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Model of discrete dynamics of asset price relations based on the minimal arbitrage principle

100%
Kostanjčar Z., Hengster-Movrić K., Jeren B.
Open Physics
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2011
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vol. 9
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issue 3
865-873
EN
In this paper we present a deterministic and a probabilistic model of the dynamics of the price relations for a number of assets on the market. The formalism is based on the asset space introduced in a theory by Illinski. We derive, from an action functional for the system of price relations in that space, the corresponding difference equations, which constitute the deterministic description. Furthermore, we obtain the probability density function of the probabilistic model of market dynamics from the same action functional. The deterministic solution corresponds to a geometric sequence for the interest, whereas the derived probability density describes the probability of the next value of the price relations in dependence on their prior value. The formalism is completely developed for systems (markets) with two and three assets, but exactly the same approach is applicable to the systems consisting of an arbitrary number of assets.
2
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Self-similarity principle: the reduced description of randomness

100%
Nigmatullin R., Machado J., Menezes R.
Open Physics
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2013
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vol. 11
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issue 6
724-739
EN
A new general fitting method based on the Self-Similar (SS) organization of random sequences is presented. The proposed analytical function helps to fit the response of many complex systems when their recorded data form a self-similar curve. The verified SS principle opens new possibilities for the fitting of economical, meteorological and other complex data when the mathematical model is absent but the reduced description in terms of some universal set of the fitting parameters is necessary. This fitting function is verified on economical (price of a commodity versus time) and weather (the Earth’s mean temperature surface data versus time) and for these nontrivial cases it becomes possible to receive a very good fit of initial data set. The general conditions of application of this fitting method describing the response of many complex systems and the forecast possibilities are discussed.
3
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Evolutionary dynamics of imatinib-treated leukemic cells by stochastic approach

100%
Pizzolato N., Valenti D., Adorno D., Spagnolo B.
Open Physics
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2009
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vol. 7
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issue 3
541-548
EN
The evolutionary dynamics of a system of cancerous cells in a model of chronic myeloid leukemia (CML) is investigated by a statistical approach. Cancer progression is explored by applying a Monte Carlo method to simulate the stochastic behavior of cell reproduction and death in a population of blood cells which can experience genetic mutations. In CML front line therapy is represented by the tyrosine kinase inhibitor imatinib which strongly affects the reproduction of leukemic cells only. In this work, we analyze the effects of a targeted therapy on the evolutionary dynamics of normal, first-mutant and cancerous cell populations. Several scenarios of the evolutionary dynamics of imatinib-treated leukemic cells are described as a consequence of the efficacy of the different modelled therapies. We show how the patient response to the therapy changes when a high value of the mutation rate from healthy to cancerous cells is present. Our results are in agreement with clinical observations. Unfortunately, development of resistance to imatinib is observed in a fraction of patients, whose blood cells are characterized by an increasing number of genetic alterations. We find that the occurrence of resistance to the therapy can be related to a progressive increase of deleterious mutations.
4
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Influence of a Range of Interaction among Agents on Efficiency and Effectiveness of Knowledge Transfer within an Organisation

100%
Paradowski K., Kowalska-Styczeń A., Malarz K.
Acta Physica Polonica A
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2018
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vol. 133
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issue 6
1470-1476
EN
In this study we examined how the size of non-formal groups between organisation members affect the transfer of knowledge in the context of the efficiency and effectiveness of this process. To analyse the dynamics of the transfer of knowledge the cellular automata model was used. The model is based on local interactions between members of the organisation, that take place in the nearest neighbourhood. These groups of close neighbours are represented by von Neumann's neighbourhood (four nearest-neighbours) and Moore's neighbourhood (four nearest-neighbours and four next-nearest neighbours) and complex neighbourhood (four nearest neighbours, four next-nearest neighbours and four next-next-neighbours). The results of the simulation show the influence of the size of the neighbourhood on the efficiency of knowledge transfer.
5
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Robust diagnostics of complex chemical processes: Main problems and possible solutions

75%
Kościelny J. M., Syfert M.
Chemical and Process Engineering
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2018
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vol. 39
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issue 2
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