Tootfinder

Modular analogs of character formulas and minimal lifts of modular forms
Patrick B. Allen, Preston Wake
https://arxiv.org/abs/2509.21426 https://arxiv.org/…

Modular analogs of character formulas and minimal lifts of modular forms
If $f$ is a mod-$3$ eigenform of weight 2 and level $Γ_0(\ell^2)$ for a prime $\ell$ such that $\ell \equiv -1 \pmod{3}$, and $\ell$ is a vexing prime for $f$, we show that there is no obstruction to finding a minimal lift of $f$, but that there is an obstruction to finding a nonminimal lift. The key new ingredient that we prove is a modular analog of the standard character formula for a cuspidal representation of $\mathrm{GL}_2(\mathbb{F}_\ell)$, an enhancement that allows us to easily comput…

Towards Modular and Accessible AUV Systems
Mingxi Zhou, Farhang Naderi, Yuewei Fu, Tony Jacob, Lin Zhao, Manavi Panjnani, Chengzhi Yuan, William McConnell, Emir Cem Gezer
https://arxiv.org/abs/2509.24864

Towards Modular and Accessible AUV Systems
This paper reports the development of a new open- access modular framework, called Marine Vehicle Packages (MVP), for Autonomous Underwater Vehicles. The framework consists of both software and hardware designs allowing easy construction of AUV for research with increased customizability and sufficient payload capacity. This paper will present the scalable hardware system design and the modular software design architecture. New features, such as articulated thruster integra- tion and high-level…

iOS warnt nun vor langsamen Netzteilen
Mittlerweile hat Apple eine iOS-Funktion eingeführt, die erkennt, sobald das iPhone nur bedingt Saft erhält. Das kann man tun.
https://www.heise.de/news/iOS-warnt-…

Modularity and random graphs
Colin McDiarmid, Fiona Skerman
https://arxiv.org/abs/2509.22066 https://arxiv.org/pdf/2509.22066

Modularity and random graphs
This work will appear as a chapter in a forthcoming volume titled `Topics in Probabilistic Graph Theory'. For a given graph $G$, each partition of the vertices has a modularity score, with higher values indicating that the partition better captures community structure in $G$. The modularity $q^*(G)$ of $G$ is the maximum over all vertex-partitions of the modularity score, and satisfies $0\leq q^*(G)< 1$. Modularity lies at the heart of the most popular algorithms for community detection. In t…

Rolling with modular symmetry: quintessence and de Sitter in heterotic orbifolds
Hansel Gordillo-Ruiz, Miguel Hernandez-Segura, Ignacio Portillo-Castillo, Saul Ramos-Sanchez, Ivonne Zavala
https://arxiv.org/abs/2509.22781

Rolling with modular symmetry: quintessence and de Sitter in heterotic orbifolds
Modular invariance is a fundamental symmetry in string compactifications, constraining both the structure of the effective theory and the dynamics of moduli and matter fields. It has also gained renewed importance in the context of swampland conjectures and, independently, flavour physics. We investigate a modular-invariant scalar potential arising from heterotic orbifolds, where the flavour structure and moduli dynamics are jointly shaped by the underlying geometry. Focusing on a string-inspir…

ConQuER: Modular Architectures for Control and Bias Mitigation in IQP Quantum Generative Models
Xiaocheng Zou, Shijin Duan, Charles Fleming, Gaowen Liu, Ramana Rao Kompella, Shaolei Ren, Xiaolin Xu
https://arxiv.org/abs/2509.22551

ConQuER: Modular Architectures for Control and Bias Mitigation in IQP Quantum Generative Models
Quantum generative models based on instantaneous quantum polynomial (IQP) circuits show great promise in learning complex distributions while maintaining classical trainability. However, current implementations suffer from two key limitations: lack of controllability over generated outputs and severe generation bias towards certain expected patterns. We present a Controllable Quantum Generative Framework, ConQuER, which addresses both challenges through a modular circuit architecture. ConQuER e…

Non-Holomorphic $A_4$ Modular Symmetry in Type-I Seesaw: Implications for Neutrino Masses and Leptogenesis
Swaraj Kumar Nanda (SOA University), Maibam Ricky Devi (Gauhati University), Sudhanwa Patra (IIT Bhilai)
https://arxiv.org/abs/2509.22108

Non-Holomorphic $A_4$ Modular Symmetry in Type-I Seesaw: Implications for Neutrino Masses and Leptogenesis
We propose a minimal extension of the Standard Model with right-handed neutrinos, governed by a non-holomorphic $A_{4}$ modular flavor symmetry. Within this model framework, the light neutrino masses are generated via the popular type-I seesaw mechanism in which the structure of the Dirac neutrino Yukawa couplings is decided by nonholomorphic modular forms. Unlike conventional flavor models with ad hoc flavon fields, the structure of Dirac and Majorana mass matrices is entirely determined by a …

N78 Frequency Band Modular RIS Design and Implementation
Sefa Kayrakl{\i}k, Recep Ba\c{s}, Hasan O\u{g}uzhan \c{C}al{\i}\c{s}kan, Samed \c{S}ahino\u{g}lu, Sercan Erdo\u{g}an, \.Ilhami \"Unal, \.Ibrahim H\"okelek, K{\i}van\c{c} Nurdan, Ali G\"or\c{c}in
https://arxiv.org/abs/2509.24355…

N78 Frequency Band Modular RIS Design and Implementation
Reconfigurable intelligent surface (RIS), capable of dynamically controlling wireless propagation characteristics using reflecting antenna elements, is a promising technology for enhancing signal coverage and improving end-user connectivity in next-generation wireless networks. This paper presents a complete design flow of a modular RIS prototype operating at the n78 frequency band, starting from the simulations to the prototype development and testing. An RIS prototype includes one master and …

Modular curves of prime-power level with infinitely many quadratic points
Michael Cerchia, Rakvi
https://arxiv.org/abs/2509.22895 https://arxiv.org/pdf/25…

Modular curves of prime-power level with infinitely many quadratic points
We completely determine the $1085$ open subgroups $H$ of $\operatorname{GL}_2(\widehat{\mathbb{Z}})$ of prime-power level that satisfy $-I \in H$ and $\operatorname{det}(H)=\widehat{\mathbb{Z}}^{\times}$ for which the corresponding modular curve $X_H$ has infinitely many quadratic points. When $g(X_H)\geq 2$ this is equivalent to determining all the hyperelliptic modular curves of prime-power level and all the bielliptic modular curves of prime-power level that admit a degree two map to a posit…

Modular Heights of Unitary Shimura Varieties
Ziqi Guo
https://arxiv.org/abs/2509.24363 https://arxiv.org/pdf/2509.24363

Modular Heights of Unitary Shimura Varieties
The goal of this paper is to prove a formula expressing the modular height of a unitary Shimura variety over a CM number field in terms of the logarithm derivative of the Hecke L-function associated with the CM extension. In a more specific term, we will introduce a global canonical integral model of such a unitary Shimura variety, and compute the arithmetic top self-intersection number of a canonical arithmetic line bundle with Hermitian metric on such integral model. At the same time, we also…