Related papers: Lattices Without a Big Constant and With Noise
We consider the problem of finding the minimum of inhomogeneous Gaussian lattice sums: Given a lattice $L \subseteq \mathbb{R}^n$ and a positive constant $\alpha$, the goal is to find the minimizers of $\sum_{x \in L} e^{-\alpha \|x -…
Consider the design based situation where an $r$-regular set is sampled on a random lattice. A fast algorithm for estimating the integrated mean curvature based on this observation is to use a weighted sum of $2\times \dotsm \times 2$…
The spectral gradient method is known to be a powerful low-cost tool for solving large-scale optimization problems. In this paper, our goal is to exploit its advantages in the stochastic optimization framework, especially in the case of…
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
We propose a new pivotal method for estimating high-dimensional matrices. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A\_0$ corrupted by noise. We propose a new method for estimating…
In this manuscript, a purely data driven statistical regularization method is proposed for extracting the information from big data with randomly distributed noise. Since the variance of the noise maybe large, the method can be regarded as…
We present a lattice formulation of non-Abelian Lifshitz-type gauge theories. Due to anisotropic scaling of space and time, the theory is asymptotically free even in five dimensions. We show results of Monte Carlo simulations that suggest a…
The evaluation of abstractive summarization models typically uses test data that is identically distributed as training data. In real-world practice, documents to be summarized may contain input noise caused by text extraction artifacts or…
In this paper, we develop a sliding method for the fractional Laplacian. We first obtain the key ingredients needed in the sliding method either in a bounded domain or in the whole space, such as narrow region principles and maximum…
Implicit samplers are algorithms for producing independent, weighted samples from multi-variate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two…
In this paper we explore some applications of a certain technique (that we call the Freese's technique), which is a tool for identifying certain lattices as sublattices of the congruence lattice of a given algebra. In particular we will…
We have developed a new method that uses wavelet analysis to remove interference fringe patterns from images. This method is particularly useful for flat fields in the common case where fringes vary between the calibration and object data.…
We propose a determinant-free approach for simulation-based Bayesian inference in high-dimensional Gaussian models. We introduce auxiliary variables with covariance equal to the inverse covariance of the model. The joint probability of the…
Lattice Field theory allows to extract properties of particles in strongly coupled quantum field theories by studying Euclidean vacuum expectation values. When estimated from numerical Monte Carlo simulations these are typically affected by…
Lattice simulation of supersymmetric gauge theories is not straightforward. In some cases the lack of manifest supersymmetry just necessitates cumbersome fine-tuning, but in the worse cases the chiral and/or Majorana nature of fermions…
In the present paper, employing properties of the complete elliptic integrals of the first and second kind, we deduce closed-form formulae for the lattice sums and other new formulae. Applications to the effective properties of regular and…
Scalings in which the graph Laplacian approaches a differential operator in the large graph limit are used to develop understanding of a number of algorithms for semi-supervised learning; in particular the extension, to this graph setting,…
We consider the problem of reconstructing a low rank matrix from noisy observations of a subset of its entries. This task has applications in statistical learning, computer vision, and signal processing. In these contexts, "noise"…
We leverage generative large language models for language learning applications, focusing on estimating the difficulty of foreign language texts and simplifying them to lower difficulty levels. We frame both tasks as prediction problems and…
We develop a lensless compressive imaging architecture, which consists of an aperture assembly and a single sensor, without using any lens. An anytime algorithm is proposed to reconstruct images from the compressive measurements; the…