Tootfinder

Bounds on bending in terms of the Schwartzian derivative and Teichm\"uller distance
Martin Bridgeman, Ming Hong Tee
https://arxiv.org/abs/2509.12493 https://

Bounds on bending in terms of the Schwartzian derivative and Teichmüller distance
Locally-univalent maps $f: Δ\rightarrow \hat{\mathbb{C}}$ can be parametrized by their Schwartzian derivatives $Sf$, a quadratic differential whose norm $\|Sf\|_\infty$ measures how close $f$ is to being Möbius. In particular, by Nehari, if $\|Sf\|_\infty < 1/2$ then $f$ is univalent and if $f$ is univalent then $\|Sf\|_\infty < 3/2$. Thurston gave another parametrization associating to $f$ a bending measured lamination $β_f$ which has a natural norm $\|β_…

An elementary derivation of 3-cycles for a quadratic map
Arpad Benyi, Ioan Casu
https://arxiv.org/abs/2510.12558 https://arxiv.org/pdf/2510.12558

An elementary derivation of 3-cycles for a quadratic map
We present an elementary derivation of the period-three cycles for the real quadratic map $x\mapsto x^2+c$, a fundamental model in one-dimensional discrete dynamics. Using symmetric polynomials, we obtain a complete algebraic characterization of 3-cycles and determine explicit conditions for their existence and stability, without reliance on computer algebra. Through conjugacy with the logistic map, we recover the classical threshold values of the logistic parameter corresponding to the emergen…

A Dark Matter Model with Quadratic Equation of State: Background Evolution and Structure Formation
Kazem Rezazadeh, Ebrahim Yusofi, Alireza Talebian
https://arxiv.org/abs/2509.11138

A Dark Matter Model with Quadratic Equation of State: Background Evolution and Structure Formation
We propose that dark matter (DM) possesses a quadratic equation of state, which becomes significant at high densities, altering the Universe's evolution during its early stages. We derive the modified background evolution equations for the Hubble parameter $H(z)$ and the DM density parameter $Ω_{\text{dm}}(z)$. We then perturb the governing equations to study the linear growth of matter fluctuations, computing the observable growth factor $fσ_8(z)$. Finally, we compare the model with the late…

A Collaborative Framework for Quantum Optimisation and Quantum Neural Networks: Credit Feature Selection and Image Classification
JiaNing Long, Xuechen Liang
https://arxiv.org/abs/2509.11110

A Collaborative Framework for Quantum Optimisation and Quantum Neural Networks: Credit Feature Selection and Image Classification
This paper investigates the efficacy of quantum computing in two distinct machine learning tasks: feature selection for credit risk assessment and image classification for handwritten digit recognition. For the first task, we address the feature selection challenge of the German Credit Dataset by formulating it as a Quadratic Unconstrained Binary Optimization (QUBO) problem, which is solved using quantum annealing to identify the optimal feature subset. Experimental results show that the result…

Class numbers of Imaginary bicyclic biquadratic number fields
Anuj Jakhar, Ravi Kalwaniya, Mahesh Kumar Ram
https://arxiv.org/abs/2509.13153 https://arxiv.…

Class numbers of Imaginary bicyclic biquadratic number fields
For any fixed positive integer $n$, we provide a method to compute all imaginary bicyclic biquadratic number fields with class number $n$, along with their class group structures, using the list of all imaginary quadratic number fields whose class numbers divide $2n$. We apply this method to list all imaginary bicyclic biquadratic number fields with class numbers $4$, $6$ and $7$. We also present the class group structure of each subfield of these fields.

High-Gain Voltage-Multiplier Coupled Quadratic Boost Converter: A New Design for Small Scale PV Integration
Safa Mohammed Sali, Hoach The Nguyen, Ameena Saad Al-Sumaiti
https://arxiv.org/abs/2509.09789

High-Gain Voltage-Multiplier Coupled Quadratic Boost Converter: A New Design for Small Scale PV Integration
This paper introduces a single-switch high-gain voltage-multiplier coupled quadratic boost converter (HGVM-QBC), developed from the conventional quadratic boost converter (QBC). The proposed topology is designed to achieve higher voltage gain, lower semiconductor voltage stress, and continuous current operation, making it particularly suitable for small-scale photovoltaic (PV) systems. By incorporating a voltage multiplier cell into the QBC, the converter significantly improves voltage boosting…

Wasserstein error estimates between telegraph processes and Brownian motion
Gerardo Barrera, Jani Lukkarinen, Mikko S. Pakkanen
https://arxiv.org/abs/2509.11871 https://

Wasserstein error estimates between telegraph processes and Brownian motion
We provide non-asymptotic error bounds in the path Wasserstein distance with quadratic integral cost between suitable functionals of the telegraph process and the corresponding functional of Brownian motion with explicit diffusivity constant. These results cover, in particular, the well-known example of the exponential integral functional of the geometric Brownian motion. The non-asymptotic error bounds tend to zero in the so-called Kac regime. Moreover, the error bounds remain valid when the f…

InfGen: A Resolution-Agnostic Paradigm for Scalable Image Synthesis
Tao Han, Wanghan Xu, Junchao Gong, Xiaoyu Yue, Song Guo, Luping Zhou, Lei Bai
https://arxiv.org/abs/2509.10441

InfGen: A Resolution-Agnostic Paradigm for Scalable Image Synthesis
Arbitrary resolution image generation provides a consistent visual experience across devices, having extensive applications for producers and consumers. Current diffusion models increase computational demand quadratically with resolution, causing 4K image generation delays over 100 seconds. To solve this, we explore the second generation upon the latent diffusion models, where the fixed latent generated by diffusion models is regarded as the content representation and we propose to decode arbit…

Implementing the Quantum Approximate Optimization Algorithms for QUBO problems Across Quantum Hardware Platforms: Performance Analysis, Challenges, and Strategies
Teemu Pihkakoski, Aravind Plathanam Babu, Pauli Taipale, Petri Liimatta, Matti Silveri
https://arxiv.org/abs/2510.12336

Implementing the Quantum Approximate Optimization Algorithms for QUBO problems Across Quantum Hardware Platforms: Performance Analysis, Challenges, and Strategies
Quantum computers are expected to offer significant advantages in solving complex optimization problems that are challenging for classical computers. Quadratic Unconstrained Binary Optimization (QUBO) problems represent an important class of problems with relevance in finance and logistics. The Quantum Approximate Optimization Algorithm (QAOA) is a prominent candidate for solving QUBO problems on near-term quantum devices. In this paper, we investigate the performance of both the standard QAOA …

Composition laws of binary quadratic forms and isolations of quadratic forms
Jangwon Ju, Daejun Kim, Kyoungmin Kim, Mingyu Kim, Byeong-Kweon Oh
https://arxiv.org/abs/2508.07916 …

Composition laws of binary quadratic forms and isolations of quadratic forms
A positive definite and integral quadratic form $f$ is called irrecoverable if there is a quadratic form $F$ such that it represents all proper subforms of $f$, whereas it does not represent $f$ itself. In this case, $F$ is called an isolation of $f$. In this article, we prove that there does not exist a binary isolation of any unary quadratic form. We also prove that there does not exist a ternary isolation of any binary quadratic form. Furthermore, if the form class group of a primitive binar…