3 Search Results for "Wang, Chu"

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.8
Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues

Authors: Gary L. Miller, Noel J. Walkington, and Alex L. Wang

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
We present two graph quantities Psi(G,S) and Psi_2(G) which give constant factor estimates to the Dirichlet and Neumann eigenvalues, lambda(G,S) and lambda_2(G), respectively. Our techniques make use of a discrete Hardy-type inequality due to Muckenhoupt.
Cite as

Gary L. Miller, Noel J. Walkington, and Alex L. Wang. Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{miller_et_al:LIPIcs.APPROX-RANDOM.2019.8,
  author =	{Miller, Gary L. and Walkington, Noel J. and Wang, Alex L.},
  title =	{{Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.8},
  URN =		{urn:nbn:de:0030-drops-112236},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.8},
  annote =	{Keywords: Hardy, Muckenhoupt, Laplacian, eigenvalue, effective resistance}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.17
Self-Sustaining Iterated Learning

Authors: Bernard Chazelle and Chu Wang

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
An important result from psycholinguistics (Griffiths & Kalish, 2005) states that no language can be learned iteratively by rational agents in a self-sustaining manner. We show how to modify the learning process slightly in order to achieve self-sustainability. Our work is in two parts. First, we characterize iterated learnability in geometric terms and show how a slight, steady increase in the lengths of the training sessions ensures self-sustainability for any discrete language class. In the second part, we tackle the nondiscrete case and investigate self-sustainability for iterated linear regression. We discuss the implications of our findings to issues of non-equilibrium dynamics in natural algorithms.
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Bernard Chazelle and Chu Wang. Self-Sustaining Iterated Learning. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chazelle_et_al:LIPIcs.ITCS.2017.17,
  author =	{Chazelle, Bernard and Wang, Chu},
  title =	{{Self-Sustaining Iterated Learning}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.17},
  URN =		{urn:nbn:de:0030-drops-81711},
  doi =		{10.4230/LIPIcs.ITCS.2017.17},
  annote =	{Keywords: Iterated learning, language evolution, iterated Bayesian linear regression, non-equilibrium dynamics}
}
Document
DOI: 10.4230/LIPIcs.STACS.2012.477
Randomized Communication Complexity for Linear Algebra Problems over Finite Fields

Authors: Xiaoming Sun and Chengu Wang

Published in: LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)

Abstract
Finding the singularity of a matrix is a basic problem in linear algebra. Chu and Schnitger [SC95] first considered this problem in the communication complexity model, in which Alice holds the first half of the matrix and Bob holds the other half. They proved that the deterministic communication complexity is Omega(n^2 log p) for an n by n matrix over the finite field F_p. Then, Clarkson and Woodruff [CW09] introduced the singularity problem to the streaming model. They proposed a randomized one pass streaming algorithm that uses O(k^2 log n) space to decide if the rank of a matrix is k, and proved an Omega(k^2) lower bound for randomized one-way protocols in the communication complexity model. We prove that the randomized/quantum communication complexity of the singularity problem over F_p is Omega(n^2 log p), which implies the same space lower bound for randomized streaming algorithms, even for a constant number of passes. The proof uses the framework by Lee and Shraibman [LS09], but we choose Fourier coefficients as the witness for the dual approximate norm of the communication matrix. Moreover, we use Fourier analysis to show the same randomized/quantum lower bound when deciding if the determinant of a non-singular matrix is a or b for non-zero a and b.
Cite as

Xiaoming Sun and Chengu Wang. Randomized Communication Complexity for Linear Algebra Problems over Finite Fields. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 477-488, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{sun_et_al:LIPIcs.STACS.2012.477,
  author =	{Sun, Xiaoming and Wang, Chengu},
  title =	{{Randomized Communication Complexity for Linear Algebra Problems over Finite Fields}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{477--488},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{D\"{u}rr, Christoph and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.477},
  URN =		{urn:nbn:de:0030-drops-34385},
  doi =		{10.4230/LIPIcs.STACS.2012.477},
  annote =	{Keywords: communication complexity, streaming, matrix, singularity, determinant}
}
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