arXiv preprints from January 1, 2026 through July 28, 2026 — 14:14:44 EST
Relying on the Lebesgue-type decomposition of positive operators, this work introduces a rigorous notion of localization probability of a quantum state within a given subspace of its Hilbert space. A non-negative operator A is uniquely decomposed as A=B+C, where B is the maximal positive operator supported inside the chosen subspace...
In this Article, I explore the impending conflict between the protection of civil rights and artificial intelligence (AI). While both areas of law have amassed rich and well-developed areas of scholarly work and doctrinal support, a growing body of scholars are interrogating the intersection between them. This Article argues that the...
The Moran process is a foundational model of genetic drift and mutation in finite populations. In its standard two-allele form with population size $n$, allele counts, and hence allele frequencies, change through stochastic replacement and mutation, yet converge to a stationary distribution. This distribution undergoes a qualitative...
The Bern-Carrasco-Johansson (BCJ) double-copy construction reveals a fundamental structural connection between gauge and gravity theories. At its core, the BCJ double copy is directly due to a duality between the algebraic relations of a color root and those of a kinematic root. We generalize this principle beyond the conventional Lie...
Background: Pneumonia remains a leading cause of morbidity and mortality among children worldwide, emphasizing the need for accurate and efficient diagnostic support tools. Deep learning has shown strong potential in medical image analysis, particularly for chest X-ray interpretation. This study compares two state-of-the-art...
Tuberculosis (TB) is an airborne disease caused by the pathogen Mycobacterium tuberculosis. In 2023, it returned to being the leading cause of death from an infectious agent globally, replacing COVID-19; in the nineteenth century, one in seven of all humans died of tuberculosis. More than 10 million people are diagnosed with TB every...
Accurately localizing 3D objects like pedestrians, cyclists, and other vehicles is essential in Autonomous Driving. To ensure high detection performance, Autonomous Vehicles complement RGB cameras with LiDAR sensors, but effectively combining these data sources for 3D object detection remains challenging. We propose LCF3D, a novel...
We consider epidemic and ecological models to investigate their coupled dynamics. Starting with the classical Susceptible-Infected-Recovered (SIR) model for basic epidemic behavior and the predator-prey (Lotka-Volterra, LV) system for ecological interactions, we then combine these frameworks into a coupled...
Luminous infrared galaxies are key sites of obscured stellar mass assembly at z > 0.5. Their star formation rates (SFRs) are often estimated using the luminosities of the 6.2 micron and 11.2 micron polycyclic aromatic hydrocarbon (PAH) features, or those of the [Ne II] and [Ne III] fine-structure lines, as they are minimally affected...
Organizations and enterprises across domains such as healthcare, finance, and scientific research are increasingly required to extract collective intelligence from distributed, siloed datasets while adhering to strict privacy, regulatory, and sovereignty requirements. Federated Learning (FL) enables collaborative model building...
Variable scoping dictates how and where variables are accessible within programming languages, playing a crucial role in code efficiency and organization. This paper examines the distinct scoping rules in SAS and R, focusing on SAS's dynamic scoping and R's lexical scoping. In SAS, dynamic scoping utilizes symbol tables, resolving...
One of the earliest mechanisms proposed for plasma heating was magnetic pumping (MP). However, its significance for astrophysical phenomena, including particle acceleration, has yet to be appreciated. MP-energized particles tap energy from magnetic-field oscillations. A particle's momentum component perpendicular to the local B-field...
This work presents an end-to-end pipeline for generating, refining, and evaluating adversarial patches to compromise facial biometric systems, with applications in forensic analysis and security testing. We utilize FGSM to generate adversarial noise targeting an identity classifier and employ a diffusion model with reverse diffusion...
Modern logical reasoning with LLMs primarily relies on employing complex interactive frameworks that decompose the reasoning process into subtasks solved through carefully designed prompts or requiring external resources (e.g., symbolic solvers) to exploit their strong logical structures. While interactive approaches introduce...
Solar eruptions arise from instabilities or loss of equilibria in the solar atmosphere, but routinely inferring the precise magnetic and plasma properties that lead to eruptions is not currently practical using synoptic solar observations. Data driven simulations offer an appealing alternative. We test our boundary data-driven...
Generalised axion-like scalar fields provide a well-motivated framework for describing the late-time acceleration of the Universe. As the field evolves, it rolls down its potential and, depending on its mass and initial conditions, it may either still be approaching the minimum or already oscillating around it. These two dynamical...
Partially coherent light is typically studied in the context of freely propagating continuous fields. Recent developments have indicated the existence of a `coherence advantage' in multimode optical communications, where partially coherent light outperforms coherent light. However, exploiting partial coherence in such applications...
We investigate how a thermodynamical first-order phase transition affects the dynamical chaotic behaviour of a given model. To this effect, we analyze the model of Berkooz, Brukner, Jia and Mamroud that interpolates between the double-scaled SYK model and an integrable chord Hamiltonian. This model exhibits a first-order transition,...
For a broad class of polynomial potentials $V$, with an important and instructive representative being $V(x) = x^{2a} + i x^b$, $x \in \mathbb R$, $a, b \in \mathbb N$, we show that the system of spectral projections $\{P_n\}_n$ of an anharmonic operator $L = - (\mathrm{d}/ \mathrm{d}x)^2 + V(x)$ does not generate a (Riesz) basis in...
The Milky Way's Galactic Center hosts the black hole Sagittarius A* (Sgr A*), which provides us with a close-up view into supermassive black hole accretion and feedback. Recent works have shown that the winds from $\sim 30$ Wolf-Rayet (WR) stars orbiting Sgr A* at about 4 arcsec are important contributors to feeding the supermassive...
This paper extends the affine Springer theory developed by Bouthier, Kazhdan, and the second author (see [BKV]) to the mixed characteristic case. In particular, we introduce a theory of perfectly placid perfect infinity stacks and establish their dimension theory. Furthermore, we prove that, in the Witt vector setting, the Chevalley...
Using the transport-of-intensity approach for free-space optical propagation in the paraxial regime, we show that diffraction is fundamentally related to the Fisher information associated with models of the transverse intensity distribution. By interpreting intensity as a probability density, we show that a) free-space diffraction...
Milky Way halo substructures identified in dynamical space are known to suffer from contamination from the Milky Way in-situ stars, which makes their accreted origins uncertain. We present detailed chemical abundances of 35 stars belonging to two sets of dynamically tagged groups, Rg8 and Rg9, to investigate their accreted nature....
Cylindrical Algebraic Decompositions (CADs) endowed with additional topological properties have found applications beyond their original logical setting, including algorithmic optimizations in CAD construction, robot motion planning, and the algorithmic study of the topology of semi-algebraic sets. In this paper, we construct explicit...
Cloud-cloud collisions are expected to trigger star formation by compressing gas into dense, gravitationally unstable regions. However, the role of magnetic fields in this process is unclear. We use SPH to model head-on collisions between two uniform density clouds, each with mass $500 \,$M$_{\odot}$, initial radius 2 pc, and embedded...