Extinction in Lotka-Volterra model

Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra model of predator-prey competition. Fluctuation effects due to discreteness of the populations destroy the mean-field stability and eventually drive the system toward extinction of one or both species. We show that the corresponding extinction time scales as a certain power-law of the population sizes. This behavior should be contrasted with the extinction of models stable in the mean-field approximation. In the latter case the extinction time scales exponentially with size.Comment: 11 pages, 17 figure

Small quenches and thermalization

We study the expectation values of observables and correlation functions at long times after a global quantum quench. Our focus is on metallic (“gapless”) fermionic many-body models and small quenches. The system is prepared in an eigenstate of an initial Hamiltonian, and the time evolution is performed with a final Hamiltonian which differs from the initial one in the value of one global parameter. We first derive general relations between time-averaged expectation values of observables as well as correlation functions and those obtained in an eigenstate of the final Hamiltonian. Our results are valid to linear and quadratic order in the quench parameter g and generalize prior insights in several essential ways. This allows us to develop a phenomenology for the thermalization of local quantities up to a given order in g. Our phenomenology is put to a test in several case studies of one-dimensional models representative of four distinct classes of Hamiltonians: quadratic ones, effectively quadratic ones, those characterized by an extensive set of (quasi-) local integrals of motion, and those for which no such set is known (and believed to be nonexistent). We show that for each of these models, all observables and correlation functions thermalize to linear order in g. The more local a given quantity, the longer the linear behavior prevails when increasing g. Typical local correlation functions and observables for which the term O(g) vanishes thermalize even to order g2. Our results show that lowest-order thermalization of local observables is an ubiquitous phenomenon even in models with extensive sets of integrals of motion

Evolutionary branching in a stochastic population model with discrete mutational steps

Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a trait, and also by population sizes, and that mutations lead to small changes in trait value. Then, traditionally, the evolutionary dynamics is studied in the limit of vanishing mutational step sizes. In the present approach, small but non-negligible mutational steps are considered. By means of theoretical analysis in the limit of infinitely large populations, as well as computer simulations, we demonstrate how discrete mutational steps affect the patterns of evolutionary branching. We also argue that the average time to the first branching depends in a sensitive way on both mutational step size and population size.Comment: 12 pages, 8 figures. Revised versio

Numerical study of the scaling properties of SU(2) lattice gauge theory in Palumbo non-compact regularization

In the framework of a non-compact lattice regularization of nonabelian gauge theories we look, in the SU(2) case, for the scaling window through the analysis of the ratio of two masses of hadronic states. In the two-dimensional parameter space of the theory we find the region where the ratio is constant, and equal to the one in the Wilson regularization. In the scaling region we calculate the lattice spacing, finding it at least 20% larger than in the Wilson case; therefore the simulated physical volume is larger.Comment: 24 pages, 7 figure

Stochastic Description of Aircraft Simulation Models and Numerical Approaches

Der Artikel befasst sich mit der Unsicherheitsquantifizierung eines Flugzeugsimulationsmodells. Mathematisch gesehen handelt es sich bei dem Flugzeugmodell um ein System von Differentialgleichungen zweiter Ordnung. Dabei hängt das System von Eingangsparametern ab, die der Masse, der Aerodynamik und der Struktur des Flugzeugs zugeordnet sind. Die aerodynamischen Eingangsparameter sind als Zufallsvariablen und -prozesse modelliert, deren Wahrscheinlichkeitsverteilungen nach dem Maximum-Entropie-Prinzip und verfügbaren experimentellen Daten ausgewählt werden. Für das Flugdynamikmodell wird die Unsicherheitsentwicklung der Flugzustandsverläufe mittels sogenannter nicht-intrusiver numerischer Verfahren abgeschätzt. Die Verfahren sind beispielsweise direkte Integrationsverfahren, stochastische Kollokationsverfahren und Pseudo-Galerkin Verfahren. Diese numerischen Verfahren basieren auf Stichproben von Flugzustandsverläufen, welche durch das Lösen der zugehörigen deterministischen gewöhnlichen Differentialgleichungen erhalten werden.This paper is concerned with the uncertainty quantification of an aircraft simulation model. Mathematically speaking the aircraft model represents a system of second order differential equations dependent on a set of input parameters related to the mass, aerodynamics and the structure of the aircraft. The input aerodynamic parameters are modelled as random variables and processes whose probability distributions are chosen according to the maximum entropy principle and available experimental data. For a flight dynamics model the evolution of uncertainties in the aircraft state trajectory is estimated with the help of so-called non-intrusive numerical approaches, examples of which are the direct integration method, the stochastic collocation approach and the pseudo-Galerkin method. These numerical methods rely on a set of samples of aircraft state trajectories simply obtained by solving the corresponding systems of deterministic ordinary differential equations

Complex population dynamics as a competition between multiple time-scale phenomena

The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The mean-field level of description allows to highlight the delicate interplay between the different time-scale processes in the resulting complex dynamics of the system. We clarify the influence of the amplitude and period of the environmental changes on the critical value of the selection pressure corresponding to a phase-transition "extinct-alive" of the population. However, the intrinsic stochasticity and the dynamically-built in correlations among the individuals, as well as the role of the mutation-induced variety in population's evolution are not appropriately accounted for. A more refined level of description, which is an individual-based one, has to be considered. The inherent fluctuations do not destroy the phase transition "extinct-alive", and the mutation amplitude is strongly influencing the value of the critical selection pressure. The phase diagram in the plane of the population's parameters -- selection and mutation is discussed as a function of the environmental variation characteristics. The differences between a smooth variation of the environment and an abrupt, catastrophic change are also addressesd.Comment: 15 pages, 12 figures. Accepted for publication in Phys. Rev.

baobabLUNA: the solution space of sorting by reversals

Summary: Computing the reversal distance and searching for an optimal sequence of reversals to transform a unichromosomal genome into another are useful algorithmic tools to analyse real evolutionary scenarios. Currently, these problems can be solved by at least two available softwares, the prominent of which are GRAPPA and GRIMM. However, the number of different optimal sequences is usually huge and taking only the distance and/or one example is often insufficient to do a proper analysis. Here, we offer an alternative and present baobabLUNA, a framework that contains an algorithm to give a compact representation of the whole space of solutions for the sorting by reversals problem

Changes in temperature and water depth of a small mountain lake during the past 3000 years in Central Kamchatka reflected by a chironomid record

© 2016 Elsevier Ltd and INQUA.We investigated chironomid assemblages of a well-dated sediment core from a small seepage lake situated at the eastern slope of the Central Kamchatka Mountain Chain, Far East Russia. The chironomid fauna of the investigated Sigrid Lake is dominated by littoral taxa that are sensitive to fluctuations of the water level. Two groups of taxa interchangeably dominate the record responding to the changes in the lake environment during the past 2800 years. The first group of littoral phytophilic taxa includes Psectrocladius sordidellus-type, Corynoneura arctica-type and Dicrotendipes nervosus-type. The abundances of the taxa from this group have the strongest influence on the variations of PCA 1, and these taxa mostly correspond to low water levels, moderate temperatures and slightly acidified conditions. The second group of taxa includes Microtendipes pedellus-type, Tanytarsus lugens-type, and Tanytarsus pallidicornis-type. The variations in the abundances of these taxa, and especially of M. pedellus-type, are in accordance with PCA 2 and correspond to the higher water level in the lake, more oligotrophic and neutral pH conditions. Water depths (WD) were reconstructed, using a modern chironomid-based temperature and water depth calibration data set (training set) and inference model from East Siberia (Nazarova et al., 2011). Mean July air temperatures (T July) were inferred using a chironomid-based temperature inference model based on a modern calibration data set for the Far East (Nazarova et al., 2015). The application of transfer functions resulted in reconstructed T July fluctuations of approximately 3 °C over the last 2800 years. Low temperatures (11.0-12.0 °C) were reconstructed for the periods between ca 1700 and 1500 cal yr BP (corresponding to the Kofun cold stage) and between ca 1200 and 150 cal yr BP (partly corresponding to the Little Ice Age [LIA]). Warm periods (modern T July or higher) were reconstructed for the periods between ca 2700 and 1800 cal yr BP, 1500 and 1300 cal yr BP and after 150 cal yr BP. WD reconstruction revealed that the lake level was lower than its present level at the beginning of the record between ca 2600 and 2300 cal yr BP and ca 550 cal yr BP. Between ca 2300 and 700 cal yr BP as well as between 450 and 150 cal yr BP, the lake level was higher than it is today, most probably reflecting more humid conditions

Changes in temperature and water depth of a small mountain lake during the past 3000 years in Central Kamchatka reflected by a chironomid record

© 2016 Elsevier Ltd and INQUA We investigated chironomid assemblages of a well-dated sediment core from a small seepage lake situated at the eastern slope of the Central Kamchatka Mountain Chain, Far East Russia. The chironomid fauna of the investigated Sigrid Lake is dominated by littoral taxa that are sensitive to fluctuations of the water level. Two groups of taxa interchangeably dominate the record responding to the changes in the lake environment during the past 2800 years. The first group of littoral phytophilic taxa includes Psectrocladius sordidellus-type, Corynoneura arctica-type and Dicrotendipes nervosus-type. The abundances of the taxa from this group have the strongest influence on the variations of PCA 1, and these taxa mostly correspond to low water levels, moderate temperatures and slightly acidified conditions. The second group of taxa includes Microtendipes pedellus-type, Tanytarsus lugens-type, and Tanytarsus pallidicornis-type. The variations in the abundances of these taxa, and especially of M. pedellu s-type, are in accordance with PCA 2 and correspond to the higher water level in the lake, more oligotrophic and neutral pH conditions. Water depths (WD) were reconstructed, using a modern chironomid-based temperature and water depth calibration data set (training set) and inference model from East Siberia (Nazarova et al., 2011). Mean July air temperatures (T July) were inferred using a chironomid-based temperature inference model based on a modern calibration data set for the Far East (Nazarova et al., 2015). The application of transfer functions resulted in reconstructed T July fluctuations of approximately 3 °C over the last 2800 years. Low temperatures (11.0–12.0 °C) were reconstructed for the periods between ca 1700 and 1500 cal yr BP (corresponding to the Kofun cold stage) and between ca 1200 and 150 cal yr BP (partly corresponding to the Little Ice Age [LIA]). Warm periods (modern T July or higher) were reconstructed for the periods between ca 2700 and 1800 cal yr BP, 1500 and 1300 cal yr BP and after 150 cal yr BP. WD reconstruction revealed that the lake level was lower than its present level at the beginning of the record between ca 2600 and 2300 cal yr BP and ca 550 cal yr BP. Between ca 2300 and 700 cal yr BP as well as between 450 and 150 cal yr BP, the lake level was higher than it is today, most probably reflecting more humid conditions

A condition on delay for differential equations with discrete state-dependent delay

Parabolic differential equations with discrete state-dependent delay are studied. The approach, based on an additional condition on the delay function introduced in [A.V. Rezounenko, Differential equations with discrete state-dependent delay: uniqueness and well-posedness in the space of continuous functions, Nonlinear Analysis: Theory, Methods and Applications, 70 (11) (2009), 3978-3986] is developed. We propose and study a state-dependent analogue of the condition which is sufficient for the well-posedness of the corresponding initial value problem on the whole space of continuous functions $C$. The dynamical system is constructed in $C$ and the existence of a compact global attractor is proved