Arithmetic Circuits and the Hadamard Product of Polynomials

Motivated by the Hadamard product of matrices we define the Hadamard product of multivariate polynomials and study its arithmetic circuit and branching program complexity. We also give applications and connections to polynomial identity testing. Our main results are the following. 1. We show that noncommutative polynomial identity testing for algebraic branching programs over rationals is complete for the logspace counting class \ceql, and over fields of characteristic $p$ the problem is in \ModpL/\Poly. 2.We show an exponential lower bound for expressing the Raz-Yehudayoff polynomial as the Hadamard product of two monotone multilinear polynomials. In contrast the Permanent can be expressed as the Hadamard product of two monotone multilinear formulas of quadratic size.Comment: 20 page

Relationship between Horizontal Flow Velocity and Cell Lifetime for Supergranulation

A study of 50 supergranular cells obtained from SOHO Dopplergrams was undertaken in order to investigate the relationship between the lifetime ($T$) and the horizontal flow velocity ($v_h$) of the cells. For this sample we find that the two parameters are correlated with a relation $v_h\propto T^{0.5}$ and $T$ is identified with the eddy turn-over time. This is in agreement with the turbulent convective model of the solar atmosphere where the velocity spectrum of supergranular field given by '$v_h \propto L^{1/3}$' can be identified with the Kolmogorov spectrum for the eddy size $L$.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

Dynamic Stability Enhancement of Power Systems Using Neural-Network Controlled Static-Compensator

This paper aims at enhancement of dynamic stability of power systems using artificial neural network (ANN) controlled static VAR compensator (SVC). SVC is proven the fact that it improves the dynamic stability of power systems apart from reactive power compensation; it has multiple roles in the operation of power systems. The auxiliary control signals to SVC play a very important role in mitigating the rotor electro-mechanical low frequency oscillations. Artificial neural network based controller is designed using the generator speed deviation, as a modulated signal to SVC, to generate the desired damping, is proposed in this paper. The ANN is trained using conventional controlled data and hence replaces the conventional controller. The ANN controlled SVC is used to improve the dynamic performance of power system by reducing the steady-state error and for its fast settling. The simulations are carried out for multi-machine power system (MMPS) at different operating conditions