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

Wine research has as its core components the disciplines of sensory analysis, viticulture, and oenology. Wine quality is an important concept for each of these disciplines, as well as for both wine producers and consumers. Any technique that could help producers to understand the nature of wine quality and how consumers perceive it, will help them to design even more effective marketing strategies. However, predicting a wine’s quality presents wine science modelling with a real challenge. We used sample data from Pinot noir wines from different regions of New Zealand to develop a mathematical model that can predict wine quality, and applied dimensional analysis with the Buckingham Pi theorem to determine the mathematical relationship among different chemical and physiochemical compounds. This mathematical model used perceived wine quality indices investigated by wine experts and industry professionals. Afterwards, machine learning algorithms are applied to validate the relevant sensory and chemical concepts. Judgments of wine intrinsic attributes, including overall quality, were made by wine professionals to two sets of 18 Pinot noir wines from New Zealand. This study develops a conceptual and mathematical framework to predict wine quality, and then validated these using a large dataset with machine learning approaches. It is worth noting that the predicted wine quality indices are in good agreement with the wine experts’ perceived quality ratings.

/pdf/understanding-quality-of-pinot-noir-wine-can-modelling-and-13mcwxmx.pdf

Understanding Quality of Pinot Noir Wine: Can Modelling and Machine Learning Pave the Way?

The master equation is a first-order integro-differential equation, which relates any function with the derivatives (function value or dependent variable). The function usually represents the physical or chemical quantities, while the derivative represents the changes with respect to time.

A Review and Challenges in Chemical Master Equation

Regulation of Meiosis Initiation before the Commitment Point in Budding Yeast: A Review of Biology, Molecular Mechanisms and Related Mathematical Models

The price of the New Zealand wool clip has steadily decreased over the years and the incumbent practitioners are looking for ways to increase the price. The price of the wool is determined by the marketing approaches that are adopted. An auction system is one of the wool marketing approaches and a total of 45% of the New Zealand wool clip is traded via auction (WIN, 2007).This auction is the English open out-cry public auction which has been running for the last 150 years in New Zealand. The key players of the auction (buyers, brokers and growers) as well as the New Zealand government are trying to understand the reasons behind the steady decrease in the price of the New Zealand wool clip. Further, the incumbent practitioners are questioning the auction system and looking for alternative ways of wool marketing. In this study, an attempt is made to model auction data. The data is available from the only auction centre in the South Island of New Zealand in Christchurch. Analytical approaches are used in developing the models from the data. Before fitting the data into the models, the database is thoroughly cleaned and a necessary and sufficient set of the parameters is produced by developing the approximation equations. The probability distributions of the parameters in the data base are observed. Best fitted distributions for all physical parameters are observed in terms of three measures namely mean square error, the chi-square and Kolmogorov-Smirnov (K-S) goodness-of-fit hypothesis tests. The cleaned database is used in the models. The models are developed to predict the price of the different types of wool. The price from the auction centre and the predicted price are compared. The models based on linear regression analysis, multiple regression analysis and principal component analysis are developed. The developed regression models are tested for the goodness-of-fit against coefficient of determination, R 2 , which describes the proportion of variability in the data set accounted for by the model. The model from the principal component analysis is used for the possible dimensionality reduction in the data set. The developed models and the physical parameters of wool are discussed. The role of physical parameters that account for the price of wool in the auction system is investigated. It is hoped that the analysis of auction database and the developed models will help the practitioners of the New Zealand wool industry in better understanding the role of physical parameters of wool and the price formation of it.

/pdf/investigating-the-price-of-the-new-zealand-wool-clip-using-56jyiw42az.pdf

Investigating the price of the New Zealand wool clip using modelling approaches

Cows with specialised characteristics and requirements can be aggregated into different herds for targeted nutri-tional management and to facilitate on-farm segregation of raw milk for the production of high-value niche dairy products, offering improved economic returns. Rapid methods for independent verification of product quality and origin are desirable to support validation and traceability of such products. This study examined the use of near infrared spectroscopy (NIRS) to segregate raw milk from individual cows of multiple breeds from different herds fed on the same or differing feeding regimes, and to correlate and evaluate the efficacy of the predictions for crude protein and the milk fatty acid (FA) phenotypes for each of the herds. Reference values and near infrared spectra were obtained from representative freeze-dried raw milk samples (n = 220) collected from 847 lactating cows of 3 breeds from the Lincoln University dairy farm in New Zealand. The feed sources (i.e. pasture or pasture with lucerne silage) significantly influenced the protein and the FA values, and these differences were reflected in NIRS analyses. The partial least square regression models for crude protein determination showed excellent results, whereas for the most dominant FA, they were not appreciable. Maximum separation was obtained between the herds on the same feeding regime (mean specificity = 95.2%) using the partial least square discriminant analysis, and its overall performance in differentiating the objects was better than that of the soft independent modelling of class analogy. The multiclass analyses conducted in this study offer improvements to current approaches for evaluating and validating raw milk for the manufacture of specific dairy products, and for enhancing product traceability.

/pdf/efficacy-of-near-infrared-spectroscopy-to-segregate-raw-milk-2pypqkvc87.pdf

Don Kulasiri

Papers

Understanding Quality of Pinot Noir Wine: Can Modelling and Machine Learning Pave the Way?

A Review and Challenges in Chemical Master Equation

Regulation of Meiosis Initiation before the Commitment Point in Budding Yeast: A Review of Biology, Molecular Mechanisms and Related Mathematical Models

Investigating the price of the New Zealand wool clip using modelling approaches

Efficacy of near infrared spectroscopy to segregate raw milk from individual cows between herds for product innovation and traceability