Computational Intelligence and Complexity Measures for Chaotic Information Processing

This dissertation investigates the application of computational intelligence methods in the analysis of nonlinear chaotic systems in the framework of many known and newly designed complex systems. Parallel comparisons are made between these methods. This provides insight into the difficult challenges facing nonlinear systems characterization and aids in developing a generalized algorithm in computing algorithmic complexity measures, Lyapunov exponents, information dimension and topological entropy. These metrics are implemented to characterize the dynamic patterns of discrete and continuous systems. These metrics make it possible to distinguish order from disorder in these systems. Steps required for computing Lyapunov exponents with a reorthonormalization method and a group theory approach are formalized. Procedures for implementing computational algorithms are designed and numerical results for each system are presented. The advance-time sampling technique is designed to overcome the scarcity of phase space samples and the buffer overflow problem in algorithmic complexity measure estimation in slow dynamics feedback-controlled systems. It is proved analytically and tested numerically that for a quasiperiodic system like a Fibonacci map, complexity grows logarithmically with the evolutionary length of the data block. It is concluded that a normalized algorithmic complexity measure can be used as a system classifier. This quantity turns out to be one for random sequences and a non-zero value less than one for chaotic sequences. For periodic and quasi-periodic responses, as data strings grow their normalized complexity approaches zero, while a faster deceasing rate is observed for periodic responses. Algorithmic complexity analysis is performed on a class of certain rate convolutional encoders. The degree of diffusion in random-like patterns is measured. Simulation evidence indicates that algorithmic complexity associated with a particular class of 1/n-rate code increases with the increase of the encoder constraint length. This occurs in parallel with the increase of error correcting capacity of the decoder. Comparing groups of rate-1/n convolutional encoders, it is observed that as the encoder rate decreases from 1/2 to 1/7, the encoded data sequence manifests smaller algorithmic complexity with a larger free distance value

Topics in chaotic secure communication

Results in nonlinear dynamics and chaos during this decade have been applied to problems in secure communications with limited success. Most of these applications have been based on the chaotic synchronization property discovered by Pecora and Carroll in 1989 [37]. Short [44, 45, 48] demonstrated the effectiveness of nonlinear dynamic (NLD) forecasting methods in breaking this class of communication schemes. In response, investigators have proposed enhancements to the basic synchronization technique in an attempt to improve the security properties. In this work two of these newer communication systems will be analyzed using NLD forecasting and other techniques to determine the level of security they provide. It will be shown that the transmitted waveform alone allows an eavesdropper to extract the message. During the course of this research, a new impulsively initialized, binary chaotic communication scheme has been developed, which eliminates the most significant weaknesses of its predecessors. This new approach is based on symbolic dynamics and chaotic control, and may be implemented using one-dimensional maps, which gives the designer more control over the statistics of the transmitted binary stream. Recent results in a certain class of one-dimensional chaotic maps will be discussed in this context. The potential for using NLD techniques in problems from standard digital communications will also be explored. The two problems which will be addressed are bit errors due to channel effects and co-channel interference. It will be shown that NLD reconstruction methods provide a way to exploit the short-term determinism that is present in these types of communication signals

Design and Implementation of Secure Chaotic Communication Systems

Chaotic systems have properties such as ergodicity, sensitivity to initial conditions/parameter mismatches, mixing property, deterministic dynamics, structure complexity, to mention a few, that map nicely with cryptographic requirements such as confusion, diffusion, deterministic pseudorandomness, algorithm complexity. Furthermore, the possibility of chaotic synchronization, where the master system (transmitter) is driving the slave system (receiver) by its output signal, made it probable for the possible utilization of chaotic systems to implement security in the communication systems. Many methods like chaotic masking, chaotic modulation, inclusion, chaotic shift keying (CSK) had been proposed however, many attack methods later showed them to be insecure. Different modifications of these methods also exist in the literature to improve the security, but almost all suffer from the same drawback. Therefore, the implementation of chaotic systems in security still remains a challenge. In this work, different possibilities on how it might be possible to improve the security of the existing methods are explored. The main problem with the existing methods is that the message imprint could be found in the dynamics of the transmitted signal, therefore by some signal processing or pattern classification techniques, etc, allow the exposition of the hidden message. Therefore, the challenge is to remove any pattern or change in dynamics that the message might bring in the transmitted signal

Design and implementation of secure chaotic communication systems

Chaotic systems have properties such as ergodicity, sensitivity to initial conditions/parameter mismatches, mixing property, deterministic dynamics, structure complexity, to mention a few, that map nicely with cryptographic requirements such as confusion, diffusion, deterministic pseudorandomness, algorithm complexity. Furthermore, the possibility of chaotic synchronization, where the master system (transmitter) is driving the slave system (receiver) by its output signal, made it probable for the possible utilization of chaotic systems to implement security in the communication systems. Many methods like chaotic masking, chaotic modulation, inclusion, chaotic shift keying (CSK) had been proposed however, many attack methods later showed them to be insecure. Different modifications of these methods also exist in the literature to improve the security, but almost all suffer from the same drawback. Therefore, the implementation of chaotic systems in security still remains a challenge. In this work, different possibilities on how it might be possible to improve the security of the existing methods are explored. The main problem with the existing methods is that the message imprint could be found in the dynamics of the transmitted signal, therefore by some signal processing or pattern classification techniques, etc, allow the exposition of the hidden message. Therefore, the challenge is to remove any pattern or change in dynamics that the message might bring in the transmitted signal.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Recurrence network analysis of EEG signals: A Geometric Approach

Understanding the neuronal dynamics of dynamical diseases like epilepsy is of fundamental importance. For instance, establishing the presence of deterministic chaos can open up possibilities that can lead to potential medical applications, including timely prevention of seizures. Additionally, understanding the dynamics of interictal activity can greatly aid the localization of epileptic foci without the need for recording seizures. Recurrences, a fundamental property of dynamical systems, are useful for characterizing nonlinear systems. Recurrence networks, which are obtained by reinterpreting the recurrence matrix as an adjacency matrix of a complex network, are useful in characterizing the structural or geometric properties of the underlying system. Recurrence network analysis has established itself as a versatile tool in the field of nonlinear time series analysis and its applicability in investigating neural dynamics remains unexplored. Certain recurrence network measures are particularly sensitive to the presence of unstable periodic orbits (UPOs), which are important for detecting determinism and are the backbone of chaotic attractors.In this thesis, we introduce recurrence network analysis as a tool for nonlinear time series analysis of epileptic electroencephalographic (EEG) signals. We present novel results based on the application of recurrence network analysis combined with surrogate testing to intracranial and extracranial epileptic EEG signals. In addition, using paradigmatic examples of dynamical systems, we present theoretical results exploring the effect of increasing noise levels on recurrence network measures.Using paradigmatic model systems, we first demonstrate that recurrence network measures can distinguish between deterministic (chaos) and stochastic processes, even at short data lengths (≈ 200 samples). In particular, our results from theoretical simulations show that recurrence network measures, particularly transitivity, local clustering coefficient, assortativity, and betweenness centrality can successfully distinguish between deterministic chaotic and stochastic processes (after additional embedding) due to their sensitivity to the presence of UPOs. Our results also show that recurrence network measures like transitivity and average path length are robust against noise and perform better than the Complexity-Entropy plane method at short data lengths. Furthermore, our results show that the effect of noise on the recurrence network measures can be minimized by increasing the recurrence rate.For the analysis of real-world data such as EEG signals, we combined the recurrence network approach with surrogate data to test for the structural complexity in healthy and epileptic EEG signals. Here our results point to an increasing complexity of EEG recordings when moving from healthy to epileptic conditions. Furthermore, we used both univariate network measure and bivariate cross-network measure to distinguish between the structural properties of interictal EEG signals recorded from epileptic and nonepileptic brain areas. Here, our results clearly demonstrated that interictal EEG signals recorded from epileptic areas are more deterministic and interdependent compared to interictal activity recorded from nonepileptic areas. Finally, we show that recurrence network analysis can be applied to uncover the dynamical transitions in neural signals using short segments of data (≈ 150 to 500 samples). To demonstrate this, we used two kinds of neural data - epileptic EEG data and local field potential (LFP) signals recorded during a visuomotor task. We observed that the temporal fluctuations observed in the recurrence network measures are consistent with the dynamical transitions underlying the epileptic and task-based LFP signals.To conclude, recurrence network analysis analysis can capture the complexity in the organization of EEG data in different dynamical states in a more elaborated fashion compared to other approaches such as nonlinear prediction error or correlation dimension. By means of the recurrence network measures, this difference can be assessed not only qualitatively (as when using as tests for nonlinearity), but also quantitatively. Thus, coupled with its ability to operate on short-window sizes and robustness to noise, recurrence network analysis can be a powerful tool to analyze the dynamics of multi-scale neural signals

Multimedia

The nowadays ubiquitous and effortless digital data capture and processing capabilities offered by the majority of devices, lead to an unprecedented penetration of multimedia content in our everyday life. To make the most of this phenomenon, the rapidly increasing volume and usage of digitised content requires constant re-evaluation and adaptation of multimedia methodologies, in order to meet the relentless change of requirements from both the user and system perspectives. Advances in Multimedia provides readers with an overview of the ever-growing field of multimedia by bringing together various research studies and surveys from different subfields that point out such important aspects. Some of the main topics that this book deals with include: multimedia management in peer-to-peer structures & wireless networks, security characteristics in multimedia, semantic gap bridging for multimedia content and novel multimedia applications

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity