Generalised Pattern Matching Revisited

In the problem of $\texttt{Generalised Pattern Matching}\ (\texttt{GPM})$ [STOC'94, Muthukrishnan and Palem], we are given a text $T$ of length $n$ over an alphabet $\Sigma_T$, a pattern $P$ of length $m$ over an alphabet $\Sigma_P$, and a matching relationship $\subseteq \Sigma_T \times \Sigma_P$, and must return all substrings of $T$ that match $P$ (reporting) or the number of mismatches between each substring of $T$ of length $m$ and $P$ (counting). In this work, we improve over all previously known algorithms for this problem for various parameters describing the input instance: * $\mathcal{D}\,$ being the maximum number of characters that match a fixed character, * $\mathcal{S}\,$ being the number of pairs of matching characters, * $\mathcal{I}\,$ being the total number of disjoint intervals of characters that match the $m$ characters of the pattern $P$. At the heart of our new deterministic upper bounds for $\mathcal{D}\,$ and $\mathcal{S}\,$ lies a faster construction of superimposed codes, which solves an open problem posed in [FOCS'97, Indyk] and can be of independent interest. To conclude, we demonstrate first lower bounds for $\texttt{GPM}$. We start by showing that any deterministic or Monte Carlo algorithm for $\texttt{GPM}$ must use $\Omega(\mathcal{S})$ time, and then proceed to show higher lower bounds for combinatorial algorithms. These bounds show that our algorithms are almost optimal, unless a radically new approach is developed

On the Expressiveness of Intensional Communication

The expressiveness of communication primitives has been explored in a common framework based on the pi-calculus by considering four features: synchronism (asynchronous vs synchronous), arity (monadic vs polyadic data), communication medium (shared dataspaces vs channel-based), and pattern-matching (binding to a name vs testing name equality). Here pattern-matching is generalised to account for terms with internal structure such as in recent calculi like Spi calculi, Concurrent Pattern Calculus and Psi calculi. This paper explores intensionality upon terms, in particular communication primitives that can match upon both names and structures. By means of possibility/impossibility of encodings, this paper shows that intensionality alone can encode synchronism, arity, communication-medium, and pattern-matching, yet no combination of these without intensionality can encode any intensional language.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127

Matching bias in syllogistic reasoning: Evidence for a dual-process account from response times and confidence ratings

We examined matching bias in syllogistic reasoning by analysing response times, confidence ratings, and individual differences. Roberts’ (2005) “negations paradigm” was used to generate conflict between the surface features of problems and the logical status of conclusions. The experiment replicated matching bias effects in conclusion evaluation (Stupple & Waterhouse, 2009), revealing increased processing times for matching/logic “conflict problems”. Results paralleled chronometric evidence from the belief bias paradigm indicating that logic/belief conflict problems take longer to process than non-conflict problems (Stupple, Ball, Evans, & Kamal-Smith, 2011). Individuals’ response times for conflict problems also showed patterns of association with the degree of overall normative responding. Acceptance rates, response times, metacognitive confidence judgements, and individual differences all converged in supporting dual-process theory. This is noteworthy because dual-process predictions about heuristic/analytic conflict in syllogistic reasoning generalised from the belief bias paradigm to a situation where matching features of conclusions, rather than beliefs, were set in opposition to logic

The College Admissions problem with lower and common quotas

We study two generalised stable matching problems motivated by the current matching scheme used in the higher education sector in Hungary. The first problem is an extension of the College Admissions problem in which the colleges have lower quotas as well as the normal upper quotas. Here, we show that a stable matching may not exist and we prove that the problem of determining whether one does is NP-complete in general. The second problem is a different extension in which, as usual, individual colleges have upper quotas, but, in addition, certain bounded subsets of colleges have common quotas smaller than the sum of their individual quotas. Again, we show that a stable matching may not exist and the related decision problem is NP-complete. On the other hand, we prove that, when the bounded sets form a nested set system, a stable matching can be found by generalising, in non-trivial ways, both the applicant-oriented and college-oriented versions of the classical Gale–Shapley algorithm. Finally, we present an alternative view of this nested case using the concept of choice functions, and with the aid of a matroid model we establish some interesting structural results for this case

Learning labelled dependencies in machine translation evaluation

Recently novel MT evaluation metrics have been presented which go beyond pure string matching, and which correlate better than other existing metrics with human judgements. Other research in this area has presented machine learning methods which learn directly from human judgements. In this paper, we present a novel combination of dependency- and machine learning-based approaches to automatic MT evaluation, and demonstrate greater correlations with human judgement than the existing state-of-the-art methods. In addition, we examine the extent to which our novel method can be generalised across different tasks and domains

Determining Lines of Constant Physics in the Confinement Phase of the SU(2) Higgs Model

We present a method for finding lines of constant physics in the confinement phase of the SU(2) Higgs model on the lattice. The model is considered at finite values of the cut-off where it behaves like an effective field theory with three independent couplings. In particular, a renormalised quantity sensitive to a variation of the bare Higgs quartic self-coupling is constructed from generalised Binder cumulants. Numerical results for the non-perturbative matching of the bare parameters of the model between beta=2.2 and beta=2.4 are presented.Comment: 10 pages, 4 figures, small changes in the introductio

Higher-order port-graph rewriting

The biologically inspired framework of port-graphs has been successfully used to specify complex systems. It is the basis of the PORGY modelling tool. To facilitate the specification of proof normalisation procedures via graph rewriting, in this paper we add higher-order features to the original port-graph syntax, along with a generalised notion of graph morphism. We provide a matching algorithm which enables to implement higher-order port-graph rewriting in PORGY, thus one can visually study the dynamics of the systems modelled. We illustrate the expressive power of higher-order port-graphs with examples taken from proof-net reduction systems.Comment: In Proceedings LINEARITY 2012, arXiv:1211.348

A Double Sigma Model for Double Field Theory

We define a sigma model with doubled target space and calculate its background field equations. These coincide with generalised metric equation of motion of double field theory, thus the double field theory is the effective field theory for the sigma model.Comment: 26 pages, v1: 37 pages, v2: references added, v3: updated to match published version - background and detail of calculations substantially condensed, motivation expanded, refs added, results unchange