A finite population model of mlecular evolution: theory and computation

This article is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work has impacted antiviral treatment and vaccine design strategies. Yet, predictions of the quasispecies model are at best viewed as a guideline, primarily because it assumes an infinite population size, whereas realistic population sizes can be quite small. In this paper we consider a population genetics-based model aimed at understanding the evolution of such organisms with finite population sizes and present a rigorous study of the convergence and computational issues that arise therein. Our first result is structural and shows that, at any time during the evolution, as the population size tends to infinity, the distribution of genomes predicted by our model converges to that predicted by the quasispecies model. This justifies the continued use of the quasispecies model to derive guidelines for intervention. While the stationary state in the quasispecies model is readily obtained, due to the explosion of the state space in our model, exact computations are prohibitive. Our second set of results are computational in nature and address this issue. We derive conditions on the parameters of evolution under which our stochastic model mixes rapidly. Further, for a class of widely used fitness landscapes we give a fast deterministic algorithm which computes the stationary distribution of our model. These computational tools are expected to serve as a framework for the modeling of strategies for the deployment of mutagenic drugs.

Analytical theory and stability analysis of an elongated nanoscale object under external torque

We consider the rotational motion of an elongated nanoscale object in a fluid under an external torque. The experimentally observed dynamics could be understood from analytical solutions of the Stokes equation, with explicit formulae derived for the dynamical states as a function of the object dimensions and the parameters defining the external torque. Under certain conditions, multiple analytical solutions to the Stokes equations exist, which have been investigated through numerical analysis of their stability against small perturbations and their sensitivity towards initial conditions. These experimental results and analytical formulae are general enough to be applicable to the rotational motion of any isolated elongated object at low Reynolds numbers, and could be useful in the design of non-spherical nanostructures for diverse applications pertaining to microfluidics and nanoscale propulsion technologies.

Conformal perturbation theory and higher spin entanglement entropy on the torus

We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential mu, the deformation is related at high temperatures to a higher spin black hole in hs0] theory on AdS(3) spacetime. We calculate the order mu(2) corrections to the single interval Renyi and entanglement entropies on the torus using the bosonized formulation. A consistent result, satisfying all checks, emerges upon carefully accounting for both perturbative and winding mode contributions in the bosonized language. The order mu(2) corrections involve integrals that are finite but potentially sensitive to contact term singularities. We propose and apply a prescription for defining such integrals which matches the Hamiltonian picture and passes several non-trivial checks for both thermal corrections and the Renyi entropies at this order. The thermal corrections are given by a weight six quasi-modular form, whilst the Renyi entropies are controlled by quasi-elliptic functions of the interval length with modular weight six. We also point out the well known connection between the perturbative expansion of the partition function in powers of the spin-three chemical potential and the Gross-Taylor genus expansion of large-N Yang-Mills theory on the torus. We note the absence of winding mode contributions in this connection, which suggests qualitatively different entanglement entropies for the two systems.

Pyrolysis of 3-carene: Experiment, Theory and Modeling

Thermal decomposition studies of 3-carene, a bio-fuel, have been carried out behind the reflected shock wave in a single pulse shock tube for temperature ranging from 920 K to 1220 K. The observed products in thermal decomposition of 3-carene are acetylene, allene, butadiene, isoprene, cyclopentadiene, hexatriene, benzene, toluene and p-xylene. The overall rate constant for 3-carene decomposition was found to be k/s(-1) = 10((9.95 +/- 0.54)) exp(-40.88 +/- 2.71 kcal mol(-1) /RT). Ab-initio theoretical calculations were carried out to find the minimum energy pathway that could explain the formation of the observed products in the thermal decomposition experiments. These calculations were carried out at B3LYP/6-311 + G(d,p) and G3 level of theories. A kinetic mechanism explaining the observed products in the thermal decomposition experiments has been derived. It is concluded that the linear hydrocarbons are the primary products in the pyrolysis of 3-carene.

Pattern formation in thin films of polymer solutions: Theory and simulations

Self-assembly has been recognized as an efficient tool for generating a wide range of functional, chemically, or physically textured surfaces for applications in small scale devices. In this work, we investigate the stability of thin films of polymer solutions. For low concentrations of polymer in the solution, long length scale dewetting patterns are obtained with wavelength approximately few microns. Whereas, for concentrations above a critical value, bimodal dispersion curves are obtained with the dominant wavelength being up to two orders smaller than the usual dewetting length scale. We further show that the short wavelength corresponds to the phase separation in the film resulting in uniformly distributed high and low concentration regions. Interestingly, due to the solvent entropy, at very high concentration values of polymer, a re-entrant behaviour is observed with the dominant length scale now again corresponding to the dewetting wavelength. Thus, we show that the binary films of polymer solutions provide additional control parameters that can be utilized for generating functional textured surfaces for various applications. (C) 2016 AIP Publishing LLC.

Practical Criterion for Universal Laws and Practical Methods for Construction of Co-variance Sets

给出相对论力学中普遍定律的实用判别法和协变集的实用构造法,还给出实现非普遍定律的“可导出性”的一种实用方法．

Gestão museológica : questões teóricas e práticas = Museum management : theory and practice

Texto em português e inglês.

Use of aerial survey and aerophotogrammetry methods in monitoring manatee populations

We evaluated the use of strip-transect survey methods for manatees through a series of replicate aerial surveys in the Banana River, Brevard County, Florida, during summer 1993 and summer 1994. Transect methods sample a representative portion of the total study area, thus allowing for statistical extrapolation to the total area. Other advantages of transect methods are less flight time and less cost than total coverage, ease of navigation, and reduced likelihood of double-counting. Our objectives were: (1) to identify visibility biases associated with the transect survey method and to adjust the counts accordingly; (2) to derive a population estimate with known variance for the Banana River during summer; and (3) to evaluate the potential value of this survey method for monitoring trends in manatee population size over time. (51 page document)