Tootfinder

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

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…

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…

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…

Systems-Level Analysis of Multisite Protein Phosphorylation: Mathematical Induction, Geometric Series, and Entropy
Iman Tavassoly, Adel Mehrpooya, Parsa Mirlohi, Zahra Abbaspourasadollah
https://arxiv.org/abs/2507.15050

Systems-Level Analysis of Multisite Protein Phosphorylation: Mathematical Induction, Geometric Series, and Entropy
Multisite protein phosphorylation plays a pivotal role in regulating cellular signaling and decision-making processes. In this study, we focus on the mathematical underpinnings and informational aspects of sequential, distributive phosphorylation systems. We first provide rigorous steady-state solutions derived using geometric series arguments and formal mathematical induction, demonstrating that the distribution of phosphorylation states follows a geometric progression determined by the kinase…

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…

Modeling Bulimia Nervosa in the Digital Age: The Role of Social Media
Brenda Murillo, Fabio Sanchez
https://arxiv.org/abs/2506.03491 https://

Modeling Bulimia Nervosa in the Digital Age: The Role of Social Media
Globalization has fundamentally reshaped societal dynamics, influencing how individuals interact and perceive themselves and others. One significant consequence is the evolving landscape of eating disorders such as bulimia nervosa (BN), which are increasingly driven not just by internal psychological factors but by broader sociocultural and digital contexts. While mathematical modeling has provided valuable insights, traditional frameworks often fall short in capturing the nuanced roles of soci…