Related papers: Generalization of the Ball-Collision Algorithm

We propose a generalized structure of Bell inequalities for arbitrary d-dimensional bipartite systems, which includes the existing two types of Bell inequalities introduced by Collins-Gisin-Linden-Massar-Popescu [Phys. Rev. Lett. 88, 040404…

In this paper we present a combination framework for polynomial complexity analysis of term rewrite systems. The framework covers both derivational and runtime complexity analysis. We present generalisations of powerful complexity…

This overview paper describes the particle methods developed for the implementation of the a class of Bayes filters formulated using the random finite set formalism. It is primarily intended for the readership already familiar with the…

In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically,…

This work discusses how to derive upper bounds for the expected generalisation error of supervised learning algorithms by means of the chaining technique. By developing a general theoretical framework, we establish a duality between…

Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…

In this paper we introduce the notion of generalized Lie algebroid and we develop a new formalism necessary to obtain a new solution for the Weistein's Problem. Many applications emphasize the importance and the utility of this new…

We generalize the quantum Arimoto-Blahut algorithm by Ramakrishnan et al. (IEEE Trans. IT, 67, 946 (2021)) to a function defined over a set of density matrices with linear constraints so that our algorithm can be applied to optimizations of…

We present a generalization of the well known Next-Closure algorithm working on semilattices. We prove the correctness of the algorithm and apply it on the computation of the intents of a formal context.

Three extensions and reinterpretations of nonclassical probabilities are reviewed. (i) We propose to generalize the probability axiom of quantum mechanics to self-adjoint positive operators of trace one. Furthermore, we discuss the…

We analyze the generalization ability of joint-training meta learning algorithms via the Gibbs algorithm. Our exact characterization of the expected meta generalization error for the meta Gibbs algorithm is based on symmetrized KL…

The paper considers the convergence of the complex block Jacobi diagonalization methods under the large set of the generalized serial pivot strategies. The global convergence of the block methods for Hermitian, normal and $J$-Hermitian…

The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].

We propose a generalization of Heisenbergs' matrix mechanics based on many-index objects. It is shown that there exists a solution describing a harmonic oscillator and many-index objects lead to a generalization of spin algebra.

In this article, a formulation of a point-collocation method in which the unknown function is approximated using global expansion in tensor product Bernstein polynomial basis is presented. Bernstein polynomials used in this study are…

We propose a novel approach in the study of transport phenomena in dense systems or systems with long range interactions where multiple particle interactions must be taken into consideration. Within Boltzmann's kinetic formalism, we study…

We propose a class of generalizations of the geometric entanglement for pure states by exploiting the matrix product state formalism. This generalization is completely divested from the notion of separability and can be freely tuned as a…

We present a general approach to deriving bounds on the generalization error of randomized learning algorithms. Our approach can be used to obtain bounds on the average generalization error as well as bounds on its tail probabilities, both…

The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas--e.g., deductive databases, theorem proving, static…

The principal innovative idea in this paper is to transform the original complex nonlinear modeling problem into a combination of linear problem and very simple nonlinear problems. The key step is the generalized linearization of nonlinear…