Peter Hegarty | University of Surrey (original) (raw)

Papers by Peter Hegarty

The classical multi-agent rendezvous problem asks for a deterministic algorithm by which nnn poin... more The classical multi-agent rendezvous problem asks for a deterministic algorithm by which nnn points scattered in a plane can move about at constant speed and merge at a single point, assuming each point can use only the locations of the others it sees when making decisions and that the visibility graph as a whole is connected. In time complexity analyses of such algorithms, only the number of rounds of computation required are usually considered, not the amount of computation done per round. In this paper, we consider Omega(n2logn)\Omega(n^2 \log n)Omega(n2logn) points distributed independently and uniformly at random in a disc of radius nnn and, assuming each point can not only see but also, in principle, communicate with others within unit distance, seek a randomised merging algorithm which asymptotically almost surely (a.a.s.) runs in time O(n), in other words in time linear in the radius of the disc rather than in the number of points. Under a precise set of assumptions concerning the communication capabilities of neighboring points, we describe an algorithm which a.a.s. runs in time O(n) provided the number of points is o(n3)o(n^3)o(n3). Several questions are posed for future work.

We consider the Hegselmann-Krause bounded confidence dynamics for n equally spaced opinions on th... more We consider the Hegselmann-Krause bounded confidence dynamics for n equally spaced opinions on the real line, with gaps equal to the confidence bound r, which we take to be 1. We prove rigorous results on the evolution of this configuration, which confirm hypotheses previously made based on simulations for small values of n. Namely, for every n, the system evolves as follows: after every 5 time steps, a group of 3 agents become disconnected at either end and collapse to a cluster at the subsequent step. This continues until there are fewer than 6 agents left in the middle, and these finally collapse to a cluster, if n is not a multiple of 6. In particular, the final configuration consists of 2*[n/6] clusters of size 3, plus one cluster in the middle of size n (mod 6), if n is not a multiple of 6, and the number of time steps before freezing is 5n/6 + O(1). We also consider the dynamics for arbitrary, but constant, inter-agent spacings d \in [0, 1] and present three main findings. Firstly we prove that the evolution is periodic also at some other, but not all, values of d, and present numerical evidence that for all d something "close" to periodicity nevertheless holds. Secondly, we exhibit a value of d at which the behaviour is periodic and the time to freezing is n + O(1), hence slower than that for d = 1. Thirdly, we present numerical evidence that, as d --> 0, the time to freezing may be closer, in order of magnitude, to the diameter d(n-1) of the configuration rather than the number of agents n.

Sondow et al have studied Ramanujan primes (RPs) and observed numerically that, while half of all... more Sondow et al have studied Ramanujan primes (RPs) and observed numerically that, while half of all primes are RPs asymptotically, one obtains runs of consecutives RPs (resp. non-RPs) which are statistically significantly longer than one would expect if one was tossing an unbiased coin. In this discussion paper we attempt a heuristic explanation of this phenomenon. Our heuristic follows naturally from the Prime Number Theorem, but seems to be only partly satisfactory. It motivates why one should obtain long runs of both RPs and non-RPs, and also longer runs of non-RPs than of RPs. However, it also suggests that one should obtain longer runs of RPs than have so far been observed in the data, and this issue remains puzzling.

Eprint Arxiv 0712 4399, Dec 1, 2007

The inverse problem for partition irregular forms seems to be more complicated. The simplest exam... more The inverse problem for partition irregular forms seems to be more complicated. The simplest example of such a form is x_1 - x_2, and for this form we provide some partial results. Several remaining open problems are discussed.

Ars Combinatoria Waterloo Then Winnipeg, 2004

Integers, 2009

We prove that the strategy of this game resembles closely that of a variant of Wythoff Nim--a var... more We prove that the strategy of this game resembles closely that of a variant of Wythoff Nim--a variant with a blocking manoeuvre on p−1p-1p−1 diagonal positions. In fact, we show a slightly more general result in which we have relaxed the notion of what an imitation is.

We present an example of a regular opinion function which, as it evolves in accordance with the d... more We present an example of a regular opinion function which, as it evolves in accordance with the discrete-time Hegselmann-Krause bounded confidence dynamics, always retains opinions which are separated by more than two. This confirms a conjecture of Blondel, Hendrickx and Tsitsiklis.

AbstRAct. We propose a generalisation of the Cameron-Erdxos conjecture for sumfree sets to arbitr... more AbstRAct. We propose a generalisation of the Cameron-Erdxos conjecture for sumfree sets to arbitrary non-translation invariant linear equations over Z in three or more variables and, using well-known methods from graph theory, prove a weak form of the conjecture for a ...

The notion of "balance" is fundamental for sociologists who study social networks. In formal math... more The notion of "balance" is fundamental for sociologists who study social networks. In formal mathematical terms, it concerns the distribution of triad configurations in actual networks compared to random networks of the same edge density. On reading Charles Kadushin's recent book "Understanding Social Networks", we were struck by the amount of confusion in the presentation of this concept in the early sections of the book. This confusion seems to lie behind his flawed analysis of a classical empirical data set, namely the karate club graph of Zachary. Our goal here is twofold. Firstly, we present the notion of balance in terms which are logically consistent, but also consistent with the way sociologists use the term. The main message is that the notion can only be meaningfully applied to undirected graphs. Secondly, we correct the analysis of triads in the karate club graph. This results in the interesting observation that the graph is, in a precise sense, quite "unbalanced". We show that this lack of balance is characteristic of a wide class of starlike-graphs, and discuss possible sociological interpretations of this fact, which may be useful in many other situations.

J Homosexual, 2001

Abstract Previous studies which have measured beliefs about sexual orientation with either a sing... more Abstract Previous studies which have measured beliefs about sexual orientation with either a single item, or a one-dimensional scale are discussed. In the present study beliefs were observed to vary along two dimensions: the immutability of sexual orientation and the ...

We present a family of finite, non-abelian groups and propose that there are members of this fami... more We present a family of finite, non-abelian groups and propose that there are members of this family whose commuting graphs are connected and of arbitrarily large diameter. If true, this would disprove a conjecture of Iranmanesh and Jafarzadeh. While unable to prove our claim, we present a heuristic argument in favour of it. We also present the results of simulations which yielded explicit examples of groups whose commuting graphs have all possible diameters up to and including 10. Previously, no finite group whose commuting graph had diameter greater than 6 was known.

Integers the Electronic Journal of Combinatorial Number Theory, 2006

For k ≥ 3 and sufficiently large n depending on k, Sujith Vijay recently provided non-trivial low... more For k ≥ 3 and sufficiently large n depending on k, Sujith Vijay recently provided non-trivial lower and upper bounds for the size of the largest subset of {1, 2, . . . , n} such that no element divides k others. The gap between his lower and upper bounds is, however, substantial, and here we provide a better upper bound which significantly reduces this gap for large k.

IEEE Transactions on Automatic Control, 2015

Discrete & Computational Geometry, 2015

Eprint Arxiv 0712 4399, Dec 1, 2007

Ars Combinatoria Waterloo Then Winnipeg, 2004

Integers, 2009

J Homosexual, 2001

Integers the Electronic Journal of Combinatorial Number Theory, 2006

IEEE Transactions on Automatic Control, 2015

Discrete & Computational Geometry, 2015

Teachers College Record, 2011

It would be an understatement to describe Private Practices as a volume that is long overdue; the... more It would be an understatement to describe Private Practices as a volume that is long overdue; the lingering damage caused by the pathologizing of homosexuality in American psychiatry has hitherto lead to a lack of sustained, reasonable, critical attention to the life and work of gay psychiatrist Harry Stack Sullivan (1892Sullivan ( -1949. The Sullivan literature has also been characterized by supposition about the 'private' man behind the public image. In her first book, Naoko Wake has broken with this tradition, drawn on original evidence from case notes, conferences, and other documents, and pieced together an original and important account of the relationship between the more private and the more public thoughts of this difficult figure.

History and Philosophy of Psychology , 2010

Elizabeth Reis has written a detailed, scholarly, accessible short book about the different ways ... more Elizabeth Reis has written a detailed, scholarly, accessible short book about the different ways that intersex bodies and lives have been problematized in American history. Students will enjoy engaging with this book in classes on the history of science, gender studies, American culture, and sexuality studies. Scholars in these fields will enjoy a very detailed account of how so many strands of American culture meet in the legal, newspaper, medical and autobiographical accounts of intersex lives and bodies. Reis work is both an update and a compliment to Alice Dreger"s (2000) Hermaphrodites and the Medical Invention of Sex. Her champions are also the group of activists and scholars clustered around the Intersex Society of North America, including Dreger. These activists and scholars issued new challenges to harmful medical mistreatments of intersex people which had been orthodox since the 1950s due to the peculiarly hegemonic theories of the psychologist John Money. Reis" history ends with a discussion of 21 st century concensus on intersex care, which acknowledges the validity of many of the charges of harm brought by ISNA and other activists in the 1990s, and adopts a historically different position from the Money protocols on matters such as early surgical intervention, patient deception, and nomenclature. However, in spite of the high ethical and political stakes in this domain, the strength of this book is that it clearly shows that we continue to live in history and that we should expect no small measure of uncertainty a propos of intersex bodies and lives in the decades ahead.

History and Philosophy of Psychology, 2007

Archives of Sexual Behavior, 2007

Feminism & Psychology, 2002

Journal of The History of Sexuality, 2001

Journal of Sex and Marital Therapy, 2000

Journal of Lesbian Studies, 1999

What is the relationship between intelligence and sex? In recent decades, studies of the controve... more What is the relationship between intelligence and sex? In recent decades, studies of the controversial histories of both intelligence testing and of human sexuality in the United States have been increasingly common—and hotly debated. But rarely have the intersections of these histories been examined. In Gentlemen’s Disagreement, Peter Hegarty enters this historical debate by recalling the debate between Lewis Terman—the intellect who championed the testing of intelligence— and pioneering sex researcher Alfred Kinsey, and shows how intelligence and sexuality have interacted in American psychology.

Through a fluent discussion of intellectually gifted onanists, unhappily married men, queer geniuses, lonely frontiersmen, religious ascetics, and the two scholars themselves, Hegarty traces the origins of Terman’s complaints about Kinsey’s work to show how the intelligence testing movement was much more concerned with sexuality than we might remember. And, drawing on Foucault, Hegarty reconciles these legendary figures by showing how intelligence and sexuality in early American psychology and sexology were intertwined then and remain so to this day.