Partition Symmetrical Entropy Functions*
|
|
|
- Edward Wade
- 5 years ago
- Views:
Transcription
1 Partition Symmetrical Entropy Functions* Jayant Apte ASPITRG *Chen, Qi; Yeung, Raymond W., Partition Symmetrical Entropy Functions, arxiv: v1 [cs.it]
2 Outline Sneak Peak Background: Basic facts from convex analysis Matroids reboot Partitions Group action Reboot New Regions and : Points fixed under action of a variable permutation group with set of orbits = partition Symmetrical properties of and : how we get rid of symmetries with and For which variable permutation groups?
3 Outline Sneak Peak Background: Basic facts from convex analysis Matroids reboot Partitions Group action Reboot New Regions and : Points fixed under action of a variable permutation group with set of orbits = partition Symmetrical properties of and : how we get rid of symmetries with and For which variable permutation groups?
4 Entropy function
5 Entropy function region
6 Entropy function region
7 Partition Symmetrical Entropy Functions
8 New Regions
9 Results
10 Results
11 Outline Sneak Peak Background: Basic facts from convex analysis Matroids reboot Partitions Group action Reboot New Regions and : Points fixed under action of a variable permutation group with set of orbits = partition Symmetrical properties of and : how we get rid of symmetries with and For which variable permutation groups?
12 Convex Cones
13 Convex Cones
14 Convex Cones
15
16 Outline Sneak Peak Background: Basic facts from convex analysis Matroids reboot Partitions Group action Reboot New Regions and : Points fixed under action of a variable permutation group with set of orbits = partition Symmetrical properties of and : how we get rid of symmetries with and For which variable permutation groups?
17 Matroid
18 Free Expansion
19 Free Expansion
20 Free expansion as a tool to prove that a polymatroid is almost entropic
21 Uniform matroid
22 Outline Sneak Peak Background: Basic facts from convex analysis Matroids reboot Partitions Group action Reboot New Regions and : Points fixed under action of a variable permutation group with set of orbits = partition Symmetrical properties of and : how we get rid of symmetries with and For which variable permutation groups?
23 Partitions Image courtesy: Wereldburger758 CC 3.0
24 Partitions Image courtesy: Wereldburger758 CC 3.0
25 Partitions OEIS A Image courtesy: Wereldburger758 CC 3.0
26 Partitions OEIS A Image courtesy: Wereldburger758 CC 3.0
27 Partitions
28 Outline Sneak Peak Background: Basic facts from convex analysis Matroids reboot Partitions Group action Reboot New Regions and : Points fixed under action of a variable permutation group with set of orbits = partition Symmetrical properties of and : how we get rid of symmetries with and For which variable permutation groups?
29 Permutation groups from orbits(partition)
30
31 Orbits and fixed set under action
32 Orbits and fixed set under action
33 Orbits and fixed set under action
34 Set-wise orbits and invariance
35 Set-wise orbits and invariance
36 Outline Sneak Peak Background: Basic facts from convex analysis Matroids reboot Partitions Group action Reboot New Regions and : Points fixed under action of a variable permutation group with set of orbits = partition Symmetrical properties of and : how we get rid of symmetries with and For which variable permutation groups?
37 Dimension of fixed space
38 Dimension of fixed space
39 Partition refinement and containment relationships of fixed spaces
40 Partition refinement and containment relationships of fixed spaces
41 Partition refinement and containment relationships of fixed spaces
42 Partition refinement and containment relationships of fixed spaces
43 Partition refinement and containment relationships of fixed spaces
44 Partition refinement and containment relationships of fixed spaces
45 New Regions
46 Equivalence classes of partitions and regions
47
48
49
50
51
52 Example Type 1 facets Type 2 facets Everybody in same orbit! One orbit per
53
54
55
56
57
58
59
60
61
62
63 Bummer!
64 Bummer! QED
65
66 1 2 l t
67 1 2 l t
68 1 2 l t
69 1 2 t 1 2 t t 1 2 t X X X X X X X X X X X X X X
70 1 2 t 1 2 t
71 1 2 t 1 2 t
72
Symmetries in Entropy Space
1 Symmetries in Entropy Space Jayant Apte, Qi Chen, John MacLaren Walsh Department of Electrical and Computer Engineering Drexel University Philadelphia, PA jwalsh@ece.drexel.edu Thanks to NSF CCF-1421828
Symmetries in the Entropy Space
Symmetries in the Entropy Space Jayant Apte, Qi Chen, John MacLaren Walsh Abstract This paper investigates when Shannon-type inequalities completely characterize the part of the closure of the entropy
Exploiting Symmetry in Computing Polyhedral Bounds on Network Coding Rate Regions
Exploiting Symmetry in Computing Polyhedral Bounds on Network Coding Rate Regions Jayant Apte John Walsh Department of Electrical and Computer Engineering Drexel University, Philadelphia NetCod, 205 NSF
Symmetry in Network Coding
Symmetry in Network Coding Formalization, Graph-theoretic Characterization, and Computation Jayant Apte John Walsh Department of Electrical and Computer Engineering Drexel University, Philadelphia ISIT,
Non-isomorphic Distribution Supports for Calculating Entropic Vectors
Non-isomorphic Distribution Supports for Calculating Entropic Vectors Yunshu Liu & John MacLaren Walsh Adaptive Signal Processing and Information Theory Research Group Department of Electrical and Computer
Bounding the Entropic Region via Information Geometry
Bounding the ntropic Region via Information Geometry Yunshu Liu John MacLaren Walsh Dept. of C, Drexel University, Philadelphia, PA 19104, USA yunshu.liu@drexel.edu jwalsh@coe.drexel.edu Abstract This
Extremal Entropy: Information Geometry, Numerical Entropy Mapping, and Machine Learning Application of Associated Conditional Independences.
Extremal Entropy: Information Geometry, Numerical Entropy Mapping, and Machine Learning Application of Associated Conditional Independences A Thesis Submitted to the Faculty of Drexel University by Yunshu
Multiterminal Networks: Rate Regions, Codes, Computations, & Forbidden Minors
Multiterminal etworks: Rate Regions, Codes, Computations, & Forbidden Minors Ph D Thesis Proposal Congduan Li ASPITRG & MAL Drexel University congduanli@gmailcom October 5, 204 C Li (ASPITRG & MAL) Thesis
Characterizing the Region of Entropic Vectors via Information Geometry
Characterizing the Region of Entropic Vectors via Information Geometry John MacLaren Walsh Department of Electrical and Computer Engineering Drexel University Philadelphia, PA jwalsh@ece.drexel.edu Thanks
Entropic Vectors: Polyhedral Computation & Information Geometry
Entropic Vectors: Polyhedral Computation & Information Geometry John MacLaren Walsh Department of Electrical and Computer Engineering Drexel University Philadelphia, PA jwalsh@ece.drexel.edu Thanks to
Symmetry in Network Coding
Symmetry in Network Coding Jayant Apte, John MacLaren Walsh Drexel University, Dept. of ECE, Philadelphia, PA 19104, USA jsa46@drexel.edu, jwalsh@coe.drexel.edu Abstract We establish connections between
Introduction to Lexicographic Reverse Search: lrs
Introduction to Lexicographic Reverse Search: lrs June 29, 2012 Jayant Apte ASPITRG Outline Introduction Lexicographic Simplex Algorithm Lex-positive and Lex min bases The pitfalls in reverse search Lexicographic
Received: 1 September 2018; Accepted: 10 October 2018; Published: 12 October 2018
entropy Article Entropy Inequalities for Lattices Peter Harremoës Copenhagen Business College, Nørre Voldgade 34, 1358 Copenhagen K, Denmark; harremoes@ieee.org; Tel.: +45-39-56-41-71 Current address:
on Newton polytopes, tropisms, and Puiseux series to solve polynomial systems
on Newton polytopes, tropisms, and Puiseux series to solve polynomial systems Jan Verschelde joint work with Danko Adrovic University of Illinois at Chicago Department of Mathematics, Statistics, and Computer
Matroid Bounds on the Region of Entropic Vectors
Matroid Bounds on the Region of Entropic Vectors Congduan Li, John MacLaren Walsh, Steven Weber Drexel University, Dept of ECE, Philadelphia, PA 19104, USA congduanli@drexeledu, jwalsh@coedrexeledu, sweber@coedrexeledu
On Multi-source Multi-sink Hyperedge Networks: Enumeration, Rate Region Computation, & Hierarchy
On Multi-ource Multi-ink Hyperedge Network: Enumeration, Rate Region Computation, & Hierarchy Ph D Diertation Defene Congduan Li ASPITRG & MANL Drexel Univerity congduanli@gmailcom May 9, 05 C Li (ASPITRG
. Relationships Among Bounds for the Region of Entropic Vectors in Four Variables
. Relationships Among Bounds for the Region of Entropic Vectors in Four Variables John MacLaren Walsh and Steven Weber Department of Electrical and Computer Engineering, Drexel University, Philadelphia,
Entropy Vectors and Network Information Theory
Entropy Vectors and Network Information Theory Sormeh Shadbakht and Babak Hassibi Department of Electrical Engineering Caltech Lee Center Workshop May 25, 2007 1 Sormeh Shadbakht and Babak Hassibi Entropy
Albert W. Marshall. Ingram Olkin Barry. C. Arnold. Inequalities: Theory. of Majorization and Its Applications. Second Edition.
Albert W Marshall Ingram Olkin Barry C Arnold Inequalities: Theory of Majorization and Its Applications Second Edition f) Springer Contents I Theory of Majorization 1 Introduction 3 A Motivation and Basic
The Inflation Technique for Causal Inference with Latent Variables
The Inflation Technique for Causal Inference with Latent Variables arxiv:1609.00672 (Elie Wolfe, Robert W. Spekkens, Tobias Fritz) September 2016 Introduction Given some correlations between the vocabulary
Algebraic matroids are almost entropic
accepted to Proceedings of the AMS June 28, 2017 Algebraic matroids are almost entropic František Matúš Abstract. Algebraic matroids capture properties of the algebraic dependence among elements of extension
Algorithms for Computing Network Coding Rate Regions via Single Element Extensions of Matroids
Algorithms for Computing Network Coding Rate Regions via Single Element Extensions of Matroids Jayant Apte, Congduan Li, John MacLaren Walsh Drexel University, Dept. of ECE, Philadelphia, PA 19104, USA
QUADRANT MARKED MESH PATTERNS IN 132-AVOIDING PERMUTATIONS III
#A39 INTEGERS 5 (05) QUADRANT MARKED MESH PATTERNS IN 3-AVOIDING PERMUTATIONS III Sergey Kitaev Department of Computer and Information Sciences, University of Strathclyde, Glasgow, United Kingdom sergey.kitaev@cis.strath.ac.uk
On Multi-source Multi-Sink Hyperedge Networks: Enumeration, Rate Region. Computation, and Hierarchy. A Thesis. Submitted to the Faculty
On Multi-source Multi-Sink Hyperedge Networks: Enumeration, Rate Region Computation, and Hierarchy A Thesis Submitted to the Faculty of Drexel University by Congduan Li in partial fulfillment of the requirements
A Dynamic Programming Approach to Counting Hamiltonian Cycles in Bipartite Graphs
A Dynamic Programming Approach to Counting Hamiltonian Cycles in Bipartite Graphs Patric R. J. Östergård Department of Communications and Networking Aalto University School of Electrical Engineering P.O.
Network Combination Operations Preserving the Sufficiency of Linear Network Codes
Network Combination Operations Preserving the Sufficiency of Linear Network Codes Congduan Li, Steven Weber, John MacLaren Walsh ECE Department, Drexel University Philadelphia, PA 904 Abstract Operations
Permutation Groups. John Bamberg, Michael Giudici and Cheryl Praeger. Centre for the Mathematics of Symmetry and Computation
Notation Basics of permutation group theory Arc-transitive graphs Primitivity Normal subgroups of primitive groups Permutation Groups John Bamberg, Michael Giudici and Cheryl Praeger Centre for the Mathematics
Secret Sharing. Qi Chen. December 14, 2015
Secret Sharing Qi Chen December 14, 2015 What is secret sharing? A dealer: know the secret S and distribute the shares of S to each party A set of n parties P n {p 1,, p n }: each party owns a share Authorized
A computational approach for determining rate regions and codes using entropic vector bounds
1 A computational approach for determining rate regions and codes using entropic vector bounds Congduan Li, John MacLaren Walsh, Steven Weber Drexel University, Dept. of ECE, Philadelphia, PA 19104, USA
LECTURE 10 LECTURE OUTLINE
LECTURE 10 LECTURE OUTLINE Min Common/Max Crossing Th. III Nonlinear Farkas Lemma/Linear Constraints Linear Programming Duality Convex Programming Duality Optimality Conditions Reading: Sections 4.5, 5.1,5.2,
Quantum Marginal Problems
Quantum Marginal Problems David Gross (Colgone) Joint with: Christandl, Doran, Lopes, Schilling, Walter Outline Overview: Marginal problems Overview: Entanglement Main Theme: Entanglement Polytopes Shortly:
Entropy inequalities and linear rank inequalities
1 Entropy inequalities and linear rank inequalities Randall Dougherty (Center for Communications Research, San Diego) Chris Freiling (California State University, San Bernardino) Ken Zeger (University
Entropic and informatic matroids
Entropic and informatic matroids Emmanuel Abbe Abstract This paper studies dependencies between random variables by means of information theoretic functionals such as the entropy and the mutual information.
Learning with Submodular Functions: A Convex Optimization Perspective
Foundations and Trends R in Machine Learning Vol. 6, No. 2-3 (2013) 145 373 c 2013 F. Bach DOI: 10.1561/2200000039 Learning with Submodular Functions: A Convex Optimization Perspective Francis Bach INRIA
A new computational approach for determining rate regions and optimal codes for coded networks
A new computational approach for determining rate regions and optimal codes for coded networks Congduan Li, Jayant Apte, John MacLaren Walsh, Steven Weber Drexel University, Dept. of ECE, Philadelphia,
LoProp: local property calculations with quantum chemical methods
LoProp: local property calculations with quantum chemical methods Laura Gagliardi Dipartimento di Chimica Fisica F. Accascina Università degli Studi di Palermo Italy Gunnar Karlström, Jesper Krogh, and
Counting chains in noncrossing partition lattices
Counting chains in noncrossing partition lattices Nathan Reading NC State University NCSU Algebra Seminar, November 16, 2007 1 Counting chains in noncrossing partition lattices Classical noncrossing partitions
Extremal Entropy: Information Geometry, Numerical Entropy Mapping, and Machine Learning Application of Associated Conditional Independences
Extremal Entropy: Information Geometry, Numerical Entropy Mapping, and Machine Learning Application of Associated Conditional Independences Ph.D. Dissertation Defense Yunshu Liu Adaptive Signal Processing
DISCRIMINANTS, SYMMETRIZED GRAPH MONOMIALS, AND SUMS OF SQUARES
DISCRIMINANTS, SYMMETRIZED GRAPH MONOMIALS, AND SUMS OF SQUARES PER ALEXANDERSSON AND BORIS SHAPIRO Abstract. Motivated by the necessities of the invariant theory of binary forms J. J. Sylvester constructed
LECTURE 3 LECTURE OUTLINE
LECTURE 3 LECTURE OUTLINE Differentiable Conve Functions Conve and A ne Hulls Caratheodory s Theorem Reading: Sections 1.1, 1.2 All figures are courtesy of Athena Scientific, and are used with permission.
FINITENESS OF RELATIVE EQUILIBRIA OF THE FOUR-BODY PROBLEM
FINITENESS OF RELATIVE EQUILIBRIA OF THE FOUR-BODY PROBLEM MARSHALL HAMPTON AND RICHARD MOECKEL Abstract. We show that the number of relative equilibria of the Newtonian four-body problem is finite, up
Part II: Integral Splittable Congestion Games. Existence and Computation of Equilibria Integral Polymatroids
Kombinatorische Matroids and Polymatroids Optimierung in der inlogistik Congestion undgames im Verkehr Tobias Harks Augsburg University WINE Tutorial, 8.12.2015 Outline Part I: Congestion Games Existence
Studies of reaction dynamics and spectroscopy of hydrocarbons in plasma
Studies of reaction dynamics and spectroscopy of hydrocarbons in plasma Bastiaan J. Braams and Joel M. Bowman IAEA CRP on Plasma Modelling Vienna; June 18, 2007 Outline Our project Potential energy surfaces
Linearly Representable Entropy Vectors and their Relation to Network Coding Solutions
2009 IEEE Information Theory Workshop Linearly Representable Entropy Vectors and their Relation to Network Coding Solutions Asaf Cohen, Michelle Effros, Salman Avestimehr and Ralf Koetter Abstract In this
How to Use Undiscovered Information Inequalities: Direct Applications of the Copy Lemma
How to Use Undiscovered Information Inequalities: Direct Applications of the Copy Lemma Emirhan Gürpınar ENS de Lyon, France Email: emirhan.gurpinar@ens-lyon.fr Andrei Romashchenko LIRMM, University of
On the structure of the 5 x 5 copositive cone
On the structure of the 5 x 5 copositive cone Roland Hildebrand 1 Mirjam Dür 2 Peter Dickinson Luuk Gijbens 3 1 Laboratory Jean Kuntzmann, University Grenoble 1 / CNRS 2 Mathematics Dept., University Trier
LECTURE 12 LECTURE OUTLINE. Subgradients Fenchel inequality Sensitivity in constrained optimization Subdifferential calculus Optimality conditions
LECTURE 12 LECTURE OUTLINE Subgradients Fenchel inequality Sensitivity in constrained optimization Subdifferential calculus Optimality conditions Reading: Section 5.4 All figures are courtesy of Athena
Nonlinear Discrete Optimization
Nonlinear Discrete Optimization Technion Israel Institute of Technology http://ie.technion.ac.il/~onn Billerafest 2008 - conference in honor of Lou Billera's 65th birthday (Update on Lecture Series given
1440 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 44, NO. 4, JULY On Characterization of Entropy Function via Information Inequalities
1440 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 44, NO. 4, JULY 1998 On Characterization of Entropy Function via Information Inequalities Zhen Zhang, Senior Member, IEEE, Raymond W. Yeung, Senior Member,
Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order
Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order Arvind Ayyer (Bangalore) Roger E. Behrend (Cardiff) Ilse Fischer (Vienna) 1 Outline Introduction: ASMs and DASASMs
Characterising Probability Distributions via Entropies
1 Characterising Probability Distributions via Entropies Satyajit Thakor, Terence Chan and Alex Grant Indian Institute of Technology Mandi University of South Australia Myriota Pty Ltd arxiv:1602.03618v2
( ) 2 = #$ 2 % 2 + #$% 3 + # 4 % 4
PC 477 The Early Universe Lectures 9 & 0 One is forced to make a choice of vacuum, and the resulting phenomena is known as spontaneous symmetry breaking (SSB.. Discrete Goldstone Model L =! µ"! µ " # V
arxiv: v2 [cond-mat.mes-hall] 31 Mar 2016
![arxiv: v2 [cond-mat.mes-hall] 31 Mar 2016](/thumbs/92/108544281.jpg "arxiv: v2 [cond-mat.mes-hall] 31 Mar 2016")
Journal of the Physical Society of Japan LETTERS Entanglement Chern Number of the ane Mele Model with Ferromagnetism Hiromu Araki, Toshikaze ariyado,, Takahiro Fukui 3, and Yasuhiro Hatsugai, Graduate
SEVEN NEW CHAMPION LINEAR CODES. 1. Introduction
SEVEN NEW CHAMPION LINEAR CODES GAVIN BROWN AND ALEXANDER M. KASPRZYK Abstract. We exhibit seven linear codes exceeding the current best known minimum distance d for their dimension k and block length
Boij-Söderberg Theory
? September 16, 2013 Table of contents? 1? 2 3 4 5 6 Preface? In this presentation we try to give an outline on a new theory on free resolutions. This theory is named after two Swedish mathematicians Mats
Ehrhart Positivity. Federico Castillo. December 15, University of California, Davis. Joint work with Fu Liu. Ehrhart Positivity
University of California, Davis Joint work with Fu Liu December 15, 2016 Lattice points of a polytope A (convex) polytope is a bounded solution set of a finite system of linear inequalities, or is the
LECTURE 4 LECTURE OUTLINE
LECTURE 4 LECTURE OUTLINE Relative interior and closure Algebra of relative interiors and closures Continuity of convex functions Closures of functions Reading: Section 1.3 All figures are courtesy of
LECTURE 25: REVIEW/EPILOGUE LECTURE OUTLINE
LECTURE 25: REVIEW/EPILOGUE LECTURE OUTLINE CONVEX ANALYSIS AND DUALITY Basic concepts of convex analysis Basic concepts of convex optimization Geometric duality framework - MC/MC Constrained optimization
Conditional Information Inequalities for Entropic and Almost Entropic Points
1 Conditional Information Ineualities for Entropic and Almost Entropic Points Tarik Kaced and Andrei Romashchenko Abstract We study conditional linear information ineualities, i.e., linear ineualities
GENERALIZED INFORMATION ENTROPIES IN QUANTUM PHYSICS
GENERALIZED INFORMATION ENTROPIES IN QUANTUM PHYSICS Mariela Portesi 1, S. Zozor 2, G.M. Bosyk 1, F. Holik 1, P.W. Lamberti 3 1 IFLP & Dpto de Fisica, CONICET & Univ. Nac. de La Plata, Argentina 2 GIPSA-Lab,
EE595A Submodular functions, their optimization and applications Spring 2011
EE595A Submodular functions, their optimization and applications Spring 2011 Prof. Jeff Bilmes University of Washington, Seattle Department of Electrical Engineering Winter Quarter, 2011 http://ee.washington.edu/class/235/2011wtr/index.html
Derangements with an additional restriction (and zigzags)
Derangements with an additional restriction (and zigzags) István Mező Nanjing University of Information Science and Technology 2017. 05. 27. This talk is about a class of generalized derangement numbers,
Approximating Submodular Functions. Nick Harvey University of British Columbia
Approximating Submodular Functions Nick Harvey University of British Columbia Approximating Submodular Functions Part 1 Nick Harvey University of British Columbia Department of Computer Science July 11th,
Quantum to Classical Randomness Extractors
Quantum to Classical Randomness Extractors Mario Berta, Omar Fawzi, Stephanie Wehner - Full version preprint available at arxiv: 1111.2026v3 08/23/2012 - CRYPTO University of California, Santa Barbara
Contents. Objectives Asymmetric Time World Lines Three Arrows of Time entropy memory expanding universe Wormholes Grand Unification Recap.
//07 Physics for Majors Today s Class The Arrow of Time Entropy/Memory/Expanding Universe Wormholes and Time Travel Unification Class Ideas from Hawking Section Why is space symmetric and time not? Last
Combining the cycle index and the Tutte polynomial?
Combining the cycle index and the Tutte polynomial? Peter J. Cameron University of St Andrews Combinatorics Seminar University of Vienna 23 March 2017 Selections Students often meet the following table
Local RG, Quantum RG, and Holographic RG. Yu Nakayama Special thanks to Sung-Sik Lee and Elias Kiritsis
Local RG, Quantum RG, and Holographic RG Yu Nakayama Special thanks to Sung-Sik Lee and Elias Kiritsis Local renormalization group The main idea dates back to Osborn NPB 363 (1991) See also my recent review
Self-complementary strongly regular graphs revisited
Self-complementary strongly regular graphs revisited Ferenc Szöllősi (joint work in part with Patric Östergård) szoferi@gmail.com Department of Communications and Networking, Aalto University Talk at CoCoA15
5. Grassmannians and the Space of Trees In this lecture we shall be interested in a very particular ideal. The ambient polynomial ring C[p] has ( n
![5. Grassmannians and the Space of Trees In this lecture we shall be interested in a very particular ideal. The ambient polynomial ring C[p] has ( n](/thumbs/89/97533670.jpg "5. Grassmannians and the Space of Trees In this lecture we shall be interested in a very particular ideal. The ambient polynomial ring C[p] has ( n")
5. Grassmannians and the Space of Trees In this lecture we shall be interested in a very particular ideal. The ambient polynomial ring C[p] has ( n d) variables, which are called Plücker coordinates: C[p]
Equivariant semidefinite lifts and sum of squares hierarchies
Equivariant semidefinite lifts and sum of squares hierarchies Pablo A. Parrilo Laboratory for Information and Decision Systems Electrical Engineering and Computer Science Massachusetts Institute of Technology
Orbit coherence in permutation groups
Orbit coherence in permutation groups John R. Britnell Department of Mathematics Imperial College London j.britnell@imperial.ac.uk Groups St Andrews 2013 Joint work with Mark Wildon (RHUL) Orbit partitions
Shannon-type Inequalities, Submodular Width, and Disjunctive Datalog
Shannon-type Inequalities, Submodular Width, and Disjunctive Datalog Hung Q. Ngo (Stealth Mode) With Mahmoud Abo Khamis and Dan Suciu @ PODS 2017 Table of Contents Connecting the Dots Output Size Bounds
Capacity Theorems for Distributed Index Coding
Capacity Theorems for Distributed Index Coding 1 Yucheng Liu, Parastoo Sadeghi, Fatemeh Arbabjolfaei, and Young-Han Kim Abstract arxiv:1801.09063v1 [cs.it] 27 Jan 2018 In index coding, a server broadcasts
Introduction to Curves. Modelling. 3D Models. Points. Lines. Polygons Defined by a sequence of lines Defined by a list of ordered points
Introduction to Curves Modelling Points Defined by 2D or 3D coordinates Lines Defined by a set of 2 points Polygons Defined by a sequence of lines Defined by a list of ordered points 3D Models Triangular
GROUP THEORY IN PHYSICS
GROUP THEORY IN PHYSICS Wu-Ki Tung World Scientific Philadelphia Singapore CONTENTS CHAPTER 1 CHAPTER 2 CHAPTER 3 CHAPTER 4 PREFACE INTRODUCTION 1.1 Particle on a One-Dimensional Lattice 1.2 Representations
Coding for Computing. ASPITRG, Drexel University. Jie Ren 2012/11/14
Coding for Computing ASPITRG, Drexel University Jie Ren 2012/11/14 Outline Background and definitions Main Results Examples and Analysis Proofs Background and definitions Problem Setup Graph Entropy Conditional
EMERGENT GRAVITY AND COSMOLOGY: THERMODYNAMIC PERSPECTIVE
EMERGENT GRAVITY AND COSMOLOGY: THERMODYNAMIC PERSPECTIVE Master Colloquium Pranjal Dhole University of Bonn Supervisors: Prof. Dr. Claus Kiefer Prof. Dr. Pavel Kroupa May 22, 2015 Work done at: Institute
Orbitopes. Marc Pfetsch. joint work with Volker Kaibel. Zuse Institute Berlin
Orbitopes Marc Pfetsch joint work with Volker Kaibel Zuse Institute Berlin What this talk is about We introduce orbitopes. A polyhedral way to break symmetries in integer programs. Introduction 2 Orbitopes
AN ELEMENTARY THEOREM IN GEOMETRIC INVARIANT THEORY
AN ELEMENTARY THEOREM IN GEOMETRIC INVARIANT THEORY BY DAVID MUMFORD Communicated by Raoul Bott, May 18, 1961 The purpose of this note is to prove the key theorem in a construction of the arithmetic scheme
Haruhiko Ogasawara. This article gives the first half of an expository supplement to Ogasawara (2015).
Economic Review (Otaru University of Commerce, Vol.66, No. & 3, 9-58. December, 5. Expository supplement I to the paper Asymptotic expansions for the estimators of Lagrange multipliers and associated parameters
Genuine three-partite entangled states with a hidden variable model
Genuine three-partite entangled states with a hidden variable model Géza Tóth 1,2 and Antonio Acín 3 1 Max-Planck Institute for Quantum Optics, Garching, Germany 2 Research Institute for Solid State Physics
1 Solution of a Large-Scale Traveling-Salesman Problem... 7 George B. Dantzig, Delbert R. Fulkerson, and Selmer M. Johnson
Part I The Early Years 1 Solution of a Large-Scale Traveling-Salesman Problem............ 7 George B. Dantzig, Delbert R. Fulkerson, and Selmer M. Johnson 2 The Hungarian Method for the Assignment Problem..............
Mutual Information in Conformal Field Theories in Higher Dimensions
Mutual Information in Conformal Field Theories in Higher Dimensions John Cardy University of Oxford Conference on Mathematical Statistical Physics Kyoto 2013 arxiv:1304.7985; J. Phys. : Math. Theor. 46
Introduction Examples More Properties. Eulerian Numbers. Armin Straub. 23-Apr 2007
23-Apr 2007 Outline Introduction Abstract Definition Simple Properties Occurrence in Probability Theory Asymptotics Generating Functions Abstract Definition Simple Properties Abstract Definition Definition
Production of triply heavy baryons and six free heavy quarks at
Production of triply heavy baryons and six free heavy quarks at LHC October 25, 2012 OUTLINE. Triply heavy baryons production.overview of the triply heavy baryons..the production of the triply heavy baryons..
The Central Curve in Linear Programming
joint work with Jesús De Loera and Bernd Sturmfels The Central Path of a Linear Program Linear Program: Maximize x R n c x s.t. A x = b and x 0. The Central Path of a Linear Program Linear Program: Maximize
Krieger s finite generator theorem for ergodic actions of countable groups
Krieger s finite generator theorem for ergodic actions of countable groups Brandon Seward University of Michigan UNT RTG Conference Logic, Dynamics, and Their Interactions II June 6, 2014 Brandon Seward
Error Correcting Index Codes and Matroids
Error Correcting Index Codes and Matroids Anoop Thomas and B Sundar Rajan Dept of ECE, IISc, Bangalore 5612, India, Email: {anoopt,bsrajan}@eceiiscernetin arxiv:15156v1 [csit 21 Jan 215 Abstract The connection
Symbolic extensions for partially hyperbolic diffeomorphisms
for partially hyperbolic diffeomorphisms Todd Fisher tfisher@math.byu.edu Department of Mathematics Brigham Young University Workshop on Partial Hyperbolicity Entropy Topological entropy measures the exponential
DAY 139 EQUATION OF A HYPERBOLA
DAY 139 EQUATION OF A HYPERBOLA INTRODUCTION In our prior conic sections lessons, we discussed in detail the two conic sections, the parabola, and the ellipse. The hyperbola is another conic section we
Uniformly Additive Entropic Formulas
Uniformly Additive Entropic Formulas Andrew Cross, Ke Li, Graeme Smith JILA and Department of Physics, University of Colorado Boulder QMATH2016 Georgia Tech October 9, 2016 Information theory: optimal
Sets avoiding norm 1 in R n
Sets avoiding norm 1 in R n Christine Bachoc Université de Bordeaux, IMB Computation and Optimization of Energy, Packing, and Covering ICERM, Brown University, April 9-13, 2018 Christine Bachoc (Université
Bipartite Matchings. Andreas Klappenecker
Bipartite Matchings Andreas Klappenecker Matching Number m(g) = number of edges in a maximally large matching. Why is m(g) < 4? m(g) = W iff A
Phonons and lattice dynamics
Chapter Phonons and lattice dynamics. Vibration modes of a cluster Consider a cluster or a molecule formed of an assembly of atoms bound due to a specific potential. First, the structure must be relaxed
Smooth Ergodic Theory and Nonuniformly Hyperbolic Dynamics
CHAPTER 2 Smooth Ergodic Theory and Nonuniformly Hyperbolic Dynamics Luis Barreira Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal E-mail: barreira@math.ist.utl.pt url:
Nucleon Pair Approximation to the nuclear Shell Model
Nucleon Pair Approximation to the nuclear Shell Model Yiyuan Cheng Department of Physics and Astronomy, Shanghai Jiao Tong University, China RCNP, Osaka university, Japan Collaborators: Yu-Min Zhao, Akito
Fluctuation theorems. Proseminar in theoretical physics Vincent Beaud ETH Zürich May 11th 2009
Fluctuation theorems Proseminar in theoretical physics Vincent Beaud ETH Zürich May 11th 2009 Outline Introduction Equilibrium systems Theoretical background Non-equilibrium systems Fluctuations and small
Cayley s Hyperdeterminant, the Principal Minors of a Symmetric Matrix and the Entropy Region of 4 Gaussian Random Variables
Forty-Sixth Annual Allerton Conference Allerton House, UIUC, Illinois, USA September 23-26, 2008 Cayley s Hyperdeterminant, the Principal Minors of a Symmetric Matrix and the Entropy Region of 4 Gaussian
Improved Slender-set Linear Cryptanalysis
1 / 37 Improved Slender-set Linear Cryptanalysis Guo-Qiang Liu 1 Chen-Hui Jin 1 Chuan-Da Qi 2 1 Information Science Technology Institute Zhengzhou, Henan, China 2 Xinyang Normal University Xinyang, Henan,
Polyhedral Methods for Positive Dimensional Solution Sets
Polyhedral Methods for Positive Dimensional Solution Sets Danko Adrovic and Jan Verschelde www.math.uic.edu/~adrovic www.math.uic.edu/~jan 17th International Conference on Applications of Computer Algebra