Relation between the Kantorovich-Wasserstein metric and the Kullback-Leibler divergence

We discuss a relation between the Kantorovich-Wasserstein (KW) metric and the Kullback-Leibler (KL) divergence. The former is defined using the optimal transport problem (OTP) in the Kantorovich formulation. The latter is used to define entropy and mutual information, which appear in variational problems to find optimal channel (OCP) from the rate distortion and the value of information theories. We show that OTP is equivalent to OCP with one additional constraint fixing the output measure, and therefore OCP with constraints on the KL-divergence gives a lower bound on the KW-metric. The dual formulation of OTP allows us to explore the relation between the KL-divergence and the KW-metric using decomposition of the former based on the law of cosines. This way we show the link between two divergences using the variational and geometric principles

Opposing effects of final population density and stress on Escherichia coli mutation rate

Evolution depends on mutations. For an individual genotype, the rate at which mutations arise is known to increase with various stressors (stress-induced mutagenesis-SIM) and decrease at high final population density (density-associated mutation-rate plasticity-DAMP). We hypothesised that these two forms of mutation-rate plasticity would have opposing effects across a nutrient gradient. Here we test this hypothesis, culturing Escherichia coli in increasingly rich media. We distinguish an increase in mutation rate with added nutrients through SIM (dependent on error-prone polymerases Pol IV and Pol V) and an opposing effect of DAMP (dependent on MutT, which removes oxidised G nucleotides). The combination of DAMP and SIM results in a mutation rate minimum at intermediate nutrient levels (which can support 7 × 10  cells ml ). These findings demonstrate a strikingly close and nuanced relationship of ecological factors-stress and population density-with mutation, the fuel of all evolution

Comparative study of hydrogen stability in hydrogenated amorphous and crystalline silicon

Populations of individuals exist in a wide range of sizes, from billions of microorganisms to fewer than ten individuals in some critically endangered species. In any evolutionary system, there is significant evolutionary pressure to evolve sequences that are both fit and robust; at high mutation rates, individuals with greater mutational robustness can outcompete those with higher fitness, a concept that has been referred to as survival-of-the-flattest. Previous studies have not found a relationship between population size and the mutation rate that can be tolerated before fitter individuals are outcompeted by those that have a greater mutational robustness. However, using a genetic algorithm with a simple two-peak fitness landscape, we show that the mutation rates at which the high, narrow peak and the lower, broader peak are lost for increasing population sizes can be approximated by exponential functions. In addition, there is evidence for a continuum of mutation rates representing a transition from survival-of-the-fittest to survival-of-the-flattest and subsequently to the error catastrophe. The effect of population size on the critical mutation rate is shown to be particularly noticeable in small populations. This provides new insight into the factors that can affect survival-of-the-flattest in small populations, and has implications for populations under threat of local extinction

Swarm intelligence based algorithms: a critical analysis

Many optimization algorithms have been developed by drawing inspiration from swarm intelligence (SI). These SI-based algorithms can have some advantages over traditional algorithms. In this paper, we carry out a critical analysis of these SI-based algorithms by analyzing their ways to mimic evolutionary operators. We also analyze the ways of achieving exploration and exploitation in algorithms by using mutation, crossover and selection. In addition, we also look at algorithms using dynamic systems, self-organization and Markov chain framework. Finally, we provide some discussions and topics for further research