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We propose a novel method for the extraction of unresolved point sources from CMB maps. This method is based on the analysis of the phase distribution of the Fourier components for the observed signal and unlike most other methods of…
Motivated by the spurious variance loss encountered during covariance propagation in atmospheric and other large-scale data assimilation systems, we consider the problem for state dynamics governed by the continuity and related hyperbolic…
Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…
In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions…
A theory of nonlinear signal propagation in multi-span wavelength division multiplexed coherent transmission systems that employ the semiconductor optical amplifier as in-line amplifiers is presented for the first time. The rigorous…
We establish explicit lower bounds for advection-diffusion equations in three settings: a polynomial $\dot H^{-1}$ bound for inviscid shears with $u\in L^\infty_t W^{1,1}_y$, a uniform positive lower bound on the mixing scale for diffusive…
In our companion paper "Multidimensional rational covariance extension with applications to spectral estimation and image compression" we discussed the multidimensional rational covariance extension problem (RCEP), which has important…
Recently anomaly detection (AD) has become an important application for target detection in hyperspectral remotely sensed images. In many applications, in addition to high accuracy of detection we need a fast and reliable algorithm as well.…
We experimentally validate a machine learning-enabled Raman amplification framework, capable of jointly shaping the signal power evolution in two domains: frequency and fiber distance. The proposed experiment addresses the amplification in…
Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…
Intersecting manifold segmentation has been a focus of research, where individual manifolds, that intersect with other manifolds, are separated to discover their distinct properties. The proposed method is based on the intuition that when a…
The extended Davis-Kahan theorem makes use of polynomial matrix transformations to produce bounds at least as tight as the standard Davis-Kahan theorem. The optimization problem of finding transformation parameters resulting in optimal…
For high-dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and noise accumulation. Therefore, researchers proposed independence rules to…
AdamW has become one of the most effective optimizers for training large-scale models. We have also observed its effectiveness in the context of federated learning (FL). However, directly applying AdamW in federated learning settings poses…
We apply the stationary phase method developed in (Assier, Shanin \& Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by a quarter-plane. The wave field is written as a double Fourier transform of an unknown spectral…
In certain scientific domains, there is a need for tensor operations. To facilitate tensor computations,computer algebra systems are employed. In our research, we have been using Cadabra as the main computer algebra system for several…
In this work we train three decision-tree based ensemble machine learning algorithms (Random Forest Classifier, Adaptive Boosting and Gradient Boosting Decision Tree respectively) to study quasar selection in the variable source catalog in…
Recent research in feature learning has been extended to sequence data, where each instance consists of a sequence of heterogeneous items with a variable length. However, in many real-world applications, the data exists in the form of…
Various technologies, including computer vision models, are employed for the automatic monitoring of manual assembly processes in production. These models detect and classify events such as the presence of components in an assembly area or…
Global expression analyses using microarray technologies are becoming more common in genomic research, therefore, new statistical challenges associated with combining information from multiple studies must be addressed. In this paper we…