随机过程动态自适应小波独立网格多尺度模拟

在随机过程数值仿真中,由多项式混沌展开谱方法得到求解展开系数的确定性偶合方程组。该方程组比相应的确定性仿真时增大许多。并且当多项式展开阶数和随机空间维数提高时,方程维数急剧增加。由于待求未知分量为表征不同尺度波动的混沌展开模,形成节点意义下的的多尺度问题,传统的网格细分自适应逼近不再适用。为此我们采用了小波的多尺度离散,并建立基于空间细化的动态自适应系统,让每个求解点上的多个未知分量有各自独立的小波网格。本文以随机对流扩散方程为例,进行了二个算例的数值实验,论证了此方法的优点。     

Minimalist molecular model for nanopore selectivity

Using a simple model it is shown that the cost of constraining a hydrated potassium ion inside a narrow nanopore is smaller than the cost of constraining the smaller hydrated sodium ion. The former allows for a greater distortion of its hydration shell and can therefore maintain a better coordination. We propose that in this way the larger ion can go through narrow pores more easily. This is relevant to the molecular basis of ion selective nanopores and since this mechanism does not depend on the molecular details of the pore, it could also operate in all sorts of nanotubes, from biological to synthetic.     

Correlations of record events as a test for heavy-tailed distributions

A record is an entry in a time series that is larger or smaller than all previous entries. If the time series consists of independent, identically distributed random variables with a superimposed linear trend, record events are positively (negatively) correlated when the tail of the distribution is heavier (lighter) than exponential. Here we use these correlations to detect heavy-tailed behavior in small sets of independent random variables. The method consists of converting random subsets of the data into time series with a tunable linear drift and computing the resulting record correlations.     

A fully vectorial effective index method to analyse the propagation properties of microstructured fiber

Based on numerical simulation, we theoretically study the linear and nonlinear properties of microstructured fiber. Using the fully vectorial effective index method, we calculate the effective refractive index for different air hole size. We show how the linear properties such as spot size, numerical aperture, splice loss and bend loss can be controled by changing the air hole size. We also propose the same method for analysing effective area and self-phase modulation of microstructured fiber for different designing parameters. We compare all our results with other numerical methods.     

The Role of Instrumental Variables in Causal Inference Based on Independence of Cause and Mechanism

Causal inference methods based on conditional independence construct Markov equivalent graphs and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal discovery can be inferred for two observations. In our contribution, we pose a challenge to reconcile these two research directions. We study the role of latent variables such as latent instrumental variables and hidden common causes in the causal graphical structures. We show that methods based on the independence of cause and mechanism indirectly contain traces of the existence of the hidden instrumental variables. We derive a novel algorithm to infer causal relationships between two variables, and we validate the proposed method on simulated data and on a benchmark of cause-effect pairs. We illustrate by our experiments that the proposed approach is simple and extremely competitive in terms of empirical accuracy compared to the state-of-the-art methods.     

Multiple time scale analysis of two models for the peroxidase-oxidase reaction

A multiple time scale analysis of two four-variable models of the peroxidase-oxidase reaction, the DOP, and the Olsen model, is carried out. It is shown that autonomous limit cycle oscillations are exhibited by the fast subsets of these two models, but only in certain regions of parameter space, confirming the prior suggestion that the slow variable (NADH) is not essential for oscillatory behavior. However, it is found that the slow variable is essential for oscillatory behavior over other ranges of parameter values, and is always essential for complex oscillatory and chaotic behavior. This latter conclusion is based on a study involving driving the fast subset with a sinusoidally varying (NADH). This study suggests the level of coupling between fast and slow variables of an autonomous system necessary to cause the chaos observed in the DOP model. Further study of the driven system allows for the identification of a natural period of the nonoscillatory but bistable fast subsystem and a set of rules for applying a parametric driving in such a way as to generate a more complete Farey sequence from a truncated Farey sequence. These conclusions are used to compare the very similar DOP and Olsen models, which, nevertheless, exhibit quite different Farey sequences and routes to chaos. (c) 1995 American Institute of Physics.     

Evaluation of the scientific impact,productivity and biological age based upon the h‐index in three Latin American countries: the materials science case

We discuss the scientific impact of Latin American scientists in the field of materials science. The analysis is based on the h‐index as the scientometric index used to quantify the scientific productivity of an individual. In particular, we focus our analysis in México, Chile and Colombia. We compare the level of productivity between all these countries. We also analyzed the h‐index as function of the biological age, by using the first year of publication of a given scientists as a reference and discussed the general distribution of its quantification. We do not find a clear relationship between these two quantities. Based in our results we propose some political measures that these countries could implement to improve productivity as well as scientific development in this field.     

Fast tunable coupler for superconducting qubits

A major challenge in the field of quantum computing is the construction of scalable qubit coupling architectures. Here, we demonstrate a novel tunable coupling circuit that allows superconducting qubits to be coupled over long distances. We show that the interqubit coupling strength can be arbitrarily tuned over nanosecond time scales within a sequence that mimics actual use in an algorithm. The coupler has a measured on/off ratio of 1000. The design is self-contained and physically separate from the qubits, allowing the coupler to be used as a module to connect a variety of elements such as qubits, resonators, amplifiers, and readout circuitry over distances much larger than nearest-neighbor. Such design flexibility is likely to be useful for a scalable quantum computer.     

Causality-based criteria for a negative refractive index must be used with care

Using the principle of causality as expressed in the Kramers-Kronig relations, we derive a generalized criterion for a negative refractive index that admits imperfect transparency at an observation frequency omega. It also allows us to relate the global properties of the loss (i.e., its frequency response) to its local behavior at omega. However, causality-based criteria rely on the group velocity, not the Poynting vector. Since the two are not equivalent, we provide some simple examples to compare the two criteria.     

Torus Fibrations and Localization of Index II

We give a framework of localization for the index of a Dirac-type operator on an open manifold. Suppose the open manifold has a compact subset whose complement is covered by a family of finitely many open subsets, each of which has a structure of the total space of a torus bundle. Under an acyclic condition we define the index of the Dirac-type operator by using the Witten-type deformation, and show that the index has several properties, such as excision property and a product formula. In particular, we show that the index is localized on the compact set.     

Fluorescence lifetime distributions in membrane systems

Membranes are complex biological systems that display heterogeneity at all spatial scales. At a molecular level, the heterogeneity arises from lipid and protein composition. At the cellular level, heterogeneity is due to membrane organization and large scale morphology. A quantitative evaluation of membrane heterogeneity at a microscopic level is very important for several fields of membrane studies. We have developed a method for the analysis of the decay of fluorescent membrane probes that can provide a quantity sensitive to membrane heterogeneity. This method is based on the analysis of the fluorescence decay using continuous lifetime distributions. The major challenge in the interpretation of the analysis results is in the identification, at a molecular level, of the mechanisms that influence the fluorescence decay. In this review we illustrate the principles of data analysis and we show examples of identification of the measured parameters with specific variables that affect membrane heterogeneity.     

Statistical properties of agent-based models in markets with continuous double auction mechanism

Real world markets display power-law features in variables such as price fluctuations in stocks. To further understand market behavior, we have conducted a series of market experiments on our web-based prediction market platform which allows us to reconstruct transaction networks among traders. From these networks, we are able to record the degree of a trader, the size of a community of traders, the transaction time interval among traders and other variables that are of interest. The distributions of all these variables show power-law behavior. On the other hand, agent-based models have been proposed to study the properties of real financial markets. We here study the statistical properties of these agent-based models and compare them with the results from our web-based market experiments. In this work, three agent-based models are studied, namely, zero-intelligence (ZI), zero-intelligence-plus (ZIP) and Gjerstad-Dickhaut (GD). Computer simulations of variables based on these three agent-based models were carried out. We found that although being the most naive agent-based model, ZI indeed best describes the properties observed in real markets. Our study suggests that the basic ingredient to produce the observed properties from real world markets could in fact be the result of a continuously evolving dynamical system with basic features similar to the ZI model.     

Rapid nondestructive analysis of threading dislocations in wurtzite materials using the scanning electron microscope

We describe the use of electron channeling contrast imaging in the scanning electron microscope to rapidly and reliably image and identify threading dislocations (TDs) in materials with the wurtzite crystal structure. In electron channeling contrast imaging, vertical TDs are revealed as spots with black-white contrast. We have developed a simple geometric procedure which exploits the differences observed in the direction of this black-white contrast for screw, edge, and mixed dislocations for two electron channeling contrast images acquired from two symmetrically equivalent crystal planes whose g vectors are at 120° to each other. Our approach allows unambiguous identification of all TDs without the need to compare results with dynamical simulations of channeling contrast.     

First-principles constitutive equation for suspension rheology

Using mode-coupling theory, we derive a constitutive equation for the nonlinear rheology of dense colloidal suspensions under arbitrary time-dependent homogeneous flow. Generalizing previous results for simple shear, this allows the full tensorial structure of the theory to be identified. Macroscopic deformation measures, such as the Cauchy-Green tensors, thereby emerge. So does a direct relation between the stress and the distorted microstructure, illuminating the interplay of slow structural relaxation and arbitrary imposed flow. We present flow curves for steady planar and uniaxial elongation and compare these to simple shear. The resulting nonlinear Trouton ratios point to a tensorially nontrivial dynamic yield condition for colloidal glasses.     

Concise presentation of the Coulomb electrostatic potential of a uniformly charged cube

We use a novel method to calculate in closed form the Coulomb electrostatic potential created by a uniformly charged cube at an arbitrary point in space. We apply a suitable transformation of variables that allows us to obtain a simple presentation of the electrostatic potential in one-dimensional integral form. The final concise closed form expression of the Coulomb electrostatic potential of the uniformly charged cube is obtained after completing the calculation of the resulting one-dimensional integrals. Such integrals consist of combinations of products of error functions and power functions that can be solved exactly despite their intimidating appearance. The exact analytic formula for the Coulomb electrostatic potential that we derive reflects the symmetry of the cube and is easy to implement. We illustrate its use by calculating the exact values of the electrostatic potential at some points of symmetry such as the center of cube, center of face of cube, center of edge of cube and corner of cube.     

A simple technique for evaluation of transmission coefficient at the splice with angular offset and transverse offset for first higher mode propagation in graded index fibers

We present simple and accurate analytical expressions for transmission coefficient at the splice with angular offset and transverse offset in case of first higher mode propagation in graded index fibers. We employ the simple series expression for first higher order modal field for graded index fiber. The evaluation of the concerned parameters based on our formalism requires very little computations. Here, we show that our estimations match excellently well with the exact results in case of step and parabolic index fibers. Further, splice being highly tolerant for longitudinal separation, our analysis is judiciously restricted to the case of transverse and angular mismatches only. The analysis should find application in dual mode graded index fiber in all optical technology.     

The structure of MgO-SiO2 glasses at elevated pressure

The magnesium silicate system is an important geophysical analogue and neutron diffraction data from glasses formed in this system may also provide an initial framework for understanding the structure-dependent properties of related liquids that are important during planetary formation. Neutron diffraction data collected in situ for a single composition (38 mol% SiO(2)) magnesium silicate glass sample shows local changes in structure as pressure is increased from ambient conditions to 8.6 GPa at ambient temperature. A method for obtaining the fully corrected, total structure factor, S(Q), has been developed that allows accurate structural characterization as this weakly scattering glass sample is compressed. The measured S(Q) data indicate changes in chemical ordering with pressure and the real-space transforms show an increase in Mg-O coordination number and a distortion of the local environment around magnesium ions. We have used reverse Monte Carlo methods to compare the high pressure and ambient pressure structures and also compare the high pressure form with a more silica-poor glass (Mg(2)SiO(4)) that represents the approach to a more dense, void-free and topologically ordered structure. The Mg-O coordination number increases with pressure and we also find that the degree of continuous connectivity of Si-O bonds increases via a collapse of interstices.     

Compatibility of Subsystem States

We examine the possible states of subsystems of a system of bits or qubits. In the classical case (bits), this means the possible marginal distributions of a probability distribution on a finite number of binary variables; we give necessary and sufficient conditions for a set of probability distributions on all proper subsets of the variables to be the marginals of a single distribution on the full set. In the quantum case (qubits), we consider mixed states of subsets of a set of qubits; in the case of three qubits we find quantum Bell inequalities—necessary conditions for a set of two-qubit states to be the reduced states of a mixed state of three qubits. We conjecture that these conditions are also sufficient.     

Pitch identification of simultaneous dichotic two-tone complexes

The optimum processor theory of Goldstein can, in principle, account for pitch perception phenomena involving simultaneous dichotic complex tones. The frequency-coding noise function, which is the only free parameter of the model, was estimated with pitch identification data of two simultaneous two-tone complexes presented to different ears. This "sigma" function was found to have a shape similar to that of the function derived from data on identification performance for single pitches. The sigmas in the simultaneous pitch identification experiment are larger by an amount that differs from subject to subject. By using different methods of data analysis it was found that the pitch estimation processes for the two tones are independent for most subjects. This allows a simple extension of Goldstein's optimum processor theory.     

Knowledge Discovery for Higher Education Student Retention Based on Data Mining: Machine Learning Algorithms and Case Study in Chile

Data mining is employed to extract useful information and to detect patterns from often large data sets, closely related to knowledge discovery in databases and data science. In this investigation, we formulate models based on machine learning algorithms to extract relevant information predicting student retention at various levels, using higher education data and specifying the relevant variables involved in the modeling. Then, we utilize this information to help the process of knowledge discovery. We predict student retention at each of three levels during their first, second, and third years of study, obtaining models with an accuracy that exceeds 80% in all scenarios. These models allow us to adequately predict the level when dropout occurs. Among the machine learning algorithms used in this work are: decision trees, k-nearest neighbors, logistic regression, naive Bayes, random forest, and support vector machines, of which the random forest technique performs the best. We detect that secondary educational score and the community poverty index are important predictive variables, which have not been previously reported in educational studies of this type. The dropout assessment at various levels reported here is valid for higher education institutions around the world with similar conditions to the Chilean case, where dropout rates affect the efficiency of such institutions. Having the ability to predict dropout based on student’s data enables these institutions to take preventative measures, avoiding the dropouts. In the case study, balancing the majority and minority classes improves the performance of the algorithms.