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

2017
*
arXiv
*
pre-print

This fundamental

arXiv:1702.02937v1
fatcat:yos2mgknknejnnq5fj3hnd4wiu
*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*. ...##
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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

2010
*
Journal of Mathematical Physics
*

By employing

doi:10.1063/1.3464263
fatcat:if5n6vj2lnejnccvnvvh7jvpoe
*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. ...##
###
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? ...

##
###
Bounds on the permanent and some applications
[article]

2014
*
arXiv
*
pre-print

We give new lower

arXiv:1408.0976v1
fatcat:oqzbsvd7vrghtkwdtmwxm56rkm
*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. ...##
###
The Distance Approach to Approximate Combinatorial Counting
[article]

2000
*
arXiv
*
pre-print

As an

arXiv:math/0005263v1
fatcat:2z4jliry3jcedhrcjwb2dmpwgq
*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. ...##
###
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

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. ...

##
###
Bounds on the Permanent and Some Applications

2014
*
2014 IEEE 55th Annual Symposium on Foundations of Computer Science
*

We show that the

doi:10.1109/focs.2014.18
dblp:conf/focs/GurvitsS14
fatcat:7zoyitmbfrb67gdvw4z2w6gudm
*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. ...##
###
Maximum Entropy Distributions: Bit Complexity and Stability
[article]

2019
*
arXiv
*
pre-print

Our main result shows

arXiv:1711.02036v2
fatcat:ku2wxvg3drgx7eccjmpb7g3l7e
*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] . ...##
###
Permanent magnet synchronous motor dynamic modeling with genetic algorithm performance improvement

2010
*
International Journal of Engineering, Science and Technology
*

The proposed model would be used

doi:10.4314/ijest.v2i2.59152
fatcat:4afrkmrorngrvmken5fusmcyiy
*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 ...##
###
Approximate counting via random optimization

1997
*
Random structures & algorithms (Print)
*

For example, the computation

doi:10.1002/(sici)1098-2418(199709)11:2<187::aid-rsa6>3.3.co;2-#
fatcat:5x7svpnzkjgbljxa6abht6mh2i
*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 . ...##
###
Approximate counting via random optimization

1997
*
Random structures & algorithms (Print)
*

For example, the computation

doi:10.1002/(sici)1098-2418(199709)11:2<187::aid-rsa6>3.0.co;2-o
fatcat:2k6d2aeeirhfvkqizsuusiui2e
*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 . ...##
###
Real Stable Polynomials and Matroids: Optimization and Counting
[article]

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. ...

##
###
List of contents

2003
*
Applied Mathematics Letters
*

Convection Dominated Flows
An

doi:10.1016/s0893-9659(03)90138-8
fatcat:sgh4wgebmnfchpedljenuojy2m
*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 ...
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