Related papers: Epsilon-approximations and epsilon-nets
Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…
We focus on the analysis of planar shapes and solid objects having thin features and propose a new mathematical model to characterize them. Based on our model, that we call an epsilon-shape, we show how thin parts can be effectively and…
We give a general framework for approximations to combinatorial assemblies, especially suitable to the situation where the number $k$ of components is specified, in addition to the overall size $n$. This involves a Poisson process, which,…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…
Random network models, constrained to reproduce specific statistical features, are often used to represent and analyze network data and their mathematical descriptions. Chief among them, the configuration model constrains random networks by…
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…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per…
Network control refers to a very large and diverse set of problems including controllability of linear time-invariant dynamical systems, where the objective is to select an appropriate input to steer the network to a desired state. There…
Proximal nested sampling was introduced recently to open up Bayesian model selection for high-dimensional problems such as computational imaging. The framework is suitable for models with a log-convex likelihood, which are ubiquitous in the…
The distributions of the random distances associated with hexagons, rhombuses and triangles have been derived and verified in the existing work. All of these geometric shapes are related to each other and have various applications in…
We consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with…
The average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we…
The coarsest approximation of the structure of a complex network, such as the Internet, is a simple undirected unweighted graph. This approximation, however, loses too much detail. In reality, objects represented by vertices and edges in…
There has been an ever-increasing interest in multidisciplinary research on representing and reasoning with imperfect data. Possibilistic networks present one of the powerful frameworks of interest for representing uncertain and imprecise…
Recently, a framework for the approximation of the entire set of $\epsilon$-efficient solutions (denote by $E_\epsilon$) of a multi-objective optimization problem with stochastic search algorithms has been proposed. It was proven that such…
We study the approximation properties of convolutional architectures applied to time series modelling, which can be formulated mathematically as a functional approximation problem. In the recurrent setting, recent results reveal an…
Measuring the similarity between patches in images is a fundamental building block in various tasks. Naturally, the patch-size has a major impact on the matching quality, and on the consequent application performance. We try to use large…
Precision predictions combined with precise measurements are a major tool in sharpening our understanding of the fundamental laws underlying microscopic as well as macroscopic systems. Here, I present a few remarkable examples covering the…
We formulate conditions for convergence of Laws of Large Numbers and show its links with of the parts of mathematical analysis such as summation theory, convergence of orthogonal series. We present also applications of the Law of Large…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…