18123350
Generalized distance functions
We obtain a generalized version of the well-known distance function family L/sub p/ norm. We prove that the new functions satisfy distance function properties. By using these functions, convex symmetric shapes can be described as loci, the set of points which are in equal distance from a given point. We also show that these symmetric convex shapes can be easily parameterized. We also show these distance functions satisfy a Lipschitz-type condition. We provide a fast ray marching algorithm for rendering shapes described by these distance functions. These distance functions can be used as building blocks for some implicit modeling tools such as soft objects, constructive soft geometry, function representations (freps) or ray quadrics.
5242879
Interactive rind modeling
In this paper, we describe a technique, with roots in topological graph theory, that we call rind modeling. It provides for the easy creation of surfaces resembling peeled and punctured rinds. We show how the method's two main steps of: 1) creation of a shell or crust like the rind of an orange, and 2) opening holes in the crust by punching or peeling can be encapsulated into a real time semi-automatic interactive algorithm. We include a number of worked examples, some by students in a first modeling course, that demonstrate the ease with which a large variety of intricate rind shapes can be created.
31382426
Strong Fault-Tolerance: Parallel Routing in Networks with Faults
A d-regular network G is strongly fault-tolerant if for any copy Gf of G with at most d - 2 faulty nodes, every pair of nonfaulty nodes u and v in Gf admits min{df(u), df (v)} node-disjoint paths in Gf from u to v, where df(u) and df(v) are the degrees of the nodes u and v in Gf. We show that popular network structures, such as hypercube and star networks, are strongly fault-tolerant. We develop efficient algorithms that construct the maximum number of node-disjoint paths of optimal or nearly optimal length in these networks with faulty nodes. Our algorithms are optimal in terms of their running time.
16331940
Optimal Parallel Routing in Star Networks
Star networks have recently been proposed as attractive alternatives to the popular hypercube for interconnecting processors on a parallel computer. In this paper, we present an efficient algorithm that constructs an optimal parallel routing in star networks. Our result improves previous results for the problem.
1021255
A minimal and complete set of operators for the development of robust manifold mesh modelers
In this paper, we identify a minimal and complete set of fundamental operators, which is necessary and sufficient for performing all homeomorphic and topological operations on 2- manifold mesh structures. Efficient algorithms are developed for the implementation of these operators. We also developed a set of powerful, user-friendly, and effective operators at the level of user-interface. Using these operators, we have developed a prototype system for robust, interactive, and user-friendly modeling of orientable 2-manifold meshes. Users of our system can perform a large set of homeomorphic and topological changes with these user-interface level operators. Our system is topologically robust in the sense that users will never create invalid 2-manifold mesh structure with these operators. In our system, the homeomorphic and topological surgery operations can be applied alternatively on 2-manifold meshes. With our system, users can blend surfaces, construct rinds, and open holes on these rind shapes. With our system, the shapes that look like solid, non-manifold, or 2-manifold with boundary can be manipulated. The system also provides automatic texture mapping during topology changes.
2261180
Graph Ear Decompositions and Graph Embeddings
Ear decomposition of a graph has been extensively studied in relation to graph connectivity. In this paper, a connection of ear decomposition to graph embeddings is exhibited. It is shown that constructing a maximum-paired ear decomposition of a graph and constructing a maximum-genus embedding of the graph are polynomial-time equivalent. Applications of this connection are discussed.
38425768
The Logic of Only Knowing as a Unified Framework for Non-Monotonic Reasoning
We propose to use the logic of only knowing (OL) by Levesque [6] as a unified framework that encompasses various non-monotonic formalisms and logic programming. OL is a modal logic which can be used to formalize an agent's introspective reasoning and to answer epistemic queries to databases. The OL logic allows one to formally express the statement “α is all I know” (in symbols, Oα) and to perform inferencing based on only-knowing, which is very useful for commonsense reasoning. Another nice thing about the OL logic is that it has a clear model-theoretic semantics and a simple proof theory, which is sound for the quantificational case, and both sound and complete for the prepositional case.
41316192
Efficient Learning of Pseudo-Boolean Functions from Limited Training Data
Pseudo-Boolean functions are generalizations of Boolean functions. We present a new method for learning pseudo-Boolean functions from limited training data. The objective of learning is to obtain a function f which is a good approximation of the target function f*. We define suitable criteria for the “goodness” of an approximating function. One criterion is to choose a function f that minimizes the “expected distance” with respect to a distance function d (over pairs of pseudo-Boolean functions) and the uniform distribution over all feasible pseudo-Boolean functions. We define two alternative “distance measures” over pairs of pseudo-Boolean functions, and show that they are are actually equivalent with respect to the criterion of minimal expected distance. We outline efficient algorithms for learning pseudo-Boolean functions according to these criteria. Other reasonable distance measures and “goodness” criteria are also discussed.
16592812
A web-based virtual laboratory on a frequency modulation experiment
With the rapid proliferation of Internet technologies, accessing and operating engineering instruments remotely anytime anywhere is fast becoming a reality. This paper presents a new Web-based virtual laboratory on a frequency modulation experiment for the teaching of an undergraduate course on communication principles in the National University of Singapore (NUS). The laboratory requires only a common Web browser to access and incorporate schemes for reducing data traffic and authenticating users. It enables students to have a natural hands-on experience of using an expensive spectrum analyzer on a one-to-one basis and provides a solution for distant engineering education. The system uses a double client-server structure where access to the experiment is via two rounds of client-server processing. The virtual laboratory can be accessed at the Web site http://vlab.ee.nus.edu.sg/vlab/freqmod/index.html.
5704334
Making subsequence time series clustering meaningful
The startling claim was made that sequential time series clustering is meaningless. This has important consequences for a significant amount of work in the literature, since such a claim invalidates this work's contribution. In this paper, we show that sequential time series clustering is not meaningless, and that the problem highlighted in these works stem from their use of the Euclidean distance metric as the distance measure in the subsequence vector space. As a solution, we consider quite a general class of time series, and propose a regime based on two types of similarity that can exist between subsequence vectors, which give rise naturally to an alternative distance measure to Euclidean distance in the subsequence vector space. We show that, using this alternative distance measure, sequential time series clustering can indeed be meaningful. We repeat a key experiment in the work on which the "meaningless" claim was based, and show that our method leads to a successful clustering outcome.
11313417
Correlated MIMO Rayleigh fading systems with transmit channel state information
We analyze the capacity of correlated multiple-input-multiple-output (MIMO) channels when channel state information (CSI) is available at both the transmitter and the receiver. We show that the achievable rate by using simple beamforming can approach this capacity when the MIMO channels are highly correlated. To simplify the coding/decoding and power adaption, we apply truncated channel inversion (TCI) in MIMO correlated channels and evaluate the achievable rates. The results show that in highly correlated MIMO fading channels, beamforming combined with TCI can get close to capacity. This provides a simplified near optimum coding, as beamforming with TCI requires only one code designed for the AWGN channel and one coder/decoder pair.