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Analysis of immunotherapy models in the context of cancer dynamics

100%
Szymańska Z.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 3
407-418
EN
A basic mathematical model of the immune response when cancer cells are recognized is proposed. The model consists of six ordinary differential equations. It is extended by taking into account two types of immunotherapy: active immunotherapy and adoptive immunotherapy. An analysis of the corresponding models is made to answer the question which of the presented methods of immunotherapy is better. The analysis is completed by numerical simulations which show that the method of adoptive immunotherapy seems better for the patient at least in some cases.
2
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Dynamics of social networks: A deterministic approach

100%
Pearson D. W., McCartney M.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
|
nr 4
545-551
EN
Our aim is to model the dynamics of social networks, which comprises the problem of how people get to know each other, like each other, detest each other, etc. Most existing models are stochastic in nature and, obviously, based on random events. Our approach is deterministic and based on ordinary differential equations. This should not be seen as a challenge to stochastic models, but rather as a complement.
3
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Algebraic condition for decomposition of large-scale linear dynamic systems

100%
Górecki H.
International Journal of Applied Mathematics and Computer Science
|
2009
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tom 19
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nr 1
107-111
EN
The paper concerns the problem of decomposition of a large-scale linear dynamic system into two subsystems. An equivalent problem is to split the characteristic polynomial of the original system into two polynomials of lower degrees. Conditions are found concerning the coefficients of the original polynomial which must be fulfilled for its factorization. It is proved that knowledge of only one of the symmetric functions of those polynomials of lower degrees is sufficient for factorization of the characteristic polynomial of the original large-scale system. An algorithm for finding all the coefficients of the decomposed polynomials and a general condition of factorization are given. Examples of splitting the polynomials of the fifth and sixth degrees are discussed in detail.
4
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A new approach to nonlinear modelling of dynamic systems based on fuzzy rules

88%
Bartczuk Ł., Przybył A., Cpałka K.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 3
603-621
EN
For many practical weakly nonlinear systems we have their approximated linear model. Its parameters are known or can be determined by one of typical identification procedures. The model obtained using these methods well describes the main features of the system's dynamics. However, usually it has a low accuracy, which can be a result of the omission of many secondary phenomena in its description. In this paper we propose a new approach to the modelling of weakly nonlinear dynamic systems. In this approach we assume that the model of the weakly nonlinear system is composed of two parts: a linear term and a separate nonlinear correction term. The elements of the correction term are described by fuzzy rules which are designed in such a way as to minimize the inaccuracy resulting from the use of an approximate linear model. This gives us very rich possibilities for exploring and interpreting the operation of the modelled system. An important advantage of the proposed approach is a set of new interpretability criteria of the knowledge represented by fuzzy rules. Taking them into account in the process of automatic model selection allows us to reach a compromise between the accuracy of modelling and the readability of fuzzy rules.
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