Biological applications of the theory of birth-and-death processes

In this review, we discuss the applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principles of the theory of these processes are briefly described. Birth-and-death processes, with some straightforward additions such as innovation, are a simple, natural formal framework for modeling a vast variety of biological processes such as population dynamics, speciation, genome evolution, including growth of paralogous gene families and horizontal gene transfer, and somatic evolution of cancers. We further describe how empirical data, e.g., distributions of paralogous gene family size, can be used to choose the model that best reflects the actual course of evolution among different versions of birth-death-and-innovation models. It is concluded that birth-and-death processes, thanks to their mathematical transparency, flexibility and relevance to fundamental biological process, are going to be an indispensable mathematical tool for the burgeoning field of systems biology.Comment: 29 pages, 4 figures; submitted to "Briefings in Bioinformatics

Exploring young students creativity: The effect of model eliciting activities

The aim of this paper is to show how engaging students in real-life mathematical situations can stimulate their mathematical creative thinking. We analyzed the mathematical modeling of two girls, aged 10 and 13 years, as they worked on an authentic task involving the selection of a track team. The girls displayed several modeling cycles that revealed their thinking processes, as well as cognitive and affective features that may serve as the foundation for a methodology that uses model-eliciting activities to promote the mathematical creative process

Sequential and asynchronous processes driven by stochastic or quantum grammars and their application to genomics: a survey

We present the formalism of sequential and asynchronous processes defined in terms of random or quantum grammars and argue that these processes have relevance in genomics. To make the article accessible to the non-mathematicians, we keep the mathematical exposition as elementary as possible, focusing on some general ideas behind the formalism and stating the implications of the known mathematical results. We close with a set of open challenging problems.Comment: Presented at the European Congress on Mathematical and Theoretical Biology, Dresden 18--22 July 200

COLLABORATIVE SYSTEMS AND MATHEMATICAL MODELS FOR LEADING ECONOMIC PROCESSES

A collaborative system is an interdisciplinary field located at the intersection of economics, computer science, management and sociology. These systems are focused on building connections between people, equipment and information. In the context of collaborative systems, the mathematical models used to simulate business processes provide information for building applications that help optimizing the business processes and contribute to sustaining economic decisions.collaborative system, mathematical model, simulation, repair, maintenance

The check problem of food thermal processes: A mathematical solution

To calculate the sterilizing value U, and hence, the microbial lethality F in thermal processes of the canned food, starting from the knowledge of heating time B, a mathematical modeling was carried out. Therefore it\u2019s useful to verify the desired microbial destruction (check problem) and it was obtained by reversing the mathematical approach carried out in a previous work [23] for the design problem, namely to calculate the retort heating time B, starting from a desired lethality F and, hence from the fh/U parameter. A comparison between the predicted fh/U, related to the lethality F calculated with the mathematical model of the present work and the desired Stumbo\u2019s values of fh/U, provided the following statistical indices: a mean relative error MRE=1.18\ub12.11%, a mean absolute error MAE=1.61\ub111.7 and a determination coefficient R2=0.991, better than ANN models. The mathematical procedure, quickly usable also with a spreadsheet, replaces the 57 Stumbo\u2019s tables and 18512 data sets in the Ball formula method

Delayed and rushed motions through time change

We introduce a definition of delayed and rushed processes in terms of lifetimes of base processes and time-changed base processes. Then, we consider time changes given by subordinators and their inverse processes. Our analysis shows that, quite surprisingly, time-changing with inverse subordinators does not necessarily imply delay of the base process. Moreover, time-changing with subordinators does not necessarily imply rushed base process.Comment: to appear on ALEA - Latin American Journal of Probability and Mathematical Statistic