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We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…
Scan line levelling, a ubiquitous and often necessary step in AFM data processing, can cause a severe bias on measured roughness parameters such as mean square roughness or correlation length. Although bias estimates have been formulated,…
Relighting of human images enables post-photography editing of lighting effects in portraits. The current mainstream approach uses neural networks to approximate lighting effects without explicitly accounting for the principle of physical…
We propose and investigate two new methods to approximate $f({\bf A}){\bf b}$ for large, sparse, Hermitian matrices ${\bf A}$. The main idea behind both methods is to first estimate the spectral density of ${\bf A}$, and then find…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
The push to train ever larger neural networks has motivated the study of initialization and training at large network width. A key challenge is to scale training so that a network's internal representations evolve nontrivially at all…
When measuring the roughness of rough surfaces, the limited sizes of scanned areas lead to its systematic underestimation. Levelling by polynomials and other filtering used in real-world processing of atomic force microscopy data increases…
The price of instruments and observing time on modern telescopes is quickly increasing with the size of the primary mirror. Therefore, it is worth revisiting the data reduction algorithms to extract every bit of scientific information from…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data,…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
Spectral algorithms leverage spectral regularization techniques to analyze and process data, providing a flexible framework for addressing supervised learning problems. To deepen our understanding of their performance in real-world…
Images taken with modern detectors require calibration via flat fielding to obtain the same flux scale across the whole image. One method for obtaining the best possible flat fielding accuracy is to derive a photometric model from dithered…
The spectral analysis of the electromagnetic field on the background of a infinitely thin flat plasma layer is carried out. This model is loosely imitating a single base plane from graphite and it is of interest for theoretical studies of…
This paper proposes a sparse regression method that continuously interpolates between Forward Stepwise selection (FS) and the LASSO. When tuned appropriately, our solutions are much sparser than typical LASSO fits but, unlike FS fits,…
Graph is a highly generic and diverse representation, suitable for almost any data processing problem. Spectral graph theory has been shown to provide powerful algorithms, backed by solid linear algebra theory. It thus can be extremely…
The spectral clustering algorithm is often used as a binary clustering method for unclassified data by applying the principal component analysis. To study theoretical properties of the algorithm, the assumption of conditional…
An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of…
The paper aims at removing the aliasing effects of the whole focal stack generated from a sparse-sampled {4D} light field, while keeping the consistency across all the focal layers. We first explore the structural characteristics embedded…
Astrophysical explorations are underpinned by large-scale stellar spectroscopy surveys, necessitating a paradigm shift in spectral fitting techniques. Our study proposes three enhancements to transcend the limitations of the current…