Tootfinder

Reasoning with Preference Constraints: A Benchmark for Language Models in Many-to-One Matching Markets
Marylou Fauchard, Florian Carichon, Margarida Carvalho, Golnoosh Farnadi
https://arxiv.org/abs/2509.13131

Reasoning with Preference Constraints: A Benchmark for Language Models in Many-to-One Matching Markets
Recent advances in reasoning with large language models (LLMs) have demonstrated strong performance on complex mathematical tasks, including combinatorial optimization. Techniques such as Chain-of-Thought and In-Context Learning have further enhanced this capability, making LLMs both powerful and accessible tools for a wide range of users, including non-experts. However, applying LLMs to matching problems, which require reasoning under preferential and structural constraints, remains underexplo…

Counting Salem numbers arising from arithmetic hyperbolic orbifolds
Michelle Chu, Plinio G. P. Murillo, Otto Romero, Lola Thompson
https://arxiv.org/abs/2508.08003 https://

Counting Salem numbers arising from arithmetic hyperbolic orbifolds
The relationship between Salem numbers and short geodesics has been fruitful in quantitative studies of arithmetic hyperbolic orbifolds, particularly in dimensions 2 and 3. In this article, we push these connections even further. The primary goals are: (1) to bound the proportion of Salem numbers of degree up to $n+1$ in the commensurability class of classical arithmetic lattices in any odd dimension $n$; (2) to improve lower bounds for the strong exponential growth of averages of multiplicitie…

Knotted DNA Configurations in Bacteriophage Capsids: A Liquid Crystal Theory Approach
Pei Liu, Zhijie Wang, Tamara Christiani, Mariel Vazquez, M. Carme Calderer, Javier Arsuaga
https://arxiv.org/abs/2509.10410

Knotted DNA Configurations in Bacteriophage Capsids: A Liquid Crystal Theory Approach
Bacteriophages, viruses that infect bacteria, store their micron long DNA inside an icosahedral capsid with a typical diameter of 40 nm to 100 nm. Consistent with experimental observations, such confinement conditions induce an arrangement of DNA that corresponds to a hexagonal chromonic liquid-crystalline phase, and increase the topological complexity of the genome in the form of knots. A mathematical model that implements a chromonic liquid-crystalline phase and that captures the changes in t…

The Linear Reliability Channel
Alexander Mariona, Ken R. Duffy, Muriel M\'edard
https://arxiv.org/abs/2509.08079 https://arxiv.org/pdf/2509.08079

The Linear Reliability Channel
We introduce and analyze a discrete soft-decision channel called the linear reliability channel (LRC) in which the soft information is the rank ordering of the received symbol reliabilities. We prove that the LRC is an appropriate approximation to a general class of discrete modulation, continuous noise channels when the noise variance is high. The central feature of the LRC is that its combinatorial nature allows for an extensive mathematical analysis of the channel and its corresponding hard-…

Performative Market Making
Charalampos Kleitsikas, Stefanos Leonardos, Carmine Ventre
https://arxiv.org/abs/2508.04344 https://arxiv.org/pdf/2508.04344

Performative Market Making
Financial models do not merely analyse markets, but actively shape them. This effect, known as performativity, describes how financial theories and the subsequent actions based on them influence market processes, by creating self-fulfilling prophecies. Although discussed in the literature on economic sociology, this deeply rooted phenomenon lacks mathematical formulation in financial markets. Our paper closes this gap by breaking down the canonical separation of diffusion processes between the …

AI-Assisted Fixes to Code Review Comments at Scale
Chandra Maddila, Negar Ghorbani, James Saindon, Parth Thakkar, Vijayaraghavan Murali, Rui Abreu, Jingyue Shen, Brian Zhou, Nachiappan Nagappan, Peter C. Rigby
https://arxiv.org/abs/2507.13499

AI-Assisted Fixes to Code Review Comments at Scale
Aim. There are 10s of thousands of code review comments each week at Meta. We developed Metamate for Code Review (MetaMateCR) that provides AI-assisted fixes for reviewer comments in production at scale. Method. We developed an internal benchmark of 64k data points to fine-tune Llama models. Once our models achieve reasonable offline results, we roll them into production. To ensure that our AI-assisted fixes do not negatively impact the time it takes to do code reviews…

Dynamic Hybrid Modeling: Incremental Identification and Model Predictive Control
Adrian Caspari, Thomas Bierweiler, Sarah Fadda, Daniel Labisch, Maarten Nauta, Franzisko Wagner, Merle Warmbold, Constantinos C. Pantelides
https://arxiv.org/abs/2506.18344

Dynamic Hybrid Modeling: Incremental Identification and Model Predictive Control
Mathematical models are crucial for optimizing and controlling chemical processes, yet they often face significant limitations in terms of computational time, algorithm complexity, and development costs. Hybrid models, which combine mechanistic models with data-driven models (i.e. models derived via the application of machine learning to experimental data), have emerged as a promising solution to these challenges. However, the identification of dynamic hybrid models remains difficult due to the…

Diophantine approximation on abelian varieties; a conjecture of M. Waldschmidt
Lior Fishman, David Lambert, Keith Merrill, David Simmons
https://arxiv.org/abs/2506.19060

Diophantine approximation on abelian varieties; a conjecture of M. Waldschmidt
Following the work of Waldschmidt, we investigate problems in Diophantine approximation on abelian varieties. First we show that a conjecture of Waldschmidt for a given simple abelian variety is equivalent to a well-known Diophantine condition holding for a certain matrix related to that variety. We then posit a related but weaker conjecture, and establish the upper bound direction of that conjecture in full generality. For rank 1 elliptic curves defined over a number field $K \subset \mathbb{R…

AlgoTune: Can Language Models Speed Up General-Purpose Numerical Programs?
Ori Press, Brandon Amos, Haoyu Zhao, Yikai Wu, Samuel K. Ainsworth, Dominik Krupke, Patrick Kidger, Touqir Sajed, Bartolomeo Stellato, Jisun Park, Nathanael Bosch, Eli Meril, Albert Steppi, Arman Zharmagambetov, Fangzhao Zhang, David Perez-Pineiro, Alberto Mercurio, Ni Zhan, Talor Abramovich, Kilian Lieret, Hanlin Zhang, Shirley Huang, Matthias Bethge, Ofir Press

AlgoTune: Can Language Models Speed Up General-Purpose Numerical Programs?
Despite progress in language model (LM) capabilities, evaluations have thus far focused on models' performance on tasks that humans have previously solved, including in programming (Jimenez et al., 2024) and mathematics (Glazer et al., 2024). We therefore propose testing models' ability to design and implement algorithms in an open-ended benchmark: We task LMs with writing code that efficiently solves computationally challenging problems in computer science, physics, and mathematics. Our AlgoTu…

On the Sierpinski triangle and its generalizations
L. De Carli, A. Echezabal, I. Morell
https://arxiv.org/abs/2506.20456 https://arxi…

On the Sierpinski triangle and its generalizations
By examining arithmetic operations between decimal numbers in a given base m we uncover fractal structures that generalize the Sierpinski triangle