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Preprint Teks lengkap
The Grothendieck ring of a non-divisible ordered abelian group is trivial
We consider the model-theoretic Grothendieck ring of definable sets in ordered abelian groups. It is well-known that $\mathrm{K} \mathbb{Q} \cong \mathbb{Z}[T]/(T^2 + T)$ and $\mathrm{K} \mathbb{Z} =0$, but surprisingly little is known about other cases. We present a short computation which shows…
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On the Convergence of Proximal Algorithms for Weakly-convex Min-max Optimization
We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially simplified proof compared to previous ones. It allows us to…
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Preprint Teks lengkap
On Generalizations of Maiorana-McFarland and $\mathcal{PS}_{ap}$ Functions
We study generalizations of two classical primary constructions of Boolean bent functions, namely the Maiorana-McFarland ($MM$) class and the (Desarguesian) partial spread ($\mathcal{PS}_{ap}$) class. The construction of bent functions lying outside the completed $MM$ class has attracted…
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Emergent-Coupling-Based Ansatz Evaluated on a Superconducting Quantum Processor
The performance of the variational quantum eigensolver depends critically on the choice of ansatz. In this work, we experimentally evaluate the emergent-coupling-based ansatz (ECBA), a physically motivated variational ansatz for disordered systems. The ECBA is based on a renormalization…
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On Legendrian Thurston-Bennequin-symmetrical graphs
This article reviews the development of Legendrian graph theory in the standard contact 3-sphere ($S^3, ξ_{std}$). We provide a generalized criterion under which the total Thurston-Bennequin invariant of a Legendrian graph (sum of tb of all cycles of the Legendrian graph) can be computed from the…
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Courtroom-Style Multi-Agent Debate with Progressive RAG and Role-Switching for Controversial Claim Verification
Large language models (LLMs) remain unreliable for high-stakes claim verification due to hallucinations and shallow reasoning. While retrieval-augmented generation (RAG) and multi-agent debate (MAD) address this, they are limited by one-pass retrieval and unstructured debate dynamics. We propose a…
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Video Generation Models as World Models: Efficient Paradigms, Architectures and Algorithms
The rapid evolution of video generation has enabled models to simulate complex physical dynamics and long-horizon causalities, positioning them as potential world simulators. However, a critical gap still remains between the theoretical capacity for world simulation and the heavy computational…
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Bogoliubov flat bands in twisted layered materials
Flat bands have attracted considerable interest in condensed matter physics because they provide a fertile platform for realizing strongly correlated and topological quantum phases. To date, however, most studies have focused on flat bands in normal-state electronic structures, such as those found…
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Complete Walsh spectra for a permutation-inverse family of Boolean functions
Let $q=2^e$ with $e$ even, and let $\mathbb{F}_{q^2}$ be the finite field of order $q^2$. Put $d=(q^2+q+1)/3$, and consider the permutation polynomial $$σ(X)=X+X^d+X^{dq}\in\mathbb{F}_{q^2}[X].$$ For $α\in\mathbb{F}_q^*$, define the Boolean function $$…
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Preprint Teks lengkap
Andromeda XXXVI: discovery of a new ultra-faint dwarf galaxy towards M31
We present deep imaging of Andromeda XXXVI (And XXXVI), a dwarf galaxy discovered through visual inspection of the Pan-Andromeda Archaeological Survey, using observations obtained with the OSIRIS+@GTC instrument. The colour-magnitude diagram of And XXXVI shows a well-defined red giant branch (RGB)…
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Preprint Teks lengkap
ConceptWeaver: Weaving Disentangled Concepts with Flow
Pre-trained flow-based models excel at synthesizing complex scenes yet lack a direct mechanism for disentangling and customizing their underlying concepts from one-shot real-world sources. To demystify this process, we first introduce a novel differential probing technique to isolate and analyze…
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Preprint Teks lengkap
Tooling for digital accessibility in mathematics: Quickly build compliant course websites that benefit all students
Public universities in the US must now meet digital accessibility (DA) standards under 2024 updates to Title II of the ADA. For math instructors, course materials must be screen-reader parsable, which standard LaTeX-to-PDF workflows cannot achieve. Despite MathML's availability as a web standard…
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Preprint Teks lengkap
Asymptotic Solutions of Radiating Stars
We investigate the evolution of the surface of radiating stars by studying the asymptotic behaviour of exact solutions initiated via the stationary boundary condition. This boundary condition leads to a master equation in the form of a second-order nonlinear differential equation that describes the…
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A connection between Gravitational Scalar-Tensor theories and Generalized Hybrid theories
We establish a correspondence between higher-derivative gravitational scalar-tensor theories of the form $Ψ(R,(\nabla R)^2,\Box R)$ and generalized hybrid metric-Palatini models $f(R,\mathcal{R})$. Restricting to the physically relevant case of linear dependence on $\Box R$, we make explicit that…
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Preprint Teks lengkap
Next-Token Prediction and Regret Minimization
We consider the question of how to employ next-token prediction algorithms in adversarial online decision-making environments. Specifically, if we train a next-token prediction model on a distribution $\mathcal{D}$ over sequences of opponent actions, when is it the case that the induced online…
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Preprint Teks lengkap
Monoids generated by projections
We define and explore semireflection monoids on a finite-dimensional vector space. These are monoids generated by semireflections: linear maps fixing a subspace of codimension 1. We mostly focus on the case of projection monoids (where the generating semireflections are non-invertible). After…
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Transfer and Norm for Finite Group Schemes
We develop the theory of transfer and norm maps for finite group schemes, extending classical results from finite group theory to a context where induction and restriction are not necessarily bi-adjoint. In the additive setting, we construct a transfer map for both modules and $\rm Ext $ groups and…
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Bridging the Geometry Mismatch: Frequency-Aware Anisotropic Serialization for Thin-Structure SSMs
The segmentation of thin linear structures is inherently topology allowbreak-critical, where minor local errors can sever long-range connectivity. While recent State-Space Models (SSMs) offer efficient long-range modeling, their isotropic serialization (e.g., raster scanning) creates a geometry…
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Preprint Teks lengkap
JW-VL: A Vision-Language Model for Solar Physics
Vision-Language Models (VLMs) have achieved breakthrough progress in general knowledge domains, yet adaptation to specialized scientific fields remains challenging due to multimodal representation shifts and the limited integration of domain-specific knowledge. To address the limitations of…
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Preprint Teks lengkap
Process Development and First Cryogenic Operation of Compact Germanium Ring-Contact HPGe Prototypes
Rare-event experiments such as LEGEND-1000 require high-purity germanium (HPGe) detectors with excellent energy resolution, low electronic noise, and scalable low-background packaging. The germanium ring-contact (GeRC) concept addresses this need through a recessed ring-and-groove electrode…
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