Tootfinder

Towards Data-Driven Metrics for Social Robot Navigation Benchmarking
Pilar Bachiller-Burgos, Ulysses Bernardet, Luis V. Calderita, Pranup Chhetri, Anthony Francis, Noriaki Hirose, No\'e P\'erez, Dhruv Shah, Phani T. Singamaneni, Xuesu Xiao, Luis J. Manso
https://arxiv.org/abs/2509.01251

Towards Data-Driven Metrics for Social Robot Navigation Benchmarking
This paper presents a joint effort towards the development of a data-driven Social Robot Navigation metric to facilitate benchmarking and policy optimization. We provide our motivations for our approach and describe our proposal for storing rated social navigation trajectory datasets. Following these guidelines, we compiled a dataset with 4427 trajectories -- 182 real and 4245 simulated -- and presented it to human raters, yielding a total of 4402 rated trajectories after data quality assurance…

Bessmertny\u{i} realizations of symmetric multivariate rational matrix functions over any field
Jason Elsinger, Ian Orzel, Aaron Welters
https://arxiv.org/abs/2509.00553 https:/…

Bessmertnyĭ realizations of symmetric multivariate rational matrix functions over any field
In this paper, we prove the following. First, every square matrix whose entries are multivariable rational functions over a field $\mathbb{F}$ has a Bessmertnyĭ realization, i.e., is the Schur complement of an affine linear square matrix pencil with coefficients in $\mathbb{F}$. Second, if the matrix is also symmetric and the characteristic of the field $\mathbb{F}$ is not two then it has a symmetric Bessmertnyĭ realization (i.e., the pencil can be chosen to consist of symmetric matrices) and…

1,000 Swiss glaciers already gone, and the melting is speeding up #Switzerland

1,000 Swiss glaciers already gone, and the melting is speeding up
Swiss glaciers lost nearly 3% of their volume in 2025, following a snow-poor winter and scorching summer heatwaves. The melt has been so extreme that some glaciers lost more than two meters of ice thickness in a single season. Scientists caution that the decline is destabilizing mountains, raising risks of rock and ice avalanches. Long-term monitoring efforts are now more critical than ever.

Weak-strong uniqueness for general cross-diffusion systems with volume filling
Maria Heitzinger, Ansgar J\"ungel
https://arxiv.org/abs/2509.25978 https://

Weak-strong uniqueness for general cross-diffusion systems with volume filling
The weak-strong uniqueness of solutions to a broad class of cross-diffusion systems with volume filling is established. In general, the diffusion matrices are neither symmetric nor positive definite. This issue is overcome by supposing that the equations possess a Boltzmann-type entropy structure, which ensures the existence of bounded weak solutions. In this framework, general conditions on the mobility matrix are identified that allow for the proof of the weak-strong uniqueness property by me…

Almost paracontact metric 3-dimensional Walker manifolds
Galia Nakova, Cornelia-Livia Bejan
https://arxiv.org/abs/2509.21809 https://arxiv.org/pdf/2509.218…

Almost paracontact metric 3-dimensional Walker manifolds
In this paper we construct and study almost paracontact metric structures $(φ,ξ,η,g)$ on a 3-dimensional Walker manifold $(M,g)$ with respect to a local basis only by the coordinate functions of a unit space-like vector field $ξ$, globally defined on $M$ and a function $f$ on $M$, characterizing the Lorentzian metric $g$. Necessary and sufficient conditions are obtained for $M$, endowed with these structures, to fall in one of the following classes of 3-dimensional almost paracontact metric…

Faster Inference of Cell Complexes from Flows via Matrix Factorization
Til Spreuer, Josef Hoppe, Michael T. Schaub
https://arxiv.org/abs/2508.21372 https://

Faster Inference of Cell Complexes from Flows via Matrix Factorization
We consider the following inference problem: Given a set of edge-flow signals observed on a graph, lift the graph to a cell complex, such that the observed edge-flow signals can be represented as a sparse combination of gradient and curl flows on the cell complex. Specifically, we aim to augment the observed graph by a set of 2-cells (polygons encircled by closed, non-intersecting paths), such that the eigenvectors of the Hodge Laplacian of the associated cell complex provide a sparse, interpre…

MTRec: Learning to Align with User Preferences via Mental Reward Models
Mengchen Zhao, Yifan Gao, Yaqing Hou, Xiangyang Li, Pengjie Gu, Zhenhua Dong, Ruiming Tang, Yi Cai
https://arxiv.org/abs/2509.22807

MTRec: Learning to Align with User Preferences via Mental Reward Models
Recommendation models are predominantly trained using implicit user feedback, since explicit feedback is often costly to obtain. However, implicit feedback, such as clicks, does not always reflect users' real preferences. For example, a user might click on a news article because of its attractive headline, but end up feeling uncomfortable after reading the content. In the absence of explicit feedback, such erroneous implicit signals may severely mislead recommender systems. In this paper, we pr…

Balanced Fibonacci word rectangles, and beyond
Jeffrey Shallit, Ingrid Vukusic
https://arxiv.org/abs/2509.25994 https://arxiv.org/pdf/2509.25994

Balanced Fibonacci word rectangles, and beyond
Following a recent paper of Anselmo et al., we consider $m \times n$ rectangular matrices formed from the Fibonacci word, and we show that their balance properties can be solved with a finite automaton. We also generalize the result to every Sturmian characteristic word corresponding to a quadratic irrational.

Russian oil refinery in Samara Oblast in flames after drone attack, media reports: https://benborges.xyz/2025/08/28/russian-oil-refinery-in-samara.html

MATRIX: Multi-Agent simulaTion fRamework for safe Interactions and conteXtual clinical conversational evaluation
Ernest Lim, Yajie Vera He, Jared Joselowitz, Kate Preston, Mohita Chowdhury, Louis Williams, Aisling Higham, Katrina Mason, Mariane Melo, Tom Lawton, Yan Jia, Ibrahim Habli
https://arxiv.org/abs/2508.19163

MATRIX: Multi-Agent simulaTion fRamework for safe Interactions and conteXtual clinical conversational evaluation
Despite the growing use of large language models (LLMs) in clinical dialogue systems, existing evaluations focus on task completion or fluency, offering little insight into the behavioral and risk management requirements essential for safety-critical systems. This paper presents MATRIX (Multi-Agent simulaTion fRamework for safe Interactions and conteXtual clinical conversational evaluation), a structured, extensible framework for safety-oriented evaluation of clinical dialogue agents. MATRIX …