Related papers: Symbolic dynamics and semigroup theory
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval…
We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing and quantum linguistic with the…
Group polarization, the phenomenon where individuals become more extreme after interacting, has been gaining attention, especially with the rise of social media shaping people's opinions. Recent interest has emerged in formal reasoning…
Language emergence and evolution has recently gained growing attention through multi-agent models and mathematical frameworks to study their behavior. Here we investigate further the Naming Game, a model able to account for the emergence of…
Some aspects of the physical nature of language are discussed. In particular, physical models of language must exist that are efficiently implementable. The existence requirement is essential because without physical models no communication…
This chapter aims to provide a clear and understandable picture of constructive semigroups with apartness in Bishop's style of constructive mathematics, BISH. Our theory is partly inspired by the classical case, but it is distinguished from…
This presentation explains why models with a dynamical symmetry often work extraordinarily well even in the presence of large symmetry breaking interactions. A model may be a caricature of a more realistic system with a "quasi-dynamical"…
We associate to each discrete partial dynamical system a universal C*-algebra generated by partial isometries satisfying relations given by a Boolean algebra connected to the discrete partial dynamical system in question. We show that for…
The modelling, specification and study of the semantics of concurrent reactive systems have been interesting research topics for many years now. The aim of this thesis is to exploit the strengths of the (co)algebraic framework in modelling…
We develop a semigroup-theoretic analogue of liaison for relative ideals of a numerical semigroup. Two parallel linkage notions are proposed: a theory based on translates of the semigroup and a theory based on translates of the canonical…
This work proposes a first approach towards a neo-Gibbsian thermodynamic theory for social systems, grounded in quantifiable economic and cultural parameters, while deliberately avoiding direct analogies with classical thermodynamic…
The most developed aspect of the theory of finite semigroups is their classification in pseudovarieties. The main motivation for investigating such entities comes from their connection with the classification of regular languages via…
The symbolic dynamics technique is well-known for low-dimensional dynamical systems and chaotic maps, and lies at the roots of the thermodynamic formalism of dynamical systems. Here we show that this technique can also be successfully…
Quasistationarity is ubiquitous in complex dynamical systems. In brain dynamics there is ample evidence that event-related potentials reflect such quasistationary states. In order to detect them from time series, several segmentation…
We define a semidirect product groupoid of a system of partially defined local homeomorphisms $T=(T_{1},..., T_{r})$. We prove that this construction gives rise to amenable groupoids. The associated algebra is a Cuntz-like algebra. We use…
In this work, a symbolic dynamical formulation based upon discrete iterative mappings derived from the Collatz conjecture is introduced. It is demonstrated that this formulation naturally induces a ternary alphabet useful for characterizing…
Homophily and social influence are the fundamental mechanisms that drive the evolution of attitudes, beliefs and behaviour within social groups. Homophily relates the similarity between pairs of individuals' attitudinal states to their…
The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as directed graphs and regarded up to isomorphism), the sum of…
Deep learning is bringing remarkable contributions to the field of argumentation mining, but the existing approaches still need to fill the gap toward performing advanced reasoning tasks. In this position paper, we posit that…
We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…