Group Testing with Blocks of Positives and Inhibitors

The main goal of group testing is to identify a small number of specific items among a large population of items. In this paper, we consider specific items as positives and inhibitors and non-specific items as negatives. In particular, we consider a novel model called group testing with blocks of positives and inhibitors. A test on a subset of items is positive if the subset contains at least one positive and does not contain any inhibitors, and it is negative otherwise. In this model, the input items are linearly ordered, and the positives and inhibitors are subsets of small blocks (at unknown locations) of consecutive items over that order. We also consider two specific instantiations of this model. The first instantiation is that model that contains a single block of consecutive items consisting of exactly known numbers of positives and inhibitors. The second instantiation is the model that contains a single block of consecutive items containing known numbers of positives and inhibitors. Our contribution is to propose efficient encoding and decoding schemes such that the numbers of tests used to identify only positives or both positives and inhibitors are less than the ones in the state-of-the-art schemes. Moreover, the decoding times mostly scale to the numbers of tests that are significantly smaller than the state-of-the-art ones, which scale to both the number of tests and the number of items.     

Memory distribution in complex fitness landscapes

In a co-evolutionary context, the survive probability of individual elements of a system depends on their relation with their neighbors. The natural selection process depends on the whole population, which is determined by local events between individuals. Particular characteristics assigned to each individual, as larger memory, usually improve the individual fitness, but an agent possesses also endogenous characteristics that induce to re-evaluate her fitness landscape and choose the best-suited kind of interaction, inducing a non-absolute value of the outcomes of the interaction. In this work, a novel model with agents combining memory and rational choice is introduced, where individual choices in a complex fitness landscape induce changes in the distribution of the number of agents as a function of time. In particular, the tail of this distribution is fat compared with distributions for agents interacting only with memory.     

FRW-Cosmological Model for Conharmonically Flat Space Time

This paper deals with FRW-Cosmological model of the universe for conharmonically flat space time. Einstein field equations with variable cosmological term are solved by using a law of variation for Hubble’s parameter, which is related to average scale factor. A new class of exact solution of the field equation has been obtained in which cosmological-term decreases with cosmic time. A detailed study of physical and kinematical properties of the model is also carried out.     

Adaptation dynamics of the quasispecies model

We study the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local peaks separated by low fitness valleys. We mainly focus on the Eigen’s model that describes the deterministic dynamics of an infinite number of self-replicating molecules. In the stationary state, for small mutation rates such a population forms a quasispecies which consists of the fittest genotype and its closely related mutants. The quasispecies dynamics on rugged fitness landscape follow a punctuated (or steplike) pattern in which a population jumps from a low fitness peak to a higher one, stays there for a considerable time before shifting the peak again and eventually reaches the global maximum of the fitness landscape. We calculate exactly several properties of this dynamical process within a simplified version of the quasispecies model.      

Diffusive Limit of a Two Dimensional Kinetic System of Partially Quantized Particles

A quantum-classical coupled system which models the diffusive transport of electrons partially confined in semiconductors nanostructures was presented in Ben Abdallah and Méhats (Proc. Edinb. Math. Soc. 49:513–549, 2006). In this model, electrons are assumed to behave like wave in the confinement direction and to have a classical behaviour in a diffusive regime in the transport direction parallel to the electron gas. It was formally derived from a kinetic system for partially quantized particles thanks to a diffusive limit when the mean free path becomes small with respect to the macroscopic length scale. This paper is devoted to the rigorous study of this limit for a transport in one dimension. In the transport direction, the motion of particles is described by a 1D Boltzmann equation. A Boltzmann-Schrödinger-Poisson system is then considered. Existence of renormalized solutions relying on the study of a quasistatic Schrödinger-Poisson system and on an entropy estimate is established. Its diffusive limit is then considered.     

A comparative study of Dirac quasinormal modes of charged black holes in higher dimensions

In this work we study the Dirac quasinormal modes of higher dimensional charged black holes. Higher dimensional Reissner–Nordström type black holes as well as charged black holes in Einstein–Gauss–Bonnet theories are studied for fermionic perturbations using WKB method. A comparative study of the quasinormal modes in the two different theories of gravity has been performed. The behavior of the frequencies with the variation of black hole parameters as well as with the variation of space-time dimensions is studied. We also study the large multipole number limit of the black hole potential in order to look for an analytic expression for the frequencies.     

Facile synthesis and characterization of high-performance NiMoO<Subscript>4</Subscript> · <Emphasis Type="Italic">x</Emphasis>H<Subscript>2</Subscript>O nanorods electrode material for supercapacitors

One-dimensional NiMoO₄ · xH₂O nanorods were synthesized by a facile template-free hydrothermal method as a potential electrode material for supercapacitors. The influences of reaction temperature, reaction time, and nickel source on the properties of resultant samples were investigated. Electrochemical data reveal that the as-synthesized one-dimensional NiMoO₄ · xH₂O nanorod superstructures can deliver a remarkable specific capacitance (SC) of 1131 F g^?1 at a current density of 1 A g^?1 and remain as high as 914 F g^?1 at 10 A g^?1 in a 6 M KOH aqueous solution. Moreover, there is only 6.2 % loss of the maximum SC after 1000 continuous charge–discharge cycles at the high current density of 10 A g^?1. Such outstanding electrochemical performance may be owing to the unique one-dimensional hierarchical structures, which can facilitate the electrolyte ions and electrons to easily contact the NiMoO₄ nanorod building blocks and then allow for sufficient faradaic reactions to take place, even at high current densities.     

A three-level analytic model for alkali metal vapor lasers: part I. Narrowband optical pumping

A three-level analytic model for optically pumped alkali metal vapor lasers is developed by considering the steady-state rate equations for the longitudinally averaged number densities of the ground ²S_1/2 and first excited ²P_3/2, and ²P_1/2 states. The threshold pump intensity includes both the requirements to fully bleach the pump transition and exceed optical losses, typically about 200  W/cm². Slope efficiency depends critically on the fraction of incident photons absorbed and the overlap of pump and resonator modes, approaching the quantum efficiency of 0.95–0.98, depending on the alkali atom. For marginal cavity transmission losses, peak performance is achieved for low output coupling mirror reflectivity. For efficient operation, the collisional relaxation between the two upper levels should be fast to prevent bottlenecking. By assuming a statistical distribution between the upper two levels, the limiting analytic solution for the quasi two-level system is achieved. For properly designed gain conditions, the quasi two-level solution is usually achievable and represents ideal performance.     

Recombination dramatically speeds up evolution of finite populations

We study the role of recombination, in the form of bacterial transformation, in speeding up Darwinian evolution. This is done by adding a new process to a previously studied Markov model of evolution on a smooth fitness landscape; this new process allows alleles to be exchanged with those in the surrounding medium. Our results, both numerical and analytic, indicate that, for a wide range of intermediate population sizes, recombination dramatically speeds up the rate of evolutionary advance.     

基于人工鱼群优化分块的多聚焦图像融合

在多聚焦图像的融合过程中,对源图像采用固定大小的分块会导致融合后的图像存在块效应、边缘模糊甚至聚焦错误。为了克服此问题,提出了一种新的基于人工鱼群优化分块的多聚焦图像融合方法。首先,将源图像分解成互不重叠的方块,利用聚焦准则选取清晰度高的方块,将已选择的方块合并重构成初始融合图像。然后,利用改进的人工鱼群优化算法,根据一定的适应度值,寻找最优大小的分块方式,获得更优的融合图像。 该方法与基于空域、频域及其他优化算法的融合方法进行了多个实验比较,结果表明,该方法获得的融合图像具有较好的客观质量和主观视觉感觉。     

基于人工鱼群优化分块的多聚焦图像融合

在多聚焦图像的融合过程中,对源图像采用固定大小的分块会导致融合后的图像存在块效应、边缘模糊甚至聚焦错误。为了克服此问题,提出了一种新的基于人工鱼群优化分块的多聚焦图像融合方法。首先,将源图像分解成互不重叠的方块,利用聚焦准则选取清晰度高的方块,将已选择的方块合并重构成初始融合图像。然后,利用改进的人工鱼群优化算法,根据一定的适应度值,寻找最优大小的分块方式,获得更优的融合图像。该方法与基于空域、频域及其他优化算法的融合方法进行了多个实验比较,结果表明,该方法获得的融合图像具有较好的客观质量和主观视觉感觉。     

Solution of the Schrödinger equation in terms of classical paths

An expression in terms of classical paths is derived for the Laplace transform $\text{Ω(s)}$ of the Green function G of the Schrödinger equation with respect to $\text{1}\text{h}\text{?}$. For an analytic potential V(r), the function Ω is also analytic in the plane of the complex action variable s; its singularities lie at the values $\text{S}$ of the action along each possible (complex) classical path, including the paths which reflect from singularities of the potential. Accordingly, G may be written as a sum of terms, each of which is associated with such a classical path, and contains the factor $\text{exp}\text{(}\text{iS}\text{h}\text{?}\text{)}$. This expansion formally solves the problem of constructing waves out of the corresponding (complex) classical paths. A similar expression, in terms of closed paths, is derived for the density ? of eigenvalues of the Schrödinger equation. In situations when the eigenvalues are dense, ? is well approximated by the contributions of the shortest closed paths: while the path of vanishing length corresponds to the Thomas-Fermi approximation and its smooth corrections, the other paths yield contributions which oscillate and are damped as $\text{exp}\text{(}\text{iS}\text{h}\text{?}\text{)}$. This result also holds for nonanalytic potentials V(r). If the spectrum is continuous, closed classical paths yield oscillations in the scattering phase-shift. The analysis is also extended to multicomponent wave functions (describing, e.g., motion of particles with spin, or coupled channel scattering); along a classical path, the internal degree of freedom varies adiabatically, except through points at which it is not coupled to the potential, where it may undergo discrete changes.     

Fluctuation Results for General Block Spin Ising Models

Journal of Statistical Physics - We study a block spin mean-field Ising model, i.e. a model of spins in which the vertices are divided into a finite number of blocks with each block having a fixed...     

Rotation numbers of periodic orbits in the Hénon map

For invertible, area-contracting maps of the plane, it is common for a basin of attraction to have a fractal basin boundary. Certain periodic orbits on the basin boundary are distinguished by being accessible (by a path) from the interior of the basin. A numerical study is made of the accessible periodic orbits for the Hénon family of maps. Theoretical results on rotary homoclinic tangencies are given, which describe the appearance of the accessible saddles, and organize them in a natural way according to the continued fractions expansions of their rotation numbers.Partially supported by the National Science FoundationPartially supported by a contract from the Applied and Computational Mathematics Program of DARPA     

Tunneling paths in multi-dimensional semiclassical dynamics

In light of the fundamental importance and renewed interest of the tunnel phenomena, we review the recent development of semiclassical tunneling theory, particularly from the view point of “tunneling path”, beginning from a simple one-dimensional formula to semiclassical theories making use of the analytic continuation, in time, coordinates, or momentum, which are the stationary solutions of semiclassical approximations to the Feynman path integrals. We also pay special attention to the instanton path and introduce various conventional and/or intuitive ideas to generate tunneling paths, to which one-dimensional tunneling theory is applied. Then, we review the recent progress in generalized classical mechanics based on the Hamilton–Jacobi equation, in which both the ordinary Newtonian solutions and the instanton paths are regarded as just special cases. Those new complex-valued solutions are generated along real-valued paths in configuration space. Such non-Newtonian mechanics is introduced in terms of a quantity called “parity of motion”. As many-body effects in tunneling, illustrative numerical examples are presented mainly in the context of the Hamilton chaos and chemical reaction dynamics, showing how the multidimensional tunneling is affected by the system parameters such as mass combination and anisotropy of potential functions.     

动态测量的高光谱图像压缩感知

针对高光谱图像相邻波段之间具有强光谱相关性的特点,为了提高高光谱图像压缩感知的重构效果,本文提出一种利用边缘信息设计动态测量率的压缩感知算法。首先,通过随机投影的分块压缩感知方法对每个图像块以固定测量率采样,重构出单波段图像作为其他波段的先验信息,并对其提取出图像边缘区域;然后,根据每个图像块边缘信息的丰富程度来自适应分配测量值。在固定总测量数的前提下,对不同图像块分配不同的测量次数。最后,利用分配好的测量次数对其余波段进行采集和重构。仿真结果表明,在相同总测量数情况下,本文提出的动态测量算法重构出的高光谱图像质量（PSNR）与传统固定测量压缩感知策略相比提高了1~4 dB,相比较下的重构时间也减少,在成功重构高光谱图像的基础上更增强了细节处的图像质量。     

Pore size assessment based on wall collision broadening of spectral lines of confined gas: experiments on strongly scattering nanoporous ceramics with fine-tuned pore sizes

Wall collision broadening of absorption lines of gases confined in porous media is a recently opened domain of high-resolution spectroscopy. Here, we present an experimental investigation of its application for pore size assessment. We report on the manufacturing of nanoporous zirconia ceramics with well-defined pore sizes fine-tuned from 50 to 150 nm. The resulting pore structure is characterized using mercury intrusion porosimetry, and the optical properties of these strongly scattering materials are measured using femtosecond photon time-of-flight spectroscopy (transport mean free paths found to be tuned from 2.3 to 1.2 μm as the pore size increase). Wall collision line broadening is studied by performing near-infrared (760 nm) high-resolution diode laser spectroscopy of confined oxygen molecules. A simple method for quantitative estimation of the pore size is outlined and shown to produce results in agreement with mercury intrusion porosimetry. At the same time, the need for improved understanding of wall collision broadening is emphasized.     

Evolutionary Accessibility in Tunably Rugged Fitness Landscapes

The adaptive evolution of a population under the influence of mutation and selection is strongly influenced by the structure of the underlying fitness landscape, which encodes the interactions between mutations at different genetic loci. Theoretical studies of such landscapes have been carried out for several decades, but only recently experimental fitness measurements encompassing all possible combinations of small sets of mutations have become available. The empirical studies have spawned new questions about the accessibility of optimal genotypes under natural selection. Depending on population dynamic parameters such as mutation rate and population size, evolutionary accessibility can be quantified through the statistics of accessible mutational pathways (along which fitness increases monotonically), or through the study of the basin of attraction of the optimal genotype under greedy (steepest ascent) dynamics. Here we investigate these two measures of accessibility in the framework of Kauffman’s LK-model, a paradigmatic family of random fitness landscapes with tunable ruggedness. The key parameter governing the strength of genetic interactions is the number K of interaction partners of each of the L sites in the genotype sequence. In general, accessibility increases with increasing genotype dimensionality L and decreases with increasing number of interactions K. Remarkably, however, we find that some measures of accessibility behave non-monotonically as a function of K, indicating a special role of the most sparsely connected, non-trivial cases K=1 and 2. The relation between models for fitness landscapes and spin glasses is also addressed.     

Optical ray paths in a quasi-periodic waveguide or a multipass cavity with smoothly varying properties

Ray paths in a quasi-periodic optical system (waveguide of cavity) with smoothly varying properties have been constructed along the ray path. The ray-transfer matrix is constructed for a large number of ray paths; it has been shown that the conventional stability condition (the modulus of the ray-transfer matrix trace for a ray path is smaller than two) does not ensure the boundedness of the beam path after a large number of paths.     

Two building blocks of microwave photonics filters in the presence of group delay ripple: a comparative survey

We have developed an analytic approach to investigate the effect of group delay ripple of the dispersive devices on the performance of two major building blocks of microwave-photonic filters. Firstly, performance of PM-based block in the presence of an arbitrary group delay ripple (GDR) is analyzed and compared with the ripple-free case to reveal the destructive effects of added group delay ripple. In the next step, we repeat the proposed approach for the AM-based one; again, the performance is compared with the ripple-free case. Two distortion metrics are also introduced to quantify this distortion. Comparison of the performance of two building blocks in the presence of group delay ripple unveils some interesting characteristics of microwave-photonic filters which have not been mentioned so far. We also add a general survey of two analyzed building blocks to present their respective most significant advantages and shortcomings. The simulated Optisystem results conform to our proposed analytical approach and verify the theoretical model.