606 research outputs found

    Dual Descriptions of SO(10) SUSY Gauge Theories with Arbitrary Numbers of Spinors and Vectors

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    We examine the low energy structure of N=1 supersymmetric SO(10) gauge theory with matter chiral superfields in N_Q spinor and N_f vector representations. We construct a dual to this model based upon an SU(N_f+2N_Q-7) x Sp(2N_Q-2) gauge group without utilizing deconfinement methods. This product theory generalizes all previously known Pouliot-type duals to SO(N_c) models with spinor and vector matter. It also yields large numbers of new dual pairs along various flat directions. The dual description of the SO(10) theory satisfies multiple consistency checks including an intricate renormalization group flow analysis which links it with Seiberg's duality transformations. We discuss its implications for building grand unified theories that contain all Standard Model fields as composite degrees of freedom.Comment: 36 pages, harvmac and tables macros, 1 figur

    Covariance Estimation: The GLM and Regularization Perspectives

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    Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent high-dimensional data environment where enforcing the positive-definiteness constraint could be computationally expensive. We provide a survey of the progress made in modeling covariance matrices from two relatively complementary perspectives: (1) generalized linear models (GLM) or parsimony and use of covariates in low dimensions, and (2) regularization or sparsity for high-dimensional data. An emerging, unifying and powerful trend in both perspectives is that of reducing a covariance estimation problem to that of estimating a sequence of regression problems. We point out several instances of the regression-based formulation. A notable case is in sparse estimation of a precision matrix or a Gaussian graphical model leading to the fast graphical LASSO algorithm. Some advantages and limitations of the regression-based Cholesky decomposition relative to the classical spectral (eigenvalue) and variance-correlation decompositions are highlighted. The former provides an unconstrained and statistically interpretable reparameterization, and guarantees the positive-definiteness of the estimated covariance matrix. It reduces the unintuitive task of covariance estimation to that of modeling a sequence of regressions at the cost of imposing an a priori order among the variables. Elementwise regularization of the sample covariance matrix such as banding, tapering and thresholding has desirable asymptotic properties and the sparse estimated covariance matrix is positive definite with probability tending to one for large samples and dimensions.Comment: Published in at http://dx.doi.org/10.1214/11-STS358 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Low Complexity Blind Equalization for OFDM Systems with General Constellations

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    This paper proposes a low-complexity algorithm for blind equalization of data in OFDM-based wireless systems with general constellations. The proposed algorithm is able to recover data even when the channel changes on a symbol-by-symbol basis, making it suitable for fast fading channels. The proposed algorithm does not require any statistical information of the channel and thus does not suffer from latency normally associated with blind methods. We also demonstrate how to reduce the complexity of the algorithm, which becomes especially low at high SNR. Specifically, we show that in the high SNR regime, the number of operations is of the order O(LN), where L is the cyclic prefix length and N is the total number of subcarriers. Simulation results confirm the favorable performance of our algorithm

    Exact S-Matrix for 2D String Theory

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    We formulate simple graphical rules which allow explicit calculation of nonperturbative c=1c=1 SS-matrices. This allows us to investigate the constraint of nonperturbative unitarity, which indeed rules out some theories. Nevertheless, we show that there is an infinite parameter family of nonperturbatively unitary c=1c=1 SS-matrices. We investigate the dependence of the SS-matrix on one of these nonperturbative parameters. In particular, we study the analytic structure, background dependence, and high-energy behavior of some nonperturbative c=1c=1 SS-matrices. The scattering amplitudes display interesting resonant behavior both at high energies and in the complex energy plane.Comment: 42p

    Mathematical modelling techniques in process design

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    Crystal Structure of Human TWEAK in Complex with the Fab Fragment of a Neutralizing Antibody Reveals Insights into Receptor Binding.

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    The tumor necrosis factor-like weak inducer of apoptosis (TWEAK) is a multifunctional cytokine playing a key role in tissue regeneration and remodeling. Dysregulation of TWEAK signaling is involved in various pathological processes like autoimmune diseases and cancer. The unique interaction with its cognate receptor Fn14 makes both ligand and receptor promising targets for novel therapeutics. To gain insights into this important signaling pathway, we determined the structure of soluble human TWEAK in complex with the Fab fragment of an antibody selected for inhibition of receptor binding. In the crystallized complex TWEAK is bound by three Fab fragments of the neutralizing antibody. Homology modeling shows that Fab binding overlaps with the putative Fn14 binding site of TWEAK. Docking of the Fn14 cysteine rich domain (CRD) to that site generates a highly complementary interface with perfectly opposing charged and hydrophobic residues. Taken together the presented structure provides new insights into the biology of TWEAK and the TWEAK/Fn14 pathway, which will help to optimize the therapeutic strategy for treatment of related cancer types and autoimmune diseases
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