Adaptive Frequency Neural Networks for Dynamic Pulse and Metre Perception.

Beat induction, the means by which humans listen to music and perceive a steady pulse, is achieved via a perceptualand cognitive process. Computationally modelling this phenomenon is an open problem, especially when processing expressive shaping of the music such as tempo change.To meet this challenge we propose Adaptive Frequency Neural Networks (AFNNs), an extension of Gradient Frequency Neural Networks (GFNNs).GFNNs are based on neurodynamic models and have been applied successfully to a range of difficult music perception problems including those with syncopated and polyrhythmic stimuli. AFNNs extend GFNNs by applying a Hebbian learning rule to the oscillator frequencies. Thus the frequencies in an AFNN adapt to the stimulus through an attraction to local areas of resonance, and allow for a great dimensionality reduction in the network.Where previous work with GFNNs has focused on frequency and amplitude responses, we also consider phase information as critical for pulse perception. Evaluating the time-based output, we find significantly improved re-sponses of AFNNs compared to GFNNs to stimuli with both steady and varying pulse frequencies. This leads us to believe that AFNNs could replace the linear filtering methods commonly used in beat tracking and tempo estimationsystems, and lead to more accurate methods

Superconductivity-Induced Anderson Localisation

We have studied the effect of a random superconducting order parameter on the localization of quasi-particles, by numerical finite size scaling of the Bogoliubov-de Gennes tight-binding Hamiltonian. Anderson localization is obtained in d=2 and a mobility edge where the states localize is observed in d=3. The critical behavior and localization exponent are universal within error bars both for real and complex random order parameter. Experimentally these results imply a suppression of the electronic contribution to thermal transport from states above the bulk energy gap.Comment: 4 pages, revtex file, 3 postscript figure

Forming disk galaxies in wet major mergers. I. Three fiducial examples

Using three fiducial Nbody+SPH simulations, we follow the merging of two disk galaxies with a hot gaseous halo component each, and examine whether the merger remnant can be a spiral galaxy. The stellar progenitor disks are destroyed by violent relaxation during the merging and most of their stars form a classical bulge, while the remaining form a thick disk and its bar. A new stellar disk forms subsequently and gradually in the remnant from the gas accreted mainly from the halo. It is vertically thin and well extended in its equatorial plane. A bar starts forming before the disk is fully in place, contrary to what is assumed in idealised simulations of isolated bar-forming galaxies. It has morphological features such as ansae and boxy/peanut bulges. Stars of different ages populate different parts of the box/peanut. A disky pseudobulge forms also, so that by the end of the simulation, all three types of bulges coexist. The oldest stars are found in the classical bulge, followed by those of the thick disk, then by those in the thin disk. The youngest stars are in the spiral arms and the disky pseudobulge. The disk surface density profiles are of type II (exponential with downbending), and the circular velocity curves are flat and show that the disks are submaximum in these examples: two clearly so and one near-borderline between maximum and submaximum. On average, only roughly between 10 and 20% of the stellar mass is in the classical bulge of the final models, i.e. much less than in previous simulations.Comment: 17 pages, 8 figures, accepted for publication in ApJ. V2: replaced Figure 4 with correct versio

(2,0) theory on circle fibrations

We consider (2,0) theory on a manifold M_6 that is a fibration of a spatial S^1 over some five-dimensional base manifold M_5. Initially, we study the free (2,0) tensor multiplet which can be described in terms of classical equations of motion in six dimensions. Given a metric on M_6 the low energy effective theory obtained through dimensional reduction on the circle is a Maxwell theory on M_5. The parameters describing the local geometry of the fibration are interpreted respectively as the metric on M_5, a non-dynamical U(1) gauge field and the coupling strength of the resulting low energy Maxwell theory. We derive the general form of the action of the Maxwell theory by integrating the reduced equations of motion, and consider the symmetries of this theory originating from the superconformal symmetry in six dimensions. Subsequently, we consider a non-abelian generalization of the Maxwell theory on M_5. Completing the theory with Yukawa and phi^4 terms, and suitably modifying the supersymmetry transformations, we obtain a supersymmetric Yang-Mills theory which includes terms related to the geometry of the fibration.Comment: 24 pages, v2 References added, typos correcte

Deconstructing graviphoton from mass-deformed ABJM

Mass-deformed ABJM theory has a maximally supersymmetric fuzzy two-sphere vacuum solution where the scalar fields are proportional to the TGRVV matrices. We construct these matrices using Schwinger oscillators. This shows that the ABJM gauge group that corresponds to the fuzzy two-sphere geometry is $U(N)\times U(N-1)$. We deconstruct the graviphoton term in the D4 brane theory. The normalization of this term is fixed by topological reasons. This gives us the correct normalization of the deconstructed U(1) gauge field and fixes the Yang -Mills coupling constant to the value which corresponds to M5 brane compactified on \mb{R}^ {1,2} \times S^3/{\mb{Z}_k}. The graviphoton term also enable us to show that the zero mode contributions to the partition functions for the D4 and the M5 brane agree.Comment: 26 page