The Hopf algebra of odd symmetric functions

We consider a q-analogue of the standard bilinear form on the commutative ring of symmetric functions. The q=-1 case leads to a Z-graded Hopf superalgebra which we call the algebra of odd symmetric functions. In the odd setting we describe counterparts of the elementary and complete symmetric functions, power sums, Schur functions, and combinatorial interpretations of associated change of basis relations.Comment: 43 pages, 12 figures. v2: some correction

The differential graded odd nilHecke algebra

We equip the odd nilHecke algebra and its associated thick calculus category with digrammatically local differentials. The resulting differential graded Grothendieck groups are isomorphic to two different forms of the positive part of quantum sl(2) at a fourth root of unity.Comment: 53 page

The odd nilHecke algebra and its diagrammatics

We introduce an odd version of the nilHecke algebra and develop an odd analogue of the thick diagrammatic calculus for nilHecke algebras. We graphically describe idempotents which give a Morita equivalence between odd nilHecke algebras and the rings of odd symmetric functions in finitely many variables. Cyclotomic quotients of odd nilHecke algebras are Morita equivalent to rings which are odd analogues of the cohomology rings of Grassmannians. Like their even counterparts, odd nilHecke algebras categorify the positive half of quantum sl(2).Comment: 48 pages, eps and xypic diagram

Probes of Lorentz Violation in Neutrino Propagation

It has been suggested that the interactions of energetic particles with the foamy structure of space-time thought to be generated by quantum-gravitational (QG) effects might violate Lorentz invariance, so that they do not propagate at a universal speed of light. We consider the limits that may be set on a linear or quadratic violation of Lorentz invariance in the propagation of energetic neutrinos, v/c=[1 +- (E/M_\nuQG1)] or [1 +- (E/M_\nu QG2}^2], using data from supernova explosions and the OPERA long-baseline neutrino experiment. Using the SN1987a neutrino data from the Kamioka II, IMB and Baksan experiments, we set the limits M_\nuQG1 > 2.7(2.5)x10^10 GeV for subluminal (superluminal) propagation, respectively, and M_\nuQG2 >4.6(4.1)x10^4 GeV at the 95% confidence level. A future galactic supernova at a distance of 10 kpc would have sensitivity to M_\nuQG1 > 2(4)x10^11 GeV for subluminal (superluminal) propagation, respectively, and M_\nuQG2 > 2(4)x10^5 GeV. With the current CNGS extraction spill length of 10.5 micro seconds and with standard clock synchronization techniques, the sensitivity of the OPERA experiment would reach M_\nuQG1 ~ 7x10^5 GeV (M_\nuQG2 ~ 8x10^3 GeV) after 5 years of nominal running. If the time structure of the SPS RF bunches within the extracted CNGS spills could be exploited, these figures would be significantly improved to M_\nuQG1 ~ 5x10^7 GeV (M_\nuQG2 ~ 4x10^4 GeV). These results can be improved further if similar time resolution can be achieved with neutrino events occurring in the rock upstream of the OPERA detector: we find potential sensitivities to M_\nuQG1 ~ 4x10^8 GeV and M_\nuQG2 ~ 7x10^5 GeV.Comment: 33 pages, 22 figures, version accepted for publication in Physical Review

Exploration of Possible Quantum Gravity Effects with Neutrinos II: Lorentz Violation in Neutrino Propagation

It has been suggested that the interactions of energetic particles with the foamy structure of space-time thought to be generated by quantum-gravitational (QG) effects might violate Lorentz invariance, so that they do not propagate at a universal speed of light. We consider the limits that may be set on a linear or quadratic violation of Lorentz invariance in the propagation of energetic neutrinos, v/c=[1 +- (E/M_\nuQG1)] or [1 +- (E/M_\nu QG2}^2], using data from supernova explosions and the OPERA long-baseline neutrino experiment.Comment: 8 pages, 6 figures, proceedings for invited talk by A.Sakharov at DISCRETE'08, Valencia, Spain; December 200

What factors influence Fair Access students to consider university and what do they look for?

This paper reports the findings of a participatory mixed methods study into the perceptions of Fair Access students on the factors which led them to consider accessing Higher Education. The study consisted of focus groups with thirteen first year Fair Access Students (female n=9, male n=4) studying at the university. The data from which was analysed thematically, identifying five themes (what others say, going to university to escape, influence of habitus, location and what the university offered). These five themes formed the basis of a Likert type questionnaire which was completed by 239 students (n=168 Fair Access, n=71 non-Fair Access). It was evident that students from Fair Access backgrounds have the same high aspirations as their non-Fair Access counterparts, as do their families. However they can be discouraged and disadvantaged in the application system due to a variety of reasons; within compulsory education (perceptions of teachers as well as a lack of careers advice and support), intuitional habitus of Higher Education Institutions (provision of pre-access information and support) as well as not identifying themselves as coming from a widening participation background, thus reducing the likelihood of a contextual offer. All of these could impact on the ability of an individual from a WP background being successful in obtaining a place to study in Higher Education

Space-Time Foam may Violate the Principle of Equivalence

The interactions of different particle species with the foamy space-time fluctuations expected in quantum gravity theories may not be universal, in which case different types of energetic particles may violate Lorentz invariance by varying amounts, violating the equivalence principle. We illustrate this possibility in two different models of space-time foam based on D-particle fluctuations in either flat Minkowski space or a stack of intersecting D-branes. Both models suggest that Lorentz invariance could be violated for energetic particles that do not carry conserved charges, such as photons, whereas charged particles such electrons would propagate in a Lorentz-inavariant way. The D-brane model further suggests that gluon propagation might violate Lorentz invariance, but not neutrinos. We argue that these conclusions hold at both the tree (lowest-genus) and loop (higher-genus) levels, and discuss their implications for the phenomenology of quantum gravity.Comment: 20 pages, 4 figures, the version accepted for publication in the International Journal of Modern Physics

Chord Segmentation and Recognition using EM-Trained Hidden Markov Models

Automatic extraction of content description from commercial audio recordings has a number of important applications, from indexing and retrieval through to novel musicological analyses based on very large corpora of recorded performances. Chord sequences are a description that captures much of the character of a piece in a compact form and using a modest lexicon. Chords also have the attractive property that a piece of music can (mostly) be segmented into time intervals that consist of a single chord, much as recorded speech can (mostly) be segmented into time intervals that correspond to specific words. In this work, we build a system for automatic chord transcription using speech recognition tools. For features we use "pitch class profile" vectors to emphasize the tonal content of the signal, and we show that these features far outperform cepstral coefficients for our task. Sequence recognition is accomplished with hidden Markov models (HMMs) directly analogous to subword models in a speech recognizer, and trained by the same Expectation-Maximization (EM) algorithm. Crucially, this allows us to use as input only the chord sequences for our training examples, without requiring the precise timings of the chord changes— which are determined automatically during training. Our results on a small set of 20 early Beatles songs show frame-level accuracy of around 75% on a forced-alignment task