Related papers: Bilateral Inversion Principles
Motivated by the study of reversal behaviour of myxobacteria, in this article we are interested in a kinetic model for reversal dynamics, in which particles with directions close to be opposite undergo binary collision resulting in…
Inverse classification is the process of perturbing an instance in a meaningful way such that it is more likely to conform to a specific class. Historical methods that address such a problem are often framed to leverage only a single…
A key challenge in example-based program synthesis is the gigantic search space of programs. To address this challenge, various work proposed to use abstract interpretation to prune the search space. However, most of existing approaches…
The inversion of nabla Laplace transform, corresponding to a causal sequence, is considered. Two classical methods, i.e., residual calculation method and partial fraction method are developed to perform the inverse nabla Laplace transform.…
In this work, we introduce the notion of regularization of bifunctions in a similar way as the well- known convex, quasiconvex and lower semicontinuous regularizations due to Crouzeix. We show that the Equilibrium Problems associated to…
Focusing, introduced by Jean-Marc Andreoli in the context of classical linear logic, defines a normal form for sequent calculus derivations that cuts down on the number of possible derivations by eagerly applying invertible rules and…
Abstraction and realization are bilateral processes that are key in deriving intelligence and creativity. In many domains, the two processes are approached through rules: high-level principles that reveal invariances within similar yet…
A binary relation on graphs is recursively enumerable if and only if it can be computed by a formula in monadic second-order logic. The latter means that the formula defines a set of graphs, in the usual way, such that each "computation…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
The aim of this paper is to highlight a hitherto unknown computational aspect of Nonstandard Analysis pertaining to Reverse Mathematics (RM). In particular, we shall establish RM-equivalences between theorems from Nonstandard Analysis in a…
We study an alternative model of infinitary term rewriting. Instead of a metric on terms, a partial order on partial terms is employed to formalise convergence of reductions. We consider both a weak and a strong notion of convergence and…
Dual Horn clauses mirror key properties of Horn clauses. This paper explores the ``other side of the looking glass'' to reveal some expected and unexpected symmetries and their practical uses. We revisit Dual Horn clauses as enablers of a…
We generalize and analyse the method for computing lower bounds of the principal eigenvalue proposed in our previous paper (I. Sebestova, T. Vejchodsky, SIAM J. Numer. Anal. 2014). This method is suitable for symmetric elliptic eigenvalue…
The two squares theorem of Fermat is a gem in number theory, with a spectacular one-sentence "proof from the Book". Here is a formalisation of this proof, with an interpretation using windmill patterns. The theory behind involves…
This paper deals with retraction - intended as isomorphic embedding - in intersection types building left and right inverses as terms of a lambda calculus with a bottom constant. The main result is a necessary and sufficient condition two…
We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude…
Lazy evaluation is a powerful tool that enables better compositionality and potentially better performance in functional programming, but it is challenging to analyze its computation cost. Existing works either require manually annotating…
Existing tools for explaining complex models and systems are associational rather than causal and do not provide mechanistic understanding. We propose a new notion called counterfactual explainability for causal attribution that is…
We show that the quadratic measure need not be postulated, but follows from the compatibility of two structural features of physical processes: linear reversible evolution prior to the formation of persistent records, and multiplicative…
The arithmetic function of two variables is defined. Some properties of the function are given along with the formula that is an analog of the so-called Mobius' inversion formula. A heuristic statement is suggested.