Integrated Calendar

The images of distant galaxies are magnified and sheared by mass fluctuations
encountered along the line of sight. Shear fields due to weak gravitational lensing have characteristic coherent patterns. We describe the topological defects in the shear field in terms of the curvature of an imaginary surface whose height function is given by the lensing potential. The resulting defects can then be identified as umbilical points of the potential surface produced by ellipsoidal halos. This enables to infer the correlation function of the lensing potential at large redshifts by measuring the abundance of defects in shear maps.

Abstract: I remind the basic features of the BFKL approach, based on general properties of high energy scattering amplitudes: analyticity, unitarity, crossing symmetry and renormalizability. The Steinmann relations allow us to write a simple representation for the production amplitudes in the multi-Regge kinematics. It turns out, that the gluon in QCD and supersymmetric gauge models is reggeized. Pomeron, Odderon and other colorless reggeons are composite states of the reggeized gluons. Their wave functions satisfy the BFKL and BKP equations. In the leading logarithmic approximations (LLA) of the multi-color QCD the BKP equation has a number of remarkable properties: Moebius invariance, holomorphic separability and duality symmetry. Moreover, it coincides with the Schroedinger equation for a closed integrable spin chain. It is shown, that in the N=4 supersymmetric model the BDS ansatz for the production amplitudes does not satisfy the Steinmann relations because it does not take into account the contribution of the Mandelstam cuts appearing in planar diagrams at certain physical regions. The equation for the wave functions describing composite states corresponding to these cuts in LLA turns out to be integrable and corresponds to an open Heisenberg spin chain. The Baxter equation for this spin chain is reduced to a simple recurrent relation and the corresponding Baxter function is expressed in terms of gamma-functions. As a result, the Mandelstam cut contributions in N=4 SUSY can be calculated in an explicit form.

What is the temporal precision of cortical activity? It is clear that the wide range of coding schemes occur on different time scales: Millisecond scale characterizes direct sensory events, tens to hundreds of milliseconds scale characterizes attention processes, while different states of alertness can last many seconds. It seems that there is a direct relationship between the time scale and the spatial resolution in cortical activity. The activity involved in a direct sensory process is well defined in small areas; for example an orientation column. On the other hand an attention process involves huge populations and maybe even the whole cortex.

In my talk I will try to bridge the gap between the recordings of single neurons (intracellular and extracellular recordings) and the recordings of large populations of neurons (EEG, LFP,VSD or fMRI) in order to understand the spatio-temporal organization underlying the function of cortical neuronal population and it's relation to brain connectivity.

I will relate to the following topics:

- What is the size of the neuronal population that contributes to the population activity in different cognitive states?

- What is the degree of synchronization within this population?

- What is the relationship between the population activity and the activity of single cortical neurons?

- The dynamic of coherent activity in neuronal assemblies - ongoing & evoked activity