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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Structured Matrices Approach for Legendre Pairs
勒让德对 结构化 矩阵方法
2023/4/17
Legendre Pairs are combinatorial objects with a rich 20+ years history. Their main application is that they furnish a structured form of the Hadamard conjecture and they have been studied by several a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Branching random walks driven by products of random matrices
随机矩阵 乘积驱动 分支随机 游走
2023/4/18
A branching random walk is a system of particles, where each particle gives birth to new particles of the next generation, which move on $\mathbb R^d$ according to some probability law. In this talk, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Products of random matrices
随机矩阵 乘积 极限定理收敛率
2023/4/19
Let $(g_n)_{n\geq 1}$ be a sequence of independent and identically distributed random matrices of type $d \times d $ with real coefficients. Consider the products $G_n : = g_n \ldots g_1$ and the rand...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Estimating Factor-Based Spot Volatility Matrices with Noisy and Asynchronous High-Frequency Data
噪声 异步高频 数据估算 因子 现货波动率 矩阵
2023/5/4
With noisy and asynchronous high-frequency data collected for an ultra-large number of assets, we estimate high-dimensional spot volatility matrices satisfying a low-rank plus sparse structure. A loca...
2018随机矩阵与自由概率论研讨会（Workshop on Random Matrices and Free Probability Theory）
2018 随机矩阵与自由概率论 研讨会
2017/12/20
The workshop will explore large-N asymptotics of random matrices, in connection with the operator-algebra models of their limiting behavior that appear in free probability theory. The behavior or rand...
Eigenvalues of products of unitary matrices and Lagrangian involutions
Unitary representations Parabolic bundles Lagrangian involutions
2015/12/17
This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a puncturedsphere with fixedlocal monodromy. The submanifoldis definedvia products of inv...
SMALL POLYNOMIAL MATRIX PRESENTATIONS OF NONNEGATIVE MATRICES
SMALL POLYNOMIAL MATRIX NONNEGATIVE MATRICES
2015/9/29
We investigate the use of polynomial matrices to give efficient presentations of nonnegative matrices exhibiting prescribed spectral and algebraic behavior.
Given square matrices B and B0 with a poset-indexed block structure (for which an ij block is zero unless i 1 j), when are there invertible matrices U and V with this required-zero-block structure suc...
PATH METHODS FOR STRONG SHIFT EQUIVALENCE OF POSITIVE MATRICES
PATH METHODS STRONG SHIFT EQUIVALENCE POSITIVE MATRICES
2015/9/29
In the early 1990’s, Kim and Roush developed path methods for establishing strong shift equivalence (SSE) of positive matrices over a dense subring U of R. This paper gives a detailed, unified and gen...
STRONG SHIFT EQUIVALENCE AND THE GENERALIZED SPECTRAL CONJECTURE FOR NONNEGATIVE MATRICES
STRONG SHIFT EQUIVALENCE GENERALIZED SPECTRAL CONJECTURE NONNEGATIVE MATRICES
2015/9/29
Given matrices A and B shift equivalent over a dense subring R of R,with A primitive, we show that B is strong shift equivalent over R to a primitive matrix. This result shows that the weak form of th...
Learning Low Rank Matrices from O(n) Entries
Random items matrix reconstruction matrix the stochastic matrix
2015/8/21
How many random entries of an n × nα, rank r matrix are necessary to reconstruct the matrix within an accuracy δ? We address this question in the case of a random matrix with bounded rank, whereby the...
Spectral Regularization Algorithms for Learning Large Incomplete Matrices
collaborative filtering nuclear norm spectral regularization netflix prize large scale convex optimization
2015/8/21
We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and...
The LASSO risk for gaussian matrices
Noisy linear observation vector image processing the matrix sequence
2015/8/20
We consider the problem of learning a coecient vector x0 2 R N from noisy linear observation y = Ax0 + w 2 R n. In many contexts (ranging from model selection to image processing) it is desirable to ...
HOPF MONOIDS FROM CLASS FUNCTIONS ON UNITRIANGULAR MATRICES
Unitriangular matrix class function superclass function
2015/8/14
We build, from the collection of all groups of unitriangular matrices, Hopf
monoids in Joyal’s category of species. Such structure is carried by the collection of
class function spaces on those grou...
THE APOLLONIAN STRUCTURE OF INTEGER SUPERHARMONIC MATRICES
APOLLONIAN STRUCTURE INTEGER SUPERHARMONIC MATRICES
2015/8/14
We prove that the set of quadratic growths attainable by integervalued superharmonic functions on the lattice Z2 has the structure of an Apollonian circle packing. This completely characterizes the PD...