A fundamental and well-studied problem in computational geometry is range searching, where the goal is to preprocess a set, S, of geometric objects (e.g., points in the plane) so that the subset S ′ ⊆ S that is contained in a query range (e.g., an axes-parallel rectangle) can be reported efficiently. However, in many situations, what is of interest is to generate a more informative "summary" of the output, obtained by applying a suitable aggregation function on S ′ . Examples of such aggregation functions include count, sum, min, max, mean, median, mode, and top-k that are usually computed on a set of weights defined suitably on the objects. Such range-aggregate query problems have been the subject of much recent research in both the database and the computational geometry communities.In this paper, we further generalize this line of work by considering aggregation functions on point-sets that measure the extent or "spread" of the objects in the retrieved set S ′ . The functions considered here include closest pair, diameter, and width. The challenge here is that these aggregation functions (unlike, say, count) are not efficiently decomposable in the sense that the answer to S ′ cannot be inferred easily from answers to subsets that induce a partition of S ′ . Nevertheless, we have been able to obtain space-and query-time-efficient solutions to several such problems including: closest pair queries with axes-parallel rectangles on point sets in the plane and on random point-sets in R d (d ≥ 2), closest pair queries with disks on random point-sets in the plane, diameter queries on point-sets in the plane, and guaranteedquality approximations for diameter and width queries in the plane. Our results are based on a combination of geometric techniques, including multilevel range trees, Voronoi Diagrams, Euclidean Minimum Spanning Trees, sparse representations of candidate outputs, and proofs of (expected) upper bounds on the sizes of such representations.
This paper presents a new haptic-based virtual environment system for diagnosis and rehabilitation of Traumatic Brain Injury (TBI) patients. By using the latest technologies, including Virtual Reality (VR), haptic force feedback and telecommunications, the system can work as an alternative to traditional labor intensive and expensive diagnosis and rehabilitation procedures for TBI patients. This paper also introduces a general approach to the design and prototyping of a haptic-based VR system for motor skill assessment and rehabilitation. A numerical model is presented to describe and record the motor skill assessment results and parameterize the rehabilitation training process. The prototype system demonstrates the potential for using advanced information and haptic-based VR technologies to build more effective and intelligent tools for healthcare. The specific techniques developed in this research can be used for motor-skill evaluation in clinical practice.
Abstract-Mobile robots can be used as mobile hubs to provide communication services on-demand. This capability is especially valuable in disaster response scenarios where there is no communication infrastructure. In such scenarios, mobile hubs can provide a communication infrastructure in a dynamic fashion.In this paper, we study the problem of building a communication bridge between a source s and a destination t with mobile robots. Given a set of robots P and their initial locations, our goal is to find a subset S of robots and their final locations such that the robots in S create a communication bridge between s and t in their final locations. We introduce a new optimization problem for building communication bridges. The objective is to minimize the number of hubs (i.e. |S|) while simultaneously minimizing the robots' motion. The two mobility measures studied in this paper are: (i) maximum travel distance and (ii) total travel distance of the robots. For a geometric version of the problem where the robots must move onto the line segment [s, t], we present polynomial time algorithms which use the minimum number of hubs while remaining within a constant factor of a given motion measure.Note to Practitioners -Mobile robotic hubs can provide connectivity service in applications such as disaster response where the underlying communication infrastructure is broken. In such applications, often a communication bridge between two sites (e.g. a command center and a specific site) must be established. In such scenarios, robots can autonomously deploy themselves and create a communication bridge.In this work, we study the efficient use of mobile robots to create a communication bridge between a source s and a destination t. This yields a challenging resource allocation problem in which mobility and communication constraints must be addressed simultaneously. Specifically we study the following problem: Given s and t, and the initial locations of the mobile hubs, find their final locations so as to minimize the number of hubs used in the bridge and (either maximum or total) distance traveled by the hubs. We present efficient, provably correct approximation algorithms for a special version of this optimization problem in which the hubs are required to move onto the line segment [s, t]. From a practical perspective, this special case is important because on the open plane it minimizes the overall number of hubs on the bridge. Thus, our algorithms can be used in scenarios such as robots operating in open spaces (land, water, or air). From a theoretical perspective, it provides an important first step toward the solution of the general problem where the hubs can be placed at arbitrary locations.
The T-loop may be preferred whenever minimal tipping is performed. The PG spring may be preferred over other springs whenever a higher magnitude of displacement is desired. Closed coil springs may be preferred whenever a reasonable magnitude of displacement is required and reasonable tipping is allowed.
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