Nonparametric Estimation of Nonlinear Dynamics by Local Linear Approximation

This chapter discusses nonparametric estimation of nonlinear dynamical system models by a method of metric-based local linear approximation. By specifying a metric such as the standard metric or the square metric on the Euclidean space and a weighting function based on such as the exponential function or the cut-off function, it is possible to estimate values of an unknown vector field from experimental data. It can be shown the local linear fitting with the Gaussian kernel, or the local polynomial modeling of degree one, is included in the class of the proposed method. In addition, conducting simulation studies for estimating random oscillations, the chapter shows the method numerically works well.

Optimal Variability and Complexity

Management seeks to provoke system optimization throughout ever changing environmental and internal conditions. Typically, perturbations to stable organizations are unpredictable and difficult to define, except from within a chaos perspective. How should management staff set up their workforce to be best responsive to these changes? It is proposed that a dynamic systems theoretical approach to the organization of the management system would foster the ideal scenario. This approach lends well to the inclusion of discovery learning strategies that promote the valuable use of optimal variability in the exploration and self-discovery of optimal solutions to existent and novel problems. In this text, the authors walk the reader through a brief history of the development of the systems perspective on human movement optimization. Next, they extend the related discoveries to applications within management systems. It is hoped that a new appreciation for complexity and beneficial aspects of variability is conveyed.

Recurrence Quantification Analysis of Financial Markets

Recurrence quantification analysis is a nonlinear time series analysis technique that detects deterministic dependencies in time series. This technique is particularly appropriate for modeling financial time series since it requires no assumptions on stationarity, statistical distribution, and minimum number of observations. This chapter illustrates two applications of recurrence quantification analysis to financial data: a set of international stock indices, and zero-coupon yields of US government bonds.

A Comparative Study of Four Different Satellite Image Classification Techniques for Geospatial Management

Satellite imagery interpretation has become the technology of choice for a host of developmental, scientific, and administrative management work. The huge repository of geospatial data and information that are available as satellite imageries datasets from platforms such as Google Earth need to be classified and understood for natural resources management, urban planning, and sustainable development. The classification and analysis procedures involve algorithms like maximum likelihood classifier, isodata, fuzzy-logic classifier, and artificial neural network based classifier. Amongst these classifiers the optimum has to be selected for classifications which involve multiple features and classes. Herein lies the motivation for the present research, which can facilitate the selection of one amongst the many algorithms available to a decision maker/manager. The aforementioned techniques are applied for classification, and the respective accuracies in the classes of forestry, rock, water, built-up area, and dry river bed have been tabulated and verified from ground truth. The comparison is based on time and space complexity of the algorithms considering also the accuracy. It is found that traditional methods like MLC and Isodata offer good time and space consumption performance over the recent more adaptable algorithms as fuzzy and ANN. But the latter group excels in accuracy of assessment. The study suggests points and cases for ranking the techniques as best, 2nd best, and so on, where each technique could be optimally utilised for a given geospatial dataset based on its contents.

Cognition and Complexity

Contemporary knowledge work places create tremendous challenges for employees and managers. High levels of “cognitive capital” are required to cope with the rapidly evolving complexity of work. This chapter presents an agent-based model of the dynamics of cognitive capital in a simulated workplace. Factors such as stress, sleep insufficiency, and excessive work function to reduce the cognitive capital among workers. The cognitive capital in this microworld is tracked among agents suffering from stress, sleep insufficiency and excessive work. The authors also explore how cognitive capital changes under varying cognitive enrichment scenarios. Simulation results reveal a range of behaviors typical of complex systems, showing evidence of periods of both stability and instability. The authors also see symmetry breaking behavior as the dynamics of cognitive capital create drastic change.

DemoscopoPhysics

Inspired from the application of physics in economy (Econophysics) and society (Sociophysics), the authors introduce the term DemoscopoPhysics as the latest interdisciplinary research field that applies theories and methods originally developed by physicists in order to predict election results by using mainly Non Linear Dynamics (chaotic dynamics). For this purpose, they applied chaotic analysis on samples from political survey for the Euro election results in Hellas, Greece in 2009, and also for the Hellenic National elections of October 4, 2009 in order to predict election results.

Drifting into Failure

The Gaussian copula, an equation first published by David Li in 2000, was a beautiful thing—in isolation. Its intention was to price collaterized debt obligations, and work out whether they were moving in the same direction. The copula was an enabler of mortgaging the most hopeless of homeowner prospects. Millions of securities could be traded on the back of a single number (a security is something that shows ownership, or right of ownership of stocks or bonds, or the right to ownership connected with derivatives that get their value from some underlying asset). As more and more webs of interactions and relationships and interdependencies and feedback loops started growing around it, however, it became part of a complex system. The copula became the trigger of a recession that swelled the number of homeless families in the US by 30% inside of two years (Associated Press, 2010). It ended up bringing global lending to a virtual standstill, triggering a worldwide financial crisis and a deep recession. How did a once good idea like this drift into failure, and how can such a risk of collapse be managed? That is what this chapter is about.

Chaotic Essence inside the Organizational Reality

In the chaotic reality of the human civilizations, organizations were always seen as bastions of order. Even in the extreme cases of organizations that sought to bring chaos and confusion, their purpose was generally to clear the present situation and bring a new order. Except the cases of some extreme sects and marginal crime organizations, almost all organizations strive to bring their own existential definitions of order. In this process, management has been the tool of bringing order to organization. Even though modern management is a relatively new concept, all through the history the elements of management such as superior-subordinate relation, persuasion, direction, and administration were seen (Starbuck, 2003; Wren, 2004). But underneath the idealistic goal of bringing order, all organizations are suffering from the chaotic essence that is in their midst. In the organizational theory literature, this chaotic essence is either ignored or it is treated as a problem of good implementation of managerial control. And this problem has been treated in a surprisingly linear way whereas non-linearity of the organizational reality is not considered.

Nonlinear Correlation of Stock and Commodity Indices in Emerging and Developed Market

The interrelationship between stock and commodity markets has been an issue of interest for both the academia and practitioners in the field of investment and wealth management. Traditionally, commodity has been a popular avenue for diversification in a mixed portfolio. However, this works well as long as there is little or no correlation between the two markets. This chapter presents an empirical investigation of the daily movement of stock and commodity index of two different countries to throw some light on the interrelationship between stock and commodity market. The uniqueness of this study lies in the choice of markets as also the methodology. The authors have chosen a developed market, viz., the US market, and an emerging market, viz., the Indian market. This study uses the major stock and commodity indices respectively for both countries for a period of three years. For analysis the authors have used the tools from nonlinear dynamics like recurrence analysis, power spectrum analysis, and delay based cross-correlation function. The investigation revealed that the dynamics of the time path of daily movement of Indian stock and commodity exchanges are much similar in nature while those of the US market are quite different. This chapter also models the respective time series using Geometric Brownian Motion and finds that the Indian data set performed much better than the US ones. This has a strong impact on strategy for designing mixed portfolios in Indian market.

Chaos and Complexity in Financial Statements

Conceptual issues and the basis for the use of financial statements from the perspective of complexity and chaos are proposed. After analyzing the implications that these perspectives have for financial statements, basic accounting equation is examined from the view of complex logic through the mechanisms of the circumscription. Besides, the phase spaces arising from the relationship between indicators of financial health, such as total assets, stakeholder’s equity, profit and loss, or cash flow at end of year, are analyzed; also, the relationship among ratios of sustainability, liquidity, and profitability is revisited. The management discussion & analysis and notes to financial statements sections of financial statements are subjected to new interpretations, based on the beliefs logic and complex and chaotic metaphorical narratives. Finally, a critical perspective on the use of chaos and complexity in the analysis of financial statements is introduced.