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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse problem for the harmonic measure
谐波测量 反问题 双曲群
2023/4/17
Sample paths of a random walk on a hyperbolic group are known to converge to the Gromov boundary. The distribution of the exit point is called the harmonic measure. I will discuss the following invers...
We show that the simple group PSL2(Fp) occurs as the Galois group of an extensionof the rationals for all primes p ≥ 5. We obtain our Galois extensions by studying the Galois action on the second étal...
MODULAR FORMS AND SOME CASES OF THE INVERSE GALOIS PROBLEM
MODULAR FORMS SOME CASES INVERSE GALOIS PROBLEM
2015/8/26
We prove new cases of the inverse Galois problem by considering the residual Galois representations arising from a fixed newform. Specific choices of weight 3 newforms will show thatthere are Galois e...
Inverse semigroups determined by their partial automorphism monoids
Inverse semigroups partial automorphism monoids Rings and Algebras
2011/9/20
Abstract: The partial automorphism monoid of an inverse semigroup is an inverse monoid consisting of all isomorphisms between its inverse subsemigroups. We prove that a tightly connected fundamental i...
Abstract: A partial automorphism of a semigroup $S$ is any isomorphism between its subsemigroups, and the set all partial automorphisms of $S$ with respect to composition is the inverse monoid called ...
The Convex Geometry of Linear Inverse Problems
Convex optimization semidefinite programming atomic norms
2011/1/17
In applications throughout science and engineering one is often faced with the challenge of
solving an ill-posed inverse problem, where the number of available measurements is smaller
than the dimen...
An Inverse Power Method for Nonlinear Eigenproblems with Applications in 1-Spectral Clustering and Sparse PCA
Inverse Power Method for Nonlinear Eigenproblems Applications 1-Spectral Clustering Sparse PCA
2011/3/2
Many problems in machine learning and statistics can be formulated as (generalized)eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding crit...
Let W be a complete local commutative Noetherian ring with residue field k of positive characteristic p. We study the inverse problem for the versal deformation rings RW(, V )
relative to W...
Regularization of statistical inverse problems and the Bakushinskii veto
statistical inverse problems the Bakushinskii veto
2010/11/22
In the deterministic context Bakushinskii's theorem excludes the existence of purely data driven convergent regularization for ill-posed problems. We will prove in the present work that in the statist...
Generalized $1$-harmonic Equation and The Inverse Mean Curvature Flow
Generalized $1$-harmonic Equation The Inverse Mean Curvature Flow
2010/11/19
We introduce and study generalized $1$-harmonic equations (1.1). Using some ideas and techniques in studying $1$-harmonic functions from [W1] (2007), and in studying nonhomogeneous $1$-harmonic funct...
The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initi...
Suppose $\mathbf{F}$ is a field different from $\mathbf{F}_{2},$ the field with two elements. Let $M_{n}(\mathbf{F})$ and $S_{n}(\mathbf{{F})}$ be the space of $n\times n$ full matrices and the spac...
On the Block Independence in $G$-Inverse and Reflexive Inner Inverse of A Partitioned Matrix
$G$-inverse reflexive inner inverse partitioned matrices block independence QQQQQ-SVD
2007/12/11
By applying the multiple quotient singular value decomposition QQQQQ-SVD, we study the block independence in $g$-inverse and reflexive inner inverse of $2\times 2$ partitioned matrices, and prove a co...
Generalized Inverse Estimator and comparison with Least Squares Estimator
Inverse Estimator Least Squares Estimator
2010/3/4
Trenkler [13] described an iteration estimator. This estimator is defined as follows: for 0 < g < 1/li \max \[ \hat{b}m, g = g \summi=0 (1-g X'X)i X'y , \] where li are eigenvalues of X'X. In this pap...
