Tootfinder

Close points on a modular hyperbola
Tsz Ho Chan
https://arxiv.org/abs/2506.04087 https://arxiv.org/pdf/2506.04087

Close points on a modular hyperbola
In this paper, we continue the study of small squares containing at least two points on a modular hyperbola $x y \equiv c \pmod{p}$. We deduce a lower bound for its side length. We also investigate what happens if the ``distances" between two such points are special type of numbers like prime numbers, squarefree numbers or smooth numbers as well as more general multiplicatively closed sets or almost dense sets.

This https://arxiv.org/abs/2501.09805 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qbi…

Multiplex Nodal Modularity: A novel network metric for the regional analysis of amnestic mild cognitive impairment during a working memory binding task
Modularity is a well-established concept for assessing community structures in various single and multi-layer networks, including those in biological and social domains. Brain networks are known to exhibit community structure at local, meso, and global scale. However, modularity is limited as a metric to a global scale describing the overall strength of community structure, overlooking important variations in community structure at node level. To address this limitation, we extended modularity …

Quasi-equivalence of Gaussian states and energy estimates for functions of modular Hamiltonians
Adriano Chialastri, Ko Sanders
https://arxiv.org/abs/2506.03907

Quasi-equivalence of Gaussian states and energy estimates for functions of modular Hamiltonians
To compare two Gaussian states of the Weyl-CCR algebra of a free scalar QFT we study three closely related perspectives: (i) quasi-equivalence of the GNS-representations, (ii) differences of the total energy (on some Cauchy surface), and (iii) differences between functions of the modular Hamiltonians. (For perspective (ii) we will only consider real linear free scalar quantum fields on ultrastatic spacetimes.) These three perspectives are known to be related qualitatively, due to work of Araki …

MOTIF: Modular Thinking via Reinforcement Fine-tuning in LLMs
Purbesh Mitra, Sennur Ulukus
https://arxiv.org/abs/2507.02851 https://a…

MOTIF: Modular Thinking via Reinforcement Fine-tuning in LLMs
Recent advancements in the reasoning capabilities of large language models (LLMs) show that employing group relative policy optimization (GRPO) algorithm for reinforcement learning (RL) training allows the models to use more thinking/reasoning tokens for generating better responses. However, LLMs can generate only a finite amount of tokens while maintaining attention to the previously generated tokens. This limit, also known as the context size of an LLM, is a bottleneck in LLM reasoning with a…

Tracing the Interactions of Modular CMA-ES Configurations Across Problem Landscapes
Ana Nikolikj, Mario Andr\'es Mu\~noz, Eva Tuba, Tome Eftimov
https://arxiv.org/abs/2507.02331

Tracing the Interactions of Modular CMA-ES Configurations Across Problem Landscapes
This paper leverages the recently introduced concept of algorithm footprints to investigate the interplay between algorithm configurations and problem characteristics. Performance footprints are calculated for six modular variants of the CMA-ES algorithm (modCMA), evaluated on 24 benchmark problems from the BBOB suite, across two-dimensional settings: 5-dimensional and 30-dimensional. These footprints provide insights into why different configurations of the same algorithm exhibit varying perfo…

This https://arxiv.org/abs/2411.04900 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Modular domain walls and gravitational waves
We discuss modular domain walls and gravitational waves in a class of supersymmetric models where quark and lepton flavour symmetry emerges from modular symmetry. In such models a single modulus field $τ$ is often assumed to be stabilised at or near certain fixed point values such as $τ= {\rm i}$ and $τ= ω$ (the cube root of unity), in its fundamental domain. We show that, in the global supersymmetry limit of certain classes of potentials, the vacua at these fixed points may be degenerate, …

State Similarity in Modular Superconducting Quantum Processors with Classical Communications
Bujiao Wu, Changrong Xie, Peng Mi, Zhiyi Wu, Zechen Guo, Peisheng Huang, Wenhui Huang, Xuandong Sun, Jiawei Zhang, Libo Zhang, Jiawei Qiu, Xiayu Linpeng, Ziyu Tao, Ji Chu, Ji Jiang, Song Liu, Jingjing Niu, Yuxuan Zhou, Yuxuan Du, Wenhui Ren, Youpeng Zhong, Tongliang Liu, Dapeng Yu

State Similarity in Modular Superconducting Quantum Processors with Classical Communications
As quantum devices continue to scale, distributed quantum computing emerges as a promising strategy for executing large-scale tasks across modular quantum processors. A central challenge in this paradigm is verifying the correctness of computational outcomes when subcircuits are executed independently following circuit cutting. Here we propose a cross-platform fidelity estimation algorithm tailored for modular architectures. Our method achieves substantial reductions in sample complexity compar…

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Flotilla: A scalable, modular and resilient federated learning framework for heterogeneous resources
Roopkatha Banerjee, Prince Modi, Jinal Vyas, Chunduru Sri Abhijit, Tejus Chandrashekar, Harsha Varun Marisetty, Manik Gupta, Yogesh Simmhan
https://arxiv.org/abs/2507.02295

Flotilla: A scalable, modular and resilient federated learning framework for heterogeneous resources
With the recent improvements in mobile and edge computing and rising concerns of data privacy, Federated Learning(FL) has rapidly gained popularity as a privacy-preserving, distributed machine learning methodology. Several FL frameworks have been built for testing novel FL strategies. However, most focus on validating the learning aspects of FL through pseudo-distributed simulation but not for deploying on real edge hardware in a distributed manner to meaningfully evaluate the federated aspects…

EU lässt Handelserleichterungen für die Ukraine auslaufen
Die EU hat Handelsvorteile für die Ukraine auslaufen lassen, mit denen das von Russland angegriffene Land drei Jahre unterstützt wurde. Um Mitternacht mitteleuropäischer Zeit sind nach Angaben der EU-Kommission Übergangsregelungen in Kraft getreten, die andauern sollen, bis Verhandlungen über ein neues Handelsabkommen abgeschlossen sind.
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EU lässt Handelserleichterungen für die Ukraine auslaufen
Wenige Monate nach Beginn der russischen Invasion brachte die EU Zollvorteile für die Ukraine auf den Weg. Diese sind jetzt ausgelaufen. Die EU-Kommission will sich zügig um ein neues Handelsabkommen bemühen.