Abstract:
Let $k$ be a field. Then Gaussian elimination over $k$ and the Euclidean division algorithm for the univariate polynomial ring $k[x]$ allow us to write any matrix in $SL_n(k)$ or $SL_n(k[x])$, $n\geq 2$, as a product of elementary matrices. Suslin's stability theorem states that the same is true for the multivariate polynomial ring $SL_n(k[x_1,\ldots ,x_m])$ with $n\geq 3$. As Gaussian elimination gives us an algorithmic way of finding an explicit factorization of the given matrix into elementary matrices over a field, we develop a similar algorithm over polynomial rings.

Abstract:
Traditional approaches to quantifier scope typically need stipulation to exclude readings that are unavailable to human understanders. This paper shows that quantifier scope phenomena can be precisely characterized by a semantic representation constrained by surface constituency, if the distinction between referential and quantificational NPs is properly observed. A CCG implementation is described and compared to other approaches.

Abstract:
We describe a class of supersymmetric gauged linear sigma-model, whose target space is the infinite dimensional space of bundles on a Calabi-Yau 3- or 2-fold. This target space can be considered the configuration space of D-branes wrapped around the Calabi-Yau. We propose that this model can be used to define matrix string theory compactifications. In the infrared limit the model flows to a superconformal non-linear sigma-model whose target space is the moduli space of BPS configurations of branes on the compact space, containing the moduli space of semi-stable bundles. We argue that the bulk degrees of freedom decouple in the infrared limit if semi-stability implies stability. We study topological versions of the model on Calabi-Yau 3-folds. The resulting B-model is argued to be equivalent to the holomorphic Chern-Simons theory proposed by Witten. The A-model and half-twisted model define the quantum cohomology ring and the elliptic genus, respectively, of the moduli space of stable bundles on a Calabi-Yau 3-fold.

Abstract:
We investigate the gravitational lensing properties of dark matter halos with Burkert profiles. We derive an analytic expression for the lens equation and use it to compute the magnification, impact parameter and image separations for strong lensing. For the scaling relation that provides the best fits to spiral-galaxy rotation curve data, Burkert halos will not produce strong lensing, even if this scaling relation extends up to masses of galaxy clusters. Tests of a simple model of an exponential stellar disk superimposed on a Burkert-profile halo demonstrate that strong lensing is unlikely without an additional concentration of mass in the galaxy center (e.g. a bulge). The fact that most strong lenses on galactic scales are elliptical galaxies suggests that a strong central concentration of baryons is required to produce image splitting. This solution is less attractive for clusters of galaxies, which are generally considered to be dark-matter dominated even at small radii. There are three possible implications of these results: (1) dark halos may have a variety of inner profiles (2) dark matter halos may not follow a single scaling relation from galaxy scale up to cluster scale and/or (3) the splitting of images (even by clusters of galaxies) may in general be due to the central concentration of baryonic material in halos rather than dark matter.

Abstract:
The influences of an impurity on the spin and the charge transport of one-dimensional antisymmetric spin filter are investigated using bosonization and Keldysh formulation and the results are highlighted against those of spinful Luttinger liquids. Due to the dependence of the electron spin orientation on wave number the spin transport is not affected by the impurity, while the charge transport is essentially identical with that of spinless one-dimensional Luttinger liquid.

Abstract:
It is found that the induced gravity with conformal couplings requires the conformal invariance in both classical and quantum levels for consistency. This is also true for the induced gravity with an extended conformal coupling interacting with torsion.

Abstract:
A ground state energy variational calculation of anyon gas with Hamiltonian included the interaction of spins of particles with anyon vector potential induced, i.e. statistical, magnetic field exhibits exact cancelation of terms connected with fractional statistics. This leads to bosonization of anyons due to coupling of their spins with statistical magnetic field. We presume that at the dense gas fluctuations of effective spins destroy the coupling and bosons become anyons. At the assumption that pseudogap (PG) boundary is temperature independent and when anyons are fermions we use this model to interpret experimental phase diagrams of Tallon and Loram hole and electron doped High-T_c superconductors below PG energy E_g and find the qualitative and quantitative agreement. We do the hypothesis that phase transition (PT) of bosons into Bose-Einstein condensate is not of second order, but of first order, close to second one, PG regime is meta stable phase of bosons, and E_g=0 is the critical point of this PT. Bosons undergo PT into fermions on PG boundary. Described in the literature non-Fermi quasi-particles might be related to bosons with effective spins.

Abstract:
This paper studies a network of observers for a distributed estimation problem, where each observer assesses a portion of output of a given LTI system. The goal of each observer is to compute a state estimate that asymptotically converges to the state of the LTI system. We consider there is a sparsity constraint that restricts interconnections between observers. We provide a sufficient condition for the existence of parameters for the observers which achieve the convergence of the state estimates to the state of the LTI system. In particular, this condition can be written in terms of the eigenvalues of the Laplacian matrix of the underlying communication graph and the spectral radius of the dynamic matrix of the LTI system.

Abstract:
Although deep convolutional neural networks(CNNs) have achieved remarkable results on object detection and segmentation, pre- and post-processing steps such as region proposals and non-maximum suppression(NMS), have been required. These steps result in high computational complexity and sensitivity to hyperparameters, e.g. thresholds for NMS. In this work, we propose a novel end-to-end trainable deep neural network architecture, which consists of convolutional and recurrent layers, that generates the correct number of object instances and their bounding boxes (or segmentation masks) given an image, using only a single network evaluation without any pre- or post-processing steps. We have tested on detecting digits in multi-digit images synthesized using MNIST, automatically segmenting digits in these images, and detecting cars in the KITTI benchmark dataset. The proposed approach outperforms a strong CNN baseline on the synthesized digits datasets and shows promising results on KITTI car detection.