Foreword by Walter J. Freeman. The induction of unconsciousness using anesthetic agents demonstrates that the cerebral cortex can operate in two very different behavioral modes: alert and responsive vs. unaware and quiescent. But the states of wakefulness and sleep are not single-neuron properties---they emerge as bulk properties of cooperating populations of neurons, with the switchover between states being similar to the physical change of phase observed when water freezes or ice melts. Some brain-state transitions, such as sleep cycling, anesthetic induction, epileptic seizure, are obvious and detected readily with a few EEG electrodes; others, such as the emergence of gamma rhythms during cognition, or the ultra-slow BOLD rhythms of relaxed free-association, are much more subtle. The unifying theme of this book is the notion that all of these bulk changes in brain behavior can be treated as phase transitions between distinct brain states. Modeling Phase Transitions in the Brain contains chapter contributions from leading researchers who apply state-space methods, network models, and biophysically-motivated continuum approaches to investigate a range of neuroscientifically relevant problems that include analysis of nonstationary EEG time-series; network topologies that limit epileptic spreading; saddle--node bifurcations for anesthesia, sleep-cycling, and the wake--sleep switch; prediction of dynamical and noise-induced spatiotemporal instabilities underlying BOLD, alpha-, and gamma-band Hopf oscillations, gap-junction-moderated Turing structures, and Hopf-Turing interactions leading to cortical waves.
This intriguing book was born out of the many discussions the authors had in the past 10 years about the role of scale-free structure and dynamics in producing intelligent behavior in brains. The microscopic dynamics of neural networks is well described by the prevailing paradigm based in a narrow interpretation of the neuron doctrine. This book broadens the doctrine by incorporating the dynamics of neural fields, as first revealed by modeling with differential equations (K-sets). The book broadens that approach by application of random graph theory (neuropercolation). The book concludes with diverse commentaries that exemplify the wide range of mathematical/conceptual approaches to neural fields. This book is intended for researchers, postdocs, and graduate students, who see the limitations of network theory and seek a beachhead from which to embark on mesoscopic and macroscopic neurodynamics.
Phase transitions--changes between different states of organization in a complex system--have long helped to explain physics concepts, such as why water freezes into a solid or boils to become a gas. How might phase transitions shed light on important problems in biological and ecological complex systems? Exploring the origins and implications of sudden changes in nature and society, Phase Transitions examines different dynamical behaviors in a broad range of complex systems. Using a compelling set of examples, from gene networks and ant colonies to human language and the degradation of diverse ecosystems, the book illustrates the power of simple models to reveal how phase transitions occur. Introductory chapters provide the critical concepts and the simplest mathematical techniques required to study phase transitions. In a series of example-driven chapters, Ricard Solé shows how such concepts and techniques can be applied to the analysis and prediction of complex system behavior, including the origins of life, viral replication, epidemics, language evolution, and the emergence and breakdown of societies. Written at an undergraduate mathematical level, this book provides the essential theoretical tools and foundations required to develop basic models to explain collective phase transitions for a wide variety of ecosystems.
This book introduces new concepts in the phenomenon of 1st order phase transitions. It discusses the concept of kinetic arrest at a certain temperature, with this temperature being dependent on the second control variable (magnetic field, or pressure). It discusses interesting manifestations of this phenomenon when the 1st order transition is broadened, i.e. occurs over a finite range of temperatures. Many examples of this phenomenon, observed recently in many materials, will also be discussed.
This book is a collection of articles by leading researchers working at the cutting edge of neuro-computational modelling of neurological and psychiatric disorders. Each article contains model validation techniques used in the context of the specific problem being studied. Validation is essential for neuro-inspired computational models to become useful tools in the understanding and treatment of disease conditions. Currently, the immense diversity in neuro-computational modelling approaches for investigating brain diseases has created the need for a structured and coordinated approach to benchmark and standardise validation methods and techniques in this field of research. This book serves as a step towards a systematic approach to validation of neuro-computational models used for studying brain diseases and should be useful for all neuro-computational modellers.
Sleep and anesthesia resemble in many ways at a first glance. The most prominent common feature of course is the loss of consciousness, i.e. the loss of awareness of external stimuli. However a closer look at the loss of consciousness reveals already a difference between sleep and anesthesia: anesthesia is induced by an anesthetic drug whereas we may fall asleep without external cause. Other questions may arise about the difference of the two effects: do we dream during surgery under anesthesia, do we feel pain during sleep? Essentially, we may ask: what is common and what are the differences between sleep and anesthesia? To answer these questions, we may take a look at the neural origin of both effects and the involved physiological pathways. In which way do they resemble? Moreover, we ask what are the detailed features of normal sleep and general anesthesia as applied during surgery and which features exist in both phenomena? If yes in which way? To receive answers to these questions, it is necessary to consider several experimental techniques that reveal underlying neural mechanisms of sleep and anesthesia. Moreover, theoretical models of neural activity may model both phenomena and comes up with predictions or even theories on the underlying mechanisms. Such models may attack several different description levels, from the microscopic level of single neurons to the macroscopic level of neural populations. Such models may give deeper insight into the phenomena if their assumptions are based on experimental findings and their predictions can be compared to experimental results. This comparison step is essential for valuable theoretical models. The book is motivated by two successful workshops on anesthesia and sleep organized during the Computational Neuroscience Conferences in Toronto in 2007 and in Berlin 2009. It aims to cover all the previous aspects with a focus on the link to experimental findings. It elucidates important issues in theoretical models that at the same time reflect some current major research interests. Moreover it considers some diverse issues which are very important to get an overview of the fields. For instance, the book discusses not only neural activity in the brain but also the effects of general anesthesia on the cardio-vascular system and the spinal cord in the context of analgesia. In addition, it considers different experimental techniques on various spatial scales, such as fMRI and EEG-experiments on the macroscopic scale and single neuron and LFP-measurements on the microscopic scale. In total all book chapters reveal aspects of the neural correlates of sleep and anesthesia motivated by experimental data. This focus on the neural mechanism in the light of experimental data is the common feature of the topics and the chapters. In addition, the book aims to clarify the shared physiological mechanisms of both phenomena, but also reveal their physiological differences.
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.