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Clifford Algebras and approximating the permanent
, 2002
"... We study approximation algorithms for the permanent of an n * n (0, 1) matrix A based on the following simple idea: obtain a random matrix B by replacing each 1entry of A independently by+e, where e is a random basis element of a suitable algebra; then output  det(B)2. This estimator is always ..."
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Cited by 21 (2 self)
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We study approximation algorithms for the permanent of an n * n (0, 1) matrix A based on the following simple idea: obtain a random matrix B by replacing each 1entry of A independently by+e, where e is a random basis element of a suitable algebra; then output  det(B)2. This estimator is always
Clifford algebras and approximating the permanent (Extended Abstract)
 ACM STOC
, 2002
"... We study approximation algorithms for the permanent of an n \Theta n (0; 1) matrix A based on the following simple idea: obtain a random matrix B by replacing each 1entry of A independently by \Sigma e, where e is a random basis element of a suitable algebra; then output j det(B)j 2. This estimato ..."
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We study approximation algorithms for the permanent of an n \Theta n (0; 1) matrix A based on the following simple idea: obtain a random matrix B by replacing each 1entry of A independently by \Sigma e, where e is a random basis element of a suitable algebra; then output j det(B)j 2
CLIFFORD ALGEBRAS AND SPINORS1
, 2010
"... Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on neutrino masses. It has a more mathematical flavour than the ..."
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Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on neutrino masses. It has a more mathematical flavour than
Clifford Networks
, 1995
"... This thesis is concerned with an extension of feedforward networks, Clifford networks,which use multideminsional values from Clifford algebras as weight and activation values. An extended back propagation algorithm is derived and results are proved which show Clifford networks can approzimate any ..."
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This thesis is concerned with an extension of feedforward networks, Clifford networks,which use multideminsional values from Clifford algebras as weight and activation values. An extended back propagation algorithm is derived and results are proved which show Clifford networks can approzimate any
Reductions in Computational Complexity using Clifford Algebras
"... A number of combinatorial problems known to be of NP time complexity can be reduced to class P within a particular algebraic context. For example, the problem of determining whether or not a graph contains a Hamiltonian cycle is known to be NPcomplete. By considering entries of Λ k, where Λ is an a ..."
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Cited by 9 (5 self)
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A number of combinatorial problems known to be of NP time complexity can be reduced to class P within a particular algebraic context. For example, the problem of determining whether or not a graph contains a Hamiltonian cycle is known to be NPcomplete. By considering entries of Λ k, where Λ
The Toolbox Revisited: Paths to Degree Completion from High School Through
 DEPARTMENT OF EDUCATION
, 2006
"... The views expressed herein are those of the author and do not necessarily represent the positions or policies of the U.S. Department of Education. No official endorsement by the U.S. Department of Education of any product, commodity, service, or enterprise mentioned in this publication is intended o ..."
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Cited by 262 (0 self)
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The views expressed herein are those of the author and do not necessarily represent the positions or policies of the U.S. Department of Education. No official endorsement by the U.S. Department of Education of any product, commodity, service, or enterprise mentioned in this publication is intended or should be inferred. This document is in the public domain. Authorization to reproduce it in whole or in part is granted. While permission to reprint this publication is not necessary, the citation should be:
Approximating the Permanent via Nonabelian Determinants
, 2009
"... Since the celebrated work of Jerrum, Sinclair, and Vigoda, we have known that the permanent of a {0, 1} matrix can be approximated in randomized polynomial time by using a rapidly mixing Markov chain to sample perfect matchings of a bipartite graph. A separate strand of the literature has pursued th ..."
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Cited by 4 (0 self)
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(d). Thus our results do not provide a new polynomialtime approximation scheme for the permanent. Indeed, they suggest that the algebraic approach to approximating the permanent faces significant obstacles. We obtain these results using diagrammatic techniques in which we express matrix products
Solving Systems of Polynomial Equations
 AMERICAN MATHEMATICAL SOCIETY, CBMS REGIONAL CONFERENCES SERIES, NO 97
, 2002
"... One of the most classical problems of mathematics is to solve systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely applied across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, ..."
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Cited by 221 (14 self)
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, statistics, machine learning, control theory, and numerous other areas. The set of solutions to a system of polynomial equations is an algebraic variety, the basic object of algebraic geometry. The algorithmic study of algebraic varieties is the central theme of computational algebraic geometry. Exciting
Menelaus’ theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy
 J. Phys. A: Math. Gen
, 2002
"... It is shown that the integrable discrete Schwarzian KP (dSKP) equation which constitutes an algebraic superposition formula associated with, for instance, the Schwarzian KP hierarchy, the classical Darboux transformation and quasiconformal mappings encapsulates nothing but a fundamental theorem of ..."
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Cited by 25 (6 self)
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of ancient Greek geometry. Thus, it is demonstrated that the connection with Menelaus ’ theorem and, more generally, Clifford configurations renders the dSKP equation a natural object of inversive geometry on the plane. The geometric and algebraic integrability of dSKP lattices and their reductions
Results 1  10
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1,822