Search

To study the relationship between the dynamics of the COVID-19 pandemic and the state of the economy, the authors developed a stochastic model that covers the epidemic and economic blocks and the system of relationships between them. Based on the three-sector Lorenz model, they have proposed an approach to analyze the interrelationships between economic sectors related to food production, food supply chains, and the healthcare industry. The model combines the above economic sectors in a single structure and considers each sector in terms of productivity, the number of jobs, and the structural disturbance levels. The authors carried out model studies to analyze the dependence of the dynamics of the pandemic on the initial conditions and parameters for managing the epidemic process and the impact of the pandemic on changes in the balance of supply and demand in sectors of the economy related to food production, food transportation, and the healthcare industry. [ABSTRACT FROM AUTHOR]

The authors have developed a mathematical model to determine the conditions whereby the rate of increase of greenhouse gas (GHG) concentrations in the atmosphere is minimized, and the given level of life quality of the population is maintained. The model combines in a holistic structure the economic sectors described in the same way. Each of them is considered in terms of the level of productivity, number of jobs, and the level of structural disturbances (the six-sector Lorenz model with variable coefficients that depend on the GHG level). The model makes it possible to investigate how changes in the GHG level and the relationships between different sectors of the economy affect the risks to sustainable development and the general level of the life quality of the population. The authors have determined conditions for the emergence of turbulent operating modes, which lead to an increase in the total number of structural disturbances and a decrease in the aggregate level of productivity. They also proposed an approach to assessing the level of threats to sustainable development under climate changes. [ABSTRACT FROM AUTHOR]

The approach to estimating distribution parameters with a priori constraints has been developed. The Lorentz six-sector model has been constructed. Based on this model, the authors have studied the relationships between food, energy, water resources, supply systems, epidemic, and social situations. They also have investigated the impact of the successive transitions of interconnected sectors to the deterministic chaos regime on the operation mode of the whole system. The method of risk assessment for food security and risk management has been elaborated. [ABSTRACT FROM AUTHOR]

We establish the mixing property for a family of Lebesgue measure preserving toral maps composed of two piecewise linear shears, the first of which is non-monotonic. The maps serve as a basic model for the ‘stretching and folding’ action in laminar fluid mixing, in particular flows where boundary conditions give rise to non-monotonic flow profiles. The family can be viewed as the parameter space between two well-known systems, Arnold’s Cat Map and a map due to Cerbelli and Giona, both of which possess finite Markov partitions and straightforward to prove mixing properties. However, no such finite Markov partitions appear to exist for the present family, so establishing mixing properties requires a different approach. In particular, we follow a scheme of Katok and Strelcyn, proving strong mixing properties with respect to the Lebesgue measure on two open parameter spaces. Finally, we comment on the challenges in extending these mixing windows and the potential for using the same approach to prove mixing properties in similar systems. [ABSTRACT FROM AUTHOR]

Complex systems such as river flow do not obey the law of linearity but most often than not behave in a nonlinear manner. In this study, the dynamics of the River Niger discharge along two stations located in Nigeria were investigated using the methods of phase space reconstruction, correlation dimension and Lyapunov exponent. The analysis was carried out by using the daily data for three different periods — 1914–1939 (period 1), 1940–1964 (period 2), and 1966–1991 (period 3) spanning before and after the Kainji dam construction. Time delay embedding values at Baro and Lokoja for the three time periods were used to reconstruct the phase space of the river discharge at both locations. The embedding dimension represents the number of variables to completely describe the system. The presence of chaos was confirmed with positive values of Lyapunov exponents in both locations at the three different periods considered. The Lyapunov exponents at Baro were in the range 0.0014–0.0150 while the range at Lokoja was 0.007–0.0145. Significant correlation dimension values obtained at Baro (2.11–2.81) and Lokoja (2.28–4.51) are indicative of low dimensional chaos. A possible explanation for this could be the temporal sequence in the dam installation. The forecast horizon, the inverse of the largest Lyapunov exponents, gives a prediction boundary on a chaotic time series. In this study, the forecast horizon for both locations is expected to be in the range of 40–58 days into the future. [ABSTRACT FROM AUTHOR]

This work is an adaptation of the Katok Closing Lemma for non-singular, endomorphisms on a compact Riemannian manifold. In special, it appears the idea of the proof of the hyperbolicity as well as the admissibility of local stable-unstable manifolds of a proper periodic point in adapted Katok Closing Lemma. [ABSTRACT FROM AUTHOR]

Ecological footprint has been widely accepted as an indicator of environmental performance in recent years since it considers carbon dioxide emissions, the collapse of fisheries, the change in land use, and deforestation. This paper investigates, if exists, the convergence in per capita ecological footprint among G20 countries by employing the annual data for the period 1961 to 2014. A bootstrap-based panel KPSS test with structural breaks and club convergence test are carried out. Eventually, this paper is expected to contribute to the literature of natural resources and ecology/environment by (1) monitoring the panel variable of ecological footprint, (2) launching stochastic and deterministic convergence analyses, and (3) estimating the club convergence parameters. In conclusion, the confirmative results in favor of environmental convergence are obtained by exhibiting the stochastic and deterministic convergences and deriving the output of merging clubs. [ABSTRACT FROM AUTHOR]

Electroencephalograms of 220 patients with post-coma disorders of consciousness after severe traumatic brain injury were analyzed using nonlinear multidimensional analysis, and the results were compared with those of standard linear time-amplitude analysis. Quantitative multichannel EEGs were recorded in the course of one-year-long clinical restorative treatment and rehabilitation. We tried to identify informative indices obtained using nonlinear analysis, which most closely correlated with the dynamics of the syndromes of altered consciousness (classification according to Dobrokhotova [34]). The diagnostic informational value of the results of nonlinear analysis of quantitative EEGs and sensitivity of this methodical approach in predicting positive/negative dynamics of consciousness recovery were estimated. Results of mapping of the values of entropy, dimension of the brain dynamic systems (complexity), parameters of the attractors, and multifractal properties of EEGs in different patient groups are described. It is concluded that the obtained results of nonlinear analysis demonstrate sertain advantages in prediction of the clinical course of post-coma disturbances of consciousness after brain trauma. [ABSTRACT FROM AUTHOR]

Background and aims: The changing soils is a never-ending process moderated by numerous biotic and abiotic factors. Among these factors, trees may play a critical role in forested landscapes by having a large imprint on soil texture and chemical properties. During their evolution, soils can follow convergent or divergent development pathways, leading to a decrease or an increase in soil spatial complexity. We hypothesized that trees can be a strong local factor intensifying, blocking or modifying pedogenetic processes, leading to local changes in soil complexity (convergence, divergence, or polygenesis). These changes are hypothetically controlled by regionally predominating soil formation processes.Methods: To test the main hypothesis, we described the pedomorphological features of soils under tree stumps of fir, beech and hemlock in three soil regions: Haplic Cambisols (Turbacz Reserve, Poland), Entic Podzols (Žofínský Prales Reserve, Czech Republic) and Albic Podzols (Upper Peninsula, Michigan, USA). Soil profiles under the stumps, as well as control profiles on sites currently not occupied by trees, were analyzed in the laboratory for 20 physical and chemical properties. In total, we analyzed 116 soil samples. The age of trees and time of tree death were determined using the radiometry (14C), dendrochronology and repeated tree censuses. To process the data, we used multivariate statistics, namely, redundancy analyses (RDAs) and principal component analyses (PCAs). The statistical significance of variables was tested using Kruskal-Wallis, Dunn, and permutation tests. To reach the main aims of the present study, we examined the dataset at three levels of data complexity: 1) soil regions, 2) microsite (i.e., tree stump versus control site), and 3) soil horizon.Results: Living tree roots and empty or infilled root channels were the most important pedogenic factors that affected the dimensions of soil horizons and the moisture in the root zone under tree stumps. Microsites explained almost 6% of the soil variability (p < 0.001, F = 13.99), demonstrating that trees significantly impacted soil chemical properties in the root zone in all regions. In the Albic Podzols soil region, we found evidence of “basket” podzolization. Our results suggest the rapid eluviation of organic matter-sesquioxide complexes under the stump, probably leading to local soil divergence in Albic Podzols. However, soil analyses under the stumps in the Haplic Cambisols soil region suggested local polygenetic changes in soils (e.g., hydromorphic processes). The thickness of the A and B horizons increased, and soil chemistry changed under trees in the Entic Podzol soil region compared to the control profiles.Conclusions: In addition to regional environmental factors that manifest themselves in regional pedogenesis and that have a key role in modifying the influence of trees on the soil, the tree species can specifically modify pedogenic processes under standing trees. Trees may influence rate of pedogenesis (hemlock in Albic Podzol region) or even soil evolutionary pathways (beech in Haplic Cambisol region). [ABSTRACT FROM AUTHOR]

Inherent part of evolutionary algorithms that are based on Darwin’s theory of evolution and Mendel’s theory of genetic heritage, are random processes since genetic algorithms and evolutionary strategies are used. In this paper, we present extended experiments (of our previous) of selected evolutionary algorithms and test functions showing whether random processes really are needed in evolutionary algorithms. In our experiments we used differential evolution and SOMA algorithms with functions 2ndDeJong, Ackley, Griewangk, Rastrigin, SineWave and StretchedSineWave. We use n periodical deterministic processes (based on deterministic chaos principles) instead of pseudo-random number generators (PRGNs) and compare performance of evolutionary algorithms powered by those processes and by PRGNs. Results presented here are numerical demonstrations rather than mathematical proofs. We propose the hypothesis that a certain class of deterministic processes can be used instead of PRGNs without lowering the performance of evolutionary algorithms. [ABSTRACT FROM AUTHOR]

Numerical-analytical methods for finding periodic solutions of highly nonlinear autonomous and nonautonomous systems of ordinary differential equations are considered. Algorithms for finding initial conditions corresponding to a periodic solution are proposed. The stability of the found periodic solutions is analyzed using corresponding variational systems. The possibility of studying the evolution of periodic solutions in a strange attractor zone and on its boundaries is discussed, and interactive software implementations of the proposed algorithms are described. Numerical examples are given. [ABSTRACT FROM AUTHOR]

In this paper, by analyzing the best chaotic sequences generated by sixteen different chaotic maps, a novel chaos optimization algorithm is presented. It can intelligently base on different chaotic maps to select different strategies so as to map the chaotic variables into the optimization variables. For the proposed algorithm, the obtained best values, the run time, and the role of the first and the second stage search by using different chaotic maps are also analyzed and compared. The simulation results implemented on several classic test functions demonstrate that the proposed algorithm has a high performance and an outstanding efficiency. [ABSTRACT FROM AUTHOR]

We investigate the appearance of chaos in a microbial 3-species model motivated by a potentially chaotic real world system (as characterized by positive Lyapunov exponents (Becks et al., Nature 435, 2005). This is the first quantitative model that simulates characteristic population dynamics in the system. A striking feature of the experiment was three consecutive regimes of limit cycles, chaotic dynamics and a fixed point. Our model reproduces this pattern. Numerical simulations of the system reveal the presence of a chaotic attractor in the intermediate parameter window between two regimes of periodic coexistence (stable limit cycles). In particular, this intermediate structure can be explained by competition between the two distinct periodic dynamics. It provides the basis for stable coexistence of all three species: environmental perturbations may result in huge fluctuations in species abundances, however, the system at large tolerates those perturbations in the sense that the population abundances quickly fall back onto the chaotic attractor manifold and the system remains. This mechanism explains how chaos helps the system to persist and stabilize against migration. In discrete populations, fluctuations can push the system towards extinction of one or more species. The chaotic attractor protects the system and extinction times scale exponentially with system size in the same way as with limit cycles or in a stable situation. [ABSTRACT FROM AUTHOR]

The studies of the processes that can significantly influence the predictability in population dynamics are reviewed and the results of mathematical simulations of population dynamics are compared to the time series obtained in field observations. Considerable attention is given to the chaotic changes in population abundance. Some methods of numerical analysis of chaoticity and predictability of the time series are considered. The importance of comparing the results of mathematical simulation and observation data is tightly linked to problems in detecting chaos in the dynamics of natural populations and estimating the prevalence of chaotic regimes in nature. Insight into these problems can allow identification of the functional role of chaotic regimes in population dynamics. [ABSTRACT FROM AUTHOR]

Delay differential equations can have 'chaotic' solutions that can be used to mimic Brownian motion. Since a Brownian motion is random in its velocity, it is reasonable to think that a random number generator might be constructed from such a model. In this preliminary study, we consider one specific example of this and show that it satisfies criteria commonly employed in the testing of random number generators (from TestU01's very stringent 'Big Crush' battery of tests). A technique termed digit discarding, commonly used in both this generator and physical RNGs using laser feedback systems, is discussed with regard to the maximal Lyapunov exponent. Also, we benchmark the generator to a contemporary common method: the multiple recursive generator, MRG32k3a. Although our method is about 7 times slower than MRG32k3a, there is in principle no apparent limit on the number of possible values that can be generated from the scheme we present here. [ABSTRACT FROM AUTHOR]

The mere means principle says it is impermissible to treat someone as merely a means to someone else's ends. I specify this principle with two conditions: a victim is used as merely a means if the victim does not want the treatment by the agent and the agent wants the presence of the victim's body. This principle is a specification of the doctrine of double effect which is compatible with moral intuitions and with a restricted kind of libertarianism. An extension of this mere means principle, where not only using but also considering someone as merely a means is immoral, can explain and unify other deontological principles: doing versus allowing, partiality in imperfect duties of beneficence, and the asymmetry of procreational duties. A loop trolley dilemma is often presented as a counterexample of the mere means principle, but I argue that this dilemma generates a moral illusion, comparable to perceptual illusions. [ABSTRACT FROM AUTHOR]

Scott Sehon recently argued that the standard notion of determinism employed in the Consequence Argument makes it so that, if our world turns out to be deterministic, then an interventionist God is logically impossible. He further argues that because of this, we should revise our notion of determinism. In this paper I show that Sehon's argument for the claim that the truth of determinism, in this sense, would make an interventionist God logically impossible ultimately fails. I then offer and respond to a weaker version of the argument for the claim that we should revise our notion of determinism. [ABSTRACT FROM AUTHOR]

We consider a class of multi-player games with perfect information and deterministic transitions, where each player controls exactly one non-absorbing state, and where rewards are zero for the non-absorbing states. With respect to the average reward, we provide a combinatorial proof that a subgame-perfect $$\varepsilon $$ -equilibrium exists, for every game in our class and for every $$\varepsilon > 0$$ . We believe that the proof of this result is an important step towards a proof for the more general hypothesis that all perfect information stochastic games, with finite state space and finite action spaces, have a subgame-perfect $$\varepsilon $$ -equilibrium for every $$\varepsilon > 0$$ with respect to the average reward criterium. [ABSTRACT FROM AUTHOR]

Hardly any of the observed black hole accretion disks in X-ray binaries and active galaxies shows constant flux. When the local stochastic variations of the disk occur at specific regions where a resonant behaviour takes place, there appear the quasi-periodic oscillations (QPOs). If the global structure of the flow and its non-linear hydrodynamics affects the fluctuations, the variability is chaotic in the sense of deterministic chaos. Our aim is to solve a problem of the stochastic versus deterministic nature of the black hole binary variabilities. We use both observational and analytic methods. We use the recurrence analysis and we study the occurence of long diagonal lines in the recurrence plot of observed data series and compare it to the surrogate series. We analyze here the data of two X-ray binaries - XTE J1550-564 and GX 339-4 observed by Rossi X-ray Timing Explorer. In these sources, the non-linear variability is expected because of the global conditions (such as the mean accretion rate) leading to the possible instability of an accretion disk. The thermal-viscous instability and fluctuations around the fixedpoint solution occurs at high accretion rate, when the radiation pressure gives dominant contribution to the stress tensor. [ABSTRACT FROM AUTHOR]

In this paper, we present a new pseudorandom number generator (PRNG) on graphics processing units (GPU). This PRNG is based on the so-called chaotic iterations. It is firstly proven to be chaotic according to the Devaney's formulation. We, thus, propose an efficient implementation for GPU that successfully passes the BigCrush tests, deemed to be the hardest battery of tests in TestU01. Experiments show that this PRNG can generate about 20 billion of random numbers per second on Tesla C1060 and NVidia GTX280 cards. It is then established that under reasonable assumptions, the proposed PRNG can be cryptographically secure. A chaotic version of the Blum-Goldwasser asymmetric key encryption scheme is finally proposed. [ABSTRACT FROM AUTHOR]

Deterministic physical theories are not beyond the reach of scientific discovery. From this fact I show that David Lewis was mistaken to think that small counterfactual perturbations from deterministic worlds involve violations of those world's laws. [ABSTRACT FROM AUTHOR]

Vocal individuality provides a method of personalization for multiple avian species. However, expression of individual vocal features depends on necessity of recognition. Here we focused on chick vocalizations of demoiselle, Siberian and red-crowned cranes that differ by their body size, developmental rates and some ecological traits. Cranes are territorial during summer, but gather in large flocks during autumn and winter. Nevertheless, parents keep feeding their chicks, even on winter grounds, despite the potential of confusing their own and alien chicks. Here we aimed to compare expression of individuality and sex in calls of three crane species between solitary and gregarious periods of a chick's life, and between species. We found significant individual patterns of acoustic variables in the calls of all three species both before and after fledging. However, only red-crowned crane chicks increased expression of individuality significantly after the fledging. Also, we found that chicks of all three species significantly increased occurrence of non-linear phenomena, i.e., irregular oscillations of sound-producing membranes (biphonations, sidebands, and deterministic chaos), in their calls after fledging. Non-linear phenomena can be a way of increasing the potential for individual recognition as well as avoiding habituation of parents to their chicks' calls. The older chicks are, the less their parents feed them, and chicks benefit from keeping the permanent attention of their parents in the course of early ontogeny. [ABSTRACT FROM AUTHOR]

We analyze the yearly mean sunspot-number data covering the period 1700 to 2012. We show that the yearly sunspot number is a low-dimensional deterministic chaotic system. We perform future predictions trying to forecast the solar activity during the next five years (2013 - 2017). We provide evidence that the yearly sunspot-number data can be used for long-term predictions. To test and prove that our model is able to predict the Maunder Minimum period (1645 - 1715), we perform long-term post-facto predictions comparing them with the observed sunspot-number values. We also perform long-term future predictions trying to forecast the solar activity up to 2102. Our predictions indicate that the present Cycle 24 is expected to be a low-peak cycle. We conclude that the level of solar activity is likely to be reduced significantly during the next 90 years, somewhat resembling the Maunder Minimum period. [ABSTRACT FROM AUTHOR]

Ed Lorenz, rightfully acclaimed as the father of the 'Butterfly Effect', was an American mathematician and meteorologist whose early work on weather prediction convinced the world at large about the unpredictability of weather. His seminal work on a simplified model for convections in the atmosphere led to the modern theory of 'Chaos'-the third revolutionary discovery of 20th century, the other two being relativity and quantum physics. The possibility of unpredictability in certain nonlinear systems was vaguely mentioned earlier by J C Maxwell and clearly asserted later by H Poincaré. But it was the work of Lorenz in 1963 that indicated clearly that the sensitive dependence on the initial conditions (also called 'SIC'-ness) of such systems can lead to unpredictable states. This strange and exotic behavior was named the 'Butterfly Effect1' by him in a lecture that he delivered in December 1972 in Washington DC. [ABSTRACT FROM AUTHOR]

Edward Lorenz discovered nonperiodic behavior in deterministic nonlinear systems and laid the foundation of chaos theory. He showed that chaos exhibits sensitive dependence on initial conditions implying that long-range weather prediction is difficult because of errors in the observations used as initial conditions. Lorenz described the intricate structure of chaotic attractors and quantified predictability. His important contributions in meteorology include energy cycle, slow manifold and general circulation. [ABSTRACT FROM AUTHOR]

Red deer stags ( Cervus elaphus) give two distinct types of roars during the breeding season, the 'common roar' and the 'harsh roar.' Harsh roars are more frequent during contexts of intense competition, and characterized by a set of features that increase their perceptual salience, suggesting that they signal heightened arousal. While common roars have been shown to encode size information and mediate both male competition and female choice, to our knowledge, the specific function of harsh roars during male competition has not yet been studied. Here, we investigate the hypothesis that the specific structure of male harsh roars signals high arousal to competitors. We contrast the behavioral responses of free ranging, harem-holding stags to the playback of harsh roars from an unfamiliar competitor with their response to the playback of common roars from the same animal. We show that males react less strongly to sequences of harsh roars than to sequences of common roars, possibly because they are reluctant to escalate conflicts with highly motivated and threatening unfamiliar males in the absence of visual information. While future work should investigate the response of stags to harsh roars from familiar opponents, our observations remain consistent with the hypothesis that harsh roars may signal motivation during male competition, and illustrate how intrasexual selection can contribute to the diversification of male vocal signals. [ABSTRACT FROM AUTHOR]

Stochasticity, noisiness, and ergodicity are the key concepts behind many natural processes and its modeling is an important part of their implementation. There is a handful of soft-computing methods that are directly inspired by nature or stochastic natural processes. The implementation of such a nature-inspired optimization and search methods usually depends on streams of integer and floating point numbers generated in course of their execution. The pseudo-random numbers are utilized for in-silico emulation of probability-driven natural processes such as arbitrary modification of genetic information (mutation, crossover), partner selection, and survival of the fittest (selection, migration) and environmental effects (small random changes in motion direction and velocity). Deterministic chaos is a well known mathematical concept that can be used to generate sequences of seemingly random real numbers within selected interval in a predictable and well controllable way. In the past, it has been used as a basis for various pseudo-random number generators (PRNGs) with interesting properties. This work provides an empirical comparison of the behavior of selected nature-inspired optimization algorithms using different PRNGs and chaotic systems as sources of stochasticity. [ABSTRACT FROM AUTHOR]

The dynamic characteristics of solar metric radio bursts with intermediate drifting patterns (fiber bursts) as they evolve at fixed frequency are examined. The data were recorded using the radio polarimeter of the Trieste Astronomical Observatory. The aim is to determine if the underlying process can be described as a deterministic chaos. Correlation dimensions and Hurst exponent are estimated showing deterministic chaotic system of low dimension. [ABSTRACT FROM AUTHOR]

In present paper, an effect of delayed frictional healing on complex dynamics of simple model of earthquake nucleation is analyzed, following the commonly accepted assumption that frictional healing represents the main mechanism for fault restrengthening. The studied model represents a generalization of Burridge-Knopoff single-block model with Dieterich-Ruina's rate and state dependent friction law. The time-dependent character of the frictional healing process is modeled by introducing time delay τ in the friction term. Standard local bifurcation analysis of the obtained delay-differential equations demonstrates that the observed model exhibits Ruelle-Takens-Newhouse route to chaos. Domain in parameters space where the solutions are stable for all values of time delay is determined by applying the Rouché theorem. The obtained results are corroborated by Fourier power spectra and largest Lyapunov exponents techniques. In contrast to previous research, the performed analysis reveals that even the small perturbations of the control parameters could lead to deterministic chaos, and, thus, to instabilities and earthquakes. The obtained results further imply the necessity of taking into account this delayed character of frictional healing, which renders complex behavior of the model, already captured in the case of more than one block. [ABSTRACT FROM AUTHOR]

This paper tells the story how a MAPLE-assisted quest for an interesting undergraduate problem in trigonometric series led some 'amateurs' to the discovery that the one-parameter family of deterministic trigonometric series [InlineEquation not available: see fulltext.], p>1, exhibits both order and apparent chaos, and how this has prompted some professionals to offer their expert insights. As to order, an elementary (undergraduate) proof is given that [InlineEquation not available: see fulltext.] ∀ t∈ℝ, with explicitly computed constant α. As to chaos, the seemingly erratic fluctuations about this overall trend are discussed. Experts' commentaries are reproduced as to why the fluctuations of [InlineEquation not available: see fulltext.] are presumably not Gaussian. Inspired by a central limit type theorem of Marc Kac, a well-motivated conjecture is formulated to the effect that the fluctuations of the ⌈ t⌉-th partial sum of [InlineEquation not available: see fulltext.], when properly scaled, do converge in distribution to a standard Gaussian when t→∞, though-provided that p is chosen so that the frequencies { n} are rationally linear independent; no conjecture has been forthcoming for rationally dependent { n}. Moreover, following other experts' tip-offs, the interesting relationship of the asymptotics of [InlineEquation not available: see fulltext.] to properties of the Riemann ζ function is exhibited using the Mellin transform. [ABSTRACT FROM AUTHOR]

Fifty years after the invention of the laser diode, and forty years after the butterfly effect signified the unpredictability of deterministic chaos, it is commonly believed that a laser diode behaves like a damped nonlinear oscillator and cannot be driven into chaotic operation without additional forcing or parameter modulation. Here, we counter that belief and report the first example of a free-running laser diode generating chaos. The underlying physics comprises a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time series and show, theoretically, the bifurcations leading to single- and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles noise-driven mode hopping, but shows opposite statistical properties. Our findings open up new research areas for the creation of controllable and integrated sources of optical chaos. [ABSTRACT FROM AUTHOR]

The possibility of making measurements with a magnetic modulation converter under deterministic chaos conditions is considered. The converter construction principle is discussed. [ABSTRACT FROM AUTHOR]

A nonlinear time-varying one-degree-of-freedom system, which is used for the modelling of the buckling of a loaded beam in Euler's problem, is considered. For a slowly changing load, the deterministic approach in this problem fails if the trajectories pass through the separatrix. An expression for the probability of possible outcomes of the evolution of the oscillations is obtained. The analytical and numerical results are compared. [ABSTRACT FROM AUTHOR]

The factors influencing the trajectory of long-range α-particle in the cold ternary fission of Cf are discussed. The trajectory of the α-particle is studied by considering the influence of the force on the α-particle due to Coulomb and proximity potentials and is found to have sensitive dependence on the initial position and initial energy of the α-particle. The sensitivity to initial conditions signifies the presence of deterministic chaos which is characterized by Lyapunov exponent (LE). The LE is calculated using Wolf's algorithm and found positive which implies that the objectives of trajectory calculations are restricted. [ABSTRACT FROM AUTHOR]

F-ATPase is a catalytic part of the FF-ATP synthase molecular motor. The cooperative hydrolysis of ATP at three catalytic sites of F-ATPase is accompanied by the rotation of the central γ-subunit inside a cylinder formed by three α-subunits and three β-subunits. Experimental works of different authors have shown that the γ-subunit rotates with irregular dwells. A simple kinetic model suggested in this article provides an explanation as to why dwells occur during the rotation of F-ATPase. According to this model, rotation dwells happen as a result of deterministic chaos, which in turn occurs at rate constants that are close to those demonstrated experimentally. The time duration of dwells in the model is in agreement with that observed experimentally. Our model explains the known irregular occupancy of catalytic sites of F-ATPase by nucleotides. [ABSTRACT FROM AUTHOR]

Many economic events involve initial observations that substantially deviate from long-run steady state. Such initial conditions are known to affect the power of univariate unit root tests diversely, whereas their impact on multivariate tests is largely unknown. This paper investigates the impact of the initial condition on the power of tests for cointegration rank, such as Johansen's widely used likelihood ratio test, tests with prior adjustment for deterministic terms, and a test based on the eigenvalues of the companion matrix. We find that the power of the likelihood ratio test is increasing in the magnitude of the initial condition, whereas the power of the other tests is generally decreasing. We exploit these findings in an application to price convergence. [ABSTRACT FROM AUTHOR]

Capital rationing is a major problem in managerial decision making. The classical mathematical formulation of the problem relies on a multi-dimensional knapsack model with known input parameters. Since capital rationing is carried out in conditions where uncertainty is the rule rather than the exception, the hypothesis of deterministic data limits the applicability of deterministic formulations in real settings. This paper proposes a stochastic version of the capital rationing problem which explicitly accounts for uncertainty. In particular, a mathematical formulation is provided in the framework of stochastic programming with joint probabilistic constraints and a novel solution approach is proposed. The basic model is also extended to include specific risk measures. Preliminary computational results are presented and discussed. [ABSTRACT FROM AUTHOR]

A proposal for an objective interpretation of probability is introduced and discussed: probabilities as deriving from ranges in suitably structured initial-state spaces. Roughly, the probability of an event on a chance trial is the proportion of initial states that lead to the event in question within the space of all possible initial states associated with this type of experiment, provided that the proportion is approximately the same in any not too small subregion of the space. This I would like to call the 'natural-range conception' of probability. Providing a substantial alternative to frequency or propensity accounts of probability in a deterministic setting, it is closely related to the so-called 'method of arbitrary functions'. It is explicated, confronted with certain problems, and some ideas how these might be overcome are sketched and discussed. [ABSTRACT FROM AUTHOR]

Identifying the respective functions of distinct call types is an important step towards understanding the diversification of mammal vocal repertoires. Red deer ( Cervus elaphus) stags give two distinct types of roars during the rut, termed 'common roars' and 'harsh roars'. This study tests the hypothesis that harsh roars function to raise and maintain female attention to calling males. To this end, we examined the response of female red deer to playback sequences of common roar bouts including a bout of harsh roars midway through the sequence. We found that females not only substantially increased their attention to the bout of harsh roars but also then maintained overall higher attention levels to subsequent common roar bouts. Our results suggest that the specific acoustic characteristics of male red deer harsh roar bouts may have evolved to engage and maintain the attention of female receivers during the breeding season. More generally, they indicate a possible evolutionary path for the diversification of male sexual vocal repertoires. [ABSTRACT FROM AUTHOR]

Arnold and Stahlecker (Stat Pap 44:107-115, 2003) considered the prediction of future values of the dependent variable in the linear regression model with a relative squared error and deterministic disturbances. They found an explicit form for a minimax linear affine solution d* of that problem. In the paper we generalize this result proving that the decision rule d* is also minimax when the class $${\mathcal{D}}$$ of possible predictors of the dependent variable is unrestricted. Then we show that d* remains minimax in $${\mathcal{D}}$$ when the disturbances are random with the mean vector zero and the known positive definite covariance matrix. [ABSTRACT FROM AUTHOR]

What is a pattern? How do we come to recognize patterns never seen before? Quantifying the notion of pattern and formalizing the process of pattern discovery go right to the heart of physical science. Over the past few decades physics' view of nature's lack of structure-its unpredictability-underwent a major renovation with the discovery of deterministic chaos, overthrowing two centuries of Laplace's strict determinism in classical physics. Behind the veil of apparent randomness, though, many processes are highly ordered, following simple rules. Tools adapted from the theories of information and computation have brought physical science to the brink of automatically discovering hidden patterns and quantifying their structural complexity. [ABSTRACT FROM AUTHOR]

The aim of this article is to provide additional evidence about the order of integration of constant price GDP per capita in a selection of countries. It does so by taking into account the possibility of non-linear deterministic trends and of asymmetric adjustment towards equilibrium. We find evidence of a global stationary ESTAR process around a nonlinear deterministic trend in almost half of the selected countries. These results show that nonlinearities affect real GDP series. By neglecting them, one can draw misleading conclusions from unit root tests. Specifically, the article questions the so-called stylised fact of a near unit root which has so influenced macroeconomic thought over the past two decades. [ABSTRACT FROM AUTHOR]

Nested words provide a natural model of runs of programs with recursive procedure calls. The usual connection between monadic second-order logic (MSO) and automata extends from words to nested words and gives us a natural notion of regular languages of nested words. In this paper we look at some well-known aspects of regular languages-their characterization via fixed points, deterministic and alternating automata for them, and synchronization for defining regular relations-and extend them to nested words. We show that mu-calculus is as expressive as MSO over finite and infinite nested words, and the equivalence holds, more generally, for mu-calculus with past modalities evaluated in arbitrary positions in a word, not only in the first position. We introduce the notion of alternating automata for nested words, show that they are as expressive as the usual automata, and also prove that Muller automata can be determinized (unlike in the case of visibly pushdown languages). Finally we look at synchronization over nested words. We show that the usual letter-to-letter synchronization is completely incompatible with nested words (in the sense that even the weakest form of it leads to an undecidable formalism) and present an alternative form of synchronization that gives us decidable notions of regular relations. [ABSTRACT FROM AUTHOR]

Influence of the difference between the transmitter and receiver parameters on the quality of communication using chaotic carrier is numerically investigated. The deterministic chaos generator based on a nonlinear element with the transfer characteristic in the form of a composition of quadratic functions is proposed. [ABSTRACT FROM AUTHOR]

We study electrical current in two-dimensional periodic Lorentz gas in the presence of a twist force on the scatterers. In this deterministic system, billiard orbits are still geodesics between collisions, but do not reflect elastically when reaching the boundary. When the horizon is finite, i.e. the free flights between collisions are bounded, the resulting current J is proportional to the strength of the twist force measured by ε. We also prove the existence of a unique SRB measure, for which the Pesin entropy formula and Young's expression for the fractal dimension are valid. [ABSTRACT FROM AUTHOR]

We study the problem of the amount of information required to perform fast broadcasting in tree networks. The source located at the root of a tree has to disseminate a message to all nodes. In each round each informed node can transmit to one child. Nodes do not know the topology of the tree but an oracle knowing it can give a string of bits of advice to the source which can then pass it down the tree with the source message. The quality of a broadcasting algorithm with advice is measured by its competitive ratio: the worst case ratio, taken over n-node trees, between the time of this algorithm and the optimal broadcasting time in the given tree. Our goal is to find a trade-off between the size of advice and the best competitive ratio of a broadcasting algorithm for n-node trees. We establish such a trade-off with an approximation factor of O( n), for an arbitrarily small positive constant ε. This is the first communication problem for which a trade-off between the size of advice and the efficiency of the solution is shown for arbitrary size of advice. [ABSTRACT FROM AUTHOR]

It is shown how, given an arbitrary dynamical system, other systems can be manufactured which are isochronous (periodic in all their degrees of freedom with an arbitrarily assigned fixed period T) and whose dynamics coincides exactly with that of the original system over a fraction 1 − σ of that period where σ is a number that can be arbitrarily assigned in the range 0 < σ < 1. The treatment is in the context of autonomous dynamical systems whose equations of motion feature infinitely differentiable functions of the dependent variables. It is argued that this possibility suggests that it would be useful to devise measures of the degree of complexity of a dynamical system which are associated with finite portions of its time evolution-hence going beyond the standard characterizations of the chaotic behavior of a dynamical system (via its Lyapunov coefficients or its ergodic properties), requiring its observation over infinite time. [ABSTRACT FROM AUTHOR]

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP's) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space ℝ. The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter ε>0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, , Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as ε goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as ε goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition. [ABSTRACT FROM AUTHOR]