On the classical WN(l)W_N^{(l)} algebras

We analyze the W_N^l algebras according to their conjectured realization as the second Hamiltonian structure of the integrable hierarchy resulting from the interchange of x and t in the l^{th} flow of the sl(N) KdV hierarchy. The W_4^3 algebra is derived explicitly along these lines, thus providing further support for the conjecture. This algebra is found to be equivalent to that obtained by the method of Hamiltonian reduction. Furthermore, its twisted version reproduces the algebra associated to a certain non-principal embedding of sl(2) into sl(4), or equivalently, the u(2) quasi-superconformal algebra. The general aspects of the W_N^l algebras are also presented.Comment: 28 page

New remarks on the linear constraint self-dual boson and Wess-Zumino terms

In this work we prove in a precise way that the soldering formalism can be applied to the Srivastava chiral boson (SCB), in contradiction with some results appearing in the literature. We have promoted a canonical transformation that shows directly that the SCB is composed of two Floreanini-Jackiw's particles with the same chirality which spectrum is a vacuum-like one. As another conflictive result we have proved that a Wess-Zumino term used in the literature consists of the scalar field, once again denying the assertion that the WZ term adds a new degree of freedom to the SCB theory in order to modify the physics of the system.Comment: 6 pages, Revtex. Final version to appear in Physical Review

On the Classical W4(2)W_{4}^{(2)} Algebra

We consider the classical \w42 algebra from the integrable system viewpoint. The integrable evolution equations associated with the \w42 algebra are constructed and the Miura maps , consequently modifications, are presented. Modifying the Miura maps, we give a free field realization the classical \w42 algebra. We also construct the Toda type integrable systems for it.Comment: 14 pages, latex, no figure

Conformal chiral boson models on twisted doubled tori and non-geometric string vacua

We derive and analyze the conditions for quantum conformal and Lorentz invariance of the duality symmetric interacting chiral boson sigma-models, which are conjectured to describe non-geometric string theory backgrounds. The one-loop Weyl and Lorentz anomalies are computed for the general case using the background field method. Subsequently, our results are applied to a class of (on-shell) Lorentz invariant chiral boson models which are based on twisted doubled tori. Our findings are in agreement with those expected from the effective supergravity approach, thereby firmly establishing that the chiral boson models under consideration provide the string worldsheet description of N=4 gauged supergravities with electric gaugings. Furthermore, they demonstrate that twisted doubled tori are indeed the doubled internal geometries underlying a large class of non-geometric string compactifications. For compact gaugings the associated chiral boson models are automatically conformal, a fact that is explained by showing that they are actually chiral WZW models in disguise.Comment: 37 pages; v2: minor improvements, version to appear in Nucl. Phys.

New possibilities for the gauging of chiral bosons

We study a new mechanism for the electromagnetic gauging of chiral bosons showing that new possibilities emerge for the interacting theory of chiral scalars. We introduce a chirally coupled gauge field necessary to mod out the degree of freedom that obstructs gauge invariance in a system of two opposite chiral bosons soldering them together.Comment: 11 pages, Latex. Accepted for publication in Physical Review

Receptive Field Inference with Localized Priors

The linear receptive field describes a mapping from sensory stimuli to a one-dimensional variable governing a neuron's spike response. However, traditional receptive field estimators such as the spike-triggered average converge slowly and often require large amounts of data. Bayesian methods seek to overcome this problem by biasing estimates towards solutions that are more likely a priori, typically those with small, smooth, or sparse coefficients. Here we introduce a novel Bayesian receptive field estimator designed to incorporate locality, a powerful form of prior information about receptive field structure. The key to our approach is a hierarchical receptive field model that flexibly adapts to localized structure in both spacetime and spatiotemporal frequency, using an inference method known as empirical Bayes. We refer to our method as automatic locality determination (ALD), and show that it can accurately recover various types of smooth, sparse, and localized receptive fields. We apply ALD to neural data from retinal ganglion cells and V1 simple cells, and find it achieves error rates several times lower than standard estimators. Thus, estimates of comparable accuracy can be achieved with substantially less data. Finally, we introduce a computationally efficient Markov Chain Monte Carlo (MCMC) algorithm for fully Bayesian inference under the ALD prior, yielding accurate Bayesian confidence intervals for small or noisy datasets

Neural processing of natural sounds

Natural sounds include animal vocalizations, environmental sounds such as wind, water and fire noises and non-vocal sounds made by animals and humans for communication. These natural sounds have characteristic statistical properties that make them perceptually salient and that drive auditory neurons in optimal regimes for information transmission.Recent advances in statistics and computer sciences have allowed neuro-physiologists to extract the stimulus-response function of complex auditory neurons from responses to natural sounds. These studies have shown a hierarchical processing that leads to the neural detection of progressively more complex natural sound features and have demonstrated the importance of the acoustical and behavioral contexts for the neural responses.High-level auditory neurons have shown to be exquisitely selective for conspecific calls. This fine selectivity could play an important role for species recognition, for vocal learning in songbirds and, in the case of the bats, for the processing of the sounds used in echolocation. Research that investigates how communication sounds are categorized into behaviorally meaningful groups (e.g. call types in animals, words in human speech) remains in its infancy.Animals and humans also excel at separating communication sounds from each other and from background noise. Neurons that detect communication calls in noise have been found but the neural computations involved in sound source separation and natural auditory scene analysis remain overall poorly understood. Thus, future auditory research will have to focus not only on how natural sounds are processed by the auditory system but also on the computations that allow for this processing to occur in natural listening situations.The complexity of the computations needed in the natural hearing task might require a high-dimensional representation provided by ensemble of neurons and the use of natural sounds might be the best solution for understanding the ensemble neural code