| 2007-12-12, godz. 14:15, s. 2180 |
|
| MC RTN 503661 Miniworkshop: Recent Trends in Applications of Mathematics |
| 14:15-15:15 Mark Chaplain, Dundee University, "Mathematical modelling
of cancer cell invasion of tissue: local and non-local models and the effect of adhesion"
15:30-15:45 Monika Piotrowska, Universitet Witten/Herdecke, "Different Approaches to Cancer Modelling"
15:50-16:05 Irina Vaseva, Novosibirskij Universitet, "Numerical analysis of PDEs"
16:10-16:25 Krzysztof Psiuk-Maksymowicz, Goeteborg Universitet,
"Modelling of solid tumour growth and radionuclide therapy" |
| 2007-05-30, godz. 16:15, s. 5840 |
| Monika Joanna Piotrowska (Uniwersytet Warszawski)
|
| Homeorhesis in the motion of an individual |
| Połączone seminarium RTN i Zakł. 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, system-relevant range. Nonliving systems do not perform
homeorhesis. Mathematically, homeorhesis is the asymptotic convergence (in the infinite-time 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, system-relevant 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 numerical-simulation results.
[1] Mamontov, E., 2007, Modelling homeorhesis by ordinary differential equations, Mathl Comput. Modelling 45(5-6), pp. 694-707.
[2] Mamontov, E., 2007, Dynamic-equilibrium solutions of ordinary differential equations and their role in applied problems, Appl. Math. Lett., accepted (paper AML5947).
[3] E. Mamontov, K. Psiuk-Maksymowicz and A. Koptioug,
Stochastic mechanics in the context of the properties
of living systems, Mathl Computer Modelling 44(7-8): 595-607 (2006)
[4] E. Mamontov, Homeorhesis and evolutionary properties of living systems: From ordinary differential equations to the active-particle generalized kinetics theory, In: 10th Evolutionary Biology Meeting at Marseilles, September 20-22, 2006 (Association pour l'Etude de l'Evolution Biologique, Centre Regional de Documentation Pedagogique, Marseille, France, 2006), pp. 28-29, abstract; the 13-page PDF file for the full oral presentation can be downloaded from
http://www.up.univ-mrs.fr/evol-cgr/home_page/meeting2006.php |
| 2007-05-16, godz. 16:00, s. 5840 |
| U. Foryś, P. Rybka, N. Kalev-Kronik, Y. Kogan, T. Liu (Uniwersytet Warszawski i Inst. for Medical Biomath.(Israel))
|
| Workshop on Mathematical Modelling of Tumour Growth |
|
| 2006-06-28, godz. 14:15, s. 5810 |
| Prof. Urszula Ledzewicz (Southern Illinois University)
|
| An Optimal Control Approach to Mathematical Models of Tumor Anti-Angiogenesis |
|
| 2006-03-29, godz. 14:15, s. 5850 |
| Philipp Getto (Uniwersytet Warszawski)
|
| Modelling and analysis of RSV-infection of cells |
|
| 2006-03-28, godz. 10:15, s. 5081 |
| Adam Bobrowski (IM PAN)
|
| Om limitations and insufficiency of the Trotter-Kato theorem, with applications to a model of stochastic gene expression II |
|
| 2006-03-21, godz. 10:00, s. 5081 |
| Adam Bobrowski (IM PAN)
|
| On limitations and insufficiency of the Trotter-Kato theorem, with applications to a model of stochastic gene expression |
|
| 2006-02-22, godz. 14:15, s. 5850 |
| Remigiusz Kowalczyk (Uniwersytet Warszawski)
|
| On the local existence to the aggregation equation |
|
| 2006-01-18, godz. 14:15, s. 5850 |
| Urszula Foryś (Uniwersytet Warszawski)
|
| Modelling of brain tumour dynamics |
|
| 2006-01-11, godz. 14:15, s. 5850 |
| Marek Galewski |
| The Existence and Stability of Solutions for Mutlidimensional Wave Equation - A Variational Approach |
|
| 2005-12-14, godz. 14:15, s. 5850 |
| Gabriela Lorelai Litcanu (Uniwersytet Warszawski)
|
| Propagation phenomena in reaction-diffusion equations |
|
| 2005-11-30, godz. 14:15, s. 5850 |
| Cristian Morales Rodrigo (Uniwersytet Warszawski)
|
| Models of tumour invasion |
|
| 2005-11-23, godz. 14:15, s. 5850 |
| Jacek Banasiak ((University of KwaZulu-Natal, Durban))
|
| Honest and dishonest processes in the applied sciences |
|
| 2005-11-16, godz. 14:15, s. 5850 |
| Cristian Morales-Rodrigo (Uniwersytet Warszawski)
|
| Mathematical Models of Tumour Invasion |
|
| 2005-11-09, godz. 14:15, s. 5850 |
| Piotr Gwiazda (Uniwersytet Warszawski)
|
| Structured Models and the Entropy Method |
|
| 2005-10-05, godz. 14:15, s. 5850 |
| Monika Piotrowska (Uniwersytet w Witten)
|
| Oscillations in a G0 Model of Hematopoietic Stem Cells |
|
| 2005-09-29, godz. 12:30, s. 5840 |
| Professor Benoit Perthame (ENS, Paris)
|
| Chemotaxis: parabolic, hyperbolic and kinetic models. |
|
| 2005-09-29, godz. 12:30, s. 5840 |
| Professor Benoit Perthame (ENS, Paris)
|
| Chemotaxis: parabolic, hyperbolic and kinetic models. |
|
| 2005-09-29, godz. 12:30, s. 5840 |
| Professor Benoit Perthame (ENS, Paris)
|
| Chemotaxis: parabolic, hyperbolic and kinetic models. |
|
| 2005-09-28 , godz. 12:15, s. 5840 |
| Professor Benoit Perthame (ENS, Paris)
|
| Population laws and the entropy structure. |
|
| 2005-06-06, godz. 10:45-11:45, s. 5820 |
| Mark Chaplain |
| Modelling the immune response to cancer |
| 7.06.2005, 10:15 - 11:15 "Modelling tumour - induced angiogenesis"
8.06.2005, 10:15 - 11:15 "Modelling cancer invasion and metastasis"
|
| 2005-05-04, godz. 16:00, s. 3130 |
| Philipp Getto (Uniwersytet Warszawski)
|
| On applicability of certain structured population models to cell division |
|
| 2005-04-27, godz. 16:00, s. 3130 |
| Remigiusz Kowalczyk (Uniwersytet Warszawski)
|
| Modelling cell aggregation in vasculogenesis c.d. |
|
| 2005-04-06, godz. 16:00, s. 3130 |
| Remigiusz Kowalczyk (Uniwersytet Warszawski)
|
| Modelling cell aggregation in vasculogenesis |
|
| 2005-03-16, godz. 16:00, s. 3130 |
| Igor Doktorski (Institute for Applied Mathematics, Heidelberg)
|
| Modeling growth of cell cultures |
| Understanding and describing growth of cell colonies, like bacterial cultures, tumors, thrombi etc. is an important and challenging aim formodelers and mathematicians. Despite of many biological differences between specific cell
colonies, they all have some important features in common, which will be used to derive a "first principle" model.
With regard to quantitative predictions, it is of outmost importance to consider both mechanics and chemistry of the system.
>From a mathematical point of view, the model is a "multi-component" model: a coupled system of visco-elastic and transport equations with source terms. Additional reaction-diffusion equations describe the chemical part of the system. The strong coupling between both characterises the biochemical part of the system.
In my talk, I will concentrate on a model system - a biofilm. Biofilms are three-dimensional submerged bacterial cultures. They are responsible for many infections in hospitals, huge energy losses in industry, but can be also used for "catalysing" bio-chemical processes in
bio-reactors.
|
| 2005-01-19, godz. 16:00, s. 3130 |
| Monika Piotrowska (Uniwersytet Warszawski)
|
| Hopf Bifurcation for Ordinary Differential Equation with two Discrete Delays (continuation) |
|
| 2005-01-12, godz. 16:00, s. 3130 |
| Monika Piotrowska (Uniwersytet Warszawski)
|
| Występowanie bifurkacji Hopfa dla pewnego typu równań różniczkowych zwyczajnych z dwoma opóźnieniami |
|
| 2004-12-08, godz. 14:30, s. 3130 |
| 1. Cristian Morales Rodrigo (Warsaw University) 2. Mark Chaplain (Dundee University) 3. Anna Marciniak-Czochra (University of Heidelberg) |
| 1. Some elliptic equations with nonlinear boundary conditions. 2. Mathematical modelling of cell cytoskeleton biomechanics and cell membrane deformations. 3. Derivation of macroscopic receptor-based model using homogenization techniques. |
| Miniworkshop: Recent Trends in Applications of Mathematics to Biology and Medicine I |
| 2004-12-01, godz. 16:00, s. 3130 |
| Marek Bodnar (Uniwersytet Warszawski)
|
| Mathematical properties of an integro-differential equation arising as a limit of individual cell-based models |
|
| 2004-11-24, godz. 16:00, s. 3130 |
| Urszula Foryś (Uniwersytet Warszawski)
|
| Zvii Agur modele angiogenezy |
|
| 2004-11-10, godz. 16:00, s. 3130 |
| Remigiusz Kowalczyk (Uniwersytet Warszawski)
|
| Istnienie słabych rozwiązań dla pewnego układu równań różniczkowych cząstkowych typu paraboliczno-eliptycznego c.d. |
|
| 2004-11-03, godz. 16:00, s. 3130 |
| Remigiusz Kowalczyk (Uniwersytet Warszawski)
|
| Istnienie słabych rozwiązań dla pewnego układu równań różniczkowych cząstkowych typu paraboliczno-eliptycznego |
|
| 2004-10-20, godz. 16:00, s. 3130 |
| Remigiusz Kowalczyk (Uniwersytet Warszawski)
|
| Funkcja Lapunova dla równań chemotaksji |
|
| 2004-10-13, godz. 16:00, s. 3130 |
| Roman Chernina (Institute of Math., NAS Ukraine, Kiev)
|
| Nonlinear reaction-diffusion systems with variable diffusivities: lie symmetries and exact solution |
|
| 2004-06-21, godz. 10:00, s. 5820 |
| Juan J.L. Velazquez (Universidad Complutense de Madrid)
|
| Singular behaviours in chemotaxis models |
|
| 2004-05-10, godz. 10:00-12:00, s. 2180 |
| prof. Vincenzo Capasso (Universita' di Milano)
|
| On the social behaviour of Biological Populations |
|
| 2004-04-22, godz. 14:15, s. 2070 |
| Remigiusz Kowalczyk (Uniwersytet Warszawski)
|
| O oszacowaniach a priori dla rozwiązań modelu chemotaksji - c.d. |
|
| 2004-03-18, godz. 14:15, s. 2070 |
| Remigiusz Kowalczyk (Uniwersytet Warszawski)
|
| O oszacowaniach a priori dla rozwiązań modelu chemotaksji - c.d. |
|
| 2004-03-11, godz. 14:15, s. 2070 |
| Remigiusz Kowalczyk (Uniwersytet Warszawski)
|
| O oszacowaniach a priori dla rozwiązań modelu chemotaksji - c.d. |
|
| 2004-03-04, godz. 14:15, s. 2070 |
| Monika Piotrowska (Uniwersytet Warszawski)
|
| Stabilność i bifurkacje Hopfa dla RR z dwoma opóźnieniami cd. |
|
| 2004-02-24, godz. 12:00, s. 2180 |
| Mark Chaplain (Dundee) |
| Mathematical modelling of solid tumour growth: Applications of Turing pre-pattern theory |
|
| 2004-02-19, godz. 14:15, s. 2070 |
| Monika Piotrowska (Uniwersytet Warszawski)
|
| Stabilnosc i bifurkacje Hopfa dla RR z 2 opoznieniami |
|
| 2004-02-12, godz. 14:15, s. 3030 |
| Monika Piotrowska (Uniwersytet Warszawski)
|
| Stabilność i bifurkacje Hopfa dla RR z 2 opóźnieniami |
|
| 2004-01-14, godz. 14:15, s. 3030 |
| Remigiusz Kowalczyk (Uniwersytet Warszawski)
|
| O ograniczeniu a priori rozwiązań dla modelu chemotaksji z nieliniową dyfuzją |
|
| 2004-01-07, godz. 14:15, s. 3030 |
| Monika Piotrowska (Uniwersytet Warszawski)
|
| Stabilność i bifurkacje Hopfa dla RR z dwoma opóźnieniami |
|
| 2003-12-17, godz. 14:15, s. 3030 |
| Joanna Jaroszewska (UJ) |
| Stabilność w uogólnionym modelu Lasoty-Mackeya-Tyrchy cyklu komórkowego |
|
| 2003-12-10, godz. 14:15, s. 3030 |
| Monika Piotrowska (Uniwersytet Warszawski)
|
| Stabilność i bifurkacje w RR z 2 opóźnieniami |
|
| 2003-12-03, godz. 14:15, s. 3030 |
| Urszula Foryś (Uniwersytet Warszawski)
|
| Równania reakcji-dyfuzji w biomatematyce (na podstawie M. Herrero) c.d. |
|
| 2003-11-26, godz. 14:15, s. 3030 |
| Urszula Foryś (Uniwersytet Warszawski)
|
| Równania reakcji-dyfuzji w biomatematyce (na podstawie M. Herrero) |
|
| 2003-11-10, godz. 16:00, s. 3130 |
| Remigiusz Kowalczyk (Uniwersytet Warszawski)
|
| Istnienie słabych rozwiązań dla pewnego układu równań różniczkowych cząstkowych typu paraboliczno-eliptycznego - c.d. |
|
| 2003-05-15, godz. 14:15, s. 5830 |
| Urszula Foryś (Uniwersytet Warszawski)
|
| Linearyzacja równania reakcji-dyfuzji z opóźnieniem |
|
| 2003-05-08, godz. 14:15, s. 5830 |
| Piotr Rybka (Uniwersytet Warszawski)
|
| Zagadnienia ze swobodną granicą na przykładzie modelu wzrostu guza |
|
| 2003-04-24, godz. 14:15, s. 5830 |
| Remigiusz Kowalczyk (Politecnico di Torino)
|
| On the chemotactic model describing cell agregation |
|
| 2003-04-10, godz. 14:15, s. 5830 |
| Zuzanna Szymańska (Uniwersytet Warszawski)
|
| Model matematyczny nekrotycznej części guza nowotworowego - cz. 2 |
|
| 2003-04-03, godz. 14:15, s. 5830 |
| Zuzanna Szymańska (Uniwersytet Warszawski)
|
| Model matematyczny nekrotycznej części guza nowotworowego |
|
| 2003-03-20, godz. 14:15, s. 5830 |
| M. Kolev i M. Lachowicz (Uniwersytet Warszawski)
|
| "Informacja o Workshopie w Dreźnie" i "Dwuliniowe równania r-c II" |
|
| 2003-03-13, godz. 14:15, s. 5830 |
| Mirosław Lachowicz (Uniwersytet Warszawski)
|
| Dwuliniowe równania różniczkowo-całkowe i ich zastosowania |
|
| 2003-02-27, godz. 14:15, s. 5830 |
| Jacek Banasiak (University of Natal)
|
| Chaotic linear dynamical systems with applications. |
|
