Space dependent adhesion forces mediated by transient elastic linkages : new convergence and global existence results

In the first part of this work we show the convergence with respect to an asymptotic parameter {\epsilon} of a delayed heat equation. It represents a mathematical extension of works considered previously by the authors [Milisic et al. 2011, Milisic et al. 2016]. Namely, this is the first result involving delay operators approximating protein linkages coupled with a spatial elliptic second order operator. For the sake of simplicity we choose the Laplace operator, although more general results could be derived. The main arguments are (i) new energy estimates and (ii) a stability result extended from the previous work to this more involved context. They allow to prove convergence of the delay operator to a friction term together with the Laplace operator in the same asymptotic regime considered without the space dependence in [Milisic et al, 2011]. In a second part we extend fixed-point results for the fully non-linear model introduced in [Milisic et al, 2016] and prove global existence in time. This shows that the blow-up scenario observed previously does not occur. Since the latter result was interpreted as a rupture of adhesion forces, we discuss the possibility of bond breaking both from the analytic and numerical point of view

Mathematical modeling of tumor therapy with oncolytic viruses: Effects of parametric heterogeneity on cell dynamics

One of the mechanisms that ensure cancer robustness is tumor heterogeneity, and its effects on tumor cells dynamics have to be taken into account when studying cancer progression. There is no unifying theoretical framework in mathematical modeling of carcinogenesis that would account for parametric heterogeneity. Here we formulate a modeling approach that naturally takes stock of inherent cancer cell heterogeneity and illustrate it with a model of interaction between a tumor and an oncolytic virus. We show that several phenomena that are absent in homogeneous models, such as cancer recurrence, tumor dormancy, an others, appear in heterogeneous setting. We also demonstrate that, within the applied modeling framework, to overcome the adverse effect of tumor cell heterogeneity on cancer progression, a heterogeneous population of an oncolytic virus must be used. Heterogeneity in parameters of the model, such as tumor cell susceptibility to virus infection and virus replication rate, can lead to complex, time-dependent behaviors of the tumor. Thus, irregular, quasi-chaotic behavior of the tumor-virus system can be caused not only by random perturbations but also by the heterogeneity of the tumor and the virus. The modeling approach described here reveals the importance of tumor cell and virus heterogeneity for the outcome of cancer therapy. It should be straightforward to apply these techniques to mathematical modeling of other types of anticancer therapy.Comment: 45 pages, 6 figures; submitted to Biology Direc

From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond

The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observations in the twentieth century. The connection between the two areas was first observed through Montgomery's work on the pair correlation of zeros of the Riemann zeta function. As its generalizations and consequences have motivated much of the following work, and to this day remains one of the most important outstanding conjectures in the field, it occupies a central role in our discussion below. We describe some of the many techniques and results from the past sixty years, especially the important roles played by numerical and experimental investigations, that led to the discovery of the connections and progress towards understanding the behaviors. In our survey of these two areas, we describe the common mathematics that explains the remarkable universality. We conclude with some thoughts on what might lie ahead in the pair correlation of zeros of the zeta function, and other similar quantities.Comment: Version 1.1, 50 pages, 6 figures. To appear in "Open Problems in Mathematics", Editors John Nash and Michael Th. Rassias. arXiv admin note: text overlap with arXiv:0909.491

Pharmacokinetic Analysis of Gd-DTPA Enhancement in dynamic three-dimensional MRI of breast lesions

The purpose of this study was to demonstrate that dynamic MRI covering both breasts can provide sensitivity for tumor detection as well as specificity and sensitivity for differentiation of tumor malignancy. Three-dimensional gradient echo scans were used covering both breasts. Before Gd-DTPA bolus injection, two scans were obtained with different flip angles, and after injection, a dynamic series followed. Thirty-two patients were scanned according to this protocol. From these scans, in addition to enhancement, the value of T1 before injection was obtained. This was used to estimate the concentration of Gd-DTPA as well as the pharmacokinetic parameters governing its time course. Signal enhancement in three-dimensional dynamic scanning was shown to be a sensitive basis for detection of tumors. In our series, all but two mam-mographically suspicious lesions did enhance, and in three cases, additional enhancing lesions were found, two of which were in the contralateral breast. The parameter most suited for classification of breast lesions into benign or malignant was shown to be the pharmacokinetically defined permeability k31, which, for that test, gave a sensitivity of 92% and a specificity of 70%. Our three-dimensional dynamic MRI data are sensitive for detection of mammographically occult breast tumors and specific for classification of these as benign or malignant

International Conference on Dynamic Control and Optimization - DCO 2021: book of abstracts

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Genetic algorithm for multi-gravity assist interplanetary trajectory optimisation

This master thesis presents the development of a genetic algorithm for optimizing multiplanetary gravity assist trajectories. The algorithm was designed to address the challenges of finding the most efficient trajectory for a spacecraft traveling into deep space using multiple planets while performing gravity-assist maneuvers. Given a model for the interplanetary trajectory, the algorithm is able to find a feasible optimal solution. The proposed approach was tested on a set of real missions and was shown to produce solutions more optimal than the real ones given our trajectory model. The results demonstrate the effectiveness of evolutionary algorithms, in concrete genetic algorithms, in finding optimal multi-planetary gravity assist trajectories, making it a valuable tool for mission planning in space exploration

Bifurcation analysis of the Topp model

In this paper, we study the 3-dimensional Topp model for the dynamicsof diabetes. We show that for suitable parameter values an equilibrium of this modelbifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests thatnear this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arisethrough period doubling cascades of limit cycles.Keywords Dynamics of diabetes · Topp model · Reduced planar quartic Toppsystem · Singular point · Limit cycle · Hopf-saddle-node bifurcation · Perioddoubling bifurcation · Shilnikov homoclinic orbit · Chao

Simulation Modeling

The book presents some recent specialized works of a theoretical and practical nature in the field of simulation modeling, which is being addressed to a large number of specialists, mathematicians, doctors, engineers, economists, professors, and students. The book comprises 11 chapters that promote modern mathematical algorithms and simulation modeling techniques, in practical applications, in the following thematic areas: mathematics, biomedicine, systems of systems, materials science and engineering, energy systems, and economics. This project presents scientific papers and applications that emphasize the capabilities of simulation modeling methods, helping readers to understand the phenomena that take place in the real world, the conditions of their development, and their effects, at a high scientific and technical level. The authors have published work examples and case studies that resulted from their researches in the field. The readers get new solutions and answers to questions related to the emerging applications of simulation modeling and their advantages