Results 1  10
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1,198
IS LOGICALLY NONTRIVIAL
"... Abstract. If we express the statement of the unitdistance preserving theorem (that every mapping from R n to R n that preserves unit distance is linear) in terms of quantifiers and logical connectives, then we get a formula that is very close to formulas from elementary geometry. A. Tarski has prov ..."
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Abstract. If we express the statement of the unitdistance preserving theorem (that every mapping from R n to R n that preserves unit distance is linear) in terms of quantifiers and logical connectives, then we get a formula that is very close to formulas from elementary geometry. A. Tarski has
Periodic Instantons with Nontrivial Holonomy
, 1998
"... We present the detailed derivation of the charge one periodic instantons or calorons with nontrivial holonomy for SU(2). We use a suitable combination of the Nahm transformation and ADHM techniques. Our results rely on our ability to compute explicitly the relevant Green’s function in terms of ..."
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Cited by 60 (2 self)
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We present the detailed derivation of the charge one periodic instantons or calorons with nontrivial holonomy for SU(2). We use a suitable combination of the Nahm transformation and ADHM techniques. Our results rely on our ability to compute explicitly the relevant Green’s function in terms
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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with a single loop • Unless all the conditional probabilities are deter ministic, belief propagation will converge. • There is an analytic expression relating the cor rect marginals to the loopy marginals. The ap proximation error is related to the convergence rate of the messages the faster
USACH/99/06 FERMIONS ON NONTRIVIAL TOPOLOGIES
, 1999
"... An exact expression for the Green function of a purely fermionic system moving on the manifold ℜ × Σ D−1 where Σ D−1 is a (D − 1)torus is found. This expression involves the bosonic analog of χn = einθ corresponding to the irreducible representation for the nth class of homotopy but in the fermion ..."
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An exact expression for the Green function of a purely fermionic system moving on the manifold ℜ × Σ D−1 where Σ D−1 is a (D − 1)torus is found. This expression involves the bosonic analog of χn = einθ corresponding to the irreducible representation for the nth class of homotopy
Nontrivial Equilibrium in an Economy with Stochastic Rationing
 National Bureau of Economic Research, Working Paper 322
, 1979
"... program in economic fluctuations. Any opinions expressed are those of the authors and not those of the National Bureau of Economic Research. The authors wish to thank Kenneth J. Arrow and Jerry Green for stimulating conversations. * A grant from the Finnish Cultural Foundation is gratefully acknowl ..."
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Cited by 1 (1 self)
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program in economic fluctuations. Any opinions expressed are those of the authors and not those of the National Bureau of Economic Research. The authors wish to thank Kenneth J. Arrow and Jerry Green for stimulating conversations. * A grant from the Finnish Cultural Foundation is gratefully
USACH/99/11 FERMIONS ON NONTRIVIAL TOPOLOGIES
, 2000
"... An exact expression for the Green function of a purely fermionic system moving on the manifold ℜ × Σ D−1, where Σ D−1 is a (D − 1)torus, is found. This expression involves the bosonic analog of χn = einθ corresponding to the irreducible representation for the nth class of homotopy and in the fermi ..."
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An exact expression for the Green function of a purely fermionic system moving on the manifold ℜ × Σ D−1, where Σ D−1 is a (D − 1)torus, is found. This expression involves the bosonic analog of χn = einθ corresponding to the irreducible representation for the nth class of homotopy
A New Proof that Alternating Links are NonTrivial
, 2008
"... We use a simple geometric argument and small cancellation properties of link groups to prove that alternating links are nontrivial. Unlike most other proofs of this result, this proof uses only classic results in topology and combinatorial group theory. 1 Statement of Results A link is said to be t ..."
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Cited by 1 (0 self)
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We use a simple geometric argument and small cancellation properties of link groups to prove that alternating links are nontrivial. Unlike most other proofs of this result, this proof uses only classic results in topology and combinatorial group theory. 1 Statement of Results A link is said
NonTrivial Realizations of Virtual Link Diagrams
, 2005
"... A realization of a virtual link diagram is obtained by choosing over/under markings for each virtual crossing. Any realization can also be obtained from some representation of the virtual link. (A representation of a virtual link is a link diagram on an oriented 2dimensional surface.) We prove that ..."
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that if a minimal genus representation meets certain criteria then there is a minimal genus representation resulting in a knotted realization. Acknowledgement.The views expressed herein are those of the author and do not purport to reflect the position of the United States Military Academy,
UNITDISTANCE PRESERVING THEOREM IS LOGICALLY NONTRIVIAL
"... Abstract. If we express the statement of the unitdistance preserving theorem (that every mapping from R n to R n that preserves unit distance is linear) in terms of quantifiers and logical connectives, then we get a formula that is very close to formulas from elementary geometry. A. Tarski has prov ..."
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Abstract. If we express the statement of the unitdistance preserving theorem (that every mapping from R n to R n that preserves unit distance is linear) in terms of quantifiers and logical connectives, then we get a formula that is very close to formulas from elementary geometry. A. Tarski has
Nontrivial Interlayer Degree Correlations in Heterogeneously Growing Multiplex Networks
"... Abstract. The multiplex network growth literature has been confined to homogeneous growth hitherto, where the number of links that each new incoming node establishes is the same across layers. This paper focuses on heterogeneous growth. We first analyze the case of two preferentially growing layers ..."
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layers and find a closedform expression for the interlayer degree distribution, and demonstrate that nontrivial interlayer degree correlations emerge in the steady state. Then we focus on the case of uniform growth. Surprisingly, interlayer correlations arise in the random case, too. Also, we
Results 1  10
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1,198