Anomalous diffusion : from life to machines

Diffusion refers to numerous phenomena, by which particles and bodies of all kinds move throughout any kind of material, has emerged as one of the most prominent subjects in the study of complex systems. Motivated by the recent developments in experimental techniques, the field had an important burst in theoretical research, particularly in the study of the motion of particles in biological environments. Just with the information retrieved from the trajectories of particles we are now able to characterize many properties of the system with astonishing accuracy. For instance, when Einstein introduced the diffusion theory back in 1905, he used the motion of microscopic particles to calculate the size of the atoms of the liquid these were suspended. Initially, most of the experimental evidence showed that such systems follow Brownian-like dynamics, i.e. the homogeneous interaction between the particles and the environment led to its stochastic, but uncorrelated motion. However, we know now that such a simple explanation lacks crucial phenomena that have been shown to arise in a plethora of physical systems. The divergence from Brownian dynamics led to the theory of anomalous diffusion, in which the particles are affected in a way or another by their interactions with the environment such that their diffusion changes drastically. For instance features such as ergodicity, Gaussianity, or ageing are now crucial for in the understanding of diffusion processes, well beyond Brownian motion. In theoretical terms, anomalous diffusion has a well-developed framework, able to explain most of the current experimental observations. However, it has been usually focused in describing the systems in terms of its macroscopic behaviour. This means that the processes are described by means of general models, able to predict the average or collective features. Even though such an approach leads to a correct description of the system and hints on the actual underlying phenomena, it lacks the understanding of the particular microscopic interactions leading to anomalous diffusion. The work presented in this Thesis has two main goals. First, we will explore how one may use microscopical (or phenomenological) models to understand anomalous diffusion. By microscopical model we refer to a model in which we will set exactly how the interactions between the various components of a system are. Then, we will explore how these interactions may be tuned in order to recover and control anomalous diffusion and how its features depend on the properties of the system. We will explore crucial topics arising in recent experimental observations, such as weak-ergodicity breaking or liquid-liquid phase separation. Second, we will survey the topic of trajectory characterization. Even if our theories are extremely well developed, without an accurate tool for studying the trajectories observed in experiments, we will be unable to correctly make any faithful prediction. In particular, we will introduce one of the first machine learning techniques that can be used for such purpose, even in systems where previous techniques failed largely.La difusión es el fenómeno por el cual partículas de todas formas y tamaños se mueven a través del entorno que les rodea. Su estudio se ha convertido en una potente herramienta para entender el comportamiento de sistemas complejos. Gracias al reciente desarrollo de diferentes técnicas experimentales, este fenómeno ha generado un enorme interés tanto desde el punto de vista experimental como del teórico, y en especial,en el estudio del movimiento de partículas microscópicas en entornos biológicos. Mediante el análisis de las trayectorias de estas partículas, no solo somos capaces de caracterizar sus propiedades, sino también las de su entorno. El propio Albert Einstein, autor junto con Marian Smoluchowski de la teoría de la difusión, demostró que era posible calcular el radio de los átomos de un líquido simplemente mediante el análisis del movimiento de una partícula suspendida en este. Esta teoría, que dio origen a lo que hoy conocemos como movimiento Browniano, consideraba que la interacción homogénea de una partícula con su entorno provocaba el movimiento aleatorio de esta última. Aunque el movimiento Browniano haya sido utilizado para describir una enorme cantidad de experimentos, hoy sabemos que existen sistemas particulares que se desvían de sus predicciones. Esta divergencia ha dado pie al desarrollo de la teoría de la difusión anómala, en la que, debido a las propiedades de las partículas y sus entornos, la difusión difiere drásticamente de las predicciones de la teoría Browniana. Algunos fenómenos como la ergodicidad, Gausianidad o el envejecimiento de difusión, particulares de la difusión anómala, son hoy en día cruciales para entender el movimiento de partículas en sistemas complejos. En términos teóricos, la difusión anómala tiene unas bases firmes, con las cuáles se explica gran parte de las observaciones experimentales más recientes. Esta teoría, sin embargo, suele centrarse en la descripción de la difusión desde un punto de vista macroscópico. Esto quiere decir: analizar un sistema mediante modelos generales, capaces de predecir propiedades colectivas o globales. Aunque las teorías macroscópicas consiguen describir correctamente la mayoría de los procesos de difusión, no tienen la capacidad de discernir qué tipo de interacciones dan lugar a la difusión anómala. El trabajo presentado en esta tesis tiene dos objetivos principales. El primero es explorar el uso de modelos microscópicos (o fenomenológicos) para entender la difusión anómala. Un modelo microscópico, en contraposición al macroscópico, describe el sistema a partir de sus propiedades específicas. En este caso, a partir del tipo de interacciones que existen entre las partículas y su entorno. El objetivo es por lo tanto entender cuáles de estas interacciones producen difusión anómala. Además, caracterizaremos los parámetros macroscópicos de la difusión, como el exponente anómalo, y mostraremos como depende de las propiedades del sistema. En el camino, exploraremos cómo fenómenos como la rotura débil de la ergodicidad (weak-ergodicity breaking) o la separación de fase aparecen en sistemas con interacciones complejas. El segundo objetivo consiste en el desarrollo de técnicas para la caracterización de trayectorias provenientes de procesos de difusión. Aunque nuestro entendimiento teórico llegue a niveles insospechados en los próximos años, sin un análisis correcto y preciso de las trayectorias experimentales, jamás podremos construir un puente entre teoría y experimentos. Por tanto, el desarrollo de técnicas con las que analizar con la mayor precisión posible dichas trayectorias es un problema igual de importante que el desarrollo teórico de la difusión. En este trabajo, estudiaremos cómo las técnicas de aprendizaje automático (Machine Learning) pueden ser utilizadas para caracterizar dichas trayectorias, llegando a niveles de precisión y análisis muy por encim

A Review of the Fractal Market Hypothesis for Trading and Market Price Prediction

This paper provides a review of the Fractal Market Hypothesis (FMH) focusing on financial times series analysis. In order to put the FMH into a broader perspective, the Random Walk and Efficient Market Hypotheses are considered together with the basic principles of fractal geometry. After exploring the historical developments associated with different financial hypotheses, an overview of the basic mathematical modelling is provided. The principal goal of this paper is to consider the intrinsic scaling properties that are characteristic for each hypothesis. In regard to the FMH, it is explained why a financial time series can be taken to be characterised by a 1/t1−1/γ role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3e1/t1−1/γ scaling law, where γ\u3e0 role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eγ\u3e0 is the Lévy index, which is able to quantify the likelihood of extreme changes in price differences occurring (or otherwise). In this context, the paper explores how the Lévy index, coupled with other metrics, such as the Lyapunov Exponent and the Volatility, can be combined to provide long-term forecasts. Using these forecasts as a quantification for risk assessment, short-term price predictions are considered using a machine learning approach to evolve a nonlinear formula that simulates price values. A short case study is presented which reports on the use of this approach to forecast Bitcoin exchange rate values

Microeconomic Structure determines Macroeconomic Dynamics. Aoki defeats the Representative Agent

Masanao Aoki developed a new methodology for a basic problem of economics: deducing rigorously the macroeconomic dynamics as emerging from the interactions of many individual agents. This includes deduction of the fractal / intermittent fluctuations of macroeconomic quantities from the granularity of the mezo-economic collective objects (large individual wealth, highly productive geographical locations, emergent technologies, emergent economic sectors) in which the micro-economic agents self-organize. In particular, we present some theoretical predictions, which also met extensive validation from empirical data in a wide range of systems: - The fractal Levy exponent of the stock market index fluctuations equals the Pareto exponent of the investors wealth distribution. The origin of the macroeconomic dynamics is therefore found in the granularity induced by the wealth / capital of the wealthiest investors. - Economic cycles consist of a Schumpeter 'creative destruction' pattern whereby the maxima are cusp-shaped while the minima are smooth. In between the cusps, the cycle consists of the sum of 2 'crossing exponentials': one decaying and the other increasing. This unification within the same theoretical framework of short term market fluctuations and long term economic cycles offers the perspective of a genuine conceptual synthesis between micro- and macroeconomics. Joining another giant of contemporary science - Phil Anderson - Aoki emphasized the role of rare, large fluctuations in the emergence of macroeconomic phenomena out of microscopic interactions and in particular their non self-averaging, in the language of statistical physics. In this light, we present a simple stochastic multi-sector growth model.Comment: 42 pages, 6 figure

GIVE-AND-TAKE KEY PROCESSING for Cloud- linked IoT

Internet of Things (IoT) is estimated there are over a billion internet users and rapidly increasing. But there are more things on the internet than there are people on the internet. This is what it has been generally mean, when it has been say internet of things. There are millions and millions of devices with sensors that are linked up together using networks that generate a sea of data. The problem is all data needs to remain secured, unchanged, and persisted at each stage of an IoT solution. This includes distributed components, communication infrastructure, back-end analytics and database servers, across potentially remote locations and adverse environments. In any case, it is helpless against eavesdropping which represents a risk to privacy and security of the client. The security of data traffic winds up plainly vital since the communications over open network happen frequently. It is along these lines basic that the data traffic over the system is encrypted. To give the QoS, the Cloud- linked IoT security is the essential part of the service providers. This paper is concentrating on issue identifying with the Cloud- linked IoT security in virtual condition. It has been propose a technique GIVE-AND-TAKE KEY PROCESSING for giving data process and security in Cloud- linked IoT using Elliptical Curve Cryptography ECC and Hash Map. Encourage, depicts the security services incorporates generation of key, encryption and decryption in virtual condition

Recent Advances in Single-Particle Tracking: Experiment and Analysis

This Special Issue of Entropy, titled “Recent Advances in Single-Particle Tracking: Experiment and Analysis”, contains a collection of 13 papers concerning different aspects of single-particle tracking, a popular experimental technique that has deeply penetrated molecular biology and statistical and chemical physics. Presenting original research, yet written in an accessible style, this collection will be useful for both newcomers to the field and more experienced researchers looking for some reference. Several papers are written by authorities in the field, and the topics cover aspects of experimental setups, analytical methods of tracking data analysis, a machine learning approach to data and, finally, some more general issues related to diffusion

A review of the fractal market hypothesis for trading and market price prediction

This paper provides a review of the Fractal Market Hypothesis (FMH) focusing on financial times series analysis. In order to put the FMH into a broader perspective, the Random Walk and Efficient Market Hypotheses are considered together with the basic principles of fractal geometry. After exploring the historical developments associated with different financial hypotheses, an overview of the basic mathematical modelling is provided. The principal goal of this paper is to consider the intrinsic scaling properties that are characteristic for each hypothesis. In regard to the FMH, it is explained why a financial time series can be taken to be characterised by a 1/t 1−1/γ scaling law, where γ > 0 is the Lévy index, which is able to quantify the likelihood of extreme changes in price differences occurring (or otherwise). In this context, the paper explores how the Lévy index, coupled with other metrics, such as the Lyapunov Exponent and the Volatility, can be combined to provide long-term forecasts. Using these forecasts as a quantification for risk assessment, short-term price predictions are considered using a machine learning approach to evolve a nonlinear formula that simulates price values. A short case study is presented which reports on the use of this approach to forecast Bitcoin exchange rate values

Applied Metaheuristic Computing

For decades, Applied Metaheuristic Computing (AMC) has been a prevailing optimization technique for tackling perplexing engineering and business problems, such as scheduling, routing, ordering, bin packing, assignment, facility layout planning, among others. This is partly because the classic exact methods are constrained with prior assumptions, and partly due to the heuristics being problem-dependent and lacking generalization. AMC, on the contrary, guides the course of low-level heuristics to search beyond the local optimality, which impairs the capability of traditional computation methods. This topic series has collected quality papers proposing cutting-edge methodology and innovative applications which drive the advances of AMC

Searching without information:a quantitative analysis of Caenorhabditis elegans locomotion

Tese de doutoramento, Biologia (Ecologia), Universidade de Lisboa, Faculdade de Ciências, 2012Animal movement accounts for an important and highly complex process that affects many ecological systems at different temporal and spatial scales. When sources of food are not accessible in the surroundings, animals move through the environment to increase their chances of locating them and by adjusting the balance between local and non-local searches. Despite of being such an important ecological process, the behavioral mechanisms of search are still not well understood. The focus of this thesis is to disentangle the behavioral mechanisms responsible for individual locomotion of Caenorhabditis elegans, while searching in a bare, homogeneous experimental setting. Considering the nature of behavioral intermittency, we use sound statistical tests and methods to characterize the spatiotemporal search patterns. Our results show that, in the absence of environmental factors, C. elegans search behavior is influenced both by past experiences (informed behavior) and by a stochastic basal (non-informed) motor output. Informed movement, which is related with previous experiences and current memory state, originates at the beginning of the experiment, a local search behavior distinguished by an intensive exploration with high number of reorientations and short crawls. The non-informed motor output is characterized by a constant temporal and spatial pattern (over the whole experiment) of reorientations and long crawls. This behavior could be thought as of a locomotion template for the organism since it is neither controlled by external cues nor by specific internal state metabolisms. The existence of these two search modes suggest that the generated movement patterns are influenced by an interplay between internal and external motor outputs that is dependent on the information gathered from the environment. These findings contribute greatly for our understanding of the behavioral mechanisms responsible for the generation of complex movement patterns.Movimento animal é um processo muito importante e altamente complexo que afecta vários sistemas ecológicos a diferentes escalas temporais e espaciais . Quando a fonte de alimento não está acessível, os animais exploram o ambiente tentando aumentar as suas chances de a localizar, e tendo que balancear, da melhor forma, a execução entre uma busca local e uma busca não-local do ambiente. Apesar do processo de busca ser um processo ecológico muito importante, ainda muito pouco se sabe sobre os seus mecanismos biológicos. O objectivo desta tese é desvendar os mecanismos biológicos responsáveis pela locomoção do nemátodo C. elegans enquanto se move num ambiente experimental homogéneo sem fonte de alimento. Considerando a natureza do comportamento intermitente, usámos testes e métodos estatísticos para caracterizar os padrões de busca espacio-temporais. Os nossos resultados mostram que, na ausência de factores ambientais, o comportamento de busca do C. elegans é influenciado por experiências passadas (comportamento com informação) e por um comportamento motor basal estocástico (comportamento sem informação). O comportamento com informação, que está relacionado com experiências passadas e com o presente estado de memória do animal, origina no início da experiência, um padrão de busca local caracterizado por uma exploração intensiva com grande número de reorientações e com movimentos contínuos curtos. O comportamento sem informação é caracterizado por um padrão temporal e espacial constante (durante toda a experiência) de reorientações e de movimentos contínuos largos. Este comportamento pode ser visto como um modo de locomoção base para o organismo uma vez que não é controlado nem por informação externa nem por um estado interno metabólico específico. A existência destes dois modos de busca sugere que os padrões de movimento gerados são influenciados pela interação entre os movimentos motores internos e externos, que é dependente da informação ambiental adquirida. Estes resultados contribuem para uma melhor compreensão dos mecanismos comportamentais responsáveis pela geração de padrões de movimento complexos.Fundação para a Ciência e a Tecnologia (FCT, SFRH/BD/32960/2006); Siemens S.A.; Santa Fé Institute e Spanish National Research Council (CSIC)

Stochastic Löwner evolution as an approach to conformal field theory

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Bursty behavioral dynamics of activity and sleep

Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha lectura: 22 de enero de 2016Una distinguida característica de la vida humana y animal son las constantes alternancias entre periodos activos dedicados a diferentes comportamientos, y periodos de inactividad dedicados a descanso y recuperación. El patrón temporal de actividad e inactividad está lleno de información de los procesos que controlan y regulan las transiciones entre estados. Tradicionalmente se había considerado que estos patrones temporales seguirían una estadística ‘normal’ como tantos otros fenómenos naturales. Pero durante las dos últimas décadas se ha ido descubriendo que muchos comportamientos, tanto en humanos como en otros animales, siguen una dinámica temporal en ráfagas y ‘sin escala’. La dinámica rafagosa se caracterizada por tener un patrón temporal donde periodos de muchos eventos cortos y frecuentes vienen separados por periodos largos de poca o ninguna actividad. La dinámica rafagosa es más irregular que la dinámica aleatoria, y es por lo tanto, más difícil de predecir. El objetivo de esta tesis doctoral ha sido estudiar la dinámica rafagosa del comportamiento espontáneo de actividad y sueño. La temática principal ha sido caracterizar la dinámica rafagosa en animales ‘simples’ y genéticamente maleables, para establecer resultados de base sobre los que construir y explorar el control neuronal subyacente de la dinámica rafagosa. La tesis consiste de tres partes principales, en las cuales hemos estudiado la dinámica de la actividad en la mosca de la fruta Drosophila melanogaster, la dinámica de sueño-vigilia en el pez cebra Danio rerio y en humanos, y estudiado las propiedades neuronales de la corriente “marcapasos” Ih que controla actividad espontánea rítmica y afecta a la rafagosidad. En Drosophila caracterizamos la dinámica locomotora y encontramos que es rafagosa. Después probamos experimentalmente una hipótesis sobre el origen de ráfagas, y descubrimos que circuitos de toma de decisiones afectan a la dinámica del comportamiento en ráfagas. Posteriormente, caracterizamos la dinámica de sueño y vigilia en el pez cebra a diferentes edades a lo largo de su vida y lo comparamos con el desarrollo de la dinámica de sueño-vigilia en humanos a diferentes edades. Encontramos que la fragmentación de la vigilia disminuye, a medida que los episodios de vigilia y vigilia nocturna total aumentan con la edad tanto en el pez cebra como en humanos. La dinámica de vigilia mostró ser altamente rafagosa, mientras que la dinámica de sueño tenía una estructura temporal más compleja de lo que ha sido predominantemente descrito. El desarrollo de la dinámica de sueño-vigilia es muy similar en las dos especies; lo que contribuye a establecer al pez cebra como un organismo modelo valioso para futuros estudios de la dinámica y regulación del sueño y de la vigilia. Finalmente, estudiamos la corriente Ih en Drosophila dado que la mutación nula del DmIh da lugar a alteraciones en el patrón de sueño-vigilia en las moscas adultas. La mutación también produce un fenotipo locomotor y de toma de decisiones en larvas, las cuales tienen un sistema nervioso más simple y una unión neuromuscular altamente caracterizada e idónea para la electrofisiología. Hallamos que el fenotipo locomotor larvario se debía a la motoneurona, que tenía una excitabilidad disminuida y una respuesta reducida a estímulos dinámicos. Los animales modelo con herramientas genéticas sofisticadas como la mosca de la fruta y el pez cebra han, por lo tanto, sido mostrados como animales valiosos para caracterizar y explorar el control y la regulación del comportamiento en ráfagas.alternations between active periods dedicated to different behaviors, and periods of inactivity dedicated to rest and recuperation. The temporal pattern of active and inactive periods is rich with information on the processes that govern and regulate the transitions among behavioral states. Traditionally these temporal patterns had been believed to follow ’normal’ statistics like so many other natural phenomena, but during the last two decades it has increasingly been discovered that many behaviors in both humans and other animals are instead governed by ’scale-free’ bursty temporal dynamics. Bursty dynamics are characterized by having a temporal pattern where periods of many short and frequent events are separated by long periods of little or no activity. Bursty dynamics are thus more irregular than random dynamics and harder to predict. The aim of this doctoral thesis has been to study the bursty behavioral dynamics of spontaneous activity and sleep. The main theme has been to characterize the bursty dynamics in genetically tractable ’simpler’ model organisms, to establish baseline results to build upon and to probe the underlying neuronal control of burstiness. The thesis consists of three main parts, in which we have studied activity dynamics in the fruit fly Drosophila melanogaster, sleep-wake dynamics in the zebrafish Danio rerio and in humans, and studied the properties of the neuronal Ih “pacemaker” current which controls spontaneous rhythmic activity and affects burstiness. In Drosophila we characterized the locomotor activity dynamics and found that it is bursty. Subsequently we experimentally tested a hypothesis on the origin of bursts, and found that decision-making circuits affect the bursty behavioral dynamics. We next characterized the sleep-wake dynamics in the zebrafish at different ages across the lifespan and compared it to the development of sleep-wake dynamics in humans at different ages. We found that nightly wake increases as wake durations become longer and less fragmented with age in both zebrafish and humans. Wake dynamics were found to be highly bursty, while sleep dynamics were found to have a more complex temporal dynamics than predominantly described. The highly similar development of sleep-wake cycles in both species contributes to establishing zebrafish as a valuable model organism for further studies of sleep-wake dynamics and regulation. Finally, we studied the Ih current as the DmIh null mutation gives rise to alterations of the sleep-wake pattern in adult fruit flies. The mutation also produces a locomotor and decision-making phenotype in larvae, which have a much simpler nervous system and a well characterized neuromuscular junction suitable for electrophysiology. We found that the larval locomotor phenotype was due to the motoneurons, which exhibited a decreased excitability and reduced responsiveness to dynamic stimuli. Model organisms with sophisticated genetical tools like the fruit fly and the zebrafish have thus been shown to be highly valuable animal models for characterizing and probing the control and regulation of behavioral burstiness