Molecular and Mathematical Biology, Chemistry, Medicine and Medical Statistics, Bioinformatics and Numerical Analysis

This second volume of Series in Advanced Sciences is devoted to Mathematics and Statistics, in particular, with applications to Biology, Medicine and Computer Science. Life Sciences have become central in scientific research for years now, both for their wide range of advanced applications and for their usefulness in the treatment of complex and/or rare diseases affecting mankind. For example, experimentalists in biology, ecology and chemistry are increasingly looking at the methods and simulation tools that mathematicians, statisticians, physicists and computer scientists can offer trying to gain insights into the physical phenomena they are involved in. This Volume opens with a thorough review by A. Tamborra and M. Bianchi on T regulatory cells and their biotechnological use. The second contribution by E. Bisquoli and V. Fusi is in the field of Chemistry and focuses on radiopharmaceutical designed for theranostic applications in medicine. M. Rocchi presents some key probabilistic-statistical techniques that were used by police investigative units on a recent Italian crime, while C. Rocchi, G. Jorio and M. Silvestrini focused on epilepsy as a medical prognostic factor in high grade gliomas. We wished that this first part of the volume, mainly involved in biological, biotechnological and medical applications ended with a mini-review based on Leonardo Urbinati\u2019s graduation thesis on the applications of the CRISPR technology in the treatment of HIV. Leonardo was a student of M. Carletti\u2019s at the Degree course in Biotechnology of the University of Urbino C. Bo in the years 2014-2017, who unexpectedly left us on December 22, 2018, right at the beginning of his master in Bioinformatics at the University of Bologna. We are so grateful to Leonardo\u2019s family for giving us the permission to let his thesis published, though in a minimum part, and thus be known by his friends and anyone else who had the privilege of being in contact with him. We sincerely thank our friend and Professor Marzia Bianchi, Leonardo\u2019s supervisor, who accepted to write the mini-review on his behalf. The second part of the volume is mainly concerned with applications of mathematics in different fields. A. Rizzo and M. Carletti propose a review in mathematical biology, regarding stochastic modeling of tumor-induced angiogenesis. The penultimate two papers deal with the mathematical modeling of bio\u2013medical problems and their solution, by means of iterative numerical methods from linear algebra and differential equations, and the related convergence issues. In particular, the sixth article discusses the influence, on convergence, of Nonnegative Matrix Factorization initialization techniques for the analysis of microarray data and the extraction of information on biological processes interactions, while the seventh article focuses on stiff differential systems, arising in bio\u2013medical applications, and presents a new strategy for stiffness detection and for switching between stiff/non-stiff solvers. The last paper presents an excursus into the history of differential equations, and describes the theoretical development of methods for the integration of first-order ordinary differential equations, from Leibniz to the Bernoulli brothers, Manfredi, Hermann and, above all, Riccati, which led to our current knowledge