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Fractionally Log-Concave and Sector-Stable Polynomials: Counting Planar Matchings and More [article]

Yeganeh Alimohammadi, Nima Anari, Kirankumar Shiragur, Thuy-Duong Vuong
2021 arXiv   pre-print
We show fully polynomial time randomized approximation schemes (FPRAS) for counting matchings of a given size, or more generally sampling/counting monomer-dimer systems in planar, not-necessarily-bipartite  ...  In order to analyze mixing properties of the multi-site Glauber dynamics, we establish two notions for generating polynomials of discrete set-valued distributions: sector-stability and fractional log-concavity  ...  Fractionally Log-Concave Polynomials In this section, first, we show that any sector-stable polynomial is a fractionally log-concave polynomial as well.  ... 
arXiv:2102.02708v2 fatcat:arzydkij3ngzlnmmqrjiqtk4oi

Domain Sparsification of Discrete Distributions using Entropic Independence [article]

Nima Anari, Michał Dereziński, Thuy-Duong Vuong, Elizabeth Yang
2021 arXiv   pre-print
Our work significantly extends the reach of prior work of Anari and Dereziński who obtained domain sparsification for distributions with a log-concave generating polynomial (corresponding to α=1).  ...  μ, as is often needed in upstream tasks such as counting and inference.  ...  This distribution is isotropic, 1 2 -sector stable [Ali+21] , and 1 2 -fractionally-log-concave, and yet, according to the worst-case analysis, it does not yield enough acceptance probability when t =  ... 
arXiv:2109.06442v2 fatcat:bpblgidim5brrebiyqmd6iktpm

Optimal Mixing Time for the Ising Model in the Uniqueness Regime [article]

Xiaoyu Chen, Weiming Feng, Yitong Yin, Xinyuan Zhang
2021 arXiv   pre-print
We refine the boosting technique developed in [CFYZ21], and prove a new boosting theorem by utilizing the entropic independence defined in [AJK+21].  ...  The theorem relates the modified log-Sobolev (MLS) constant of the Glauber dynamics for a near-critical Ising model to that for an Ising model in a sub-critical regime.  ...  R [AASV21] Yeganeh Alimohammadi, Nima Anari, Kirankumar Shiragur, and Thuy-Duong Vuong. Fractionally log-concave and sector-stable polynomials: counting planar matchings and more.  ... 
arXiv:2111.03034v1 fatcat:wyejmbuisjgxxlgxg4ls4sgayy

Mathematical and Algorithmic Analysis of Network and Biological Data [article]

Charalampos E. Tsourakakis
2014 arXiv   pre-print
This dissertation contributes to mathematical and algorithmic problems that arise in the analysis of network and biological data.  ...  of the sectors.  ...  By the planar separator theorem [281] and the planarity of RANs, this property is satisfied.  ... 
arXiv:1407.0375v1 fatcat:6s2qka5fazbl7bzxz4k3u75hzm

A Singular Mathematical Promenade [article]

Etienne Ghys
2017 arXiv   pre-print
Hopefully, some motivated undergraduates and some more advanced mathematicians will enjoy some of these panoramas.  ...  We pay a visit to Hipparchus, Newton and Gauss, but also to many contemporary mathematicians. We play with a bit of algebra, topology, geometry, complex analysis and computer science.  ...  This gives a lower bound for the growth of a n since we already counted separable permutations. lim inf 1 n log a n ≥ log(3 + 2 √ 2).  ... 
arXiv:1612.06373v4 fatcat:3x2nfhmw3jgo3lfwvyt7njnssq

Quantum Barnes Function as the Partition Function of the Resolved Conifold

Sergiy Koshkin
2008 International Journal of Mathematics and Mathematical Sciences  
Our strategy applies to more general situations, and it is to interpret the Gromov-Witten, the Donaldson-Thomas, and the Chern-Simons invariants as different characterizations of the same holomorphic function  ...  We give a short new proof of largeNduality between the Chern-Simons invariants of the 3-sphere and the Gromov-Witten/Donaldson-Thomas invariants of the resolved conifold.  ...  Auckly and D. Karp for sharing their thoughts and notes on the Gromov-Witten and the Chern-Simons theories and also for suggesting numerous corrections and improvements to the original draft.  ... 
doi:10.1155/2008/438648 fatcat:nm2ug6zu6bepjhaqnqbrnn4hoy

Decay of Correlations for Lorentz Gases and Hard Balls [chapter]

N. Chernov, L. S. Young
2000 Hard Ball Systems and the Lorentz Gas  
We discuss rigorous results and open problems on the decay of correlations for dynamical systems characterized by elastic collisions: hard balls, Lorentz gases, Sinai billiards and related models.  ...  These techniques give exponential decay of correlations for many classes of billiards and open the door to further investigations.  ...  In 1970 Sinai [Si5] undertook a systematic study of planar periodic Lorentz gases and, more generally, of planar billiards in tables with concave boundaries (now called dispersing billiards or Sinai  ... 
doi:10.1007/978-3-662-04062-1_5 fatcat:2iw7g7pt25fpzpz74so3vjxx5q

Minimum color‐degree perfect b ‐matchings

Mariia Anapolska, Christina Büsing, Martin Comis, Tabea Krabs
2020 Networks  
Schrader, and Graphs III (Wed 20, Room PP, 9:30-10:30) chaired by R. Cordone. Session chairs must remind speakers to load up slides on laptops, and keep the sessions on time.  ...  Session chairs are encouraged to be cruel and despotic as regards times allotted, since there are parallel sessions.  ...  This leads to simpler/more-compact matrix algebra and more-streamlined finite-convergence proofs.  ... 
doi:10.1002/net.21974 fatcat:4qgtutmxrrcy7anvxks4fivcii

Random Partitions and the Quantum Benjamin-Ono Hierarchy [article]

Alexander Moll
2017 arXiv   pre-print
Our results reflect the fact that at fixed ħ>0 the weight defining Fock space is already a fractional Brownian motion of variance ħ and Hurst index (-s) - 12T = + 12 - 12 = 0.  ...  As Jack polynomials are the quantum stationary states and Stanley's Cauchy kernel (1989) is the reproducing kernel, the random values of the quantum periodic Benjamin-Ono hierarchy in a coherent state  ...  If one identifies the enumeration of more and more complicated objects with higher and higher corrections, these corrections become more and more sensitive to the choice of quantization.  ... 
arXiv:1508.03063v3 fatcat:agw5xrfmfrcj3kkfjxtn5zzinm

Abstracts of Working Papers in Economic

1986 Abstracts of Working Papers in Economics  
KW Optimal Fractional Matchings. Augmenting Path Method.  ...  AB We show how optimal fractional matchings can be used to start the shortest augmenting path method for solving the (integer) matching problem.  ...  But the more general goal of increasing general saving is.  ... 
doi:10.1017/s0951007900000322 fatcat:i5ukytusmbfwvizmo34s2nebi4

Fermionic Matrix Models

Gordon W. Semenoff, Richard J. Szabo
1997 International Journal of Modern Physics A  
We discuss the properties of the adjoint fermion one-, two- and gauge invariant D-dimensional matrix models at large-N and compare them with their bosonic counterparts which are the more familiar Hermitian  ...  We derive and solve the complete sets of loop equations for the correlators of these models and use these equations to examine critical behaviour.  ...  Plefka and M. Van Raamsdonk for valuable discussions and comments on the manuscript. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada.  ... 
doi:10.1142/s0217751x97001328 fatcat:c27h5kdqrjhorkyboieequ2wd4

Abstracts of Working Papers in Economics

1990 Abstracts of Working Papers in Economics  
International coordination can exacerbate the deficit bias, and thus reduce social welfare at home and abroad.  ...  TI Government Spending and Budget Deficits in the Industrial Economies. AU Roubini, Nouriel; Sachs, Jeffrey D.  ...  Planar Network. Polynomial Algorithm. Integer Solution. Stock Volatility. AA University of Rochester.  ... 
doi:10.1017/s0951007900001534 fatcat:ctxzhimskrcllg5cpy7s6dbvdy

Isospin-Asymmetry Dependence of the Thermodynamic Nuclear Equation of State in Many-Body Perturbation Theory [article]

Corbinian Wellenhofer
2017 arXiv   pre-print
The nuclear equation of state is an essential quantity in nuclear astrophysics and governs the properties of neutron stars and core-collapse supernov\ae.  ...  The first-order nuclear liquid-gas phase transition is analyzed with respect to its dependence on temperature and the neutron-to-proton ratio.  ...  [399] . 30 We note that the temperature dependence ofF sym and TS sym approaches linear behavior in the limit of vanishing density,F sym (T, ρ → 0) = −TS sym (T, ρ → 0) = T ln 2.  ... 
arXiv:1707.09222v2 fatcat:zxotb4bi45cwfceggmcg4i35aq

Geometric Aspects of Spectral Theory

Michiel van den Berg, Daniel Grieser, Thomas Hoffmann-Ostenhof, Iosif Polterovich
2012 Oberwolfach Reports  
featured presentations on some of the most fascinating recent developments in the subject, including five survey talks given by top experts, as well as reports on the progress made by graduate students and  ...  The scale log λ/ √ λ is sharp.  ...  If Ω is a simply connected planar set then P (Ω) gives the torsional rigidity of a cylindrical beam of cross section Ω, and more generally the torsion function plays a role in a variety of areas including  ... 
doi:10.4171/owr/2012/33 fatcat:4u2lgrvogfbjldyun42obedgau

Hub Location Problems: The Location of Interacting Facilities [chapter]

Bahar Y. Kara, Mehmet R. Taner
2011 International Series in Operations Research and Management Science  
Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.  ...  The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they  ...  -004-F and CONICYT FBO16.  ... 
doi:10.1007/978-1-4419-7572-0_12 fatcat:skbs7zlmqjb5pk2swpw3yxemna
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