Spl Rfr Research Articles

A fine-grained modality classification for global predicates

Specifying and detecting predicates in a distributed execution is an important problem. Distributed execution observation has classically used two modalities-Possibly(/spl Phi/) and Definitely(/spl Phi/)-for predicate /spl Phi/. Based on the temporal interactions of intervals, the author identified a complete, orthogonal set of relationships /spl Rfr/; between pairs of intervals in a distributed execution. We show how to map the rich, orthogonal classification of modalities of pairwise interval interactions, to the classical coarse-grained classification, Possibly(/spl Phi/) and Definitely(/spl Phi/), for specifying predicates defined on any number of processes. This increases the power of expressing the temporal modalities under which predicates can be specified, beyond the current Possibly/Definitely classification. We give some timestamp-based tests for the orthogonal modalities in the refined classification.

Pattern classification using fuzzy relational calculus

Our aim is to design a pattern classifier using fuzzy relational calculus (FRC) which was initially proposed by Pedrycz (1990). In the course of doing so, we first consider a particular interpretation of the multidimensional fuzzy implication (MFI) to represent our knowledge about the training data set. Subsequently, we introduce the notion of a fuzzy pattern vector to represent a population of training patterns in the pattern space and to denote the antecedent part of the said particular interpretation of the MFI. We introduce a new approach to the computation of the derivative of the fuzzy max-function and min-function using the concept of a generalized function. During the construction of the classifier based on FRC, we use fuzzy linguistic statements (or fuzzy membership function to represent the linguistic statement) to represent the values of features (e.g., feature F/sub 1/ is small and F/sub 2/ is big) for a population of patterns. Note that the construction of the classifier essentially depends on the estimate of a fuzzy relation /spl Rfr/ between the input (fuzzy set) and output (fuzzy set) of the classifier. Once the classifier is constructed, the nonfuzzy features of a pattern can be classified. At the time of classification of the nonfuzzy features of the testpatterns, we use the concept of fuzzy masking to fuzzify the nonfuzzy feature values of the testpatterns. The performance of the proposed scheme is tested on synthetic data. Finally, we use the proposed scheme for the vowel classification problem of an Indian language.

Numerical optimization on the euclidean group with applications to camera calibration

We present the cyclic coordinate descent (CCD) algorithm for optimizing quadratic objective functions on SE(3), and apply it to a class of robot sensor calibration problems. Exploiting the fact that SE(3) is the semidirect product of SO(3) and /spl Rfr//sup 3/, we show that by cyclically optimizing between these two spaces, global convergence can be assured under a mild set of assumptions. The CCD algorithm is also invariant with respect to choice of fixed reference frame (i.e., left invariant, as required by the principle of objectivity). Examples from camera calibration confirm the simplicity, efficiency, and robustness of the CCD algorithm on SE(3), and its wide applicability to problems of practical interest in robotics.

Statistical characterization of the Jones matrix of long fibers affected by polarization mode dispersion (PMD)

The unitary transfer matrix of a fiber affected by polarization mode dispersion (PMD) is analyzed using the Stokes representation of its eigenmodes and its retardation angle, or equivalently through its Pauli coordinates. We develop a statistical theory applied to these parameters and relate it to the extensive existing literature on the statistics of the PMD vector Dynamical equations are established for the Pauli coordinates. Assuming a standard white Gaussian model for the local birefringence, and using the tools of stochastic calculus, we derive the distributions of the eigenmodes, the retardation angle, the Pauli coordinates, and of the frequency derivatives of all these parameters. The evolution in space of the Pauli coordinates is also characterized as a standard Brownian motion on the unit sphere in /spl Rfr//sup 4/. An expression for the frequency autocorrelation function of the Pauli coordinates, the eigenmodes and the retardation angle is derived and their coherence bandwidth is compared to that of the PMD vector. All theoretical results are supported by simulation over an ensemble of 10000 fibers, using the standard retarder plate model.

Correlation of Fourier transforms of pulsed electric field waveform and microorganism inactivation

The real /spl Rfr/[F(/spl omega/)] and imaginary /spl Jfr/[F(/spl omega/)] Fourier transform parameters of temporal waveforms comparable to those used in PEF (pulsed electric field) studies of microorganism S/sub f/ (survival fraction) as a function of waveform have been calculated. log S/sub ft/ is a linear function of the log of the ratio of areas /spl Jfr/[F(/spl omega/)]//spl Rfr/[F(/spl omega/)] and log of /spl Jfr/[F(/spl omega/)]//spl Rfr/[F(/spl omega/)]+/spl Jfr/[F(/spl omega/)]. The correlation with the largest slope, was found for the latter ratio. The log (S/sub f/) also was found to correlate with the log of the integrated pulse magnitude M(/spl omega/) and log of temporal pulse area. The correlation coefficients are /spl ges/0.95.

Implementation of efficient algorithms for globally optimal trajectories

We consider a continuous space shortest path problem in a two-dimensional plane. This is the problem of finding a trajectory that starts at a given point, ends at the boundary of a compact set of /spl Rfr//sup 2/, and minimizes a cost function of the form /spl int//sub O//sup T/ r(x(t)) dt+q(x(T)). For a discretized version of this problem, a Dijkstra-like method that requires one iteration per discretization point has been developed by Tsitsiklis (1995). Here we develop some new label correcting-like methods based on the small label first methods of Bertsekas (1993) and Bertsekas et al. (1996). We prove the finite termination of these methods, and present computational results showing that they are competitive and often superior to the Dijkstra-like method and are also much faster than the traditional Jacobi and Gauss-Seidel methods.

Efficient algorithms for the minimum shortest path Steiner arborescence problem with applications to VLSI physical design

Given an undirected graph G=(V, E) with positive edge weights (lengths) /spl omega/: E/spl rarr//spl Rfr//sup +/, a set of terminals (sinks) N/spl sube/V, and a unique root node e/spl epsiv/N, a shortest path Steiner arborescence (hereafter an arborescence) is a Steiner tree rooted at, spanning all terminals in N such that every source-to-sink path is a shortest path in G. Given a triple (G, N, r), the minimum shortest path Steiner arborescence (MSPSA) problem seeks an arborescence with minimum weight. The MSPSA problem has various applications in the areas of physical design of very large-scale integrated circuits (VLSI), multicast network communication, and supercomputer message routing; various eases have been studied in the literature. In this paper, we propose several heuristics and exact algorithms for the MSPSA problem with applications to VLSI physical design. Experiments indicate that our heuristics generate near optimal results and achieve speedups of orders of magnitude over existing algorithms.

Gauss-Markov random fields (CMrf) with continuous indices

Gauss-Markov random fields (GMrfs) play an important role in the modeling of physical phenomena. The paper addresses the second-order characterization and the sample path description of GMrf's when the indexing parameters take values in bounded subsets of /spl Rfr//sup d/, d/spl ges/1. Using results of Pitt (1994), we give conditions for the covariance of a GMrf to be the Green's function of a partial differential operator and, conversely, for the Green's function of an operator to be the covariance of a GMrf. We then develop a minimum mean square error representation for the field in terms of a partial differential equation driven by correlated noise. The paper establishes for GMrf's on /spl Rfr//sup d/ second-order characterizations that parallel the corresponding results for GMrf's on finite lattices.

The min-max function differentiation and training of fuzzy neural networks

This paper discusses the Delta-rule and training of min-max neural networks by developing a differentiation theory for min-max functions, the functions containing min (wedge) and/or max (V) operations. We first prove that under certain conditions all min-max functions are continuously differentiable almost everywhere in the real number field R and derive the explicit formulas for the differentiation. These results are the basis for developing the Delta-rule for the training of min-max neural networks. The convergence of the new Delta-rule is proved theoretically using the stochastic theory, and is demonstrated with a simulation example.

Learning separations by Boolean combinations of half-spaces

Given two subsets S/sub 1/ and S/sub 2/ (not necessarily finite) of /spl Rfr//sup d/ separable by a Boolean combination of learning half-spaces, the authors consider the problem of (in the sense of Valiant) the separation function from a finite set of examples, i.e., they produce with a high probability a function close to the actual separating function. The authors' solution consists of a system of N perceptrons and a single consolidator which combines the outputs of the individual perceptrons; it is shown that an off-line version of this problem, where the examples are given in a batch, can be solved in time polynomial in the number of examples. The authors also provide an on-line learning algorithm that incrementally solves the problem by suitably training a system of N perceptrons much in the spirit of the classical perceptron learning algorithm. >

Restrictions on the weight distribution of binary linear codes imposed by the structure of Reed-Muller codes

The words of a binary linear /spl lsqb/n, k/spl rsqb/ code C whose weights belong to a given subset I/spl sub//spl lcub/0,1,...,n/spl rcub/ constitute a word in a certain Reed-Muller code /spl Rfr//spl Mfr/(r, k). Appropriate choices of I result in low values of the order r and thus yield restrictions on the weight distribution of C. >