Tootfinder

$\epsilon$-Distance via L\'evy-Prokhorov Lifting
Jos\'ee Desharnais, Ana Sokolova
https://arxiv.org/abs/2507.10732 https://ar…

$ε$-Distance via Lévy-Prokhorov Lifting
The most studied and accepted pseudometric for probabilistic processes is one based on the Kantorovich distance between distributions. It comes with many theoretical and motivating results, in particular it is the fixpoint of a given functional and defines a functor on (complete) pseudometric spaces. Other notions of behavioural pseudometrics have also been proposed, one of them ($ε$-distance) based on $ε$-bisimulation. $ε$-Distance has the advantages that it is intuitively easy to underst…

KV-Latent: Dimensional-level KV Cache Reduction with Frequency-aware Rotary Positional Embedding
Luohe Shi, Zuchao Li, Lefei Zhang, Guoming Liu, Baoyuan Qi, Hai Zhao
https://arxiv.org/abs/2507.11273

KV-Latent: Dimensional-level KV Cache Reduction with Frequency-aware Rotary Positional Embedding
Large language models (LLMs) based on Transformer Decoders have become the preferred choice for conversational generative AI. Despite the overall superiority of the Decoder architecture, the gradually increasing Key-Value (KV) cache during inference has emerged as a primary efficiency bottleneck, both in aspects of memory consumption and data transfer bandwidth limitations. To address these challenges, we propose a paradigm called KV-Latent. By down-sampling the Key-Value vector dimensions into…

Well-posedness and relaxation in a simplified model for viscoelastic phase separation via Hilbertian gradients flows
Moritz Immanuel Gau, Katharina Hopf
https://arxiv.org/abs/2508.10722

Well-posedness and relaxation in a simplified model for viscoelastic phase separation via Hilbertian gradients flows
This article is concerned with a gradient-flow approach to a Cahn-Hilliard model for viscoelastic phase separation introduced by Zhou et al. (Phys. Rev. E, 2006) in its variant with constant mobility. By means of time-incremental minimisation and generalised contractivity estimates, we establish the global well-posedness of the Cauchy problem for moderately regular initial data. For general finite-energy data we obtain the existence of gradient-flow solutions and a stability estimate of weak-st…

Predictive Position Control for Movable Antenna Arrays in UAV Communications: A Spatio-Temporal Transformer-LSTM Framework
Kan Yu, Kaixuan Li, Xiaowu Liu, Qixun Zhang, Zhiyong Feng
https://arxiv.org/abs/2508.10720

Predictive Position Control for Movable Antenna Arrays in UAV Communications: A Spatio-Temporal Transformer-LSTM Framework
In complex urban environments, dynamic obstacles and multipath effects lead to significant link attenuation and pervasive coverage blind spots. Conventional approaches based on large-scale fixed antenna arrays and UAV trajectory optimization struggle to balance energy efficiency, real-time adaptation, and spatial flexibility. The movable antenna (MA) technology has emerged as a promising solution, offering enhanced spatial flexibility and reduced energy consumption to overcome the bottlenecks o…

Cappell-Shaneson polynomials
Hisaaki Endo, Kazunori Iwaki, Andrei Pajitnov
https://arxiv.org/abs/2507.10885 https://arxiv.org/pdf/250…

Cappell-Shaneson polynomials
S. Cappell and J. Shaneson constructed a pair of inequivalent embeddings of $(n-1)$-spheres in homotopy $(n+1)$-spheres for every square matrix of order $n$ with special properties (a Cappell-Shaneson matrix). A Cappell-Shaneson polynomial is the characteristic polynomial of a Cappell-Shaneson matrix. In this paper, we interpret part of the definition of Cappell-Shaneson polynomial as algebraic conditions on polynomials in terms of signed reciprocal polynomial and reduction modulo primes, and g…

A Dual Quaternion Control Law for Formation Control of Multiple 3-D Rigid Bodies
Chunfeng Cui, Liqun Qi, Hao Chen, Xiangke Wang
https://arxiv.org/abs/2508.10519 https://

A Dual Quaternion Control Law for Formation Control of Multiple 3-D Rigid Bodies
This paper studies the integrated position and attitude control problem for multi-agent systems of 3D rigid bodies. While the state-of-the-art method in [Olfati-Saber and Murray, 2004] established the theoretical foundation for rigid-body formation control, it requires all agents to asymptotically converge to identical positions and attitudes, limiting its applicability in scenarios where distinct desired relative configurations must be maintained. In this paper, we develop a novel dual-quatern…

On 3-terminal positions in Hex
Eric Demer, Peter Selinger
https://arxiv.org/abs/2507.08247 https://arxiv.org/pdf/2507.08247

On 3-terminal positions in Hex
This paper is about 3-terminal regions in Hex. A 3-terminal region is a region of the Hex board that is completely surrounded by black and white stones, in such a way that the black boundary stones form 3 connected components. We characterize Hex as the universal planar Shannon game of degree 3. This ensures that every Hex position can be decomposed into 3-terminal regions. We then investigate the combinatorial game theory of 3-terminal regions. We show that there are infinitely many distinct H…

GUP, Lorentz Invariance (Non)-Violation, and Non-Commutative Geometry
Michael Bishop, Daniel Hooker, Peter Martin, Douglas Singleton
https://arxiv.org/abs/2506.11219

GUP, Lorentz Invariance (Non)-Violation, and Non-Commutative Geometry
In this work, we formulate a generalized uncertainty principle with both position and momentum operators modified from their canonical forms. We study whether Lorentz symmetry is violated and whether it can be saved with these modifications. The requirement that Lorentz invariance is not violated places restrictions on the way the position and momentum operators can be modified. We also investigate the connection between general uncertainty principle and non-commutative geometry models, e.g.,la…

A Computational Approach to Analyzing Language Change and Variation in the Constructed Language Toki Pona
Daniel Huang, Hyoun-A Joo
https://arxiv.org/abs/2508.10246 https://

A Computational Approach to Analyzing Language Change and Variation in the Constructed Language Toki Pona
This study explores language change and variation in Toki Pona, a constructed language with approximately 120 core words. Taking a computational and corpus-based approach, the study examines features including fluid word classes and transitivity in order to examine (1) changes in preferences of content words for different syntactic positions over time and (2) variation in usage across different corpora. The results suggest that sociolinguistic factors influence Toki Pona in the same way as natu…

Echoes of Agreement: Argument Driven Opinion Shifts in Large Language Models
Avneet Kaur
https://arxiv.org/abs/2508.09759 https://arxiv.org/pdf/2508.09759

Echoes of Agreement: Argument Driven Opinion Shifts in Large Language Models
There have been numerous studies evaluating bias of LLMs towards political topics. However, how positions towards these topics in model outputs are highly sensitive to the prompt. What happens when the prompt itself is suggestive of certain arguments towards those positions remains underexplored. This is crucial for understanding how robust these bias evaluations are and for understanding model behaviour, as these models frequently interact with opinionated text. To that end, we conduct experim…