Simple Synchronous and Asynchronous Algorithms for Distributed Minimax Optimization

Synchronous and asynchronous algorithms are presented for distributed minimax optimization. The objective here is to realize the minimization of the maximum of component functions over the standard multi-agent network, where each node of the network knows its own function and it exchanges its decision variable with its neighbors. In fact, the proposed algorithms are standard consensus and gossip based subgradient methods, while the original minimax optimization is recast as minimization of the sum of component functions by using a p-norm approximation. A scalable step size depending on the approximation ratio p is also presented in order to avoid slow convergence. Numerical examples illustrate that the algorithms with this step size work well even in the high approximation ratios

Mathematical model for promotion of wound closure with ATP release

To computationally investigate the recent experimental finding such that extracellular ATP release caused by exogeneous mechanical forces promote wound closure, we introduce a mathematical model, the Cellular Potts Model (CPM), which is a popular discretized model on a lattice, where the movement of a “cell” is determined by a Monte Carlo procedure. In the experiment, it was observed that there is mechanosensitive ATP release from the leading cells facing the wound gap and the subsequent extracellular Ca2+ influx. To model these phenomena, the Reaction-Diffusion equations for extracellular ATP and intracellular Ca2+ concentrations are adopted and combined with CPM, where we also add a polarity term because the cell migration is enhanced in the case of ATP release. From the numerical simulations using this hybrid model, we discuss effects of the collective cell migration due to the ATP release and the Ca2+ influx caused by the mechanical forces and the consequent promotion of wound closure

Stochastic Consensus Algorithms over General Noisy Networks

Stochastic consensus algorithms are considered for multi-agent systems over noisy unbalanced directed networks. The graph which represents a communication network of the system is assumed to contain a directed spanning tree, that is, a given digraph is weakly connected. Then two types of stochastic consensus are investigated, where one is for the agent states themselves and the other is for the time averages of the agent states. The convergence of the algorithms is investigated, which gives a stopping rule, i.e., an explicit relation between the number of iterations and the closeness of the agreement