Sharif Digital Repository

Moving of living organisms appears in many interesting problems, e.g. the growth of bacteria colonies, tumor growth, wound healing, color patterns of animals and etc. There are many ways to model such problems and PDE theory is widely used to investigate these problems. In this thesis, we study two well-known classic models. First, macroscopic “Keller–Segel” model and then kinetic “Othmer–Dunbar–Alt” System. Since these models have a nice behavior in two dimensions that they don’t have in other dimensions, we propose a way to alter them such that they behave in this way in all dimensions. Also none of the known models have the suitable dynamics in one dimension, so our model has the property... 

Inverse reinforcement learning (IRL) is one of the machine learning frameworks based on learning from humans; That is, instead of producing a decision process maximizing a predefined reward function, seeks to find the reward function based on the observed behavior of an agent. The biggest motivation of IRL is that, usually, determining a reward function for a problem is very difficult. We consider IRL in Markov decision processes; that is, the problem of extracting a reward function with the assumption of knowing the optimal behavior. IRL could be useful for apprenticeship learning to obtain skilled behavior, and for optimizing a reward function by a natural system. We first, determine a set... 

Networks of neurons produce diverse patterns of oscillations, arising from the net-work’s global properties, the propensity of individual neurons to oscillate, or a mixture of the two. Here we describe noisy limit cycles and quasi-cycles, two related mech-anisms underlying emergent oscillations in neuronal networks whose individual com- ponents, stochastic spiking neurons, do not themselves oscillate. Both mechanisms are shown to produce gamma band oscillations atthepopulation level while individualneu-rons fire at a rate much lower than the population frequency. Spike trains in a network undergoing noisy limit cycles display a preferred period which is not found in the case...