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We develop a systematic theory of microwave-induced oscillations in magnetoresistivity of a 2D electron gas in the vicinity of fractional harmonics of the cyclotron resonance, observed in recent experiments. We show that in the limit of…
MRI signal acquisition with multiple coils in a phased array is nowadays commonplace. The use of multiple receiver coils increases the signal-to-noise ratio (SNR) and enables accelerated parallel imaging methods. Some of these methods, like…
Thepaperprovesconvergenceofone-levelandmultilevelunsymmetriccollocationforsecondorderelliptic boundary value problems on the bounded domains. By using Schaback's linear discretization theory,L2 errors are obtained based on the kernel-based…
Attenuated Radon projections with respect to the weight function $W_\mu(x,y) = (1-x^2-y^2)^{\mu-1/2}$ are shown to be closely related to the orthogonal expansion in two variables with respect to $W_\mu$. This leads to an algorithm for…
Low-rank adaptation is a popular parameter-efficient fine-tuning method for large language models. In this paper, we analyze the impact of low-rank updating, as implemented in LoRA. Our findings suggest that the low-rank updating mechanism…
We have recently introduced a modification of the multiple signal classification (MUSIC) method for synthetic aperture radar. This method depends on a tunable, user-defined parameter, $\epsilon$, that allows for quantitative high-resolution…
Let R be the quotient of a polynomial ring over a field k by an ideal generated by monomials. We derive a formula for the multigraded Poincare' series of R, i.e., the generating function for the ranks of the modules in a minimal multigraded…
We consider a class of $(1,M)$-elementary step functions on the $p$-adic Vilenkin group. We prove that $(1,M)$-elementary step function generates a MRA on $p$-adic Vilenkin group iff it is generated by a rooted tree on the set of vertices…
All integrals needed to evaluate the correlated wave functions with polynomial terms of inter-electronic distance are included. For this form of the wave function, the integrals needed can be expressed as a product of integrals involving at…
Low-Rank Adaptation (LoRA) drives research to align its performance with full fine-tuning. However, significant challenges remain: (1) Simply increasing the rank size of LoRA does not effectively capture high-rank information, which leads…
We consider the problem of recovering a low-multilinear-rank tensor from a small amount of linear measurements. We show that the Riemannian gradient algorithm initialized by one step of iterative hard thresholding can reconstruct an…
To address ultimate precision in density-functional-theory calculations we employ the full-potential linearized augmented planewave + local-orbital (LAPW+lo) method and justify its usage as a benchmark method. LAPW+lo and two completely…
Multireference alignment (MRA) problem is to estimate an underlying signal from a large number of noisy circularly-shifted observations. The existing methods are always proposed under the hypothesis of a single Gaussian noise. However, the…
This is the second paper in a series where we study arithmetic applications of the multiple elliptic Gamma functions originated in mathematical physics. In the first article in this series we defined geometric families of these functions…
We construct a meromorphic function on the eigencurve that interpolates a square root of the ratio of the central values of two quadratic twists of the $L$-function at classical points.
We introduce a generating function associated to the homogeneous generators of a graded algebra that measures how far is this algebra from being finitely generated. For the case of some algebras of Frobenius endomorphisms we describe this…
We present a second-order formulation of multi-reference algebraic diagrammatic construction theory [Sokolov, A. Yu. J. Chem. Phys. 2018, 149, 204113] for simulating photoelectron spectra of strongly correlated systems (MR-ADC(2)). The…
The E2/M1 ratio (EMR) of the $\Delta$(1232) is extracted from the world data in pion photoproduction by means of an Effective Lagrangian Approach (ELA).This quantity has been derived within a crossing symmetric, gauge invariant, and chiral…
Root cause analysis (RCA) in microservice systems is challenging, requiring on-call engineers to rapidly diagnose failures across heterogeneous telemetry such as metrics, logs, and traces. Traditional RCA methods often focus on single…
Regularized linear discriminant analysis (RLDA) is a widely used tool for classification and dimensionality reduction, but its performance in high-dimensional scenarios is inconsistent. Existing theoretical analyses of RLDA often lack clear…