We compare two concepts of stochastic stability in spatial games. The classical approach to stochastic stability, introduced by Foster and Young [8], involves single configurations in the zero-noise limit. Ensemble stability discussed in [17] refers to ensembles of configurations in the limit of an infinite number of players. The above two limits may not commute. We will discuss reasons of such behaviour. We review some results concerning the effect of the number of players and the noise level on...
Many processes in natural and social sciences can be modeled by systems of interacting objects. It is usually very difficult to obtain analytic expressions describing time evolution and equilibrium behavior of such systems. Very often we rely only on computer simulations. Fortunately, in many cases one can construct useful approximation schemes and derive exact results which capture some specific features of a given process. A frequent approach is to replace interactions between objects by a mean...
We extend the classical Barabási-Albert preferential attachment procedure by allowing edge deletion. We prove that unlike in the original model, power-law exponents of degree distribution of scale-free graphs with edge deletion depend on the number of attached edges in one step of the growing process.
We discuss various models of ion transport through cell membrane channels. Recent experimental data shows that sizes of some ion channels are compared to those of ions and that only few ions may be simultaneously in any single channel. Theoretical description of ion transport in such channels should therefore take into account stochastic fluctuations and interactions between ions and between ions and channel proteins. This is not satisfied by macroscopic continuum models based on the Poisson-Nernst-Planck...
XLVI Nationalwide Conference on Applications of Mathematics, 5 - 12 September 2017, Zakopane-Kościelisko (Ł. Stettner) A brief history of Mathematics Applications Seminar. XLVII Seminar on Applications of Mathematics in Kobyla Góra (Chalfen)XXIII Nationalwide Conference on Applications of Mathematics in Biology and Medicine (Urszula Foryś). Eleventh ISDG Workshops in Warsaw (Agnieszka Wiszniewska-Matyszkiel)XLIII Conference "Mathematical Statistics" (P. Grzegorzewski)Simons Semester at Banach...
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