A General Method for the Calculation of Axis-crossing Moments Technical Report No. 5

Calculating axis-crossing moments by stochastic proces

Development of reliability methodology for systems engineering. Volume III - Theoretical investigations - An approach to a class of reliability problems Final report

Random quantities from continuous time stochastic process with application to reliability and probabilit

On certain functionals of normal processes Technical report no. 1

Probabilistic modeling and stochastic process investigations to provide measures of quality of performance and reliability for systems engineering - Chebyshev approximatio

Theory of spike timing based neural classifiers

We study the computational capacity of a model neuron, the Tempotron, which classifies sequences of spikes by linear-threshold operations. We use statistical mechanics and extreme value theory to derive the capacity of the system in random classification tasks. In contrast to its static analog, the Perceptron, the Tempotron's solutions space consists of a large number of small clusters of weight vectors. The capacity of the system per synapse is finite in the large size limit and weakly diverges with the stimulus duration relative to the membrane and synaptic time constants.Comment: 4 page, 4 figures, Accepted to Physical Review Letters on 19th Oct. 201

Semantic linking of complex properties, monitoring processes and facilities in web-based representations of the environment

Where a virtual representation of the Earth must contain data values observed within the physical Earth system, data models are required that allow the integration of data across the silos of various Earth and environmental sciences domains. Creating a mapping between the well-defined terminologies of these silos is a stubborn problem. This paper presents a generalised ontology for use within Web 3.0 services, which builds on European Commission spatial data infrastructure models. The presented ontology acknowledges that there are many complexities to the description of environmental properties which can be observed within the physical Earth system. The ontology is shown to be flexible and robust enough to describe concepts drawn from a range of Earth science disciplines, including ecology, geochemistry, hydrology and oceanography. This paper also demonstrates the alignment and compatibility of the ontology with existing systems and shows applications in which the ontology may be deployed

On smoothed probability density estimation for stationary processes

Aspects of estimation of the (marginal) probability density for a stationary sequence or continuous parameter process, are considered in this paper. Consistency and asymptotic distributional results are obtained using a class of smoothed function estimators including those of kernel type, under various decay of dependence conditions for the process. Some of the consistency results contain convergence rates which appear to be more delicate than those previously available, even for i.i.d. sequences

Palm distributions of wave characteristics in encountering seas

Distributions of wave characteristics of ocean waves, such as wave slope, waveheight or wavelength, are an important tool in a variety of oceanographic applications such as safety of ocean structures or in the study of ship stability, as will be the focus in this paper. We derive Palm distributions of several wave characteristics that can be related to steepness of waves for two different cases, namely for waves observed along a line at a fixed time point and for waves encountering a ship sailing on the ocean. The relation between the distributions obtained in the two cases is also given physical interpretation in terms of a ``Doppler shift'' that is related to the velocity of the ship and the velocities of the individual waves.Comment: Published in at http://dx.doi.org/10.1214/07-AAP480 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function

We argue that the freezing transition scenario, previously explored in the statistical mechanics of 1/f-noise random energy models, also determines the value distribution of the maximum of the modulus of the characteristic polynomials of large N x N random unitary (CUE) matrices. We postulate that our results extend to the extreme values taken by the Riemann zeta-function zeta(s) over sections of the critical line s=1/2+it of constant length and present the results of numerical computations in support. Our main purpose is to draw attention to possible connections between the statistical mechanics of random energy landscapes, random matrix theory, and the theory of the Riemann zeta function.Comment: published version with a few misprints corrected and references adde

Ground State Energy of the One-Dimensional Discrete Random Schr\"{o}dinger Operator with Bernoulli Potential

In this paper, we show the that the ground state energy of the one dimensional Discrete Random Schroedinger Operator with Bernoulli Potential is controlled asymptotically as the system size N goes to infinity by the random variable \ell_N, the length the longest consecutive sequence of sites on the lattice with potential equal to zero. Specifically, we will show that for almost every realization of the potential the ground state energy behaves asymptotically as $\frac{\pi^2}{\ell_N+1)^2}$ in the sense that the ratio of the quantities goes to one

Extreme value statistics and return intervals in long-range correlated uniform deviates

We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to minimum are such that the reference point from which the maximum is measured is itself a random quantity. We analytically calculate the limiting distributions for independent and identically distributed random variables, and use these as a reference point for correlated cases. The distributions are different from that of the maximum itself i.e., a Weibull distribution, reflecting the fact that the distribution of the reference point either dominates over or convolves with the distribution of the maximum. The functional form of the limiting distributions is unaffected by correlations, although the convergence is slower. We show that our findings can be directly generalized to a wide class of stochastic processes. We also analyze return interval distributions, and compare them to recent conjectures of their functional form