Maximum Rate of Unitary-Weight, Single-Symbol Decodable STBCs

It is well known that the Space-time Block Codes (STBCs) from Complex orthogonal designs (CODs) are single-symbol decodable/symbol-by-symbol decodable (SSD). The weight matrices of the square CODs are all unitary and obtainable from the unitary matrix representations of Clifford Algebras when the number of transmit antennas $n$ is a power of 2. The rate of the square CODs for $n = 2^a$ has been shown to be $\frac{a+1}{2^a}$ complex symbols per channel use. However, SSD codes having unitary-weight matrices need not be CODs, an example being the Minimum-Decoding-Complexity STBCs from Quasi-Orthogonal Designs. In this paper, an achievable upper bound on the rate of any unitary-weight SSD code is derived to be $\frac{a}{2^{a-1}}$ complex symbols per channel use for $2^a$ antennas, and this upper bound is larger than that of the CODs. By way of code construction, the interrelationship between the weight matrices of unitary-weight SSD codes is studied. Also, the coding gain of all unitary-weight SSD codes is proved to be the same for QAM constellations and conditions that are necessary for unitary-weight SSD codes to achieve full transmit diversity and optimum coding gain are presented.Comment: accepted for publication in the IEEE Transactions on Information Theory, 9 pages, 1 figure, 1 Tabl

Stochastic model of transcription factor-regulated gene expression

We consider a stochastic model of transcription factor (TF)-regulated gene expression. The model describes two genes: Gene A and Gene B which synthesize the TFs and the target gene proteins respectively. We show through analytic calculations that the TF fluctuations have a significant effect on the distribution of the target gene protein levels when the mean TF level falls in the highest sensitive region of the dose-response curve. We further study the effect of reducing the copy number of Gene A from two to one. The enhanced TF fluctuations yield results different from those in the deterministic case. The probability that the target gene protein level exceeds a threshold value is calculated with a knowledge of the probability density functions associated with the TF and target gene protein levels. Numerical simulation results for a more detailed stochastic model are shown to be in agreement with those obtained through analytic calculations. The relevance of these results in the context of the genetic disorder haploinsufficiency is pointed out. Some experimental observations on the haploinsufficiency of the tumour suppressor gene, Nkx3.1, are explained with the help of the stochastic model of TF-regulated gene expression.Comment: 17 pages, 11 figures. Accepted for publication in Physical Biolog

Three dimensional filamentary structures of a relativistic electron beam in Fast Ignition plasmas

The filamentary structures and associated electromagnetic fields of a relativistic electron beam have been studied by three dimensional particle-in-cell (PIC) simulations in the context of Fast Ignition fusion. The simulations explicitly include collisions in return plasma current and distinctly examine the effects of beam temperature and collisions on the growth of filamentary structures generated.Comment: 4 pages, 6 figures, submitted to Physics of Plasma

NEW SELF-GRAVITATIONAL OSCILLATORY EIGENMODE PATTERNS OF SOLAR PLASMA WITH BOLTZMANN-DISTRIBUTED ELECTRONS

We attempt to propose a simplified theoretical model to study new stationary states of the nonlinear self-gravitational fluctuation dynamics of the solar plasma with the zero-inertia electrons against weakly nonlinear perturbation within the framework of the Jeans homogenization assumption. This is based on a bi-fluidic approach with the thermal electrons treated as the Boltzmann-distributed species. The joint effects of space-charge polarization, sheath-formation, and bi-layer plasma-boundary interaction through gravito-electrostatic interplay in a spherically symmetric geometry are considered. Applying a standard multiscale technique, a unique form of extended Korteweg-de Vries-Burger (e-KdVB) equation with a new selfconsistent linear sink is methodologically developed. The origin of the unique sink lies in the spherically symmetric self-gravity contributed by the massive ions. A numerical shape-analysis with multi-parameter variation depicts the co-existence of two distinct classes of new eigenmode excitations. The fluctuation patterns evolve as oscillatory soliton-like and oscillatory shock-like patterns in judicious plasma conditions under the adiabatic electronic response. Their oscillations, arising due to resonant and non-resonant coupling phenomena with the background spectral components, get gradually damped out due to the sink. This scientific study allows us to conjecture that the model supports self-gravitational solitary (shock) waves having tails (fronts) composed of a sequence of slightly overlapping solitons with smoothly varying characteristic parameters. Our results are compared with the earlier theoretical model predictions, on-board multispace satellite data and spacecraft observations highlighting tentative future scopes

Flavor origin of dark matter and its relation with leptonic nonzero θ13 and Dirac CP phase δ

We propose a minimal extension of the standard model by including a U(1) flavor symmetry to establish a correlation between the relic abundance of dark matter, measured by WMAP and PLANCK satellite experiments and non-zero value of sinθ13 observed at DOUBLE CHOOZ, Daya Bay, RENO and T2K. The flavour symmetry is allowed to be broken at a high scale to a remnant Z2 symmetry, which not only ensures the stability to the dark matter, but also gives rise to a modification to the existing A4-based tri-bimaximal neutrino mixing. This deviation in turn suggests the required non-zero value of sinθ13. We assume the dark matter to be neutral under the existing A4 symmetry while charged under the U(1) flavor symmetry. Hence in this set-up, the non-zero value of sinθ13 predicts the dark matter charge under U(1), which can be tested at various ongoing and future direct and collider dark matter search experiments. We also point out the involvement of nonzero leptonic CP phase δ, which plays an important role in the analysi

Unifying the flavor origin of dark matter with leptonic nonzero θ13

We propose a flavor symmetric approach to unify the origin of dark matter (DM) with the nonzero θ13 in the lepton sector. In this framework, the breaking of a U(1) flavor symmetry to a remnant Z2 ensures the stability of the DM and gives rise to a modification to the existing A4-based tribimaximal neutrino mixing to attain the required nonzero values of sinθ13. This results in a range of Higgs portal coupling of the DM which can be potentially accessible at various ongoing and future direct and collider search experiments