Related papers: Boolean Models and Simultaneous Inequalities
The algebraic derivation of the numerical limits of Bell inequalities in either three or four random variables is independent of the assumption of randomness.The limits of the inequalities follow as mathematical consequences of their…
Generalisations of the bent property of a boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic boolean functions are related to simple graphs and it is shown…
For certain weak versions of the Axiom of Choice (most notably, the Boolean Prime Ideal theorem), we obtain equivalent formulations in terms of partial orders, and filter-like objects within them intersecting certain dense sets or…
The goal in function property testing is to determine whether a black-box Boolean function has a certain property or is epsilon-far from having that property. The performance of the algorithm is judged by how many calls need to be made to…
This work continues the author's article in Rus. J. Nonlinear Dynamics (2010, v.6, No.4) and contains applications of the Boolean functions method to investigation of the admissible regions and the phase topology of three algebraically…
We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main features of these inequalities are that (a) they apply to a…
We analyze the Ensemble and Polynomial Chaos Kalman filters applied to nonlinear stationary Bayesian inverse problems. In a sequential data assimilation setting such stationary problems arise in each step of either filter. We give a new…
Even the fastest SMT solvers have performance problems with regular expressions from real programs. Because these performance issues often arise from the problem representation (e.g. non-deterministic finite automata get determinized and…
We survey the recent sequence of algorithms for evaluating Boolean formulas consisting of NAND gates.
We study a linear filtering problem where the signal and observation processes are described as solutions of linear stochastic differential equations driven by time-space Brownian sheets. We derive a stochastic integral equation for the…
The article describe the model, derivation, and implementation of variational Bayesian inference for linear and logistic regression, both with and without automatic relevance determination. It has the dual function of acting as a tutorial…
For equations with the neutral term strictly delayed we construct the fundamental solution, derive a variation-of-constants formula for inhomogeneous equations, and prove growth estimates. Only unavoidable measure and integration theory, up…
We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…
Symmetries have been exploited successfully within the realms of SAT and QBF to improve solver performance in practical applications and to devise more powerful proof systems. As a first step towards extending these advancements to the…
Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as…
In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.
In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.
This paper presents a method to detect and recognize symmetries in Boolean functions. The idea is to use information theoretic measures of Boolean functions to detect sub-space of possible symmetric variables. Coupled with the new…
Partial ordinary Bell polynomials are used to formulate and prove a version of the Fa\`{a} di Bruno's formula which is convenient for handling nonlinear terms in the differential transformation. Applicability of the result is shown in two…
Bell's theorem admits several interpretations or 'solutions', the standard interpretation being 'indeterminism', a next one 'nonlocality'. In this article two further solutions are investigated, termed here 'superdeterminism' and…