Algorithms for Stochastic Games on Interference Channels

We consider a wireless channel shared by multiple transmitter-receiver pairs. Their transmissions interfere with each other. Each transmitter-receiver pair aims to maximize its long-term average transmission rate subject to an average power constraint. This scenario is modeled as a stochastic game. We provide sufficient conditions for existence and uniqueness of a Nash equilibrium (NE). We then formulate the problem of finding NE as a variational inequality (VI) problem and present an algorithm to solve the VI using regularization. We also provide distributed algorithms to compute Pareto optimal solutions for the proposed game

The context-dependence of mutations: a linkage of formalisms

Defining the extent of epistasis - the non-independence of the effects of mutations - is essential for understanding the relationship of genotype, phenotype, and fitness in biological systems. The applications cover many areas of biological research, including biochemistry, genomics, protein and systems engineering, medicine, and evolutionary biology. However, the quantitative definitions of epistasis vary among fields, and its analysis beyond just pairwise effects remains obscure in general. Here, we show that different definitions of epistasis are versions of a single mathematical formalism - the weighted Walsh-Hadamard transform. We discuss that one of the definitions, the backgound-averaged epistasis, is the most informative when the goal is to uncover the general epistatic structure of a biological system, a description that can be rather different from the local epistatic structure of specific model systems. Key issues are the choice of effective ensembles for averaging and to practically contend with the vast combinatorial complexity of mutations. In this regard, we discuss possible approaches for optimally learning the epistatic structure of biological systems.Comment: 6 pages, 3 figures, supplementary informatio

Power Allocation Games on Interference Channels with Complete and Partial Information

We consider a wireless channel shared by multiple transmitter-receiver pairs. Their transmissions interfere with each other. Each transmitter-receiver pair aims to maximize its long-term average transmission rate subject to an average power constraint. This scenario is modeled as a stochastic game under different assumptions. We first assume that each transmitter and receiver has knowledge of all direct and cross link channel gains. We later relax the assumption to the knowledge of incident channel gains and then further relax to the knowledge of the direct link channel gains only. In all the cases, we formulate the problem of finding the Nash equilibrium as a variational inequality (VI) problem and present an algorithm to solve the VI.Comment: arXiv admin note: text overlap with arXiv:1409.755