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A Generalization of Permanent Inequalities and Applications in Counting and Optimization [article]

Nima Anari, Shayan Oveis Gharan
2017 arXiv   pre-print
This fundamental inequality has been used to attack several counting and optimization problems.  ...  We use our theorem to give a new proof of Schrijver's inequality on the number of perfect matchings of a regular bipartite graph, generalize a recent result of Nikolov and Singh, and give deterministic  ...  Applications Applications in Counting In this section we prove Theorem 1.2 and we discuss several applications of our results for counting problems. We start with Schrijver's inequality.  ... 
arXiv:1702.02937v1 fatcat:yos2mgknknejnnq5fj3hnd4wiu

Page 5262 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
Summary: “We present a highly optimized method for the elimi- nation of linear variables from a Boolean combination of polyno- mial equations and inequalities.  ...  The paper gives an explicit construction of how to represent a polyno- mial in VNP by the counting operator applied to the permanent polynomial.  ... 

Matrix permanent and quantum entanglement of permutation invariant states

Tzu-Chieh Wei, Simone Severini
2010 Journal of Mathematical Physics  
By employing a recently introduced permanent inequality by Carlen, Loss and Lieb, we can prove explicit formulas of the geometric measure for permutation invariant basis states in a simple way.  ...  We point out that a geometric measure of quantum entanglement is related to the matrix permanent when restricted to permutation invariant states.  ...  A recent permanent inequality of Carlen, Loss and Lieb [6] can be employed to bypass the optimization problem.  ... 
doi:10.1063/1.3464263 fatcat:if5n6vj2lnejnccvnvvh7jvpoe

List of contents

2002 Computers and Mathematics with Applications  
and Global Attractivity in a Nonlinear Delay Periodic Model of Respiratory Dynamics A Complete Algorithm for Counting Real Solutions of Polynomials Systems of Equations and Inequalities V  ...  Global Optimization Based on a Statistical Model and Simplicial Partitioning 979 Dynamic Model of Market of Patents and Equilibria in Technology Stocks 1007 1019 Global Optimization in  ...  Four-Moduli Set (2, 2" -1, 2" + 2" _ ' -1, 2" + ' + 2" -1) Simplifies the Residue to Binary Converters Based on CRT II The Dynamic-Q Optimization Method: An Alternative to SQP?  ... 
doi:10.1016/s0898-1221(02)80027-x fatcat:xvuiqiphbrc5hmnfs5xeh4canq

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.  ...  We prove the lower bound in Section 3, and the upper bound in Sections 4 and 5. 2 Bounds for the permanent Lower bounds In general, the permanent of a nonnegative matrix may vanish.  ... 
arXiv:1408.0976v1 fatcat:oqzbsvd7vrghtkwdtmwxm56rkm

The Distance Approach to Approximate Combinatorial Counting [article]

Alexander Barvinok, Alex Samorodnitsky
2000 arXiv   pre-print
As an application, we present a new randomized polynomial time algorithm which approximates the permanent of a 0-1 matrix by solving a small number of Assignment problems.  ...  We develop general methods to obtain fast (polynomial time) estimates of the cardinality of a combinatorially defined set via solving some randomly generated optimization problems on the set.  ...  Gromov and B. Sudakov for many helpful discussions.  ... 
arXiv:math/0005263v1 fatcat:2z4jliry3jcedhrcjwb2dmpwgq

Page 474 of Mathematical Reviews Vol. , Issue 89A [page]

1989 Mathematical Reviews  
The advice is generated by simplifying the pending subproblems into trees, counting the number of consistent solutions in each simpli- fied subproblem, and comparing these counts to decide among the choices  ...  Therefore, a special case of the algorithm will lift a variable-only E-unification algorithm to the general case in which more than one operator satisfying the axioms of E and other operators which satisfy  ... 

The optimization for the inequalities of power means

Jiajin Wen, Wan-Lan Wang
2006 Journal of Inequalities and Applications  
In this paper, we will state the important background and meaning of the inequality n (a); a necessary and sufficient condition and another interesting sufficient condition that the foregoing inequality  ...  Our methods used are the procedure of descending dimension and theory of majorization; and apply techniques of mathematical analysis and permanents in algebra.  ...  from the NSF of China.  ... 
doi:10.1155/jia/2006/46782 fatcat:3w6k2b7ewncbvp6dc36ihsogm4

Bounds on the Permanent and Some Applications

Leonid Gurvits, Alex Samorodnitsky
2014 2014 IEEE 55th Annual Symposium on Foundations of Computer Science  
We show that the permanent of a doubly stochastic n × n matrix A = (a ij ) is at least as large as ∏ i,j (1 − a ij ) 1−aij and at most as large as 2 n times this number.  ...  We also give a combinatorial application of the lower bound, proving S. Friedland's "Asymptotic Lower Matching Conjecture" for the monomer-dimer problem.  ...  Another part is in its ability to count things. The permanent of a 0, 1 matrix A equals the number of perfect matchings in the bipartite graph it represents.  ... 
doi:10.1109/focs.2014.18 dblp:conf/focs/GurvitsS14 fatcat:7zoyitmbfrb67gdvw4z2w6gudm

Maximum Entropy Distributions: Bit Complexity and Stability [article]

Damian Straszak, Nisheeth K. Vishnoi
2019 arXiv   pre-print
Our main result shows a poly(m, log 1/ε) bound on the bit complexity of ε-optimal dual solutions to the maximum entropy convex program – for very general support sets and with no restriction on the marginal  ...  Applications of this result include polynomial time algorithms to compute max-entropy distributions over several new and old polytopes for any marginal vector in a unified manner, a polynomial time algorithm  ...  Brascamp-Lieb inequalities are an ultimate generalization of many inequalities used in analysis and all of mathematics, such as the Hölder inequality and Loomis-Whitney [12, 28] .  ... 
arXiv:1711.02036v2 fatcat:ku2wxvg3drgx7eccjmpb7g3l7e

Permanent magnet synchronous motor dynamic modeling with genetic algorithm performance improvement

A Shahat, H Shewy
2010 International Journal of Engineering, Science and Technology  
The proposed model would be used in many applications such as automotive, mechatronics, green energy applications, and machine drives.  ...  This paper proposes dynamic modeling simulation for ac Surface Permanent Magnet Synchronous Motor (SPMSM) with the aid of MATLAB -Simulink environment.  ...  Abd Al Menem for her effort in this research editing  ... 
doi:10.4314/ijest.v2i2.59152 fatcat:4afrkmrorngrvmken5fusmcyiy

Approximate counting via random optimization

Alexander Barvinok
1997 Random structures & algorithms (Print)  
For example, the computation of the permanent of a given 0᎐1 matrix reduces to counting bases in the intersection of two matroids.  ...  Examples of particularly interesting and difficult problems include counting forests in a given graph and counting subsets of linearly indepen-Ž . dent vectors in a given set in a vector space over GF  ...  matchings in a graph with n edges in Theorem 1.3 or when F F is the set of n . Hamiltonian circuits in a graph with n vertices in Theorem 3.1 .  ... 
doi:10.1002/(sici)1098-2418(199709)11:2<187::aid-rsa6>3.3.co;2-# fatcat:5x7svpnzkjgbljxa6abht6mh2i

Approximate counting via random optimization

Alexander Barvinok
1997 Random structures & algorithms (Print)  
For example, the computation of the permanent of a given 0᎐1 matrix reduces to counting bases in the intersection of two matroids.  ...  Examples of particularly interesting and difficult problems include counting forests in a given graph and counting subsets of linearly indepen-Ž . dent vectors in a given set in a vector space over GF  ...  matchings in a graph with n edges in Theorem 1.3 or when F F is the set of n . Hamiltonian circuits in a graph with n vertices in Theorem 3.1 .  ... 
doi:10.1002/(sici)1098-2418(199709)11:2<187::aid-rsa6>3.0.co;2-o fatcat:2k6d2aeeirhfvkqizsuusiui2e

Real Stable Polynomials and Matroids: Optimization and Counting [article]

Damian Straszak, Nisheeth K. Vishnoi
2016 arXiv   pre-print
A great variety of fundamental optimization and counting problems arising in computer science, mathematics and physics can be reduced to one of the following computational tasks involving polynomials and  ...  In this paper we present a general convex programming framework geared to solve both of these problems.  ...  We present a general framework for solving such counting and optimization problems. We start with the counting problem and later extend our solution to the optimization problem.  ... 
arXiv:1611.04548v1 fatcat:bownuefvfrdrzaegj3su3j4zzy

List of contents

2003 Applied Mathematics Letters  
Convection Dominated Flows An Optimization Approach to Multiple Sequence Alignment Partial Relaxed Monotonicity and General Auxiliary Problem Principle with Applications The Number of Walks in  ...  Born Series in Obstacle ScatteringUnique Estimation of Mortality Rates in Gompertz Survival Model Parameters Efficient and Weak Efficient Points in Vector Optimization with Generalized Cone Convexity  ... 
doi:10.1016/s0893-9659(03)90138-8 fatcat:sgh4wgebmnfchpedljenuojy2m
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