Powrót do listy seminariów 
Seminarium Zakładu Biomatematyki i Teorii Gier
Prowadzi: Urszula Foryś
20141119, godz. 14:15, s. 4050 
Wojciech Niemiro (Uniwersytet Warszawski) 
UKRYTE MODELE MARKOWA, PRZYKŁADY I ALGORYTMY 
Przedstawimy ogólny schemat ukrytych modeli Markow I parę przykładów zastosowań. W miarę naszych możliwości postaramy się skupić na zastosowaniach w biologii I chemii. Zrobimy przegląd algorytmów obliczeniowych I symulacyjnych, ze szczególnym uwzględnieniem MCMC dla ukrytych procesów z czasem ciągłym, które wydaja się najważniejsze w modelowaniu kinetyki reakcji chemicznych (i dla których mamy dość świeże wyniki własne). 
20141105, godz. 14:15, s. 4050 
Krzysztof R. Apt (Uniwersytet Warszawski) 
Potentials and their uses in strategic games 
The idea of a potential was introduced in the influential paper of
Monderer and Shapley in 1994. It is a technique that allows one to conclude that a strategic game has a Nash equilibrium. We shall discuss the main aspects of this paper and subsequently illustrate other uses of potentials in our recent work on coordination games on graphs. In each such game the players are the nodes of a graph. Each node selects a colour from a set of colours (privately) available for it. The payoff to a node is the number of neighbours who chose the same colour. These games capture the idea of coordination in a local setting strategies. We shall focus on the issue of existence of Nash equilibria, kequilibria and strong equilibria. This is a joint work with Mona Rahn, Guido Schaefer and Sunil Simon. 
20141029, godz. 14:15, s. 4050 
Małgorzata Półtorak ((dawna absolwentka MISMAPu) ) 
FUNCTIONING IN CLOSE RELATIONSHIPS: MATHEMATICAL MODEL 
I will present modified Felmlee & Greenberg (1999) model of the dynamics of relationships between two persons. Using various parameters of the model we are able to explain various types of relationships and give some suggestions to make the relationship better. 
20141022, godz. 14:15, s. 4050 
JeChiang Tsai (Chung Cheng University, Taiwan ) 
Curvature dependence of propagating velocity for a simplied calcium model 
It is known that the relation between curvature and wave speed plays a key role in the propagation of twodimensional waves in an excitable model. For typical excitable models (e.g., the FitzHughNagumo (FHN) model), such a relation is believed to obey the linear eikonal equation, which states that the relation between the normal velocity and the local curvature is approximately linear. In this talk, we show that for a caricature model of intracellular calcium dynamics, although its temporal dynamics can be investigated by analogy with the FHN model, the curvature relation does not obey the linear eikonal equation even in the limiting case. Hence this caricature calcium model may be an unexpected excitable system, whose wave propagation properties cannot be always understood by analogy with the FHN model. 
20141015, godz. 14:15, s. 4050 
Wojciech Borkowski (Instytut Studiów Społecznych im. prof. B. Zajonca, UW ) 
Dynamiczna Psychologia Społeczna 
W istniejącym już od ponad 20 lat "Ośrodku badania układów złożonych i
nowych technologii" w Instytucie Studiów Społecznych UW, zajmujemy się
zastosowaniami teorii układów złożonych i informatyki w psychologii
społecznej (dział ten bywa nazywany "dynamiczną psychologią
społeczną"), ale także w obszarach stanowiących dla niej tło 
psychologii "ja", dynamice sieci neuronowych czy, z drugiej strony,
procesów ewolucyjnych. Jednym z głównych wątków badawczych i
teoretycznych były dla nas zawsze procesy wpływu społecznego, który
uznajemy za podstawowy mechanizm sterujący uwspólnianiem informacji
adaptacyjnej w ludzkich społeczeństwach, choć w tej chwili praktyka
badań znacznie się rozszerzyła w kierunku informatyki i ekonomi.
Poza różnorodnymi metodami badań psychologicznych i socjologicznych centralną metodą badawczych jest modelowanie komputerowe dynamiki procesów psychicznych, społecznych i ewolucyjnych za pomocą symulacji komputerowych, jako że narzędzie to pozwala badać zjawiska emergentne, powszechne w tych systemach. Stosujemy szeroką gamę modeli: od automatów komórkowych, algorytmów genetycznych, sztucznych sieci neuronowych i innych modeli sieciowych, po utworzone na ich bazie "minimalistyczne modele agentowe" będące naszą główną specjalnością, oraz rozbudowane  "realistyczne" modele agentowe. Kilka dosyć aktualnych linków rozszerzających temat:  Dynamical Minimalism: Why Less is More in Psychology, Andrzej Nowak http://www.ncbi.nlm.nih.gov/pubmed/15223518, http://psr.sagepub.com/content/8/2/183.full.pdf+html  Culture Change: The Perspective of Dynamical Minimalism, Andrzej Nowak, Wouter de Raad, and Wojciech Borkowski rozdział http://global.oup.com/academic/product/advancesincultureandpsychology9780199840694  Why Simulate? To Develop a Mental Model, Andrzej Nowak, Agnieszka Rychwalska and Wojciech Borkowski http://jasss.soc.surrey.ac.uk/16/3/12.html  UKŁADY ZŁOŻONE W NAUKACH SPOŁECZNYCH Wybrane zagadnienia (książka) http://scholar.com.pl/sklep.php?md=products&id_p=2029 
20140604, godz. 14:15, s. 4050 
Paweł Ciosmak (Uniwersytet Warszawski) 
Numerical methods for the dynamics of the populations with structure 
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. 
20140514, godz. 14:15, s. 4050 
María Vela Pérez (Service de Physique de l'Etat Condensé, CEASaclay, 91191 GifsurYvette, France) 
From Individual to Collective Dynamics in Argentine Ants 
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. VelaPerez, et al. (2013), Ant foraging and geodesic paths in labyrinths: Analytical and computational results, J. Theo. Biol. 320, 100112. 
20140507, godz. 14:15, s. 4050 
Emad Attia (doktorant z Egiptu) 
On the distance between adjacent zeros of solutions of first order differential equation with distributed delays 
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. 
20140430, godz. 14:15, s. 4050 
Urszula Foryś (Uniwersytet Warszawski) 
The survey on Lyapunov functions on the basis of the article by SzeBi Hsu c.d. 
20140409, godz. 14:15, s. 4050 
Agnieszka Bartłomiejczyk (Politechnika Gdańska) Henryk Leszczyński (Uniwersytet Gdański) 
Asymptotyka rozwiązań w modelach populacyjnych o strukturze cech fizjologicznych z dyfuzją 
Badamy model ewolucyjny uwzględniający śmiertelność, wzrost, narodziny i dyfuzję z warunkami brzegowymi Fellera. Rozpoczynamy rozważania od zasady maksimum, następnie analizujemy rozwiązania rozwijane w szereg Fouriera w przestrzeni Hilberta, która wyznaczona jest przez warunki Fellera. Struktura tych rozwinięć pozwala na przewidywanie asymptotycznych własności, w szczególności tzw. profilu. 
20140402, godz. 14:15, s. 4050 
Agnieszka Dziekańska (alumni of University College Dublin, Systems Biology, Ireland) 
Computational analysis of multistable signalling biochemical networks 
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 steadystates 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 steadystates. The study introduces two methods of computation of the biochemical landscape. The first method applies the concept of the quasipotential in order to compute the gradient of trajectory of a dynamic system as it evolves to its steadystate. The second method applies stochastic simulations (Gibbs sampling) for the purpose of deriving the probability densities that correspond to steadystates of the system. Calculation of landscapes for gene regulatory or signalling networks can determine the relative stability of steadystates 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. 
20140326, godz. 14:15, s. 4050 
Krzysztof Fujarewicz (Politechnika Śląska) 
Structural sensitivity analysis of mathematical models in biology 
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 socalled 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 gradientbased optimization for various models will be presented. 
20140312, godz. 14:15, s. 4050 
Marek Bodnar (Uniwersytet Warszawski) 
General model of a cascade of reactions with time delays: global stability analysis c.d. 
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 are presented. Then the abstract result is applied for the Hes1 gene expression model. 
20140305, godz. 14:15, s. 4050 
Marek Bodnar (Uniwersytet Warszawski) 
General model of a cascade of reactions with time delays: global stability analysis 
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 are presented. Then the abstract result is applied for the Hes1 gene expression model. 
20140226, godz. 14:15, s. 4050 (ZMIANA SALI) 
Jacek Waniewski (IBIB PAN) 
Matematyczne modele transportu w czasie dializy otrzewnowej c.d. 
20140219, godz. 14:15, s. 4050 (ZMIANA SALI) 
Jacek Waniewski (IBIB PAN) 
Matematyczne modele transportu w czasie dializy otrzewnowej 
Modele opisują procesy wymiany płynu i substancji pomiędzy tkanką a: 1) krwią przepływającą przez naczynia włosowate zawarte w tkance, oraz 2) otoczeniem tkanki (np. płynem dializacyjnym w jamie otrzewnowej lub żelem nałożonym na powierzchnię skóry). Modele używane w zastosowaniach klinicznych mają charakter modeli kompartmentowych, natomiast fizjologię tych procesów można opisać modelami opartymi o równania różniczkowe cząstkowe typu równań dyfuzjakonwekcjareakcja. Pokażemy, że liniowe wersje tych równań pozwalają na wyprowadzenie ciekawych zależności dostarczających interpretacji danych klinicznych i fizjologicznych. Uwzględnienie nieliniowych interakcji charakterystycznych dla żywej tkanki wymaga prowadzenia badań numerycznych. 
20140122, godz. 14:15, s. 5840 
Maciej Cytowski, Zuzanna Szymańska (ICM UW) 
Large Scale Parallel Simulations of 3D Cell Colony Dynamics 
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 10^{9} cells, which allows for instance to describe tumor growth in its early clinical stage. 
20140115, godz. 14:15, s. 5840 
Jan Poleszczuk (MiSDoMP i IBIB PAN) 
Pulse wave propagation models 
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. 
20140108, godz. 14:15, s. 5840 
Paweł Zwoleński (IM PAN) 
Phenotypic evolution of hermaphrodites 
We consider finite, phenotypestructured 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, intraspecific 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 TjonWu 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 byproduct we obtain relatively easy proof of LasotaTraple theorem concerning asymptotic stability of TjonWu equation. Moreover, we show applications of our theorem to some biologically reasonable situations of phenotypic inheritance. 
20131211, godz. 14:15, s. 5840 
Beata Zduniak (SGGW Warszawa) 
A VENTRICULAR TACHYCARDIA AND AV NODAL DOUBLE RESPONSE TACHYCARDIA IN A MODIFIED VAN DER POL EQUATION 
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 reentry waves, which play an important role in generating a pathological heart rate. The existence of reentry may entail serious disorders, like auricular fibrillation or tachycardia. 
20131204, godz. 14:15, s. 5840 
Urszula Foryś (Uniwersytet Warszawski) 
Global stability for some types of delayed logistic equations  continuation 
This time we will focus on the main goal that is the study of simple epidemic model of vectorborne diseases proposed by Cooke which belong to the class of delayed logistic equations. 
20131120, godz. 14:15, s. 5840 
Urszula Foryś (Uniwersytet Warszawski) 
Global stability for some types of delayed logistic equations 
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 vectorborne diseases proposed by Cooke which belong
to the class of delayed logistic equations.

20131106, godz. 14:15, s. 5840 
Marek Bodnar (Uniwersytet Warszawski) 
Global stability of steady steady state of delay differential equations in neural network model 
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 onedimentional map is a strong attractor and we present an example that this is not true in dimension higher than one. 
20131023, godz. 14:15, s. 5840 
Magdalena Bogdańska (Uniwersytet Warszawski) 
Delay effects in the response of low grade gliomas to radiotherapy: a mathematical model and its therapeutical implications 
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 ﬁrstline radiation therapy and found the counterintuitive 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. 
20131016, godz. 14:15, s. 5840 
Simon Angus ((Monash University) ) 
he 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. 
20131009, godz. 14:15, s. 5840 
Simon Angus (Monash University) 
"Challenges in silico: modelling delays, death and repair in EMT6/Ro tumor cells under a variety of multidose 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 multidose 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 singledose irradiation (Angus & Piotrowska,
2013), finds that delaydeathrepair dynamics are well represented by a
reciprocal repair function (Fowler, 1999 & 2002) which includes an
unrepairable cell fraction (CarabeFernandez, 2001).

20130605, godz. 16:15, s. 5820 
Marek Bodnar (Uniwersytet Warszawski) 
Traveling waves in reactiondiffusion equations with time delay 
I will talk about traveling waves in reaction diffusion systems with delay. On the basis on some simple equation I will show problems that arise when looking for traveling fronts in equation with delay. In fact, the system for the shape of wave front can be delay differential system and finding an appropriate solution is more difficult han is the case without delay and it is necessary to use Fixed Point Theorem or some interaction scheme. 
20130515, godz. 16:15, s. 5820 
Prof. Urszula Ledzewicz (USA) 
Timing and Dosage of AntiCancer Drug Therapies: An Optimal Control Approach 
A systematic study of cancer treatment requires that we take into account not only the cancerous cells and their growth, but also various
aspects of the tumor microenvironment. Its elemets include various types
of cancer cells, sensitive and resistant to the treatment, healthy
cells, tumor vasculature, immune system and more. We shell discuss
mathematical models that describe the dynamics of tumor growth in
relation to its supproting vasculature under reciprocal angiogenic
signaling. For such models, in addition to standard direct treatments
that kill cancer cells, one can introduce the second indirect treatment
by means of angiogenic inhibitors that target the tumor vasculature. A
second indirect approach is to consider the interactions between the
tumor and the immune system, inclusing tumor surveillance. Here a
classical, minimally parametrized model of tumorimmune interactions
will be discussed in connection with optimizing the treatment that
combined traditional chemotherapy with a stimulatory effect of the
immune system. We will also outline some future work on a more complex
model wich encompasses more elements of the microenvironment and
multitarget therapies. This will naturally lead to the topic of
metronomic chemotherapy, a new direction in cancer treatment where the
various aspects of the tumor microenvironment being targeted by one
cytotoxic drug applied accord to a properly chosen "metronomic" protocol
which involves between 20% and 80% MTD. It has been observed in
experimental studies that such treatment has lower toxicity, lowe drug
resistance and in addition exhibits antiagiogenic and immune system
stimulatory effects. The challenges concerning the modeling and
mathematical analysis for metronomic chemotherapy will be addressed.

20130508, godz. 16:15, s. 5820 
Marzena Dołbniak (Gliwice) 
Protocols of antiangiogenic and combined anticancer therapy 
In brief introduction information about negative results obtained after
single antiangiogenic treatment and reasons for use antiangiogenic
factors to normalization of chaotic and unregulated tumor vessels are
presented. I discussed several simple ordinary differential equation
(ODE) models of tumor growth taking into account the development of its
vascular network. Different biological aspects are considered from the
simplest model of Hahnfeldt et al. proposed in 1999 [4]; by modification
included influence of vessel density and ”pruning”
effect (d’OnofrioGandolfi [3]); or separation endothelial
cells for mature and immature (Benzekry et al. [2]); to the model in
which separation of sensitive and resistance cancer cells after
chemotherapy occur (Świerniak [5]). Some of these models can be used in
clinical oncology to optimize antiangiogenic and cytostatic drugs
delivery so as to ensure maximum efficiency.
I am aware that there is a big gap between the simulated and the real world and it this why I try to focus on several questions. The first is how modifications of the basic model improves the fit between the simulated therapy protocol and the real clinical results. The second question is how the dynamics of this model will look like after implementing protocols already used in medicine. Simple models of continuous and periodic protocols of combined therapy are implemented. Discussion on the dynamics of the models and their complexity is presented. 
20130424, godz. 16:15, s. 5820 
Łukasz Płociniczak (Politechnika Wrocławska) 
A New Mathematical Model of Corneal Topography 
Sight is the most important sense that we posses. It is crucial to understand the mechanics of vision in order to treat various diseases that may occur and disturb regular seeing. The eye's main part responsible for about twothirds of refractive power is the cornea. Cornea is transparent, shelllike structure situated in the frontal part of the eye. It is one of the most sensitive parts of human body and its various irregularities can cause many seeing disorders. Precise knowledge of corneal shape is very important and accurate mathematical models are necessary to fully understand biomechanics of cornea. We present a new model of corneal geometry based on a nonlinear membrane equation. We establish existence of solution and provide some estimates. When fitting with data we use its simplied form and find that mean error is of order of a few percent. Also, we are concerned with determining some unknown parameters when the solution is known (usually with a noise). This is one example of so called Inverse Problems. They are usually more difficult to solve and analyze than direct ones. Moreover, they often are illposed, that is, not necessarily have unique solution which is continuous with respect to the initial data. We propose some regularization methods and apply them to the real corneal data. We struggle with two types of different inverse problems. The first one concerns constant parameter case. It turns out that determination of these constants is a nonlinear problem in two unknowns to which solution we develop an iteration scheme and prove rates of convergence. The second problem is linear one and concerns the case when one of unknown parameters is not necessarily constant. the end we obtain a stable method of determining unknown parameters of our differential equation from the knowledge of corneal shape. These parameters may have direct relation to some biomechanical properties of the eye and can be used to provide some insights of corneal structure. 
20130417, godz. 16:15, s. 5820 
Urszula Foryś (Uniwersytet Warszawski) 
News from IMBM: modelling of prostate cancer immunotherapy 
Abstract: During my visit in IMBM in January I have discussed the idea
of new project with the team of Prof. Zvia Agur. We have decided to
focus on the modelling of prostate cancer immunotherapy. I will present
the model which was published in PlosOne recently. It is the system of
several ODEs, however most of them are linear. It occurs that for one
boost of immunotherapy this large system has simple, in fact
onedimensional dynamics. I will also present the analysis for impulsive
treatment and give conditions sufficient to cure. At the end I will
focus on the proposed changes in the model equations that are of our
interest now.

20130410, godz. 16:15, s. 5820 
Michal Komorowski (IPPT Homing+) 
The concept of information at the interface between statistics and systems biology 
The purpose of the talk is to discuss intricacies of quantifying information in some problems arising at the interface between statistic and biology. Behaviour generated by interacting molecules, cells or tissues is not random but focuses on sustaining life processes. Sustaining life, however, is to the large extend based on information storage, transmission and processing with examples ranging from the iconic DNA doublehelix through signal transduction pathways to proteomic and metabolic networks. Understanding how information is processed in living cells and organism is therefore one of the crucial elements to understand how life is sustained. Fisher and Shannon as most well known concepts. It has been originally associated with a precision parameters can be estimated in an experiment. Alternative approach by C. Shannon arose on the basic of communication theory and was later assimilated by statistical sciences. posterior distribution, Shannon Information, Fisher Information and Jeffrey's prior. Using examples of experimental design techniques and signal transduction pathways I will demonstrate how statistical theory can be used to better understand biological systems at the cellular level. 
20130320, godz. 16:15, s. 5820 
Andrea Quartarone (University of Messina, Italy) and Tatiana V. Ryabukha (MIMUW and NANU, Ukraine) 
Stability of the solutions of the mesoscopic equation that corresponds to the replicator equation. 
The replicator equation is a deterministic nonlinear equation arising in
evolutionary game theory describing the evolving lifeforms in terms of
frequencies of strategies. It is related to a mean field approach and
therefore it has a macroscopic character: the description is referred to
the frequencies (densities) of agents playing the corresponding
strategies. However, the macroscopic approach is not sufficient to
describe the dynamics of complex living systems by reducing the
complexity of the overall systems. In some applications to consider the
agents as discrete interacting units is important in order to capture
the complexity of (biological) phenomena.
We propose a class of kinetic type equations that describe the replicator dynamics at the mesoscopic level. Under suitable assumptions we show the asymptotic (exponential) stability of the solutions to such kinetic equations in the case when the corresponding macroscopic equation is asymptotically stable. To obtain the mesoscopic model corresponding to the replicator equation we follow the techniques developed by N. Bellomo with coautors applying tools of the kinetic theory of active particles for complex living systems. In perspective, the obtained results could be used for analysing the asymptotic behaviour in time of mathematical model which describes tumourimmune system competition. 
20130313, godz. 16:15, s. 5820 
Jan Poleszczuk (MISDoMP Uniwersytet Warszawski) 
Cellular senescence — a key player in radiotherapy and radiation induced bystander effect? 
I'm going to present a novel biological hypothesis which combines two hitherto distinct phenomena: cellular senescence and radiation induced bystander effects. Hypothesis gives a new insight into the principles governing the tumor response to ionizing radiation and provides elegant explanation for the various types of bystander effects. Basic analysis based on a mathematical models reveals that the radiationdose survival curves, and hence the tumor cure probabilities are highly dependent on the amount of cellular senescence triggered by the ionizing radiation or by the bystander signals. 
20130306, godz. 16:15, s. 5820 
Agnieszka WiszniewskaMatyszkiel (Uniwersytet Warszawski) 
Applications of large dynamic games to modelling markets and exploitation of ecosystems 
20130227, godz. 16:15, s. 5820 
Agnieszka WiszniewskaMatyszkiel (Uniwersytet Warszawski) 
Applications of large dynamic games to modelling markets and exploitation of ecosystems 
I'm going to present my results on large games  mainly games with a continuum of players and their economic applications. Games with a continuum of players may be regarded as an equivalent of continuum  microscale models of physics. They were developed to model situation in which the number of interacting agents, called players (human beings, animals or even particles),is large enough to make the influence of a single player on some global variables negligible. 
20130123, godz. WYJĄTKOWO o 16:30, s. 5820 
Martin Parisot (MIMUW ERCIM) 
Intermediate Modeling between Kinetic Equations and Hydrodynamic Limits: Application to the SpitzerHarm regime 
This work is devoted to the study of a problem resulting from plasma physics: heat transfer of electrons in a plasma close to Maxwellian equilibrium. A formal derivation from the Vlasov equations is proposed. A hierarchy of intermediate models between the kinetic equations and the hydrodynamic limit is described. In particular, a new system 
20121212, godz. 16:15, s. 5820 
Urszula Foryś (Uniwersytet Warszawski) 
Constructing Lyapunov functionals IV 
20121205, godz. 16:15, s. 5820 
Urszula Foryś (Uniwersytet Warszawski) 
Constructing Lyapunov functionals III 
20121128, godz. 16:15, s. 5820 
Urszula Foryś (Uniwersytet Warszawski) 
Constructing Lyapunov functionals II 
20121121, godz. 16:15, s. 5820 
Urszula Foryś (Uniwersytet Warszawski) 
Constructing Lyapunov functionals 
During the talk we will recall/summarise methods allowing to construct Lyapunov functionals for ODEs. We will start from linear ODEs and then switch to some nonlinear examples. 
20121107, godz. 16:15, s. 5820 
Marek Bodnar (Uniwersytet Warszawski) 
Linear Chain Trick, distributed delays, and stability of steady states 
The seminar is devoted to the theory of delay differential equations with distributed delays or in other words with memory. The Linear Chain Trick is discussed and I show under which condition an equation with distributed delays is equivalent to the system of ordinary differential equations. The stability of steady states will be discussed. I show that the equation with distributed delays is more stable than with a discrete delay in the sense that steady states are stable for a wider range of parameters. 
20121024, godz. 16:15, s. 5820 
Jan Karbowski (MIMUW i IBIB PAN) 
Translating neural activity into behavior 
How neural activity in the brain generates a particular behavior is not well understood. The focus of the talk will be on modeling neural circuit responsible for forward and backward locomotion in the nematode C. elegans. In particular, I will discuss an optimal pattern of connections 
20121017, godz. 16:15, s. 5820 
Piotr Szopa (Uniwersytet Warszawski) 
Cellular calcium dynamics 
During the talk I want to describe key aspects of cellular 
20121010, godz. 16:15, s. 5820 
Ishtiaq Ali (Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan, and MIMUW) 
Numerical Solutions of Delay Differential Equations Using Spectral Methods 
In this talk I shall present an efficient numerical approach for delay differential equations with vanishing proportional delays based on spectral methods. We develop a spectral approach for the pantograph typedelay differential equations. A Legendre spectralcollocation method is employed to obtain highly accurate numerical approximations to the exact solution. The exponential convergence was obtained theoretically which was confirmed by some numerical examples, provided the data in the given pantograph delay differential equation are smooth. We also discuss briefly the case of nonlinear and system of pantographtype delay 
20120516, godz. 16:15, s. 5820 
Monika Piotrowska (Uniwersytet Warszawski) 
Noisesustained fluctuations in stochastic dynamics with a delay 
20120509, godz. 16:15, s. 5820 
Jan Poleszczuk (MISDOMP) 
The impact of time delays on synchronizability in stochastic systems 
20120425, godz. 16:15, s. 5820 
Bogdan Kaźmierczak (IPPT) 
Spatially extended model of kinasereceptor interaction in cells 
We consider a spatiallyextended model describing mutual 
20120418, godz. 16:15, s. 5820 
Marina Dolfin (University of Messina) 
MODELLING Th1Th2 CELL BALANCE DURING T CELL MEDIATED IMMUNE RESPONSE 
Experimental observations show the relevance of Th1Th2 cell balance in hypersensitive reactions. We propose a theoretical model of T cell mediated immune response focusing on Th1Th2 cell balance, in the mathematical framework of the theory of reacting fluid mixtures with proliferative events. In our model the proliferative events, i.e. events which are not mass preserving, are the clonal expansions of Th1 and Th2 cells. Smooth approximate solutions of the resulting PDE's system are analyzed by using a doublescale approach enlightening some features regarding the multiscale complexity of the phenomenon under observation. 
20120404, godz. 16:15, s. 5820 
Jurij Kozicki (UMCS) 
Markov Dynamics in a Spatial Ecological Model with Dispersion and Competition Part II but hopefully selfcontained 
20120328, godz. 16:15, s. 5820 
Beata Zduniak (Uniwersytet Warszawski) 
INFLUENCE OF DELAYED FEEDBACK ON MODIFIED VAN DER POL OSCILLATOR 
Modified van der Pol equation can be used to describe the activity of elements of electrical conduction system of human heart: sinoatrial node (SA), atrioventicular node (AV), and His Purkinje system. This model has a number of interesting properties allowing do reconstruct phenomena observed in physiological experiments as well as in Holter 
20120321, godz. 16:15, s. 5820 
Jacek Banasiak (KwaZuluNatal, Durban) 
Classical solutions of fragmentationcoagulation equations with unbounded coagulation rates 
So far fragmentationcoagulation equations with strong coagulation have been analysed using weak compactness techniques which only yielded weak solutions. Recently we have proved that the fragmentation operator is sectorial which, combined with some interpolation techniques, allowed for proving classical solvability of such equations for large classes of fragmentation and coagulation rates. 
20120314, godz. 16:15, s. 5820 
Jurij Kozicki (UMCS) 
Markov Dynamics in a Spatial Ecological Model with Dispersion and Competition 
The evolution of an individualbased spatial ecological model with dispersion and competition is studied. In the model, an infinite number of individuals, point particles in R^d, reproduce themselves, compete, and die at random. These events are described by a Markov generator, which determines the evolution of states understood as probability measures on the space of particle configurations. The main result is a statement that the corresponding correlation functions evolve in a scale of Banach spaces and remain subPoissonian, and hence no clustering occurs, if the 
20120307, godz. 16:15, s. 5820 
Urszula Foryś (Uniwersytet Warszawski) 
On some SIRC epidemic model and vaccination strategies 
We consider a model of SIRC type, taking into account four groups: susceptible, infected, removed and carriers. We study the dynamics in two interesting cases: when a positive steady state does not exist and when it exists. Efficient vaccination strategies are proposed which are based on 
20120229, godz. 16:15, s. 5820 
Tatyana Ryabukha (Institute of Mathematics, National Academy of Sciences of Ukraine and MIMUW) 
Equilibrium solutions for a microscopic model of population dynamics 
Mirosław Lachowicz (MIMUW) 
20120222, godz. 16:15, s. 5820 
Urszula Foryś (Uniwersytet Warszawski) 
Chinese reminiscences 
20120118, godz. 16:15, s. 5820 
Jędrzej Jabłoński (Uniwersytet Warszawski) 
Modeling mortality of a sizestructured population using optimization approach to predator's behaviour (case of fish and Daphnia) 
Existing models of fish predation are either descriptive or lack realistic assumptions on predator's motion. Presented model fills this gap. The pure optimization approach gives answers not only about prey mortality, but also about predator's trajectory and speed. 
20111214, godz. 16:15, s. 5820 
Tatiana Ryabukha (Institute of Mathematics, National Academy of Sciences of Ukraine and MIMUW) 
The Liouville Equation for a Stochastic Particle System 
20111207, godz. 16:15, s. 5820 
Marek Bodnar (Uniwersytet Warszawski) 
Friction dominated dynamics of interacting particles locally close to a crystallographic lattice towards conclusion but of course self contained 
20111130, godz. 16:15, s. 5820 
Marek Bodnar (Uniwersytet Warszawski) 
Friction dominated dynamics of interacting particles locally close to a crystallographic lattice. Selfcontained continuation 
20111123, godz. 16:15, s. 5820 
Karol Wawrzyniak (ICM UW & National Centre for Nuclear Research) 
On Phenomenology, Dynamics and some Applications of the Minority Game 

20111116, godz. 16:15, s. 5820 
Marek Bodnar (Uniwersytet Warszawski) 
Friction dominated dynamics of interacting particles locally close to a crystallographic lattice 
We study a system of particles, in general ddimensional space, that interact by means of pair potential and adjust their positions according to the gradient flow dynamics induced by the total energy of the system. We consider the case when the range of the interaction is of the same order as the mean interparticle distance. It is also assumed that particles, locally, are located close to some crystallographic lattice. An appropriate system of equations that describes the evolution of macroscopic deformation of the crystallographic lattice, as well as the system that describe the evolution of the main crystallographic directions is derived. Well posedness of the derived system is studied as well as the stability of the particle system. Same examples of potentials that yield stable and unstable systems are given. 
20111019, godz. 16:15, s. 5820 
Roman Cherniha, (Institute of Mathematics of NASU, National University 'KyivMohyla Academy ') 
Mathematical model for fluidglucosealbumin transport in dialysis and its steadystate solutions 
Mathematical description of fluid and solute transport between blood and 
20111012, godz. 16:15, s. 5820 
Maria VelaPerez (IE University, Segovia) 
Geodesic paths in simple graphs for some social insects 
Social insects are an important example of complex collective behavior. In particular, ant colonies develop diff erent 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 [2], we will consider ants as random walkers where the probability to move in one or another direction is influenced by the concentration of pheromone near them (reinforced random walks). We are mainly interested not in an individual random walker but rather on a large number of random walkers, their collective behavior, and the possibility for them to aggregate forming geodesic paths between two points in some simple networks. We investigate the behavior of ants in a two node network and in a three node network (with and without directionality constraint). Our analytical and computational results show that in order for the ants to follow shortest paths between nest and food, it is necessary to superimpose to the ants' random walkthe chemotactic reinforcement. It is also needed a certain degree of persistence so that ants tend to move preferably without changing their direction much. Another important fact is the number of ants, since we will show that the speed for finding minimal paths increases very fast with it. Bibliography [1] B. Holldobler and K. Wilson. The ants, Berlin: Springer, 1990 [2] M. VelaPerez, M. A. Fontelos and J. J. L. Velazquez. Ant foraging and minimal paths in simple graphs, submitted for publication 
20110601, godz. 16:15, s. 5820 
Tatiana Ryabukha (Institute of Mathematics, National Academy of Sciences of Ukraine and MIMUW) 
Nonequilibrium cluster expansions in the theory of manyparticle dynamical systems 
This talk deals with analytical methods in statistical mechanics. It's 
20110525, godz. 16:15, s. 5820 
Adam Bobrowski (Politechnika Lubelska) 
From diffusions on graphs to Markov chains via asymptotic state lumping 
We show that finitestate Markov chains may be approximated by fast 
20110518, godz. 16:15, s. 5820 
Tadeusz Płatkowski (Uniwersytet Warszawski) 
Game dynamics for players with complex personalities 
We consider populations of individuals who are engaged in nperson public good games or in twoperson non symmetric or symmetric social dilemma games. The players imitate the most attractive strategies, and the choice is motivated not only by their payoffs, but also by their popularity in the population. The aggregated parameter which determines the influence of these two factors on the strategy choice of the players is identified with the sensitivity to reinforcements parameter in the Hernstein's Matching Law of mathematical psychology. The idea of of imitating the most successful, and the copying the most popular strategies leads to stabilization of cooperation in the populations of individuals in the considered classes of games. The level of cooperation depends on the sensitivity to reinforcements. We discuss the existence of equilibria and their stability for such populations. A unique threshold of the sensitivity is found, below which the polymorphic equilibria are stable, and above which they are unstable. 
20110504, godz. 16:15, s. 5820 
Urszula Foryś (Uniwersytet Warszawski) 
More on linear differential systems with small delays 
We'll study the aysymptotic dynamics of linear systems of DDEs with small delays. It can be shown that asymptotically such systems behave as the socalled special solutions and for linear DDEs these solutions coincide with fundamental solutions. Moreover, we are able to calculate the limitof X^{1}(t)x(f)(t) as t tends to infinity, where X(t) is the fundamental matrix (a special solution matrix) and x(f) is the solution to DDe with the initial function f at t=0. This limit can be expressed in terms of the basis of the generalised eigenspace for the formal adjoint equation. 
20110420, godz. 16:15, s. 5820 
Wizytówka Biomatematyki i Teorii Gier 
Przedstawiamy się cd 1. Tatiana Ryabukha Institute of Mathematics, National Academy of Sciences of Ukraine On solutions of classical and dual BBGKY hierarchies 2. Jacek Miękisz On games, genes, and delays O grach, genach i czasowych opóźnieniach 3. Urszula Foryś Delays in different natural phenomena Opóźnienia w różnych procesach naturalnych 4. Monika Piotrowska About the fascinating delays and cellular automata O fascynujących opóźnieniach i automatach komórkowych 5. Jan Poleszczuk Cancer stem cell hypothesis, tumor angiogenesis and influence of delay on biochemical networks Hipoteza komórek macierzystych nowotworu, angiogeneza oraz wpływ opóźnień na przebieg reakcji chemicznych 
20110406, godz. 16:15, s. 5820 
Wizytówka Biomatematyki i Teorii Gier 
Przedstawiamy się 1. Tatiana Ryabukha, Institute of Mathematics, National Academy of Sciences of Ukraine, On interplay between statistical mechanics and life sciences in science globalization perspective 2. Mirosław Lachowicz, Markov jumps everywhere, Markowskie skoki wszędzie 3. Tadeusz Płatkowski, Some models of cooperation, O kilku modelach kooperacji 4. Agnieszka WiszniewskaMatyszkiel, Dynamic games, continuum of players and expectations, Gry dynamiczne, continuum graczy i oczekiwania 5. Jacek Miękisz, On games, genes, and delays, O grach, genach i czasowych opóźnieniach 6. Urszula Foryś, Delays in different natural phenomena, Opóźnienia w różnych procesach naturalnych 7. Monika Piotrowska, About the fascinating delays and cellular automata, O fascynujących opóźnieniach i automatach komórkowych 8. Jan Poleszczuk, Cancer stem cell hypothesis, tumor angiogenesis and influence of delay on biochemical networks, Hipoteza komórek macierzystych nowotworu, angiogeneza oraz wpływ opóźnień na przebieg reakcji chemicznych 
20110330, godz. 16:15, s. 5820 
Urszula Foryś (Uniwersytet Warszawski) 
Small delays 
20110316, godz. 16:15, s. 5820 
Marta Kulik (UW) 
Hipoteza Zielonej Ziemi  model komputerowy 
Wszechobecność roślin zielonych zainspirowała Hairstona, Smitha i Slobodkina do opracowania ogólnej teorii kontroli populacji lądowych. W Hipotezie Zielonej Ziemi (HSS) zauważyli oni, że do znacznego uszczuplenia populacji roślin dochodzi niezmiernie rzadko, liczebność (biomasa) roślinożerców zatem nie może być limitowana przez zasoby. Z drugiej strony nie ogranicza ich również środowisko abiotyczne, stąd czynnikiem ograniczającym jest drapieżnictwo. Stworzony został komputerowy model ewolucji testujący hipotezę, że względne dostosowanie roślinożerców jest niższe niż roślin (i szczytowych drapieżników), co wyklucza osiągnięcie przez nie wysokiego zagęszczenia, bliskiego pojemności środowiska. Założono istnienie trzech populacji, należących do jednego łańcucha troficznego (populacje roślin, roślinożerców i mięsożerców). Osobniki w każdej z populacji określono za pomocą binarnych sekwencji ich genotypów. Dostosowanie osobników, wyrażające ich zdolność do korzystania z zasobów oraz obrony przed drapieżnikami, oszacowano licząc zgodne allele w odpowiednich genotypach. Rozrodczość oraz śmiertelność w każdym kroku czasowym były funkcją dostosowania i liczebności populacji. Analiza zmienności genetycznej pokazała, że najwyższa różnorodność genetyczna występowała w populacji roślinożerców. Zgodnie z przewidywaniami, dostosowanie roślinożerców oraz poziom wypełnienia ich pojemności środowiska były istotnie niższe niż wartości otrzymywane dla skrajnych poziomów troficznych (roślin i drapieżników). Model powstał we współpracy z prof. Piotrem Dawidowiczem oraz prof. Dariuszem Wrzoskiem. 
20110302, godz. 16:15, s. 5820 
Urszula Foryś (Uniwersytet Warszawski) 
Small time delays 
20110223, godz. 16:15, s. 5820 
Urszula Foryś (Uniwersytet Warszawski) 
Small time delays 
20110216, godz. 16:15, s. 5820 
Natalia Bielczyk (Uniwersytet Warszawski) 
Dynamical Models of Dyadic Interactions with Time Delay 
We will discuss a general class of linear models of dyadic interactions with a constant discrete time delay. In such models, changes of stability of stationary points occur for various intervals of parameters which determine the intensity of interactions. Conditions guaranteeing arbitrary number (that is zero, one or more) switches are formulated and the relevant theorems are proved. A systematic analysis of all generic cases is carried out. Possible generalizations to triadic interactions will also be presented. The talk is based on the joint work with U. Foryś and T. Płatkowski. 
20110119, godz. 16:15, s. 5820 
Michał Matuszak (UMK Toruń) 
Coevolution of networks and strategies 
Evolution of cooperation, within a framework of Prisoner's Dilemma game, on scalefree graphs will be discussed. We will present coevolutionary stochastic dynamics which lead to scalefree graphs with various exponents. 
20110112, godz. 16:15, s. 5820 
Urszula Foryś (Uniwersytet Warszawski) 
Still more on small time delays 
20110104, godz. 16:15, s. 5820 
Urszula Foryś (Uniwersytet Warszawski) 
More on small time delays 
20101208, godz. 16:15, s. 5820 
Urszula Foryś (Uniwersytet Warszawski) 
Equations with small delays 
I'll present a review of known results concerning equations with small delays. This talk will be mainly focused on linear and semilinear delay differential equations with small delays. 
20101124, godz. 16:15, s. 5820 
Kazimierz Piechór (IPPT PAN) 
Mechanochemiczny model waskulogenezy i angiogenezy, liniowa stabilność modelu, fale biegnące 
20101103, godz. 16:15, s. 5820 
Piotr Pokarowski (Uniwersytet Warszawski) 
A minimal proteinlike lattice model 
I will summarize results of my papers with Andrzej Kolinski. We have designed a minimal model of protein folding that reproduces in a qualitative way the most pronounced features of globular proteins. Using Monte Carlo simulations we have estimated a set of parameters for which the native state is the global minimum of conformational energy. This implies the minimality of our force field. Then we have found such interaction parameters for which the model satisfies the thermodynamic hypothesis and folding transition is maximally cooperative. Contrary to HP models, long range interactions are consistent with statistical contact potentials within an average protein environment and not with the transfer energies of residues from water. Cooperativity depends on protein architecture: it is the highest for the beta motif and the lowest for the alpha motif. 
20101027, godz. 16:15, s. 5820 
Mirosław Lachowicz (Uniwersytet Warszawski) 
DNA 
Few remarks on the possible mathematical description of the process of denaturation of DNA 
20101020, godz. 16:15, s. 5820 
Michał Matuszak (UMK) 
Smooth Conditional Trajectory Evaluation in Dynamical Gaussian Networks 
The seminar will present possibilities of applying Gaussian networks in realistic animation of virtual characters and optimal redeployment in multiagent environments. It will be achieved by solving the variational equations for FreidlinWentzell action functionals. 
20100526, godz. 16:15, s. 5820 
Roman Cherniha (NAS of Ukraine and University Kyiv Mohyla Academy) 
Symmetries and exact solutions of the diffusive LotkaVolterra system 
Lie and conditional symmetries of the classical LotkaVolterra sys tem inthe case of one space variable are completely described and sets of suchsymmetries in explicit form are constructed. These symmetries are used toreduce the classical LotkaVolterra systems with correctly specifiedcoefficients to ODE systems and examples of exact solutions in explicitform are found. The properties of the obtained solutions are examined withthe aim to provide the relevant interpretation for population dynamics.

20100519, godz. 16:15, s. 5820 
Irena Lasiecka, profesor wizytujący w ramach projektu Nowoczesny Uniwersytet programu Kapitał Ludzki Unii Europejskiej (University of Virginia) 
Boundary stabilization of a 3D Navier Stokes flow in the neighborhood of an unstable equilibrium 
Połączone seminarium: Równania Fizyki Matematycznej i Biomatematyka i Teoria GierWe shall consider a 3D Navier Stokes flow defined in the neighborhood of an unstable equilibrium. For large Reynolds numbers, the steady state solutions are unstable and cause turbulence in their surroundings. Our goal is to construct a feedback operator, supported on the boundary of the domain, which will produce local exponential stability of such steadystate solution. The construction is based on solvability of optimization problem with "high" gain (unbounded) functional cost. This leads to the analysis of existence and uniqueness of the associated nonstandard Riccati equations with boundary controls. 
20100428, godz. 16:15, s. 5820 
Monika Piotrowska (Uniwersytet Warszawski) 
Family of angiogenesis models with discrete delays 
We will discuss a family of models with delays describing the process of angiogenesis, that is a physiological process involving the growth of new blood vessels from preexisting ones. This family includes the well known models of tumour angiogenesis proposed by Hahnfeldt et al. and Ergun et al. and is based on the Gompertz type of the tumour growth. The family of considered models depends on two time delays and a parameter which reflects how strongly the vessels dynamics depends on the ratio between tumour and vessels volume. 
20100421, godz. 16:15, s. 5820 
Jacek Miekisz (Uniwersytet Warszawski) 
Gry ewolucyjne na grafach 
Będziemy rozważać Zamieć Śnieżną na grafach regularnych i z losowym doborem graczy oraz Dylemat Więźniaa bezskalowych grafach losowych BarabasiAlberty. 
20100414, godz. 16:15, s. 5820 
Ryszard Rudnicki (US i IMPAN) 
O własnościach gatunków semelpatrycznych 
Gatunek semelpatryczny, to taki, którego przedstawiciele rozmnażają się raz w życiu i umierają. Będziemy dodatkowo zakładać, że długość życia osobników n jest stała. Przedstawimy model strukturywiekowej populacji semelpatrycznej z dyskretnym czasem. Dla n=1 model redukuje się do funkcji jednej zmiennej. W tym przypadku naszkicujemy dowód twierdzenia o globalnej stabilności punktu stałego w oparciu o twierdzenieSzarkowskiego.Dla n>1 model sprowadza się do transformacji w przestrzeni nwymiarowej. Model ten ma zaskakujące własności. Między inny dla n parzystych rozwiązanie stacjonarne nigdy nie jest stabilne. Również asymptotyka długoczasowa jest zaskakująca. Konkurencja wewnątrz gatunkowa prowadzi do eliminacji wszystkich roczników za wyjątkiem jednego. Jest to zgodne z obserwacjami biologicznymi np. różnych gatunków owadów. 
20100331, godz. 16:15, s. 5820 
Jacek Miekisz (Uniwersytet Warszawski) 
Gry ewolucyjne na grafach regularnych i losowych 
Główne pytanie: jak struktura grafu wpływa na poziom kooperacji to znaczy postać miary stacjonarnej odpowiedniego łańcucha Markowa? Odpowiedź na seminarium. 
20100324, godz. 16:15, s. 5820 
Jacek Miękisz (Uniwersytet Warszawski) 
Gry ewolucyjne na grafach 
Od pewnego czasu wiadomo, że struktura przestrzenna sprzyja zachowaniom kooperacyjnym. Przedstawię wyniki dotyczące poziomu kooperacji w grach typu Dylemat Więźnia, Zamieć Śnieżna oraz JeleńZając. 
20100317, godz. 16:15, s. 5820 
Jarosław Bihun ((Narodowy Uniwersytet im. Jurija Fedkowycza w Czerniowcach)) 
Averaging in Multifrequency Systems of DifferentialFunctional Equations 
This work is devoted to the development and justification of averaging 
20100310, godz. 16:15, s. 5820 
Krzysztof Mogielski i Tadeusz Płatkowski (MIMUW) (Uniwersytet Warszawski) 
A Mechanism of Dynamical Interactions for TwoPerson Social Dilemmas 
We propose a new mechanism of interactions between game  theoretical 
20100303, godz. 16:15, s. 5820 
Tomasz Lipniacki (IPPT) 
Przestrzenna regulacja kaskady kinaz 
20100120, godz. 16:15, s. 5820 
Michał Ramsza (SGH) 
Twierdzenie MarkusaYamabe w teorii gier ewolucyjnych 
Podczas prezentacji zostanie przedstawione twierdzenie MarkusaYamabe (Markus, Yamabe, 1960) o globalnej asymptotycznej stabilności. Twierdzenie zostanie przedstawione w uproszczonej wersji przystosowanej do zastosowania w teorii gier ewolucyjnych. Jako przykład zastosowania zostaną podane dwa różne dowody twierdzenia o globalnej asymptotycznej stabilności równowagi w symetrycznej jednookresowej grze przetargowej w dynamice testowania i porównań binarnych. 
20100113, godz. 16:15, s. 5820 
Jakub Kowalski (Uniwersytet Wrocławski) 
Ewolucja populacji  model Penna 
Przedstawię założenia teoretyczne modelu zarówno z punktu widzenia matematyki, jak i biologii, a także powiem, do jakich wniosków prowadzą symulacje z jego wykorzystaniem. 
20100106, godz. 16:15, s. 5820 
Marek Bodnar (Uniwersytet Warszawski) 
Effects of time delay on stability for simple linear DDEs 
We illustrate the influence of time delay on the stability of steady state for some simple linear delay differential equations. We prove that for one DDE with one discrete delay the only stability switch that can occur while delay is increasing is from the stable case to the unstable one. We also justify that in the case of several discrete delays if the steady state is unstable in the case without delays then it remains unstable for positive delays and we give an example showing that for two discrete delays while enlarging them, we can have the following stability switch: stable  unstable  stable  unstable. We also present an example of a system of two linear DDEs with one discrete delay tau, such that the steady state is unstable for tau = 0 and is stable for some tau>0. 
20091216, godz. 16:15, s. 5820 
Monika Piotrowska (Uniwersytet Warszawski) 
O pracy Tembine, Altmana i ElAzouzi czyli o symetrycznych i asymetrycznych opóźnieniach w grach ewolucyjnych. 
Zajmiemy się tematyką opóźnień w symetrycznych grach ewolucyjnych, gdzie z każdą czystą strategią powiązane jest dyskretne opóźnienie pojawiające się w równaniach replikatorowych. 
20091209, godz. 16:15, s. 5440 (wyjatkowo inna sala) 
Benoit Perthame (Pierre & Marie Curie University, Paris) 
Adaptive evolution: a population view 
Połączone Seminarium Biomatematyka i Teoria Gier i Seminar Ph.D. Programme Mathematical Methods in Natural Sciences Więcej informacji na http://mmns.mimuw.edu.pl/perthame/ Seminarium będzie samozawierające się 
20091202, godz. 16:15, s. 5820 
Marek Bodnar (Uniwersytet Warszawski) 
Stability of the expected value and boundness of the variance of some stochastic timedelay differential equations  conclusion 
20091125, godz. 16:15, s. 5820 
Marek Bodnar (Uniwersytet Warszawski) 
Stability of the expected value and boundness of the variance of some stochastic timedelay differential equations 
20091118, godz. 16:15, s. 5820 
Daniel Wójcik (Nencki Institute of Experimental Biology) 
Simple point process models of neural spike trains 
A necessary ingredient for a quantitative theory of neural coding is appropriate spike kinematics: a precise description of spike trains  sequences of standard voltage impulses used for communication between neurons. While summarizing experiments by complete spike time collections is clearly inefficient and probably unnecessary, the most common probabilistic model used in neurophysiology, the inhomogeneous Poisson process, often seems too crude. Recently a more general model, the inhomogeneous Markov interval (IMI) model (Berry & Meister, 1998; Kass & Ventura, 2001), was considered, which takes into account both the current experimental time and the time from the last spike. In my talk I will discuss the nature of neural data to be understood and show how they naturally fall into point process description. I will introduce some basic point process models (Poisson and renewal processes) reaching IMI models in some general framework. Then I will propose a direct method of estimation that is easy to implement, fast, and conceptually simple. The method will be illustrated with an analysis of sample data from the cat's superior colliculus. Zapraszam, Jacek Miękisz 
20091104, godz. 16:15, s. 5820 
Marek Bodnar (Uniwersytet Warszawski) 
Stability of the expected value and boundness of the variance of some stochastic timedelay differential equation and its application to the hemapoietic stem cell regulation system 
The results of work of J. Lei and M. Mackey (SIAM J. Appl. Math., 67, 387407 (2007)) will be presented. We will study the stability of the trivial solution of a stochastic delay differential equation in the presence of an additive and multiplicative white noise. We will show the conditions guaranteeing that the expected value of the solution converges to zero and that the variance is bounded. We will also give a condition for unboudness of the variance. The results will be applied to the hemapoietic stem cell regulation system. 
20091028, godz. 16:15, s. 5820 
Mirosław Lachowicz (Uniwersytet Warszawski) 
Denaturacja DNA i pewne równania różniczkowocałkowe 
Zostanie przedstawiona pewna klasa równań różniczkowocałkowych i dość desperacka próba opisu zjawiska denaturacji DNA (pękania wiązań wodorowych)pod wpływem temperatury  tzw. topnienie DNA. 
20091007, godz. 16:15, s. 5820 
Ofer Biham (Racah Insitute of Physics, The Hebrew University, Jerusalem) 
Stochastic analysis of toggle switch and toxinantitoxin modules 
Regulation processes in cells are performed by networks of interacting genes, which regulate each other's expression. To analyze the function of genetic networks, we simulate the dynamics of small functional modules using stochastic methods which take into account the effects of fluctuations. In this talk I will consider two genetic modules  the toggle switch (encoded synthetically on plasmids) and the toxinantitoxin system (I will focus on the hipBA module in E. coli). I will show that in such modules, which include feedback, fluctuations give rise to crucial quantitative and qualitative effects. For the toggle switch I will show how the details of the system architecture affect the bistable state and the switching time. For the hipBA toxinantitoxin system, I will focus on its role in the phenomenon of bacterial persistence. 
20090603, godz. 16:15, s. 5840 
Jan Poleszczuk (Uniwersytet Warszawski) 
Validity of delayed differential equations in biochemical reactions systems 
It is well known that the time evolution of spatially homogeneous mixture composition consisting of molecules from N different species that can react through M chemical channels can be deterministically described by some set of ordinary differential equations. The method of generating stochastic simulations of such systems was developed by D.T. Gillespie. There is a high correspondence between quantitative results obtained by these two methods. Recently, to incorporate the fact that some reactions take some time or to reduce complexity of systems there were introduced delays in reactions. Therefore, ordinary differential equations have been reformulated as delay differential equations. To incorporate delay in the stochastic algorithm, some modifications of the Gillespie algorithm were introduced. We investigate validity of deterministic descriptions of two delayed reactions presented in some papers with the usage of stochastic algorithm. Comparison of deterministic and stochastic result revealed that in both delayed reactions the natural formulation of DDEs for those reactions brings assumptions which are not consistent with reactionsdescriptions. Therefore, we propose also another deterministic descriptions for those reactions from which the general idea of formulating deterministic descriptions for delayed reactions can be seen. 
20090520, godz. 16:15, s. 5840 
Agnieszka WiszniewskaMatyszkiel (Uniwersytet Warszawski) 
Evolutionary games with continuous strategy spaces 
20090513, godz. 16:15, s. 5840 
Agnieszka WiszniewskaMatyszkiel (Uniwersytet Warszawski) 
Evolutionary games with continuous strategy spaces 
20090506, godz. 16:15, s. 5840 
Agnieszka WiszniewskaMatyszkiel (Uniwersytet Warszawski) 
Evolutionary games with continuous strategy spaces 
We shall consider evolutionary games based on games with continuous strategy spaces. Properties of replicator and adaptive dynamics will be described. The sequence of presentations will be based on papers of Oechsler & Riedel, Cressman, Hofbauer & Cressman and Doebeli, Hauert & Killingback. 
20090429, godz. 16:15, s. 5840 
Jan Zakrzewski (Uniwersytet Warszawski) 
Stochastic fluctuations in selection model based on evolutionary game theory 
20090422, godz. 16:15, s. 5840 
Jan Zakrzewski (Uniwersytet Warszawski) 
Stochastic fluctuations in selection model based on evolutionary game theory 
We will investigate frequencydependent selection model (with one locus, two alleles, two phenotypes and finite population) based on evolutionary game theory. Next we will include stochastic fluctuations in the model, and convert deterministic equation into the master equation. The master equation will be approximated with FokkerPlanck equation, which we will use to predict mean and variance of both allele and phenotypic frequency. Based on Y. Tao, R. Cressman, B. Zhang, and X. Zheng Theoretical and Population Biology 74 (2008) 263272 
20090408, godz. 16:15, s. 5840 
Monika Piotrowska (Uniwersytet Warszawski) 
Co powinniśmy wiedzieć o Stochastycznych Równaniach Różniczkowych z Opóźnieniem II 
20090401, godz. 16:15, s. 5840 
Monika Piotrowska (Uniwersytet Warszawski) 
Co powinniśmy wiedzieć o Stochastycznych Równaniach Różniczkowych z Opóźnieniem 
Celem wystapienia jest zaprezentowanie podstawowych definicji i twierdzen (bez dowodow) teorii stochastycznych rownaniach rozniczkowych z opoznieniami czasowymi. 
20090318, godz. 16:15, s. 5840 
Jan Karbowski, Institute of Biocybernetics and Biomedical Engineering,Polish Academy of Sciences 
COMPUTATIONAL NEURODYNAMICS  HOW NERVOUS SYSTEM GENERATES MOTION? 
The ambitious objective of computational neuroscience is to find general rules of brain organization and function. By organization we usually mean the pattern of connections between neurons, and by function the dynamics of neural networks in some context. In this talk, I will focus on undulatory locomotion of a tiny worm called C. elegans. This animal is a good system for biological modeling because we know a great deal about its cellular and molecular organization. I will present some results concerning C. elegans biomechanics, its neural structure, and oscillatory neural dynamics leading to worm locomotion. 
20090311, godz. 16:15, s. 5840 
Tadeusz Płatkowski (Uniwersytet Warszawski) 
Equilibria in populations of agents with complex personality profiles for 2player games 
We propose a theory of evolution of social systems which generalizes the standard proportional fitness rule of the evolutionary game theory, and a formalism of social interactions in which the actors' choice behavior is controlled by parameters which describe their ability to control the relation between a sequence of stimulus and a sequence of responses. The formalism is applied to describe the dynamics of twoperson oneshot games played in infinite populations. In particular it predicts the nonzero level of cooperation in the long run for the Prisoner's Dilemma games. 
20090304, godz. 16:15, s. 5840 
Marek Bodnar (Uniwersytet Warszawski) 
Small delay approximation of stochastic delay differential equation 
20090225, godz. 16:15, s. 5840 
Marek Bodnar (Uniwersytet Warszawski) 
Small delay approximation of stochastic delay differential equation 
20090218, godz. 16:15, s. 5840 
Marek Bodnar (Uniwersytet Warszawski) 
Small delay approximation of stochastic delay differential equation 
We will review the article by Steve Guillouzic, Ivan L'Heureux, and Andre Longtin Phys. Rev E 59: 3970 (1999). 
20090114, godz. 16:15, s. 5840 
Urszula Foryś (Uniwersytet Warszawski) 
Wpływ szumu na bifurkacje Hopfa w równaniu różniczkowym z opóżnieniem 
Rozpatrzymy specyficzne równanie różniczkowe z opóźnieniem dyskretnym, w którym przy zmianie opóźnienia występuje bifurkacja Hopfa. Następnie do tego równania zostanie wprowadzony element stochastyczny na zasadzie procesu OrnsteinaUhlenbecka (z białym szumem Gaussowskim). Omówimy wyniki analizy numerycznej, a w przypadku asymptotycznym otrzymamy równoważne zagadnienie różnicowe. 
20081217, godz. 16:15, s. 5840 
Mirosław Lachowicz (Uniwersytet Warszawski) 
Stochastyczne równania różniczkowe typu LotkiVolterry 
Omowione zostana uklady rownan rozniczkowych typu LotkiVolterry ze stochastycznym zaburzeniem. Pokazany zostanie wplyw stochastycznego zaburzenia na zachowanie rozwiazan. 
20081210, godz. 16:15, s. 5840 
Mirosław Lachowicz (Uniwersytet Warszawski) 
Stochastyczne równania różniczkowe z opóżnieniem 
Miesiąc temu, 10 listopada, zmarł Kiyosi Ito, twórca teorii stochastycznych równań różniczkowych http://wwwgroups.dcs.stand.ac.uk/~history/Biographies/ Ito.html. Podczas seminarium omówione zostaną układy równań różniczkowych typu LotkiVolterry z opóźnieniem i ze stochastycznym zaburzeniem. Pokazany zostanie wpływ stochastycznego zaburzenia na zachowanie rozwiązań. 
20081203, godz. 16:15, s. 5840 
Jacek Miękisz (Uniwersytet Warszawski) 
Smalldelay expansions in simple stochastic models with time delay 
20081126, godz. 16:15, s. 5840 
Jacek Banasiak (University of KwaZuluNatal i Politechnika Łódzka) 
O liczbie cząsteczek w procesach koagulacji i fragmentacji 
Choc w procesach fragmentacji tworza sie przez rozpad nowe czasteczki, matematyczna analiza tych procesow prowadzona jest w przestrzeni kontrolujacej ewolucje masy. Jest to spowodowane tym, ze w tej przestrzeni operator fragmentacji jest dyssypatywny, podczas gdy liczba czasteczek moze wybuchowo rosnac do nieskonczonosci. Z drugiej strony, mozliwosc kontrolowania liczby czasteczek w procesie fragmentacji ma istotne znaczenie przy analizie pelnego rownania fragmentacji i koagulacji. W trakcie wykladu omowimy zastosowanie teorii operatorow o dodatnich rezolwentach do uzyskania oszacowan liczby czasteczek produkowanych w trakcie fragmentacji, zatrzymamy sie na kilku patologiach modelu, i wskazemy mozliwosci zastosowania tych wynikow do kontroli momentow rozwiazan rownania koagulacji i fragmentacji. 
20081119, godz. 16:15, s. 5840 
Jacek Miękisz (Uniwersytet Warszawski) 
Stochastic dynamics with time delay  methematical problems and physical results 
We will discuss Master, FokkerPlanck and Langevin equations with time delay in the context of gene expression. 
20081105, godz. 16:15, s. 5840 
Jacek Miękisz (Uniwersytet Warszawski) 
Stochastic models of gene expression with time delay 
We will present an elementary introduction to stochastic models of gene expression. Master, FokkerPlanck, and Langevin equations will be discussed. We will review a simple model of protein production which can be completely solved, that is one can obtain analytical expressions for the expected value and the variance of the number of protein molecules (Thattai and Oudenaarden, PNAS, 86148619, 2001). Then we will discuss some simplified models with time delay and report on work in progress. 
20081022, godz. 14:15 (!), s. 5840 
Malgorzata Kubalinska (Politechnika Lubelska) 
Model typu FisheraWrighta ze zmienna wielkoscia populacji i mutacjami w postaci procesu punktowego 
Koalescencja Kingmana jest jednym z wazniejszych pojec genetyki populacyjnej. Jednak przybliza ona tylko proces dokadnej koalescencji (proces tworzenia drzew genealogicznych w modelu FisheraWrighta). Przedstawimy model populacji zbudowany w oparciu o proces dokladnej koalescencji z mutacjami opisanymi za pomoc modelu nieskoczenie wielu miejsc. Zbadamy, widziane jako funkcja wielkosci populacji, asymptotyczne zachowanie rozkladow i momentow pary procesow punktowych zwiazanych z czteroelementowa probka wylosowana z takiej populacji (pierwszy element tej pary to roznica symetryczna, tzw. niezgranie, miedzy mutacjami pierwszego i drugiego elementu probki, a drugi to roznica symetryczna miedzy mutacjami trzeciego i czwartego elementu). Sprawdzimy na ile model z czasem dyskretnym rozni sie od modelu z czasem ciaglym (zbudowanym w oparciu o koalescencje Kingmana z mutacjami modelowanymi za pomoca procesu punktowego). 
20081015, godz. 16:15, s. 5840 
Jacek Miękisz (Uniwersytet Warszawski) 
Dyskretne opóźnienia 
20081008, godz. 16:15, s. 5840 
Zebranie organizacyjne ZBiTG 
20081001, godz. 16:15, s. 2180 
Mark Chaplain (University of Dundee) 
Multiscale mathematical modelling of cancer growth 
20080604, godz. 16:15, s. 5840 
Christian Maes ((Katholieke Universiteit Leuven)) 
Large deviations in nonreversible Markov processes 
We show differences in the structure of dynamical fluctuations for Markov processes between the reversible and nonreversible case. The rate function for the occupation statistics is connected with the entropy production, and the study of current fluctuations involves characterizations of the largest eigenvalue of some nonnormal matrices. This is a joint work with Karel Netocny. 
20080528, godz. 16:1518.00, s. 5840 
Zuzanna Szymanska (ICM UW) 
Mathematical modelling of the influence of heat shock proteins on cancer invasion of tissue 
Tumour cell invasion is crucial for cancer metastasis, which is the main cause of cancer mortality. An important group of proteins involved in cancer invasion are the Heat Shock Proteins (HSPs). According to experimental data, inhibition of one of these proteins, Hsp90, slows down cancer cells while they are invading tissue. To test different biological hypotheses regarding how precisely Hsp90 influences tumour invasion, we use a model of solid tumour growth which accounts for the interactions between Hsp90 dynamics and the migration of cancer cells and, alternatively, between Hsp90 dynamics and the synthesis of matrix degrading enzymes (MDEs). The model consists of a system of reactiondiffusiontaxis partial differential equations describing interactions between cancer cells, MDE, and the host tissue (ECM). Using numerical simulations we investigate the effects of the administration of Hsp90 inhibitors on the dynamics of tumour invasion. 
20080514, godz. 16:1518.00, s. 5840 
Urszula Foryś (Uniwersytet Warszawski) 
Delays again 
20080423, godz. 16:15, s. 5840 
Delays, delays 
20080416, godz. 16:15, s. 5840 
Delays, informal discussion goes on 
20080409, godz. 16:15, s. 5840 
Tomasz Lipniacki (IPPT) 
Interplay between bistability and stochasticity in Tcell signaling 
The stochastic dynamics of Tcell receptor (TCR) signaling are studied using a mathematical model intended to capture kinetic proofreading (sensitivity to ligandreceptor binding kinetics) and negative and positive feedback regulation. The model incorporates proteinprotein interactions and reproduces several experimental observations about the behavior of TCR signaling. Analysis of the model indicates that TCR signaling dynamics are marked by significant stochastic fluctuations and bistability which is caused by the competition between the positive and negative feedbacks. Stochastic fluctuations are such that singlecell trajectories differ qualitatively from the trajectory predicted by the deterministic approximation of the dynamics. Moreover, because of the bistability, the average of singlecell trajectories differs markedly from the deterministic trajectory. Bistability combined with stochastic fluctuations allows for switchlike responses to signals, which may help a T cell to make committed cellfate decisions. 
20080312, godz. 16:15, s. 5840 
Mats Bodin (IM PAN) 
Modeling copying behavior in animals  informal discussion 
Decisionmaking plays a central role in animal groups, and ultimately results from the natural selection. We look at the evolution of copying behavior, where individuals gain information by watching others, as part of decisionmaking. 
20080305, godz. 16:15, s. 5840 
Jacek Miękisz (Uniwersytet Warszawski) 
How to model delays  informal discussion 
20080123, godz. 16:15, s. 5840 
Kazimierz Sobczyk (IPPT i UW) 
Złożone mikrostruktury materialne; modelowanie i propagacja fal stochastycznych. Complex material microstructures; modelling and stochastic wave propagations 
20080116, godz. 16:15, s. 5840 
Kazimierz Sobczyk (Uniwersytet Warszawski i IPPT) 
Dynamika stochastyczna i niezawodność układów z degradacją 
20080109, godz. 16:15, s. 5840 
Urszula Foryś (Uniwersytet Warszawski) 
Delays 
20071219, godz. 16:15, s. 5840 
Urszuka Foryś (Uniwersytet Warszawski) 
Discrete Marchuk's model with time delay 
20071205, godz. 16:15, s. 5840 
Urszula Foryś (Uniwersytet Warszawski) 
Discrete models with time delays: logistic equation and Marchuk's model 
Tydzień temu seminarium zostało odwołane. We will consider discrete dynamical systems with time delays. The basic properties will be explain on two examples:discrete logistic equation and the discrete version of Marchuk's model of an immune system. We introduce time delay to the discrete logistic equation in different possible ways and compare the properties of such models with the classic model. It occurs that these properties depend strongly on the way of introducing delay. We also study a discrete version of Marchuk's model where time delay is introduced like in the original model. We compare the properties of discrete and continuous models. 
20071121, godz. 16:15, s. 5840 
Cristian MoralesRodrigo (Uniwersytet Warszawski) 
Cellmatrix interactions in cancer invasion 
SEMINARIUM WSPÓLNE Z SEMINARIUM RTN 
20071010, godz. 16:15, s. 5840 
Monika Joanna Piotrowska (Uniwersytet Warszawski) 
A Calibrated Cellular Automata Model of in vitro Cultivated Multicellular Tumour Spheroids 
SEMINARIUM WSPÓLNE Z SEMINARIUM RTN. In this paper we present a quasitwo dmimensional Cellular Automata (CA)model describing the dynamics of the in vitro cultivated multicellular spheroid obtained from EMT6/Ro (mammary carcinoma) cell line. The CA model is coupled to the experimental data and shows extremely good agreement across a wide range of outputs including bulk growth kinetics, necrotic core formation and kinetics and response to environmental glucose levels. 
20070606, godz. 16:15, s. 5840 
Marek Bodnar and Remigiusz Kowalczyk (Uniwersytet Warszawski) 
Stochastic models in genetics 
20070530, godz. 16:15, s. 5840 
Monika Joanna Piotrowska (Uniwersytet Warszawski) 
Homeorhesis in the motion of an individual 
Połączone seminarium RTN i Zakładu Biomatematyki i Teorii Gier Homeorhesis is an inherent dynamical feature of any living system. Homeorhesis is a peculiar qualitative and quantitative independence of the exogenous signals acting on the system and varying within a certain, systemrelevant range. Nonliving systems do not perform homeorhesis. Mathematically, homeorhesis is the asymptotic convergence (in the infinitetime limit) of certain dynamic equilibria of the dynamical model that describes a living system (see [1], [2]). Preliminary results on the homeorhesis modelling in terms of ordinary differential equations (ODEs) are developed in [3, Appendix], [1], and [2]. In this case, both the actual mode and creode of the system are two dynamic equilibria [2] which correspond to the actual exogenous signal and the most favoured exogenous signal, respectively. In these terms, homeorhesis is the property of a living system that its actual mode in the course of time tends to its creode for any actual exogenous signal (within a certain, systemrelevant range). Homeorhesis is a fundamental notion in theoretical biology (and in a more general field, theory of living matter). It is an inherent feature of any living system. Nevertheless, the literature on dynamical modelling in sociology does not include works on homeorhesis. The purpose of the present work is to fill this gap. Report [4] suggests the simplest model for homeorhesis. The present work specifies this model in the case of the motion of a single individual and illustrates the treatment with numericalsimulation results. [1] Mamontov, E., 2007, Modelling homeorhesis by ordinary differential equations, Mathl Comput. Modelling 45(56), pp. 694707. [2] Mamontov, E., 2007, Dynamicequilibrium solutions of ordinary differential equations and their role in applied problems, Appl. Math. Lett., accepted (paper AML5947). [3] E. Mamontov, K. PsiukMaksymowicz and A. Koptioug, Stochastic mechanics in the context of the properties of living systems, Mathl Computer Modelling 44(78): 595607 (2006) [4] E. Mamontov, Homeorhesis and evolutionary properties of living systems: From ordinary differential equations to the activeparticle generalized kinetics theory, In: 10th Evolutionary Biology Meeting at Marseilles, September 2022, 2006 (Association pour l'Etude de l'Evolution Biologique, Centre Regional de Documentation Pedagogique,Marseille, France, 2006), pp. 2829, abstract; the 13page PDF file for the full oral presentation can be downloaded from http://www.up.univmrs.fr/evolcgr/home_page/meeting2006.php 
20070523, godz. 16:00, s. 5840 
1. Marek Bodnar and Remigiusz Kowalczyk 2. Ting Liu (Uniwersytet Warszawski) 
1. Stochastic models in genetics. 2. From von Foerster to delay equations in the model of cell cycle. 
20070516, godz. 16:00, s. 5840 
U. Foryś (UW), P. Rybka (UW), N. KalevKronik i Y. Kogan (Inst. for Medical Biomath. Israel) T. Liu (UW) (Uniwersytet Warszawski) 
Workshop on Mathematical Modelling of Tumour Growth 
1. Apomixis, just questions. 2. Interactions between GBM brain tumour and immune system. 3. Interactions between GBM brain tumour and immune system  mathematical modelling. 4. From von Foerster to delay equations in the model of cell cycle. Workshop wspólny Zakładu Biomatematyki i Teorii Gier i RTN 
20070425, godz. 16:15, s. 5840 
Janusz A. Hołyst (Faculty of Physics, Center of Excellence for Complex Systems Research, Warsaw University of Technology) 
Universal scaling of distances in complex networks 
Universal scaling of distances between vertices of ErdosRenyi random graphs, scalefree BarabasiAlbert models,
science collaboration networks, biological networks,
Internet Autonomous Systems and public transport networks are observed. A mean distance distance between two nodes of degrees k_i and k_j equals to 
20070418, godz. 16:15, s. 5840 
Agnieszka WiszniewskaMatyszkiel (Uniwersytet Warszawski) 
A new kind of equilibrium in dynamic games with beliefs 
20070404, godz. 16:15, s. 5840 
Agnieszka WiszniewskaMatyszkiel (Uniwersytet Warszawski) 
A new kind of equilibrium in dynamic games with beliefs 
We shall introduce a new notion of equilibrium  beliefdistorted Nash equilibrium (BDNE)  in discrete time dynamic games in which players do not have perfect information about strategies chosen by the other players and form some expectations about them. A game in the strategic form is generally a triple of objects: the set of players (with, possibly, some structure imposed), their strategy sets and payoff functions defined on the set of profiles of strategies.The usual concept of Nash equilibrium requires that at an equilibrium profile every player (almost every in the case of infinitely many players represented as a measure space) maximizes his payoff as the function of his strategy given the strategies of the remaining players. In the concepts of beliefdistorted Nash equilibrium we assume that at each stage of the game players maximize another functions related both to the original payoff functions and players' beliefs about future behaviour of the system. Various notions of self verification are introduced. Equivalence between a BDNE for perfect foresight beliefs and Nash equilibrium is proven. The concepts are illustrated by examples of exploitation of a common renewable resource and a repeated minority game. 
20070314, godz. 16:15, s. 5840 
Adam Lipowski (Dept. of Physics, A.Mickiewicz University, Poznań) 
On the ecological and evolutionary dynamics of preypredator systems 
I will discuss some aspects of the dynamics of interacting populations.In particular, I will talk about oscillatory behaviour and environmentally induced largescale synchronization (Moran effect) in lattice models of preypredator systems. More complicated models with coevolution of many interacting species will be also examined. In such models the number of species and some other characteristics show longtime periodic behaviour. Such a scenario is confronted with a possibility of periodicity of mass extinctions in the Earth ecosystem, as suggested by Raup and Sepkoski. 
20070308, godz. 12:30, s. 2100 
Antoni Leon Dawidowicz (Institute of Mathematics, Jagiellonian University) 
The Lasota equation and its properties 
Połączone seminarium Zakładów: Równań Fizyki Matematycznej, Biomatematyki i Teorii Gier oraz Research Training Network Modeling, Mathematical Methods and Computer Simulations of Tumour Growth and Therapy 
20070124, godz. 16:15, s. 5840 
Daniel K. Wójcik (Instytut Biologii Doświadczalnej im. M. Nenckiego) 
Introduction to nonequilibrium work relations 
Nonequilibrium work relations discovered by Chris Jarzynski are an example of symmetries found recently for several classes of nonequilibrium problems. These symmetries typically connect probability of a given process with that of its "reverse". I will briefly introduce Jarzynski relations, sketch a proof in a special case and illustrate them with a recent experiment on stretching DNA. 
20061220, godz. 14:15, s. 5840 
Michalina Błażkiewicz 
An attempt of mathematical description of kinematic parameters of hurdles, especially of the hurdle stride 
The main objective of this presentation is utilization of mathematical apparatus for description of some kinematic parameters of hurdle race and analysis of position of limbs and of body centre of gravity during hurdle stride. The detailed objectives concern description of technique of hurdles of 100/110m and analysis of different aspects of efficiency of hurdle stride. Using mathematical analysis and calculus of variations (methods of Lagrange) I could answer a following question: What should be the athletes speed on a data distance L to have minimum time of run? On the other hand, the utilization of basic kinematics and dynamics laws allows to answer the following question: Who has major predisposition for hurdles: short or high athletes? For analysis of hurdle stride it was used the APAS (Ariel Performance Analysis System). We analysed the international champion 100m hurdles for women. 
20061206, godz. 16:15, s. 5840 
Urszula Foryś (Uniwersytet Warszawski) 
Generalization of the Greenspan MCS model to ndimensional case 
In tumour dynamics there is a well known model of spherical growth underthe diffusion of nutrient. The basic concept of multicellular spheroid (MCS) in 3D was proposed by Greenspan. I'll show the formal generalization of this concept in ndimensional case. I'll focus on the dependence of the model dynamics on the dimension parameter n, especially in comparison of two standard cases  for n=3 and n=2. 
20061129, godz. 16:15, s. 5840 
Tadeusz Płatkowski (Uniwersytet Warszawski) 
Cooperation in Multiperson Prisoner's Dilemma Games  Social Loafing 
Social loafing is the tendency for individuals to expend less effort when working collectively compared with when working individually. Such reduction of commonly appearing prosocial behavior was observed in the past by psychologists. Generally, the experiments on social loafing confronted individual's efforton task in participation of two persons and several persons. It was observed that decrease of motivation to perform collective tasks changed when number of men had increased,however, not in the linear proportion, but rather exponential. We develop a mathematical model which takes into account various aspects of the phenomena, using multiperson Prisoner's Dilemma (PD) Games. The model  a 2D system of nonlinear ODE takes into account evolution of the aspiration level in the population and mean frequency of the cooperative behavior. In particular we study limiting properties of the cooperation level in function of the order of the PD game. 
20061122, godz. 14:15, s. 5840 
Radosław Wieczorek (IMPAN Katowice) 
From individual behavior of phytoplankton to evolution equation 
Phytoplankton, a mass of small plants (mostly algae) living in the water, comes out to be the main source of nutrient in oceans. That is why understanding of its bahaviour becomes so important and has been widely investigated. An individual based model, that describes spatial movement and processes of fragmentation and coagulation of phytoplankton structures, will be presented. The individuals in this model are phytoplankton aggregates (a number of cells joined by some organic glue) that move in the space, may split into smaller ones and have the possibility of joining together. After the formulation of the model in the setting of measurevalued stochastic process, we investigate its behaviour in the limit where the number of individuals grows to infinity. As a result of something like central limit theorem for our processes, we obtain the evolution equation on the density of the massspatial distribution of phytoplankton population. 
20061115, godz. 16:15, s. 5840 
Ting Liu (Uniwersytet Warszawski) 
Nonlinear impulse partial differential equations with delay 
20061108, godz. 16:15, s. 5840 
Urszula Foryś (Uniwersytet Warszawski) 
Review on Delay Differential Equations, a continuation 
20061025, godz. 16:15, s. 5840 
Urszula Foryś (Uniwersytet Warszawski) 
Review on Delay Differential Equations, continuation but in fact the beginning 
20061018, godz. 16:15, s. 5840 
Urszula Foryś (Uniwersytet Warszawski) 
Review on Delay Differential Equations 
We introduce the basic notation used in the theory of DDE, formulate the basic theorems and show some examples of the infuence of delays on the dynamics of the system. 
20060524, godz. 16:15, s. 5840 
Dorin Marinescu (Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Bucharest) 
Simulation methods for Boltzmanntype equations 
We report on the numerical approximation of the solution of a general class of nonlinear Boltzmann like equations. We provide a discretized version of the equations approximating the above class of equations. The numerical implementation of this scheme it is not possible due to the powerlike growth of the computational numerical effort. For this reason we introduce stochastic techniques to diminish the numerical effort. Finally, one obtains a probabilistic convergent scheme solving the initial equations. 
20060517, godz. 16:15, s. 5840 
Krzysztof Argasiński (Uniwersytet Jagielloński) 
Sex ratio evolution from the point of view of dynamic large games 
On the seminar will be presented new model of sex ratio evolution related to so called dynamic evolutionary large games. This is a new technique of modelling of multipopulaton problems. The classic approach (e.g. ShawMoller or Sex Ratio Game) relies on assumption that proper fitness measure is the number of grandsons. A new model shows that this is a mathematical artifact, and selfregulation of population sex ratio is not the product of 0.5 female phenotype selection. In stable state population may be heterogenic (consisting of different individual strategies) but population sex ratio is equal to 0.5. These stable states are elements of Evolutionarily Stable Set. 
20060405, godz. 16:15, s. 5840 
Tomasz Lipniacki (IPPT) 
Stochastic regulation of NFkappaB pathway 
Living cells may be considered noisy or stochastic biochemical reactors. In eukaryotic cells, in which the number of protein or mRNA molecules is relatively large, the stochastic effects may originate in regulation of gene activity or receptors activation. The stochasticity of activator binding and dissociation is amplified by transcription and translation, since target gene activation results in a burst of mRNAs molecules, and each copy of mRNA then serves as a template for numerous protein molecules. Similarly the single receptor activation can be amplified by the transduction cascade. In the present action I expand our model of the NFkappaB (Nuclear Factor kappa B) regulatory module (Lipniacki et al., 2006. Biophys. J. 90, pp. 725742) in order to analyze cell activation at low dose of TNF (Tumor Necrosis Factor). The considered regime of activation is important in analysis of celltocell signaling. Ordinary differential equations, used for description of fast reaction channels of processes involving a large number of molecules, are combined with a stochastic switches to account for activity of genes and TNF receptors. The stochasticity in receptor activation and in gene transcription causes simulated cells to exhibit large variability. Moreover none of them behave like an "average" cell. 
20060328, godz. 10:15, s. 5081 
Adam Bobrowski (IM PAN) 
On limitations and insufficiency of the TrotterKato theorem with applications to a model of stochastic gene expression II (wspólne seminarium z RTN) 
20060321, godz. 10:00, s. 5081 
Adam Bobrowski (IM PAN) 
On limitations and insufficiency of the TrotterKato theorem, with applications to a model of stochastic gene expression 
Wspólne seminarium z RTN Modeling, Mathematical Methods and Computer Simulation of Tumour Growth and Therapy. Abstract: Motivation for the talk comes from a recent model of stochastic gene expression introduced by Lipniacki et al. (J. Theor. Biol. 238: 348367, 2006). The model involves a family of Feller processes, solutions to systems of stochastic differential equations driven by Markov chains with statedependent jump intensities, which naturally converge to a certain deterministic process. It turns out that convergence of related semigroups of operators cannot be proved by means of the classical TrotterKato theorem, and the difficulty lies in a somewhat unexpected place. Before we deal with this difficulty, to explain the source of the problem, we exhibit simple examples of convergence of equibounded semigroups that cannot be captured by means of the TrotterKato theorem. In this context we discuss the need for semigrouptheoretical tools that would supplement this theorem in dealing with convergence problems. 
20060315, godz. 16:15, s. 5840 
Jacek Miękisz (Uniwersytet Warszawski) 
Stochastic models of genetic regulatory networks 
Regulation of gene expression is a chemical process involving many coupled elementary chemical reactions modeled usually by systems of differential equations describing time evolution of molecular concentrations. However, due to low numbers of molecules involved in gene expression processes, random fluctuations may play a significant role. We will present an elementary introduction to stochastic models of such processes. Master, FokkerPlanck, and Langevin equations will be discussed. We will review a simple model of protein production which can be completely solved, that is one can obtain analytical expressions for the expected value and the variance of the number of protein molecules (Thattai and Oudenaarden, PNAS, 86148619, 2001). Then we will discuss specific models of mRNA and proteinregulated networks, present some partial results and open problems. 
20060308, godz. 16:15, s. 5840 
Mirosław Lachowicz (Uniwersytet Warszawski) 
Amplificationdeamplification process  odwołane 