On skew tau-functions in higher spin theory

Recent studies of higher spin theory in three dimensions concentrate on Wilson loops in Chern-Simons theory, which in the classical limit reduce to peculiar corner matrix elements between the highest and lowest weight states in a given representation of SL(N). Despite these "skew" tau-functions can seem very different from conventional ones, which are the matrix elements between the two highest weight states, they also satisfy the Toda recursion between different fundamental representations. Moreover, in the most popular examples they possess simple representations in terms of matrix models and Schur functions. We provide a brief introduction to this new interesting field, which, after quantization, can serve as an additional bridge between knot and integrability theories.Comment: 36 page

Knot invariants from Virasoro related representation and pretzel knots

We remind the method to calculate colored Jones polynomials for the plat representations of knot diagrams from the knowledge of modular transformation (monodromies) of Virasoro conformal blocks with insertions of degenerate fields. As an illustration we use a rich family of pretzel knots, lying on a surface of arbitrary genus g, which was recently analyzed by the evolution method. Further generalizations can be to generic Virasoro modular transformations, provided by integral kernels, which can lead to the Hikami invariants.Comment: 29 page

Porting Spotlight Range Migration Algorithm Processor from Matlab to Virtex 6

This paper describes the implementation and optimization of a Synthetic Aperture Radar process Spotlight Range Migration Algorithm processor on FPGA Virtex 6 DSP kit that fits on the chip. The mean/max error compared to a software implementation is -54/-28.74dB for 55 elements and 882 samples

FMCW rail-mounted SAR: Porting spotlight SAR imaging from MATLAB to FPGA

In this work, a low-cost laptop-based radar platform derived from the MIT open courseware has been implemented. It can perform ranging, Doppler measurement and SAR imaging using MATLAB as the processor. In this work, porting the signal processing algorithms onto a FPGA platform will be addressed as well as differences between results obtained using MATLAB and those obtained using the FPGA platform. The target FPGA platforms were a Virtex6 DSP kit and Spartan3A starter kit, the latter was also low-cost to further reduce the cost for students to access radar technology

Models of G time variations in diverse dimensions

A review of different cosmological models in diverse dimensions leading to a relatively small time variation of the effective gravitational constant G is presented. Among them: 4-dimensional general scalar-tensor model, multidimensional vacuum model with two curved Einstein spaces, multidimensional model with multicomponent anisotropic "perfect fluid", S-brane model with scalar fields and two form field etc. It is shown that there exist different possible ways of explanation of relatively small time variation of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on G-dot may be satisfied ether in some restricted interval or for all allowed values of the synchronous time variable.Comment: 27 pages, Late

Towards topological quantum computer

One of the principal obstacles on the way to quantum computers is the lack of distinguished basis in the space of unitary evolutions and thus the lack of the commonly accepted set of basic operations (universal gates). A natural choice, however, is at hand: it is provided by the quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, distinguished from the points of view of group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Observables in this case are (square modules of) the knot polynomials, and their pronounced integrality properties could provide a key to error correction. We suggest to use R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, to build a topological version of quantum computing.Comment: 14 page