoff distance. However, the spatially anisotropic nature of the side chain determines that it is challenging to identify the contact pairs. This study compares three side chain contact models: the Atom Distance criteria (ADC) model, the Isotropic Sphere Side chain (ISS) model and the Anisotropic Ellipsoid Side chain (AES) model using 424 high resolution protein structures in the …
Istart 2: Improvements For Efficiency And Effectiveness, Irwin B. Levinstein, Chutima Boonthum, Srinivasa P. Pillarisetti, Courtney Bell, Danielle S. Mcnamara
Istart 2: Improvements For Efficiency And Effectiveness, Irwin B. Levinstein, Chutima Boonthum, Srinivasa P. Pillarisetti, Courtney Bell, Danielle S. Mcnamara
Computer Science Faculty Publications
iSTART (interactive strategy training for active reading and thinking) is a Web-based reading strategy trainer that develops students' ability to self-explain difficult text as a means to improving reading comprehension. Its curriculum consists of modules presented interactively by pedagogical agents: an introduction to the basics of using reading strategies in the context of self-explanation, a demonstration of self-explanation, and a practice module in which the trainee generates self-explanations with feedback on the quality of reading strategies contained in the self-explanations. We discuss the objectives that guided the development of the second version of iSTART toward the goals of increased efficiency …
Efficient Algorithms For Graphs With Few P-4’S, Luitpold Babel, Ton Kloks, Jan Kratochvíl, Dieter Kratsch, Kaiko Müller, Stephan Olariu
Efficient Algorithms For Graphs With Few P-4’S, Luitpold Babel, Ton Kloks, Jan Kratochvíl, Dieter Kratsch, Kaiko Müller, Stephan Olariu
Computer Science Faculty Publications
We show that a large variety of NP-complete problems can be solved efficiently for graphs with 'few' P4's. We consider domination problems (domination, total domination, independent domination. connected domination and dominating clique), the Steiner tree problem, the vertex ranking problem, the pathwidth problem, the path cover number problem, the hamiltonian circuit problem, the list coloring problem and the precoloring extension problem. We show that all these problems can be solved in linear time for the class of (q,q - 4)-graphs, for every fixed q. These are graphs for which no set of at most q. vertices induces more …
A New Conjecture About Minimal Imperfect Graphs, H. Meyniel, Stephan Olariu
A New Conjecture About Minimal Imperfect Graphs, H. Meyniel, Stephan Olariu
Computer Science Faculty Publications
H. Meyniel proved that in every minimal imperfect graph, every pair of vertices is joined by a chordless path containing an odd number of edges. We conjectured that in every minimal imperfect graph, every pair of vertices is joined by a path containing an even number of edges. We give an equivalent version of this new conjecture.
The Strong Perfect Graph Conjecture For Pan-Free Graphs, Stephan Olariu
The Strong Perfect Graph Conjecture For Pan-Free Graphs, Stephan Olariu
Computer Science Faculty Publications
A graph G is perfect if for every induced subgraph F of G, the chromatic number χ(F) equals the largest number ω(F) of pairwise adjacent vertices in F. Berge's famous Strong Perfect Graph Conjecture asserts that a graph G is perfect if and only if neither G nor its complement G contains an odd chordless cycle of length at least five. Its resolution has eluded researchers for more than twenty years. We prove that the conjecture is true for a class of graphs which strictly contains the claw-free graphs.
No Antitwins In Minimal Imperfect Graphs, Stephan Olariu
No Antitwins In Minimal Imperfect Graphs, Stephan Olariu
Computer Science Faculty Publications
It is customary to call vertices x and y twins if every vertex distinct from x and y is adjacent either to both of them or to neither of them. By analogy, we shall call vertices x and yantitwins if every vertex distinct from x and y is adjacent to precisely one of them. Lovász proved that no minimal imperfect graph has twins. The purpose of this note is to prove the analogous statement for antitwins.