A Fast Linear Separability Test by Projection of Positive Points on Subspaces

A geometric and non parametric procedure for testing if two finite set of points are linearly separable is proposed. The Linear Separability Test is equivalent to a test that determines if a strictly positive point h > 0 exists in the range of a matrix A (related to the points in the two finite sets). The algorithm proposed in the paper iteratively checks if a strictly positive point exists in a subspace by projecting a strictly positive vector with equal co-ordinates (p), on the subspace. At the end of each iteration, the subspace is reduced to a lower dimensional subspace. The test is completed within r ≤ min(n, d + 1) steps, for both linearly separable and non separable problems (r is the rank of A, n is the number of points and d is the dimension of the space containing the points). The worst case time complexity of the algorithm is O(nr3) and space complexity of the algorithm is O(nd). A small review of some of the prominent algorithms and their time complexities is included. The worst case computational complexity of our algorithm is lower than the worst case computational complexity of Simplex, Perceptron, Support Vector Machine and Convex Hull Algorithms, if d

A fast algorithm for finding frequent episodes in event streams

Frequent episode discovery is a popular framework for mining data available as a long sequence of events. An episode is essentially a short ordered sequence of event types and the frequency of an episode is some suitable measure of how often the episode occurs in the data sequence. Recently,we proposed a new frequency measure for episodes based on the notion of non-overlapped occurrences of episodes in the event sequence, and showed that, such a definition, in addition to yielding computationally efficient algorithms, has some important theoretical properties in connecting frequent episode discovery with HMM learning. This paper presents some new algorithms for frequent episode discovery under this non-overlapped occurrences-based frequency definition. The algorithms presented here are better (by a factor of N, where N denotes the size of episodes being discovered) in terms of both time and space complexities when compared to existing methods for frequent episode discovery. We show through some simulation experiments, that our algorithms are very efficient. The new algorithms presented here have arguably the least possible orders of spaceand time complexities for the task of frequent episode discovery.

Fast-Group-Decodable STBCs via Codes over GF(4): Further Results

Recently in, a framework was given to construct low ML decoding complexity Space-Time Block Codes (STBCs) via codes over the finite field F4. In this paper, we construct new full-diversity STBCs with cubic shaping property and low ML decoding complexity via codes over F4 for number of transmit antennas N = 2m, m >; 1, and rates R >; 1 complex symbols per channel use. The new codes have the least ML decoding complexity among all known codes for a large set of (N, R) pairs. The new full-rate codes of this paper (R = N) are not only information-lossless and fully diverse but also have the least known ML decoding complexity in the literature. For N ≥ 4, the new full-rate codes are the first instances of full-diversity, information-lossless STBCs with low ML decoding complexity. We also give a sufficient condition for STBCs obtainable from codes over F4 to have cubic shaping property, and a sufficient condition for any design to give rise to a full-diversity STBC when the symbols are encoded using rotated square QAM constellations.

Asymptotically-Optimal, Fast-Decodable, Full-Diversity STBCs

For a family/sequence of Space-Time Block Codes (STBCs) C1, C2,⋯, with increasing number of transmit antennas Ni, with rates Ri complex symbols per channel use (cspcu), i = 1,2,⋯, the asymptotic normalized rate is defined as limi→∞ Ri/Ni. A family of STBCs is said to be asymptotically-good if the asymptotic normalized rate is non-zero, i.e., when the rate scales as a non-zero fraction of the number of transmit antennas, and the family of STBCs is said to be asymptotically-optimal if the asymptotic normalized rate is 1, which is the maximum possible value. In this paper, we construct a new class of full-diversity STBCs that have the least maximum-likelihood (ML) decoding complexity among all known codes for any number of transmit antennas N>;1 and rates R>;1 cspcu. For a large set of (R,N) pairs, the new codes have lower ML decoding complexity than the codes already available in the literature. Among the new codes, the class of full-rate codes (R=N) are asymptotically-optimal and fast-decodable, and for N>;5 have lower ML decoding complexity than all other families of asymptotically-optimal, fast-decodable, full-diversity STBCs available in the literature. The construction of the new STBCs is facilitated by the following further contributions of this paper: (i) Construction of a new class of asymptotically-good, full-diversity multigroup ML decodable codes, that not only includes STBCs for a larger set of antennas, but also either matches in rate or contains as a proper subset all other high-rate or asymptotically-good, delay-optimal, multigroup ML decodable codes available in the literature. (ii) Construction of a new class of fast-group-decodable codes (codes that combine the low ML decoding complexity properties of multigroup ML decodable codes and fast-decodable codes) for all even number of transmit antennas and rates 1 <; R ≤ 5/4.- - (iii) Given a design with full-rank linear dispersion matrices, we show that a full-diversity STBC can be constructed from this design by encoding the real symbols independently using only regular PAM constellations.

Fast Direct Torque Control of an Open-End Induction Motor Drive Using 12-Sided Polygonal Voltage Space Vectors

A torque control scheme, based on a direct torque control (DTC) algorithm using a 12-sided polygonal voltage space vector, is proposed for a variable speed control of an open-end induction motor drive. The conventional DTC scheme uses a stator flux vector for the sector identification and then the switching vector to control stator flux and torque. However, the proposed DTC scheme selects switching vectors based on the sector information of the estimated fundamental stator voltage vector and its relative position with respect to the stator flux vector. The fundamental stator voltage estimation is based on the steady-state model of IM and the synchronous frequency of operation is derived from the computed stator flux using a low-pass filter technique. The proposed DTC scheme utilizes the exact positions of the fundamental stator voltage vector and stator flux vector to select the optimal switching vector for fast control of torque with small variation of stator flux within the hysteresis band. The present DTC scheme allows full load torque control with fast transient response to very low speeds of operation, with reduced switching frequency variation. Extensive experimental results are presented to show the fast torque control for speed of operation from zero to rated.

NMR methods for fast data acquisition

NMR spectroscopy has witnessed tremendous advancements in recent years with the development of new methodologies for structure determination and availability of high-field strength spectrometers equipped with cryogenic probes. Supported by these advancements, a new dimension in NMR research has emerged which aims to increase the speed with data is collected and analyzed. Several novel methodologies have been proposed in this direction. This review focuses on the principles on which these different approaches are based with an emphasis on G-matrix Fourier transform NMR spectroscopy.

Fast Robust Pattern Classification Algorithms for Real Time Neuro-Motor Prosthetic Applications

In this paper, we give a brief review of pattern classification algorithms based on discriminant analysis. We then apply these algorithms to classify movement direction based on multivariate local field potentials recorded from a microelectrode array in the primary motor cortex of a monkey performing a reaching task. We obtain prediction accuracies between 55% and 90% using different methods which are significantly above the chance level of 12.5%.

A simple and fast scheme for code compression for VLIW processors

Summary form only given. A scheme for code compression that has a fast decompression algorithm, which can be implemented using simple hardware, is proposed. The effectiveness of the scheme on the TMS320C62x architecture that includes the overheads of a line address table (LAT) is evaluated and obtained compression rates ranging from 70% to 80%. Two schemes for decompression are proposed. The basic idea underlying the scheme is a simple clustering algorithm that partially maps a block of instructions into a set of clusters. The clustering algorithm is a greedy algorithm based on the frequency of occurrence of various instructions.

Fast algorithms for frequent episode discovery in event sequences

In this paper we consider the process of discovering frequent episodes in event sequences. The most computationally intensive part of this process is that of counting the frequencies of a set of candidate episodes. We present two new frequency counting algorithms for speeding up this part. These, referred to as non-overlapping and non-inteleaved frequency counts, are based on directly counting suitable subsets of the occurrences of an episode. Hence they are different from the frequency counts of Mannila et al [1], where they count the number of windows in which the episode occurs. Our new frequency counts offer a speed-up factor of 7 or more on real and synthetic datasets. We also show how the new frequency counts can be used when the events in episodes have time-durations as well.

An Opportunistic, Fast, and Distributed Subchannel and User-Pairing Algorithm for OFDMA

Channel-aware assignment of subchannels to users in the downlink of an OFDMA system requires extensive feedback of channel state information (CSI) to the base station. Since bandwidth is scarce, schemes that limit feedback are necessary. We develop a novel, low feedback, distributed splitting-based algorithm called SplitSelect to opportunistically assign each subchannel to its most suitable user. SplitSelect explicitly handles multiple access control aspects associated with CSI feedback, and scales well with the number of users. In it, according to a scheduling criterion, each user locally maintains a scheduling metric for each subchannel. The goal is to select, for each subchannel, the user with the highest scheduling metric. At any time, each user contends for the subchannel for which it has the largest scheduling metric among the unallocated subchannels. A tractable asymptotic analysis of a system with many users is central to SplitSelect's simple design. Extensive simulation results demonstrate the speed with which subchannels and users are paired. The net data throughput, when the time overhead of selection is accounted for, is shown to be substantially better than several schemes proposed in the literature. We also show how fairness and user prioritization can be ensured by suitably defining the scheduling metric.