Data-adaptive harmonic spectra and multilayer Stuart-Landau models

Harmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure. The corresponding eigenvalues can be grouped per Fourier frequency, and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data. These eigenvalues obey furthermore a variational principle that allows us to define naturally a multidimensional power spectrum. The eigenmodes, as far as they are concerned, exhibit a data-adaptive character manifested in their phase which allows us in turn to define a multidimensional phase spectrum. The resulting data-adaptive harmonic (DAH) modes allow for reducing the data-driven modeling effort to elemental models stacked per frequency, only coupled at different frequencies by the same noise realization. In particular, the DAH decomposition extracts time-dependent coefficients stacked by Fourier frequency which can be efficiently modeled---provided the decay of temporal correlations is sufficiently well-resolved---within a class of multilayer stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators. Applications to the Lorenz 96 model and to a stochastic heat equation driven by a space-time white noise, are considered. In both cases, the DAH decomposition allows for an extraction of spatio-temporal modes revealing key features of the dynamics in the embedded phase space. The multilayer Stuart-Landau models (MSLMs) are shown to successfully model the typical patterns of the corresponding time-evolving fields, as well as their statistics of occurrence.Comment: 26 pages, double columns; 15 figure

Genome Dynamics Are Influenced by Food Source in Allogromia laticollaris Strain CSH (Foraminifera)

Across the eukaryotic tree of life, genomes vary within populations and within individuals during their life cycle. Understanding intraspecific genome variation in diverse eukaryotes is key to elucidating the factors that underlie this variation. Here, we characterize genome dynamics during the life cycle of Allogromia laticollaris strain CSH, a member of the Foraminifera, using fluorescence microscopy and reveal extensive variation in nuclear size and DNA content. Both nuclear size and DNA content are tightly correlated across a 700-fold range in cell volume. In contrast to models in yeast where nuclear size is determined solely by cell size, the relationship in A. laticollaris CSH differs according to both life cycle stage and food source. Feeding A. laticollaris CSH a diet that includes algae results in a 2-fold increase in DNA content in reproductive cells compared with a diet of bacteria alone. This difference in DNA content likely corresponds to increased fecundity, as reproduction occurs through segregation of the polyploid nucleus into numerous daughter nuclei. Environmentally mediated variation in DNA content may be a widespread phenomenon, as it has been previously reported in the plant flax and the flagellate Euglena. We hypothesize that DNA content is influenced by food in other single-celled eukaryotes with ploidy cycles and that this genome flexibility may enable these eukaryotes to maximize fitness across changing environmental conditions

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

Quasispecies Theory for Horizontal Gene Transfer and Recombination

We introduce a generalization of the parallel, or Crow-Kimura, and Eigen models of molecular evolution to represent the exchange of genetic information between individuals in a population. We study the effect of different schemes of genetic recombination on the steady-state mean fitness and distribution of individuals in the population, through an analytic field theoretic mapping. We investigate both horizontal gene transfer from a population and recombination between pairs of individuals. Somewhat surprisingly, these nonlinear generalizations of quasi-species theory to modern biology are analytically solvable. For two-parent recombination, we find two selected phases, one of which is spectrally rigid. We present exact analytical formulas for the equilibrium mean fitness of the population, in terms of a maximum principle, which are generally applicable to any permutation invariant replication rate function. For smooth fitness landscapes, we show that when positive epistatic interactions are present, recombination or horizontal gene transfer introduces a mild load against selection. Conversely, if the fitness landscape exhibits negative epistasis, horizontal gene transfer or recombination introduce an advantage by enhancing selection towards the fittest genotypes. These results prove that the mutational deterministic hypothesis holds for quasi-species models. For the discontinuous single sharp peak fitness landscape, we show that horizontal gene transfer has no effect on the fitness, while recombination decreases the fitness, for both the parallel and the Eigen models. We present numerical and analytical results as well as phase diagrams for the different cases.Comment: 54 pages; 8 figures; 12 tables; some typos corrected; to appear in Phys. Rev.

Algorithm of calculation of energy consumption on the basis of differential model of the production task performed on machines with computer numeric control (CNC)

© Published under licence by IOP Publishing Ltd. The calculation algorithm, power consumption of all consumers involved in the operation and production tasks developed by the example of workplaces equipped with CNC machines is developed. The algorithm takes into account the actual status, operating modes and switching sequence of all electricity consumers

The influence of iron microstructure on tool capacity during cutting process

© Published under licence by IOP Publishing Ltd. An overview of machinability by cutting cast irons is given. The effect of the microstructure of cast iron on the tool's working capacity during cutting has been studied. The reasons for the tool failure during drilling are revealed

Energy planning in production shops with numerically controlled machine tools

© 2017, Allerton Press, Inc. A method is proposed for planning the energy expenditures in production buildings with numerically controlled machine tools. The calculations take account of the individual production operations, as well as the actual state of the machine-tool drives

Evolution of a behavior-linked microsatellite-containing element in the 5' flanking region of the primate AVPR1A gene

<p>Abstract</p> <p>Background</p> <p>The arginine vasopressin V1a receptor (V1aR) modulates social cognition and behavior in a wide variety of species. Variation in a repetitive microsatellite element in the 5' flanking region of the V1aR gene (<it>AVPR1A</it>) in rodents has been associated with variation in brain V1aR expression and in social behavior. In humans, the 5' flanking region of <it>AVPR1A </it>contains a tandem duplication of two ~350 bp, microsatellite-containing elements located approximately 3.5 kb upstream of the transcription start site. The first block, referred to as DupA, contains a polymorphic (GT)₂₅microsatellite; the second block, DupB, has a complex (CT)₄-(TT)-(CT)₈-(GT)₂₄polymorphic motif, known as RS3. Polymorphisms in RS3 have been associated with variation in sociobehavioral traits in humans, including autism spectrum disorders. Thus, evolution of these regions may have contributed to variation in social behavior in primates. We examined the structure of these regions in six ape, six monkey, and one prosimian species.</p> <p>Results</p> <p>Both tandem repeat blocks are present upstream of the <it>AVPR1A </it>coding region in five of the ape species we investigated, while monkeys have only one copy of this region. As in humans, the microsatellites within DupA and DupB are polymorphic in many primate species. Furthermore, both single (lacking DupB) and duplicated alleles (containing both DupA and DupB) are present in chimpanzee (<it>Pan troglodytes</it>) populations with allele frequencies of 0.795 and 0.205 for the single and duplicated alleles, respectively, based on the analysis of 47 wild-caught individuals. Finally, a phylogenetic reconstruction suggests two alternate evolutionary histories for this locus.</p> <p>Conclusion</p> <p>There is no obvious relationship between the presence of the RS3 duplication and social organization in primates. However, polymorphisms identified in some species may be useful in future genetic association studies. In particular, the presence of both single and duplicated alleles in chimpanzees provides a unique opportunity to assess the functional role of this duplication in contributing to variation in social behavior in primates. While our initial studies show no signs of directional selection on this locus in chimps, pharmacological and genetic association studies support a potential role for this region in influencing V1aR expression and social behavior.</p

Optimizing the regimes of Advanced LIGO gravitational wave detector for multiple source types

We develop here algorithms which allow to find regimes of signal-recycled Fabry-Perot--Michelson interferometer (for example, Advanced LIGO), optimized concurrently for two (binary inspirals + bursts) and three (binary inspirals + bursts + millisecond pulsars) types of gravitational waves sources. We show that there exists a relatevely large area in the interferometer parameters space where the detector sensitivity to the first two kinds of sources differs only by a few percent from the maximal ones for each kind of source. In particular, there exists a specific regime where this difference is ~0.5 for both of them. Furthermore we show that even more multipurpose regimes are also possible, that provide significant sensitivity gain for millisecond pulsars with only minor sensitivity degradation for binary inspirals and bursts.Comment: 10 pages, 14 figures, 3 tables. Minor corrections in main text are done in version 2 and two plots and one table are added for the sake of clarity of the obtained result