A unified construction of space-time codes with optimal rate-diversity tradeoff

The problem of constructing space-time (ST) block codes over a fixed, desired signal constellation is considered. In this situation, there is a tradeoff between the transmission rate as measured in constellation symbols per channel use and the transmit diversity gain achieved by the code. The transmit diversity is a measure of the rate of polynomial decay of pairwise error probability of the code with increase in the signal-to-noise ratio (SNR). In the setting of a quasi-static channel model, let n(t) denote the number of transmit antennas and T the block interval. For any n(t) <= T, a unified construction of (n(t) x T) ST codes is provided here, for a class of signal constellations that includes the familiar pulse-amplitude (PAM), quadrature-amplitude (QAM), and 2(K)-ary phase-shift-keying (PSK) modulations as special cases. The construction is optimal as measured by the rate-diversity tradeoff and can achieve any given integer point on the rate-diversity tradeoff curve. An estimate of the coding gain realized is given. Other results presented here include i) an extension of the optimal unified construction to the multiple fading block case, ii) a version of the optimal unified construction in which the underlying binary block codes are replaced by trellis codes, iii) the providing of a linear dispersion form for the underlying binary block codes, iv) a Gray-mapped version of the unified construction, and v) a generalization of construction of the S-ary case corresponding to constellations of size S-K. Items ii) and iii) are aimed at simplifying the decoding of this class of ST codes.

A Unified Approach to Encoding and Classification Using Bimodal Projection-Based Features

In general the objective of accurately encoding the input data and the objective of extracting good features to facilitate classification are not consistent with each other. As a result, good encoding methods may not be effective mechanisms for classification. In this paper, an earlier proposed unsupervised feature extraction mechanism for pattern classification has been extended to obtain an invertible map. The method of bimodal projection-based features was inspired by the general class of methods called projection pursuit. The principle of projection pursuit concentrates on projections that discriminate between clusters and not faithful representations. The basic feature map obtained by the method of bimodal projections has been extended to overcome this. The extended feature map is an embedding of the input space in the feature space. As a result, the inverse map exists and hence the representation of the input space in the feature space is exact. This map can be naturally expressed as a feedforward neural network.

A unified approach to known and unknown cases of Berge's conjecture

Berge's elegant dipath partition conjecture from 1982 states that in a dipath partition P of the vertex set of a digraph minimizing , there exists a collection Ck of k disjoint independent sets, where each dipath P?P meets exactly min{|P|, k} of the independent sets in C. This conjecture extends Linial's conjecture, the GreeneKleitman Theorem and Dilworth's Theorem for all digraphs. The conjecture is known to be true for acyclic digraphs. For general digraphs, it is known for k=1 by the GallaiMilgram Theorem, for k?? (where ?is the number of vertices in the longest dipath in the graph), by the GallaiRoy Theorem, and when the optimal path partition P contains only dipaths P with |P|?k. Recently, it was proved (Eur J Combin (2007)) for k=2. There was no proof that covers all the known cases of Berge's conjecture. In this article, we give an algorithmic proof of a stronger version of the conjecture for acyclic digraphs, using network flows, which covers all the known cases, except the case k=2, and the new, unknown case, of k=?-1 for all digraphs. So far, there has been no proof that unified all these cases. This proof gives hope for finding a proof for all k.

Fluctuations in the alpha-effect and grand solar minima

The parameters of a special type of alpha-effect known in dynamo theory as the Babcock-Leighton mechanism are estimated using the data of sunspot catalogs. The estimates support the presence of the Babcock-Leighton alpha-effect on the Sun. Fluctuations of the alpha-effect are also estimated. The fluctuation amplitude appreciably exceeds themean value, and the characteristic time for the fluctuations is comparable to the period of the solar rotation. Fluctuations with the parameters found are included in a numericalmodel for the solar dynamo. Computations show irregular changes in the amplitudes of the magnetic cycles on time scales of centuries and millennia. The calculated statistical characteristics of the grand solar minima and maxima agree with the data on solar activity over the Holocene.

Unified Continuum Damage Model for Matrix Cracking in Composite Rotor Blades

This paper deals with modeling of the first damage mode, matrix micro-cracking, in helicopter rotor/wind turbine blades and how this effects the overall cross-sectional stiffness. The helicopter/wind turbine rotor system operates in a highly dynamic and unsteady environment leading to severe vibratory loads present in the system. Repeated exposure to this loading condition can induce damage in the composite rotor blades. These rotor/turbine blades are generally made of fiber-reinforced laminated composites and exhibit various competing modes of damage such as matrix micro-cracking, delamination, and fiber breakage. There is a need to study the behavior of the composite rotor system under various key damage modes in composite materials for developing Structural Health Monitoring (SHM) system. Each blade is modeled as a beam based on geometrically non-linear 3-D elasticity theory. Each blade thus splits into 2-D analyzes of cross-sections and non-linear 1-D analyzes along the beam reference curves. Two different tools are used here for complete 3-D analysis: VABS for 2-D cross-sectional analysis and GEBT for 1-D beam analysis. The physically-based failure models for matrix in compression and tension loading are used in the present work. Matrix cracking is detected using two failure criterion: Matrix Failure in Compression and Matrix Failure in Tension which are based on the recovered field. A strain variable is set which drives the damage variable for matrix cracking and this damage variable is used to estimate the reduced cross-sectional stiffness. The matrix micro-cracking is performed in two different approaches: (i) Element-wise, and (ii) Node-wise. The procedure presented in this paper is implemented in VABS as matrix micro-cracking modeling module. Three examples are presented to investigate the matrix failure model which illustrate the effect of matrix cracking on cross-sectional stiffness by varying the applied cyclic

Role of gas in supporting grand spiral structure

The density wave theory for the grand-design two-armed spiral pattern in galaxies is successful in explaining several observed features. However, the long-term persistence of this spiral structure is a serious problem since the group transport would destroy it within about a billion years as shown in a classic paper by Toomre. In this paper, we include the low-velocity dispersion component, namely gas, on an equal footing with stars in the formulation of the density wave theory, and obtain the dispersion relation for this coupled system. We show that the inclusion of gas makes the group transport slower by a factor of few, thus allowing the pattern to persist longer - for several billion years. Though still less than the Hubble time, this helps in making the spiral structure more long-lived. Further we show that addition of gas is essential to get a stable wave for the observed pattern speed for the Galaxy, which otherwise is not possible for a one-component stellar disc.

epsilon-expansions near three dimensions from conformal field theory

We formally extend the CFT techniques introduced in arXiv: 1505.00963, to phi(2d0/d0-2) theory in d = d(0) dimensions and use it to compute anomalous dimensions near d(0) = 3, 4 in a unified manner. We also do a similar analysis of the O(N) model in three dimensions by developing a recursive combinatorial approach for OPE contractions. Our results match precisely with low loop perturbative computations. Finally, using 3-point correlators in the CFT, we comment on why the phi(3) theory in d(0) = 6 is qualitatively different.

Transceiver designs and analysis for LTI, LTV and broadcast channels - new matrix decompositions and majorization theory

Signal processing techniques play important roles in the design of digital communication systems. These include information manipulation, transmitter signal processing, channel estimation, channel equalization and receiver signal processing. By interacting with communication theory and system implementing technologies, signal processing specialists develop efficient schemes for various communication problems by wisely exploiting various mathematical tools such as analysis, probability theory, matrix theory, optimization theory, and many others. In recent years, researchers realized that multiple-input multiple-output (MIMO) channel models are applicable to a wide range of different physical communications channels. Using the elegant matrix-vector notations, many MIMO transceiver (including the precoder and equalizer) design problems can be solved by matrix and optimization theory. Furthermore, the researchers showed that the majorization theory and matrix decompositions, such as singular value decomposition (SVD), geometric mean decomposition (GMD) and generalized triangular decomposition (GTD), provide unified frameworks for solving many of the point-to-point MIMO transceiver design problems.

In this thesis, we consider the transceiver design problems for linear time invariant (LTI) flat MIMO channels, linear time-varying narrowband MIMO channels, flat MIMO broadcast channels, and doubly selective scalar channels. Additionally, the channel estimation problem is also considered. The main contributions of this dissertation are the development of new matrix decompositions, and the uses of the matrix decompositions and majorization theory toward the practical transmit-receive scheme designs for transceiver optimization problems. Elegant solutions are obtained, novel transceiver structures are developed, ingenious algorithms are proposed, and performance analyses are derived.

The first part of the thesis focuses on transceiver design with LTI flat MIMO channels. We propose a novel matrix decomposition which decomposes a complex matrix as a product of several sets of semi-unitary matrices and upper triangular matrices in an iterative manner. The complexity of the new decomposition, generalized geometric mean decomposition (GGMD), is always less than or equal to that of geometric mean decomposition (GMD). The optimal GGMD parameters which yield the minimal complexity are derived. Based on the channel state information (CSI) at both the transmitter (CSIT) and receiver (CSIR), GGMD is used to design a butterfly structured decision feedback equalizer (DFE) MIMO transceiver which achieves the minimum average mean square error (MSE) under the total transmit power constraint. A novel iterative receiving detection algorithm for the specific receiver is also proposed. For the application to cyclic prefix (CP) systems in which the SVD of the equivalent channel matrix can be easily computed, the proposed GGMD transceiver has K/log_2(K) times complexity advantage over the GMD transceiver, where K is the number of data symbols per data block and is a power of 2. The performance analysis shows that the GGMD DFE transceiver can convert a MIMO channel into a set of parallel subchannels with the same bias and signal to interference plus noise ratios (SINRs). Hence, the average bit rate error (BER) is automatically minimized without the need for bit allocation. Moreover, the proposed transceiver can achieve the channel capacity simply by applying independent scalar Gaussian codes of the same rate at subchannels.

In the second part of the thesis, we focus on MIMO transceiver design for slowly time-varying MIMO channels with zero-forcing or MMSE criterion. Even though the GGMD/GMD DFE transceivers work for slowly time-varying MIMO channels by exploiting the instantaneous CSI at both ends, their performance is by no means optimal since the temporal diversity of the time-varying channels is not exploited. Based on the GTD, we develop space-time GTD (ST-GTD) for the decomposition of linear time-varying flat MIMO channels. Under the assumption that CSIT, CSIR and channel prediction are available, by using the proposed ST-GTD, we develop space-time geometric mean decomposition (ST-GMD) DFE transceivers under the zero-forcing or MMSE criterion. Under perfect channel prediction, the new system minimizes both the average MSE at the detector in each space-time (ST) block (which consists of several coherence blocks), and the average per ST-block BER in the moderate high SNR region. Moreover, the ST-GMD DFE transceiver designed under an MMSE criterion maximizes Gaussian mutual information over the equivalent channel seen by each ST-block. In general, the newly proposed transceivers perform better than the GGMD-based systems since the super-imposed temporal precoder is able to exploit the temporal diversity of time-varying channels. For practical applications, a novel ST-GTD based system which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD DFE transceiver is also proposed.

The third part of the thesis considers two quality of service (QoS) transceiver design problems for flat MIMO broadcast channels. The first one is the power minimization problem (min-power) with a total bitrate constraint and per-stream BER constraints. The second problem is the rate maximization problem (max-rate) with a total transmit power constraint and per-stream BER constraints. Exploiting a particular class of joint triangularization (JT), we are able to jointly optimize the bit allocation and the broadcast DFE transceiver for the min-power and max-rate problems. The resulting optimal designs are called the minimum power JT broadcast DFE transceiver (MPJT) and maximum rate JT broadcast DFE transceiver (MRJT), respectively. In addition to the optimal designs, two suboptimal designs based on QR decomposition are proposed. They are realizable for arbitrary number of users.

Finally, we investigate the design of a discrete Fourier transform (DFT) modulated filterbank transceiver (DFT-FBT) with LTV scalar channels. For both cases with known LTV channels and unknown wide sense stationary uncorrelated scattering (WSSUS) statistical channels, we show how to optimize the transmitting and receiving prototypes of a DFT-FBT such that the SINR at the receiver is maximized. Also, a novel pilot-aided subspace channel estimation algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) systems with quasi-stationary multi-path Rayleigh fading channels. Using the concept of a difference co-array, the new technique can construct M^2 co-pilots from M physical pilot tones with alternating pilot placement. Subspace methods, such as MUSIC and ESPRIT, can be used to estimate the multipath delays and the number of identifiable paths is up to O(M^2), theoretically. With the delay information, a MMSE estimator for frequency response is derived. It is shown through simulations that the proposed method outperforms the conventional subspace channel estimator when the number of multipaths is greater than or equal to the number of physical pilots minus one.

Quantum measurement of a solid-state qubit: A unified quantum master equation approach

Quantum measurement of a solid-state qubit by a mesoscopic detector is of fundamental interest in quantum physics and an essential issue in quantum computing. In this work, by employing a unified quantum master equation approach constructed in our recent publications, we study the measurement-induced relaxation and dephasing of the coupled-quantum-dot states measured by a quantum-point contact. Our treatment pays particular attention on the detailed-balance relation, which is a consequence of properly accounting for the energy exchange between the qubit and detector during the measurement process. As a result, our theory is applicable to measurement at arbitrary voltage and temperature. Both numerical and analytical results for the qubit relaxation and dephasing are carried out, and important features are highlighted in concern with their possible relevance to future experiments.

A Unified Statistical and Information Theoretic Framework for Multi-modal Image Registration

We formulate and interpret several multi-modal registration methods in the context of a unified statistical and information theoretic framework. A unified interpretation clarifies the implicit assumptions of each method yielding a better understanding of their relative strengths and weaknesses. Additionally, we discuss a generative statistical model from which we derive a novel analysis tool, the "auto-information function", as a means of assessing and exploiting the common spatial dependencies inherent in multi-modal imagery. We analytically derive useful properties of the "auto-information" as well as verify them empirically on multi-modal imagery. Among the useful aspects of the "auto-information function" is that it can be computed from imaging modalities independently and it allows one to decompose the search space of registration problems.

Getting Constitutional Theory into Proportion: A Matter of Interpretation?

Gibbs, N., Getting Constitutional Theory into Proportion: A Matter of Interpretation?, Oxford Journal of Legal Studies, 27 (1), 175-191. RAE2008

A General Theory of Semi-Unification

Various restrictions on the terms allowed for substitution give rise to different cases of semi-unification. Semi-unification on finite and regular terms has already been considered in the literature. We introduce a general case of semi-unification where substitutions are allowed on non-regular terms, and we prove the equivalence of this general case to a well-known undecidable data base dependency problem, thus establishing the undecidability of general semi-unification. We present a unified way of looking at the various problems of semi-unification. We give some properties that are common to all the cases of semi-unification. We also the principality property and the solution set for those problems. We prove that semi-unification on general terms has the principality property. Finally, we present a recursive inseparability result between semi-unification on regular terms and semi-unification on general terms.

A Neural Theory of Attentive Visual Search: Interactions of Boundary, Surface, Spatial, and Object Representations

Visual search data are given a unified quantitative explanation by a model of how spatial maps in the parietal cortex and object recognition categories in the inferotemporal cortex deploy attentional resources as they reciprocally interact with visual representations in the prestriate cortex. The model visual representations arc organized into multiple boundary and surface representations. Visual search in the model is initiated by organizing multiple items that lie within a given boundary or surface representation into a candidate search grouping. These items arc compared with object recognition categories to test for matches or mismatches. Mismatches can trigger deeper searches and recursive selection of new groupings until a target object io identified. This search model is algorithmically specified to quantitatively simulate search data using a single set of parameters, as well as to qualitatively explain a still larger data base, including data of Aks and Enns (1992), Bravo and Blake (1990), Chellazzi, Miller, Duncan, and Desimone (1993), Egeth, Viri, and Garbart (1984), Cohen and Ivry (1991), Enno and Rensink (1990), He and Nakayarna (1992), Humphreys, Quinlan, and Riddoch (1989), Mordkoff, Yantis, and Egeth (1990), Nakayama and Silverman (1986), Treisman and Gelade (1980), Treisman and Sato (1990), Wolfe, Cave, and Franzel (1989), and Wolfe and Friedman-Hill (1992). The model hereby provides an alternative to recent variations on the Feature Integration and Guided Search models, and grounds the analysis of visual search in neural models of preattentive vision, attentive object learning and categorization, and attentive spatial localization and orientation.

Grandparents and parenting: towards a theory of grandparenthood

This paper explores the changing role of contemporary grandparents with many demonstrating a willingness and ability to take on parental responsibilities for their grandchildren, where they may face challenges and opportunities in difficult times. Three main forms of grand parenting are identified in the literature, those who have primary responsibility and are raising their grand children as their main carers perhaps in response to crisis situations, those who live in extended families and participate in care, and those who provide day care while the child’s parents work. The latter has increased because of the increasing frequency of divorce, single parenting and the lack of available or subsidised child care in the United Kingdom. When grandparents step into a troubled situation and attempt to offer stability and security for their grandchildren they may have to manage the combined responsibilities of family caregivers and parental figures. Grandparenthood is a tenuous role, lacking clear agreement on behaviour norms. In the culture of advice and parenting support, while care must be taken not to undermine parenting skills or make judgements about the ability to cope with the demands of childcare, an exploration of the impact on grandparents and children must be undertaken. Due to the complex web of interrelated factors the process and outcomes of care giving by grandparents is not well known in the literature. It is proposed therefore that it is timely for research to be undertaken to explore and develop a theory of Grandparenthood.