Semiflexible Chains under Tension

A functional integral formalism is used to derive the extension of a stiff chain subject to an external force. The force versus extension curves are calculated using a meanfield approach in which the hard constraint $u^2(s)=1$ is replaced by a global constraint $= 1$ where $u(s)$ is the tangent vector describing the chain and $s$ is the arc length. The theory ``quantitatively'' reproduces the experimental results for DNA that is subject to a constant force. We also treat the problems of a semiflexible chain in a nematic field. In the limit of weak nematic field strength our treatment reproduces the exact results for chain expansion parallel to the director. When the strength of nematic field is large, a situation in which there are two equivalent minima in the free energy, the intrinsically meanfield approach yields incorrect results for the dependence of the persistence length on the nematic field.Comment: 14 pages, 1 figure available upon request, submitted to J. Chem. Phy

Diffusion in a continuum model of self-propelled particles with alignment interaction

In this paper, we provide the $O(\epsilon)$ corrections to the hydrodynamic model derived by Degond and Motsch from a kinetic version of the model by Vicsek & coauthors describing flocking biological agents. The parameter $\epsilon$ stands for the ratio of the microscopic to the macroscopic scales. The $O(\epsilon)$ corrected model involves diffusion terms in both the mass and velocity equations as well as terms which are quadratic functions of the first order derivatives of the density and velocity. The derivation method is based on the standard Chapman-Enskog theory, but is significantly more complex than usual due to both the non-isotropy of the fluid and the lack of momentum conservation

L2L_2 boosting in kernel regression

In this paper, we investigate the theoretical and empirical properties of $L_2$ boosting with kernel regression estimates as weak learners. We show that each step of $L_2$ boosting reduces the bias of the estimate by two orders of magnitude, while it does not deteriorate the order of the variance. We illustrate the theoretical findings by some simulated examples. Also, we demonstrate that $L_2$ boosting is superior to the use of higher-order kernels, which is a well-known method of reducing the bias of the kernel estimate.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ160 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

An Underlying Theory for Gravity

A new direction to understand gravity has recently been explored by considering classical gravity to be a derived interaction from an underlying theory. This underlying theory would involve new degrees of freedom at a deeper level and it would be structurally different from classical gravitation. It may conceivably be a quantum theory or a non-quantum theory. The relation between this underlying theory and Einstein's gravity is similar to the connection between statistical mechanics and thermodynamics. We discuss the apparent lack of evidence of any quantum nature of gravity in this context.Comment: Contributed paper to VIIth International Conference on Gravitation and Cosmology, 14 - 19 December, 2011 GOA, INDIA. 4 page

Persistence Length of Flexible Polyelectrolyte Chains

We calculate the dependence of the electrostatic persistence length, l_e, of weakly charged flexible polyelectrolyte chains using a self-consistent variational theory. The variation of l_e with \kappa, the inverse Debye screening length, is controlled by the parameter l_0 l_B/A^2, where l_0 is the bare persistence length, l_B is the Bjerrum length, and A is the mean distance between charges along the chain. Several distinct regimes for the dependence of l_e on \kappa emerge depending on the value of l_0 l_B/A^2. We show that when l_0 l_B /A^2 << 1 we recover the classical result, l_e \propto \kappa^{-2}. For intermediate values of l_0 l_B /A^2, l_e \propto \kappa^{-1}. In this regime one can also get l_e \propto \kappa^{-y} with y < 1 depending on the strength of the Coulomb interaction. Qualitative comparisons between our theory and simulations as well as other theories are presented.Comment: 25 pages, Latex, figure available upon reques

Neutrino reactions on 138^{138}La and 180^{180}Ta via charged and neutral currents by the Quasi-particle Random Phase Approximation (QRPA)

Cosmological origins of the two heaviest odd-odd nuclei, $^{138}$La and $^{180}$Ta, are believed to be closely related to the neutrino-process. We investigate in detail neutrino-induced reactions on the nuclei. Charged current (CC) reactions, $^{138}$Ba$(\nu_e, e^{-}) ^{138}$La and $^{180}$Hf$(\nu_e, e^{-}) ^{180}$Ta, are calculated by the standard Quasi-particle Random Phase Approximation (QRPA) with neutron-proton pairing as well as neutron-neutron, proton-proton pairing correlations. For neutral current (NC) reactions, $^{139}$La$(\nu \nu^{'}) ^{139}${La}$^*$ and $^{181}$Ta$(\nu, \nu^{'}) ^{181}$Ta$^*$, we generate ground and excited states of odd-even target nuclei, $^{139}$La and $^{181}$Ta, by operating one quasi-particle to even-even nuclei, $^{138}$Ba and $^{180}$Hf, which are assumed as the BCS ground state. Numerical results for CC reactions are shown to be consistent with recent semi-empirical data deduced from the Gamow-Teller strength distributions measured in the ($^{3}$He, t) reaction. Results for NC reactions are estimated to be smaller by a factor about 4 $\sim$ 5 rather than those by CC reactions. Finally, cross sections weighted by the incident neutrino flux in the core collapsing supernova are presented for further applications to the network calculations for relevant nuclear abundances

Estimating the Spectrum in Computed Tomography Via Kullback–Leibler Divergence Constrained Optimization

Purpose We study the problem of spectrum estimation from transmission data of a known phantom. The goal is to reconstruct an x‐ray spectrum that can accurately model the x‐ray transmission curves and reflects a realistic shape of the typical energy spectra of the CT system. Methods Spectrum estimation is posed as an optimization problem with x‐ray spectrum as unknown variables, and a Kullback–Leibler (KL)‐divergence constraint is employed to incorporate prior knowledge of the spectrum and enhance numerical stability of the estimation process. The formulated constrained optimization problem is convex and can be solved efficiently by use of the exponentiated‐gradient (EG) algorithm. We demonstrate the effectiveness of the proposed approach on the simulated and experimental data. The comparison to the expectation–maximization (EM) method is also discussed. Results In simulations, the proposed algorithm is seen to yield x‐ray spectra that closely match the ground truth and represent the attenuation process of x‐ray photons in materials, both included and not included in the estimation process. In experiments, the calculated transmission curve is in good agreement with the measured transmission curve, and the estimated spectra exhibits physically realistic looking shapes. The results further show the comparable performance between the proposed optimization‐based approach and EM. Conclusions Our formulation of a constrained optimization provides an interpretable and flexible framework for spectrum estimation. Moreover, a KL‐divergence constraint can include a prior spectrum and appears to capture important features of x‐ray spectrum, allowing accurate and robust estimation of x‐ray spectrum in CT imaging