Modularity and 4D-2D spectral equivalences for large-N gauge theories with adjoint matter

In recent work, we demonstrated that the confined-phase spectrum of non-supersymmetric pure Yang-Mills theory coincides with the spectrum of the chiral sector of a two-dimensional conformal field theory in the large-$N$ limit. This was done within the tractable setting in which the gauge theory is compactified on a three-sphere whose radius is small compared to the strong length scale. In this paper, we generalize these observations by demonstrating that similar results continue to hold even when massless adjoint matter fields are introduced. These results hold for both thermal and $(-1)^F$-twisted partition functions, and collectively suggest that the spectra of large-$N$ confining gauge theories are organized by the symmetries of two-dimensional conformal field theories.Comment: 51 pages, LaTeX, 3 figure

Opinion Dynamics in Social Networks through Mean-Field Games

Emulation, mimicry, and herding behaviors are phenomena that are observed when multiple social groups interact. To study such phenomena, we consider in this paper a large population of homogeneous social networks. Each such network is characterized by a vector state, a vector-valued controlled input and a vector-valued exogenous disturbance. The controlled input of each network is to align its state to the mean distribution of other networks’ states in spite of the actions of the disturbance. One of the contributions of this paper is a detailed analysis of the resulting mean field game for the cases of both polytopic and L2 bounds on controls and disturbances. A second contribution is the establishment of a robust mean-field equilibrium, that is, a solution including the worst-case value function, the state feedback best-responses for the controlled inputs and worst-case disturbances, and a density evolution. This solution is characterized by the property that no player can benefit from a unilateral deviation even in the presence of the disturbance. As a third contribution, microscopic and macroscopic analyses are carried out to show convergence properties of the population distribution using stochastic stability theory

Detecting event-related recurrences by symbolic analysis: Applications to human language processing

Quasistationarity is ubiquitous in complex dynamical systems. In brain dynamics there is ample evidence that event-related potentials reflect such quasistationary states. In order to detect them from time series, several segmentation techniques have been proposed. In this study we elaborate a recent approach for detecting quasistationary states as recurrence domains by means of recurrence analysis and subsequent symbolisation methods. As a result, recurrence domains are obtained as partition cells that can be further aligned and unified for different realisations. We address two pertinent problems of contemporary recurrence analysis and present possible solutions for them.Comment: 24 pages, 6 figures. Draft version to appear in Proc Royal Soc

Multi-Layer Cyber-Physical Security and Resilience for Smart Grid

The smart grid is a large-scale complex system that integrates communication technologies with the physical layer operation of the energy systems. Security and resilience mechanisms by design are important to provide guarantee operations for the system. This chapter provides a layered perspective of the smart grid security and discusses game and decision theory as a tool to model the interactions among system components and the interaction between attackers and the system. We discuss game-theoretic applications and challenges in the design of cross-layer robust and resilient controller, secure network routing protocol at the data communication and networking layers, and the challenges of the information security at the management layer of the grid. The chapter will discuss the future directions of using game-theoretic tools in addressing multi-layer security issues in the smart grid.Comment: 16 page

Autonomous Robust Skill Generation Using Reinforcement Learning with Plant Variation

This paper discusses an autonomous space robot for a truss structure assembly using some reinforcement learning. It is difficult for a space robot to complete contact tasks within a real environment, for example, a peg-in-hole task, because of error between the real environment and the controller model. In order to solve problems, we propose an autonomous space robot able to obtain proficient and robust skills by overcoming error to complete a task. The proposed approach develops skills by reinforcement learning that considers plant variation, that is, modeling error. Numerical simulations and experiments show the proposed method is useful in real environments

Pursuit-Evasion Games and Zero-sum Two-person Differential Games

International audienceDifferential games arose from the investigation, by Rufus Isaacs in the 50's, of pursuit-evasion problems. In these problems, closed-loop strategies are of the essence, although defining what is exactly meant by this phrase, and what is the Value of a differential game, is difficult. For closed-loop strategies, there is no such thing as a " two-sided Maximum Principle " , and one must resort to the analysis of Isaacs' equation, a Hamilton Jacobi equation. The concept of viscosity solutions of Hamilton-Jacobi equations has helped solve several of these issues

Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems

We derive a new exact self-consistent crystalline condensate in the 1+1 dimensional chiral Gross-Neveu model. This also yields a new exact crystalline solution for the one dimensional Bogoliubov-de Gennes equations and the Eilenberger equation of semiclassical superconductivity. We show that the functional gap equation can be reduced to a solvable nonlinear equation, and discuss implications for the temperature-chemical potential phase diagram.Comment: 5 pages, 5 figures; v2 minor corrections, version for PR

Task-related modulation of anterior theta and posterior alpha EEG reflects top-down preparation

<p>Abstract</p> <p>Background</p> <p>Prestimulus EEG alpha activity in humans has been considered to reflect ongoing top-down preparation for the performance of subsequent tasks. Since theta oscillations may be related to poststimulus top-down processing, we investigated whether prestimulus EEG theta activity also reflects top-down cognitive preparation for a stimulus.</p> <p>Results</p> <p>We recorded EEG data from 15 healthy controls performing a color and shape discrimination task, and used the wavelet transformation to investigate the time course and power of oscillatory activity in the signals. We observed a relationship between both anterior theta and posterior alpha power in the prestimulus period and the type of subsequent task.</p> <p>Conclusions</p> <p>Since task-differences were reflected in both theta and alpha activities prior to stimulus onset, both prestimulus theta (particularly around the anterior region) and prestimulus alpha (particularly around the posterior region) activities may reflect prestimulus top-down preparation for the performance of subsequent tasks.</p

Inhomogeneous Condensates in the Thermodynamics of the Chiral NJL_2 model

We analyze the thermodynamical properties, at finite density and nonzero temperature, of the (1+1)-dimensional chiral Gross-Neveu model (the NJL_2 model), using the exact inhomogeneous (crystalline) condensate solutions to the gap equation. The continuous chiral symmetry of the model plays a crucial role, and the thermodynamics leads to a broken phase with a periodic spiral condensate, the "chiral spiral", as a thermodynamically preferred limit of the more general "twisted kink crystal" solution of the gap equation. This situation should be contrasted with the Gross-Neveu model, which has a discrete chiral symmetry, and for which the phase diagram has a crystalline phase with a periodic kink crystal. We use a combination of analytic, numerical and Ginzburg-Landau techniques to study various parts of the phase diagram.Comment: 28 pages, 13 figure

Event-related alpha suppression in response to facial motion

This article has been made available through the Brunel Open Access Publishing Fund.While biological motion refers to both face and body movements, little is known about the visual perception of facial motion. We therefore examined alpha wave suppression as a reduction in power is thought to reflect visual activity, in addition to attentional reorienting and memory processes. Nineteen neurologically healthy adults were tested on their ability to discriminate between successive facial motion captures. These animations exhibited both rigid and non-rigid facial motion, as well as speech expressions. The structural and surface appearance of these facial animations did not differ, thus participants decisions were based solely on differences in facial movements. Upright, orientation-inverted and luminance-inverted facial stimuli were compared. At occipital and parieto-occipital regions, upright facial motion evoked a transient increase in alpha which was then followed by a significant reduction. This finding is discussed in terms of neural efficiency, gating mechanisms and neural synchronization. Moreover, there was no difference in the amount of alpha suppression evoked by each facial stimulus at occipital regions, suggesting early visual processing remains unaffected by manipulation paradigms. However, upright facial motion evoked greater suppression at parieto-occipital sites, and did so in the shortest latency. Increased activity within this region may reflect higher attentional reorienting to natural facial motion but also involvement of areas associated with the visual control of body effectors. © 2014 Girges et al