Related papers: Entropy-Bounded Computational Geometry Made Easier…
The region of entropic vectors is a convex cone that has been shown to be at the core of many fundamental limits for problems in multiterminal data compression, network coding, and multimedia transmission. This cone has been shown to be…
In this paper we present efficient algorithmic solutions for several constrained resource allocation, management and discovery problems. We consider new types of resource allocation models and constraints, and we present new geometric…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
We propose entanglement entropy as a probe of the architecture of spacetime in quantum gravity. We argue that the leading contribution to this entropy satisfies an area law for any sufficiently large region in a smooth spacetime, which, in…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in…
We study the entropy of the black hole with torsion using the covariant form of the partition function. The regularization of infinities appearing in the semiclassical calculation is shown to be consistent with the grand canonical boundary…
Algorithmic entropy can be seen as a special case of entropy as studied in statistical mechanics. This viewpoint allows us to apply many techniques developed for use in thermodynamics to the subject of algorithmic information theory. In…
The quasi-local notion of an isolated horizon is employed to study the entropy of black holes without any particular symmetry in loop quantum gravity. The idea of characterizing the shape of a horizon by a sequence of local areas is…
Entropy production is often interpreted as a proxy for microscopic disorder or environmental roughness in stochastic systems. We test this interpretation using controlled simulations of overdamped stochastic dynamics on curved surfaces in…
The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of…
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…
We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
How much can randomness help computation? Motivated by this general question and by volume computation, one of the few instances where randomness provably helps, we analyze a notion of dispersion and connect it to asymptotic convex…
We perform numerical studies including Monte Carlo simulations of high rotational symmetry random tilings. For computational convenience, our tilings obey fixed boundary conditions in regular polygons. Such tilings are put in correspondence…
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…
The time evolution of complex systems usually can be described through stochastic processes. These processes are measured at finite resolution, what necessarily reduces them to finite sequences of real numbers. In order to relate these data…
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
Trigonometric and trigonometric-algebraic entropies are introduced. Regularity increases the entropy and the maximal entropy is shown to result when a regular $n$-gon is inscribed in a circle. A regular $n$-gon circumscribing a circle gives…