Exploration of Finite 2D Square Grid by a Metamorphic Robotic System

We consider exploration of finite 2D square grid by a metamorphic robotic system consisting of anonymous oblivious modules. The number of possible shapes of a metamorphic robotic system grows as the number of modules increases. The shape of the system serves as its memory and shows its functionality. We consider the effect of global compass on the minimum number of modules necessary to explore a finite 2D square grid. We show that if the modules agree on the directions (north, south, east, and west), three modules are necessary and sufficient for exploration from an arbitrary initial configuration, otherwise five modules are necessary and sufficient for restricted initial configurations

Parity Mixed Doublets in A = 36 Nuclei

The $\gamma$-circular polarizations ($P_{\gamma}$) and asymmetries ($A_{\gamma}$) of the parity forbidden M1 + E2 $\gamma$-decays: $^{36}Cl^{\ast} (J^{\pi} = 2^{-}; T = 1; E_{x} = 1.95$ MeV) $\rightarrow$ $^{36}Cl (J^{\pi} = 2^{+}; T = 1; g.s.)$ and $^{36}Ar^{\ast} (J^{\pi} = 2^{-}; T = 0; E_{x} = 4.97$ MeV) $\rightarrow$ $^{36}Ar^{\ast} (J^{\pi} = 2^{+}; T = 0; E_{x} = 1.97$ MeV) are investigated theoretically. We use the recently proposed Warburton-Becker-Brown shell-model interaction. For the weak forces we discuss comparatively different weak interaction models based on different assumptions for evaluating the weak meson-hadron coupling constants. The results determine a range of $P_{\gamma}$ values from which we find the most probable values: $P_{\gamma}$ = $1.1 \cdot 10^{-4}$ for $^{36}Cl$ and $P_{\gamma}$ = $3.5 \cdot 10^{-4}$ for $^{36}Ar$.Comment: RevTeX, 17 pages; to appear in Phys. Rev.

Nonlinear PDEs for Fredholm determinants arising from string equations

String equations related to 2D gravity seem to provide, quite naturally and systematically, integrable kernels, in the sense of Its-Izergin-Korepin and Slavnov. Some of these kernels (besides the "classical" examples of Airy and Pearcey) have already appeared in random matrix theory and they have a natural Wronskian structure, given by one of the operators in the string relation $[L^\pm,Q^\pm] = \pm 1$, namely $L^\pm$. The kernels are intimately related to wave functions for Gel'fand-Dickey reductions of the KP hierarchy. The Fredholm determinants of these kernels also satisfy Virasoro constraints leading to PDEs for their log derivatives, and these PDEs depend explicitly on the solutions of Painlev\'e-like systems of ODEs equivalent to the relevant string relations. We give some examples coming from critical phenomena in random matrix theory (higher order Tracy-Widom distributions) and statistical mechanics (Ising models).Comment: Accepted for publication on the AMS Contemporary Mathematics Series, 36 page

Identification of temperature profile and heat transfer on a dielectric membrane for gas sensors by `COSMOS' program simulation

The application of commercial 3-D software `COSMOS' for the design and thermal analysis of the low power consumption test structures with dielectric membrane for gas microsensors is presented. Within this work, the simulation provides the estimation of the temperature profile on the active area and the whole membrane including the four bridges and the heating efficiency in the temperature range 20-500 °C. Unravelling of the heat loss mechanisms in terms of radiation, convection, conduction by air and solid materials during heat transfer on the dielectric membrane is reported for the first time as a mean to evaluate by 3-D simulation the contribution of technological processes and lay-out design to the total heat losses

A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics

We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the Relative Entropy Rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of suitable observables in path space for the Relative Entropy Rate and the corresponding Fisher Information Matrix. The stationary regime is crucial for stochastic dynamics and here allows us to address the sensitivity analysis of complex systems, including examples of processes with complex landscapes that exhibit metastability, non-reversible systems from a statistical mechanics perspective, and high-dimensional, spatially distributed models. All these systems exhibit, typically non-gaussian stationary probability distributions, while in the case of high-dimensionality, histograms are impossible to construct directly. Our proposed methods bypass these challenges relying on the direct Monte Carlo simulation of rigorously derived observables for the Relative Entropy Rate and Fisher Information in path space rather than on the stationary probability distribution itself. We demonstrate the capabilities of the proposed methodology by focusing here on two classes of problems: (a) Langevin particle systems with either reversible (gradient) or non-reversible (non-gradient) forcing, highlighting the ability of the method to carry out sensitivity analysis in non-equilibrium systems; and, (b) spatially extended Kinetic Monte Carlo models, showing that the method can handle high-dimensional problems

From the Hitchin section to opers through nonabelian Hodge

For a complex simple simply connected Lie group $G$, and a compact Riemann surface $C$, we consider two sorts of families of flat $G$-connections over $C$. Each family is determined by a point ${\mathbf u}$ of the base of Hitchin's integrable system for $(G,C)$. One family $\nabla_{\hbar,{\mathbf u}}$ consists of $G$-opers, and depends on $\hbar \in {\mathbb C}^\times$. The other family $\nabla_{R,\zeta,{\mathbf u}}$ is built from solutions of Hitchin's equations, and depends on $\zeta \in {\mathbb C}^\times, R \in {\mathbb R}^+$. We show that in the scaling limit $R \to 0$, $\zeta = \hbar R$, we have $\nabla_{R,\zeta,{\mathbf u}} \to \nabla_{\hbar,{\mathbf u}}$. This establishes and generalizes a conjecture formulated by Gaiotto

Efficient Multi-Robot Motion Planning for Unlabeled Discs in Simple Polygons

We consider the following motion-planning problem: we are given $m$ unit discs in a simple polygon with $n$ vertices, each at their own start position, and we want to move the discs to a given set of $m$ target positions. Contrary to the standard (labeled) version of the problem, each disc is allowed to be moved to any target position, as long as in the end every target position is occupied. We show that this unlabeled version of the problem can be solved in $O(n\log n+mn+m^2)$ time, assuming that the start and target positions are at least some minimal distance from each other. This is in sharp contrast to the standard (labeled) and more general multi-robot motion-planning problem for discs moving in a simple polygon, which is known to be strongly NP-hard

On a modular property of N=2 superconformal theories in four dimensions

In this note we discuss several properties of the Schur index of N=2 superconformal theories in four dimensions. In particular, we study modular properties of this index under SL(2,Z) transformations of its parameters.Comment: 23 page, 2 figure

Peso al nacer de niños brasileños menores de dos años

Low birth weight is associated with increased risk of dying in the first year of life. This study was motivated by recent changes in the determination of birth weight patterns with the advent of the perinatal epidemiological transition. We analyzed data from the Brazilian National Survey of Demographic and Health of Children and Women including only children < 24 months. Prevalence of low birth weight in Brazil was 6.1%. Risk factors included female gender, residence in the South and Southeast geographic regions, low maternal education, and maternal smoking. The low birth weight profile changed, with higher prevalence in more economically developed regions, reflecting the neonatal epidemiological transition determined by changes in patterns of childbirth care and incorporation of perinatal life support technologies, in addition to the previously known biological risks associated with poverty and misinformation.El bajo peso al nacer tiene una gran relación con el riesgo de morir en el primer año de vida. Estudios muestran su asociación con problemas de desarrollo en la infancia y enfermedades en la vida adulta. Dada la importancia de este indicador, el objetivo de este estudio fue investigar los factores sociales, demográficos, biológicos y ambientales involucrados en su determinación. Se analizaron los datos de la Investigación Nacional de Demografía y Salud del Niño y de la Mujer (PNDS-2006), incluyendo solamente niños menores de 24 meses de vida. La prevalencia de bajo peso al nacer en Brasil fue de un 6,1%. Los factores de riesgo identificados fueron sexo femenino, residir en las macrorregiones Sur y Sudeste y ser hijo de madres con baja escolaridad o tabaquistas. Hubo cambios en el perfil de bajo peso al nacer, con mayor prevalencia en regiones más desarrolladas económicamente, reflejando la transición epidemiológica perinatal, caracterizada por cambios en los padrones de asistencia al parto e incorporación de los avances tecnológicos en la asistencia perinatal, además de factores de riesgo biológicos conocidos, asociados a la pobreza y a la desinformación.O baixo peso ao nascer tem grande relação com risco de morrer no primeiro ano de vida. Estudos mostram sua associação com problemas de desenvolvimento na infância e doenças na vida adulta. Dada a importância desse indicador, o objetivo deste estudo foi investigar os fatores sociais, demográficos, biológicos e ambientais envolvidos na sua determinação. Analisaram-se dados da Pesquisa Nacional de Demografia e Saúde da Criança e da Mulher (PNDS-2006), incluindo apenas crianças menores de 24 meses de vida. A prevalência de baixo peso ao nascer no Brasil foi de 6,1%. Os fatores de risco identificados foram sexo feminino, residir nas macrorregiões Sul e Sudeste e ser filho de mães com baixa escolaridade ou tabagistas. Houve mudanças no perfil do baixo peso ao nascer, com maior prevalência em regiões mais desenvolvidas economicamente, refletindo a transição epidemiológica perinatal, caracterizada por mudanças nos padrões de assistência ao parto e incorporação dos avanços tecnológicos na assistência perinatal, além de fatores de risco biológicos conhecidos associados à pobreza e à desinformação.Universidade Federal de São Paulo (UNIFESP)UNIFESPSciEL