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Statistical Fluctuations in Evolutionary and Population Dynamics
In this thesis, we study collective phenomena that arise from microscopic fluctuations at the individual level of two different living populations. First, we study evolutionary dynamics of two-species competitions in a well-mixed environment subject to population size fluctuations. We demonstrate a mechanism for neutral evolution such that population size fluctuations favor a fixation of one species over the other. An effective evolutionary dynamics for fluctuation-induced selection is derived. We then investigate strong mutualism, in a limit where a varying population size can strongly influence the evolutionary dynamics. We determine fixation probabilities as well as mean fixation times ta...
Unpredictable Dynamics in Congestion Games
We study the dynamics of simple congestion games with two resources where a continuum of agents behaves according to a simplified version of Experience-Weighted Attraction algorithm. The dynamics is characterized by the intensity of choice capturing rationality of the total population of agents and a discount factor capturing a type of memory loss where past outcomes matter exponentially less than the recent ones. Finally, our system adds a third parameter, which captures the asymmetry of the cost functions of the two resources. We show that for any discount factor the system will be destabilized for a sufficiently large intensity of choice, but dependent on the asymmetry of costs, and its relation to the discount factor, the system will stay predictable or become unpredictable and chaotic. Moreover, as memory loss increases the chaotic regime will give place to the attracting periodic orbit of period 2.
Quantum Phase Transitions
Describing the physical properties of quantum materials near critical points with long-range many-body quantum entanglement, this book introduces readers to the basic theory of quantum phases, their phase transitions and their observable properties. This second edition begins with a new section suitable for an introductory course on quantum phase transitions, assuming no prior knowledge of quantum field theory. It also contains several new chapters to cover important recent advances, such as the Fermi gas near unitarity, Dirac fermions, Fermi liquids and their phase transitions, quantum magnetism, and solvable models obtained from string theory. After introducing the basic theory, it moves on to a detailed description of the canonical quantum-critical phase diagram at non-zero temperatures. Finally, a variety of more complex models are explored. This book is ideal for graduate students and researchers in condensed matter physics and particle and string theory.
Corks and Curls
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Simple Adaptive Strategies: From Regret-matching To Uncoupled Dynamics
This volume collects almost two decades of joint work of Sergiu Hart and Andreu Mas-Colell on game dynamics and equilibria. The starting point was the introduction of the adaptive strategy called regret-matching, which on the one hand is simple and natural, and on the other is shown to lead to correlated equilibria. This initial finding — boundedly rational behavior that yields fully rational outcomes in the long run — generated a large body of work on the dynamics of simple adaptive strategies. In particular, a natural condition on dynamics was identified: uncoupledness, whereby decision-makers do not know each other's payoffs and utilities (so, while chosen actions may be observable, t...
Generating Random Networks and Graphs
This book describes how to correctly and efficiently generate random networks based on certain constraints. Being able to test a hypothesis against a properly specified control case is at the heart of the 'scientific method'.
Large Networks and Graph Limits
Recently, it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks. To develop a mathematical theory of very large networks is an important challenge. This book describes one recent approach to this theory, the limit theory of graphs, which has emerged over the last decade. The theory has rich connections with other approaches to the study of large networks, such as ``property testing'' in computer science and regularity partition in graph theory. It has several applications in extremal graph theory, including the exact formulations and partial answers to very general questions, such as which problems in extremal graph ...
Random Fields and Spin Glasses
The book introduces some useful and little known techniques in statistical mechanics and field theory including multiple Legendre transforms, supersymmetry, Fourier transforms on a tree, infinitesimal permutations and Ward Takahashi Identities."--Jacket.
Quantum Geometry
Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.
MATLAB for Brain and Cognitive Scientists
An introduction to a popular programming language for neuroscience research, taking the reader from beginning to intermediate and advanced levels of MATLAB programming. MATLAB is one of the most popular programming languages for neuroscience and psychology research. Its balance of usability, visualization, and widespread use makes it one of the most powerful tools in a scientist's toolbox. In this book, Mike Cohen teaches brain scientists how to program in MATLAB, with a focus on applications most commonly used in neuroscience and psychology. Although most MATLAB tutorials will abandon users at the beginner's level, leaving them to sink or swim, MATLAB for Brain and Cognitive Scientists take...
