arXiv preprints from January 1, 2026 through September 23, 2026 — 01:39:02 EST
We construct an irreducible rational curve of degree 10 in $CP^2$ which has 12 triple points and a union of three rational quartics with 19 triple points. This gives counter-examples to a conjecture by Dimca, Harbourne, and Sticlaru. We also prove that there exists an analytic family $C_u$ of curves of degree 10 with 12 triple points...
We consider supercritical long-range percolation on transitive graphs of polynomial growth. In this model, any two vertices $x$ and $y$ of the underlying graph $G$ connect by a direct edge with probability $1-\exp(-βJ(x,y))$, where $J(x,y)$ is a function that is invariant under the automorphism group of $G$, and we assume that $J$...
Deploying geospatial foundation models on resource-constrained edge devices demands compact architectures that maintain high downstream performance. However, their large parameter counts and the accuracy loss often induced by compression limit practical adoption. In this work, we leverage manifold-constrained optimization framework...
In operator-algebraic AQFT one routinely moves back and forth between two kinds of structure: inclusions of local algebras coming from inclusions of regions, and bimodules/intertwiners that implement the standard $L^2$-based constructions used to compare and compose observables. The obstruction to making this interplay genuinely...
The increased use of Large Language Models (LLMs) in sensitive domains leads to growing interest in how their confidence scores correspond to fairness and bias. This study examines the alignment between LLM-predicted confidence and human-annotated bias judgments. Focusing on gender bias, the research investigates probability...
Remote sensing change detection fundamentally relies on the effective fusion and discrimination of bi-temporal features. Prevailing paradigms typically utilize Siamese encoders bridged by explicit difference computation modules, such as subtraction or concatenation, to identify changes. In this work, we challenge this complexity with...
In this paper we present a systematic study of continuous local iterated function systems. We prove local iterated function systems admit compact attractors and, under a contractivity assumption, construct their code space and present an extended shift that describes admissible compositions. In particular, the possible combinatorial...
We study $\mathbb Z_2\times\mathbb Z_2$ bi-graded Lie algebras. We describe their properties in relation to Lie superalgebras with some compatible structures. Then we focus on the approach to the Lie group--algebra correspondence based on Harish-Chandra pairs and provide some examples of application of it in the bi-graded setting.
We study the bond percolation on finite graphs induced by the level-sets of zero-average Gaussian free field on the associated metric graph above a given height (level) parameter $h \in \mathbb{R}$. We characterize the near- and off-critical phases of this model for any expanders family $\mathcal{G}_n = (V_n, E_n)$ with uniformly...
We propose a topology-optimization framework for optimizing finite structures of arbitrary shape by combining density-based methods with level-set approaches. We first optimize regular polygonal structures to suppress the photonic density of states and find that the best performing polygon is consistent with a tiling of space with...
We construct rigorous Anderson-type lower bounds on the ground-state energy of the spin-$S$ Heisenberg antiferromagnet on the pyrochlore lattice. By formulating and optimizing a hierarchy of local cluster motifs ordered by size, we generate a sequence of increasingly tight bounds. A seven-site "hourglass" cluster composed of two...
The rotation velocities of disc galaxies trace dark matter halo structure, providing direct constraints on the galaxy--halo connection. We construct a Bayesian forward model to connect the dark matter halo population predicted by $Λ$CDM with an observed sample of disc galaxies (SPARC) through their maximum rotation velocities. Our...
We present a general theoretical approach for the quantitative description of parametric excitation of spin-wave modes in confined micromagnetic systems. This type of problem belongs to a broader class of nonlinear modal dynamics that arise across many areas of physics and engineering. The ferromagnetic sample is driven by parallel...
Large collections of matrices arise throughout modern machine learning, signal processing, and scientific computing, where they are commonly compressed by concatenation followed by truncated singular value decomposition (SVD). This strategy enables parameter sharing and efficient reconstruction and has been widely adopted across...
With the increasing deployment of large language models (LLMs) in affective agents and AI systems, maintaining a consistent and authentic LLM personality becomes critical for user trust and engagement. However, existing work overlooks a fundamental psychological consensus that personality traits are dynamic and context-dependent. To...
This paper considers the source coding problem with broadcast side information. The side information is sent to two receivers through a noisy broadcast channel. We provide an outer bound of the rate--distortion--bandwidth (RDB) quadruples and achievable RDB quadruples when the helper uses a separation-based scheme. Some special cases...
Large language models (LLMs) are increasingly used as conversational partners for learning, yet the interactional dynamics supporting users' learning and engagement are understudied. We analyze the linguistic and interactional features from both LLM and participant chats across 397 human-LLM conversations about socio-political issues...
The European Space Agency (ESA), driven by its ambitions on planned lunar missions with the Argonaut lander, has a profound interest in reliable crater detection, since craters pose a risk to safe lunar landings. This task is usually addressed with automated crater detection algorithms (CDA) based on deep learning techniques. It is...
Large language models (LLMs) are increasingly evaluated on their ability to perform multi-hop reasoning, i.e., to combine multiple pieces of information into a coherent inference. We introduce KinshipQA, a benchmark designed to probe this capability through reasoning over kinship relations. The central contribution of our work is a...
We prove the combinatorial invariance of the coefficient of $q$ in Kazhdan--Lusztig polynomials for arbitrary Coxeter groups. As a result, we obtain the Combinatorial Invariance Conjecture, of Lusztig and of Dyer, also for Bruhat intervals of length at most $6$. We also prove the Gabber--Joseph conjecture for the second-highest $Ext$...
Portfolio optimization under cardinality constraints transforms the classical Markowitz mean-variance problem from a convex quadratic problem into an NP-hard combinatorial optimization problem. This paper introduces a novel approach using THRML (Thermodynamic HypergRaphical Model Library), a JAX-based library for building and sampling...
We establish necessary and sufficient conditions for the existence of an LU factorization $A=LU$ for an arbitrary square matrix $A$, including singular and rank-deficient cases, without the use of row or column permutations. We prove that such a factorization exists if and only if the nullity of every leading principal submatrix is...
System logs are crucial for monitoring and diagnosing modern computing infrastructure, but their scale and complexity require reliable and efficient automated interpretation. Since severity levels are predefined metadata in system log messages, having a model merely classify them offers limited standalone practical value, revealing...
For generic theories of nonlinear electrodynamics (NLED) we investigate the implications of (a)causality on spherically-symmetric solutions of the Einstein-NLED equations that are asymptotic to a Reissner-Nordström (RN) spacetime. Equal-charge dyonic RN black holes are shown to be exact, but unstable, solutions of (acausal)...
Effective shift transitions are crucial for cybersecurity incident response teams, yet there is limited guidance on managing these handovers. This exploratory study aimed to develop guidelines for such transitions through the analysis of existing literature and consultation with practitioners. Two draft guidelines (A and B) were...