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High Dimensional Normality of Noisy Eigenvectors
We study joint eigenvector distributions for large symmetric matrices in the presence of weak noise. Our main result asserts that every submatrix in the orthogonal matrix of eigenvectors converges toExpand
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Distribution of orders in number fields
AbstractIn this paper, we study the distribution of orders of bounded discriminants in number fields. We use the zeta functions introduced by Grunewald, Segal, and Smith. In order to carry out ourExpand
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Antitussive activity of Althaea officinalis L. polysaccharide rhamnogalacturonan and its changes in guinea pigs with ovalbumine-induced airways inflammation.
AIM The presented studies were aimed on experimental confirmation of Althaea officinalis polysaccharide rhamnogalacturonan antitussive effect and its changes in conditions of allergic inflammation.Expand
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An Improved Lower Bound for Sparse Reconstruction from Subsampled Hadamard Matrices
TLDR
We give a short argument that yields a new lower bound on the number of subsampled rows from a bounded, orthonormal matrix necessary to form a matrix with the restricted isometry property. Expand
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Systematyka gleb Polski
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Sparse Reconstruction from Hadamard Matrices: A Lower Bound
TLDR
We give a short argument that yields a new lower bound on the number of subsampled rows from a bounded, orthonormal matrix necessary to form a matrix with the restricted isometry property. Expand
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Counting Subrings of ${\mathbb Z}^n$ of finite index
In this article we investigate the number of subrings of $\Z^d$ using subring zeta functions and $p$-adic integration.
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Elliptic Curves and the Mordell-Weil Theorem
This paper introduces the notion of elliptic curves with an emphasis on elliptic curves defined over Q and their rational points. Some algebraic number theory and algebraic geometry is developed inExpand
Comparison theorem for some extremal eigenvalue statistics
We introduce a method for the comparison of some extremal eigenvalue statistics of random matrices. For example, it allows one to compare the maximal eigenvalue gap in the bulk of two generalizedExpand
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Eigenvector Statistics of L\'{e}vy Matrices
We analyze statistics for eigenvector entries of heavy-tailed random symmetric matrices (also called Levy matrices) whose associated eigenvalues are sufficiently small. We show that the limiting lawExpand
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