Coexistence of critical sensitivity and subcritical specificity can yield optimal population coding

The vicinity of phase transitions selectively amplifies weak stimuli, yielding optimal sensitivity to distinguish external input. Along with this enhanced sensitivity, enhanced levels of fluctuations at criticality reduce the specificity of the response. Given that the specificity of the response is largely compromised when the sensitivity is maximal, the overall benefit of criticality for signal processing remains questionable. Here it is shown that this impasse can be solved by heterogeneous systems incorporating functional diversity, in which critical and subcritical components coexist. The subnetwork of critical elements has optimal sensitivity, and the subnetwork of subcritical elements has enhanced specificity. Combining segregated features extracted from the different subgroups, the resulting collective response can maximise the tradeoff between sensitivity and specificity measured by the dynamic-range-to-noise-ratio. Although numerous benefits can be observed when the entire system is critical, our results highlight that optimal performance is obtained when only a small subset of the system is at criticality.Comment: 7 pages, 4 figure

Quantum Gibbs distribution from dynamical thermalization in classical nonlinear lattices

We study numerically time evolution in classical lattices with weak or moderate nonlinearity which leads to interactions between linear modes. Our results show that in a certain strength range a moderate nonlinearity generates a dynamical thermalization process which drives the system to the quantum Gibbs distribution of probabilities, or average oscillation amplitudes. The effective dynamical temperature of the lattice varies from large positive to large negative values depending on energy of initially excited modes. This quantum Gibbs distribution is drastically different from usually expected energy equipartition over linear modes corresponding to a regime of classical thermalization. Possible experimental observations of this dynamical thermalization are discussed for cold atoms in optical lattices, nonlinear photonic lattices and optical fiber arrays.Comment: 15 pages, 12 figures. Small modifs., video abstract 107MB at http://www.quantware.ups-tlse.fr/dima/video/gibbs2013.mp

Effective run-and-tumble dynamics of bacteria baths

{\it E. coli} bacteria swim in straight runs interrupted by sudden reorientation events called tumbles. The resulting random walks give rise to density fluctuations that can be derived analytically in the limit of non interacting particles or equivalently of very low concentrations. However, in situations of practical interest, the concentration of bacteria is always large enough to make interactions an important factor. Using molecular dynamics simulations, we study the dynamic structure factor of a model bacterial bath for increasing values of densities. We show that it is possible to reproduce the dynamics of density fluctuations in the system using a free run-and-tumble model with effective fitting parameters. We discuss the dependence of these parameters, e.g., the tumbling rate, tumbling time and self-propulsion velocity, on the density of the bath

Spaceability and algebrability of sets of nowhere integrable functions

We show that the set of Lebesgue integrable functions in $[0,1]$ which are nowhere essentially bounded is spaceable, improving a result from [F. J. Garc\'{i}a-Pacheco, M. Mart\'{i}n, and J. B. Seoane-Sep\'ulveda. \textit{Lineability, spaceability, and algebrability of certain subsets of function spaces,} Taiwanese J. Math., \textbf{13} (2009), no. 4, 1257--1269], and that it is strongly $\mathfrak{c}$-algebrable. We prove strong $\mathfrak{c}$-algebrability and non-separable spaceability of the set of functions of bounded variation which have a dense set of jump discontinuities. Applications to sets of Lebesgue-nowhere-Riemann integrable and Riemann-nowhere-Newton integrable functions are presented as corollaries. In addition we prove that the set of Kurzweil integrable functions which are not Lebesgue integrable is spaceable (in the Alexievicz norm) but not 1-algebrable. We also show that there exists an infinite dimensional vector space $S$ of differentiable functions such that each element of the $C([0,1])$-closure of $S$ is a primitive to a Kurzweil integrable function, in connection to a classic spaceability result from [V. I. Gurariy, \textit{Subspaces and bases in spaces of continuous functions (Russian),} Dokl. Akad. Nauk SSSR, \textbf{167} (1966), 971-973].Comment: Accepted for publication in 201

Dynamics and thermalization of Bose-Einstein condensate in Sinai oscillator trap

We study numerically the evolution of Bose-Einstein condensate in the Sinai oscillator trap described by the Gross-Pitaevskii equation in two dimensions. In the absence of interactions this trap mimics the properties of Sinai billiards where the classical dynamics is chaotic and the quantum evolution is described by generic properties of quantum chaos and random matrix theory. We show that, above a certain border, the nonlinear interactions between atoms lead to the emergence of dynamical thermalization which generates the statistical Bose-Einstein distribution over eigenmodes of the system without interactions. Below the thermalization border the evolution remains quasi-integrable. Such a Sinai oscillator trap, formed by the oscillator potential and a repulsive disk located in the vicinity of the center, had been already realized in rst experiments with the Bose-Einstein condensate formation by Ketterle group in 1995 and we argue that it can form a convenient test bed for experimental investigations of dynamical of thermalization. Possible links and implications for Kolmogorov turbulence in absence of noise are also discussed.Comment: 11 pages, 14 figures. Final version. Accepted forpublication at Phys. Rev. A. Additional information available at http://www.quantware.ups-tlse.fr/QWLIB/sinaioscillator

Run-and-tumble particles in speckle fields

The random energy landscapes developed by speckle fields can be used to confine and manipulate a large number of micro-particles with a single laser beam. By means of molecular dynamics simulations, we investigate the static and dynamic properties of an active suspension of swimming bacteria embedded into speckle patterns. Looking at the correlation of the density fluctuations and the equilibrium density profiles, we observe a crossover phenomenon when the forces exerted by the speckles are equal to the bacteria's propulsion

Analisis Pengaruh Financial Leverage Terhadap Return on Equity Dan Earning Per Share Pada PT Sampoerna Agro,tbk. Dan Entitas Anak

This study aims to determine the level of financial leverage, the magnitude of Return onEquity (ROE), as well as the effect of financial leverage on ROE and Earning Per Share in PTSampoerna Agro Tbk. And Subsidiaries for the year 2009 to 2013. The analysis of thisresearch includes the analysis of the level of financial leverage and financial leverage ratios,analysis of ROE, the analysis of the effect of Financial Leverage on ROE and Earnings PerShare, a simple correlation analysis, analysis simple regression, and F test. The resultsshowed that the DFL at PT Sampoerna Agro Tbk. And Subsidiaries in 2009 up to 2013continued to increase. Earning Per Share (EPS) of the company tends to fluctuate, as well asROE at PT Sampoerna Agro Tbk. and Subsidiaries. I suggest that the companies need to payattention to risk too because investors avoid stocks with high risk and add assets to boost theproductivity of the company

Dynamical thermalization of Bose-Einstein condensate in Bunimovich stadium

We study numerically the wavefunction evolution of a Bose-Einstein condensate in a Bunimovich stadium billiard being governed by the Gross-Pitaevskii equation. We show that for a moderate nonlinearity, above a certain threshold, there is emergence of dynamical thermalization which leads to the Bose-Einstein probability distribution over the linear eigenmodes of the stadium. This distribution is drastically different from the energy equipartition over oscillator degrees of freedom which would lead to the ultra-violet catastrophe. We argue that this interesting phenomenon can be studied in cold atom experiments.Comment: 6 pages, 6 figures. Accepted in Europhysics Letters. Video is available at http://www.quantware.ups-tlse.fr/QWLIB/becstadium

Renormalization group in super-renormalizable quantum gravity

One of the main advantages of super-renormalizable higher derivative quantum gravity models is the possibility to derive exact beta functions, by making perturbative one-loop calculations. We perform such a calculation for the Newton constant by using the Barvinsky-Vilkovisky trace technology. The result is well-defined in a large class of models of gravity in the sense that the renormalization group beta functions do not depend on the gauge-fixing condition. Finally, we discuss the possibility to apply the results to a large class of nonlocal gravitational theories which are free of massive ghost-like states at the tree-level.Comment: 21 pages, journal version, improved and with two new appendice