N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

Computational Analysis of Microarray Data

Most of our knowledge of biodiversity and its causes in the deep-sea benthos derives from regional-scale sampling studies of the macrofauna. Improved sampling methods and the expansion of investigations into a wide variety of habitats have revolutionized our understanding of the deep sea. Local species diversity shows clear geographic variation on spatial scales of 100-1000 km. Recent sampling programs have revealed unexpected complexity in community structure at the landscape level that is associated with large-scale oceanographic processes and their environmental consequences. We review the relationships between variation in local species diversity and the regional-scale phenomena of boundary constraints, gradients of productivity, sediment heterogeneity, oxygen availability, hydrodynamic regimes, and catastrophic physical disturbance. We present a conceptual model of how these interdependent environmental factors shape regional-scale variation in local diversity. Local communities in the deep sea may be composed of species that exist as metapopulations whose regional distribution depends on a balance among global-scale, landscape-scale, and small-scale dynamics. Environmental gradients may form geographic patterns of diversity by influencing local processes such as predation, resource partitioning, competitive exclusion, and facilitation that determine species coexistence. The measurement of deep-sea species diversity remains a vital issue in comparing geographic patterns and evaluating their potential causes. Recent assessments of diversity using species accumulation curves with randomly pooled samples confirm the often-disputed claim that the deep sea supports higher diversity than the continental shelf. However, more intensive quantitative sampling is required to fully characterize the diversity of deep-sea sediments, the most extensive habitat on Earth. Once considered to be constant, spatially uniform, and isolated, deep-sea sediments are now recognized as a dynamic, richly textured environment that is inextricably linked to the global biosphere. Regional studies of the last two decades provide the empirical background necessary to formulate and test specific hypotheses of causality by controlled sampling designs and experimental approaches.

Environmental influences on regional deep-sea species diversity

Machine Learning for Childhood Acute Lymphoblastic Leukaemia Gene Expression Data Analysis: A Review

Modeling protein-protein interactions in axon initial segment to understand their potential impact on action potential initiation

Chapter 4 - Solving Stochastic Differential Equations

This paper presents 3 NN case studies. In the first, fracture toughness of wood was predicted using an expanded MLP network from experimentally measured crack angle, stiffness, density and moisture content. The data is characterized by noise but the model produced physically meaningful nonlinear trends with an R2 value of 0.67. In the second study, hydraulic conductivity (K m/day) was estimated from ground water solute concentration data collected for a range of K values. Four separate NN needed to be developed for four sub-ranges of K to reduce error. In order to determine the appropriate range of K for a particular system concentration data were clustered into 4 groups using SOM. The hybrid-model was applied to an experimental aquifer and only 10% difference was found between experimental and NN estimations of K. In the third study, digital images of lamb chops were used to collect values for 102 geometric and textural variables for meat grading. Principal component analysis reduced the variables to twelve. Three- and four-layer MLP networks and discriminant function analysis (DFA) were performed on the data and the classification accuracy from 3-layer MLP was 83% and was 12% better than that from DFA.

/pdf/three-neural-network-case-studies-in-biology-and-natural-55ovaykxqb.pdf

Three neural network case studies in biology and natural resource management

Most Artificial Neural Networks that are widely used today focus on approximating deterministic input-output mapping of nonlinear phenomena, and therefore, they can be well trained to represent the average behaviour of a nonlinear system. However, most natural phenomena are not only nonlinear but also highly variable. Deterministic neural networks do not adequately represent the variability observed in the natural settings of a system and therefore cannot capture the complexity of the whole system behaviour that is characterised by noise. This chapter implements a class of neural networks named Stochastic Neural Networks (SNNs) to simulate internal stochastic properties of natural and biological systems. Developing a suitable mathematical model for SNNs is based on the canonical representation of stochastic processes by means of Karhunen-Loeve Theorem. In the implementation of this mathematical formulation for modelling nonlinear random processes from observed data, SNN is represented as a network of embedded deterministic neural networks, each representing a significant eigenfunction characterised by data, juxtaposed with random noise represented by White noise characterised by the corresponding eigenvalues. Two successful examples, including one from biology, are presented in the chapter to confirm the validity of the proposed SNN. Furthermore, analysis of internal working of SNNs provides an in-depth view of how SNNs work giving meaningful insights.

Don Kulasiri

Papers

Machine Learning for Childhood Acute Lymphoblastic Leukaemia Gene Expression Data Analysis: A Review

Modeling protein-protein interactions in axon initial segment to understand their potential impact on action potential initiation

Chapter 4 - Solving Stochastic Differential Equations

Three neural network case studies in biology and natural resource management

Stochastic Neural Networks for Modelling Random Processes from Observed Data