Our seminars take place on Wednesdays, 14:15-15:45 in room 4050
2014-06-04: Paweł Ciosmak (MIMUW)
Title: Numerical methods for the dynamics of the populations with structure.
Abstract: In many situations the description of the dynamics of a population requires taking into account its structure. In the case of one real structural parameter, like the age or size of an individual, nonlinear first order hyperbolic equations are often applied. We will present the escalator boxcar train method, which can be used to solve these equations, and discuss its convergence.
2014-05-29: Jan Wehr (University of Arizona), s.2180, godz.14.15
Title: Active Brownian motion
Abstract: Active Brownian particles - often called microswimmers - propel themselves in various ways while undergoing di ffusive motion. They appear naturally in numerous applications, in particular in physics and in biologoy. An ideal mathematical tool to study microswimmer motion is the theory of stochastic diff erential equations. While general mathematical foundations of this theory are very well established, specific problems arising in applications call for new ideas and are a very active area of current research. In this talk I will show some recent examples of mathematical problems involving active Brownian particles, including systems with time delay and di ffusion of particles on surfaces. The results have been obtained jointly with Austin McDaniel at the University of Arizona and with Giovanni Volpe and his group at Bilkent University.
2014-05-14: María Vela Pérez (Service de Physique de l'Etat Condensé, CEA-Saclay, 91191 Gifsur-Yvette, France)
Title: From Individual to Collective Dynamics in Argentine Ants
Abstract: Social insects are an important example of complex collective behavior. In particular, ant colonies develop different tasks as foraging, building and allocation [1]. While they search for food they deposit a pheromone that it is considered as a crucial element in the mechanism for finding minimal paths. The experimental observations suggest that the model should include the presence of pheromone and the persistence (tendency to follow straight paths in the absence of other effects). In our study, based on the experimental data described in [2], we develop a model in the plane to describe the behavior of Argentine Ants when foraging in the plane.
Following the ideas explained in [3] we consider ants as random walkers. We treat them as pure random walkers when they detect an amount of pheromone that is below a certain threshold. The idea is that ants, once out of the nest, start foraging for food and do it following a random walk with the probability distribution for the change in direction that is fitted, from experimental data, to a distribution with fat tails. Once the ant detects an amount of pheromone concentration above the threshold, the motion changes to a reinforced random walk where a component of the change in the ant's direction is proportional to the gradient of the amount of pheromone.
[1] B. Holldobler and K. Wilson, The ants, Berlin: Springer, 1990
[2] A. Perna, et al. (2012) Individual rules for trail pattern formation in Argentine ants (Linepithema humile). PLOS Comput Biol 8(7):e1002592.
[3] M. Vela-Perez, et al. (2013), Ant foraging and geodesic paths in labyrinths: Analytical and computational results, J. Theo. Biol. 320, 100-112.
2014-05-07: Emad Attia (PhD student from Egypt)
Title: On the distance between adjacent zeros of solutions of first order differential equation with distributed delays
Abstract: The results of many publications that estimated the upper bound of the distance between adjacent zeros of any solution of first order delay differential equation will be displayed. We show some fundamental results for the lower bound of of the distance between adjacent zeros of any solution of first order delay differential equation. New estimations of the upper bound of the distance between successive zeros of any solution of a first order differential equation with distributed will be discussed.
2014-04-30: Urszula Foryś (WMIM UW)
Abstract: I will continue my talk about Lyapunov functions and functionals on the base of the article "A survey of constructing Lyapunov functions for mathematical models in population biology" by Sze-Bi Hsu. Some ideas for the model with diffusion will be included.
2014-04-23: Urszula Foryś (WMIM UW)
Abstract: I will continue my talk about Lyapunov functions and functionals. Now, on the base of the article "A survey of constructing Lyapunov functions for mathematical models in population biology" by Sze-Bi Hsu. Some ideas for the model with diffusion will be included.
2014-04-09: Agnieszka Bartłomiejczyk (Gdańsk University of Technology) i Henryk Leszczyński (University of Gdańsk)
2014-04-02: Agnieszka Dziekańska (alumna of University College Dublin, Systems Biology, Ireland)
Title: Computational analysis of multi-stable signalling biochemical networks.
Abstract: In this talk, two novel approaches to investigate systemic properties of signalling biochemical networks will be introduced. The first approach focuses on the analysis of information processing in signalling networks performed by the application of information theory. Molecular components of any signalling network are constantly subject to intracellular fluctuations in gene expression. The study applies the concept of Shannon’s entropy and channel capacity to investigate how fluctuations in the level of network components affect information processing capacity in biochemical networks. A sensitivity analysis of channel capacity could be applied to detect the nodes whose perturbations do not translate to significant changes in channel capacity and therefore do not play an important role in information transduction across the network. However, such a detailed analysis can be performed only in presence of high quality mathematical models of signalling networks. Lack of such models poses a main obstacle in current applications of IT in Systems Biology. The second approach concentrates on computation of steady-states of biochemical networks by the application of the concept of the biochemical landscape. The biochemical landscape quantifies the propensity of the system to settle in any of the possible steady-states. The study introduces two methods of computation of the biochemical landscape. The first method applies the concept of the quasi-potential in order to compute the gradient of trajectory of a dynamic system as it evolves to its steady-state. The second method applies stochastic simulations (Gibbs sampling) for the purpose of deriving the probability densities that correspond to steady-states of the system. Calculation of landscapes for gene regulatory or signalling networks can determine the relative stability of steady-states to fluctuations present in the network. The concept of an attractor positioned on the landscape surface could represent the discrete phenotypes of many human diseases such as cancer. It could also provide an explanation of the origin and development of the diseases and influence the current method of drug discovery.
2014-03-26: Krzysztof Fujarewicz (Politechnika Śląska)
Title: Structural sensitivity analysis of mathematical models in biology
Abstract: Sensitivity analysis plays very important and useful role during modeling and analysis of dynamical systems. It answers the question how changes in model parameters affects the model solution. The answer to this question can be useful in solving of many tasks, such as: estimation of model parameters, design of experiments, or the optimization of the structure of the model. Typically, the sensitivity functions with respect to model parameters are calculated but it is possible to perform the sensitivity analysis w.r.t. initial conditions or signals stimulating the system. During the presentation the so-called structural sensitivity analysis will be presented. It assumes that the system is presented in a structural form: as a block diagram. It simplifies the rules for the adjoint system creation and may be treated as a special case of so called automatic differentiation. The adjoint sensitivity analysis for systems of ordinary differential equation (ODE), delayed differential equations (DDE) and cellular automata used for solving partial differential (PDE) will be formulated. Results of application of the approach to parameter estimation and gradient-based optimization for various models will be presented.
2014-03-12: Marek Bodnar (WMIM UW)
Title: General model of a cascade of reactions with time delays: global stability analysis - continuation
2014-03-05: Marek Bodnar (WMIM UW)
Title: General model of a cascade of reactions with time delays: global stability analysis
Abstract: I discuss a general model of a cascade of reactions with discrete as well as distributed delays, which arose in the context of Hes1 gene expression. For the abstract general model sufficient conditions for global stability will be presented. Then the abstract result is applied for the Hes1 gene expression model.
2014-02-26: Jacek Waniewski (IBIB PAN)
2014-02-19: Jacek Waniewski (IBIB PAN)
2014-01-22: Maciej Cytowski, Zuzanna Szymańska (ICM UW)
Title: Large Scale Parallel Simulations of 3-D Cell Colony Dynamics
Abstract: Biological processes are inherentlyvery complex and involve many unknown relationships and mechanisms at different scales. Despite many efforts, one still cannot explain all the observed phenomena and, if necessary, make any desirable changes in the dynamics. Recently, it has become apparent that the opportunity lies in complementing the traditional, heuristic experimental approach with mathematical modelling and computer simulations. Achieving a realistic simulation scale is still a huge challenge, however it is necessary to understand and control complex biological processes. In this paper we present a novel high performance computational approach allowing simulations of 3D cell colony dynamics in realistic, previously unavailable scale. Due to the high parallel scalability we are able to simulate cell colonies composed of 109 cells, which allows for instance to describe tumor growth in its early clinical stage.
2014-01-15: Jan Poleszczuk (MiSDoMP i IBIB PAN)
Title: Pulse wave propagation models
Abstract: During the seminar I will present the state of the art of mathematical methods utilized in the modeling of the pulse wave propagation (PWP) through the arterial tree. In the spatially distributed approach, the whole arterial tree is divided into segments that are assumed to be straight compliant vessels (each segment may have different characteristics), some of which bifurcate into two subsequent smaller vessels. A typical blood vessel segment is modeled as an axisymmetric compliant cylinder with wall assumed to be impermeable (or permeable only to a small extent). The assumption about the axisymmetry allows to reduce the continuous flow into one spatial dimension, i.e. position along the vessel. The relation between pressure p and flow q for each vascular segment is derived from conservation of mass and the momentum equations by assuming fully developed incompressible Newtonian flow in a straight vessel. In other approach, each arterial segment is lumped and spatial information about the flow is lost. This approach allows to express the system as the electrical circuit analog, with capacitors and resistors as the main components. Obviously, these models are simpler than the distributed ones and the mathematical complications are kept to a minimum. They can also yield useful insight into the behavior of the system under investigation.
2014-01-08: Paweł Zwoleński (IM PAN)
Title: Phenotypic evolution of hermaphrodites
Abstract: We consider finite, phenotype-structured population of hermaphrodites, and build an individual based model which describes interactions between the individuals. The model contains such elements as mating of individuals (random or assortative), inheritance of phenotypic traits including mutations, intra-specific competition and mortality. Here offspring’s phenotype depends on parential traits. We consider the limit passage with the number of individuals to infinity, what leads us to continuous distribution of phenotypic traits in the population. The model is described by evolution equation in the space of measures, which contains nonlinear operators. The first of the operators is in charge of mating of individuals and inheritance, the other corresponds to the competition. The limiting version of the model for random mating is an evolutionary equation, containing bilinear operator. The particular case of the equation is Tjon-Wu equation which appears in the description of the energy distribution of colliding particles. In the case of random mating, under suitable conditions we prove the asymptotic stability result: distribution of the phenotypic traits in the population converges to a stationary distribution. As a by-product we obtain relatively easy proof of Lasota-Traple theorem concerning asymptotic stability of Tjon-Wu equation. Moreover, we show applications of our theorem to some biologically reasonable situations of phenotypic inheritance.
2013-12-11: Beata Zduniak (SGGW Warszawa)
Title: A VENTRICULAR TACHYCARDIA AND AV NODAL DOUBLE RESPONSE TACHYCARDIA IN A MODIFIED VAN DER POL EQUATION
Abstract: A modified van der Pol equation is a mathematical model used to recreate physiological behaviour in the conducting heart's system. The use of certain values for coupled terms allows to simulate circulating re-entry waves, which play an important role in generating a pathological heart rate. The existence of re-entry may entail serious disorders, like auricular fibrillation or tachycardia.
2013-12-04: Urszula Foryś (Uniwersytet Warszawski)
Title: Global stability for some types of delayed logistic equations - continuation
Abstract: This time we will focus on the main goal that is the study of simple epidemic model of vector-borne diseases proposed by Cooke which belong to the class of delayed logistic equations.
2013-11-20: Urszula Foryś (Uniwersytet Warszawski)
Title: Global stability for some types of delayed logistic equations
Abstract: We will focus on proving global stability for three different types of delayed logistic equation. Our main goal will be to study simple epidemic model of vector-borne diseases proposed by Cooke which belong to the class of delayed logistic equations.
2013-11-06, Marek Bodnar (University of Warsaw)
Title: Global stability of steady steady state of delay differential equations in neural network model
Abstract: We prove that a strong attractor of a discrete map implies global stability of a corresponding system of delay differential equations. We apply this result to a delayed Hopfield's model. We prove also that every attractor one-dimentional map is a strong attractor and we present an example that this is not true in dimension higher than one.
2013-10-23: Magdalena Bogdańska (University of Warsaw)
Title: Delay effects in the response of low grade gliomas to radiotherapy: a mathematical model and its therapeutical implications
Abstract: Low grade gliomas (LGGs) are a group of primary brain tumors, which are highly infiltrative and generally incurable but have median survival time of more than 5 years because of low proliferation. Management of LGGs has historically been controversial because these patients are typically young, with few, if any, neurological symptoms. Recently Pallud et al. studied patients with LGGs treated with first-line radiation therapy and found the counter-intuitive result that tumors with a fast response to the therapy had a worse prognosis than those responding late. We construct a mathematical model describing the basic facts of glioma progression. Radiation therapy included in our mathematical model captures the essentials of the dynamics and explains the relationship between proliferation, response to the therapy and prognosis. It can also provide an explanation to the observations of Pallud et al. and it can be used to explore different radiation regimes. Using the model we propose radiation fractionation schemes that might be therapeutically useful by helping to evaluate the tumor malignancy. It could help the oncologists in making the best possible decision on when and how act on the tumor.
2013-10-16: Simon Angus (Monash University)
Title: The Similarity of Human Interest Amongst the Nations
Abstract: Are Australians more like Americans, British, New Zealanders or Indonesians? What shapes human interests more: contemporary events or events from long ago? This talk aims to answer these questions with a novel data source and new statistical technologies. Whilst several attempts have been made to get at cultural similarity amongst peoples of Earth, thus far all have relied on survey data. In contrast, we take a 'big data' approach to the question and utilise Google Trends data -- aggregate search volume data by Google across 38 nations -- to construct a model of the similarity of human interest amongst nations. We use this model to produce synthetic similarities for out of sample ties enabling a hierarchical interest similarity presentation of the major and minor divisions in international human interest.
2013-10-09: Simon Angus (Monash University)
Title: Challenges in silico: modelling delays, death and repair in EMT6/Ro tumor cells under a variety of multi-dose irradiation protocols
Abstract: In silico (computational) techniques offer the potential to investigate efficiently many aspects of tumour development and progression. In particular, a calibrated, dynamic, in silico tumour model could be used to probe the combinatorially extensive, and largely unexplored, irradiation protocol space (dose size and timing sequence) in a facile way, with the potential to discover large gains in efficacy within a given total dose envelope, meriting further clinical investigation. However, to do this, the tumour model must present realistic delay, death and repair dynamics under multi-dose irradiation. Given that the exact mechanism of repair, cell cycle delay and death is not perfectly understood, the calibration approach itself allows for the testing of various theoretical assumptions. Our study, building on our previous work with single-dose irradiation (Angus & Piotrowska, 2013), finds that delay--death--repair dynamics are well represented by a reciprocal repair function (Fowler, 1999 & 2002) which includes an unrepairable cell fraction (Carabe-Fernandez, 2001).
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