arXiv subjects

Daniel Cicala

Publications and source records attributed to Daniel Cicala.

7 recordsLinked to original sources

arXiv2025

A Mathematical Model of Opinion Dynamics with Application to Vaccine Denial

Public health outcomes can be heavily influenced by the landscape of public opinion; hence, it is important to understand how that landscape changes over time. For one, opinions on public health issues are responsive to official pronouncements, whether from the governmental or professional medical establishments. Additionally, in today's world of high speed communication, opinion can also be highly responsive to the broadcast opinions of "influencers" whose large numbers of followers assure them of a broad reach. To understand the opinion landscape in a general sense, we develop an ordinary differential equation model for opinion change that is based primarily on attraction to the opinions of prominent sources. The individual opinion change model is then used to develop a Fokker-Planck-type partial differential equation model for the overall opinion landscape. This model is shown to have a stable equilibrium solution, and the dependence of the equilibrium solution on key model parameters is illustrated with examples based on opinion regarding vaccination.

physics.soc-ph↗

arXiv2024

Incorporating changeable attitudes toward vaccination into an SIR infectious disease model

We develop a mechanistic model that classifies individuals both in terms of epidemiological status (SIR) and vaccination attitude (willing or unwilling), with the goal of discovering how disease spread is influenced by changing opinions about vaccination. Analysis of the model identifies existence and stability criteria for both disease-free and endemic disease equilibria. The analytical results, supported by numerical simulations, show that attitude changes induced by disease prevalence can destabilize endemic disease equilibria, resulting in limit cycles.

math.DS↗

arXiv2020

Rewriting Structured Cospans

We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is adhesive or a topos. These results guarantee that double pushout rewriting can be applied in this setting. We then define structured cospan grammars and construct their associated languages via a 2-categorical framework, capturing both network composition and rewrite dynamics. As an application, we show that for graphs, hypergraphs, Petri nets, and their typed variants, any grammar induces the same language as its corresponding discrete grammar. This equivalence enables an inductive characterization of rewriting, thereby generalizing classical results from graph transformation to a broader class of categorical models.

math.CT↗

arXiv2019

Rewriting Structured Cospans: A Syntax For Open Systems

The concept of a system has proliferated through natural and social sciences. While myriad theories of systems exist, there is no mathematical general theory of systems. In this thesis, we take a first step towards formulating such a theory. Our focus is on developing a syntax for compositional systems equipped with a rewriting theory. We pull from category theory and linguistics to accomplish this. The basic syntactical unit is a structured cospan and rewriting is introduced via the double pushout method. Two versions of rewriting are proposed: one that tracks intermediate steps and another disregards them. Benefits and drawbacks of both versions are discussed. We apply our results to the decomposition of closed systems, obtaining a structurally inductive viewpoint of rewriting such systems.

math.CT↗

arXiv2017

Spans of cospans in a topos

For a topos $\mathbf{T}$, there is a bicategory $\mathbf{MonicSp(Csp(T))}$ whose objects are those of $\mathbf{T}$, morphisms are cospans in $\mathbf{T}$, and 2-morphisms are isomorphism classes of monic spans of cospans in $\mathbf{T}$. Using a result of Shulman, we prove that $\mathbf{MonicSp(Csp(T))}$ is symmetric monoidal, and moreover, that it is compact closed in the sense of Stay. We provide an application which illustrates how to encode double pushout rewrite rules as $2$-morphisms inside a compact closed sub-bicategory of $\mathbf{MonicSp(Csp(Graph))}$.

math.CT↗

arXiv2017

Categorifying the ZX-calculus

We build a symmetric monoidal and compact closed bicategory by combining spans and cospans inside a topos. This can be used as a framework in which to study open networks and diagrammatic languages. We illustrate this framework with Coecke and Duncan's zx-calculus by constructing a bicategory with the natural numbers for 0-cells, the zx-calculus diagrams for 1-cells, and rewrite rules for 2-cells.

math.CT↗

arXiv2016

Spans of cospans

We discuss the notion of a span of cospans and define, for them, horizonal and vertical composition. These compositions satisfy the interchange law if working in a topos $\mathbf{C}$ and if the span legs are monic. A bicategory is then constructed from $\mathbf{C}$-objects, $\mathbf{C}$-cospans, and doubly monic spans of $\mathbf{C}$-cospans. The primary motivation for this construction is an application to graph rewriting.

math.CT↗