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A Tight Analysis of Bethe Approximation for Permanent [article]

Nima Anari, Alireza Rezaei
2019 arXiv   pre-print
Our bound is tight, and when combined with previously known inequalities lower bounding the permanent, fully resolves the quality of Bethe approximation for permanent.  ...  We show this by proving that the Bethe approximation of the permanent, a quantity computable in polynomial time, is at least as large as the permanent divided by √(2)^n.  ...  Bethe approximation of the permanent The algorithm we analyze has, in fact, been studied very extensively and its output is known as the Bethe approximation of the permanent, or Bethe permanent for short  ... 
arXiv:1811.02933v2 fatcat:7hxms2beffdynjxhgl5pygrthi

Approximating the Permanent with Belief Propagation [article]

Bert Huang, Tony Jebara
2009 arXiv   pre-print
This work describes a method of approximating matrix permanents efficiently using belief propagation.  ...  We formulate a probability distribution whose partition function is exactly the permanent, then use Bethe free energy to approximate this partition function.  ...  In Section 3, we discuss Bethe free energy and introduce belief propagation as a method of finding a suitable set of pseudo-marginals for the Bethe approximation.  ... 
arXiv:0908.1769v1 fatcat:hnzyblw3tzam7k4lzntw75b5kq

Approximating the Permanent with Fractional Belief Propagation [article]

M. Chertkov, A. B. Yedidia
2013 arXiv   pre-print
We discuss schemes for exact and approximate computations of permanents, and compare them with each other.  ...  Specifically, we analyze the Belief Propagation (BP) approach and its Fractional Belief Propagation (FBP) generalization for computing the permanent of a non-negative matrix.  ...  ABY acknowledges support of the Undergraduate Research Assistant Program at LANL and he is also grateful to CNLS at LANL for its hospitality.  ... 
arXiv:1108.0065v4 fatcat:tos42as7yfhohkur27l34wr6di

The Bethe permanent of a non-negative matrix

Pascal O. Vontobel
2010 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
Bethe approximation; Bethe permanent; graph cover; partition function; perfect matching; permanent; sum-product algorithm It has recently been observed that the permanent of a non-negative matrix, i.e.  ...  , of a matrix containing only non-negative real entries, can very well be approximated by solving a certain Bethe free energy function minimization problem with the help of the sum-product algorithm.  ...  Of course, nobody would use the Bethe permanent to approximate the permanent of a 2 × 2 matrix, however, it gives some good insights on the strengths and the weaknesses of the Bethe approximation to the  ... 
doi:10.1109/allerton.2010.5706926 fatcat:j4dpjurjlnhg3hxp4j4nycsxsu

The Bethe and Sinkhorn Permanents of Low Rank Matrices and Implications for Profile Maximum Likelihood [article]

Nima Anari, Moses Charikar, Kirankumar Shiragur, Aaron Sidford
2020 arXiv   pre-print
We achieve these results by providing new bounds on the quality of approximation of the Bethe and Sinkhorn permanents (Vontobel, 2012 and 2014).  ...  As a by-product of our work we establish a surprising connection between the convex relaxation in prior work (CSS19) and the well-studied Bethe and Sinkhorn approximations.  ...  We thank the anonymous reviewer for pointing out the alternative proof of the quality of scaled Sinkhorn and Bethe approximations on approximating the permanent of matrices with a bounded number of distinct  ... 
arXiv:2004.02425v1 fatcat:ueqgbx6oundqtamybbor4ptj6i

The Bethe Permanent of a Nonnegative Matrix

Pascal O. Vontobel
2013 IEEE Transactions on Information Theory  
It has recently been observed that the permanent of a non-negative square matrix, i.e., of a square matrix containing only non-negative real entries, can very well be approximated by solving a certain  ...  We also present a combinatorial characterization of the Bethe permanent in terms of permanents of so-called lifted versions of the matrix under consideration.  ...  Of course, nobody would use the Bethe permanent to approximate the permanent of a 2 × 2 matrix, however, it gives some good insights on the strengths and the weaknesses of the Bethe approximation to the  ... 
doi:10.1109/tit.2012.2227109 fatcat:vszcjawh4zavhggvtbfyahh5dm

Inhibition of flexor tone

Beth U. Coon, William R. Mattingly
2004 Journal of Hand Therapy  
In fact, three of the patients discharged from therapy have subsequently returned for fab- rication of a replacement of their “permanent adaptive splint.”  ...  Inhibition of Flexor Tone. Beth U. Coon, PT, CHT, William R.  ... 
doi:10.1197/j.jht.2003.10.027 fatcat:3swz2ts53rfq7mks3zd5dgvuha

Loop calculus and bootstrap-belief propagation for perfect matchings on arbitrary graphs

M Chertkov, A Gelfand, J Shin
2013 Journal of Physics, Conference Series  
We present two novel problem formulations - one for computing the PF of a Perfect Matching (PM) and one for finding MWPMs - that build upon the inter-related Bethe Free Energy, Belief Propagation (BP),  ...  We then study the zero-temperature version of this Bootstrap-BP formula for approximately solving the MWPM problem.  ...  For decades the three fields developed BP and the homonymous Bethe-Peierls approximation independently.  ... 
doi:10.1088/1742-6596/473/1/012007 fatcat:xuoe4pmbxvc7jgsk6ht5dxutky

Bounds on the size of balls over permutations with the infinity metric

Moshe Schwartz, Pascal O. Vontobel
2015 2015 IEEE International Symposium on Information Theory (ISIT)  
We focus on the regime of balls with radius r = ρ · (n−1), ρ ∈ [0, 1], i.e., a radius that is a constant fraction of the maximum possible distance. We provide new bounds on the size of such balls.  ...  We study the size (or volume) of balls in the metric space of permutations, S n , under the infinity metric.  ...  Bethe-Permanent-Based Lower Bound We recall that a doubly-stochastic matrix is a square n × n matrix with non-negative real entries for which the sum of each row and each column is 1.  ... 
doi:10.1109/isit.2015.7282752 dblp:conf/isit/SchwartzV15 fatcat:ji6lauzhkzgv7ecfzharale6oi

Bounds on the permanent and some applications [article]

Leonid Gurvits, Alex Samorodnitsky
2014 arXiv   pre-print
We give new lower and upper bounds on the permanent of a doubly stochastic matrix. Combined with previous work, this improves on the deterministic approximation factor for the permanent.  ...  We also give a combinatorial application of the lower bound, proving S. Friedland's "Asymptotic Lower Matching Conjecture" for the monomer-dimer problem.  ...  of its Bethe Approximation.  ... 
arXiv:1408.0976v1 fatcat:oqzbsvd7vrghtkwdtmwxm56rkm

Predicting the Future of Permanent-Magnet Materials

Ralph Skomski, Priyanka Manchanda, Pankaj K. Kumar, B. Balamurugan, Arti Kashyap, D. J. Sellmyer
2013 IEEE transactions on magnetics  
Concerning the choice of the hard phase, both a high magnetization and a high anisotropy are necessary.  ...  Our analysis of aligned hard-soft nanostructures shows that soft-in-hard geometries are better than hard-in-soft geometries and that embedded soft spheres are better than sandwiched soft layers.  ...  However, the Slater-Bethe-Néel curve is a crude approximation, and our VASP calculations show that strong ferromagnetic (FM) exchange can exist even for very short Mn-Mn distances.  ... 
doi:10.1109/tmag.2013.2248139 fatcat:hkaxjpx4t5btxdybomrtu5boam

Approximating the Bethe partition function [article]

Adrian Weller, Tony Jebara
2013 arXiv   pre-print
yields a fully polynomial-time approximation scheme (FPTAS) for attractive models without any degree restriction.  ...  When belief propagation (BP) converges, it does so to a stationary point of the Bethe free energy F, and is often strikingly accurate.  ...  Acknowledgments We are grateful to Kui Tang for help with coding, and to David Sontag, Kui Tang, Nicholas Ruozzi and Tomaz Slivnik for helpful discussions.  ... 
arXiv:1401.0044v1 fatcat:3yx55nmvrrcanng5zmhrdykege

Correlations in rare-earth transition-metal permanent magnets

R. Skomski, P. Manchanda, A. Kashyap
2015 Journal of Applied Physics  
On an independentelectron level, the use of a single Slater determinant with broken spin symmetry introduces Hund's rule correlations, which govern the behavior of rare-earth ions and of alloys described  ...  by the local spin density approximation (LSDA) and LSDA þ U approximations to DFT.  ...  Sellmyer for the discussion of various details. This research is supported by DOE (DE-FG02-04ER46152) and NCMN.  ... 
doi:10.1063/1.4917003 fatcat:l7jnhg26wbevljwhmcv37qxhci

Robust Multiple-Range Coherent Quantum State Transfer

Bing Chen, Yan-Dong Peng, Yong Li, Xiao-Feng Qian
2016 Scientific Reports  
At the weak interaction regime, our system is effectively equivalent to a three level system of which a coherent superposition of the two carrier states constitutes a dark state.  ...  In our scheme, an information carrier (a qubit) and its remote partner are both adiabatically coupled to the same data bus, i.e., an N}-site tight-binding chain that has a single defect at the center.  ...  We will present a detail analysis of the peculiar properties of Hamiltonian ˆM  which used as a quantum channel for quantum state transfer via Bethe ansatz method 47 .  ... 
doi:10.1038/srep28886 pmid:27364891 pmcid:PMC4929469 fatcat:zvfbwqbokjgtpkgloqsys2zbsa

Accurate description of charged excitations in molecular solids from embedded many-body perturbation theory

Jing Li, Gabriele D'Avino, Ivan Duchemin, David Beljonne, Xavier Blase
2018 Physical review B  
We present a novel hybrid quantum/classical (QM/MM) approach to the calculation of charged excitations in molecular solids based on the many-body Green's function GW formalism.  ...  polarization, which is accounted for combining quantum and classical polarizabilities, and crystal field effects, that can impact energy levels by up to ±0.6 eV.  ...  On general grounds, the analysis of Eq.  ... 
doi:10.1103/physrevb.97.035108 fatcat:zlrdd7fcp5ewxizwbfqlpqt2jq
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