In this paper we formally verify that the Uniform Candy Distribution Puzzle is self-stabilizing: Given a valid start configuration, eventually the Puzzle will evolve to a ‘stable’ situation in which it will remain. In terms of verification, the Uniform Candy Distribution Puzzle forms a scalable parametrized distributed system: The Puzzle comes in various sizes, for each size of the Puzzle there...

The present paper is a continuation of the work, carried out in [4] and [5] of investigating the relationship between a Gaussian process and its reproducing kernel Hilbert subspace. Our main result gives a characterization of the topological support of a Gaussian measure defined on a linear topological space of functions on an arbitrary set. As special cases we consider Gaussian processes on Ba...

Interpretation of Algebraic Polynomial Systems (Extended Abstract) Patrick Cousot 1 and Radhia Cousot 2 1 LIENS, ~cole Normale Sup4neure, 45 rue d'Ulm, 75230 Paris cedex 05, France [email protected] http://www.dmi.ens.fr/-cousot 2 LIX, CNRS & Ecole Polytechnique, 91140 Palaiseau cedex, France [email protected] http://lix.polytechnique.fr/-rcousot Abstract. We define a hierarchy of co...

We present a spectral theory of uniform hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of “symmetric hyperdeterminants” of hypermatrices, a.k.a. multidimensional arrays. Symmetric hyperdeterminants share many properties with determinants, but the context of multilinear algebra is substantiall...

We introduce a vector-valued version of uniform algebra, called the function space over algebra. The diameter two properties algebra on an infinite compact Hausdorff are investigated. Every nonempty relatively weakly open subset unit ball $$A(K, (X, \tau ))$$ dimensional has two, where $$\tau $$ is locally convex topology Banach X compatible to dual pair. Under assumption equipped with norm bei...

In this paper, the largest and the smallest observations are considered, at the time when a new record of either kind (upper or lower) occurs based on a sequence of independent random variables with identical continuous distributions. We prove that sequences of the residual or past entropy of the current records characterizes F in the family of continuous distributions. The exponential and the ...

In this paper, we study several analytic and graph-theoretic properties of asymptotic expanders. We show that expanders can be characterised in terms their uniform Roe algebra. Moreover, use to provide uncountably many new counterexamples the coarse Baum–Connes conjecture. Finally, vertex-transitive are actually particular, gives a C⁎-algebraic characterisation for graphs. achieve these results...

This paper investigates calculus rules for the limiting Fréchet-subdifferential of infimum value functions of locally Lipschitzian and non-Lipschitzian functions. It is not required that the infimum is attained.

Received (received date) Revised (revised date) Communicated by (Name) The article analyzes similarity of closed polygonal curves with respect to the Fréchet metric, which is stronger than the well-known Hausdorff metric and therefore is more appropriate in some applications. An algorithm is described that determines whether the Fréchet distance between two closed polygonal curves with m and n ...

Connections between Bayesian nonparametric inference and the classes of prob-ability measures with known marginals (Frechet classes) are investigated. Inparticular, a class of Dirichlet processes with parameters proportional to prob-ability measures in a Frechet class will be considered.Relations between two statistical characters are then studied, by presentinga...