Related papers: Boolean Models and Simultaneous Inequalities
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…
In this article, we extensively develop Carleman estimates for the wave equation and give some applications. We focus on the case of an observation of the flux on a part of the boundary satisfying the Gamma conditions of Lions. We will then…
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…
Floquet theory is a powerful tool in the analysis of many physical phenomena, and extended to spatial coordinates provides the basis for Bloch's theorem. However, in its original formulation it is limited to linear systems with periodic…
Boolean networks (BNs) are widely used to model the qualitative dynamics of biological systems. Besides the logical rules determining the evolution of each component with respect to the state of its regulators, the scheduling of component…
Machine learning techniques are used to predict theoretical constraints such as unitarity and boundedness from below in extensions of the Standard Model. This approach has proven effective for models incorporating additional SU(2) scalar…
For the quantum stochastic processes generated by the Boolean Commutation Relations, we prove the following version of De Finetti Theorem: each of such Boolean process is exchangeable if and only if it is independent and identically…
We introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assumption is used in our analysis. The operator defining the…
In Bounded Model Checking both the system model and the checked property are translated into a Boolean formula to be analyzed by a SAT-solver. We introduce a new encoding technique which is particularly optimized for managing quantitative…
In this paper, an extension of the generalized free matrix based inequality is introduced in a unified form suitable for the estimation of integrals and sums of quadratic functions. The equivalences of several known variants are shown,…
Boolean automata networks (aka Boolean networks) are space-time discrete dynamical systems, studied as a model of computation and as a representative model of natural phenomena. A collection of simple entities (the automata) update their…
Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
The author has recently introduced an abstract algebraic framework of analogical proportions within the general setting of universal algebra. This paper studies analogical proportions in the boolean domain consisting of two elements 0 and 1…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
We use the method of similar operators to study a mixed problem for a differential equation with an involution and an operator-valued potential function. The differential operator defined by the equation is transformed into a similar…
We consider the Stokes phenomenon for the solutions of some partial differential equations with variable coefficients in two complex variables, where initial data are holomorphic. We use the theory of (moment) summability and the theory of…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
A univariate polynomial equation is presented. It provides models of the thermal lattice Boltzmann equation. The models can be accurate up to any required level and can be applied to regular lattices, which allow efficient and accurate…
For all Einstein-Podolsky-Rosen-type experiments on deterministic systems the Bell inequality holds, unless non-local interactions exist between certain parts of the setup. Here we show that in nonlinear systems the Bell inequality can be…