Related papers: Estimation of the infinitesimal generator by squar…
We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact…
Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…
Several finite difference methods are proposed for the infinitesimal generator of 1D asymmetric $\alpha$-stable L\'{e}vy motions, based on the fact that the operator becomes a multiplier in the spectral space. These methods take the general…
In nonequilibrium statistical physics, quantifying the nearest (and higher-order) neighbors and free volumes of particles in many-body systems is crucial to elucidating the origin of macroscopic collective phenomena, such as glass/granular…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to…
Consider the mutually catalytic branching process with finite branching rate $\gamma$. We show that as $\gamma\to\infty$, this process converges in finite-dimensional distributions (in time) to a certain discontinuous process. We give…
Spectral gaps, Kramers escape rates, and position-dependent relaxation timescales are dynamical invariants encoded in the infinitesimal generator $\Lop$ of a stochastic flow. We show that weak projection of the governing It\^{o} SDE onto…
This paper introduces a general method to approximate the convolution of an arbitrary program with a Gaussian kernel. This process has the effect of smoothing out a program. Our compiler framework models intermediate values in the program…
Strategies for the generation of periodic discrete structures with identical two-point correlation are developed. Starting from a pair of root structures, which are not related by translation, phase inversion or axis reflections, child…
In this paper we answer the following question: what is the infinitesimal generator of the diffusion process defined by a kernel that is normalized such that it is bi-stochastic with respect to a specified measure? More precisely, under the…
We develop an accelerated algorithm for computing an approximate eigenvalue decomposition of bistochastic normalized kernel matrices. Our approach constructs a low rank approximation of the original kernel matrix by the pivoted partial…
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…
Coarse-grained models are a core computational tool in theoretical chemistry and biophysics. A judicious choice of a coarse-grained model can yield physical insight by isolating the essential degrees of freedom that dictate the…
The infinitesimal generator of a one-dimensional strictly $\alpha$-stable process can be represented as a weighted sum of (right and left) Riemann-Liouville fractional derivatives of order $\alpha$ and one obtains the fractional Laplacian…
In all but special circumstances, measurements of time-dependent processes reflect internal structures and correlations only indirectly. Building predictive models of such hidden information sources requires discovering, in some way, the…
Dielectric microstructures have generated much interest in recent years as a means of accelerating charged particles when powered by solid state lasers. The acceleration gradient (or particle energy gain per unit length) is an important…
The quasicontinuum approximation is a method to reduce the atomistic degrees of freedom of a crystalline solid by piecewise linear interpolation from representative atoms that are nodes for a finite element triangulation. In regions of the…
This report presents some fundamental mathematical results towards elucidating the information-geometric underpinnings of evolutionary modelling schemes for (quasi-)stationary discrete stochastic processes. The model class under…
We present an alternative way to determine the unknown parameter associated to a gaussian approximation in a generic two-dimensional model. Instead of the standard variational approach, we propose a procedure based on a quantitative…