24/11/2014, 11:00 — 12:00 — Room P3.10, Mathematics Building
Sinai Robins, Brown University
Cone theta functions and rationality of spherical volumes
20/11/2014, 15:00 — 16:00 — Room P3.10, Mathematics Building
Javad Hatami, IBB-Institute for Biotechnology and Biosciences, IST, Univ Lisbon
A Mathematical Approach To Model Human Megakaryopoiesis Process in vitro
Megakaryopoiesis is a complex process, which is commenced with the proliferation and the differentiation of hematopoietic stem cells (HSC) into megakaryocytes (Mk), followed by maturation and polyploidy of Mk and ended by platelet biogenesis. An in vitro two-stage protocol including HSC expansion and Mk lineage commitment of human umbilical cord blood cells (hUCB) were established [1]. In the first stage, hUCB CD34+-enriched cells were expanded in co-culture with bone marrow human mesenchymal stem cells (BM hMSC) in a cytokines cocktail pre-optimized for CD34+ expansion. In the second stage, expanded cells were differentiated toward Mk lineage using a cocktail containing TPO and IL-3 in a serum-free medium. Phenotypic characterization of cells was performed by Flow cytometry. In order to describe the fate of HSC during the megakaryopoiesis, a mathematical approach was used based on kinetic modeling of cell expansion and differentiation. This kind of modeling, which computes the concentration of each subset during the time, can provide significant insight into the limiting step involved in the protocol and how the interaction of different factors can affect the outcome of megakaryopoiesis process. A set of ordinary differentiation equation (ODE) were used to analyze the proliferation and differentiation of UCB CD34+ cells, as evaluated by the number of HSC (CD34+ cells), Mk (CD41+ cells) and platelets (CD42b+ cells). These ODEs were solved and a general solution for each subset was fitted to the experimental result, using least square method, to determine the unknown coefficient factors. The establishment of such reliable kinetic model will be useful for development of an efficient bioreactor system devoted for production of specific hematopoietic product.References:1. Hatami J, Andrade PZ, Bacalhau D, Cirurgião F, Ferreira FC, et al. (2014) Proliferation extent of CD34+ cells as a key parameter to maximize megakaryocytic differentiation of umbilical cord blood-derived hematopoietic stem/progenitor cells in a two-stage culture protocol. Biotechnology Reports 4: 50-55.
06/11/2014, 15:00 — 16:00 — Room P3.10, Mathematics Building
Anca-Maria Toader, CMAF and Faculdade de Ciências da Universidade de Lisboa
The Adjoint Method in Optimization of Eigenvalues and Eigenmodes
The Adjoint Method goes back to the works of Pontryagin in the framework of Ordinary Differential Equations. In the eighties, J. Cea employed the Adjoint Method in a practical way, from the perspective of Lagrange multipliers. Since then, applications of the Adjoint Method were successfully used in Shape Optimization, Topology Optimization and very recently to optimize eigenvalues and eigenmodes (eigenvectors).
The main contribution of this study is to show how the Adjoint Method is applied to the optimization of eigenvalues and eigenmodes. The general case of an arbitrary cost function will be detailed. In this framework, the direct problem does not involve a bilinear form and a linear form as usual in other applications. However, it is possible to follow the spirit of the method and deduce $N$ adjoint problems and obtain $N$ adjoint states, where $N$ is the number of eigenmodes taken into account for optimization.
An optimization algorithm based on the derivative of the cost function is developed. This derivative depends on the derivatives of the eigenmodes and the Adjoint Method allows one to express it in terms of the the adjoint states and of the solutions of the direct eigenvalue problem.
This method was applied in [1] for material identification purposes in the framework of free material design. In [2] this study is applied to optimization of microstructures, modeled by Bloch wave techniques.
References
- S. Oliveira, A.-M. Toader, P. Vieira, Damage identification in a concrete dam by fitting measured modal parameters. Nonlinear Analysis: Real World Applications, 13, Issue 6, 2888-2899, 2012.
- C. Barbarosie, A.-M. Toader, The Adjoint Method in the framework of Bloch Waves (in preparation).
09/10/2014, 14:30 — 15:30 — Room P3.10, Mathematics Building
Sílvia Barbeiro, CMUC, Department of Mathematics, University of Coimbra
Modeling electromagnetic wave’s propagation in human eye’s structure
In this talk we will discuss the a mathematical model that describes the electromagnetic wave’s propagation through the eye’s structures in order to create a virtual OCT scan. Our model is based on time-dependent Maxwell’s equations. We use the discontinuous Galerkin method for the integration in space and a low-storage Runge-Kutta method for the integration in time. In the model we consider anisotropic permittivity tensors which arise naturally in our application of interest. We illustrate the performance of the method with some numerical experiments.
09/09/2014, 11:30 — 12:30 — Room P3.10, Mathematics Building
Maria Specovius-Neugebauer, University of Kassel, Germany
The time periodic Stokes system in a layer: asymptotic behavior at infinity
While there are numerous papers on the time decay of solutions to the Stokes and Navier-Stokes initial boundary value in various types of domains only few results are devoted to the spatial decay. In this talk we consider the solutions to the time periodic Stokes problem in a layer where the data are also time periodic and smooth with bounded support for simplicity. The results were obtained in a joint work with Konstantin Pileckas,Vilnius.
23/07/2014, 11:00 — 13:00 — Room P3.10, Mathematics Building
Willi Jäger, Maria Neuss-Radu, University of Heidelberg, University of Erlangen-Nuremberg (resp.)
Interactions of the fluid and solid phases in complex media — coupling reactive flows, transport and mechanics, and applications to medical processes.
Modelling reactive flows, diffusion, transport and mechanical interactions in media consisting of multiple phases, e.g. of a fluid and a solid phase in a porous medium, is giving rise to many open problems for (multi-scale) analysis and simulation. In this lecture, the following processes are studied:
- diffusion, transport, and reaction of substances in the fluid and the solid phases,
- mechanical interactions of the fluid and solid phases,
- change of the mechanical properties of the solid phase by chemical reactions,
- volume changes (“growth”) of the solid phase.
These processes occur for instance in soil and in porous materials, but also in biological membranes, tissues and in bones. The model equations consist of systems of nonlinear partial differential equations, with initial-boundary conditions and transmission conditions on fixed or free boundaries, mainly in complex domains. The coupling of processes on different scales is posing challenges to the mathematical analysis as well as to computing. In order to reduce the complexity, effective macroscopic equations have to be derived, including the relevant information from the micro-scale.
In case of processes in tissues, a homogenization limit leads to an effective, mechanical system, containing a pressure gradient, which satisfies a generalized, time-dependent Darcy law, a Biot-law, where the chemical substances satisfy diffusion-transport-reaction equations and are influencing the mechanical parameters.
The interaction of the fluid and the material transported in a vessel with its flexible wall, incorporating material and changing its structure and mechanical behavior, is a process important e.g. in the vascular system (plaque-formation) or in porous media.
The modeling and analytic aspects addressed in our talk are also highly relevant for the study of inflammatory processes.
The lecture is based on recent results obtained in cooperation with A. Mikelic, F. Weller and Y. Yang.
05/06/2014, 16:00 — 17:00 — Room P3.10, Mathematics Building
Alexander G. Ramm, Department of Mathematics, Kansas State University
Wave scattering by many small particles and creating materials with desired refraction coefficients
Many-body wave scattering problems are solved asymptotically, as the size \(a\) of the particles tends to zero and the number of the particles tends to infinity.
Acoustic, quantum-mechanical, and electromagnetic wave scattering by many small particles is studied. This theory allows one to give a recipe for creating materials with a desired refraction coefficient.
One can create material with negative refraction, that is, the group velocity in this material is directed opposite to the phase velocity. One can create material with some desired wave-focusing properties. For example, one can create a new material which scatters plane wave mostly in a fixed given solid angle.
15/05/2014, 15:00 — 16:00 — Room P3.10, Mathematics Building
Jahed Naghipoor, CMUC, Universidade de Coimbra
A non-Fickian reaction diffusion equation for polymeric stent
embedded in the arterial wall
In recent years, mathematical modeling of cardiovascular drug
delivery systems has become an effective tool to gain deeper
insights in the cardiovascular diseases like atherosclerosis.. In
the case of coronary biodegradable stent which is a tiny expandable
biocompatible metallic mesh tube covered by biodegradable polymer,
it leads to a deeper understanding of the drug release mechanisms
from polymeric stent into the arterial wall. A coupled non-Fickian
model of a cardiovascular drug delivery system using a
biodegradable drug eluting stent is proposed in this talk. Energy
estimates are used to study the qualitative behavior of the model.
The numerical results are obtained using an IMEX finite element
method. The influence of arterial stiffness in the sorption of drug
eluted from the stent is analyzed. The results presented in this
talk open new perspectives to adapt the drug delivery profile to
the needs of the patient.
27/03/2014, 15:00 — 16:00 — Room P3.10, Mathematics Building
Arvet Pedas, Institute of Applied Mathematics, Tartu University, Estonia
High-order methods for Volterra integral equations with weak
singularities
We consider the numerical solution of some classes of linear
Volterra integral equations with singularities. We apply to them a
smoothing transformation so that the exact solution of the
resulting equation does not contain any singularities in its
derivatives up to a certain order. After that the regularized
equation is solved by a piecewise polynomial collocation method on
a mildly graded or uniform grid. Global convergence estimates are
derived and some superconvergence results are given.
27/03/2014, 14:00 — 15:00 — Room P3.10, Mathematics Building
Ruediger Weiner, Institut für Mathematik, University of Halle, Germany
Global error control with explicit peer methods
Step size control in the numerical solution of initial value
problems is usually based on the
control of the local error. We present numerical tests showing that
this may lead to high global errors, i.e. the real error is much
larger than the prescribed tolerance. There is a tolerance
proportionality, with more stringent tolerances also the global
error is reduced. However, tolerance and achieved global error may
differ by several magnitudes. A very simple idea to overcome this
problem is to use two methods of different orders with same step
size sequences and local error control for the lower order method.
Then the difference of the numerical approximations of both methods
is an estimate of the global error of the lower order method. This
strategy was implemented for pairs of explicit peer methods in
Matlab . Numerical tests show the reliability of this approach. The
numerical costs are comparable with those of ode45, but in contrast
to ode45 the required accuracy is achieved.
13/03/2014, 14:30 — 15:30 — Room P3.10, Mathematics Building
Elias Gudino, CMUC, Universidade de Coimbra
A 3D model for mechanistic control of drug release
A 3D mathematical model for sorption/desorption by a cylindrical
polymeric matrix with dispersed drug is proposed. The model is
based on a system of partial differential equations coupled with
boundary conditions over a moving boundary. We assume that the
penetrant diffuses into a swelling matrix and causes a deformation
which induces a stress driven diffusion and consequently a
non-Fickian mass flux. A physically sound non linear dependence
between strain and penetrant concentration is considered and
introduced in a Boltzmann integral with a kernel computed from a
Maxwell-Wiechert model. Numerical simulations show how the
mechanistic behavior can have a role in drug delivery design.
11/12/2013, 14:00 — 16:00 — Room V1.08, Civil Engineering Building, IST
Marco Leite, UCL Institute of Neurology and Instituto de Sistemas e Robótica, IST
Modelling populations of integrate and fire neurons: a
Fokker-Planck approach to population density dynamics
Much of the phenomenology of interest in the field of
neuroscience arises from the interaction of large populations of
densely interconnected neurons (~\(10^5\) neurons per
mm3 of mammal cortex, averaging \(10^4\) connections per
neuron). Different levels of abstraction may be adopted when
modelling such systems, and these need to be well suited with
regards to the phenomena one is interested in studying. Here we aim
at the study of the (sparse) synchronization of neurons observed
during electrophysiologically recorded fast oscillatory behavior of
networks of large populations. For that we use a ubiquitous
simplified neuronal model - the conductance based leaky integrate
and fire neuron. This model may be described by a one dimensional
stochastic differential equation. Under mean field assumptions we
may describe, using a linear Fokker-Planck equation, the behavior
of a single population of uncoupled neurons with a PDE. The
coupling of different populations will render this Fokker-Planck
equation strongly non-linear. In this presentation I will also
explore some details of such modelling approaches, namely: the
non-natural boundary conditions generated by the neuronal firing
mechanism and the numerical scheme used to deal with the
brittleness from there ensued. I will also present results on the
types of behavior, data, and statistics that such modelling
approach is able to predict, e.g. neuronal (a)synchrony, neuronal
input currents, firing rates, inter spike intervals, etc... This
type of approach allows for a computationally tractable and
scalable study of networks of populations of neurons. In the future
we plan to implement parameter estimation algorithms to this family
of models.
26/11/2013, 15:00 — 16:00 — Room P3.10, Mathematics Building
G. E. Chatzarakis, School of Pedagogical and Technological Education, Athens, Greece
Oscillations of Difference Equations of Several Deviating Arguments
Sufficient conditions are given for the oscillation of all solutions of a certain retarded linear difference equation and for its (dual) advanced difference equation.
Examples illustrating the results are also given.
See also
https://www.math.tecnico.ulisboa.pt/~plima/Chatzar.pdf
26/11/2013, 14:00 — 15:00 — Room P3.10, Mathematics Building
I. P. Stavroulakis, University of Ioannina, Greece
Oscillations of Delay and Difference Equations
Results are presented about the oscillation of all solutions of a certain class of first order linear retarded differential equations and their discrete analogues.
See also
https://www.math.tecnico.ulisboa.pt/~plima/Stavrou.pdf
13/11/2013, 15:30 — 16:30 — Room P9, Mathematics Building
Julia Tsyganova, Ulyanovsk State University, Ulyanovsk, Russia
Parameter Identification in Stochastic Dynamic Systems based on API Approach (with applications in Biology)
In this talk, we discuss the following two problems. First, we present the Auxiliary Performance Functional (API) developed by Prof. I.V. Semushin and study its role in the state and parameter estimation of linear discrete-time stochastic systems. The minimization procedure of the API with respect to parameters of the Data Model is then considered. Our approach differs from what has been done earlier in the adaptive filtering theory. We may mention that the minimization with respect to the parameters of the Adaptive Filter instead of the Data Model was considered previously. Second, we concern with robust array adaptive filters grounded in SR and UD covariance matrix factorizations used for the API gradient evaluation in identification algorithms. As a reallife example, we consider an application of the API approach to linear time-invariant statespace stochastic MIMO filter systems arising in human body temperature daily variation adaptive stochastic modeling. Simulation results and conclusions are also provided. Key words: linear stochastic system, parameter estimation, model identification, Auxiliary Performance Functional (API) approach, state sensitivity evaluation methods, stochastic modeling, homeostasis, thermoregulation.
13/11/2013, 14:30 — 15:30 — Room P9, Mathematics Building
Andrey Tsyganov, Ulyanovsk State Pedagogical University, Ulyanovsk, Russia
Parallel Algorithms for NFA State Minimization Problem
This talk will start with an introduction, where we present the Laboratory of Mathematical Modeling which was recently established in Ulyanovsk State Pedagogical University. The report will cover its hardware and software facilities and main areas of conducted research: cosmology, molecular biology, combinatorial optimization, parameter identification. Then we will switch to the main subject of the talk. We consider the state minimization problem for nondeterministic finite automata (NFA) which is known to be computationally hard (PSPACE-complete) and introduce ReFaM – a software tool for its solution. This software tool provides a number of parallel algorithms: parallel versions of exact Kameda- Weiner and Melnikov methods as well as their hybrids with popular metaheurstics (genetic algorithm, simulated annealing, etc.). All parallel algorithms are implemented using MPI and OpenMP techniques. We discuss the implementation details and provide the results of numerical experiments
04/09/2013, 16:00 — 17:00 — Room P3.10, Mathematics Building
Kazuaki Nakane, Division of Health Sciences, Osaka University, Japan
A Homology-based Algorithm for the Analysis of Structures
Observations of the microstructure of objects by means of a
microscope are carried out in different technical fields. The state
organization of iron with quenching-annealing and the human tissue
by biopsy are typical examples. Since the results of such
observations depend on the skills of the technician, objective
methods are required for the quantification of structures. When the
observed structures are very complex, the performance of pattern
recognition and Fourier methods is not satisfactory. In this talk,
I will introduce an algorithm based on the concept of homology. By
applying this method, we obtain rigorous quantitative estimates of
a structure. Several examples of its application will be presented.
12/07/2013, 11:30 — 12:30 — Room P3.10, Mathematics Building
Jevgenija Pavlova, CEMAT, Instituto Superior Técnico, Lisbon
Modeling the Coagulation Dynamics in Human Blood
Blood coagulation is an extremely complex biological process in which blood forms clots to prevent bleeding, following by their dissolution and the subsequent repair of the injured tissue. The process involves different interactions between the plasma, the vessel wall and platelets having a huge impact of the flowing blood on the thrombus growth regularization. The blood coagulation model we are working on consists of a system of reaction-advection-diffusion equations, describing the cascade of biochemical reactions, coupled with rheological models for the blood flow (Newtonian, shear-thinning and viscoelastic models). We introduce the effect of blood slip at the vessel wall emphasizing an extra supply of activated platelets to the clotting site. We expect that such contribution could be dominant, resulting in the acceleration of thrombin production and eventually of the whole clot progression. Such model will have the capacity to predict effects of specific perturbations in the hemostatic system that can’t be done by laboratory tests, and will assist in clinical diagnosis and therapies of blood coagulation diseases. A mathematical model and numerical results for thrombus development will be presented. The chain of biochemical reactions interacting with the platelets, resulting in a fibrin-platelets clot formation and the additional blood flow influence on thrombus development will be discussed.
20/03/2013, 16:30 — 17:30 — Room P3.10, Mathematics Building
Mikhail Bulatov, Institute of System Dynamics and Control Theory, Irkutsk, Russia
Analytical and Numerical Methods for Integral-Algebraic Equations
In the present talk we will discuss some properties of
Integral-Algebraic Equations (IAE) and their numerical solution.
Concerning analytical methods, me will consider IAE with kernels of
convolution type and weakly singular kernels. We will also discuss
the regularization of IAE. The discussion of numerical methods will
start with the case of systems of Volterra integral equations of
the first kind. Then we will describe multistep methods for IAE.
13/03/2013, 16:30 — 17:30 — Room P3.10, Mathematics Building
Werner Varnhorn, Kassel University, Germany
The Navier–Stokes Equations: A never ending challenge?
More than 2500 years after the famous statement πάντα
ῥεῖ by Heracleitos the investigation of the mechanical and
dynamical behavior of fluid flow is more than ever of fundamental
importance. Due to a large number of technical, experimental and
computational innovations and related theoretical problems the
investigation of fluid flow represents a challenging and exciting
subject requiring a wide variety of profound mathematical methods,
efficient numerical algorithms and complex experimental
simulations. Fascinating from the mathematical point of view, of
course, is the fact that the fundamental equations of
Navier–Stokes, formulated the first time by the French engineer
Navier in 1822, could not be solved in the general
three–dimensional case up to now. So the famous American Clay
Mathematics Institute created the Navier–Stokes Millennium Price
Problem and offered one Million US–Dollar for its solution,
stating: „Although the Navier–Stokes equations were written
down in the 19th Century, our understanding of them remains
minimal. The challenge is to make substantial progress toward a
mathematical theory, which will unlock the secrets hidden in the
Navier–Stokes equations“.
The lecture introduces the Navier–Stokes equations from an
historical and physical point of view, touches some fundamental
mathematical problems of viscous incompressible fluid flow and ends
up with new regularity results.
