arXiv preprints from January 1, 2026 through July 28, 2026 — 09:50:35 EST
The dynamics of the left translation semigroup $\{T_t\}_{t \geq 0}$ on weighted $L^p$ spaces over a directed metric tree $L(G)$ is investigated. Necessary and sufficient conditions on the weight family $ρ$ for the strong continuity of the semigroup are provided. Furthermore, hypercyclicity and weak mixing properties are characterized...
Models of neutron and strange stars are considered in the approximation of a uniform density distribution. A universal algebraic equation, valid for any equation of state, is used to find the approximate mass of a star of a given density without resorting to the integration of differential equations. Equations of state for neutron...
Electric prosthetic hands should be lightweight to decrease the burden on the user, shaped like human hands for cosmetic purposes, and designed with motors enclosed inside to protect them from damage and dirt. Additionally, in-hand manipulation is necessary to perform daily activities such as transitioning between different postures,...
Autonomous 3D scanning of open-world target structures via drones remains challenging despite broad applications. Existing paradigms rely on restrictive assumptions or effortful human priors, limiting practicality, efficiency, and adaptability. Recent foundation models (FMs) offer great potential to bridge this gap. This paper...
We formulate a quantum mechanical system consisting of a single discrete state coupled to an infinite ladder of equally-spaced states, the coupling between the two being given by a Lorentzian profile. Various limits of this system correspond to well-known models from quantum optics, namely, the narrow resonance limit gives the Rabi...
Electroencephalogram (EEG)-based brain-computer interfaces (BCIs) face significant deployment challenges due to inter-subject variability, signal non-stationarity, and computational constraints. While test-time adaptation (TTA) mitigates distribution shifts under online data streams without per-use calibration sessions, existing TTA...
We estimate key parameters for the Galactic globular clusters NGC1904 and NGC4372 and update the parameters for NGC288, NGC362, NGC5904, NGC6205, and NGC6218, which were analysed in our previous papers. We fit various colour-magnitude diagrams (CMDs) of the clusters using isochrones from the DSED and BaSTI. The CMDs are constructed...
Zinc sulphide (ZnS) is a non-toxic, wide-bandgap II-VI semiconductor with well-established optoelectronic properties. This work presents a systematic, concentration-dependent comparison of PEG and PVP across two scalable aqueous routes, linking ligand chemistry to crystallite size and bandgap shifts. ZnS quantum dots (QDs) were...
As large language models (LLMs) continue to improve in reasoning and decision-making, there is a growing need for realistic and interactive environments where their abilities can be rigorously evaluated. We present VirtualEnv, a next-generation simulation platform built on Unreal Engine 5 that enables fine-grained benchmarking of LLMs...
This paper is an introduction to Coxeter polyhedra in spherical, Euclidean, and hyperbolic geometries. It consists of essentially two parts that could be read independently. In the first we introduce non-obtuse polyhedra in the spherical, Euclidean, and hyperbolic spaces, and prove various fundamental theorems originated from Andreev,...
We study a weak form of formality for differential graded algebras, called $A_3$-formality, for the cohomology of pro-p Demushkin groups at odd primes p. We show that the differential graded $\mathbb{F}_p$-algebras of continuous cochains of Demushkin groups with q-invariant not equal 3 are $A_3$-formal, whereas Demushkin groups with...
Multivariate Time-Series (MTS) clustering is crucial for signal processing and data analysis. Although deep learning approaches, particularly those leveraging Contrastive Learning (CL), are prominent for MTS representation, existing CL-based models face two key limitations: 1) neglecting clustering information during positive/negative...
Coherence transfer is a multi-disciplinary topic of interest, including chemistry, biology and physics. In quantum technologies, achieving non-local coherent coupling between solid-state qubits is of the utmost importance. Here, we demonstrate that excitons - i.e. electron-hole pairs bound by the Coulomb force within a quantum well -...
Medical time series data, such as EEG and ECG, are vital for diagnosing neurological and cardiovascular diseases. However, their precise interpretation faces significant challenges due to high annotation costs, leading to data scarcity, and the limitations of traditional contrastive learning in capturing complex temporal patterns. To...
The Levenshtein sequence reconstruction problem studies the reconstruction of a transmitted sequence from multiple erroneous copies of it. A fundamental question in this field is to determine the minimum number of erroneous copies required to guarantee correct reconstruction of the original sequence. This problem is equivalent to...
We study the problem of estimating the mutation rate between two sequences from noisy sequencing reads. Existing alignment-free methods typically assume direct access to the full sequences. We extend these methods to the sequencing framework, where only noisy reads from the sequences are observed. We use a simple model in which both...
We study differentially private ordinary least squares (DP-OLS) with bounded data $(X,Y)$ via sketching-based mechanisms. While Gaussian sketching approaches have been explored for DP-OLS \citep{sheffet2017differentially}, they are typically viewed as less competitive than the Adaptive Sufficient Statistics Perturbation (AdaSSP)...
Access to reliable maternal healthcare information is a major challenge in rural India due to limited medical resources and infrastructure. With over 830 million internet users and nearly half of rural women online, digital tools offer new opportunities for health education. This study evaluates large language models (LLMs) like...
This work addresses an enumeration problem on weighted bi-colored plane trees with prescribed vertex data, with all vertices labeled distinctly. We give a bijection proof of the enumeration formula originally due to Kochetkov, hence affirmatively answer a question of Adrianov-Pakovich-Zvonkin. The argument is purely combinatorial and...
Small-scale discrepancies in the standard Lambda cold dark matter paradigm have motivated the exploration of alternative dark matter (DM) models, such as warm dark matter (WDM). We investigate the constraining power of galaxy scaling relations on cosmological, astrophysical, and WDM parameters through a joint analysis of hydrodynamic...
Type IIn supernovae (SNe IIn) are hydrogen-rich explosions embedded in dense circumstellar medium (CSM), which gives rise to their characteristic narrow hydrogen emission lines. The nature of their progenitors and pre-explosion mass loss remains, however, poorly understood. Using high-resolution Hubble Space Telescope (HST) imaging,...
We show that the holonomy group of a connected Riemannian locally symmetric space (not necessarily complete) without local flat factor is compact and has finite index in its normalizer in the orthogonal group.
We give a self-contained introduction to linear algebraic and semialgebraic groups over real closed fields, and we generalize several key results about semisimple Lie groups to algebraic and semialgebraic groups over real closed fields. We prove that a torus in a semisimple algebraic group is maximal $\mathbb{R}$-split if and only if...
Universal time-temperature scaling of conductivity spectra in disordered solids has been explained by thermally activated hopping of noninteracting particles over random energy barriers. An open problem is whether the random barrier model accounts for site energy disorder in real materials. Through mapping many-particle hopping in a...
Most numerical methods for time integration use real-valued time steps. Complex time steps, however, can provide an additional degree of freedom, as we can select the magnitude of the time step in both the real and imaginary directions. We show that specific paths in the complex time plane lead to expanded stability regions, providing...