The Eighth Congress of Romanian Mathematicians

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List of talks

I. Algebra and Number Theory

Special session: Local rings and homological algebra. Special session dedicated to Prof. Nicolae Radu

II. Algebraic, Complex and Differential Geometry and Topology

Special session: Geometry and Topology of Differentiable Manifolds and Algebraic Varieties

III. Real and Complex Analysis, Potential Theory

IV. Ordinary and Partial Differential Equations, Variational Methods, Optimal Control

Special session: Optimization and Games Theory

V. Functional Analysis, Operator Theory and Operator Algebras, Mathematical Physics

Special session: Spectral Theory and Applications in Mathematical Physics

Special session: Dynamical Systems and Ergodic Theory

VI. Probability, Stochastic Analysis, and Mathematical Statistics

VII. Mechanics, Numerical Analysis, Mathematical Models in Sciences

Special session: Mathematical Modeling of Some Medical and Biological Processes

Special session: Mathematical Models in Astronomy

VIII. Theoretical Computer Science, Operations Research and Mathematical Programming

Special session: Logic in Computer Science

IX. History and Philosophy of Mathematics

Mathematical Modeling of Some Medical and Biological Processes (special session) 

(this list is in updating process)

University Politehnica of Bucharest, Romania
Title: Stability analysis of some equilibrium points in a complex model for blood cells’ evolution in CML (details)
The complex model considers the competition between the populations of healthy and leukemic stem-like short-term and mature leukocytes and the influence of the T-lymphocytes on the evolution of leukemia. Delay differential equations are used in a modified Mackey-Glass approach, with the consideration of asymmetric division and feedback functions for the action of the immune system. This research is focused on the linear stability analysis of equilibrium points. As the characteristic equations for some equilibrium points are very complex, the existence of a Lyapunov-Krasovskii functional is investigated. Also, treatment with Imatinib is introduced in the model and new stability properties are investigated. This research is supported by the CNCS Grant PNII-ID-PCE-3-0198 and by POSDRU/159/1.5/S/132395.
BALAN Vladimir
University Politehnica of Bucharest, Romania
Title: Spectral aspects of anisotropic metric models in the Garner oncologic framework (details)
%================================= % CMR-2015 * TALK * Balan-Stojanov %================================= \documentclass[11pt]{article}\begin{document}\thispagestyle{empty}\begin{abstract} % The present talk discusses three natural Finsler models, which naturally relate to the classical Garner dynamical system, which describes the evolution of the active and quiescent cancer cell populations. % The statistically fit metric structures are determined from the energy of the deformed field of the biological model, assuming that severe disease circumstances occur, and it is shown that the subsequently derived geometric objects are able to provide an evaluation of the overall cancer cell population growth.\par % The spectral characteristics of the Cartan tensor, the comparison between the $Z-$ and $H-$eigendata of the constructed Randers, $m-$th root and Euclidean structures, and the applicative advantages of the developed geometric models, are discussed.\\[2mm] % 2010 \textit{Mathematics Subject Classification:} 53B40, 53C60, 37C75, 65F30, 15A18, 15A69.\\[1mm] % \end{abstract}\end{document} %=================================
"Grigore T. Popa" University of Medicine and Pharmacy of Iasi, Romania
Title: Numerical simulations of a two noncompeting species chemotaxis model (details)
In this study we present the results of the numerical simulations of a two-species chemotaxis model. This model represents a regularized extension of the Patlak-Keller-Segel (PKS) system to the case of the chemotaxis motion of two noncompeting species that produce the same chemoattractant. We perform several experiments by applying a strong stability preserving (SSP) implicit-explicit Runge-Kutta method to study the behaviour of the obtained spiky solutions.
Technical University of Iasi, Romania
Title: Mathematical insights and integrated strategies for the control of Aedes aegypti mosquito (details)
We propose and investigate a delayed model for the dynamics and control of a mosquito population which is subject to an integrated strategy that includes pesticide release, the use of mechanical controls and the use of the sterile insect technique (SIT). The existence of positive equilibria is characterized in terms of two threshold quantities, being observed that the ``richer" equilibrium (with more mosquitoes in the aquatic phase) has better chances to be stable, while a longer duration of the aquatic phase has the potential to destabilize both equilibria. It is also found that the stability of the trivial equilibrium appears to be mostly determined by the value of the maturation rate from the aquatic phase to the adult phase. A nonstandard finite difference (NSFD) scheme is devised to preserve the positivity of the approximating solutions and to keep consistency with the continuous model. The resulting discrete model is transformed into a delay-free model by using the method of augmented states, a necessary condition for the existence of optimal controls then determined. The particularities of different control regimes under varying environmental temperature are investigated by means of numerical simulations. It is observed that a combination of all three controls has the highest impact upon the size of the aquatic population. At higher environmental temperatures, the oviposition rate is seen to possess the most prominent influence upon the outcome of the control measures.
ION Anca Veronica
"Gh. Mihoc - C. Iacob" Institute of Mathematical Statistics and Applied Mathematics, Bucharest, Romania
Title: Qualitative and numerical study of a system of delay differential equations modeling leukemia (details)
This work is a review of some previous works of ours concerning the investigation of a system of two delay differential equations, system that models the periodic chronic myelogenous leukemia. The system consists of two equations, one for the proliferating cells and one for the so-called resting cells, and depends on five parameters. The equation for resting cells is independent of the other one. For this equation we study the stability of the two equilibria, the Hopf bifurcation, and the Bautin bifurcation. Then we study the behavior of the proliferating cells (that is determined by that of the resting cells).
Universitatea de Vest din Timisoara, Romania
Title: Dynamical analysis of a fractional-order Hindmarsh-Rose model (details)
This work is dedicated to the stability and bifurcation analysis of a model of neuronal activity of Hindmarsh-Rose type and of fractional order. First, a two-dimensional model is considered, with respect to the membrane potential in the axon and the transport rate of sodium and potassium ions through fast ion channels. This model is later complemented by the addition of a third-order fractional differential equation that takes into account a slow adaptation current. The main purpose of this paper is to demonstrate that existing mathematical models of neuronal activity can be improved by using fractional derivatives instead of classical integer-order derivatives and that these new models reflect a better understanding of the biological reality, as suggested by the experimental results. Results of numerical simulations are also presented to validate the theoretical results.
LITCANU Gabriela
Institute of Mathematics "O. Mayer", Romania
Title: About patterns driven by chemotaxis (details)
The pattern formation is a key process in the development of living systems. It describes the interplays between members of species at the intercellular or intracellular levels. We consider a coupled chemotaxis-haptotaxis system which describes a large variety of biological or medical phenomena. We investigate how both the change of parameters of the system and the singularities of the chemosensitivity term can generate pattern formation.
NEAMTU Mihaela
West University of Timisoara, Romania
Title: Hopf bifurcation analysis for the model of the hypothalamic-pituitary-adrenal axis with distributed time delay (details)
In the present paper we analyze the mathematical model of the hypothalamus-pituitary-adrenal axis. Since there is a spatial separation between the brain, where the hypothalamus and pituitary are situated, and the kidney, where the adrenal glands are situated, time is needed for transportation of the hormones between the glands. Thus, the distributed time delays are considered as both weak and Dirac kernels. The model, described by a nonlinear differential system with distributed time delay, is analyzed regarding the stability and bifurcation behavior. The last part contains some numerical simulations to illustrate the effectiveness of our results. Moreover, the behavior of the fractional differential time delay model is simulated.
United States Naval Academy, USA and Romania
Title: Border-Collision Bifurcations in A Piece-Wise Smooth Planar Dynamical System Associated with Cardiac Potential (details)
The talk addresses the bifurcations of a two-dimensional non-linear dynamical system introduced by Kline and Baker to model cardiac rhythmic response to periodic stimulation. The dynamical behavior of this continuous (but only piece-wise smooth) model transitions from simple (a unique attracting cycle) to complicated (co-existence of stable cycles) as the stimulus period is decreased from large towards zero. The first bifurcation, of discontinuous period-doubling type, results from the collision of two cycles with a switching manifold. For stimuli periods just shorter than collision time, of the two cycles about to collide, the 2:1 escalator is stable and the alternans solution is unstable; with those co-exists a stable 1-escalator whose orbit lays away from the switching manifold. The principal results show that the dynamical system associated with the collision exhibits two distinct types of domains of attraction, some impossible in smooth dynamics.
Babes-Bolyai University of Cluj-Napoca, Romania
Title: Mathematical models of stem cell transplantation (details)
We present simple mathematical models expressed as three-dimensional ordinary differential systems for describing the dynamics of three cell lines after allogeneic and autologous stem cell transplantation [1], [3]. The evolution ultimately leads either to the normal hematopoietic state achieved by the expansion of normal cells and the elimination of the cancer cells, or to the leukemic hematopoietic state characterized by the proliferation of the cancer line and the suppression of the normal cells. A theoretical basis for the control of post-transplant evolution is provided for the allogeneic transplant [4]. Thus, we describe several scenarios of change of system parameters by which a bad post-transplant evolution can be corrected and turned into a good one, and we propose therapy planning algorithms for guiding the correction treatment [2]. We also conclude about the effectiveness of the autologous transplantation as therapeutic procedure for AML [3]. References: [1] R. Precup et al., Mathematical modeling of cell dynamics after allogeneic bone marrow transplantation, Int. J. Biomath. 5 (2012), 1250026, 1--18. [2] R. Precup et al., A planning algorithm for correction therapies after allogeneic stem cell transplantation, J. Math. Model. Algor. 11 (2012), 309--323. [3] R. Precup, Mathematical understanding of the autologous stem cell transplantation, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity 10 (2012), 155--167. [4] R. Precup, M-A Serban, D Trif, Asymptotic stability for a model of cell dynamics after allogeneic bone marrow transplantation, Nonlinear Dyn. Syst. Theory 13 (2013), 79--92.
State University of New York at New Paltz, United States
Title: Dynamic Networks: From Connectivity to Temporal Behavior (details)
Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. We illustrate how the hardwired structure (adjacency graph) can affect dynamics (temporal behavior) for two particular types of networks: one with discrete and one with continuous temporal updates. The nodes are coupled according to a connectivity scheme that obeys certain constrains, but also incorporates random aspects. We develop new measures (such as probabilistic bifurcations and extensions of Julia sets) to compare the effects of different ways of increasing connectivity: by altering edge weights versus edge density versus edge configuration. We determine that the adjacency spectrum is a poor predictor of dynamics, that increasing the number of connections is not equivalent to strengthening them, and that there is no single factor among those we tested that governs the stability of the system. We discuss the potential applications of our results towards increasing our understanding of neural dynamics and genetic replication processes.
University Politehnica of Bucharest, Romania
Title: Optimal control of Imatinib treatment in a competition model of Chronic Myelogenous Leukemia with immune response (details)
In this work, we present an optimal control strategy for a delay differential system with application to the drug therapy of Chronic Myelogenous Leukemia. The mathematical model is represented by a nonlinear system of five equations from population dynamics which is based on the competition between normal cells and leukemic cells (stem-like and mature). The effect of the immune system through anti-leukemia T-cells is also included in the model. The effect of Imatinib therapy is introduced in the form of several factors controlling cell multiplication and mortality for leukemia cell populations and the evolution of immune cell population. The optimal control method is applied to eliminate the leukemic cells whilst minimizing the amount of drug. In order to derive necessary optimality conditions in the form of Pontryagin’s minimum principle, discretization methods are applied and the delayed control problem is augmented to a nondelayed problem to which Pontryagin’s minimum principle is applicable. The obtained results are illustrated by numerical simulations and discussed in view of the optimal treatment approach.
Purdue University Calumet, USA
Title: A hybrid mathematical model for cell motility in angiogenesis (details)
The process of angiogenesis is regulated by the interactions between various cell types such as endothelial cells and macrophages, and by biochemical factors. In this talk, we present a hybrid mathematical model in which cells are treated as discrete units in a continuum field of a chemoattractant that evolves according to a system of reaction-diffusion equations, whereas the discrete cells serve as sources/sinks in this continuum field. It incorporates a realistic model for signal transduction and VEGF production and release, and gives insights into the aggregation patterns and the factors that influence stream formation. The model allows us to explore how changes in the microscopic rules by which cells determine their direction and duration of movement affect macroscopic formations. In particular, it serves as a tool for investigating tumor-vessel signaling and the role of mechano-chemical interactions of the cells with the substratum.