Nasze seminarium zakładowe odbywa się w środy 14:15-15:45 w sali 4050
2017-01-25: Adam Korpusik (doktorant MIM i UWM)
Tytuł: On the nonlocal discretization of basic mathematical models of viral infection
Streszczenie: I will present two nonstandard finite difference schemes designed for the numerical simulation of basic mathematical models of viral infection. The proposed methods preserve the non-negativity and equilibria (along with their stability conditions), as well as the presence (or absence) of oscillations. All of these qualitative features of the original continuous models are preserved independently of the chosen step-size of the simulation.
2017-01-18: Jacek Sadowski (MINI PW)
Tytuł: Differential equations with coeffcients in Sobolev spaces
Streszczenie: I would like to talk about ordinary and delay differential equations with coefficients in Sobolev spaces. An example of a differential system with measurable singular right hand side is the system of motion of n-bodies. When we deal with nonsmooth differential equations, then some obstacles appear: for instance the superposition f(t,y(t)) does not have to be measurable. A candidate for a solution of such problem is the concept of the trace operator defining the trace on a graph on a curve.
2017-01-11: Piotr Bajger (doktorant MISDoMP)
Tytuł: Optimal therapy for heterogeneous tumours
Streszczenie: I will discuss a model for a growth of a heterogeneous tumour from a point of view of optimal control. The main issue is how to choose an appropriate objective functional so that two goals are achieved: the tumour overall volume does not become too large over the course of the treatment and at the same time the "switch" of a tumour to a more resistant phenotype is avoided. Due to the non-linear nature of the problem, theoretical analysis quickly becomes difficult, hence numerical results will be presented.
2016-12-21: Faiz Alhag (doktorant MIM)
Tytuł: Analytical solution of optima and open loop Nash equilibrium in oil war model with finite time horizon
Streszczenie: Recently, there have been numerous international wars about natural non-renewable resource in Iran-Iraq, China Sea-the east China, Sudan -south Sudan and unfortunately nowadays my home (Yemen) and Saudi Arabia and other locations. The current case study focuses on any neighboring two countries that have access to the same natural non-renewable resource (oil), which is divided symmetrically by the border. We consider both cooperative and Nash equilibrium result in the pre - war phase.
2016-12-14: Mateusz Dębowski (doktorant MIM)
Tytuł: When zombie attack: mathematical modelling of an outbreak of zombie infection.
Streszczenie: I will present a model based on work by Philip Munz, Ioan Hudea, Joe Imad and Robert Smith. I will show the basic model for zombie infection, analytical results, numerical simulations and modification including quarantine or a cure. The main question is: how we should react when zombie attack? At the end of my presentation we will get to know the answer.
2016-11-30: Kamila Łyczek (doktorantka MIM)
Tytuł: Optimization in infinite time horizon
Streszczenie: Pontryagin's maximum principle is used in optimal control theory to find the best possible control for taking a dynamical system from one state to another, especially in the presence of constraints for the state or input controls. It has as a special case the Euler–Lagrange equation of the calculus of variations. Maximum principle cannot be used for infinite-horizon optimal control problems, which appear for example in many fields of economics. Typically, the initial state is fixed and the terminal state (at infinity) is free in such problems, while the utility functional to be maximized is given by an improper integral on the time interval. S. M. Aseev and V. M. Veliov have formulated a proper version of the Pontryagin's maximum principle for the infinite-horizon problem. I will talk what could happend when we use normal form of maximum principle for infinite time, about results of Aseev and Velov, and about a plan how to expand this optimization for dynamical games.
2016-11-23: Marcin Choiński (doktorant MIM)
Tytuł: Criss-cross modeling of TB
Streszczenie: We consider a criss-cross model describing tuberculosis epidemic dynamics. The case in study considers Warmian-Masurian province of Poland and is related to actions of active detecting of tuberculosis in homeless people subpopulation. In the model the population is divided into subpopulations of non-homeless and homeless people. Each of the subpopulation consists of two groups - susceptible and infected people. The analysis of model will be presented. The most important property of the model is related to its Malthusian origin. This means that in general the size of the whole population (meaning homeless and non-homeless together) grows unboundedly or the population goes to extinction. It can also happen that the subpopulation of non-homeless people goes to extinction while the subpopulation of homeless people grows unboundedly, which seems to be absurd. Therefore, we propose a modification of this model.
2016-11-16: Rajani Singh (doktorantka MIM)
Tytuł: A Linear-Quadratic Common Resource Extraction Game with Many Players and Binding Constraints
Streszczenie: We analyse a linear quadratic multistage game of extraction of a common renewable resource by many players with state dependent constraints for exploitation and infinite time horizon. We analyse social optimum and Nash equilibrium for feedback information structure and compare the results obtained in both. For Nash equilibria, we obtain a value function that is contrary to intuitions from standard linear quadratic games. We also study introduction of a tax in order to enforce socially optimal behaviour of the players. Besides, this game constitutes a counterexample to two techniques regarded as standard in computation of Nash equilibrium and/or optimal control.
2016-11-09: Michał Górski (doktorant MISDoMP)
Tytuł: Komputerowe wspomaganie poszukiwania przestępców
2016-11-02: Prof. Priti Kumar Roy, Jadavpur University Kolkata, Indie
Tytuł: Therapeutic Approach with Keratinocyte Anomalies: Mathematical insights on Psoriasis
Streszczenie: Psoriasis is a long-lasting autoimmune disease characterized by patches of abnormal skin. Psoriasis is non-infective but it can be genetically inherited and basically is a product of cell proliferation signal mismatch. There is no cure for psoriasis. However, various treatments can help control the symptoms. Biologics are any pharmaceutical drug product manufactured in, extracted from, or semi synthesized from biological sources. Different from chemically synthesized pharmaceuticals, they include vaccines, blood, or blood components, somatic cells, gene therapies, tissues, recombinant therapeutic protein, and living cells used in cell therapy. Biologics can be composed of sugars, proteins, or nucleic acids or complex combinations of these substances, chemokines and cytokines or may be living cells or tissues. Mathematical modelling of Psoriatic ailment is an important hallmark in Psoriasis treatment and the treatments can be administered based on the sensitivity of the model outputs. A systematic and cell biological process based model system is constructed on strict biological foundations and it is extended further on functional cell cycle dynamics of the affected keratinocytes. We objectify on strict mathematical sense to introduce novel treatment process for the suffering people, integrating knowledge of both the domains in a composite form of nonlinear differential equations. Further, we have constructed some control profiles of the cellular process to limit Psoriasis using optimal control theory and also deduce the maximum cost effective drug treatment using cost function. We have also derived the signal cascade of cellular memory effects on such destabilized system producing Psoriasis with the incorporation of fractional order system and memory operator (α) to establish links among the cell and the control therapeutic approach through optimal drug dosing within the fractional-order system reducing the Keratinocyte cell population more significantly.
2016-10-26: Jan Poleszczuk (IBIB)
Tytuł: Usefulness of mathematical modeling at cancer center: personal experience
Streszczenie: I will talk about my experience of being a Postdoctoral fellow at Moffitt Cancer Center in Department of Integrated Mathematical Oncology (by briefly describing projects that I was involved in). I will discuss pros and cons of working close to the clinic and why I've decided to move back to Poland.
2016-10-19: Prof. Priti Kumar Roy from Jadavpur University Kolkata, Indie
Tytuł: Biodiesel: From Ecology (Jatropha Curcas) to Production Through Mathematical Aspect
Streszczenie: Biodiesel is one of promising renewable energy and used as an alternative of conventional mineral fuels. Jatropha curcas plant is the most cost effective sources of biodiesel. The plant can be cultivated in wastelands and grows on almost any type of territory, even on sandy and saline soils. However, the plant is affected by different pests that causes crop damages and hamper maximum production of seeds. Judicious agricultural practices and effective crop management of Jatropha curcas is preliminary requisite to get maximum yield of oil. We study the control of pests through biopesticides and chemical insecticides simultaneously, which destroys pests quickly and results in maximum seeds to obtain oil from which the biodiesel is produced. Application of bio-pesticides is a costly as well as time dependent process but it is ecologically safer. Our model is developed with a view to maximize the cost benefit in response to the managerial operations applied. Taking account of the ecological management of the pests in farming of Jatropha plant and incorporating the industrial production of biodiesel from its fruits we have developed some mathematical models to study and predict how we can maximize our oil production integrating the ecological and industrial management with our mathematical perceptive. Our numerical and analytical results provide an idea of the cost effective biodiesel production, which satisfies our hypothesis.
2016-10-12: Marek Bodnar and Magdalena Bogdańska
Tytuł: TOG: Therapy optimization in glioblastoma: An integrative human data-based approach using mathematical models
Streszczenie: We will talk about the TOG project, which is a collaborative project dedicated to acquire data from patients and integrate those data into mathematical approaches able to characterize the disease evolution. The final goal of the project is to use that knowledge to improve glioblastoma treatments. In the project almost 20 scientific centres are involved, between them there are many hospitals and medical centres. During the seminar we will present a brief review of the workshop that took place on October 3-4 in Cuenca. In particular we will show models that describe creation of pseudopalisades by glioblastoma cells. We will present also a model that indicates that increase of the time between radiotherapy doses may be beneficial for the patient.
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