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We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for…
A novel recurrence formula for moments with respect to M\"{u}ntz-Legendre polynomials is proposed and applied to construct a numerical method for solving generalized Gauss quadratures with power function weight for M\"{u}ntz systems. These…
Special matrix functions have recently been investigated for regions of convergence, integral representations and the systems of matrix differential equation that these functions satisfy. In this paper, we find the recursion formulas for…
Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs operating on integers. To this end, a variety of acceleration techniques has been proposed. However, all of them are monolithic:…
We extend the synthetic theories of discrete and Gaussian categorical probability by introducing a diagrammatic calculus for reasoning about hybrid probabilistic models in which continuous random variables, conditioned on discrete ones,…
The explicit formula for the elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure for the solution of systems of linear equations is applied to error analysis. Stability conditions in terms of relative…
We express quantum computations (with measurements) using the arrow calculus extended with monadic constructions. This framework expresses quantum programming using well-understood and familiar classical patterns for programming in the…
We consider a modal logic that can formalise statements about uncertainty and beliefs such as `I think that my wallet is in the drawer rather than elsewhere' or `I am confused whether my appointment is on Monday or Tuesday'. To do that, we…
We study sums of arithmetic functions, defined on Gaussian integers and taken over those pairs of integers whose coordinates give rise to a singular system.
A situation calculus is presented that provides a solution to the frame problem for hierarchical situations, that is, situations that have a modular structure in which parts of the situation behave in a relatively independent manner. This…
In this paper, we will explicitly calculate Gauss sums for the general linear groups and the special linear groups over $\Bbb Z_n$, where $\Bbb Z_n=\Bbb Z/n \Bbb Z$ and $n>0$ is an integer. For $r$ being a positive integer, the formulae of…
While almost all existing works which optimally solve just-in-time scheduling problems propose dedicated algorithmic approaches, we propose in this work mixed integer formulations. We consider a single machine scheduling problem that aims…
We report on a package of routines for the computer algebra system Maple which supports the explicit determination of the geometric quantities, field equations, equations of motion, and conserved quantities of General Relativity in the…
In this paper, we introduce a novel task for machine learning in healthcare, namely personalized modeling of the female hormonal cycle. The motivation for this work is to model the hormonal cycle and predict its phases in time, both for…
Periods are defined as integrals of semialgebraic functions defined over the rationals. Periods form a countable ring not much is known about. Examples are given by taking the antiderivative of a power series which is algebraic over the…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
The purpose of these notes is to provide the details of the Jacobian ring computations carried out in [1], based on the computer algebra system Magma [2].
We present a new formula for the gauge charge in the causal formalism for the QCD case.
Name-passing calculi are foundational models for mobile computing. Research into these models has produced a wealth of results ranging from relative expressiveness to programming pragmatics. The diversity of these results call for…
Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…