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310
An explicit counterexample to the LagariasWang finiteness conjecture
 Adv. Math
"... Abstract. The joint spectral radius of a finite set of real d × d matrices is defined to be the maximum possible exponential rate of growth of long products of matrices drawn from that set. A set of matrices is said to have the finiteness property if there exists a periodic product which achieves th ..."
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Cited by 20 (7 self)
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of pairs of 2 × 2 matrices which contains a counterexample. Similar results were subsequently given by V. D. Blondel, J. Theys and A. A. Vladimirov and by V. S. Kozyakin, but no explicit counterexample to the finiteness conjecture has so far been given. The purpose of this paper is to resolve this issue
AN EXPLICIT COUNTEREXAMPLE TO THE EQUIVARIANT K =2 CONJECTURE
"... Abstract. We construct an explicit example of a geometrically finite Kleinian group G with invariant component Ω in the Riemann sphere Ĉ such that any quasiconformal map from Ω to the boundary of the convex hull of Ĉ − Ωin H 3 which extends to the identity map on their common boundary in Ĉ, and whic ..."
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Abstract. We construct an explicit example of a geometrically finite Kleinian group G with invariant component Ω in the Riemann sphere Ĉ such that any quasiconformal map from Ω to the boundary of the convex hull of Ĉ − Ωin H 3 which extends to the identity map on their common boundary in Ĉ
Convergence Properties of the NelderMead Simplex Method in Low Dimensions
 SIAM Journal of Optimization
, 1998
"... Abstract. The Nelder–Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder–Mead algorithm. This paper pr ..."
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Cited by 598 (3 self)
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Abstract. The Nelder–Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder–Mead algorithm. This paper
1 Counterexamples
"... to a proposed Stam inequality on finite groups Venkat Anantharam, Fellow, IEEE, Abstract — Gibilisco and Isola have recently proposed a definition of Fisher information for random variables taking values in a finite group that is analogous to the definition for real valued random variables with a de ..."
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explicit counterexamples. Finite group, Fisher information, Groupvalued random variables, Stam inequality.
Counterexamples to the correlated stability conjecture
"... We demonstrate explicit counterexamples to the Correlated Stability Conjecture (CSC), which claims that the horizon of a black brane is unstable precisely if that horizon has a thermodynamic instability, meaning that its matrix of susceptibilities has a negative eigenvalue. These examples involve p ..."
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We demonstrate explicit counterexamples to the Correlated Stability Conjecture (CSC), which claims that the horizon of a black brane is unstable precisely if that horizon has a thermodynamic instability, meaning that its matrix of susceptibilities has a negative eigenvalue. These examples involve
Counterexamples to the correlated stability conjecture
"... We demonstrate explicit counterexamples to the Correlated Stability Conjecture (CSC), which claims that the horizon of a black brane is unstable precisely if that horizon has a thermodynamic instability, meaning that its matrix of susceptibilities has a negative eigenvalue. These examples involve p ..."
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We demonstrate explicit counterexamples to the Correlated Stability Conjecture (CSC), which claims that the horizon of a black brane is unstable precisely if that horizon has a thermodynamic instability, meaning that its matrix of susceptibilities has a negative eigenvalue. These examples involve
Counterexamples for timed probabilistic reachability
 FORMATS. VOLUME 3829 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2005
"... The inability to provide counterexamples for the violation of timed probabilistic reachability properties constrains the practical use of CSL model checking for continuous time Markov chains (CTMCs). Counterexamples are essential tools in determining the causes of property violations and are requir ..."
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Cited by 21 (10 self)
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The inability to provide counterexamples for the violation of timed probabilistic reachability properties constrains the practical use of CSL model checking for continuous time Markov chains (CTMCs). Counterexamples are essential tools in determining the causes of property violations
Directed Explicit StateSpace Search in the Generation of Counterexamples for Stochastic Model Checking
, 2009
"... Current stochastic model checkers do not make counterexamples for property violations readily available. In this paper we apply directed explicit state space search to discrete and continuoustime Markov chains in order to compute counterexamples for the violation of PCTL or CSL properties. Directe ..."
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Cited by 24 (8 self)
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Current stochastic model checkers do not make counterexamples for property violations readily available. In this paper we apply directed explicit state space search to discrete and continuoustime Markov chains in order to compute counterexamples for the violation of PCTL or CSL properties
Counterexamples to a Proposed Stam Inequality on Finite Groups
"... Abstract—Gibilisco and Isola have recently proposed a definition of Fisher information for random variables taking values in a finite group that is analogous to the definition for real valued random variables with a density. Based on this Fisher information concept, they claim to prove a Stam inequa ..."
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inequality for finitegroup valued random variables that is analogous to the one in the case of real values. In this note we show these results, unfortunately, do not hold for nonabelian groups in general, by constructing explicit counterexamples. Index Terms—Finite group, Fisher information, group
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