Reaching an Optimal Consensus: Dynamical Systems that Compute Intersections of Convex Sets

In this paper, multi-agent systems minimizing a sum of objective functions, where each component is only known to a particular node, is considered for continuous-time dynamics with time-varying interconnection topologies. Assuming that each node can observe a convex solution set of its optimization component, and the intersection of all such sets is nonempty, the considered optimization problem is converted to an intersection computation problem. By a simple distributed control rule, the considered multi-agent system with continuous-time dynamics achieves not only a consensus, but also an optimal agreement within the optimal solution set of the overall optimization objective. Directed and bidirectional communications are studied, respectively, and connectivity conditions are given to ensure a global optimal consensus. In this way, the corresponding intersection computation problem is solved by the proposed decentralized continuous-time algorithm. We establish several important properties of the distance functions with respect to the global optimal solution set and a class of invariant sets with the help of convex and non-smooth analysis

Virtual reality and consciousness inference in dreaming

This article explores the notion that the brain is genetically endowed with an innate virtual reality generator that – through experience-dependent plasticity – becomes a generative or predictive model of the world. This model, which is most clearly revealed in rapid eye movement (REM) sleep dreaming, may provide the theater for conscious experience. Functional neuroimaging evidence for brain activations that are time-locked to rapid eye movements (REMs) endorses the view that waking consciousness emerges from REM sleep – and dreaming lays the foundations for waking perception. In this view, the brain is equipped with a virtual model of the world that generates predictions of its sensations. This model is continually updated and entrained by sensory prediction errors in wakefulness to ensure veridical perception, but not in dreaming. In contrast, dreaming plays an essential role in maintaining and enhancing the capacity to model the world by minimizing model complexity and thereby maximizing both statistical and thermodynamic efficiency. This perspective suggests that consciousness corresponds to the embodied process of inference, realized through the generation of virtual realities (in both sleep and wakefulness). In short, our premise or hypothesis is that the waking brain engages with the world to predict the causes of sensations, while in sleep the brain’s generative model is actively refined so that it generates more efficient predictions during waking. We review the evidence in support of this hypothesis – evidence that grounds consciousness in biophysical computations whose neuronal and neurochemical infrastructure has been disclosed by sleep research

Re-Examining the Association Between Unexpected Earnings and Abnormal Security Returns in the Present of Financial Leverage

This study re-examines the theoretical prediction of Dhaliwal et al. (1991) about the association between leverage and earnings response coefficients (ERCs). Since leverage and default risk are endogenous, the estimation using leverage to proxy for default risk may produce biased results. We use a propensity score matching method to deal with this endogeneity and introduce dividend payouts as another proxy for default risk. We find that higher default risk firms are consistently associated with lower ERCs. Our findings suggest that a combination of dividend payouts and leverage is a more refined proxy for default risk

Preface: Special Topic on Supramolecular Self-Assembly at Surfaces

Supramolecular self-assembly at surfaces is one of the most exciting and active fields in Surface Science today. Applications can take advantage of two key properties: (i) versatile pattern formation over a broad length scale and (ii) tunability of electronic structure and transport properties, as well as frontier orbital alignment. It provides a new frontier for Chemical Physics as it uniquely combines the versatility of Organic Synthesis and the Physics of Interfaces. The Journal of Chemical Physics is pleased to publish this Special Topic Issue, showcasing recent advances and new directions