Resolvent Positive Linear Operators Exhibit the Reduction Phenomenon

The spectral bound, s(a A + b V), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in b \in R. This is shown here, through an elementary lemma, to imply that s(a A + b V) is also convex in a > 0, and notably, \partial s(a A + b V) / \partial a <= s(A) when it exists. Diffusions typically have s(A) <= 0, so that for diffusions with spatially heterogeneous growth or decay rates, greater mixing reduces growth. Models of the evolution of dispersal in particular have found this result when A is a Laplacian or second-order elliptic operator, or a nonlocal diffusion operator, implying selection for reduced dispersal. These cases are shown here to be part of a single, broadly general, `reduction' phenomenon.Comment: 7 pages, 53 citations. v.3: added citations, corrections in introductory definitions. v.2: Revised abstract, more text, and details in new proof of Lindqvist's inequalit

Fitness landscape of the cellular automata majority problem: View from the Olympus

In this paper we study cellular automata (CAs) that perform the computational Majority task. This task is a good example of what the phenomenon of emergence in complex systems is. We take an interest in the reasons that make this particular fitness landscape a difficult one. The first goal is to study the landscape as such, and thus it is ideally independent from the actual heuristics used to search the space. However, a second goal is to understand the features a good search technique for this particular problem space should possess. We statistically quantify in various ways the degree of difficulty of searching this landscape. Due to neutrality, investigations based on sampling techniques on the whole landscape are difficult to conduct. So, we go exploring the landscape from the top. Although it has been proved that no CA can perform the task perfectly, several efficient CAs for this task have been found. Exploiting similarities between these CAs and symmetries in the landscape, we define the Olympus landscape which is regarded as the ''heavenly home'' of the best local optima known (blok). Then we measure several properties of this subspace. Although it is easier to find relevant CAs in this subspace than in the overall landscape, there are structural reasons that prevent a searcher from finding overfitted CAs in the Olympus. Finally, we study dynamics and performance of genetic algorithms on the Olympus in order to confirm our analysis and to find efficient CAs for the Majority problem with low computational cost

Some topics in theoretical population genetics: Editorial commentaries on a selection of Marc Feldman's TPB papers.

This article consists of commentaries on a selected group of papers of Marc Feldman published in Theoretical Population Biology from 1970 to the present. The papers describe a diverse set of population-genetic models, covering topics such as cultural evolution, social evolution, and the evolution of recombination. The commentaries highlight Marc Feldman's role in providing mathematically rigorous formulations to explore qualitative hypotheses, in many cases generating surprising conclusions

On the Neutrality of Flowshop Scheduling Fitness Landscapes

Solving efficiently complex problems using metaheuristics, and in particular local searches, requires incorporating knowledge about the problem to solve. In this paper, the permutation flowshop problem is studied. It is well known that in such problems, several solutions may have the same fitness value. As this neutrality property is an important one, it should be taken into account during the design of optimization methods. Then in the context of the permutation flowshop, a deep landscape analysis focused on the neutrality property is driven and propositions on the way to use this neutrality to guide efficiently the search are given.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome : Italy (2011

Impact of Epistasis and Pleiotropy on Evolutionary Adaptation

Evolutionary adaptation is often likened to climbing a hill or peak. While this process is simple for fitness landscapes where mutations are independent, the interaction between mutations (epistasis) as well as mutations at loci that affect more than one trait (pleiotropy) are crucial in complex and realistic fitness landscapes. We investigate the impact of epistasis and pleiotropy on adaptive evolution by studying the evolution of a population of asexual haploid organisms (haplotypes) in a model of N interacting loci, where each locus interacts with K other loci. We use a quantitative measure of the magnitude of epistatic interactions between substitutions, and find that it is an increasing function of K. When haplotypes adapt at high mutation rates, more epistatic pairs of substitutions are observed on the line of descent than expected. The highest fitness is attained in landscapes with an intermediate amount of ruggedness that balance the higher fitness potential of interacting genes with their concomitant decreased evolvability. Our findings imply that the synergism between loci that interact epistatically is crucial for evolving genetic modules with high fitness, while too much ruggedness stalls the adaptive process.Comment: 20 pages, 8 figures, plus 10 supporting figure

An Evolutionary Reduction Principle for Mutation Rates at Multiple Loci

A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event models. A multivariate form of the reduction principle is found: reduction results at individual loci combine topologically to produce a surface of mutation rate alterations that are neutral for a new modifier allele. New mutation rates survive if and only if they fall below this surface - a generalization of the hyperplane found by Zhivotovsky et al. (1994) for a multilocus recombination modifier. Increases in mutation rates at some loci may evolve if compensated for by decreases at other loci. The strength of selection on the modifier scales in proportion to the number of germline cell divisions, and increases with the number of loci affected. Loci that do not make a difference to marginal fitnesses at equilibrium are not subject to the reduction principle, and under fine tuning of mutation rates would be expected to have higher mutation rates than loci in mutation-selection balance. Other results include the nonexistence of 'viability analogous, Hardy-Weinberg' modifier polymorphisms under multiplicative mutation, and the sufficiency of average transmission rates to encapsulate the effect of modifier polymorphisms on the transmission of loci under selection. A conjecture is offered regarding situations, like recombination in the presence of mutation, that exhibit departures from the reduction principle. Constraints for tractability are: tight linkage of all loci, initial fixation at the modifier locus, and mutation distributions comprising transition probabilities of reversible Markov chains.Comment: v3: Final corrections. v2: Revised title, reworked and expanded introductory and discussion sections, added corollaries, new results on modifier polymorphisms, minor corrections. 49 pages, 64 reference

Development and Validation of a Model for Hydrogen Reduction of JSC-1A

Hydrogen reduction of lunar regolith has been proposed as a viable technology for oxygen production on the moon. Hydrogen reduces FeO present in the lunar regolith to form metallic iron and water. The water may be electrolyzed to recycle the hydrogen and produce oxygen. Depending upon the regolith composition, FeO may be bound to TiO2 as ilmenite or it may be dispersed in glassy substrates. Some testing of hydrogen reduction has been conducted with Apollo-returned lunar regolith samples. However, due to the restricted amount of lunar material available for testing, detailed understanding and modeling of the reduction process in regolith have not yet been developed. As a step in this direction, hydrogen reduction studies have been carried out in more detail with lunar regolith simulants such as JSC-1A by NASA and other organizations. While JSC-1A has some similarities with lunar regolith, it does not duplicate the wide variety of regolith types on the moon, for example, it contains almost no ilmenite. Nonetheless, it is a good starting point for developing an understanding of the hydrogen reduction process with regolith-like material. In this paper, a model utilizing a shrinking core formulation coupled with the reactor flow is described and validated against experimental data on hydrogen reduction of JSC-1A

Language control and parallel recovery of language in individuals with aphasia

Background: The causal basis of the different patterns of language recovery following stroke in bilingual speakers is not well understood. Our approach distinguishes the representation of language from the mechanisms involved in its control. Previous studies have suggested that difficulties in language control can explain selective aphasia in one language as well as pathological switching between languages. Here we test the hypothesis that difficulties in managing and resolving competition will also be observed in those who are equally impaired in both their languages even in the absence of pathological switching. Aims: To examine difficulties in language control in bilingual individuals with parallel recovery in aphasia and to compare their performance on different types of conflict task. Methods & procedures: Two right-handed, non-native English-speaking participants who showed parallel recovery of two languages after stroke and a group of non-native English-speaking, bilingual controls described a scene in English and in their first language and completed three explicit conflict tasks. Two of these were verbal conflict tasks: a lexical decision task in English, in which individuals distinguished English words from non-words, and a Stroop task, in English and in their first language. The third conflict task was a non-verbal flanker task. Outcomes & Results: Both participants with aphasia were impaired in the picture description task in English and in their first language but showed different patterns of impairment on the conflict tasks. For the participant with left subcortical damage, conflict was abnormally high during the verbal tasks (lexical decision and Stroop) but not during the non-verbal flanker task. In contrast, for the participant with extensive left parietal damage, conflict was less abnormal during the Stroop task than the flanker or lexical decision task. Conclusions: Our data reveal two distinct control impairments associated with parallel recovery. We stress the need to explore the precise nature of control problems and how control is implemented in order to develop fuller causal accounts of language recovery patterns in bilingual aphasia