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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-...
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
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 ...
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...
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...
Exact Risk Analysis of Wavelet Regression     Orthogonal series denoising  Squared error       font style='font-size:12px;'> 2015/8/20
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...
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...
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...
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...
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. ...
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 solution of some new planar polygon models. Plus aspects of a ”new” SAW model.
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...
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...

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