Tootfinder

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…

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…

Regierung: Apples Lieferkette in Indien schuf sechsstellige Anzahl Jobs
350.000 Menschen sollen auf dem Subkontinent mittlerweile für Apples Lieferanten arbeiten. Das wurde in fünf Jahren erreicht.
ht…

PMODE: Theoretically Grounded and Modular Mixture Modeling
Robert A. Vandermeulen
https://arxiv.org/abs/2508.21396 https://arxiv.org/pdf/2508.21396

PMODE: Theoretically Grounded and Modular Mixture Modeling
We introduce PMODE (Partitioned Mixture Of Density Estimators), a general and modular framework for mixture modeling with both parametric and nonparametric components. PMODE builds mixtures by partitioning the data and fitting separate estimators to each subset. It attains near-optimal rates for this estimator class and remains valid even when the mixture components come from different distribution families. As an application, we develop MV-PMODE, which scales a previously theoretical approach …

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…

#idw #Hitzewellen in Nord- und Mitteleuropa extremer und chaotischer
Hitzewellen in Europa werden nicht nur häufiger und heißer, sondern auch unberechenbarer. Eine Studie (erschienen in Nature Communications) des Klimaforschers Goratz Beobide-Arsuaga vom Earth and Society Research Hub (ESRAH) der Univer…

Hitzewellen in Nord- und Mitteleuropa extremer und chaotischer

Modular differential equations of minimal orders of the elliptic genus of Calabi--Yau varieties
Dmitrii Adler, Valery Gritsenko
https://arxiv.org/abs/2509.25954 https://

Modular differential equations of minimal orders of the elliptic genus of Calabi--Yau varieties
We study modular differential equations (MDEs) of high orders for weak Jacobi forms and find necessary conditions for weak Jacobi forms to satisfy MDEs of order 3 with respect to the heat operator. We investigate all possible MDEs for the elliptic genus of six-dimensional manifolds with a trivial first Chern class. We prove that the minimal possible order of the MDE for the elliptic genus of a strict six-dimensional Calabi--Yau variety is four, and find MDEs of order 7 for hyperkähler varietie…

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 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…

A framework for proving quantum modularity: Application to Witten's asymptotic expansion conjecture
Yuya Murakami
https://arxiv.org/abs/2508.21710 https://

A framework for proving quantum modularity: Application to Witten's asymptotic expansion conjecture
We address two linked problems at the interface of quantum topology and number theory: deriving asymptotic expansions of the Witten--Reshetikhin--Turaev invariants for 3-manifolds and establishing quantum modularity of false theta functions. Previous progress covers Seifert homology 3-spheres for the former and rank-one cases for the latter, both of which rely on single-variable integral representations. We extend these results to negative definite plumbed 3-manifolds and to general false theta…