Statistical Mechanics for Network Structure and Evolution

In this thesis, we address problems in complex networks using the methods of statistical mechanics and information theory. We particularly focus on the thermodynamic characterisation of networks and entropic analysis on statistics and dynamics of network evolution. After a brief introduction of background and motivation behind the thesis in Chapter 1, we provide a review of relevant literature in Chapter 2, and elaborate the main methods from Chapter 3 to Chapter 6. In Chapter 3, we explore the normalised Laplacian matrix as the Hamiltonian operator of the network which governs the particle occupations corresponding to Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics. The relevant partition functions derive the thermodynamic quantities in revealing network structural characterisations. Chapter 4 further decomposes the global network entropy in three statistics on edge-connection components. This decompensation reflects the detailed distribution of entropy across the edges of a network, and is particularly useful if the analysis of non-homogeneous networks with a strong community and hub structure is being attempted. Furthermore, Chapter 5 and Chapter 6 provide the theoretical approaches to analyse the dynamic network evolution and the application of the real-world networks. In Chapter 5, we investigate both undirected and directed network evolution using the Euler-Lagrange equation. This variational principle is based on the von Neumann entropy for time-varying network structure. The presented model not only provides an accurate simulation of the degree statistics in network evolution, but also captures the topological variations taking place when the structure of a network changes violently. Chapter 6 studies the fMRI regional brain interaction networks using directed graphs. We further develop a novel method for characterising networks using Bose-Einstein entropy and the Jensen-Shannon divergence. It offers a high discrimination among patients with suspected Alzheimer's disease. Finally, Chapter 7 concludes the thesis and discusses the limitations of our methodologies, which also supplies the potential research in the future

Dissipation and spontaneous symmetry breaking in brain dynamics

We compare the predictions of the dissipative quantum model of brain with neurophysiological data collected from electroencephalograms resulting from high-density arrays fixed on the surfaces of primary sensory and limbic areas of trained rabbits and cats. Functional brain imaging in relation to behavior reveals the formation of coherent domains of synchronized neuronal oscillatory activity and phase transitions predicted by the dissipative model.Comment: Restyled, slight changes in title and abstract, updated bibliography, J. Phys. A: Math. Theor. Vol. 41 (2008) in prin

Early Detection of Alzheimer’s Disease : Detecting Asymmetries with a Return Random Walk Link Predictor

Alzheimer’s disease has been extensively studied using undirected graphs to represent the correlations of BOLD signals in different anatomical regions through functional magnetic resonance imaging (fMRI). However, there has been relatively little analysis of this kind of data using directed graphs, which potentially offer the potential to capture asymmetries in the interactions between different anatomical brain regions. The detection of these asymmetries is relevant to detect the disease in an early stage. For this reason, in this paper, we analyze data extracted from fMRI images using the net4Lap algorithm to infer a directed graph from the available BOLD signals, and then seek to determine asymmetries between the left and right hemispheres of the brain using a directed version of the Return Random Walk (RRW). Experimental evaluation of this method reveals that it leads to the identification of anatomical brain regions known to be implicated in the early development of Alzheimer’s disease in clinical studies

Spin-Mediated Consciousness: Theory, Experimental Studies, Further Development & Related Topics

We postulate that consciousness is intrinsically connected to quantum spin since the latter is the origin of quantum effects in both Bohm and Hestenes quantum formulisms and a fundamental quantum process associated with the structure of space-time. Applying these ideas to the particular structures and dynamics of the brain, we have developed a detailed model of quantum consciousness. We have also carried out experiments from the perspective of our theory to test the possibility of quantum-entangling the quantum entities inside the brain with those of an external chemical substance. We found that applying magnetic pulses to the brain when an anaesthetic was placed in between caused the brain to feel the effect of said anaesthetic as if the test subject had actually inhaled the same. We further found that drinking water exposed to magnetic pulses, laser light or microwave when an anaesthetic was placed in between also causes brain effects in various degrees. Additional experiments indicate that the said brain effect is indeed the consequence of quantum entanglement. Recently we have studied non-local effects in simple physics systems. We have found that the pH value, temperature and gravity of a liquid in the detecting reservoirs can be non-locally affected through manipulating another liquid in a remote reservoir quantum-entangled with the former. In particular, the pH value changes in the same direction as that being manipulated; the temperature can change against that of local environment; and the gravity can change against local gravity. We suggest that they are mediated by quantum entanglement between nuclear and/or electron spins in treated liquid and discuss the profound implications of these results. This paper now also includes materials on further development of the theory and related topics.Comment: 92 pages; expanded content; minor corrections; for additional information, please visit http://quantumbrain.or

Nonlinear Dynamics

This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students

Serotonin and brain function: a tale of two receptors

Previous attempts to identify a unified theory of brain serotonin function have largely failed to achieve consensus. In this present synthesis, we integrate previous perspectives with new and older data to create a novel bipartite model centred on the view that serotonin neurotransmission enhances two distinct adaptive responses to adversity, mediated in large part by its two most prevalent and researched brain receptors: the 5-HT1A and 5-HT2A receptors. We propose that passive coping (i.e. tolerating a source of stress) is mediated by postsynaptic 5-HT1AR signalling and characterised by stress moderation. Conversely, we argue that active coping (i.e. actively addressing a source of stress) is mediated by 5-HT2AR signalling and characterised by enhanced plasticity (defined as capacity for change). We propose that 5-HT1AR-mediated stress moderation may be the brain’s default response to adversity but that an improved ability to change one’s situation and/or relationship to it via 5-HT2AR-mediated plasticity may also be important – and increasingly so as the level of adversity reaches a critical point. We propose that the 5HT1AR pathway is enhanced by conventional 5-HT reuptake blocking antidepressants such as the selective serotonin reuptake inhibitors (SSRIs), whereas the 5-HT2AR pathway is enhanced by 5-HT2AR-agonist psychedelics. This bipartite model purports to explain how different drugs (SSRIs and psychedelics) that modulate the serotonergic system in different ways, can achieve complementary adaptive and potentially therapeutic outcomes

A Survey on Graph Kernels

Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their design, such as the nature of their extracted graph features, their method of computation and their applicability to problems in practice. In an extensive experimental evaluation, we study the classification accuracy of a large suite of graph kernels on established benchmarks as well as new datasets. We compare the performance of popular kernels with several baseline methods and study the effect of applying a Gaussian RBF kernel to the metric induced by a graph kernel. In doing so, we find that simple baselines become competitive after this transformation on some datasets. Moreover, we study the extent to which existing graph kernels agree in their predictions (and prediction errors) and obtain a data-driven categorization of kernels as result. Finally, based on our experimental results, we derive a practitioner's guide to kernel-based graph classification