A Tutorial on Time-Evolving Dynamical Bayesian Inference

In view of the current availability and variety of measured data, there is an increasing demand for powerful signal processing tools that can cope successfully with the associated problems that often arise when data are being analysed. In practice many of the data-generating systems are not only time-variable, but also influenced by neighbouring systems and subject to random fluctuations (noise) from their environments. To encompass problems of this kind, we present a tutorial about the dynamical Bayesian inference of time-evolving coupled systems in the presence of noise. It includes the necessary theoretical description and the algorithms for its implementation. For general programming purposes, a pseudocode description is also given. Examples based on coupled phase and limit-cycle oscillators illustrate the salient features of phase dynamics inference. State domain inference is illustrated with an example of coupled chaotic oscillators. The applicability of the latter example to secure communications based on the modulation of coupling functions is outlined. MatLab codes for implementation of the method, as well as for the explicit examples, accompany the tutorial.Comment: Matlab codes can be found on http://py-biomedical.lancaster.ac.uk

Inference of Time-Evolving Coupled Dynamical Systems in the Presence of Noise

A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of the coupling functions and other parameters to be followed. It is based on phase dynamics, with Bayesian inference of the time-evolving parameters achieved by shaping the prior densities to incorporate knowledge of previous samples. The method is tested numerically and applied to reveal and quantify the time-varying nature of cardiorespiratory interactions.Comment: 5 pages, 3 figures, accepted for Physical Review Letter

Dynamical inference:where phase synchronization and generalized synchronization meet

Synchronization is a widespread phenomenon that occurs among interacting oscillatory systems. It facilitates their temporal coordination and can lead to the emergence of spontaneous order. The detection of synchronization from the time series of such systems is of great importance for the understanding and prediction of their dynamics, and several methods for doing so have been introduced. However, the common case where the interacting systems have time-variable characteristic frequencies and coupling parameters, and may also be subject to continuous external perturbation and noise, still presents a major challenge. Here we apply recent developments in dynamical Bayesian inference to tackle these problems. In particular, we discuss how to detect phase slips and the existence of deterministic coupling from measured data, and we unify the concepts of phase synchronization and general synchronization. Starting from phase or state observables, we present methods for the detection of both phase and generalized synchronization. The consistency and equivalence of phase and generalized synchronization are further demonstrated, by the analysis of time series from analog electronic simulations of coupled nonautonomous van der Pol oscillators. We demonstrate that the detection methods work equally well on numerically simulated chaotic systems. In all the cases considered, we show that dynamical Bayesian inference can clearly identify noise-induced phase slips and distinguish coherence from intrinsic coupling-induced synchronization

Coupling functions enable secure communications

Secure encryption is an essential feature of modern communications, but rapid progress in illicit decryption brings a continuing need for new schemes that are harder and harder to break. Inspired by the time-varying nature of the cardiorespiratory interaction, here we introduce a new class of secure communications that is highly resistant to conventional attacks. Unlike all earlier encryption procedures, this cipher makes use of the coupling functions between interacting dynamical systems. It results in an unbounded number of encryption key possibilities, allows the transmission/reception of more than one signal simultaneously, and is robust against external noise. Thus, the information signals are encrypted as the time-variations of linearly-independent coupling functions. Using predetermined forms of coupling function, we can apply Bayesian inference on the receiver side to detect and separate the information signals while simultaneously eliminating the effect of external noise. The scheme is highly modular and is readily extendable to support different communications applications within the same general framework

Coupling functions in networks of oscillators

Networks of interacting oscillators abound in nature, and one of the prevailing challenges in science is how to characterize and reconstruct them from measured data. We present a method of reconstruction based on dynamical Bayesian inference that is capable of detecting the effective phase connectivity within networks of time-evolving coupled phase oscillators subject to noise. It not only reconstructs pairwise, but also encompasses couplings of higher degree, including triplets and quadruplets of interacting oscillators. Thus inference of a multivariate network enables one to reconstruct the coupling functions that specify possible causal interactions, together with the functional mechanisms that underlie them. The characteristic features of the method are illustrated by the analysis of a numerically generated example: a network of noisy phase oscillators with time-dependent coupling parameters. To demonstrate its potential, the method is also applied to neuronal coupling functions from single- and multi-channel electroencephalograph recordings. The crossfrequency δ, α to α coupling function, and the θ, α, γ to γ triplet are computed, and their coupling strengths, forms of coupling function, and predominant coupling components, are analysed. The results demonstrate the applicability of the method to multivariate networks of oscillators, quite generally

Neural Cross-Frequency Coupling Functions

Although neural interactions are usually characterized only by their coupling strength and directionality, there is often a need to go beyond this by establishing the functional mechanisms of the interaction. We introduce the use of dynamical Bayesian inference for estimation of the coupling functions of neural oscillations in the presence of noise. By grouping the partial functional contributions, the coupling is decomposed into its functional components and its most important characteristics-strength and form-are quantified. The method is applied to characterize the δ-to-α phase-to-phase neural coupling functions from electroencephalographic (EEG) data of the human resting state, and the differences that arise when the eyes are either open (EO) or closed (EC) are evaluated. The δ-to-α phase-to-phase coupling functions were reconstructed, quantified, compared, and followed as they evolved in time. Using phase-shuffled surrogates to test for significance, we show how the strength of the direct coupling, and the similarity and variability of the coupling functions, characterize the EO and EC states for different regions of the brain. We confirm an earlier observation that the direct coupling is stronger during EC, and we show for the first time that the coupling function is significantly less variable. Given the current understanding of the effects of e.g., aging and dementia on δ-waves, as well as the effect of cognitive and emotional tasks on α-waves, one may expect that new insights into the neural mechanisms underlying certain diseases will be obtained from studies of coupling functions. In principle, any pair of coupled oscillations could be studied in the same way as those shown here

Cardiorespiratory coupling functions, synchronization and ageing

We discuss the advent of coupling functions as a new dimension in the analysis of cardiorespiratory interactions. By decomposing the separate coupling components in a phase oscillator model, we infer the cardiorespiratory coupling functions with dynamical Bayesian inference for time-evolving and noisy coupled systems. The inferred coupling functions are themselves time-varying processes. On a longer timescale, application to ageing shows that the coupling functions and the direct influence of respiration decrease as age increases. We find that the coupling functions can give rise to synchronization transitions, and that there are no significant changes in synchronization with age

Distributed Environment for Efficient Virtual Machine Image Management in Federated Cloud Architectures

The use of Virtual Machines (VM) in Cloud computing provides various benefits in the overall software engineering lifecycle. These include efficient elasticity mechanisms resulting in higher resource utilization and lower operational costs. VM as software artifacts are created using provider-specific templates, called VM images (VMI), and are stored in proprietary or public repositories for further use. However, some technology specific choices can limit the interoperability among various Cloud providers and bundle the VMIs with nonessential or redundant software packages, leading to increased storage size, prolonged VMI delivery, stagnant VMI instantiation and ultimately vendor lock-in. To address these challenges, we present a set of novel functionalities and design approaches for efficient operation of distributed VMI repositories, specifically tailored for enabling: (i) simplified creation of lightweight and size optimized VMIs tuned for specific application requirements; (ii) multi-objective VMI repository optimization; and (iii) efficient reasoning mechanism to help optimizing complex VMI operations. The evaluation results confirm that the presented approaches can enable VMI size reduction by up to 55%, while trimming the image creation time by 66%. Furthermore, the repository optimization algorithms, can reduce the VMI delivery time by up to 51% and cut down the storage expenses by 3%. Moreover, by implementing replication strategies, the optimization algorithms can increase the system reliability by 74%

Noise in interacting biological systems

Biological systems are never isolated, usually oscillatory, and invariably subject to noise and fluctuations that may be of either internal or external origin. We present a methodological framework for studying the deterministic interactions of biological oscillatory systems, while at the same time decomposing and evaluating the noise strength. Based on dynamical Bayesian inference, the method models coupled phase oscillators in the presence of dynamical noise. We demonstrate first the potential and the precision of the method on a predefined numerical system. Then we illustrate its usefulness in detecting how the noise strengths from three human physiological systems – the heart, the lungs and the brain – are affected by general anæsthesia. The results demonstrate the potential of the method for detecting and quantifying noise from biological dynamical systems, quite generally

Coupling Functions:Dynamical Interaction Mechanisms in the Physical, Biological and Social Sciences

Dynamical systems are widespread, with examples in physics, chemistry, biology, population dynamics, communications, climatology and social science. They are rarely isolated but generally interact with each other. These interactions can be characterised by coupling functions -- which contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how each interaction occurs. Coupling functions can be used, not only to understand, but also to control and predict the outcome of the interactions. This theme issue assembles ground-breaking work on coupling functions by leading scientists. After overviewing the field and describing recent advances in the theory, it discusses novel methods for the detection and reconstruction of coupling functions from measured data. It then presents applications in chemistry, neuroscience, cardio-respiratory physiology, climate, electrical engineering and social science. Taken together, the collection summarises earlier work on coupling functions, reviews recent developments, presents the state-of-the-art, and looks forward to guide the future evolution of the field