Related papers: Formal Relationships Between Geometrical and Class…
A model for the Mandelbrot set is due to Thurston and is stated in the language of geodesic laminations. The conjecture that the Mandelbrot set is actually homeomorphic to this model is equivalent to the celebrated MLC conjecture stating…
The logical parallelism of propositional connectives and type constructors extends beyond the static realm of predicates, to the dynamic realm of processes. Understanding the logical parallelism of process propositions and dynamic types was…
We define a variety of notions of cubical sets, based on sites organized using substructural algebraic theories presenting PRO(P)s or Lawvere theories. We prove that all our sites are test categories in the sense of Grothendieck, meaning…
The well-known process algebras, such as CCS, ACP and $\pi$-calculus, capture the interleaving concurrency based on bisimilarity semantics. We did some work on truly concurrent process algebras, such as CTC, APTC and $\pi_{tc}$, capture the…
We start from two closure operators defined on the elements of a special kind of partially ordered sets, called causal nets. Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of…
Remarkable parallelism between the theory of integrable systems of first-order quasilinear PDE and some old results in projective and affine differential geometry of conjugate nets, Laplace equations, their Bianchi-Baecklund transformations…
Aspects of compatibility of topologies of parallel computing systems and tasks are investigated. The introduction of appropriate indexes based on the original topological model of parallel computations and on the nontraditional description…
Concurrent computations resemble conversations. In a conversation, participants direct utterances at others and, as the conversation evolves, exploit the known common context to advance the conversation. Similarly, collaborating software…
The recently introduced model of representations has been defined and motivated somewhat ex-nihilo. In this document, I will show that representations are related to a more ''classical'' model through a 2-adjunction. The target model is…
Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every areas of computer science. Their development was also inextricably…
Causality serves as an abstract notion of time for concurrent systems. A computation is causal, or simply valid, if each observation of a computation event is preceded by the observation of its causes. The present work establishes that this…
Topological learning is a wide research area aiming at uncovering the mutual spatial relationships between the elements of a set. Some of the most common and oldest approaches involve the use of unsupervised competitive neural networks.…
Conflict sets are loci of intersecting wavefronts emanating from $l$ different surfaces. We show that generically conflict sets are Legendrian: locally they admit the structure of wavefronts. Simple stable singularities for this problem in…
Common approaches to concurrent programming begin with languages whose semantics are naturally sequential and add new constructs that provide limited access to concurrency, as exemplified by futures. This approach has been quite successful,…
Recently machine learning techniques have become popular for analysing physical systems and solving problems occurring in quantum computing. In this paper we focus on using such techniques for finding the sequence of physical operations…
We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…
Concurrent pattern calculus (CPC) drives interaction between processes by comparing data structures, just as sequential pattern calculus drives computation. By generalising from pattern matching to pattern unification, interaction becomes…
Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and…
We consider approaches for causal semantics of Petri nets, explicitly representing dependencies between transition occurrences. For one-safe nets or condition/event-systems, the notion of process as defined by Carl Adam Petri provides a…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…