Tootfinder

Algorithms for Modular Parametrizations of Elliptic Curves over $\mathbb{Q}$
SanMin Wang
https://arxiv.org/abs/2509.14747 https://arxiv.org/pdf/2509.14747

Algorithms for Modular Parametrizations of Elliptic Curves over $\mathbb{Q}$
Let \( E \) be a complex elliptic curve with conductor \( N \) and modular invariant \( j(E) \in \mathbb{Q} \). We construct a class of modular polynomials $F_N(x,j)$ that relate the modular function $x$ on $X_0(N)$ to the $j$-invariant $j$, where $x$ is obtained by composing the first coordinate function of $E$ with the modular parametrization $φ: X_0(N) \rightarrow E$. Using $F_N(x,j)$, we can precisely determine the poles of $φ$, compute exact values of $φ$ at cusps, and develop an algori…

Lepton models from non-holomorphic $A^{\prime}_{5}$ modular flavor symmetry
Cai-Chang Li, Gui-Jun Ding
https://arxiv.org/abs/2509.15183 https://arxiv.org/p…

Lepton models from non-holomorphic $A^{\prime}_{5}$ modular flavor symmetry
In the framework of non-holomorphic modular invariance approach, we have systematically constructed all minimal lepton models based on the non-holomorphic $A^{\prime}_{5}$ modular symmetry from a bottom-up approach. In these models, the Yukawa couplings are described by polyharmonic Maaß forms of integer weights at level $N=5$. Under the assumption of Majorana neutrinos, both the Weinberg operator and the type-I seesaw mechanism are considered for neutrino mass generation. All minimal models a…

GenKOL: Modular Generative AI Framework For Scalable Virtual KOL Generation
Tan-Hiep To, Duy-Khang Nguyen, Tam V. Nguyen, Minh-Triet Tran, Trung-Nghia Le
https://arxiv.org/abs/2509.14927

GenKOL: Modular Generative AI Framework For Scalable Virtual KOL Generation
Key Opinion Leader (KOL) play a crucial role in modern marketing by shaping consumer perceptions and enhancing brand credibility. However, collaborating with human KOLs often involves high costs and logistical challenges. To address this, we present GenKOL, an interactive system that empowers marketing professionals to efficiently generate high-quality virtual KOL images using generative AI. GenKOL enables users to dynamically compose promotional visuals through an intuitive interface that inte…

The column number for 3-modular matrices
Joseph Paat, Zach Walsh, Luze Xu
https://arxiv.org/abs/2509.13463 https://arxiv.org/pdf/2509.13463

The column number for 3-modular matrices
An integer-valued matrix $\mathbf{A}$ is $Δ$-modular if each $\text{rank}(\mathbf{A}) \times \text{rank}(\mathbf{A})$ submatrix has determinant at most $Δ$ in absolute value. The column number problem is to determine the maximum number of pairwise non-parallel columns of a rank-$r$, $Δ$-modular matrix. Exact values for the column number are only known for $r \le 2$ or $Δ\le 2$. We prove that if $r$ is sufficiently large, then the maximum number of pairwise non-parallel columns of a rank-$r$…

🧑‍🤝‍🧑 Modular robots assemble into bridges, shelters and tools for outdoor tasks
#robots

Modular robots assemble into bridges, shelters and tools for outdoor tasks
Modular robots built by Dartmouth researchers are finding their feet outdoors. Engineered to assemble into structures that best suit the task at hand, the robots are pieced together from cube-shaped robotic blocks that combine rigid rods and soft, stretchy strings whose tension can be adjusted to deform the blocks and control their shape.

From Who Said What to Who They Are: Modular Training-free Identity-Aware LLM Refinement of Speaker Diarization
Yu-Wen Chen, William Ho, Maxim Topaz, Julia Hirschberg, Zoran Kostic
https://arxiv.org/abs/2509.15082

From Who Said What to Who They Are: Modular Training-free Identity-Aware LLM Refinement of Speaker Diarization
Speaker diarization (SD) struggles in real-world scenarios due to dynamic environments and unknown speaker counts. SD is rarely used alone and is often paired with automatic speech recognition (ASR), but non-modular methods that jointly train on domain-specific data have limited flexibility. Moreover, many applications require true speaker identities rather than SD's pseudo labels. We propose a training-free modular pipeline combining off-the-shelf SD, ASR, and a large language model (LLM) to d…

D. erzählte, es sei mittlerweile recht schwierig, in Innsbruck mit Gastvortragenden hernach essen zu gehen, weil viele Restaurants jetzt so früh mit der Küche aufhören würden. Kein Personal.

Russlands Schattenflotte beunruhigt EU
Die sogenannte russische Schattenflotte zur Umgehung von internationalen Ölsanktionen infolge des russischen Kriegs gegen die Ukraine bereitet der EU zunehmend Sorgen. Wie aus einem Arbeitspapier für das heutige Außenministertreffen in Luxemburg hervorgeht, wird die Größe dieser Flotte mittlerweile auf 600 bis 1.400 Tanker geschätzt. "Diese Schiffe tragen nicht…
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Die Russische Schattenflotte bereitet der EU zunehmend Sorgen
Trotz der EU-Sanktionen sind weiterhin Tanker mit russischem Öl unterwegs. Bis zu 1.400 Schiffe könnten zur sogenannten Schattenflotte gehören. Die EU-Außenbeauftragte Kallas fordert härtere Maßnahmen - auch aus Umweltgründen.

#today resting up after getting home about 5am - last light included a live French modular synth plus singing/wailing duo that was fab!

Zeta functions of abstract isogeny graphs and modular curves
Jun Bo Lau, Travis Morrison, Eli Orvis, Gabrielle Scullard, Lukas Zobernig
https://arxiv.org/abs/2509.15214 https://…

Zeta functions of abstract isogeny graphs and modular curves
We introduce a ``non-orientable'' variation of Serre's definition of a graph, which we call an abstract isogeny graph. These objects capture the combinatorics of the graphs $G(p,\ell,H)$, the $\ell$-isogeny graphs of supersingular elliptic curves with $H$-level structure. In particular they allow for the study of non-backtracking walks, primes, and zeta functions. We prove an analogue of Ihara's determinant formula for the zeta function of an abstract isogeny graph. For $B_1(N) \subseteq H \sub…