Slow manifolds for stochastic koper models with stable Lévy noises

The Koper model is a vector field in which the differential equations describe the electrochemical oscillations appearing in diffusion processes. This work focuses on the understanding of the slow dynamics of a stochastic Koper model perturbed by stable Lévy noise. We establish the slow manifold for a stochastic Koper model with stable Lévy noise and verify exponential tracking properties. We also present two practical examples to demonstrate the analytical results with numerical simulations

Ergodicity breaking and lack of a typical waiting time in area-restricted search of avian predators

Movement tracks of wild animals frequently fit models of anomalous rather than simple diffusion, mostly reported as ergodic superdiffusive motion combining area-restricted search within a local patch and larger-scale commuting between patches, as highlighted by the L\'evy walk paradigm. Since L\'evy walks are scale invariant, superdiffusive motion is also expected within patches, yet investigation of such local movements has been precluded by the lack of accurate high-resolution data at this scale. Here, using rich high-resolution movement datasets ($>\! 7 \times 10^7$ localizations) from 70 individuals and continuous-time random walk modeling, we found subdiffusive behavior and ergodicity breaking in the localized movement of three species of avian predators. Small-scale, within-patch movement was qualitatively different, not inferrable and separated from large-scale inter-patch movement via a clear phase transition. Local search is characterized by long power-law-distributed waiting times with diverging mean, giving rise to ergodicity breaking in the form of considerable variability uniquely observed at this scale. This implies that wild animal movement is scale specific rather than scale free, with no typical waiting time at the local scale. Placing these findings in the context of the static-ambush to mobile-cruise foraging continuum, we verify predictions based on the hunting behavior of the study species and the constraints imposed by their prey.Comment: 27 pages, 8 figure

The role of data in model building and prediction: a survey through examples

The goal of Science is to understand phenomena and systems in order to predict their development and gain control over them. In the scientific process of knowledge elaboration, a crucial role is played by models which, in the language of quantitative sciences, mean abstract mathematical or algorithmical representations. This short review discusses a few key examples from Physics, taken from dynamical systems theory, biophysics, and statistical mechanics, representing three paradigmatic procedures to build models and predictions from available data. In the case of dynamical systems we show how predictions can be obtained in a virtually model-free framework using the methods of analogues, and we briefly discuss other approaches based on machine learning methods. In cases where the complexity of systems is challenging, like in biophysics, we stress the necessity to include part of the empirical knowledge in the models to gain the minimal amount of realism. Finally, we consider many body systems where many (temporal or spatial) scales are at play-and show how to derive from data a dimensional reduction in terms of a Langevin dynamics for their slow components

Complex scaling behavior in animal foraging patterns

This dissertation attempts to answer questions from two different areas of biology, ecology and neuroscience, using physics-based techniques. In Section 2, suitability of three competing random walk models is tested to describe the emergent movement patterns of two species of primates. The truncated power law (power law with exponential cut off) is the most suitable random walk model that characterizes the emergent movement patterns of these primates. In Section 3, an agent-based model is used to simulate search behavior in different environments (landscapes) to investigate the impact of the resource landscape on the optimal foraging movement patterns of deterministic foragers. It should be noted that this model goes beyond previous work in that it includes parameters such as spatial memory and satiation, which have received little consideration to date in the field of movement ecology. When the food availability is scarce in a tropical forest-like environment with feeding trees distributed in a clumped fashion and the size of those trees are distributed according to a lognormal distribution, the optimal foraging pattern of a generalist who can consume various and abundant food types indeed reaches the Lévy range, and hence, show evidence for Lévy-flight-like (power law distribution with exponent between 1 and 3) behavior. Section 4 of the dissertation presents an investigation of phase transition behavior in a network of locally coupled self-sustained oscillators as the system passes through various bursting states. The results suggest that a phase transition does not occur for this locally coupled neuronal network. The data analysis in the dissertation adopts a model selection approach and relies on methods based on information theory and maximum likelihood

Stochastic 0-dimensional Biogeochemical Flux Model: Effect of temperature fluctuations on the dynamics of the biogeochemical properties in a marine ecosystem

We present a new stochastic model, based on a 0-dimensional version of the well known biogeochemical flux model (BFM), which allows to take into account the temperature random fluctuations present in natural systems and therefore to describe more realistically the dynamics of real marine ecosystems. The study presents a detailed analysis of the effects of randomly varying temperature on the lower trophic levels of the food web and ocean biogeochemical processes. More in detail, the temperature is described as a stochastic process driven by an additive self-correlated Gaussian noise. Varying both correlation time and intensity of the noise source, the predominance of different plankton populations is observed, with regimes shifted towards the coexistence or the exclusion of some populations. Finally a Fourier analysis carried out on the time series of the plankton populations shows how the ecosystem responds to the seasonal driving for different values of the noise intensit

Behavioural analysis of marine predator movements in relation to heterogeneous environments

An understanding of the spatio-temporal dynamics of marine predator populations is essential for the sustainable management of marine resources. Tagging studies are providing ever more information about the movements and migrations of marine predators and much has been learned about where these predators spend their time. However little is known about their underlying motivations, making it difficult to make predictions about how apex predators will respond to changing environments. While much progress has been made in behavioural ecology through the use of optimality models, in the marine environment the necessary costs and benefits are difficult to quantify making this approach less successful than with terrestrial studies. One aspect of foraging behaviour that has proved tractable however is the optimisation of random searches. Work by statistical physicists has shown that a specialised movement, known as Lévy flight, can optimise the rate of new prey patch encounters when new prey patches are beyond sensory range. The resulting Lévy flight foraging (LFF) hypothesis makes testable predictions about marine predator search behaviour that can be addressed with the theoretical and empirical studies that form the basis of this thesis. Results presented here resolve the controversy surrounding the hypothesis, demonstrating the optimality of Lévy searches under a broader set of conditions than previously considered, including whether observed Lévy patterns are innate or emergent. Empirical studies provide robust evidence for the prevalence of Lévy search patterns in the movements of diverse marine pelagic predators such as sharks, tunas and billfish as well as in the foraging patterns of albatrosses, overturning a previous study. Predictions from the LFF hypothesis concerning fast moving prey are confirmed leading to simulation studies of ambush predator’s activity patterns. Movement analysis is then applied to the assessment of by-catch mitigation efforts involving VMS data from long-liners and simulated sharks

採餌問題のための確率的探索戦略の設計と最適化

Autonomous robot’s search strategy is the set of rules that it employs while looking for targets in its environment. In this study, the stochastic movement of robots in unknown environments is statistically studied, using a Levy walk method. Biological systems (e.g., foraging animals) provide useful models for designing optimal stochastic search algorithms. Observations of biological systems, ranging from large animals to immune cells, have inspired the design of efficient search strategies that incorporate stochastic movement. In this study, we seek to identify the optimal stochastic strategies for autonomous robots. Given the complexity of interaction between the robot and its environment, optimization must be performed in high-dimensional parameter space. The effect of the explanatory variable on the forger robot movement with the minimum required energy was also studied using experiments done by the response surface methodology (RSM). We analyzed the extent to which search efficiency requires these characteristics, using RSM. Correlation between the involved parameters via a Lévy walk process was examined through designing a setup for the experiments to determine the interaction of the involved variables and the robot movement. The extracted statistical model represents the priority influence of those variables on the robot by developing the statistical model of the mentioned unknown area. The efficiency of a simple strategy was investigated based on Lévy walk search in two-dimensional landscapes with clumped resource distributions. We show how RSM techniques can be used to identify optimal parameter values as well as to describe how sensitive efficiency reacts to the changes in these values. Here, we identified optimal parameter for designing robot by using stochastic search pattern and applying mood-switching criteria on a mixture of speed and sensor and μ to determine how many robots are needed for a solution. Fractal criterion-based robot strategies were more efficient than those based on the resource encounter criterion, and the former was found to be more robust to changes in resource distribution as well.九州工業大学博士学位論文 学位記番号:生工博甲第358号 学位授与年月日:令和元年9月20日1 Introduction|2 Levy Walk|3 Design of Experiment (DOE)|4 Response Surface Methodology|5 Results and Discussions|6 Conclusion九州工業大学令和元年

Visually-guided timing and its neural representation

Stimulus-driven timing is a fundamental aspect of human and animal behavior. This type of timing can be subdivided into three principal axes: interval generation, storage, and evaluation. In this thesis, we present results related to each of these axes and describe their implications for how we understand timed behavior. In Chapter 2, we address interval generation, which is the process of creating an internal representation of an ongoing temporal interval. While several studies have found evidence for neural oscillators which may subserve this function, it has remained an open question whether such a mechanism can be useful for timing at even the lowest level of cortex. To address this question, we analyze electrophysiological data collected from rats performing a timing task and find evidence that, indeed, timed reward-seeking behavior tracks oscillatory states in primary visual cortex. This kind of finding raises an important question: how is this temporal information stored after the interval has been generated? This process is called interval storage, and we address the sources of noise that might corrupt it in Chapter 3. Specifically, we devise a novel timing task for humans (BiCaP) to address whether memory biases can account for performance on a classification task, in which a subject must decide whether a test interval is more similar to one or another reference interval. We find that they do, and argue that these sources of noise must be accounted for in theories of timing. In Chapter 4, we deal with interval evaluation which is the process of using this stored temporal information to make valuation decisions. We study this process through the lens of foraging behavior. Specifically, we develop and test a framework that rationalizes observed spatial search patterns of wild animals and humans by accounting for the temporal information they gather about their environment, and how they discount delayed rewards (temporal discounting). Lastly, in Chapter 5, we discuss how these processes are integrated and the implications of these findings for theories of timing