Related papers: A Simpler Approach to Linear Programming
We present an adaptation, based on program extraction in elementary linear logic, of Krivine & Leivant's system FA_2. This system allows to write higher-order equations in order to specify the computational content of extracted programs.…
Causality is one of the most fundamental notions in physics. Generalized probabilistic theories (GPTs) and the process matrix framework incorporate it in different forms. However, a direct connection between these frameworks remains…
We study the linear filtering problem for systems driven by continuous Gaussian processes with memory described by two parameters. The driving processes have the virtue that they possess stationary increments and simple semimartingale…
Fourier-Motzkin elimination, a standard method for solving systems of linear inequalities, leads to an elementary, short, and self-contained proof of von Neumann's minimax theorem.
We give the mathematical theory of duality computer in the density matrix formalism. This result complements the mathematical theory of duality computer of Gudder in the pure state formalism.
This paper is concerned with a duality-based approach to derive the linear feedback particle filter (FPF). The FPF is a controlled interacting particle system where the control law is designed to provide an exact solution for the nonlinear…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
Linear programming has played a crucial role in shaping decision-making, resource allocation, and cost reduction in various domains. In this paper, we investigate the application of overparametrized neural networks and their implicit bias…
We study the framework of abductive logic programming extended with integrity constraints. For this framework, we introduce a new measure of the simplicity of an explanation based on its degree of \emph{arbitrariness}: the more arbitrary…
We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…
We argue that reducing nonlinear programming problems to a simple canonical form is an effective way to analyze them, specially when the problem is degenerate and the usual linear independence hypothesis does not hold. To illustrate this…
We consider a homogeneous system of linear equations of the form $A_\alpha^{\otimes N} {\bf x} = 0$ arising from the distinguishability of two quantum operations by $N$ uses in parallel, where the coefficient matrix $A_\alpha$ depends on a…
This paper introduces an efficient approach to solve quadratic and nonlinear programming problems subject to linear equality constraints via the Theory of Functional Connections. This is done without using the traditional Lagrange…
Property A is a form of weak amenability for groups and metric spaces introduced as an approach to the famous Novikov higher signature conjecture, one of the most important unsolved problems in topology. We show that property A can be…
We investigate differential systems occurring in the study of particular non-isolated singularities, the so-called linear free divisors. We obtain a duality theorem for these D-modules taking into account filtrations, and deduce…
One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are…
We propose a new quantifier elimination algorithm for the theory of linear real arithmetic. This algorithm uses as subroutine satisfiability modulo this theory, a problem for which there are several implementations available. The quantifier…
We compare the accuracy, precision and reliability of different methods for estimating key system parameters for two-level systems subject to Hamiltonian evolution and decoherence. It is demonstrated that the use of Bayesian modelling and…
We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetries can be seen as solutions of a hierarchy of linear…
Ahlswede and Katona (1977) posed the following isodiametric problem in Hamming spaces: For every $n$ and $1\le M\le2^{n}$, determine the minimum average Hamming distance of binary codes with length $n$ and size $M$. Fu, Wei, and Yeung…