Related papers: Functional norms, condition numbers and numerical …

A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficient estimators can be constructed,…

Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…

We introduce and study $\ell_p$-norm-multiway-cut: the input here is an undirected graph with non-negative edge weights along with $k$ terminals and the goal is to find a partition of the vertex set into $k$ parts each containing exactly…

The subject of this paper is regularity-preserving aggregation of regular norms on finite-dimensional linear spaces. Regular norms were introduced in [5] and are closely related to ``type 2'' spaces [9, Chapter 9] playing important role in…

The bilinear assignment problem (BAP) is a generalization of the well-known quadratic assignment problem (QAP). In this paper, we study the problem from the computational analysis point of view. Several classes of neigborhood structures are…

We characterise $L_p$-norms on the space of integrable step functions, defined on a probabilistic space, via H\"older's type inequality with an optimality condition.

We present a new algorithm for computing integral bases in algebraic function fields of one variable, or equivalently for constructing the normalization of a plane curve. Our basic strategy makes use of the concepts of localization and…

The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…

Within the past years, hardware vendors have started designing low precision special function units in response to the demand of the Machine Learning community and their demand for high compute power in low precision formats. Also the…

The Heisenberg algebra is first deformed with the set of parameters ${q, l, \lambda}$ to generate a new family of generalized coherent states. In this framework, the matrix elements of relevant operators are exactly computed. A proof on…

We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…

The matrix $p \rightarrow q$ norm is a fundamental quantity appearing in a variety of areas of mathematics. This quantity is known to be efficiently computable in only a few special cases. The best known algorithms for approximately…

Through the subsequent discussion we consider a certain particular sort of (topological) algebras, which may substitute the `` structure sheaf algebras'' in many--in point of fact, in all--the situations of a geometrical character that…

In this paper, we extend the methodology developed for Support Vector Machines (SVM) using $\ell_2$-norm ($\ell_2$-SVM) to the more general case of $\ell_p$-norms with $p\ge 1$ ($\ell_p$-SVM). The resulting primal and dual problems are…

In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…

This article is a review of theoretical advances in the research field of algebraic geometry and Bayesian statistics in the last two decades. Many statistical models and learning machines which contain hierarchical structures or latent…

The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…

The task of projecting onto $\ell_p$ norm balls is ubiquitous in statistics and machine learning, yet the availability of actionable algorithms for doing so is largely limited to the special cases of $p = \left\{ 0, 1,2, \infty \right\}$.…

Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…

In this paper we present Affine.m - program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. Algorithms are based upon the properties of weights and Weyl symmetry.…