Longest Common Extensions in Sublinear Space

The longest common extension problem (LCE problem) is to construct a data structure for an input string $T$ of length $n$ that supports LCE$(i,j)$ queries. Such a query returns the length of the longest common prefix of the suffixes starting at positions $i$ and $j$ in $T$. This classic problem has a well-known solution that uses $O(n)$ space and $O(1)$ query time. In this paper we show that for any trade-off parameter $1 \leq \tau \leq n$, the problem can be solved in $O(\frac{n}{\tau})$ space and $O(\tau)$ query time. This significantly improves the previously best known time-space trade-offs, and almost matches the best known time-space product lower bound.Comment: An extended abstract of this paper has been accepted to CPM 201

Transition Property For Cube-Free Words

We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair $(u,v)$ of $d$-ary cube-free words, if $u$ can be infinitely extended to the right and $v$ can be infinitely extended to the left respecting the cube-freeness property, then there exists a "transition" word $w$ over the same alphabet such that $uwv$ is cube free. The crucial case is the case of the binary alphabet, analyzed in the central part of the paper. The obtained "transition property", together with the developed technique, allowed us to solve cube-free versions of three old open problems by Restivo and Salemi. Besides, it has some further implications for combinatorics on words; e.g., it implies the existence of infinite cube-free words of very big subword (factor) complexity.Comment: 14 pages, 5 figure

Mixing patterns and the spread of close-contact infectious diseases

Surprisingly little is known regarding the human mixing patterns relevant to the spread of close-contact infections, such as measles, influenza and meningococcal disease. This study aims to estimate the number of partnerships that individuals make, their stability and the degree to which mixing is assortative with respect to age. We defined four levels of putative at-risk events from casual (physical contact without conversation) to intimate (contact of a sexual nature), and asked university student volunteers to record details on those they contacted at these levels on three separate days. We found that intimate contacts are stable over short time periods whereas there was no evidence of repeat casual contacts with the same individuals. The contacts were increasingly assortative as intimacy increased. Such information will aid the development and parameterisation of models of close contact diseases, and may have direct use in outbreak investigations

Drawing Boundaries

In “On Drawing Lines on a Map” (1995), I suggested that the different ways we have of drawing lines on maps open up a new perspective on ontology, resting on a distinction between two sorts of boundaries: fiat and bona fide. “Fiat” means, roughly: human-demarcation-induced. “Bona fide” means, again roughly: a boundary constituted by some real physical discontinuity. I presented a general typology of boundaries based on this opposition and showed how it generates a corresponding typology of the different sorts of objects which boundaries determine or demarcate. In this paper, I describe how the theory of fiat boundaries has evolved since 1995, how it has been applied in areas such as property law and political geography, and how it is being used in contemporary work in formal and applied ontology, especially within the framework of Basic Formal Ontology

The Virtues of Thisness Presentism

Presentists believe that only present things exist. But opponents insist this view has unacceptable implications: if only present things exist, we can’t express singular propositions about the past, since the obvious propositional constituents don’t exist, nor can we account for temporal passage, or the openness of the future. According to such opponents, and in spite of the apparent ‘common sense’ status of the view, presentism should be rejected on the basis of these unacceptable implications. In this paper, I present and defend a version of presentism (‘Thisness Presentism’) that avoids the unacceptable implications. The basic strategy I employ is familiar—I postulate presently existing entities to serve as surrogates (or ‘proxies’) for non-present entities—but some of the details of my proposal are more novel, and their application to these problems is certainly novel. One overarching thesis of this paper is that Thisness Presentism is preferable to other versions of presentism since it solves important problems facing standard iterations of the view. And I assume that this is a good positive reason in favour of the underlying thisness ontology

A Qualified Kolmogorovian Account of Probabilistic Contextuality

We describe a mathematical language for determining all possible patterns of contextuality in the dependence of stochastic outputs of a system on its deterministic inputs. The central notion is that of all possible couplings for stochastically unrelated outputs indexed by mutually incompatible values of inputs. A system is characterized by a pattern of which outputs can be "directly influenced" by which inputs (a primitive relation, hypothetical or normative), and by certain constraints imposed on the outputs (such as Bell-type inequalities or their quantum analogues). The set of couplings compatible with these constraints represents a form of contextuality in the dependence of outputs on inputs with respect to the declared pattern of direct influences.Comment: Lecture Notes in Computer Science 8369, 201-212 (2014

Predicting residents' performance: A prospective study

BACKGROUND: Objective criteria for predicting residents' performance do not exist. The purpose of this study was to test the hypothesis that global assessment by an intern selection committee (ISC) would correlate with the future performance of residents. METHODS: A prospective study of 277 residents between 1992 and 1999. Global assessment at the time of interview was compared to subsequent clinical (assessed by chief residents) and cognitive performance (assessed by the American Board of Pediatrics in-service training examination). RESULTS: ISC ratings correlated significantly with clinical performance at 24 and 36 months of training (r = 0.58, P < .001; and r = 0.60, P < .001 respectively). ISC ratings also correlated significantly with in-service exam scores in the 1(st), 2(nd), and 3(rd) years of training (r = 0.35, P = .0016; r = 0.39, P = 0.0003; r = 0.50, P = 0.005 respectively). CONCLUSIONS: Global assessment by an ISC predicted residents' clinical and cognitive performances