Related papers: Restriction in Program Algebra
This paper explores in some detail a recent proposal (the Rieffel induction/refined algebraic quantization scheme) for the quantization of constrained gauge systems. Below, the focus is on systems with a single constraint and, in this…
We introduce the notion of radical parametrization of a surface, and we provide algorithms to compute such type of parametrizations for families of surfaces, like: Fermat surfaces, surfaces with a high multiplicity (at least the degree…
In this paper, we obtain results about the positive definiteness, the continuity and the level-boundedness of two optimal value functions of specific parametric optimization problems. Those two optimization problems are generalizations of…
We present an algorithm for approximating semidefinite programs with running time that is sublinear in the number of entries in the semidefinite instance. We also present lower bounds that show our algorithm to have a nearly optimal running…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
The development of machine learning in particular and artificial intelligent in general has been strongly conditioned by the lack of an appropriated framework to specify and integrate learning processes, data transformation processes and…
Classically domain theory is a rigourous mathematical structure to describe denotational semantics for programming languages and to study the computability of partial functions. Recently, the application of domain theory has also been…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some…
We study the distributional behavior of additive arithmetic functions evaluated at integers drawn from the harmonic distribution. Our main result shows that a broad family of such functions converges in law to conditioned Dickman-type…
We show that a subspace $S$ of the space of real analytical functions on a manifold that satisfies certain regularity properties is contained in the set of solutions of a linear elliptic differential equation. The regularity properties are…
We propound the thesis that there is a limitation to the number of possible structures which are axiomatically endowed with identities involving operations. In the case of algebras with a binary operation satisfying a formally reducible (to…
We study a variant of the Alt, Caffarelli, and Friedman free boundary problem with many phases and a slightly different volume term, which we originally designed to guess the localization of eigenfunctions of a Schr\"odinger operator in a…
We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary…
We initiate a formal study of reproducibility in optimization. We define a quantitative measure of reproducibility of optimization procedures in the face of noisy or error-prone operations such as inexact or stochastic gradient computations…
Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
Understanding generalization is crucial to confidently engineer and deploy machine learning models, especially when deployment implies a shift in the data domain. For such domain adaptation problems, we seek generalization bounds which are…
Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as…