This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.

When I ?rst came across the term data mining and knowledge discovery in databases, I was excited and curious to ?nd out what it was all about. I was excited because the term tends to convey a new ?eld that is in the making. I was curious because I wondered what it was doing that the other ?elds of research, such as statistics and the broad ?eld of arti?cial intelligence, were not doing. After reading up on the literature, I have come to realize that it is not much different from conventional data analysis. The commonly used de?nition of knowledge discovery in databases: “the non-trivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in data” is actually in line with the core mission of conventional data analysis. The process employed by conventional data analysis is by no means trivial, and the patterns in data to be unraveled have, of course, to be valid, novel, useful and understandable. Therefore, what is the commotion all about? Careful scrutiny of the main lines of research in data mining and knowledge discovery again told me that they are not much different from that of conventional data analysis. Putting aside data warehousing and database m- agement aspects, again a main area of research in conventional database research, the rest of the tasks in data mining are largely the main concerns of conventional data analysis.

Over the last decade, dynamical systems theory and related nonlinear methods have had a major impact on the analysis of time series data from complex systems. Recent developments in mathematical methods of state-space reconstruction, time-delay embedding, and surrogate data analysis, coupled with readily accessible and powerful computational facilities used in gathering and processing massive quantities of high-frequency data, have provided theorists and practitioners unparalleled opportunities for exploratory data analysis, modelling, forecasting, and control. Until now, research exploring the application of nonlinear dynamics and associated algorithms to the study of economies and markets as complex systems is sparse and fragmentary at best. Modelling and Forecasting Financial Data brings together a coherent and accessible set of chapters on recent research results on this topic. To make such methods readily useful in practice, the contributors to this volume have agreed to make available to readers upon request all computer programs used to implement the methods discussed in their respective chapters. Modelling and Forecasting Financial Data is a valuable resource for researchers and graduate students studying complex systems in finance, biology, and physics, as well as those applying such methods to nonlinear time series analysis and signal processing.

This book covers performance analysis of computer networks, and begins by providing the necessary background in probability theory, random variables, and stochastic processes. Queuing theory and simulation are introduced as the major tools analysts have access to. It presents performance analysis on local, metropolitan, and wide area networks, as well as on wireless networks. It concludes with a brief introduction to self-similarity. Designed for a one-semester course for senior-year undergraduates and graduate engineering students, it may also serve as a fingertip reference for engineers developing communication networks, managers involved in systems planning, and researchers and instructors of computer communication networks.

Information and computer technologies for data analysis and processing in various fields of data mining and machine learning generates the conditions for increasing the effectiveness of information processing by making it faster and more accurate. The book includes 49 scientific papers presenting the latest research in the fields of data mining, machine learning and decision-making. Divided into three sections: “Analysis and Modeling of Complex Systems and Processes”; “Theoretical and Applied Aspects of Decision-Making Systems”; and “Computational Intelligence and Inductive Modeling”, the book is of interest to scientists and developers in the field.

The brain is composed of many interconnected neurons that form a complex system, from which thought, behavior, and creativity emerge through self-organization. By studying the dynamics of this network, some basic motifs can be identified. Recent technological and computational advances have led to rapidly accumulating empirical evidence that spontaneous cortical activity exhibits scale-free and critical behavior. Multiple experiments have identified neural processes without a preferred timescale in the avalanche-like spatial propagation of activity in cortical slices and in self-similar time series of local field potentials. Even at the largest scale, scale-free behavior can be observed by looking at the power distributions of brain rhythms as observed by neuroimaging. These findings may indicate that brain dynamics are always close to critical states – a fact with important consequences for how brain accomplishes information transfer and processing. Capitalizing on analogies between the collective behavior of interacting particles in complex physical systems and interacting neurons in the cortex, concepts from non-equilibrium thermodynamics can help to understand how dynamics are organized. In particular, the concepts of phase transitions and self-organized criticality can be used to shed new light on how to interpret collective neuronal dynamics. Despite converging support for scale-free and critical dynamics in cortical activity, the implications for accompanying cognitive functions are still largely unclear. This Research Topic aims to facilitate the discussion between scientists from different backgrounds, ranging from theoretical physics, to computational neuroscience, brain imaging and neurophysiology. By stimulating interactions with the readers of Frontiers in Physiology, we hope to advance our understanding of the role of scale-freeness and criticality in organizing brain dynamics. What do these new perspectives tell us about the brain and to what extent are they relevant for our cognitive functioning? For this Research Topic, we therefore solicit reviews, original research articles, opinion and method papers, which address the principles that organize the dynamics of cortical activity. While focusing on work in the neurosciences, this Research Topic also welcomes theoretical contributions from physics or computational approaches.

Modeling of Transport Demand explains the mechanisms of transport demand, from analysis to calculation and forecasting. Packed with strategies for forecasting future demand for all transport modes, the book helps readers assess the validity and accuracy of demand forecasts. Forecasting and evaluating transport demand is an essential task of transport professionals and researchers that affects the design, extension, operation, and maintenance of all transport infrastructures. Accurate demand forecasts are necessary for companies and government entities when planning future fleet size, human resource needs, revenues, expenses, and budgets. The operational and planning skills provided in Modeling of Transport Demand help readers solve the problems they face on a daily basis. Modeling of Transport Demand is written for researchers, professionals, undergraduate and graduate students at every stage in their careers, from novice to expert. The book assists those tasked with constructing qualitative models (based on executive judgment, Delphi, scenario writing, survey methods) or quantitative ones (based on statistical, time series, econometric, gravity, artificial neural network, and fuzzy methods) in choosing the most suitable solution for all types of transport applications. - Presents the most recent and relevant findings and research - both at theoretical and practical levels - of transport demand - Provides a theoretical analysis and formulations that are clearly presented for ease of understanding - Covers analysis for all modes of transportation - Includes case studies that present the most appropriate formulas and methods for finding solutions and evaluating results

The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. Experimental technique and data analysis have seen such dramatic progress that, by now, most fundamental properties of nonlinear dynamical systems have been observed in the laboratory. Great efforts are being made to exploit ideas from chaos theory wherever the data displays more structure than can be captured by traditional methods. Problems of this kind are typical in biology and physiology but also in geophysics, economics, and many other sciences.

This dissertation will discuss the uncertainty encountered in the daily operations of businesses. The concepts will be developed by first giving an overview of probability and statistics as used in our everyday activities, such as the basic principles of probability, univariate and multivariate statistics, data clustering and mapping, as well as time sequence and spectral analysis. The examples used will be from the oil and gas exploration industry because the risks taken in this industry are normally quite large and are ideal for showing the application of the various techniques for minimizing risk. Subsequently, the discussion will deal with basic risk analysis, spatial and time variations of risk, geotechnical risk analysis, risk aversion and how it is affected by personal biases, and how to use portfolios to hedge risk together with the application of real options. Next, fractal analysis and its application to economics and risk analysis will be examined, followed by some examples showing the change in the Value at Risk under Fractal Brownian Motions. Finally, a neural network application is shown whereby some of these risks and risk factors will be combined to forecast the best possible outcome given a certain knowledge base. The chapters will discuss: Basic probability techniques and uncertainty principles Analysis and diversification for exploration projects The value and risk of information in the decision process Simulation techniques and modeling of uncertainty Project valuation and project risk return Modeling risk propensity or preference analysis of exploration projects Application of fractals to risk analysis Simultaneous prediction of strategic risk and decision attributes using multivariate statistics and neural networks"