Deterministic Sparse Pattern Matching via the Baur-Strassen Theorem

How fast can you test whether a constellation of stars appears in the night sky? This question can be modeled as the computational problem of testing whether a set of points $P$ can be moved into (or close to) another set $Q$ under some prescribed group of transformations. Consider, as a simple representative, the following problem: Given two sets of at most $n$ integers $P,Q\subseteq[N]$, determine whether there is some shift $s$ such that $P$ shifted by $s$ is a subset of $Q$, i.e., $P+s=\{p+s:p\in P\}\subseteq Q$. This problem, to which we refer as the Constellation problem, can be solved in near-linear time $O(n\log n)$ by a Monte Carlo randomized algorithm [Cardoze, Schulman; FOCS'98] and time $O(n\log^2 N)$ by a Las Vegas randomized algorithm [Cole, Hariharan; STOC'02]. Moreover, there is a deterministic algorithm running in time $n\cdot2^{O(\sqrt{\log n\log\log N})}$ [Chan, Lewenstein; STOC'15]. An interesting question left open by these previous works is whether Constellation is in deterministic near-linear time (i.e., with only polylogarithmic overhead). We answer this question positively by giving an $n\cdot(\log N)^{O(1)}$-time deterministic algorithm for the Constellation problem. Our algorithm extends to various more complex Point Pattern Matching problems in higher dimensions, under translations and rigid motions, and possibly with mismatches, and also to a near-linear-time derandomization of the Sparse Wildcard Matching problem on strings. We find it particularly interesting how we obtain our deterministic algorithm. All previous algorithms are based on the same baseline idea, using additive hashing and the Fast Fourier Transform. In contrast, our algorithms are based on new ideas, involving a surprising blend of combinatorial and algebraic techniques. At the heart lies an innovative application of the Baur-Strassen theorem from algebraic complexity theory.Comment: Abstract shortened to fit arxiv requirement

Sight, sound, the chicken and the egg: Audio-visual co-dependency in music

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Amongst the modern day abundance of audio-visual media, where sounds represent everything from the swooping of virtual cameras through 3D spaces to the pressing of buttons and receiving of emails, and conversely where VJs routinely accompany live musical performance with an increasingly sophisticated language of abstract computer animation, the notion of music as a necessarily exclusively aural medium seems somewhat out of place. Psychological theories relating to the cognition of sound, in particular physical schema, accounting for the ubiquity of vertical plane pitch metaphors in most musical cultures, provide evidence of a deep-rooted spatially informed understanding of sound thus providing a common ground for both sound and vision in music. Furthermore, Western Classical composition is rife with examples of visually conceived forms from Bach’s Crab Canon (1747) to Xenakis’ architecturally inspired Metastasis (1954). However, in practice the gap between the listener’s auditory experience and the composer’s visual concept is often insurmountable. Rising to Schaeffer’s call for “Primacy to the ear!” (Schaeffer, 1967, pp. 28-30), acousmatic composers have sought to derive music exclusively from experientially verifiable criteria. However, in its pervasiveness of other musical genres, no doubt aided by technologically and commercially driven domination of the pre-recorded over the live listening experience in the latter half of the twentieth century, such an approach has lead to the neglect of visual aspects in the live performance of much art-music. This research aims to begin to redress this balance through the composition of, largely computer realised, audio-visual works whose conception arises not from a superimposition of one medium upon another, but through the very relations between the media themselves. Utilising modern computers’ ability to synchronise physical and virtual visual events with synthesised sound in real time not only affords composers an invaluable tool for enhancing listener’s perception of formal structures but also implies causal relationships between the sonic and the visual which can provide a base of intuitive understanding on which more complex formal ideas can be built.Sponsored by the Brunel University Isambard Scholarship

Computational Group Theory

This was the seventh workshop on Computational Group Theory. It showed that Computational Group Theory has significantly expanded its range of activities. For example, symbolic computations with groups and their representations and computations with infinite groups play a major role nowadays. The talks also presented connections and applications to cryptography, number theory and the algorithmic theory of algebras

Identification and monitoring of violent interactions in video

This project shall help to bring a tool to fight against bullying in schools. It is also possible to use it in different scenes where a camera is recording a common area shared by people, such as companies, banks, prisons, or hospitals. To achieve that, the issue is approached from two main modules. The first one, a comparative study of approaches to detect violence in video, using image and video analyser Neural Networks (NN)s: a custom image analyser NN based on LeNet5, AlexNet, custom stacked long short-term memory (LSTM) and convolutional LSTM based NNs. The trainings are done with two datasets that have been subject to modifications to correct possible misinterpretations during the learning and pretraining is applied. The LeNet5 based NN is unsuccessful and tested with an independent dataset AlexNet is inaccurate. The best results are obtained with a stacked LSTM NN and a convolutional LSTM with dropout and a LSTM layer. Both NNs achieve over 90 % of accuracy with training and validation datasets, meanwhile the stacked LSTM and the convolutional NN achieve, respectively, 75 % and 100 % of accuracy with a small independent test dataset created. The convolutional LSTM needed 10 times less epochs to achieve the same result as the stacked LSTM. The second module consists of a violence detection system that applies the best solution obtained from the comparative study. The violence detection system saves the frames detected as violence with date, time and camera name and emits a sound alarm when more than a certain number of consecutive frames are evaluated as containing violence. This way the sensitivity of the system is reduced and avoids false alarms due to small mistakes done by the intelligence