A procedure concept for local reflex control of grasping

An architecture is proposed for the control of robotic devices, and in particular of anthropomorphic hands, characterized by a hierarchical structure in which every level of the architecture contains data and control function with varying degree of abstraction. Bottom levels of the hierarchy interface directly with sensors and actuators, and process raw data and motor commands. Higher levels perform more symbolic types of tasks, such as application of boolean rules and general planning operations. Layers implementation has to be consistent with the type of operation and its requirements for real time control. It is proposed to implement the rule level with a Boolean Artificial Neural Network characterized by a response time sufficient for producing reflex corrective action at the actuator level

Diversifying Top-K Results

Top-k query processing finds a list of k results that have largest scores w.r.t the user given query, with the assumption that all the k results are independent to each other. In practice, some of the top-k results returned can be very similar to each other. As a result some of the top-k results returned are redundant. In the literature, diversified top-k search has been studied to return k results that take both score and diversity into consideration. Most existing solutions on diversified top-k search assume that scores of all the search results are given, and some works solve the diversity problem on a specific problem and can hardly be extended to general cases. In this paper, we study the diversified top-k search problem. We define a general diversified top-k search problem that only considers the similarity of the search results themselves. We propose a framework, such that most existing solutions for top-k query processing can be extended easily to handle diversified top-k search, by simply applying three new functions, a sufficient stop condition sufficient(), a necessary stop condition necessary(), and an algorithm for diversified top-k search on the current set of generated results, div-search-current(). We propose three new algorithms, namely, div-astar, div-dp, and div-cut to solve the div-search-current() problem. div-astar is an A* based algorithm, div-dp is an algorithm that decomposes the results into components which are searched using div-astar independently and combined using dynamic programming. div-cut further decomposes the current set of generated results using cut points and combines the results using sophisticated operations. We conducted extensive performance studies using two real datasets, enwiki and reuters. Our div-cut algorithm finds the optimal solution for diversified top-k search problem in seconds even for k as large as 2,000.Comment: VLDB201

On fractional GJMS operators

We describe a new interpretation of the fractional GJMS operators as generalized Dirichlet-to-Neumann operators associated to weighted GJMS operators on naturally associated smooth metric measure spaces. This gives a geometric interpretation of the Caffarelli--Silvestre extension for $(-\Delta)^\gamma$ when $\gamma\in(0,1)$, and both a geometric interpretation and a curved analogue of the higher order extension found by R. Yang for $(-\Delta)^\gamma$ when $\gamma>1$. We give three applications of this correspondence. First, we exhibit some energy identities for the fractional GJMS operators in terms of energies in the compactified Poincar\'e--Einstein manifold, including an interpretation as a renormalized energy. Second, for $\gamma\in(1,2)$, we show that if the scalar curvature and the fractional $Q$-curvature $Q_{2\gamma}$ of the boundary are nonnegative, then the fractional GJMS operator $P_{2\gamma}$ is nonnegative. Third, by assuming additionally that $Q_{2\gamma}$ is not identically zero, we show that $P_{2\gamma}$ satisfies a strong maximum principle.Comment: 38 pages. Final version, to appear in Communications on Pure and Applied Mathematic

Adaptive Complex Contagions and Threshold Dynamical Systems

A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are static. In this paper we extend current theory of finite dynamical systems to cover dynamic thresholds. Three classes of parallel and sequential dynamic threshold systems are introduced and analyzed. Our main result, which is a complete characterization of their attractor structures, show that sequential systems may only have fixed points as limit sets whereas parallel systems may only have period orbits of size at most two as limit sets. The attractor states are characterized for general graphs and enumerated in the special case of paths and cycle graphs; a computational algorithm is outlined for determining the number of fixed points over a tree. We expect our results to be relevant for modeling a broad class of biological, behavioral and socio-technical systems where adaptive behavior is central.Comment: Submitted for publicatio

Application of Computable General Equilibrium Model to Derive Impacts of Surface Water Reallocation Policy

Resource /Energy Economics and Policy,