Abstract:
Binary Decision Diagrams (BDDs) can be graphically manipulated to reduce the number of nodes and hence the area. In this context, ordering of BDDs play a major role. Most of the algorithms for input variable ordering of OBDD focus primarily on area minimization. However, suitable input variable ordering helps in minimizing the power consumption also. In this particular work, we have proposed two algorithms namely, a genetic algorithm based technique and a branch and bound algorithm to find an optimal input variable order. Of course, the node reordering is taken care of by the standard BDD package buddy-2.4. Moreover, we have evaluated the performances of the proposed algorithms by running an exhaustive search program. Experi-mental results show a substantial saving in area and power. We have also compared our techniques with other state-of-art techniques of variable ordering for OBDDs and found to give superior results.

An exact and fast analytic method based on power series
is established to predict the modal field distributions, Petermann-2
spot size, the normalized propagation constant corresponding to fundamental and
first higher order mode in graded index fibers with any arbitrary power law
profile. The variation of normalized cut-off frequencies of some LP_{lm} modes in graded index fibers with different profile exponents are also shown
here and an empirical relation between them is determined.

GaAs has high three photon absorption (3PA) co-efficient
at mid-infrared wavelength like2.2mm and waveguides can be formed with this material like silicon
nano-wires. It is shown that three-photon-absorption in GaAs wire waveguide can
be utilized to form NAND gate. Three-photon-absorption is incorporated in
one-dimensional Finite Difference Time Domain (FDTD) equations.The
evolution of a probe pulse under the influence of a pump pulse through crossabsorption
in a waveguide is investigated using FDTD simulation, where the dominant
process is nonlinear three-photon-absorption. Output probe power dependence on
input pump power shows that GaAs waveguide NAND gate has higher extinction
ratio in comparison to NAND gate using two-photon-absorption in silicon
waveguide.

Abstract:
We study the phase distribution and its dynamics in spin-orbit coupled two component ultracold Bosons for finite size system. Using an inhomogeneous meanfield analysis we demonstrate how phase distribution evolves as we tune the spin-orbit coupling $\gamma$ and $t$, the spin-independent hopping. For $t>>\gamma$ we find the homogeneous superfluid phase. As we increase $\gamma$, differences in the phases of the order parameter grows leading to twisted superfluid phase. For $t \sim \gamma$ competing orderings in the phase distribution is observed. At large $\gamma$ limit a Ferro-Magnetic stripe ordering appears along the diagonal. We explain that this is due to the frustration bought in by the spin-orbit interaction. Isolated vortex formation is also shown to appear. We also investigate the possible collective modes. In deep superfluid regime we derive the equation of motion for the phases following a semi-classical approximation. Imaginary frequencies indicating the damped modes are seen to appear and the dynamics of lowest normal modes are discussed.

Abstract:
Neuroinflammation associated with Japanese encephalitis (JE) is mainly due to the activation of glial cells with subsequent release of proinflammatory mediators from them. The recognition of viral RNA, in part, by the pattern recognition receptor retinoic acid-inducible gene I (RIG-I) has been indicated to have a role in such processes. Even though neurons are also known to express this receptor, its role after JE virus (JEV) infections is yet to be elucidated.

Abstract:
The presence of seasonal effects in monthly returns has been reported in several developed and emerging stock markets. The objective of this study is to explore the interplay between the month-of-the-year effect and market crash effects on monthly returns in Indian stock markets. The study uses dummy variable multiple linear regression to assess the seasonality of stock market returns and the impact of market crashes on the same. The results of the study provide evidence for a month-of-the-year effect in Indian stock markets, particularly positive November, August, and December effects, and a negative March effect. Further, the study suggests that the incidence of market crashes reduces the seasonal effects. Keywords: seasonality, stock market returns, month-of-the-year effect, market crash effects, dummy variable regression. JEL Classification: G14

Abstract:
We develop a projection operator formalism for studying both the zero temperature equilibrium phase diagram and the non-equilibrium dynamics of the Bose-Hubbard model. Our work, which constitutes an extension of Phys. Rev. Lett. {\bf 106}, 095702 (2011), shows that the method provides an accurate description of the equilibrium zero temperature phase diagram of the Bose-Hubbard model for several lattices in two- and three-dimensions (2D and 3D). We show that the accuracy of this method increases with the coordination number $z_0$ of the lattice and reaches to within 0.5% of quantum Monte Carlo data for lattices with $z_0=6$. We compute the excitation spectra of the bosons using this method in the Mott and the superfluid phases and compare our results with mean-field theory. We also show that the same method may be used to analyze the non-equilibrium dynamics of the model both in the Mott phase and near the superfluid-insulator quantum critical point where the hopping amplitude $J$ and the on-site interaction $U$ satisfy $z_0J/U \ll 1$. In particular, we study the non-equilibrium dynamics of the model both subsequent to a sudden quench of the hopping amplitude $J$ and during a ramp from $J_i$ to $J_f$ characterized by a ramp time $\tau$ and exponent $\alpha$: $J(t)=J_i +(J_f-J_i) (t/\tau)^{\alpha}$. We compute the wavefunction overlap $F$, the residual energy $Q$, the superfluid order parameter $\Delta(t)$, the equal-time order parameter correlation function $C(t)$, and the defect formation probability $P$ for the above-mentioned protocols and provide a comparison of our results to their mean-field counterparts. We find that $Q$, $F$, and $P$ do not exhibit the expected universal scaling. We explain this absence of universality and show that our results for linear ramps compare well with the recent experimental observations.

Abstract:
We examine the large branching ratio for the process $B\to \eta^{\prime} K$ from the standpoint of R parity violating supersymmetry. We have given all possible $R_p$ violating contributions to $B\to \eta^{\prime} K$ amplitudes. We find that only two pairs of $\lambda^{\prime}$-type $R_p$ violating couplings can solve this problem after satisfying all other experimental bounds. We also analyze those modes where these couplings can appear, {\em e.g.}, $B^\pm \to \pi^{\pm}K^0$, $B^{\pm,0} \to K^{*\pm,0} \eta^{(\prime)}$, $B^{\pm} \to\phi K^{\pm}$ etc., and predict their branching ratios. Further, one of these two pairs of couplings is found to lower the branching ratio of $B^{\pm}\to\phi K^\pm$, thereby allowing larger $\xi\equiv{1\over N_c}$. This allows us to fit $B^{\pm}\to \omega K^{\pm}$ and $B^{\pm}\to \omega \pi^{\pm}$, which could not be done in the SM framework.

Abstract:
We use a time-dependent hopping expansion technique to study the non-equilibrium dynamics of strongly interacting bosons in an optical lattice in the presence of a harmonic trap characterized by a force constant $K$. We show that after a sudden quench of the hopping amplitude $J$ across the superfluid (SF)-Mott insulator(MI) transition, the SF order parameter $|\Delta_{\bf r}(t)|$ and the local density fluctuation $\delta n_{\bf r}(t)$ exhibit sudden decoherence beyond a trap-induced time scale $T_0 \sim K^{-1/2}$. We also show that after a slow linear ramp down of $J$, $|\Delta_{\bf r}|$ and the boson defect density $P_{\bf r}$ display a novel non-monotonic spatial profile. Both these phenomena can be explained as consequences of trap-induced time and length scales affecting the dynamics and can be tested by concrete experiments.

Abstract:
We study the statistics of the work distribution $P(w)$ in a $d-$dimensional closed quantum system with linear dimension $L$ subjected to a periodic drive with frequency $\omega_0$. We show that after an integer number of periods of the drive, the corresponding rate function $I(w)= -\ln[P(w)]/L^d$ satisfies an universal lower bound $I(0)\ge n_d$ and has a zero at $w=Q$, where $n_d$ and $Q$ are the defect density and residual energy generated during the drive. We supplement our results by calculating $I(w)$ for a class of $d$-dimensional integrable models and show that it has oscillatory dependence on $\omega_0$ originating from Stuckelberg interference generated during multiple passage through intermediate quantum critical points or regions during the drive. We suggest experiments to test our theory.