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SIMNRA is widely adopted by the scientific community of ion beam analysis for interpretation of nuclear scattering analysis. Taking advantage of its recognized reliability and quality of the simulations, we developed a computer program that…
The recent introduction of portable, low-field MRI (LF-MRI) into the clinical setting has the potential to transform neuroimaging. However, LF-MRI is limited by lower resolution and signal-to-noise ratio, leading to incomplete…
In this article two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz (MERA). The Tucker core tensor is…
The connection between multiple modular L-functions, as defined by Manin in [5], and modular iterated integrals was made explicit by Choie and Ihara [3] under the restrictive assumption that all modular forms involved have vanishing…
Multifunction radars (MFR) are met with complex capability requirements, involving various kinds of targets and saturating scenarios. In order to achieve these goals, radar systems use Active Electronically Scanned Array (AESA) to switch…
A rotational modulator (RM) gamma-ray imager is capable of obtaining significantly better angular resolution than the fundamental geometric resolution defined by the ratio of detector diameter to mask-detector separation. An RM imager…
We present an algorithm using transformation groups and their irreducible representations to generate an orthogonal basis for a signal in the vector space of the signal. It is shown that multiresolution analysis can be done with amplitudes…
Clinical decision-making in radiology increasingly benefits from artificial intelligence (AI), particularly through large language models (LLMs). However, traditional retrieval-augmented generation (RAG) systems for radiology question…
In this paper, we prove central limit theorems for bias reduced estimators of the structure function of several multifractal processes, namely mutiplicative cascades, multifractal random measures, multifractal random walk and multifractal…
Genetic algorithms have played an important role in engineering optimization. Traditional GAs treat each gene separately. However, biophysical studies of gene regulatory networks revealed direct associations between different genes. It…
Given a compact set $S$ and a uniformly discrete sequence $\La$, we show that "approximate interpolation" of delta--functions on $\La$ by a bounded sequence of $L^2-$functions with spectra in $S$ implies an estimate on measure of $S$…
Mendelian randomization (MR) is a powerful approach to examine the causal relationships between health risk factors and outcomes from observational studies. Due to the proliferation of genome-wide association studies (GWASs) and abundant…
We study the 2-D super-resolution multi-reference alignment (SR-MRA) problem: estimating an image from its down-sampled, circularly-translated, and noisy copies. The SR-MRA problem serves as a mathematical abstraction of the structure…
Kernel alignment measures the degree of similarity between two kernels. In this paper, inspired from kernel alignment, we propose a new Linear Discriminant Analysis (LDA) formulation, kernel alignment LDA (kaLDA). We first define two…
Many statistical problems involve the estimation of a $\left(d\times d\right)$ orthogonal matrix $\textbf{Q}$. Such an estimation is often challenging due to the orthonormality constraints on $\textbf{Q}$. To cope with this problem, we…
Thyroid ultrasound is the first-line exam for assessing thyroid nodules and determining whether biopsy is warranted. In routine reporting, radiologists produce two coupled outputs: a nodule contour for measurement and a TI-RADS risk…
In this paper, we introduce a method for fine-tuning Large Language Models (LLMs), inspired by Multi-Task learning in a federated manner. Our approach leverages the structure of each client's model and enables a learning scheme that…
In this article, we consider two proper double splittings satisfying certain conditions, of a semi-monotone rectangular matrix A and derive new comparison results for the spectral radii of the correspond ing iteration matrices. These…
For an arbitrary matrix dilation, any integer n and any integer/semi-integer c, we describe all masks that are symmetric with respect to the point c and have sum rule of order n. For each such mask, we give explicit formulas for wavelet…
The article suggests a new approach what is called a consistency method for the inversion of the spherical Radon transform in 2D with detectors on a line. It is known that there is not an exact inversion formula in 2D. By means of the…