Related papers: Modular Construction of Fixed Point Combinators an…
In the context of discrete dynamical systems and their applications, fixed points often have a clear interpretation. This is indeed a central topic of gene regulatory mechanisms modeled by Boolean automata networks (BANs), where a…
A new model of quantum computing has recently been proposed which, in analogy with a classical lambda-calculus, exploits quantum processes which operate on other quantum processes. One such quantum meta-operator takes N unitary…
One perspective on quantum algorithms is that they are classical algorithms having access to a special kind of memory with exotic properties. This perspective suggests that, even in the case of quantum algorithms, the control flow notions…
Combinatorial evolution - the creation of new things through the combination of existing things - can be a powerful way to evolve rather than design technical objects such as electronic circuits. Intriguingly, this seems to be an ongoing…
In a constructive setting, no concrete formulation of ordinal numbers can simultaneously have all the properties one might be interested in; for example, being able to calculate limits of sequences is constructively incompatible with…
By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…
Let M be a finitely generated submodule of a free module over a multivariate polynomial ring with coefficients in a discrete coherent ring. We prove that its module MLT(M ) of leading terms is countably generated and provide an algorithm…
It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras-that is, the alge- braic models of the Intuitionistic Propositional Calculus-always exist, even when these algebras…
We discuss some results concerning fixed point equations in the setting of topological *-algebras of unbounded operators. In particular, an existence result is obtained for what we have called {\em weak $\tau$ strict contractions}, and some…
We introduce the notion of reflexivity for combinatory algebras. Reflexivity can be thought of as an equational counterpart of the Meyer-Scott axiom of combinatory models, which indeed allows us to characterise an equationally definable…
This paper proposes an algorithm called Forward Composition Propagation (FCP) to explain the predictions of feed-forward neural networks operating on structured classification problems. In the proposed FCP algorithm, each neuron is…
We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wavefunctions in a coupled-cluster framework. This new…
Boolean circuits abstract away from physical details to focus on the logical structure and computational behaviour of digital components. Although such circuits have been studied for many decades, compositionality has been widely ignored or…
In this paper we consider the long-term behavior of points in ${\mathbb R}$ under iterations of continuous functions. We show that, given any Cantor set $\Lambda^*$ embedded in ${\mathbb R}$, there exists a continuous function $F^*:{\mathbb…
Let R be a commutative Noetherian ring, I and J ideals of R and M a finitely generated R-module. Let F be a covariant R-linear functor from the category of finitely generated R-modules to itself. We first show that if F is coherent, then…
In the case of monotone independence, the transparent understanding of the mechanism to validate the central limit theorem (CLT) has been lacking, in sharp contrast to commutative, free and Boolean cases. We have succeeded in clarifying it…
Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract…
We use the method of monotone iterations to obtain fixed point and coupled fixed point results for mixed monotone operators in the setting of partially ordered sets, with no additional assumptions on the partial order and with no…
Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…
We obtain a differential equation for the enumeration of the path length of general increasing trees. By using differential operators and their combinatorial interpretation we give a bijective proof of a version of Fa\`a di Bruno formula,…