Analytical solution of a multidimensional Langevin equation at high friction limits and probability passing over a two-dimensional saddle

The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.

Probability distribution of the four-phase structure invariants of isomorphously related structure factors and its applications

The probability distribution of the four-phase structure invariants (4PSIs) involving four pairs of structure factors is derived by integrating the direct methods with isomorphous replacement (IR). A simple expression of the reliability parameter for 16 types of invariant is given in the case of a native protein and a heavy-atom derivative. Test calculations on a protein and its heavy-atom derivative using experimental diffraction data show that the reliability for 4PSI estimates is comparable with that for the three-phase structure invariants (3PSIs), and that a large-modulus invariants method can be used to improve the accuracy.

Probability distribution of random wave-current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave-wave and wave-current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan-Pierson-Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. (c) 2006 Elsevier Ltd. All rights reserved.

Fuzzy ARTMAP, Slow Learning and Probability Estimation

A nonparametric probability estimation procedure using the fuzzy ARTMAP neural network is here described. Because the procedure does not make a priori assumptions about underlying probability distributions, it yields accurate estimates on a wide variety of prediction tasks. Fuzzy ARTMAP is used to perform probability estimation in two different modes. In a 'slow-learning' mode, input-output associations change slowly, with the strength of each association computing a conditional probability estimate. In 'max-nodes' mode, a fixed number of categories are coded during an initial fast learning interval, and weights are then tuned by slow learning. Simulations illustrate system performance on tasks in which various numbers of clusters in the set of input vectors mapped to a given class.

A Fuzzy ARTMAP Nonparametric Probability Estimator For Nonstationary Pattern Recognition Problem

An incremental, nonparametric probability estimation procedure using the fuzzy ARTMAP neural network is introduced. In slow-learning mode, fuzzy ARTMAP searches for patterns of data on which to build ever more accurate estimates. In max-nodes mode, the network initially learns a fixed number of categories, and weights are then adjusted gradually.

An Integrated Neural Network-Event-Related Potentials Model of Temporal and Probability Context Effects on Event Categorization

We present a neural network that adapts and integrates several preexisting or new modules to categorize events in short term memory (STM), encode temporal order in working memory, evaluate timing and probability context in medium and long term memory. The model shows how processed contextual information modulates event recognition and categorization, focal attention and incentive motivation. The model is based on a compendium of Event Related Potentials (ERPs) and behavioral results either collected by the authors or compiled from the classical ERP literature. Its hallmark is, at the functional level, the interplay of memory registers endowed with widely different dynamical ranges, and at the structural level, the attempt to relate the different modules to known anatomical structures.

Practical wireless sensor networks power consumption metrics for building energy management applications

The power consumption of wireless sensor networks (WSN) module is an important practical concern in building energy management (BEM) system deployments. A set of metrics are created to assess the power profiles of WSN in real world condition. The aim of this work is to understand and eventually eliminate the uncertainties in WSN power consumption during long term deployments and the compatibility with existing and emerging energy harvesting technologies. This paper investigates the key metrics in data processing, wireless data transmission, data sensing and duty cycle parameter to understand the system power profile from a practical deployment prospective. Based on the proposed analysis, the impacts of individual metric on power consumption in a typical BEM application are presented and the subsequent low power solutions are investigated.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Scale-wise evolution of rainfall probability density functions fingerprints the rainfall generation mechanism

© 2010 by the American Geophysical Union.The cross-scale probabilistic structure of rainfall intensity records collected over time scales ranging from hours to decades at sites dominated by both convective and frontal systems is investigated. Across these sites, intermittency build-up from slow to fast time-scales is analyzed in terms of heavy tailed and asymmetric signatures in the scale-wise evolution of rainfall probability density functions (pdfs). The analysis demonstrates that rainfall records dominated by convective storms develop heavier-Tailed power law pdfs toward finer scales when compared with their frontal systems counterpart. Also, a concomitant marked asymmetry build-up emerges at such finer time scales. A scale-dependent probabilistic description of such fat tails and asymmetry appearance is proposed based on a modified q-Gaussian model, able to describe the cross-scale rainfall pdfs in terms of the nonextensivity parameter q, a lacunarity (intermittency) correction and a tail asymmetry coefficient, linked to the rainfall generation mechanism.