Dictionary matching in a stream

We consider the problem of dictionary matching in a stream. Given a set of strings, known as a dictionary, and a stream of characters arriving one at a time, the task is to report each time some string in our dictionary occurs in the stream. We present a randomised algorithm which takes O(log log(k + m)) time per arriving character and uses O(k log m) words of space, where k is the number of strings in the dictionary and m is the length of the longest string in the dictionary

Pattern Matching in Multiple Streams

We investigate the problem of deterministic pattern matching in multiple streams. In this model, one symbol arrives at a time and is associated with one of s streaming texts. The task at each time step is to report if there is a new match between a fixed pattern of length m and a newly updated stream. As is usual in the streaming context, the goal is to use as little space as possible while still reporting matches quickly. We give almost matching upper and lower space bounds for three distinct pattern matching problems. For exact matching we show that the problem can be solved in constant time per arriving symbol and O(m+s) words of space. For the k-mismatch and k-difference problems we give O(k) time solutions that require O(m+ks) words of space. In all three cases we also give space lower bounds which show our methods are optimal up to a single logarithmic factor. Finally we set out a number of open problems related to this new model for pattern matching.Comment: 13 pages, 1 figur

Free subgroups of one-relator relative presentations

Suppose that G is a nontrivial torsion-free group and w is a word over the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\}. It is proved that for n\ge2 the group \~G= always contains a nonabelian free subgroup. For n=1 the question about the existence of nonabelian free subgroups in \~G is answered completely in the unimodular case (i.e., when the exponent sum of x_1 in w is one). Some generalisations of these results are discussed.Comment: V3: A small correction in the last phrase of the proof of Theorem 1. 4 page

Baseline Shifts do not Predict Attentional Modulation of Target Processing During Feature-Based Visual Attention

Cues that direct selective attention to a spatial location have been observed to increase baseline neural activity in visual areas that represent a to-be-attended stimulus location. Analogous attention-related baseline shifts have also been observed in response to attention-directing cues for non-spatial stimulus features. It has been proposed that baseline shifts with preparatory attention may serve as the mechanism by which attention modulates the responses to subsequent visual targets that match the attended location or feature. Using functional MRI, we localized color- and motion-sensitive visual areas in individual subjects and investigated the relationship between cue-induced baseline shifts and the subsequent attentional modulation of task-relevant target stimuli. Although attention-directing cues often led to increased background neural activity in feature specific visual areas, these increases were not correlated with either behavior in the task or subsequent attentional modulation of the visual targets. These findings cast doubt on the hypothesis that attention-related shifts in baseline neural activity result in selective sensory processing of visual targets during feature-based selective attention

Online Pattern Matching for String Edit Distance with Moves

Edit distance with moves (EDM) is a string-to-string distance measure that includes substring moves in addition to ordinal editing operations to turn one string to the other. Although optimizing EDM is intractable, it has many applications especially in error detections. Edit sensitive parsing (ESP) is an efficient parsing algorithm that guarantees an upper bound of parsing discrepancies between different appearances of the same substrings in a string. ESP can be used for computing an approximate EDM as the L1 distance between characteristic vectors built by node labels in parsing trees. However, ESP is not applicable to a streaming text data where a whole text is unknown in advance. We present an online ESP (OESP) that enables an online pattern matching for EDM. OESP builds a parse tree for a streaming text and computes the L1 distance between characteristic vectors in an online manner. For the space-efficient computation of EDM, OESP directly encodes the parse tree into a succinct representation by leveraging the idea behind recent results of a dynamic succinct tree. We experimentally test OESP on the ability to compute EDM in an online manner on benchmark datasets, and we show OESP's efficiency.Comment: This paper has been accepted to the 21st edition of the International Symposium on String Processing and Information Retrieval (SPIRE2014

The Crystallisation of Glasses from the Ternary CaF2-CaAl2Si2O8-P2 O5 System

A study of glasses from the ternary system CaF2-CaAl2Si2O8-P2O5 has been carried out. It has been shown that glasses with low phosphorus contents and high fluorite contents crystallise to fluorite. Fluorine reduces the glass transition temperature and is also required for the formation of fluorapatite (FAP). In the absence of fluorine in the glass no apatite phase is formed. Bulk nucleation of FAP is favoured for glasses with Ca:P ratios close to the apatite stoichiometry of 1.67 and with low crosslink densities. Thermal gravimetric analysis showed significant weight losses attributable to the formation of volatile silicon tetrafluoride to occur on crystallisation of the aluminium containing phases, anorthite and mullite, which supports the view that silicon tetrafluoride formation is hindered by fluorine bonding to the aluminium atoms of the glass network. Anorthite crystallisation always occurred by a surface nucleation mechanism and ap peared to be favoured by the higher silicon to aluminium ratio in these glasses compared to previously studied glass compositions. © 2001 Kluwer Academic Publishers

Siting prisons, sighting communities: geographies of objection in a planning process

This paper reviews the planning process for a Scottish prison located near a former mining village. Analysing the letters of objection submitted by residents offers an opportunity to explore local views about prison and community and to relate these to the unique social and spatial history of the area. The planning process itself structured how residents were able to express themselves and defined what counted as a relevant objection. After deconstructing this process, the paper then restores and uses as a framework for analysis three geographies of objection stripped from local responses to the development proposal: the emotional, temporal, and spatial. Emotional expressions of objection added intensity and gave meaning to claims about the historical decline of the region and also conveyed a deep sense of the proposed building site as a lived space. Particular grounds of opposition—over fear of strangers, the fragility of a local orchid, and the pollution from mining—provide an opportunity to explore the complex nature of place meaning and community identity, ultimately leading to a conclusion that the meaning of place is always in flux. The paper argues that Simmel’s classic concept of the stranger, as the outsider who comes to stay, offers a useful analytic in understanding how the quality of proximal remoteness that prisons and other unwanted developments constitute participates in a constantly evolving sense of the local

Scale Invariance and the AdS/CFT Correspondence

Using the AdS/CFT correspondence, we show that the Anti-de Sitter (AdS) rotating (Kerr) black holes in five and seven dimensions provide us with examples of non-trivial field theories which are scale, but not conformally invariant. This is demonstrated by our computation of the actions and the stress-energy tensors of the four and six dimensional field theories residing on the boundary of these Kerr-AdS black holes spacetimes.Comment: 3 pages. LaTeX, IJMP style. Contribution to proceedings of DPF 2000, held at Ohio State