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Theoretical neuroscience, like theoretical physics, attempts to discover and quantify the basic principles governing the systems it studies. Currently, however, there are very few attempts at unification across the levels of organization found in the brain. In this talk, I will describe the biological mechanisms of interest to neuroscientists, and describe a quantitative method for constructing sophisticated models of these mechanisms. Through a series of examples, I will show how the three principles that make up this method are general, allowing us to better understand a broad range of complex behaviour in a unified manner.

WMAP measurements of CMB temperature anisotropies reveal a power asymmetry: the average amplitude of temperature fluctuations in one hemisphere is larger than the average amplitude in the opposite hemisphere at the 99% confidence level. This power asymmetry may be generated during inflation by a large-amplitude superhorizon perturbation that causes the mean energy density to vary across the observable Universe. Such a superhorizon perturbation would also induce large-scale temperature anisotropies in the CMB; measurements of the CMB quadrupole and octupole (but not the dipole!) therefore constrain the perturbation\'s amplitude and wavelength. I will show how a superhorizon perturbation in a multi-field inflationary theory, the curvaton model, can produce the observed power asymmetry without generating unacceptable temperature fluctuations in the CMB. I will also discuss how this mechanism for generating the power asymmetry will be tested by forthcoming CMB experiments.

We review basic properties of effective worldvolume theory describing the dynamics of Dirichlet branes in type II supergravity backgrounds and then show that the SL(2,R) symmetry of IIB supergravity allows for the existence of new supersymmetric 7-brane configurations called Q7-branes. The Q7-branes differ from the D7-branes, in particular, by their coupling to the dilaton, axion and to `magnetic\' gauge field duals thereof. The appearance of Q7-branes and their instanton duals may indicate the existence of a new, yet unexplored, perturbative vacuum of type IIB string theory.

The general boundary state formulation is a key tool for extracting the semiclassical limit of nonpertubative theories of quantum gravity. In this talk I will discuss how this formalism works in the context of four-dimensional quantum Regge calculus with a general triangulation. A Gaussian boundary state selects a classical internal solution and peaks the path integral on it. As a result boundary observables, in particular the two-point function, can be computed order by order in a semiclassical asymptotic expansion. When the same methods are applied to a modified Regge theory that substitutes the exponential of the action by its cosine at each simplex in the triangulation, as conjectured from the semiclassical limit of spin foam models, the contributions from the sign-reversed terms are suppressed and the results match those of conventional Regge calculus. This talk is based on the results published in arXiv:0808.1107 [gr-qc].

I would like to provide a short, possibly elementary, introduction to the problem of computing string amplitudes at higher genus for superstrings. Essentially, I will recall which is the mathematical problem in defining the path integral measure (which has a well defined algebraic geometry realization for bosonic strings) and the solution proposed by d~@~YHocker and Phong for the genus 2 case. Their main results are the chiral splitted form of the measure, and its explicit expression in genus two. They proposed the splitting form to work at any genus and assumed some restriction for the explicit form which however did not permitted them to find a solution for genera higher then 2. I will tell something about the technology which permitted us to find explicit solutions for genus 3 and four. Indeed, we showed that the restrictions imposed by d~@~YHocker and Phong have no solution whereas the most general form compatible with modular invariance and clustering provide a unique solution, at least for genus 3 and 4. I will try to be as less technical as possible.

This course is aimed at advanced undergraduate and beginning graduate students, and is inspired by a book by the same title, written by Padmanabhan. Each session consists of solving one or two pre-determined problems, which is done by a randomly picked student. While the problems introduce various subjects in Astrophysics and Cosmology, they do not serve as replacement for standard courses in these subjects, and are rather aimed at educating students with hands-on analytic/numerical skills to attack new problems.

This course is aimed at advanced undergraduate and beginning graduate students, and is inspired by a book by the same title, written by Padmanabhan. Each session consists of solving one or two pre-determined problems, which is done by a randomly picked student. While the problems introduce various subjects in Astrophysics and Cosmology, they do not serve as replacement for standard courses in these subjects, and are rather aimed at educating students with hands-on analytic/numerical skills to attack new problems.

In this talk I will give an introduction to the simulation of quantum many-body systems using the so-called tensor networks. After a brief historical review, I will introduce the basics on tensor network representations of quantum states, and will explain some recent developments. In particular, in the last part of my talk I will focus on recent results obtained in the simulation of 2-dimensional quantum lattice systems of infinite size.