Computation, Volume 9, Issue 10 (October 2021) – 11 articles

This paper presents the mathematical modeling and experimental implementation of a Buck converter with hysteresis control. The system is described using a state-space model. Theoretical and simulation studies show that the zero hysteresis control leads to an equilibrium point with the implication of an infinite commutation frequency, while the use of a constant hysteresis band induces a limit cycle with a finite switching frequency. There exists a tradeoff between voltage output ripple and transistor switching frequency. An experimental prototype for the Buck power converter is built, and theoretical results are verified experimentally. In general terms, the Buck converter with the hysteresis control shows a robust control with respect to load variations, with undesired high switching frequency taking place for a very narrow hysteresis band, which is solved by tuning the hysteresis band properly. Full article

Metabolic pathway analysis is a key method to study a metabolism in its steady state, and the concept of elementary fluxes (EFs) plays a major role in the analysis of a network in terms of non-decomposable pathways. The supports of the EFs contain in particular those of the elementary flux modes (EFMs), which are the support-minimal pathways, and EFs coincide with EFMs when the only flux constraints are given by the irreversibility of certain reactions. Practical use of both EFMs and EFs has been hampered by the combinatorial explosion of their number in large, genome-scale systems. The EFs give the possible pathways in a steady state but the real pathways are limited by biological constraints, such as thermodynamic or, more generally, kinetic constraints and regulatory constraints from the genetic network. We provide results on the mathematical structure and geometrical characterization of the solution space in the presence of such biological constraints (which is no longer a convex polyhedral cone or a convex polyhedron) and revisit the concept of EFMs and EFs in this framework. We show that most of the results depend only on very general properties of compatibility of constraints with vector signs: either sign-invariance, satisfied by regulatory constraints, or sign-monotonicity (a stronger property), satisfied by thermodynamic and kinetic constraints. We show in particular that the solution space for sign-monotone constraints is a union of particular faces of the original polyhedral cone or polyhedron and that EFs still coincide with EFMs and are just those of the original EFs that satisfy the constraint, and we show how to integrate their computation efficiently in the double description method, the most widely used method in the tools dedicated to EFs computation. We show that, for sign-invariant constraints, the situation is more complex: the solution space is a disjoint union of particular semi-open faces (i.e., without some of their own faces of lesser dimension) of the original polyhedral cone or polyhedron and, if EFs are still those of the original EFs that satisfy the constraint, their computation cannot be incrementally integrated into the double description method, and the result is not true for EFMs, that are in general strictly more numerous than those of the original EFMs that satisfy the constraint. Full article

Predicting the state of a dynamic system influenced by a chaotic immersion environment is an extremely difficult task, in which the direct use of statistical extrapolation computational schemes is infeasible. This paper considers a version of precedent forecasting in which we use the aftereffects of retrospective observation segments that are similar to the current situation as a forecast. Furthermore, we employ the presence of relatively stable correlations between the parameters of the immersion environment as a regularizing factor. We pay special attention to the choice of similarity measures or distances used to find analog windows in arrays of retrospective multidimensional observations. Full article

(1) Background: The estimation of daily reproduction numbers throughout the contagiousness period is rarely considered, and only their sum R₀ is calculated to quantify the contagiousness level of an infectious disease. (2) Methods: We provide the equation of the discrete dynamics of the epidemic’s growth and obtain an estimation of the daily reproduction numbers by using a deconvolution technique on a series of new COVID-19 cases. (3) Results: We provide both simulation results and estimations for several countries and waves of the COVID-19 outbreak. (4) Discussion: We discuss the role of noise on the stability of the epidemic’s dynamics. (5) Conclusions: We consider the possibility of improving the estimation of the distribution of daily reproduction numbers during the contagiousness period by taking into account the heterogeneity due to several host age classes. Full article

A class of bivariate integer-valued time series models was constructed via copula theory. Each series follows a Markov chain with the serial dependence captured using copula-based transition probabilities from the Poisson and the zero-inflated Poisson (ZIP) margins. The copula theory was also used again to capture the dependence between the two series using either the bivariate Gaussian or “t-copula” functions. Such a method provides a flexible dependence structure that allows for positive and negative correlation, as well. In addition, the use of a copula permits applying different margins with a complicated structure such as the ZIP distribution. Likelihood-based inference was used to estimate the models’ parameters with the bivariate integrals of the Gaussian or t-copula functions being evaluated using standard randomized Monte Carlo methods. To evaluate the proposed class of models, a comprehensive simulated study was conducted. Then, two sets of real-life examples were analyzed assuming the Poisson and the ZIP marginals, respectively. The results showed the superiority of the proposed class of models. Full article

Automation is becoming ubiquitous in all laboratory activities, moving towards precisely defined and codified laboratory protocols. However, the integration between laboratory protocols and mathematical models is still lacking. Models describe physical processes, while protocols define the steps carried out during an experiment: neither cover the domain of the other, although they both attempt to characterize the same phenomena. We should ideally start from an integrated description of both the model and the steps carried out to test it, to concurrently analyze uncertainties in model parameters, equipment tolerances, and data collection. To this end, we present a language to model and optimize experimental biochemical protocols that facilitates such an integrated description, and that can be combined with experimental data. We provide probabilistic semantics for our language in terms of Gaussian processes (GPs) based on the linear noise approximation (LNA) that formally characterizes the uncertainties in the data collection, the underlying model, and the protocol operations. In a set of case studies, we illustrate how the resulting framework allows for automated analysis and optimization of experimental protocols, including Gibson assembly protocols. Full article

Genetic expression analysis is a principal tool to explain the behavior of genes in an organism when exposed to different experimental conditions. In the state of art, many clustering algorithms have been proposed. It is overwhelming the amount of biological data whose high-dimensional structure exceeds mostly current computational architectures. The computational time and memory consumption optimization actually become decisive factors in choosing clustering algorithms. We propose a clustering algorithm based on Non-negative Matrix Factorization and K-means to reduce data dimensionality but whilst preserving the biological context and prioritizing gene selection, and it is implemented within parallel GPU-based environments through the CUDA library. A well-known dataset is used in our tests and the quality of the results is measured through the Rand and Accuracy Index. The results show an increase in the acceleration of 6.22× compared to the sequential version. The algorithm is competitive in the biological datasets analysis and it is invariant with respect to the classes number and the size of the gene expression matrix. Full article

There is a myriad of career opportunities stemming from science, technology, engineering, and mathematics (STEM) disciplines. In addition to careers in corporate settings, teaching is a viable career option for individuals pursuing degrees in STEM disciplines. With national shortages of secondary STEM teachers, efforts to recruit, train, and retain quality STEM teachers is greatly important. Prior to exploring ways to attract potential STEM teacher candidates to pursue teacher training programs, it is important to understand the perceived value that potential recruits place on STEM careers, disciplines, and the teaching profession. The purpose of this study was to explore students’ perceptions of the usefulness of STEM disciplines and their value in supporting students’ careers. A novel statistical method was utilized, combining exploratory-factor analysis, the analysis of variance, generalized estimating equation evaluations under the framework of a generalized linear model, and quantile regression. Using the outputs from each statistical measure, students’ valuation of each STEM discipline and their interest in pursuing teaching as a career option were assessed. Our results indicate a high correlation of liking and perceived usability of the STE disciplines relative to careers. Conversely, our results also display a low correlation of the liking and perceived usability of mathematics relative to future careers. The significance of these diametrically related results suggests the need for promotion of the interrelatedness of mathematics and STE. Full article

We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of a class of nonlinear differential equations containing polynomial nonlinearities. We present an amended version of the methodology, which is based on the use of composite functions. The number of steps of the SEsM was reduced from seven to four in the amended version of the methodology. For the case of nonlinear differential equations with polynomial nonlinearities, SEsM can reduce the solved equations to a system of nonlinear algebraic equations. Each nontrivial solution of this algebraic system leads to an exact solution of the solved nonlinear differential equations. We prove the theorems and present examples for the use of composite functions in the methodology of the SEsM for the following three kinds of composite functions: (i) a composite function of one function of one independent variable; (ii) a composite function of two functions of two independent variables; (iii) a composite function of three functions of two independent variables. Full article

Molecularly imprinted polymers (MIPs) are synthetic receptors engineered towards the selective binding of a target molecule; however, the manner in which MIPs interact with other molecules is of great importance. Being able to rapidly analyze the binding of potential molecular interferences and determine the selectivity of a MIP can be a long tedious task, being time- and resource-intensive. Identifying computational models capable of reliably predicting and reporting the binding of molecular species is therefore of immense value in both a research and commercial setting. This research therefore sets focus on comparing the use of machine learning algorithms (multitask regressor, graph convolution, weave model, DAG model, and inception) to predict the binding of various molecular species to a MIP designed towards 2-methoxphenidine. To this end, each algorithm was “trained” with an experimental dataset, teaching the algorithms the structures and binding affinities of various molecular species at varying concentrations. A validation experiment was then conducted for each algorithm, comparing experimental values to predicted values and facilitating the assessment of each approach by a direct comparison of the metrics. The research culminates in the construction of binding isotherms for each species, directly comparing experimental vs. predicted values and identifying the approach that best emulates the real-world data. Full article

Models of computation are fundamental notions in computer science; consequently, they have been the subject of countless research papers, with numerous novel models proposed even in recent years. Amongst a multitude of different approaches, many of these methods draw inspiration from the biological processes observed in nature. P systems, or membrane systems, make an analogy between the communication in computing and the flow of information that can be perceived in living organisms. These systems serve as a basis for various concepts, ranging from the fields of computational economics and robotics to the techniques of data clustering. In this paper, such utilization of these systems—membrane system–based clustering—is taken into focus. Considering the growing number of data stored worldwide, more and more data have to be handled by clustering algorithms too. To solve this issue, bringing these methods closer to the data, their main element provides several benefits. Database systems equip their users with, for instance, well-integrated security features and more direct control over the data itself. Our goal is if the type of the database management system is given, e.g., NoSQL, but the corporation or the research team can choose which specific database management system is used, then we give a perspective, how the algorithms written like this behave in such an environment, so that, based on this, a more substantiated decision can be made, meaning which database management system should be connected to the system. For this purpose, we discover the possibilities of a clustering algorithm based on P systems when used alongside NoSQL database systems, that are designed to manage big data. Variants over two competing databases, MongoDB and Redis, are evaluated and compared to identify the advantages and limitations of using such a solution in these systems. Full article