Hitting Spheres with Brownian Motion and Sommerfeld′s Radiation Condition

AbstractBy taking the Laplace transform of the scalar wave equation an inhomogeneous problem of the Helmholtz type is obtained. For this problem a probabilistic representation of the solution exists. Using the hitting distribution of a sphere by Brownian motion, we show that this representation satisfies a Sommerfeld radiation condition

Elongation factor Tu's nucleotide binding is governed by a thermodynamic landscape unique among bacterial translation factors.

Molecular switches such as GTPases are powerful devices turning "on" or "off" biomolecular processes at the core of critical biological pathways. To develop molecular switches de novo, an intimate understanding of how they function is required. Here we investigate the thermodynamic parameters that define the nucleotide-dependent switch mechanism of elongation factor (EF) Tu as a prototypical molecular switch. EF-Tu alternates between GTP- and GDP-bound conformations during its functional cycle, representing the "on" and "off' states, respectively. We report for the first time that the activation barriers for nucleotide association are the same for both nucleotides, suggesting a guanosine nucleoside or ribose-first mechanism for nucleotide association. Additionally, molecular dynamics (MD) simulations indicate that enthalpic stabilization of GDP binding compared to GTP binding originates in the backbone hydrogen bonding network of EF-Tu. In contrast, binding of GTP to EF-Tu is entropically driven by the liberation of bound water during the GDP- to GTP-bound transition. GDP binding to the apo conformation of EF-Tu is both enthalpically and entropically favored, a feature unique among translational GTPases. This indicates that the apo conformation does not resemble the GDP-bound state. Finally, we show that antibiotics and single amino acid substitutions can be used to target specific structural elements in EF-Tu to redesign the thermodynamic landscape. These findings demonstrate how, through evolution, EF-Tu has fine-tuned the structural and dynamic features that define nucleotide binding, providing insight into how altering these properties could be exploited for protein engineering

Nonparametric Information Geometry

The differential-geometric structure of the set of positive densities on a given measure space has raised the interest of many mathematicians after the discovery by C.R. Rao of the geometric meaning of the Fisher information. Most of the research is focused on parametric statistical models. In series of papers by author and coworkers a particular version of the nonparametric case has been discussed. It consists of a minimalistic structure modeled according the theory of exponential families: given a reference density other densities are represented by the centered log likelihood which is an element of an Orlicz space. This mappings give a system of charts of a Banach manifold. It has been observed that, while the construction is natural, the practical applicability is limited by the technical difficulty to deal with such a class of Banach spaces. It has been suggested recently to replace the exponential function with other functions with similar behavior but polynomial growth at infinity in order to obtain more tractable Banach spaces, e.g. Hilbert spaces. We give first a review of our theory with special emphasis on the specific issues of the infinite dimensional setting. In a second part we discuss two specific topics, differential equations and the metric connection. The position of this line of research with respect to other approaches is briefly discussed.Comment: Submitted for publication in the Proceedings od GSI2013 Aug 28-30 2013 Pari

Scalar Quantum Field Theory in Disordered Media

A free massive scalar field in inhomogeneous random media is investigated. The coefficients of the Klein-Gordon equation are taken to be random functions of the spatial coordinates. The case of an annealed-like disordered medium, modeled by centered stationary and Gaussian processes, is analyzed. After performing the averages over the random functions, we obtain the two-point causal Green's function of the model up to one-loop. The disordered scalar quantum field theory becomes qualitatively similar to a $\lambda\phi^{4}$ self-interacting theory with a frequency-dependent coupling

Microstructure, texture and tensile properties of ultrafine/nano grained magnesium alloy processed by accumulative back extrusion

An AZ31 wrought magnesium alloy was processed by employing multipass accumulative back extrusion process. The obtained microstructure, texture and room temperature tensile properties were characterized and discussed. Ultrafine grained microstructure including nano grains were developed, where the obtained mean grain size was decreased from 8 to 0.5 µm by applying consecutive passes. The frequency of both low angle and high angle boundaries increased after processing. Strength of the experimental alloy was decreased after processing, which was attributed to the obtained texture involving the major component lying inclined to the deformation axis. Both the uniform and post uniform elongations of the processed materials were increased after processing, where a total elongation of 68 pct was obtained after six-pass deformation. The contribution of different twinning and slip mechanism was described by calculating corresponding Schmid factors. The operation of prismatic slip was considered as the major deformation contributor. The significant increase in post uniform deformation of the processed material was discussed relying on the occurrence of grain boundary sliding associated with the operation of prismatic slip.Postprint (author's final draft