Tootfinder

Non-affine Families of 8 x 8 Complex Hadamard Matrices
Tuomo Valtonen
https://arxiv.org/abs/2505.22947 https://arxiv.org/pdf/2505.229…

Non-affine Families of 8 x 8 Complex Hadamard Matrices
Six non-affine 3-parameter families of complex Hadamard matrices of order 8 are presented. These families contain Hadamard matrices that are not equivalent to any previously known Hadamard matrices in the literature. Each family arises from unimodular points of an affine variety defined by palindromic polynomials. The families are given as an image of a function that solves the corresponding system of polynomials on a domain that guarantees unimodularity of the solutions

Regularized Extragradient Methods for Solving Equilibrium Problems on Hadamard Manifolds
Shikher Sharmaa, Pankaj Gautam, Simeon Reich
https://arxiv.org/abs/2506.22391

Regularized Extragradient Methods for Solving Equilibrium Problems on Hadamard Manifolds
Employing two distinct types of regularization terms, we propose two regularized extragradient methods for solving equilibrium problems on Hadamard manifolds. The sequences generated by these extragradient algorithms converge to a solution of the equilibrium problem without requiring the Lipschitz continuity of the bifunction or imposing additional conditions on the parameters. We establish convergence results for both algorithms and derive global error bounds along with $R$-linear convergence …

A synthetic Lorentzian Cartan-Hadamard theorem
Darius Er\"os, Sebastian Gieger
https://arxiv.org/abs/2506.22197 https://arxiv.or…

A synthetic Lorentzian Cartan-Hadamard theorem
We formulate and prove a synthetic Lorentzian Cartan-Hadamard theorem. This result both transfers the corresponding statement for locally convex metric spaces established by S. Alexander and R. Bishop to the Lorentzian setting, and simultaneously generalizes the smooth Lorentzian theorem discussed by J. Beem and P. Ehrlich to the recently established framework of synthetic Lorentzian geometry. Our approach is based on an appropriate notion of local concavity for Lorentzian (pre-)length spaces, …

Resource-Efficient Hadamard Test Circuits for Nonlinear Dynamics on a Trapped-Ion Quantum Computer
Eleftherios Mastorakis, Muhammad Umer, Milena Guevara-Bertsch, Juris Ulmanis, Felix Rohde, Dimitris G. Angelakis
https://arxiv.org/abs/2507.19250

Resource-Efficient Hadamard Test Circuits for Nonlinear Dynamics on a Trapped-Ion Quantum Computer
Resource-efficient, low-depth implementations of quantum circuits remain a promising strategy for achieving reliable and scalable computation on quantum hardware, as they reduce gate resources and limit the accumulation of noisy operations. Here, we propose a low-depth implementation of a class of Hadamard test circuits, complemented by the development of a parameterized quantum ansatz specifically tailored for variational algorithms that exploit the underlying Hadamard test framework. Our find…

Lensing Without Borders: Measurements of galaxy-galaxy lensing and projected galaxy clustering in DESI DR1
S. Heydenreich, A. Leauthaud, C. Blake, Z. Sun, J. U. Lange, T. Zhang, M. DeMartino, A. J. Ross, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, F. J. Castander, T. Claybaugh, A. Cuceu, A. de la Macorra, J. DeRose, Arjun Dey, Biprateep Dey, P. Doel, N. Emas, S. Ferraro, A. Font-Ribera, J. E. Forero-Romero, C. Garcia-Quintero, E. Gazta\~naga, S. Gontcho A Gontcho, G. Gutierrez, B. Had…

Lensing Without Borders: Measurements of galaxy-galaxy lensing and projected galaxy clustering in DESI DR1
We present Galaxy-Galaxy Lensing measurements obtained by cross-correlating spectroscopically observed galaxies from the first data release of the Dark Energy Spectroscopic Instrument (DESI) with source galaxies from the Hyper Suprime-Cam Subaru Strategic Survey, the Kilo-Degree Survey, the Sloan Digital Sky Survey, and the Dark Energy Survey. Specifically, we measure the excess surface mass density $ΔΣ$ and tangential shear $γ_\mathrm{t}$ for the Bright Galaxy Sample and Luminous Red Galaxi…

VHU-Net: Variational Hadamard U-Net for Body MRI Bias Field Correction
Xin Zhu
https://arxiv.org/abs/2506.19181 https://arxiv.org/pdf…

VHU-Net: Variational Hadamard U-Net for Body MRI Bias Field Correction
Bias field artifacts in magnetic resonance imaging (MRI) scans introduce spatially smooth intensity inhomogeneities that degrade image quality and hinder downstream analysis. To address this challenge, we propose a novel variational Hadamard U-Net (VHU-Net) for effective body MRI bias field correction. The encoder comprises multiple convolutional Hadamard transform blocks (ConvHTBlocks), each integrating convolutional layers with a Hadamard transform (HT) layer. Specifically, the HT layer perfo…

🇺🇦 #NowPlaying on #BBC6Music's #6MusicArtistInResidence
Ship Sket:
🎵 Midnight Banquet
#ShipSket
https://hdmurder.bandcamp.com/track/midnight-banquet
https://open.spotify.com/track/0k1nsk67U5RwvxxG3lHWB5

This https://arxiv.org/abs/2502.13067 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Spectral geometry of the curl operator on smoothly bounded domains
We show that the spectrum of the curl operator on a generic smoothly bounded domain in three-dimensional Euclidean space consists of simple eigenvalues. The main new ingredient in our proof is a formula for the variation of curl eigenvalues under a perturbation of the domain, reminiscent of Hadamard's formula for the variation of Laplace eigenvalues under Dirichlet boundary conditions. As another application of this variational formula, we simplify the derivation of a well-known necessary condi…

Hadamard fractional Brownian motion: path properties and Wiener integration
Luisa Beghin, Alessandro De Gregorio, Yuliya Mishura
https://arxiv.org/abs/2507.13512

Hadamard fractional Brownian motion: path properties and Wiener integration
The so-called Hadamard fractional Brownian motion, as defined in Beghin et al. (2025) by means of Hadamard fractional operators, is a Gaussian process which shares some properties with standard Brownian motion (such as the one-dimensional distribution). However, it also resembles the fractional Brownian motion in many other features as, for instance, self-similarity, long/short memory property, Wiener-integral representation. The logarithmic kernel in the Hadamard fractional Brownian motion rep…

A small and interesting architecture for early fault-tolerant quantum computers
Jacob S. Nelson, Andrew J. Landahl, Andrew D. Baczewski
https://arxiv.org/abs/2507.20387 https://…

A small and interesting architecture for early fault-tolerant quantum computers
We present an architecture for early fault-tolerant quantum computers based on the smallest interesting colour code (Earl Campbell, 2016). It realizes a universal logical gate set consisting of single-qubit measurements and preparations in the X and Z bases, single- qubit Hadamard (H) gates, and three-qubit controlled-controlled-Z (CCZ) gates. State teleportations between [[4, 2, 2]] (2D) and [[8, 3, 2]] (3D) error-detecting color codes allow one to make use of the respective transversal H and …