Spectra of Modular Random Graphs

We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete. Two different types of inter-module connectivity are considered, one where the number of intermodule connections per-node diverges, and one where this number remains finite in the infinite module-size limit. In the first case, results can be understood as a perturbation of a superposition of semicircular spectral densities one would obtain for uncoupled modules. In the second case, matters can be more involved, and depend in detail on inter-module connectivities. For suitable parameters we even find near-triangular shaped spectral densities, similar to those observed in certain scale-free networks, in a system of consisting of just two coupled modules. Analytic results are presented for the infinite module-size limit; they are well corroborated by numerical simulations.Comment: 16 pages, 4 figures. to appear in J. Phys.

Large Deviations for Nonlocal Stochastic Neural Fields

We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a $Q$-Wiener process and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers' law for neural fields poses substanial difficulties but that one may transfer techniques from stochastic partial differential equations to establish a large deviation principle (LDP). Then we demonstrate that an efficient finite-dimensional approximation of the stochastic neural field equation can be achieved using a Galerkin method and that the resulting finite-dimensional rate function for the LDP can have a multi-scale structure in certain cases. These results form the starting point for an efficient practical computation of the LDP. Our approach also provides the technical basis for further rigorous study of noise-induced transitions in neural fields based on Galerkin approximations.Comment: 29 page

QCD Corrections to Hadronic Z and tau Decays

We present a brief (mainly bibliographical) report on recently performed calculations of terms of order O(\alpha_s^4 n_f^2) and O(\alpha_s^4 n_f^2 m_q^2) for hadronic Z and \tau decay rates. A few details about the analytical evaluation of the masters integrals appearing in the course of calculations are presented.Comment: revised version (some references corrected); 3 pages, talk given at International Europhysics Conference on High Energy Physics, Aachen, Germany, 17-23 July 200

Dependence of Galaxy Shape on Environment in the Sloan Digital Sky Survey

Using a sample of galaxies from the Sloan Digital Sky Survey (SDSS) Data Release 4, we study the trends relating surface brightness profile type and apparent axis ratio to the local galaxy environment. We use the SDSS parameter `fracDeV' to quantify the profile type. We find that galaxies with M_r > -18 are mostly described by exponential profiles in all environments. Galaxies with -21 < M_r < -18 mainly have exponential profiles in low density environments and de Vaucouleurs profiles in high density environments. The most luminous galaxies, with M_r < -21, are mostly described by de Vaucouleurs profiles in all environments. For galaxies with M_r < -19, the fraction of de Vaucouleurs galaxies is a monotonically increasing function of local density, while the fraction of exponential galaxies is monotonically decreasing. For a fixed surface brightness profile type, apparent axis ratio is frequently correlated with environment. As the local density of galaxies increases, we find that for -20 < M_r < -18, galaxies of all profile types become slightly rounder, on average; for -22 < M_r < -20, galaxies with exponential profiles tend to become flatter, while galaxies with de Vaucouleurs profiles become rounder; for M_r < -22, galaxies with exponential profiles become flatter, while the de Vaucouleurs galaxies become rounder in their inner regions, yet exhibit no change in their outer regions. We comment on how the observed trends relate to the merger history of galaxies.Comment: 23 pages, 7 figures, accepted by Ap

Review Essay—Adaptation and the School of War: Mars Adapting: Military Change during War

Retired Marine officer and National Defense University research fellow Frank Hoffman’s Mars Adapting is, first and foremost, a work of military theory. Hoffman initially achieved notoriety for his work and briefs about something he characterized as hybrid or compound warfare, since popularized alongside the rise in interest in gray-zone conflict. This book’s major contribution is similarly theoretical, but in the area of institutional learning, not modalities of war. Hoffman argues “for greater consideration of Organizational Learning Theory [OLT] to establish an analytical framework.

Ductile Saline Ice

Experiments have shown that tensile ductility of about 5% or more can be imparted to columnar, saline ice by pre-compressing the material by about 3.5%. This effect is similar to that observed in granular, fresh-water ice and is attributed to the operation of both dislocation creep and diffusion creep within that part of the matrix which recrystallized during the pre-compressive deformation

The relation between SAR and the electromagnetic field distribution for heterogeneous exposure conditions

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