Random walks and random numbers from supercontinuum generation

We report a numerical study showing how the random intensity and phase fluctuations across the bandwidth of a broadband optical supercontinuum can be interpreted in terms of the random processes of random walks and Lévy flights. We also describe how the intensity fluctuations can be applied to physical random number generation. We conclude that the optical supercontinuum provides a highly versatile means of studying and generating a wide class of random processes at optical wavelengths. © 2012 Optical Society of America.

Functional Transfer Theorems for Maxima of Stationary Processes

2000 Mathematics Subject Classification: 60G70, 60F12, 60G10.

Infinite-horizon policy-gradient estimation

Gradient-based approaches to direct policy search in reinforcement learning have received much recent attention as a means to solve problems of partial observability and to avoid some of the problems associated with policy degradation in value-function methods. In this paper we introduce GPOMDP, a simulation-based algorithm for generating a biased estimate of the gradient of the average reward in Partially Observable Markov Decision Processes (POMDPs) controlled by parameterized stochastic policies. A similar algorithm was proposed by Kimura, Yamamura, and Kobayashi (1995). The algorithm's chief advantages are that it requires storage of only twice the number of policy parameters, uses one free parameter β ∈ [0,1) (which has a natural interpretation in terms of bias-variance trade-off), and requires no knowledge of the underlying state. We prove convergence of GPOMDP, and show how the correct choice of the parameter β is related to the mixing time of the controlled POMDP. We briefly describe extensions of GPOMDP to controlled Markov chains, continuous state, observation and control spaces, multiple-agents, higher-order derivatives, and a version for training stochastic policies with internal states. In a companion paper (Baxter, Bartlett, & Weaver, 2001) we show how the gradient estimates generated by GPOMDP can be used in both a traditional stochastic gradient algorithm and a conjugate-gradient procedure to find local optima of the average reward. ©2001 AI Access Foundation and Morgan Kaufmann Publishers. All rights reserved.

On the computation and interpretation of auto- and cross-trispectra

This paper discusses the principal domains of auto- and cross-trispectra. It is shown that the cumulant and moment based trispectra are identical except on certain planes in trifrequency space. If these planes are avoided, their principal domains can be derived by considering the regions of symmetry of the fourth order spectral moment. The fourth order averaged periodogram will then serve as an estimate for both cumulant and moment trispectra. Statistics of estimates of normalised trispectra or tricoherence are also discussed.

Statistics of tricoherence

Statistics of the estimates of tricoherence are obtained analytically for nonlinear harmonic random processes with known true tricoherence. Expressions are presented for the bias, variance, and probability distributions of estimates of tricoherence as functions of the true tricoherence and the number of realizations averaged in the estimates. The expressions are applicable to arbitrary higher order coherence and arbitrary degree of interaction between modes. Theoretical results are compared with those obtained from numerical simulations of nonlinear harmonic random processes. Estimation of true values of tricoherence given observed values is also discussed

On the behaviour of higher-order spectral features for object recognition in the presence of various types of noise

This paper presents results on the robustness of higher-order spectral features to Gaussian, Rayleigh, and uniform distributed noise. Based on cluster plots and accuracy results for various signal to noise conditions, the higher-order spectral features are shown to be better than moment invariant features.

Spectrum sensing optimisation for dynamic primary user signal

We propose a multi-layer spectrum sensing optimisation algorithm to maximise sensing efficiency by computing the optimal sensing and transmission durations for a fast changing, dynamic primary user. Dynamic primary user traffic is modelled as a random process, where the primary user changes states during both the sensing period and transmission period to reflect a more realistic scenario. Furthermore, we formulate joint constraints to correctly reflect interference to the primary user and lost opportunity of the secondary user during the transmission period. Finally, we implement a novel duty cycle based detector that is optimised with respect to PU traffic to accurately detect primary user activity during the sensing period. Simulation results show that unlike currently used detection models, the proposed algorithm can jointly optimise the sensing and transmission durations to simultaneously satisfy the optimisation constraints for the considered primary user traffic.

Feature selection using expected attainable discrimination

We propose expected attainable discrimination (EAD) as a measure to select discrete valued features for reliable discrimination between two classes of data. EAD is an average of the area under the ROC curves obtained when a simple histogram probability density model is trained and tested on many random partitions of a data set. EAD can be incorporated into various stepwise search methods to determine promising subsets of features, particularly when misclassification costs are difficult or impossible to specify. Experimental application to the problem of risk prediction in pregnancy is described.

Dynamic stiffness matrix of a general cable element

A computational scheme for determining the dynamic stiffness coefficients of a linear, inclined, translating and viscously/hysteretically damped cable element is outlined. Also taken into account is the coupling between inplane transverse and longitudinal forms of cable vibration. The scheme is based on conversion of the governing set of quasistatic boundary value problems into a larger equivalent set of initial value problems, which are subsequently numerically integrated in a spatial domain using marching algorithms. Numerical results which bring out the nature of the dynamic stiffness coefficients are presented. A specific example of random vibration analysis of a long span cable subjected to earthquake support motions modeled as vector gaussian random processes is also discussed. The approach presented is versatile and capable of handling many complicating effects in cable dynamics in a unified manner.

Energy Harvesting WSNs for Accurately Estimating the Maximum Sensor Reading: Trade-Offs and Optimal Design

Computing the maximum of sensor readings arises in several environmental, health, and industrial monitoring applications of wireless sensor networks (WSNs). We characterize the several novel design trade-offs that arise when green energy harvesting (EH) WSNs, which promise perpetual lifetimes, are deployed for this purpose. The nodes harvest renewable energy from the environment for communicating their readings to a fusion node, which then periodically estimates the maximum. For a randomized transmission schedule in which a pre-specified number of randomly selected nodes transmit in a sensor data collection round, we analyze the mean absolute error (MAE), which is defined as the mean of the absolute difference between the maximum and that estimated by the fusion node in each round. We optimize the transmit power and the number of scheduled nodes to minimize the MAE, both when the nodes have channel state information (CSI) and when they do not. Our results highlight how the optimal system operation depends on the EH rate, availability and cost of acquiring CSI, quantization, and size of the scheduled subset. Our analysis applies to a general class of sensor reading and EH random processes.

Generalizations and extensions of the Fokker-Planck-Kolmogorov equations

The problem of determining probability density functions of general transformations of random processes is considered in this thesis. A method of solution is developed in which partial differential equations satisfied by the unknown density function are derived. These partial differential equations are interpreted as generalized forms of the classical Fokker-Planck-Kolmogorov equations and are shown to imply the classical equations for certain classes of Markov processes. Extensions of the generalized equations which overcome degeneracy occurring in the steady-state case are also obtained.

The equations of Darling and Siegert are derived as special cases of the generalized equations thereby providing unity to two previously existing theories. A technique for treating non-Markov processes by studying closely related Markov processes is proposed and is seen to yield the Darling and Siegert equations directly from the classical Fokker-Planck-Kolmogorov equations.

As illustrations of their applicability, the generalized Fokker-Planck-Kolmogorov equations are presented for certain joint probability density functions associated with the linear filter. These equations are solved for the density of the output of an arbitrary linear filter excited by Markov Gaussian noise and for the density of the output of an RC filter excited by the Poisson square wave. This latter density is also found by using the extensions of the generalized equations mentioned above. Finally, some new approaches for finding the output probability density function of an RC filter-limiter-RC filter system driven by white Gaussian noise are included. The results in this case exhibit the data required for complete solution and clearly illustrate some of the mathematical difficulties inherent to the use of the generalized equations.

Development of a triple stage heat transformer for the recycling of low temperature heat energy

Absorption heat transformers are thermodynamic systems which are capable of recycling industrial waste heat energy by increasing its temperature. Triple stage heat transformers (TAHTs) can increase the temperature of this waste heat by up to approximately 145˚C. The principle factors influencing the thermodynamic performance of a TAHT and general points of operating optima were identified using a multivariate statistical analysis, prior to using heat exchange network modelling techniques to dissect the design of the TAHT and systematically reassemble it in order to minimise internal exergy destruction within the unit. This enabled first and second law efficiency improvements of up to 18.8% and 31.5% respectively to be achieved compared to conventional TAHT designs. The economic feasibility of such a thermodynamically optimised cycle was investigated by applying it to an oil refinery in Ireland, demonstrating that in general the capital cost of a TAHT makes it difficult to achieve acceptable rates of return. Decreasing the TAHT's capital cost may be achieved by redesigning its individual pieces of equipment and reducing their size. The potential benefits of using a bubble column absorber were therefore investigated in this thesis. An experimental bubble column was constructed and used to track the collapse of steam bubbles being absorbed into a hotter lithium bromide salt solution. Extremely high mass transfer coefficients of approximately 0.0012m/s were observed, showing significant improvements over previously investigated absorbers. Two separate models were developed, namely a combined heat and mass transfer model describing the rate of collapse of the bubbles, and a stochastic model describing the hydrodynamic motion of the collapsing vapour bubbles taking into consideration random fluctuations observed in the experimental data. Both models showed good agreement with the collected data, and demonstrated that the difference between the solution's temperature and its boiling temperature is the primary factor influencing the absorber's performance.

Response to Comments on "Impacts of Biodiversity Loss on Ocean Ecosystem Services"

We show that globally declining fisheries catch trends cannot be explained by random processes and are consistent with declining stock abundance trends. Future projections are inherently uncertain but may provide a benchmark against which to assess the effectiveness of conservation measures. Marine reserves and fisheries closures are among those measures and can be equally effective in tropical and temperate areas—but must be combined with catch-, effort-, and gear restrictions to meet global conservation objectives.

The Equiprobability Bias from a Mathematical and Psychological Perspective

The equiprobability bias (EB) is a tendency to believe that every process in which randomness is involved corresponds to a fair distribution, with equal probabilities for any possible outcome. The EB is known to affect both children and adults, and to increase with probability education. Because it results in probability errors resistant to pedagogical interventions, it has been described as a deep misconception about randomness: the erroneous belief that randomness implies uniformity. In the present paper, we show that the EB is actually not the result of a conceptual error about the definition of randomness. On the contrary, the mathematical theory of randomness does imply uniformity. However, the EB is still a bias, because people tend to assume uniformity even in the case of events that are not random. The pervasiveness of the EB reveals a paradox: The combination of random processes is not necessarily random. The link between the EB and this paradox is discussed, and suggestions are made regarding educational design to overcome difficulties encountered by students as a consequence of the EB.

Statistical evidences of cyclic changes in volcanic gas chemistry composition by inverse modelling

The identification of compositional changes in fumarolic gases of active and quiescent volcanoes is one of the most important targets in monitoring programs. From a general point of view, many systematic (often cyclic) and random processes control the chemistry of gas discharges, making difficult to produce a convincing mathematical-statistical modelling. Changes in the chemical composition of volcanic gases sampled at Vulcano Island (Aeolian Arc, Sicily, Italy) from eight different fumaroles located in the northern sector of the summit crater (La Fossa) have been analysed by considering their dependence from time in the period 2000-2007. Each intermediate chemical composition has been considered as potentially derived from the contribution of the two temporal extremes represented by the 2000 and 2007 samples, respectively, by using inverse modelling methodologies for compositional data. Data pertaining to fumaroles F5 and F27, located on the rim and in the inner part of La Fossa crater, respectively, have been used to achieve the proposed aim. The statistical approach has allowed us to highlight the presence of random and not random fluctuations, features useful to understand how the volcanic system works, opening new perspectives in sampling strategies and in the evaluation of the natural risk related to a quiescent volcano