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1
Rak : rzecz o propagacji błędów w sieciach genowo-komórkowych
Świerniak A.
Śląskie Wiadomości Elektryczne
|
2015
|
Nr 3 (120)
21--27
PL
W artykule przedstawiono działalność techniczną Komitetu Automatyki Elektroenergetycznej w latach 2010-2015 przy organizacji odczytów, seminariów i konferencji oraz redagowaniu czasopism technicznych.
EN
This article presents the technical operations of the Automation Electric Power Engineering Committee in the years 2010-2015 during organization of lectures, seminars, conferences and editing of the technical journals.
2
Content available Controllability of a model of combined anticancer therapy
Klamka J., Świerniak A.
Control and Cybernetics
|
2013
|
Vol. 42, no. 1
123--138
EN
Controllability of combination of antiangiogenic treatment and chemotherapy is considered. A model used in the paper is a finite-dimensional dynamical control system described by secondo order semilinear time invariant ordinary differential state equations. Using a generalized open mapping theorem, sufficient conditions for constrained local controllability in a given time interval are formulated and proved. These conditions require verification of constrained global controllability of the associated linear second-order dynamical control system.
3
Content available Regulation of p53 by siRNA in radiation treated cells: Simulation studies
Puszyński K., Jaksik R., Świerniak A.
International Journal of Applied Mathematics and Computer Science
|
2012
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Vol. 22, no. 4
1011-1018
EN
Ionizing radiation activates a large variety of intracellular mechanisms responsible for maintaining appropriate cell functionality or activation of apoptosis which eliminates damaged cells from the population. The mechanism of such induced cellular death is widely used in radiotherapy in order to eliminate cancer cells, although in some cases it is highly limited by increased cellular radio-resistance due to aberrations in molecular regulation mechanisms of malignant cells. Despite the positive correlation between the radiation dose and the number of apoptotic cancer cells, radiation has to be limited because of extensive side effects. Therefore, additional control signals whose role will be to maximize the cancer cells death-ratio while minimizing the radiation dose and by that the potential side effects are worth considering. In this work we present the results of simulation studies showing possibilities of single gene regulation by small interfering RNA (siRNA) that can increase radio-sensitivity of malignant cells showing aberrations in the p53 signaling pathway, responsible for DNA damage-dependant apoptosis. By blocking the production of the p53 inhibitor Mdm2, radiation treated cancer cells are pushed into the apoptotic state on a level normally achievable only with high radiation doses. The presented approach, based on a simulation study originating from experimentally validated regulatory events, concerns one of the basic problems of radiotherapy dosage limitations, which, as will be shown, can be partially avoided by using the appropriate siRNA based control mechanism.
4
Content available Spatial evolutionary games and radiation induced bystander effect
Krześlak M., Świerniak A.
Archives of Control Sciences
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2011
|
Vol. 21, no. 2
135-150
EN
We present an application of evolutionary game theory to modeling of some processes important from oncological point of view. A studied phenomenon is a radiation induced bystander effect, in which three different strategies (phenotypes) of cells take part. The proposed payoff table of fitness, related to environment adaptation and genetic cell behavior, contains costs/profits of bystander effect, choice of apoptotic pathway, producing growth factors and resistance against bystander effect. We consider a game theory model including spatial cells allocation (the game is played on lattice). We discuss also different polymorphic equilibrium points dependent on model parameters, types of spatial games and players distribution.
5
Content available remote W co grają komórki rakowe?
Świerniak A., Krześlak M.
Przegląd Elektrotechniczny
|
2010
|
R. 86, nr 9
118-122
PL
W pracy przedstawiamy zastosowanie teorii gier ewolucyjnych skończonych do modelowania procesów karcenogenezy i sygnalizacji międzykomórkowej. Modele proponowane w literaturze wzbogacamy o badania oparte na dynamice replikatorów i interpretacje otrzymanych na tej podstawie wyników symulacji. Proponujemy również własne modele.
EN
We present application of finite evolution game theory for modeling of carcinogenesis and intercellular communication process. The models proposed in literature are enriched by studies of replicator dynamics and their interpretation based on simulation experiments. We propose also our original models.
6
Content available remote Identification and identifiability of models of cell signalling pathways
Fujarewicz K., Kimmel M., Świerniak A.
Przegląd Elektrotechniczny
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2008
|
R. 84, nr 5
91-94
EN
The dynamical behaviour of a cell signalling pathway may be described by means of a set of nonlinear ordinary differential equations. The data for parameter estimation are collected only at discrete time moments that are relatively rare. We show a gradient-based algorithm for parameter estimation. We also present some considerations about identifiability of cell signalling pathways. The approach is illustrated on a model of NF?B transcription factor pathway.
PL
Dynamiczne zachowanie komórkowych szlaków sygnałowych może być modelowane za pomocą nieliniowych równań różniczkowych zwyczajnych. Dane potrzebne do identyfikacji zbierane są w nielicznych, dyskretnych chwilach czasu. W artykule zamieszczamy gradientową metodę identyfikacji parametrów oraz przedstawiamy rozważania dotyczące identyfikowalności parametrów. Podejście jest zilustrowane na przykładzie modelu szlaku sygnałowego czynnika transkrypcyjnego NF?B.
7
Content available remote Angiogeneza nowotworów jako obiekt sterowania
Świerniak A., Gala G., Onofrio A., Gandolfi A.
Przegląd Elektrotechniczny
|
2008
|
R. 84, nr 4
124-127
PL
W pracy przedstawiony i przeanalizowany został model terapii skierowanej przeciwko powstającej w procesie angiogenezy nowotworów sieci naczyniowej i tym samym pośrednio umożliwiającej wyleczenie choroby. Dyskutowany jest model zaproponowany przez Hahnfeldta a także pewna jego modyfikacja. Przedstawiona analiza dotyczy warunków stabilności przekładających się na możliwość asymptotycznej anihilacji guza oraz warunków koniecznych optymalizacji protokołów terapii.
EN
A model of tumor growth taking into account its vascularization due to angiogenesis and antiangiogenic cancer chemotherapy is proposed and analised. The model is a modified Hahnfeldt model and the analysis has two goals: first of all we check stability of the equilibrium point of the model using Lyapunov first and second methods to find conditions leading to tumour eradication, and then we propose an optimization problem and give necessary conditions of its solution basing on the Pontryagin maximum principle.
8
Content available remote Direct and indirect control of cancer populations
Świerniak A.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2008
|
Vol. 56, nr 4
367-378
EN
This paper presents a brief survey of our research in which we have used control theoretic methods in modelling and control of cancer populations. We focus our attention on two classes of problems: optimization of anticancer chemotherapy taking into account both phase specificity and drug resistance, and modelling, and optimization of antiangiogenic therapy. In the case of chemotherapy the control action is directly aimed against the cancer cells while in the case of antiangiogenic therapy it is directed against normal cells building blood vessels and only indirectly it controls cancer growth. We discuss models (both finite and infinite dimensional) which are used to find conditions for tumour eradication and to optimize chemotherapy protocols treating cell cycle as an object of control. In the case of antiangiogenic therapy we follow the line of reasoning presented by Hahnfeldt et al. who proposed to use classical models of self-limiting tumour growth with variable carrying capacity defined by the dynamics of the vascular network induced by the tumour in the process of angiogenesis. In this case antiangiogenic protocols are understood as control strategies and their optimization leads to new recommendations for anticancer therapy.
9
Metoda bezkolizyjnego sterowania grupą robotów, bazująca na punktach równowagi gier niekooperacyjnych
Skrzypczyk K., Gałuszka A., Świerniak A.
Zeszyty Naukowe. Automatyka / Politechnika Śląska
|
2006
|
z. 146
129-152
PL
W pracy przedstawiono zastosowanie koncepcji punktów równowagi w grach niekooperacyjnych do bezkolizyjnego planowania ruchu grapy robotów mobilnych w dynamicznym, szybkozmiennym środowisku. Zaproponowano prawo sterowania wykorzystujące rozwiązanie niekooperacyjnego problemu decyzyjnego, umożliwiające syntezę systemu bezkolizyjnego sterowania grupą robotów. Rozwiązania problemu planowania ruchu, wykorzystujące koncepcję równowagi są dobrze znane w literaturze. Takie podejście jest wysoce efektywne, jednak tylko w przypadku gdy istnieją pojedyncze punkty równowagi. Jednakże nawet w prostych problemach nawigacyjnych pojawiają się sytuacje, w których występują rozwiązania wielokrotne, będące powodem istotnych trudności w syntezie praw sterowania. W pracy zaproponowano rozwiązanie problemu wyboru pojedynczego rozwiązania, bazujące na idei częściowej koordynacji. Do systemu wprowadzono moduł koordynatora, który staje się aktywny w sytuacjach gdy zostaje wykryte występowanie wielokrotnych punktów równowagi. W celu potwierdzenia efektywności proponowanej metody przedstawiono wyniki symulacji przeprowadzonych dla 2 i 5 robotów.
EN
In this work we present an application of the concept of non-cooperative game equilibria for the design of a collision free movement of a team of mobile robots in a dynamic environment. We propose the solution to the problem of feasible control synthesis, based on partially centralized sensory system. The control strategy based on the concept of non cooperative game equilibria is well known in the literature. It is highly efficient through phases where the solution is unique. However, even in simple navigation problems, it happens that multiple equilibria occur, which poses a problem for control synthesis and may lead to erroneous results. In this paper we present the solution to this problem based on the partial centralization idea. The coordinator module is incorporated into the system and becomes active when multiple equilibria are detected. The coordination method includes a "fair arbiter" for selection of an appropriate equilibrium solution. Simulation studies of the proposed methodology were carried out for 2,3 and 5 robots and their results are presented.
10
Content available remote On Adaptive Control for the Continuous Time-varying JLQG Problem
Czornik A., Świerniak A.
International Journal of Applied Mathematics and Computer Science
|
2005
|
Vol. 15, no 1
53-62
EN
In this paper the adaptive control problem for a continuous infinite time-varying stochastic control system with jumps in parameters and quadratic cost is investigated. It is assumed that the unknown coefficients of the system have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Under these assumptions it is shown that the optimal value of the quadratic cost can be reached based only on the values of these limits, which, in turn, can be estimated through strongly consistent estimators.
11
Content available remote Non-cooperative game approach to multi-robot planning
Gałuszka A., Świerniak A.
International Journal of Applied Mathematics and Computer Science
|
2005
|
Vol. 15, no 3
359-367
EN
A multi-robot environment with a STRIPS representation is considered. Under some assumptions such problems can be modelled as a STRIPS language (for instance, a Block World environment) with one initial state and a disjunction of goal states. If the STRIPS planning problem is invertible, then it is possible to apply the machinery for planning in the presence of incomplete information to solve the inverted problem and then to find a solution to the original problem. In the paper a planning algorithm that solves the problem described above is proposed and its computational complexity is analyzed. To make the plan precise, non-cooperative strategies are used.
12
Content available Finite dimensional models of drug resistant and phase specific cancer chemotherapy
Ledzewicz U., Schättler H., Świerniak A.
Journal of Medical Informatics & Technologies
|
2004
|
Vol. 8
IP5--14
EN
The problem of modelling drug resistance and phase specificity of cancer chemotherapy using finite dimensional models were considered. We formulate optimal control problems arising in protocol design for such models and discuss research issues resulting from these formulations.
13
Content available Are infinite dimensional models applicable in modelling and analysis of cancer chemotherapy?
Świerniak A., Kimmel M., Śmieja J., Rzeszowska-Wolny J.
Journal of Medical Informatics & Technologies
|
2004
|
Vol. 8
MM3--10
EN
Drug resistance and phase dependence have been regarded by many authors as the main obstacles against successful cancer chemotherapy. We propose a model which takes into account both these phenomena and give a tool to use phase specificity as an advantage rather than a fault and make it resistant of drug resistance. It combines models that so far have been studied separately, taking into account both the phenomenon of gene amplification and drug specificity in chemotherapy, in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix, the form of which enables decomposition of the model into two interacting subsystems. While the first one, of finite dimension, can have any form, the second one is infinite dimensional and tridiagonal.
14
Content available remote Using control theory to make cancer chemotherapy beneficial from phase dependence and resistant to drug resistance
Kimmel M., Świerniak A.
Archives of Control Sciences
|
2004
|
Vol. 14, no. 2
105-145
EN
Two major obstacles against successful chemotheraphy of cancer are (1) the cell-cycle-phase dependence of treatment, and (2) the emergence of resistance of cancer cells to cytotoxic agents. One way to understand and overcome these two problems is to apply optimal control theory to mathematical models of cell cycle dynamics. These models should include division og the cell cycle into subphase and/or the mechanisms of drug resistance. we review our relevant results in mathematical modelling and control of the cell cycle and the mechanisms of gene amplification, and estimation of parameters of the constructed models.
15
Content available remote Optimal Control for a Class of Compartmental Models in Cancer Chemotherapy
Świerniak A., Ledzewicz U., Schättler H.
International Journal of Applied Mathematics and Computer Science
|
2003
|
Vol. 13, no 3
357-368
EN
We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models B and C, are analyzed, which consider a blocking agent and a recruiting agent, respectively. In Model B a blocking agent which slows down cell growth during the synthesis allowing in consequence the synchronization of the neoplastic population is added. In Model C the recruitment of dormant cells from the quiescent phase to enable their efficient treatment by a cytotoxic drug is included. In all models the cumulative effect of the killing agent is used to model the negative effect of the treatment on healthy cells. For each model it is shown that singular controls are not optimal. Then sharp necessary and sufficient optimality conditions for bang-bang controls are given for the general class of models P and illustrated with numerical examples.
16
Content available remote Different Models of Chemotherapy Taking Into Account Drug Resistance Stemming from Gene Amplification
Śmieja J., Świerniak A.
International Journal of Applied Mathematics and Computer Science
|
2003
|
Vol. 13, no 3
297-305
EN
This paper presents an analysis of some class of bilinear systems that can be applied to biomedical modelling. It combines models that have been studied separately so far, taking into account both the phenomenon of gene amplification and multidrug chemotherapy in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix whose form allows decomposing the model into two interacting subsystems. While the first one, of a finite dimension, can have any form, the other is infinite dimensional and tridiagonal. A methodology of the analysis of such models, based on system decomposition, is presented. An optimal control problem is defined in the l1 space. In order to derive necessary conditions for optimal control, the model description is transformed into an integro-differential form. Finally, biomedical implications of the obtained results are discussed.
17
Content available Asymptotic analysis of three random branching walk models arising in molecular biology
Świerniak A., Polański A., Śmieja J., Kimmel M., Rzeszowska-Wolny J.
Control and Cybernetics
|
2003
|
Vol. 32, no 1
147-162
EN
Using asymptotic techniques based on Laplace transforms, spectral analysis and theory of feedback systems, we characterise the asymptotic behaviour of the repeat loci in microsatellite DNA and cancer cells with increasing number of copies of genes responsible for coding proteins causing drug removal or metabolisation as well as telomeres shortening, which is supposed to be the mechanism of ageing and death. These three problems are described by models in the form of infinitely many differential linear or bilinear first order equations, resulting from branching random walk processes used to represent the evolution of particles in these problems.
PL
Wykorzystując techniki asymptotyczne oparte na transformatach Laplace'a, analizę spektralną oraz teorię układów ze sprzężeniem zwrotnym w artykule scharakteryzowano zachowanie asymptotyczne powtórek w DNA mikrosatelitarnym oraz w komórkach rakowych z rosnącą liczbą kopii genów odpowiedzialnych za kodowanie białek powodujących usuwanie lub przemianę metaboliczną leków, a także skracanie telomerów, o którym się sądzi, że jest mechanizmem starzenia się i śmierci. Te trzy zagadnienia są opisywane przy pomocy modeli w postaci nieskończonej liczby liniowych lub biliniowych równań pierwszego rzędu, wynikających z procesów błądzenia, stosowanych do opisu ewolucji cząstek w tych zagadnieniach.
18
Content available remote Single nucleotide polymorphisms applied in statistical inference of population growth
Polański A., Starosolski Z., Świerniak A., Kimmel M.
Biocybernetics and Biomedical Engineering
|
2003
|
Vol. 23, no. 4
45-61
EN
We have evaluated probability distributions of estimates of parameters of population growth, based on data on frequencies of alleles of unlinked SNP sites in DNA, modeled with the use of time dependent coalescence process acting together with mutation of a very low intensity. Probability distributions of maximum likelihood estimates of the product parameter of the present population effective size and exponent coefficient, for exponential scenario, have atoms at zero and long tails to the right. For stepwise scenario, log likelihood functions typically exhibit very long lines, covering many decades of the scale, of almost the same value of log likelihood. Observational data from [14] are consistent with the hypothesis of the population growth.
19
Content available Optimal multidrug treatment in the presence of drug resistance stemming from gene amplification
Śmieja J., Świerniak A.
Journal of Medical Informatics & Technologies
|
2002
|
Vol. 3
MI13--19
EN
The paper is concerned with development of optimal treatment protocols that take into account both action of several drugs and the evolution of drug resistance. It is a result of analysis of evolution of drug resistance in cancer population but presented methodology can be applied in any case involving drug resistance stemming from gene amplification. First, a biological background is given. In subsequent sections of the paper, the developed technique is presented and some early analytical results, which form a basis for more precise modeling, are shown. Afterwards, the model description is transformed into a vector integro-differential equation, which makes it possible to define necessary conditions of optimal solution to the minimization problem arising from the search for the optimal treatment. Finally, some remarks on the model applicability are presented.
20
Content available remote On the discrete time-varying JLQG problem
Czornik A., Świerniak A.
International Journal of Applied Mathematics and Computer Science
|
2002
|
Vol. 12, no 2
203-207
EN
In the present paper optimal time-invariant state feedback controllers are designed for a class of discrete time-varying control systems with Markov jumping parameter and quadratic performance index. We assume that the coefficients have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Moreover, following the same line of reasoning, an adaptive controller is proposed in the case when system parameters are unknown but their strongly consistent estimators are available.
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