Related papers: Entropy-Bounded Computational Geometry Made Easier…
This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
We present a general framework for analyzing the complexity of subdivision-based algorithms whose tests are based on the sizes of regions and their distance to certain sets (often varieties) intrinsic to the problem under study. We call…
In a genetic algorithm, fluctuations of the entropy of a genome over time are interpreted as fluctuations of the information that the genome's organism is storing about its environment, being this reflected in more complex organisms. The…
If moments of singular measures are passed as inputs to the entropy maximization procedure, the optimization algorithm might not terminate. The framework developed in our previous paper demonstrated how input moments of measures, on a broad…
This work contains two single-letter upper bounds on the entropy rate of a discrete-valued stationary stochastic process, which only depend on second-order statistics, and are primarily suitable for models which consist of relatively large…
The goal of this paper is to explore the basic Approximate Bayesian Computation (ABC) algorithm via the lens of information theory. ABC is a widely used algorithm in cases where the likelihood of the data is hard to work with or…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
We consider the problem of performing predecessor searches in a bounded universe while achieving query times that depend on the distribution of queries. We obtain several data structures with various properties: in particular, we give data…
We consider the \emph{two-dimensional range maximum query (2D-RMQ)} problem: given an array $A$ of ordered values, to pre-process it so that we can find the position of the smallest element in the sub-matrix defined by a (user-specified)…
It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a…
A relation between the conformal anomaly and the logarithmic term in the entanglement entropy is known to exist for CFT's in even dimensions. In odd dimensions the local anomaly and the logarithmic term in the entropy are absent. As was…
We study the problem of computing the \textsc{Maxima} of a set of $n$ $d$-dimensional points. For dimensions 2 and 3, there are algorithms to solve the problem with order-oblivious instance-optimal running time. However, in higher…
We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelisable…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
An important problem in computational topology is to calculate the homology of a space from samples. In this work, we develop a statistical approach to this problem by calculating the expected rank of an induced map on homology from a…
Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfully capturing these computational…
This article demonstrates how an understanding of the geometry of a family of cost functions can be used to develop efficient numerical algorithms for real-time optimisation. Crucially, it is not the geometry of the individual functions…
In loop quantum gravity, the area element of embedded spatial surfaces is given by a well-defined operator. We further characterize the quantized geometry of such surfaces by proposing definitions for operators quantizing scalar curvature…
We present an overall picture of the advances in the description of black hole physics from the perspective of loop quantum gravity. After an introduction that discusses the main conceptual issues we present some details about the classical…