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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some Exact Formulas of the KPZ Fixed Point and Directed Landscape
KPZ不动点 定向景观 精确公式
2023/4/18
In the past twenty years, there have been huge developments in the study of the Kardar-Parisi-Zhang (KPZ) universality class, which is a broad class of physical and probabilistic models including one-...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonsplitting of the Hilbert Exact Sequence and the Principal Chebotarev Density Theorem
希尔伯特精确序列 主切 博塔列夫密度定理 非分裂
2023/4/18
Let $K/k$ be a finite Galois extension of number fields, and let $H_K$ be the Hilbert class field of $K$. We find a way to verify the nonsplitting of the short exact sequence
New Paper Published in Nature Communications titled, “Exact exchange-correlation potentials from ground-state electron densities”
Published titled Exact potentials electron densities
2019/10/10
The quest for accurate exchange-correlation functionals has long remained a grand challenge in density functional theory (DFT), as it describes the many-electron quantum mechanical behavior through a ...
Fast Slant Stack: A notion of Radon Transform for Data in a Cartesian Grid which is Rapidly Computible, Algebraically Exact, Geometrically Faithful and Invertible
Radon Transform Projection-slice theorem Sinc-Interpolation,
2015/8/21
We define a notion of Radon Transform for data in an n by n grid. It is based on summation
along lines of absolute slope less than 1 (as a function either of x or of y), with values at non-Cart...
Exact Covariance Thresholding into Connected Components for Large-Scale Graphical Lasso
sparse inverse covariance selection sparsity graphical lasso Gaussian graphical models graph connected components concentration graph large scale covariance estimation
2015/8/21
We consider the sparse inverse covariance regularization problem or graphical lasso with regularization parameter λ. Suppose the sample covariance graph formed by thresholding the entries of the sampl...
Wavelets have motivated development of a host of new ideas in nonparametric
regression smoothing. Here we apply the tool of exact risk analysis, to understand the
small sample behavior of wavelet es...
Example of exact trade-offs in linear controller design
Linear time-invariant controller robust controller linear quadratic gaussian the numerical calculation
2015/8/13
The design of a linear time-invariant controller for a given linear-time-invariant plant, like any engineering design, involves tradeoff among many desirable qualities, such as fast response to comman...
An Exact Test for Multiple Inequality and Equality Constraints in the Linear Regression Model
Multiple Inequality Equality Constraints
2015/7/31
In this article we consider the linear regression model y = X,B + a,
where e is N(O, a21). In this context we derive exact tests of the form
H: Rft ? r versus K: f E R K for the case in which a2 i...
Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information
Random matrices free probability sparsity trigonometric expansions uncertainty principle convex optimization duality in optimization total-variation minimization image reconstruction linear programming
2015/6/17
This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal f ∈ CN and a randomly chosen set of frequencies Ω. Is it pos...
Exact Matrix Completion via Convex Optimization
Matrix completion low-rank matrices convex optimization duality in optimization nuclear norm minimization random matrices noncommutative Khintchine inequality decoupling compressed sensing
2015/6/17
We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. ...
Exact Boundary Conditions for the Initial Value Problem of Convex Conservation Laws
exact boundary conditions artificial boundary conditions convex conservation laws Burgers’ (inviscid) equation
2015/5/4
The initial value problem of convex conservation laws, which includes the famous Burgers’ (inviscid) equation, plays an important rule not only in the-oretical analysis for conservation laws, but also...
Exact D-optimal designs for response surface models on a circle
Exact D-optimal designs for response surface models on a circle
2015/3/20
Exact D-optimal designs for response surface models on a circle.
Exact solution of some new planar polygon models. Plus aspects of a ”new” SAW model
planar polygon models new SAW model
2015/3/19
Exact solution of some new planar polygon models. Plus aspects of a ”new” SAW model.
Exact Solutions to the Six-Vertex Model with Domain Wall Boundary Conditions and Uniform Asymptotics of Discrete Orthogonal Polynomials on an Infinite Lattice
Statistical Mechanics Random Matrices Orthogonal Polynomials Asymptotics Riemann-Hilbert Problems
2015/1/19
In this dissertation the partition function, $Z_n$, for the six-vertex model with domain wall boundary conditions is solved in the thermodynamic limit in various regions of the phase diagram. In the f...
Exact quantum Monte Carlo process for the statistics of discrete systems
Monte carlo and discrete quantum system statistical data the grid virtual transformation
2014/12/23
We propose an exact Monte Carlo approach for the statistics of discrete quantum systems that does not employ the standard partition of the imaginary time into a mesh and does not contain small paramet...