THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

https://www.chester.ac.uk/sites/files/chester/rep377.pdf

Analysis of Fractional Differential Equations

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Signal sequences: The limits of variation

New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection—Diffusion Equations

Diabetes Mellitus is a metabolic disorder which may result in severe and potentially fatal complications if not well-treated and monitored. In this study, a quantitative analysis of the data collected using CGM (Continuous Glucose Monitoring) devices from six subjects with type 2 diabetes in good metabolic control at the University Polyclinic Agostino Gemelli, Catholic University of the Sacred Heart, is carried out. In particular, a system of random ordinary differential equations whose state variables are affected by a sequence of stochastic perturbations is proposed and used to extract more informative inferences from the patients' data. For this work, Matlab and R programs were used to find the most appropriate values of parameters (according to the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC)) in models for each patient. Specifically, the fitting was carried out by using the Particle Swarm Optimization Method to minimize the ordinary least squares error between the observed CGM data and the data from the random ODE model. Goodness of fit tests were made in order to assess whether or not the exponential distribution, whose parameter had been estimated by Maximum Likelihood Estimation, was suitable for representing the waiting times computed from the model parameters. Finally, both parametric and non-parametric density estimation of the frequency histograms associated with the variability of the glucose elimination rate from blood into the external environment were conducted and their representative parameters assessed from the data. The results show that the chosen models succeed in capturing most of the glucose fluctuations for almost every patient.

A System of Random ODEs for Representing Trends of CGM Signals

Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible S, infected I, removed R and dead people D. In order to have a cross validation, a deterministic version of such a model is also devised which is represented by a system of ordinary differential equations with delays. In the second stochastic model two further compartments are added: the class A of asymptomatic individuals and the class L of isolated infected people. Effects such as social distancing measures are easily included and the consequences are analyzed. Numerical solutions are obtained with Monte Carlo simulations. Quantitative predictions are provided which can be useful for the evaluation of political measures, e.g. the obtained results suggest that strategies based on herd immunity are too risky. Finally, the models are calibrated on data referring to the second wave of infection in Italy.

/pdf/continuous-time-stochastic-processes-for-the-spread-of-covid-59xxj4pk5c.pdf

Continuous-time stochastic processes for the spread of COVID-19 disease simulated via a Monte Carlo approach and comparison with deterministic models.

Modeling the Heating of Semiconductor Crystal Lattice Based on the Maximum Entropy Principle

The doping profile optimization in semiconductor has been tackled as a constrained optimization problem coupled with a drift-diffusion model to simulate the physical phenomenon. A new population-based algorithm, the Constrained Immunological Algorithm, has been introduced and the experimental results confirm that clearly outperforms previous state-of-theart algorithms in doping profile optimization. Supplementary Materials: more numerical results are available at http://www.dmi.unict.it/∼stracquadanio/semiconductors.html.

Vittorio Romano

Papers

A System of Random ODEs for Representing Trends of CGM Signals

Continuous-time stochastic processes for the spread of COVID-19 disease simulated via a Monte Carlo approach and comparison with deterministic models.

Modeling the Heating of Semiconductor Crystal Lattice Based on the Maximum Entropy Principle

Doping profile optimization in semiconductor design

Nonlinear Wave Propagation in AN Elastic Soil