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We consider a class of nonlinear mappings FA;N in RN indexed by symmetric random matrices A 2 RNN with independent entries. Within spin glass theory, special cases of these mappings correspond to ite...
This paper proposes a formulation to provide necessary and sufficient conditions for robust stability of a family of matrices modeling linearized power system dynamics. A construction for transforming...
Gibbs/Metropolis algorithms on a convex polytope
Polytope numbers for a polytope are a sequence of nonnegative integers that are defined by the facial information of a polytope. Every polygon is triangulable and a higher dimensional analogue of this...
In 2010, M. Studen\'y, R. Hemmecke, and Linder explored a new algebraic description of graphical models, characteristic imsets. Compare with standard imsets, characteristic imsets have several advanta...
We study the posterior contraction behavior of the latent population structure that arises in admixture models as the amount of data increases. An admixture model --- alternatively known as a topic mo...
For closed 3-manifolds Ozsv\'ath and Szab\'o, Ni, and Hedden show that there exists a certain duality between an appropriate flavour of the Heegaard Floer polytope and the Thurston norm unit ball. For...
Abstract: We show that the rate of convergence on the approximation of volumes of a convex symmetric polytope P in R^n by its dual L_{p$-centroid bodies is independent of the geometry of P. In particu...
We use the method of steepest descents to study the root distribution of the Ehrhart polynomial of the d-dimensional cross-polytope, namely Ld, as d ! 1. We prove that the distribution function of the...
We compute all dynamical degrees of monomial maps. Our approach is based on the isomorphism between the polytope algebra of P. McMullen and the universal cohomology of complete toric varieties.
We discuss a symplectic counterpart of the theory of stacky fans. First, we define a stacky polytope and construct the symplectic toric Deligne–Mumford stack associated to it. Then we establish a rel...
We present a constructive proof, that there exists a decomposition of the 2-skeleton of the k-dimensional cross polytope k into closed surfaces of genus ¤ 1, each with a transitive automorphism gro...
We present a constructive proof, that there exists a decomposition of the 2-skeleton of the k-dimensional cross polytope k into closed surfaces of genus ¤ 1, each with a transitive automorphism gro...

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