Algebraic Approaches to Space-Time Code Construction for Multiple-Antenna Communication

A major challenge in wireless communications is overcoming the deleterious effects of fading, a phenomenon largely responsible for the seemingly inevitable dropped call. Multiple-antennas communication systems, commonly referred to as MIMO systems, employ multiple antennas at both transmitter and receiver, thereby creating a multitude of signalling pathways between transmitter and receiver. These multiple pathways give the signal a diversity advantage with which to combat fading. Apart from helping overcome the effects of fading, MIMO systems can also be shown to provide a manyfold increase in the amount of information that can be transmitted from transmitter to receiver. Not surprisingly,MIMO has played, and continues to play, a key role in the advancement of wireless communication.Space-time codes are a reference to a signalling format in which information about the message is dispersed across both the spatial (or antenna) and time dimension. Algebraic techniques drawing from algebraic structures such as rings, fields and algebras, have been extensively employed in the construction of optimal space-time codes that enable the potential of MIMO communication to be realized, some of which have found their way into the IEEE wireless communication standards. In this tutorial article, reflecting the authors’interests in this area, we survey some of these techniques.

A study of symbolic processing and computational aspects in helicopter dynamics

Even research models of helicopter dynamics often lead to a large number of equations of motion with periodic coefficients; and Floquet theory is a widely used mathematical tool for dynamic analysis. Presently, three approaches are used in generating the equations of motion. These are (1) general-purpose symbolic processors such as REDUCE and MACSYMA, (2) a special-purpose symbolic processor, DEHIM (Dynamic Equations for Helicopter Interpretive Models), and (3) completely numerical approaches. In this paper, comparative aspects of the first two purely algebraic approaches are studied by applying REDUCE and DEHIM to the same set of problems. These problems range from a linear model with one degree of freedom to a mildly non-linear multi-bladed rotor model with several degrees of freedom. Further, computational issues in applying Floquet theory are also studied, which refer to (1) the equilibrium solution for periodic forced response together with the transition matrix for perturbations about that response and (2) a small number of eigenvalues and eigenvectors of the unsymmetric transition matrix. The study showed the following: (1) compared to REDUCE, DEHIM is far more portable and economical, but it is also less user-friendly, particularly during learning phases; (2) the problems of finding the periodic response and eigenvalues are well conditioned.

Single-resolution and multiresolution extended-Kalman-filter-based reconstruction approaches to optical refraction tomography

The problem of reconstruction of a refractive-index distribution (RID) in optical refraction tomography (ORT) with optical path-length difference (OPD) data is solved using two adaptive-estimation-based extended-Kalman-filter (EKF) approaches. First, a basic single-resolution EKF (SR-EKF) is applied to a state variable model describing the tomographic process, to estimate the RID of an optically transparent refracting object from noisy OPD data. The initialization of the biases and covariances corresponding to the state and measurement noise is discussed. The state and measurement noise biases and covariances are adaptively estimated. An EKF is then applied to the wavelet-transformed state variable model to yield a wavelet-based multiresolution EKF (MR-EKF) solution approach. To numerically validate the adaptive EKF approaches, we evaluate them with benchmark studies of standard stationary cases, where comparative results with commonly used efficient deterministic approaches can be obtained. Detailed reconstruction studies for the SR-EKF and two versions of the MR-EKF (with Haar and Daubechies-4 wavelets) compare well with those obtained from a typically used variant of the (deterministic) algebraic reconstruction technique, the average correction per projection method, thus establishing the capability of the EKF for ORT. To the best of our knowledge, the present work contains unique reconstruction studies encompassing the use of EKF for ORT in single-resolution and multiresolution formulations, and also in the use of adaptive estimation of the EKF's noise covariances. (C) 2010 Optical Society of America

Fuzzy Logic-Based Approaches in Water Resource System Modelling

Recent research in modelling uncertainty in water resource systems has highlighted the use of fuzzy logic-based approaches. A number of research contributions exist in the literature that deal with uncertainty in water resource systems including fuzziness, subjectivity, imprecision and lack of adequate data. This chapter presents a broad overview of the fuzzy logic-based approaches adopted in addressing uncertainty in water resource systems modelling. Applications of fuzzy rule-based systems and fuzzy optimisation are then discussed. Perspectives on the scope for further research are presented.

An algebraic theory of functional and multivalued dependencies in relational databases

Computation of the dependency basis is the fundamental step in solving the membership problem for functional dependencies (FDs) and multivalued dependencies (MVDs) in relational database theory. We examine this problem from an algebraic perspective. We introduce the notion of the inference basis of a set M of MVDs and show that it contains the maximum information about the logical consequences of M. We propose the notion of a dependency-lattice and develop an algebraic characterization of inference basis using simple notions from lattice theory. We also establish several interesting properties of dependency-lattices related to the implication problem. Founded on our characterization, we synthesize efficient algorithms for (a): computing the inference basis of a given set M of MVDs; (b): computing the dependency basis of a given attribute set w.r.t. M; and (c): solving the membership problem for MVDs. We also show that our results naturally extend to incorporate FDs also in a way that enables the solution of the membership problem for both FDs and MVDs put together. We finally show that our algorithms are more efficient than existing ones, when used to solve what we term the ‘generalized membership problem’.

Algebraic and geometric intersection numbers for free groups

We show that the algebraic intersection number of Scott and Swarup for splittings of free groups Coincides With the geometric intersection number for the sphere complex of the connected sum of copies of S-2 x S-1. (C) 2009 Elsevier B.V. All rights reserved.

Bayesian and Decision Tree Approaches for Pattern Recognition Including Feature Measurement Costs

The minimum cost classifier when general cost functionsare associated with the tasks of feature measurement and classification is formulated as a decision graph which does not reject class labels at intermediate stages. Noting its complexities, a heuristic procedure to simplify this scheme to a binary decision tree is presented. The optimizationof the binary tree in this context is carried out using ynamicprogramming. This technique is applied to the voiced-unvoiced-silence classification in speech processing.

Algebraic characterization of decentralized fixed modes

An input-output, frequency-domain characterization of decentralized fixed modes is given in this paper, using only standard block-diagram algebra, well-known determinantal expansions and the Binet-Cauchy formula.

Algebraic design techniques for reliable stabilization

In this paper we study two problems in feedback stabilization. The first is the simultaneous stabilization problem, which can be stated as follows. Given plantsG_{0}, G_{1},..., G_{l}, does there exist a single compensatorCthat stabilizes all of them? The second is that of stabilization by a stable compensator, or more generally, a "least unstable" compensator. Given a plantG, we would like to know whether or not there exists a stable compensatorCthat stabilizesG; if not, what is the smallest number of right half-place poles (counted according to their McMillan degree) that any stabilizing compensator must have? We show that the two problems are equivalent in the following sense. The problem of simultaneously stabilizingl + 1plants can be reduced to the problem of simultaneously stabilizinglplants using a stable compensator, which in turn can be stated as the following purely algebraic problem. Given2lmatricesA_{1}, ..., A_{l}, B_{1}, ..., B_{l}, whereA_{i}, B_{i}are right-coprime for alli, does there exist a matrixMsuch thatA_{i} + MB_{i}, is unimodular for alli?Conversely, the problem of simultaneously stabilizinglplants using a stable compensator can be formulated as one of simultaneously stabilizingl + 1plants. The problem of determining whether or not there exists anMsuch thatA + BMis unimodular, given a right-coprime pair (A, B), turns out to be a special case of a question concerning a matrix division algorithm in a proper Euclidean domain. We give an answer to this question, and we believe this result might be of some independent interest. We show that, given twon times mplantsG_{0} and G_{1}we can generically stabilize them simultaneously provided eithernormis greater than one. In contrast, simultaneous stabilizability, of two single-input-single-output plants, g0and g1, is not generic.

Tuning of PID controllers for water networks—different approaches

Better operational control of water networks can help reduce leakage, maintain pressure, and control flow. Proportional integral derivative (PID) controllers, with proper fine-tuning, can help water utility operators achieve targets faster without creating undue transients. The authors compared three tuning methods, in different test situations, involving flow and level control to different reservoirs. Although target values were reached with all three tuning methods, the methods’ performances varied significantly. The lowest performer among the three was the method most widely used in the industry—standard tuning by the Ziegler-Nichols method. Achieving better results was offline tuning by genetic algorithms. Achieving the best control, though, was a fuzzy logic–based online tuning approach—the FZPID controller. The FZPID controller had fewer overshoots and took significantly less time to tune the gains for each problem. This new tuning approach for PID controllers can be applied to a variety of problems and can increase the performance of water networks of any size and structure

Some direct numerical approaches to the solution of the singular nonlinear transonic integral equation

The nonlinear singular integral equation of transonic flow is examined, noting that standard numerical techniques are not applicable in solving it. The difficulties in approximating the integral term in this expression were solved by special methods mitigating the inaccuracies caused by standard approximations. It was shown how the infinite domain of integration can be reduced to a finite one; numerical results were plotted demonstrating that the methods proposed here improve accuracy and computational economy.

An algebraic algorithm for the design and analysis of linear dynamical systems

In an earlier paper [1], it has been shown that velocity ratio, defined with reference to the analogous circuit, is a basic parameter in the complete analysis of a linear one-dimensional dynamical system. In this paper it is shown that the terms constituting velocity ratio can be readily determined by means of an algebraic algorithm developed from a heuristic study of the process of transfer matrix multiplication. The algorithm permits the set of most significant terms at a particular frequency of interest to be identified from a knowledge of the relative magnitudes of the impedances of the constituent elements of a proposed configuration. This feature makes the algorithm a potential tool in a first approach to a rational design of a complex dynamical filter. This algorithm is particularly suited for the desk analysis of a medium size system with lumped as well as distributed elements.

An algebraic approach to the restoration of images

Two different matrix algorithms are described for the restoration of blurred pictures. These are illustrated by numerical examples.

Embryogenesis in flowering plants: Recent approaches and prospects

The overall architectural pattern of the mature plant is established during embryogenesis. Very little is known about the molecular processes that underlie embryo morphogenesis. Last decade has, nevertheless, seen a burst of information on the subject. The synchronous somatic embryogenesis system of carrot is largely being used as the experimental system. Information on the molecular regulation of embryogenesis obtained with carrot somatic embryos as well as observations on sandalwood embryogenic system developed in our laboratory are summarized in this review. The basic experimental strategy of molecular analysis mostly relied on a comparison between genes and proteins being expressed in embryogenic and non-embryogenic cells as well as in the different stages of embryogenesis. Events such as expression of totipotency of cells and establishment of polarity which are so critical for embryo development have been characterized using the strategy, Several genes have been identified and cloned from the carrot system, These include sequences that encode certain extracellular proteins (EPs) that influence cell proliferation and embryogenesis in specific ways and sequences of the abscisic acid (ABA) inducible late embryogenesis abundant (LEA) proteins which are most abundant and differentially expressed mRNAs in somatic embryos. That LEAs are expressed in the somatic embryos of a tree flora also is evidenced from studies on sandalwood Several undescribed or novel sequences that are enhanced in embryos were identified. A sequence of this nature exists in sandalwood embryos was demonstrated using a Cuscuta haustorial (organ-specific) cDNA probe. Somatic embryogenesis systems have been used to assess the expression of genes isolated from non-embryogenic tissues. Particular attention has been focused on both cell cycle and histone genes.