Stability of Zeno Equilibria in Lagrangian Hybrid Systems

This paper presents both necessary and sufficient conditions for the stability of Zeno equilibria in Lagrangian hybrid systems, i.e., hybrid systems modeling mechanical systems undergoing impacts. These conditions for stability are motivated by the sufficient conditions for Zeno behavior in Lagrangian hybrid systems obtained in [11]—we show that the same conditions that imply the existence of Zeno behavior near Zeno equilibria imply the stability of the Zeno equilibria. This paper, therefore, not only presents conditions for the stability of Zeno equilibria, but directly relates the stability of Zeno equilibria to the existence of Zeno behavior

Statistics of the Island-Around-Island Hierarchy in Hamiltonian Phase Space

The phase space of a typical Hamiltonian system contains both chaotic and regular orbits, mixed in a complex, fractal pattern. One oft-studied phenomenon is the algebraic decay of correlations and recurrence time distributions. For area-preserving maps, this has been attributed to the stickiness of boundary circles, which separate chaotic and regular components. Though such dynamics has been extensively studied, a full understanding depends on many fine details that typically are beyond experimental and numerical resolution. This calls for a statistical approach, the subject of the present work. We calculate the statistics of the boundary circle winding numbers, contrasting the distribution of the elements of their continued fractions to that for uniformly selected irrationals. Since phase space transport is of great interest for dynamics, we compute the distributions of fluxes through island chains. Analytical fits show that the "level" and "class" distributions are distinct, and evidence for their universality is given.Comment: 31 pages, 13 figure

Co-detection of acoustic emissions during failure of heterogeneous media: new perspectives for natural hazard early warning

A promising method for real time early warning of gravity driven rupture that considers both the heterogeneity of natural media and characteristics of acoustic emissions attenuation is proposed. The method capitalizes on co-detection of elastic waves emanating from micro-cracks by multiple and spatially separated sensors. Event co-detection is considered as surrogate for large event size with more frequent co-detected events marking imminence of catastrophic failure. Using a spatially explicit fiber bundle numerical model with spatially correlated mechanical strength and two load redistribution rules, we constructed a range of mechanical failure scenarios and associated failure events (mapped into AE) in space and time. Analysis considering hypothetical arrays of sensors and consideration of signal attenuation demonstrate the potential of the co-detection principles even for insensitive sensors to provide early warning for imminent global failure

Geometric control of particle manipulation in a two-dimensional fluid

Manipulation of particles suspended in fluids is crucial for many applications, such as precision machining, chemical processes, bio-engineering, and self-feeding of microorganisms. In this paper, we study the problem of particle manipulation by cyclic fluid boundary excitations from a geometric-control viewpoint. We focus on the simplified problem of manipulating a single particle by generating controlled cyclic motion of a circular rigid body in a two-dimensional perfect fluid. We show that the drift in the particle location after one cyclic motion of the body can be interpreted as the geometric phase of a connection induced by the system's hydrodynamics. We then formulate the problem as a control system, and derive a geometric criterion for its nonlinear controllability. Moreover, by exploiting the geometric structure of the system, we explicitly construct a feedback-based gait that results in attraction of the particle towards the rigid body. We argue that our gait is robust and model-independent, and demonstrate it in both perfect fluid and Stokes fluid

Dilemma that cannot be resolved by biased quantum coin flipping

We show that a biased quantum coin flip (QCF) cannot provide the performance of a black-boxed biased coin flip, if it satisfies some fidelity conditions. Although such a QCF satisfies the security conditions of a biased coin flip, it does not realize the ideal functionality, and therefore, does not fulfill the demands for universally composable security. Moreover, through a comparison within a small restricted bias range, we show that an arbitrary QCF is distinguishable from a black-boxed coin flip unless it is unbiased on both sides of parties against insensitive cheating. We also point out the difficulty in developing cheat-sensitive quantum bit commitment in terms of the uncomposability of a QCF.Comment: 5 pages and 1 figure. Accepted versio

Formal and practical completion of Lagrangian hybrid systems

This paper presents a method for completing Lagrangian hybrid systems models in a formal manner. That is, given a Lagrangian hybrid system, i.e., a hybrid system that models a mechanical system undergoing impacts, we present a systematic method in which to extend executions of this system past Zeno points by adding an additional domain to the hybrid model. Moreover, by utilizing results that provide sufficient conditions for Zeno behavior and for stability of Zeno equilibria in Lagrangian hybrid systems, we are able to give explicit bounds on the error incurred through the practical simulation of these completed hybrid system models. These ideas are illustrated on a series of examples, and are shown to be consistent with observed reality

Back testing multi asset value at risk : Norwegian data

This paper attempts to e stimate Value At Risk (VaR) for a multi asset Norwegian portfolio, using some of the most popular estimation methods , Variance Covariance Method, Historical Simulation and Monte Carlo Simulation . The Variance Covariance Method is applied with both time varying and constant volatility . Each VaR estimation method ’ s accurac y is tested , using Kupiec’s univariate test ing framework , for multiple single points in the left tail of the portfolio’s return distribution, and Pérignon and Smith ’s multivariate framework for a larger subset of the left tail. It compares each method ’s ov erall results for the Norwegian portfolio with those found by Wu et al. (2012) on a similar Taiwanese portfolio . And finally , based on the empirical testing , it attempts to draw a conclusion on which method is best suited for Norwegian data

Stability and Completion of Zeno Equilibria in Lagrangian Hybrid Systems

This paper studies Lagrangian hybrid systems, which are a special class of hybrid systems modeling mechanical systems with unilateral constraints that are undergoing impacts. This class of systems naturally display Zeno behavior-an infinite number of discrete transitions that occur in finite time, leading to the convergence of solutions to limit sets called Zeno equilibria. This paper derives simple conditions for stability of Zeno equilibria. Utilizing these results and the constructive techniques used to prove them, the paper introduces the notion of a completed hybrid system which is an extended hybrid system model allowing for the extension of solutions beyond Zeno points. A procedure for practical simulation of completed hybrid systems is outlined, and conditions guaranteeing upper bounds on the incurred numerical error are derived. Finally, we discuss an application of these results to the stability of unilaterally constrained motion of mechanical systems under perturbations that violate the constraint

Strategies for Scaleable Communication and Coordination in Multi-Agent (UAV) Systems

A system is considered in which agents (UAVs) must cooperatively discover interest-points (i.e., burning trees, geographical features) evolving over a grid. The objective is to locate as many interest-points as possible in the shortest possible time frame. There are two main problems: a control problem, where agents must collectively determine the optimal action, and a communication problem, where agents must share their local states and infer a common global state. Both problems become intractable when the number of agents is large. This survey/concept paper curates a broad selection of work in the literature pointing to a possible solution; a unified control/communication architecture within the framework of reinforcement learning. Two components of this architecture are locally interactive structure in the state-space, and hierarchical multi-level clustering for system-wide communication. The former mitigates the complexity of the control problem and the latter adapts to fundamental throughput constraints in wireless networks. The challenges of applying reinforcement learning to multi-agent systems are discussed. The role of clustering is explored in multi-agent communication. Research directions are suggested to unify these components