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Chris Preston

Publications and source records attributed to Chris Preston.

12 recordsLinked to original sources
arXiv2023

Cybersecurity in Motion: A Survey of Challenges and Requirements for Future Test Facilities of CAVs

The way we travel is changing rapidly, and Cooperative Intelligent Transportation Systems (C-ITSs) are at the forefront of this evolution. However, the adoption of C-ITSs introduces new risks and challenges, making cybersecurity a top priority for ensuring safety and reliability. Building on this premise, this paper presents an envisaged Cybersecurity Centre of Excellence (CSCE) designed to bolster research, testing, and evaluation of the cybersecurity of C-ITSs. We explore the design, functionality, and challenges of CSCE's testing facilities, outlining the technological, security, and societal requirements. Through a thorough survey and analysis, we assess the effectiveness of these systems in detecting and mitigating potential threats, highlighting their flexibility to adapt to future C-ITSs. Finally, we identify current unresolved challenges in various C-ITS domains, with the aim of motivating further research into the cybersecurity of C-ITSs.

cs.CR↗
arXiv2018

Some Notes on Finite Sets

These notes aim to give a gentle account to one approach to the theory of finite sets without making use of the natural numbers. They were written to be used as the basis for a student seminar. There are no real prerequisites except for a certain familiarity with the kind of mathematics seen in the first couple of years of a university mathematics course. The definition of being finite employed in these notes is usually called Kuratowski-finiteness and it is essentially that employed by Whitehead and Russell in Principia Mathematica. This is a revised and extended version of a paper with the same title from November 2015

math.HO↗
arXiv2012

Coupled one-dimensional dynamical systems

This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of self-mappings of the unit interval. There is no real mathematics to be found here (in the sense of results stated and proved) and in fact there is an almost complete lack of precise statements. The only thing on offer is the definition of the mappings and a few nice pictures showing examples of their asymptotic limit sets. There is a JavaScript program available, accessible at www.math.uni-bielefeld.de/~preston/iterates.html, which can be used to `discover' more about these mappings. The program might prove to be helpful for anyone interested in doing this.

math.DS↗
arXiv2010

Iterates of mappings which are almost continuous and open

This note presents an approach to studying the iterates of a mapping whose restriction to the complement of a finite set is continuous and open. The main examples to which the approach can be applied are piecewise monotone mappings defined on an interval or a finite graph.

math.DS↗
arXiv2010

Computing with Equations

The intention of these notes is to give a mathematical account of how I believe students could be taught to think about functional programming languages and to explain how such languages work.

cs.PL↗
arXiv2010

A Note on a Theorem of Parry

A well-known result of Bill Parry shows that a topologically transitive continuous piecewise monotone mapping with positive topological entropy is conjugate to a uniformly piecewise linear mapping with slope determined by the entropy. In this note we generalise Parry's result somewhat to what we call the class of essentially transitive mappings. This generalisation is of some interest in as much as for mappings with one turning point the converse also holds, i.e., a uniformly piecewise linear mapping with one turning point and with slope greater than 1 is essentially transitive.

math.DS↗
arXiv2010

Existence of monoids compatible with a family of mappings

These notes present an approach to obtaining monoid operations which are compatible with a given family of mappings in the sense that the mappings become left translations in the monoid. This can be applied to various situations such as the addition on the natural numbers and the integers as well as the concatenation of lists.

math.HO↗
arXiv2010

Finite Sets and Counting

We start by presenting a theory of finite sets using the approach which is essentially that taken by Whitehead and Russell in Principia Mathematica}, and which does not involve the natural numbers (or any other infinite set). This theory is then applied to prove results about structures which, like the natural numbers, satisfy the principle of mathematical induction, but do not necessarily satisfy the remaining Peano axioms.

math.HO↗
arXiv2010

Refining quasi-probability kernels

We consider the problem of modifying a quasi-probability kernel in order to improve its properties without changing the set of measures whose conditional probabilities it specifies.

math.PR↗
arXiv2009

Specifying Data Objects with Initial Algebras

This study presents a systematic approach to specifying data objects with the help of initial algebras. The primary aim is to describe the set-up to be found in modern functional programming languages such as Haskell and ML, although it can also be applied to more general situations.

cs.LO↗