Tootfinder

A Square-Root Free Algorithm for Computing Real Givens Rotations
Carlos F. Borges
https://arxiv.org/abs/2508.19431 https://arxiv.org/pdf/2508.19431

A Square-Root Free Algorithm for Computing Real Givens Rotations
We develop an accurate square-root-free algorithm for constructing real Givens rotations. On processors that support the fused multiply-add operation in hardware, the algorithm is competitive with square-root based algorithms using a hardware square-root. Unlike the square-root-free algorithms in \cite{Hsieh1993,GENTLEMAN1973,Barlow1987,Hammarling1974ANO,Ling1989EfficientLL,Hanson,Hanson2}, our approach will construct the Givens rotation directly and is therefore applicable to a much wider vari…

I upload HTML files to #Brightspace to have more control over my content (writing it in #Emacs #orgmode). It mostly works, but yesterday I discovered BS was corrupting my code examples by applying Mat…

OTMol: Robust Molecular Structure Comparison via Optimal Transport
Xiaoqi Wei, Xuhang Dai, Yaqi Wu, Yanxiang Zhao, Yingkai Zhang, Zixuan Cang
https://arxiv.org/abs/2509.01550 ht…

OTMol: Robust Molecular Structure Comparison via Optimal Transport
Root-mean-square deviation (RMSD) is widely used to assess structural similarity in systems ranging from flexible ligand conformers to complex molecular cluster configurations. Despite its wide utility, RMSD calculation is often challenged by inconsistent atom ordering, indistinguishable configurations in molecular clusters, and potential chirality inversion during alignment. These issues highlight the necessity of accurate atom-to-atom correspondence as a prerequisite for meaningful alignment.…

Quantum speed limits based on Jensen-Shannon and Jeffreys divergences for general physical processes
Jucelino Ferreira de Sousa, Diego Paiva Pires
https://arxiv.org/abs/2509.20347

Quantum speed limits based on Jensen-Shannon and Jeffreys divergences for general physical processes
We discuss quantum speed limits (QSLs) for finite-dimensional quantum systems undergoing a general physical process. These QSLs were obtained using two families of entropic measures, namely the square root of the Jensen-Shannon divergence, which in turn defines a faithful distance of quantum states, and the square root of the quantum Jeffreys divergence. The results apply to both closed and open quantum systems, and are evaluated in terms of the Schatten speed of the evolved state, as well as c…

Tauberian Theorem: Square-root singularity and Ramified covering of degree two
Guillaume Chevalier (IMAG, IMB)
https://arxiv.org/abs/2507.15394 https://

Tauberian Theorem: Square-root singularity and Ramified covering of degree two
We prove a Tauberian theorem concerning power series admitting square root singularities. More precisely we give an asymptotic expansion to any order of the coefficients of a power series admitting square-root type singularities. This article is one of a triptych with [Che25b] and [Che25c] that aims at proving an asympototic expansion to any order of the passage probability of an irreducible finite range random walk on free groups.

Quantifying the noise sensitivity of the Wasserstein metric for images
Erik Lager, Gilles Mordant, Amit Moscovich
https://arxiv.org/abs/2510.01015 https://…

Quantifying the noise sensitivity of the Wasserstein metric for images
Wasserstein metrics are increasingly being used as similarity scores for images treated as discrete measures on a grid, yet their behavior under noise remains poorly understood. In this work, we consider the sensitivity of the signed Wasserstein distance with respect to pixel-wise additive noise and derive non-asymptotic upper bounds. Among other results, we prove that the error in the signed 2-Wasserstein distance scales with the square root of the noise standard deviation, whereas the Euclide…

Efficient Decoding of Double-circulant and Wozencraft Codes from Square-root Errors
Oren Dubin, Noam Oz, Noga Ron-Zewi
https://arxiv.org/abs/2507.13548 htt…

Efficient Decoding of Double-circulant and Wozencraft Codes from Square-root Errors
We present efficient decoding algorithms from square-root errors for two known families of double-circulant codes: A construction based on Sidon sets (Bhargava, Taveres, and Shiva, \emph{IEEE IT 74}; Calderbank, \emph{IEEE IT 83}; Guruswami and Li, \emph{IEEE IT 2025}), and a construction based on cyclic codes (Chen, Peterson, and Weldon, \emph{Information and Control 1969}). We further observe that the work of Guruswami and Li implicitly gives a transformation from double-circulant codes of ce…

On Averages of Shifted Convolutions with Applications to $GL(2)$ and $GL(3)$ Fourier Coefficients
Jiseong Kim
https://arxiv.org/abs/2509.24152 https://arxi…

On Averages of Shifted Convolutions with Applications to $GL(2)$ and $GL(3)$ Fourier Coefficients
In this paper, we study the average of shifted sum for general multiplicative functions. As applications, we prove non-trivial upper bounds for weighted averages of shifted convolutions involving $GL(2)$ and $GL(3)$ Fourier coefficients without smoothing. We apply square-root cancellation on average over short intervals for $GL(2)$ Fourier coefficients with the standard Hardy-Littlewood circle method.

Reframing Three-Dimensional Morphometrics Through Functional Data Innovations
Aneesha Balachandran Pillay, Issa-Mbenard Dabo, Sophie Dabo-Niang, Dharini Pathmanathan
https://arxiv.org/abs/2509.00650

Reframing Three-Dimensional Morphometrics Through Functional Data Innovations
This study innovates geometric morphometrics by incorporating functional data analysis, the square-root velocity function (SRVF), and arc-length parameterisation for 3D morphometric data, leading to the development of seven new pipelines in addition to the standard geometric morphometrics (GM) approach.. This enables three-dimensional images to be examined from perspectives that do not neglect curvature, through the combined use of arc-length parameterisation, soft-alignment, and elastic-alignm…

Traveltime signature of 3-D edge diffractions exemplified by triple-square-root moveout
Pavel Znak, Dirk Gajewski
https://arxiv.org/abs/2508.19187 https://…

Traveltime signature of 3-D edge diffractions exemplified by triple-square-root moveout
Various underground anomalies, both natural and artificial, cause diffraction of high-frequency seismic and electromagnetic pulses emitted from the earth's surface. Backscattered, they are registered by seismic sensors and ground-penetrating radars. Most of these signals can be categorized as either point or edge diffraction. Despite the abundance of linear structures in geological formations and among buried anthropogenic objects, diffraction processing often relies on the idea of point diffra…

Normalized Square Root: Sharper Matrix Factorization Bounds for Differentially Private Continual Counting
Monika Henzinger, Nikita P. Kalinin, Jalaj Upadhyay
https://arxiv.org/abs/2509.14334

Normalized Square Root: Sharper Matrix Factorization Bounds for Differentially Private Continual Counting
The factorization norms of the lower-triangular all-ones $n \times n$ matrix, $γ_2(M_{count})$ and $γ_{F}(M_{count})$, play a central role in differential privacy as they are used to give theoretical justification of the accuracy of the only known production-level private training algorithm of deep neural networks by Google. Prior to this work, the best known upper bound on $γ_2(M_{count})$ was $1 + \frac{\log n}π$ by Mathias (Linear Algebra and Applications, 1993), and the best known lower…

Sharp Square Root Bounds for Edge Eigenvector Universality in Sparse Random Regular Graphs
Leonhard Nagel
https://arxiv.org/abs/2507.14259 https://

Sharp Square Root Bounds for Edge Eigenvector Universality in Sparse Random Regular Graphs
We study how eigenvectors of random regular graphs behave when projected onto fixed directions. For a random $d$-regular graph with $N$ vertices, where the degree $d$ grows slowly with $N$, we prove that these projections follow approximately normal distributions. Our main result establishes a Berry-Esseen bound showing convergence to the Gaussian with error $O(\sqrt{d} \cdot N^{-1/6+\varepsilon})$ for degrees $d \leq N^{1/4}$. This bound significantly improves upon previous results that had er…

First-Extinction Law for Resampling Processes
Matteo Benati, Alessandro Londei, Denise Lanzieri, Vittorio Loreto
https://arxiv.org/abs/2509.20101 https://a…

First-Extinction Law for Resampling Processes
Extinction times in resampling processes are fundamental yet often intractable, as previous formulas scale as $2^M$ with the number of states $M$ present in the initial probability distribution. We solve this by treating multinomial updates as independent square-root diffusions of zero drift, yielding a closed-form law for the first-extinction time. We prove that the mean coincides exactly with the Wright-Fisher result of Baxter et al., thereby replacing exponential-cost evaluations with a line…

Heavy flavored hydrogen molecule systems
Hui-Min Yang, Yao Ma, Shi-Lin Zhu
https://arxiv.org/abs/2507.21498 https://arxiv.org/pdf/2507.21498 https://arxiv.org/html/2507.21498
arXiv:2507.21498v1 Announce Type: new
Abstract: This study provides a comprehensive analysis of $S$-wave exotic hydrogen-like three-body systems ($pp\mu^-$, $pp\tau^-$, $\mu^-\mu^-p$, $\tau^-\tau^-p$, $p\mu^-\tau^-$) with spin-parity $J^P = 1/2^ $ and $3/2^ $, and four-body systems ($pp\mu^-\mu^-$, $pp\tau^-\tau^-$) with $J^P = 0^ $, $1^ $, and $2^ $. We use complex scaling and Gaussian expansion methods to solve the complex-scaled Schr\"{o}dinger equation and obtain possible bound and quasi-bound states. The resulting binding energies range from $-33.8$~keV to $-340$~eV. Notably, we present the first theoretical estimation of the bound-state energy levels of $pp\mu^-\mu^-$ and $pp\tau^-\tau^-$, which is of significant importance for understanding exotic few-body Coulomb systems. We further analyze spin configurations and root-mean-square radii to elucidate the spatial structure of these bound and quasi-bound states. Our results reveal that $K$-type spatial configurations play a crucial role in accurately describing bound and quasi-bound states in the hydrogen-molecule-like systems $pp\mu^-\mu^-$ and $pp\tau^-\tau^-$. Incorporating $K$-type configurations significantly alters the mass spectra of these states. Future muon colliders and muon facilities may offer promising platforms for the possible copious production of such heavy flavored hydrogen molecules and molecular ions. For instance, scattering processes such as $2\mu^- \mathrm{H_2} \to \mathrm{H_{2\mu}} 2e^-$, $\mu^- \mathrm{H_2} \to \mathrm{H_{\mu e}} e^-$, and $\mu^- \mathrm{H_2^ } \to \mathrm{H_{2\mu}^ } e^-$ could be utilized, facilitating detailed studies of intriguing states such as $\mathrm{H_{2\mu}}$, $\mathrm{H_{\mu e}}$, and $\mathrm{H_{2\mu}^ }$.
toXiv_bot_toot

Uniqueness of the Short-Time Linear Canonical Transform Phase Retrieval
Yali Dong, Rui Liu, Heying Wang
https://arxiv.org/abs/2508.18973 https://arxiv.org/…

Uniqueness of the Short-Time Linear Canonical Transform Phase Retrieval
In this paper, we focus on the problem of phase retrieval from intensity measurements of the Short-Time Linear Canonical Transform (STLCT). Specifically, we show that the STLCT allows for the unique recovery of any square-integrable function through phaseless STLCT sampling on rectangular square-root lattices. When turning to the uniform lattices, we establish counterexamples about the STLCT phase retrieval problems in L2(R). Nevertheless, for functions in band-limited function spaces, phase re…

Qrisp Implementation and Resource Analysis of a T-Count-Optimised Non-Restoring Quantum Square-Root Circuit
Heorhi Kupryianau, Marcin Niemiec
https://arxiv.org/abs/2507.12603

Qrisp Implementation and Resource Analysis of a T-Count-Optimised Non-Restoring Quantum Square-Root Circuit
Efficient quantum arithmetic operations are essential building blocks for complex quantum algorithms, yet few theoretical designs have been implemented in practical quantum programming frameworks. This paper presents the first complete implementation of the T-count optimized non-restoring quantum square root algorithm using the Qrisp quantum programming framework. The algorithm, originally proposed by Thapliyal et al., offers better resource efficiency compared to alternative methods, achieving…

Stop using root-mean-square error as a precipitation target!
Kieran M. R. Hunt
https://arxiv.org/abs/2509.08369 https://arxiv.org/pdf/2509.08369

Stop using root-mean-square error as a precipitation target!
Root-mean-square error (RMSE) remains the default training loss for data-driven precipitation models, despite precipitation being semi-continuous, zero-inflated, strictly non-negative, and heavy-tailed. This Gaussian-implied objective misspecifies the data-generating process because it tolerates negative predictions, underpenalises rare heavy events, and ignores the mass at zero. We propose replacing RMSE with the Tweedie deviance, a likelihood-based and differentiable loss from the exponential…

The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility II: An Artificial Market Generator
Guillaume Maitrier, Gr\'egoire Loeper, Jean-Philippe Bouchaud
https://arxiv.org/abs/2509.05065

The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility II: An Artificial Market Generator
This work extends and complements our previous theoretical paper on the subtle interplay between impact, order flow and volatility. In the present paper, we generate synthetic market data following the specification of that paper and show that the approximations made there are actually justified, which provides quantitative support our conclusion that price volatility can be fully explained by the superposition of correlated metaorders which all impact prices, on average, as a square-root of ex…

Conflation of Ensemble-Learned Nuclear Mass Models for Enhanced Precision
Srikrishna Agrawal, N. Chandnani, T. Ghosh, G. Saxena, B. K. Agrawal, N. Paar
https://arxiv.org/abs/2508.21771

Conflation of Ensemble-Learned Nuclear Mass Models for Enhanced Precision
Ensemble learning algorithms, the gradient boosting and bagging regressors, are employed to correct the residuals of nuclear mass excess for a diverse set of six nuclear mass models. The weighted average of these corrected residuals reduces due to their partial cancellation, yielding a significant improvement in nuclear mass predictions. Our conflated model, which integrates ensemble learning and model averaging (ELMA), achieves a root mean square error of approximately 65 keV, well below the c…

High-root topological edge-state bands
R. G. Dias, L. Madail, A. M. Marques
https://arxiv.org/abs/2508.12066 https://arxiv.org/pdf/2508.12066

High-root topological edge-state bands
This paper presents a complex band analysis of one-dimensional (1D) square and high-root topological insulators (HRTIs). We show that edge-state bands of HRTIs are sliced sections of impurity bands of a uniform tight-binding chain. A simplified topological characterization of HRTIs with generalized boundary conditions is carried out based on the existence of edge-state bands in the infinite HRTI and the restrictions imposed by the boundary conditions. Edge states in finite or semi-infinite 1D H…

Lie-RMSD: A Gradient-Based Framework for Protein Structural Alignment using Lie Algebra
Yue Hu, Zanxia Cao, Yingchao Liu
https://arxiv.org/abs/2508.17010 https://

Lie-RMSD: A Gradient-Based Framework for Protein Structural Alignment using Lie Algebra
The comparison of protein structures is a fundamental task in computational biology, crucial for understanding protein function, evolution, and for drug design. While analytical methods like the Kabsch algorithm provide an exact, closed-form solution for minimizing the Root Mean Square Deviation (RMSD) between two sets of corresponding atoms, their application is limited to this specific metric. The rise of deep learning and automatic differentiation frameworks offers a new, more flexible parad…

Regulators of the fixed elliptic curve over rank-one imaginary quadratic fields
Shenghao Hua
https://arxiv.org/abs/2507.20297 https://arxiv.org/pdf/2507.20…

Regulators of the fixed elliptic curve over rank-one imaginary quadratic fields
We establish a one-sided central limit theorem for the logarithms of regulators of a fixed rational non-CM elliptic curve $E$ over imaginary quadratic fields of rank one, motivated by the Gross--Zagier formula and a result of Radziwiłłand Soundararajan. We also establish the existence of many imaginary quadratic fields whose regulators grow at least as fast as the square root of the conductor of the field. When the central value of the $L$-function of $E$ is non-vanishing, these results a…

$TIME[t] \subseteq SPACE[O(\sqrt{t})]$ via Tree Height Compression
Logan Nye
https://arxiv.org/abs/2508.14831 https://arxiv.org/pdf/2508.14831

$TIME[t] \subseteq SPACE[O(\sqrt{t})]$ via Tree Height Compression
We prove a square-root space simulation for deterministic multitape Turing machines, showing $\TIME[t] \subseteq \SPACE[O(\sqrt{t})]$. The key step is a Height Compression Theorem that uniformly (and in logspace) reshapes the canonical left-deep succinct computation tree for a block-respecting run into a binary tree whose evaluation-stack depth along any DFS path is $O(\log T)$ for $T = \lceil t/b \rceil$, while preserving $O(b)$ work at leaves, $O(1)$ at internal nodes, and edges that are logs…

Hammering Higher Order Set Theory
Chad E. Brown, Cezary Kaliszyk, Martin Suda, Josef Urban
https://arxiv.org/abs/2509.08264 https://arxiv.org/pdf/2509.0826…

Hammering Higher Order Set Theory
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of two. Higher order automated theorem provers are particularly useful here, since the underlying framework of higher order set theory coincides with the classical extensional higher order logic of (most) higher order automated theorem provers, so no significant tr…

Training a Foundation Model for Materials on a Budget
Teddy Koker, Tess Smidt
https://arxiv.org/abs/2508.16067 https://arxiv.org/pdf/2508.16067

Training a Foundation Model for Materials on a Budget
Foundation models for materials modeling are advancing quickly, but their training remains expensive, often placing state-of-the-art methods out of reach for many research groups. We introduce Nequix, a compact E(3)-equivariant potential that pairs a simplified NequIP design with modern training practices, including equivariant root-mean-square layer normalization and the Muon optimizer, to retain accuracy while substantially reducing compute requirements. Built in JAX, Nequix has 700K paramete…

Shannon entropy for harmonic metrics on cyclic Higgs bundles II
Natsuo Miyatake
https://arxiv.org/abs/2508.12844 https://arxiv.org/pdf/2508.12844

Shannon entropy for harmonic metrics on cyclic Higgs bundles II
Let $X$ be a Riemann surface and $K_X \rightarrow X$ the canonical bundle. For each integer $r \geq 2$, each $q \in H^0(K_X^r)$, and each choice of the square root $K_X^{1/2}$ of the canonical bundle, we obtain a Higgs bundle, which is called a cyclic Higgs bundle. A diagonal harmonic metric $h = (h_1, \dots, h_r)$ on a cyclic Higgs bundle yields $r-1$-Hermitian metrics $H_1, \dots, H_{r-1}$ on $K_X^{-1} \rightarrow X$, while $h_1$, $h_r$, and $q$ yield a degenerate Hermitian metric $H_r$ on $K…

Development and testing of integrated readout electronics for next generation SiSeRO (Single electron Sensitive Read Out) devices
Tanmoy Chattopadhyay, Haley R. Stueber, Abigail Y. Pan, Sven Herrmann, Peter Orel, Kevan Donlon, Steven W. Allen, Marshall W. Bautz, Michael Cooper, Catherine E. Grant, Beverly LaMarr, Christopher Leitz, Andrew Malonis, Eric D. Miller, R. Glenn Morris, Gregory Prigozhin, Ilya Prigozhin, Artem Poliszczuk, Keith Warner, Daniel R. Wilkins

Development and testing of integrated readout electronics for next generation SiSeRO (Single electron Sensitive Read Out) devices
The first generation of Single electron Sensitive Read Out (SiSeRO) amplifiers, employed as on-chip charge detectors for charge-coupled devices (CCDs) have demonstrated excellent noise and spectral performance: a responsivity of around 800 pA per electron, an equivalent noise charge (ENC) of 3.2 electrons root mean square (RMS), and a full width half maximum (FWHM) energy resolution of 130 eV at 5.9 keV for a readout speed of 625 Kpixel/s. Repetitive Non Destructive Readout (RNDR) has also been…

Tetraquark states in the quark model
Wei-Lin Wu, Yan-Ke Chen, Yao Ma, Lu Meng, Shi-Lin Zhu
https://arxiv.org/abs/2508.11161 https://arxiv.org/pdf/2508.1116…

Tetraquark states in the quark model
We perform systematical investigations of heavy flavor tetraquark systems, including fully heavy $QQ\bar Q\bar Q$ ($Q=b,c$), doubly heavy $QQ^{(\prime)}\bar q\bar q$ ($q=u,d$), and singly heavy $Qs\bar q\bar q$ tetraquark systems, within the framework of quark potential model. We employ the Gaussian expansion method and complex scaling method to solve the four-body Hamiltonian and identify bound and resonant states. We further calculate the root mean square radii to study the spatial configurat…

The asymptotic behavior of simple eigenvalues of particle-in-well systems
Peter Hintz, Aaron Moser
https://arxiv.org/abs/2508.13545 https://arxiv.org/pdf/2…

The asymptotic behavior of simple eigenvalues of particle-in-well systems
The particle in a well in dimension one is a classical problem in quantum mechanics. We study higher-dimensional analogues of the problem, where the well is a smooth domain in $\mathbb{R}^d$. We show that simple eigenvalues and eigenfunctions of the corresponding Schrödinger operator depend smoothly on the square root $h$ of the inverse depth of the well and provide an explicit first-order expansion of the eigenvalues at $h = 0$. Our proof consists of two steps. In the first step, we constru…

Radiation of "breathing" vortex electron packets in magnetic field
G. V. Zmaga, G. K. Sizykh, D. V. Grosman, Qi Meng, Liping Zou, Pengming Zhang, D. V. Karlovets
https://arxiv.org/abs/2509.21195

Radiation of "breathing" vortex electron packets in magnetic field
When a vortex electron with an orbital angular momentum (OAM) enters a magnetic field, its quantum state is described with a nonstationary Laguerre-Gaussian (NSLG) state rather than with a stationary Landau state. A key feature of these NSLG states is oscillations of the electron wave packet's root-mean-square (r.m.s.) radius, similar to betatron oscillations. Classically, such an oscillating charge distribution is expected to emit photons. This raises a critical question: does this radiation c…

Exponential sums over primes are unbounded
Pierre-Alexandre Bazin
https://arxiv.org/abs/2508.18394 https://arxiv.org/pdf/2508.18394

Exponential sums over primes are unbounded
We prove prime exponential sums have no better than square root cancellation on average on short intervals, in the sense that $$\frac{1}{x} \sum_{-y< n\le x} \left|\sum_{\substack{n< m \le n+y\\ 1\le m \le x}} Λ(m) \mathrm{e}(αm)\right|^2 \gg y\log y$$ whenever $y \ll x^{1/3-\varepsilon}.$ This answers a question of Ramaré by proving the lower bound $$\sup_{n\le x} \left|\sum_{m\le n} Λ(m) \mathrm{e}(αm)\right| \gg x^{1/6 - \varepsilon}.$$

Improving Cram\'er-Rao Bound And Its Variants: An Extrinsic Geometry Perspective
Sunder Ram Krishnan
https://arxiv.org/abs/2509.17886 https://arxiv.org…

Improving Cramér-Rao Bound And Its Variants: An Extrinsic Geometry Perspective
This work presents a geometric refinement of the classical Cramér-Rao bound (CRB) by incorporating curvature-aware corrections based on the second fundamental form associated with the statistical model manifold. That is, our formulation shows that relying on the extrinsic geometry of the square root embedding of the manifold in the ambient Hilbert space comprising square integrable functions with respect to a fixed base measure offers a rigorous (and intuitive) way to improve upon the CRB and …

Exceptionally deficient topological square-root insulators
Subhajyoti Bid, Henning Schomerus
https://arxiv.org/abs/2508.11490 https://arxiv.org/pdf/2508.11…

Exceptionally deficient topological square-root insulators
One of the most surprising features of effectively non-Hermitian physical systems is their potential to exhibit a striking nonlinear response and fragility to small perturbations. This feature arises from spectral singularities known as exceptional points, whose realization in the spectrum typically requires fine-tuning of parameters. The design of such systems receives significant impetus from the recent conception of \emph{exceptional deficiency}, in which the entire energy spectrum is compos…

Accounting for shelf width in selecting altimetry observations for coastal sea level variability improves its agreement with tide gauges
Vandana Sukumaran, Bramha Dutt Vishwakarma
https://arxiv.org/abs/2508.20046

Accounting for shelf width in selecting altimetry observations for coastal sea level variability improves its agreement with tide gauges
A novel dynamically varying search radius algorithm is developed that takes advantage of bathymetry information to choose satellite observations that represent coastal sea level variability better. The algorithm is successfully tested at 155 tide gauge stations around the globe and demonstrates broader applicability across different coastal regimes compared to existing validation methods. This is supported by consistently higher median correlation and lower median Normalized Root Mean Square Er…

Replaced article(s) found for q-fin.TR. https://arxiv.org/list/q-fin.TR/new
[1/1]:
- The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility: A Unifying Framework
Guillaume Maitrier, Jean-Philippe Bouchaud

Experimental Validation of Provably Covert Communication Using Software-Defined Radio
Rohan Bali, Trevor E. Bailey, Michael S. Bullock, Boulat A. Bash
https://arxiv.org/abs/2508.08380

Experimental Validation of Provably Covert Communication Using Software-Defined Radio
The fundamental information-theoretic limits of covert, or low probability of detection/intercept (LPD/LPI), communication have been extensively studied for over a decade, resulting in the square root law (SRL): only $L\sqrt{n}$ covert bits can be reliably transmitted over time-bandwidth product $n$, for constant $L>0$. Transmitting more either results in detection or decoding errors. The SRL imposes significant constraints on hardware realization of mathematically-guaranteed covert communicati…

Saddle-node bifurcation during the relaminarization of turbulent puffs in pipe
Basheer Ahmad Khan, Shai Arogeti, Oriel Shoshani, Alexander Yakhot
https://arxiv.org/abs/2508.08862

Saddle-node bifurcation during the relaminarization of turbulent puffs in pipe
Turbulent puffs in a pipe persist for a long time before abruptly transitioning to laminar flow through viscous exponential decay. Direct numerical simulation results reveal a saddle-node bifurcation sequence governing the final relaminarization stage. Specifically, a universal square-root scaling law in the annihilation of critical points that is indicative of a saddle-node bifurcation. The Riccati equation has been proposed as a straightforward approach to modeling these bifurcations.

Galois theory by calculator
Thomas W. Mattman, Robertson-Figaniak, Zoe Steele
https://arxiv.org/abs/2508.18595 https://arxiv.org/pdf/2508.18595

Galois theory by calculator
We present an algorithm to determine the Galois group of an irreducible monic polynomial $f(x) \in \mathbb{Z}[x]$ of degree at most five. Following work of Conrad, Dummit, and Stauduhar this comes down to answering two questions: Is a given integer a square? and Does a given polynomial have an integral root? Since these are both easily addressed with a calculator, our algorithm amounts to Galois theory by calculator. For example, we have an implementation at Desmos.com. In an appendix we presen…

Complete harmonic metrics and subharmonic functions on the unit disc
Natsuo Miyatake
https://arxiv.org/abs/2508.12848 https://arxiv.org/pdf/2508.12848

Complete harmonic metrics and subharmonic functions on the unit disc
Let $X$ be a Riemann surface, $K_X \rightarrow X$ the canonical bundle, and $T_X\rightarrow X$ the dual bundle of the canonical bundle. For each integer $r \geq 2$, each $q \in H^0(K_X^r)$, and each choice of the square root $K_X^{1/2}$ of the canonical bundle, we obtain a Higgs bundle $(\mathbb{K}_r,Φ(q))$, which is called a cyclic Higgs bundle. A diagonal harmonic metric $h = (h_1, \dots, h_r)$ on a cyclic Higgs bundle yields $r-1$-Hermitian metrics $H_1, \dots, H_{r-1}$ on $T_X$, while $h_1…

Cancellation in Sums of Hecke Eigenvalues Over Quadratic Polynomials and Mass Equidistribution
Steven Creech
https://arxiv.org/abs/2508.18666 https://arxiv…

Cancellation in Sums of Hecke Eigenvalues Over Quadratic Polynomials and Mass Equidistribution
We study cancellation in sums of Hecke eigenvalues over irreducible quadratic polynomials over short intervals. In particular, we look at an average over bases of Hecke forms of weight $k$ in the range $\vert k-K\vert

Oscillation-Induced Frequency Generation in 1D Quantum Droplets under Harmonic-Gaussian Confinements
Jagnyaseni Jogania, Saurab Das, Ajay Nath, Jayanta Bera
https://arxiv.org/abs/2507.05902

Oscillation-Induced Frequency Generation in 1D Quantum Droplets under Harmonic-Gaussian Confinements
We explore the dynamical behavior of one-dimensional quantum droplets (QDs) governed by the extended Gross-Pitaevskii equation, under harmonic confinement supplemented by a static or time-dependent Gaussian spike (Gs) potential. Employing both variational analytical techniques and numerical simulations, we investigate the evolution of the root-mean-square (RMS) size, excitation spectrum, and phase-space dynamics of QDs. Our study reveals that while the harmonic trap sets the primary confinement…

The Fourier coefficients of the critical holomorphic multiplicative chaos
Christopher Atherfold, Joseph Najnudel
https://arxiv.org/abs/2508.13849 https://a…

The Fourier coefficients of the critical holomorphic multiplicative chaos
The holomorphic multiplicative chaos (HMC) is a holomorphic analogue of the Gaussian multiplicative chaos. It arises naturally as the limit in large matrix size of the characteristic polynomial of Haar unitary matrices, and more generally, random matrices following the Circular-$β$-Ensemble. In a previous article, Najnudel, Paquette and Simm prove that in the $L^2$ phase $β> 4$, the appropriately normalized Fourier coefficient of the HMC converges in distribution to the square root of the tot…

Fermion mass ratios from the exceptional Jordan algebra
Tejinder P. Singh
https://arxiv.org/abs/2508.10131 https://arxiv.org/pdf/2508.10131

Fermion mass ratios from the exceptional Jordan algebra
We revisit the "three generations" problem and the pattern of charged-fermion masses from the vantage of octonionic and Clifford algebra structures. Working with the exceptional Jordan algebra J3(OC) (right-handed flavor) and the symmetric cube of SU(3) (left-handed charge frame), we show that a single minimal ladder in the symmetric cube, together with the Dynkin Z2 swap (the A2 diagram flip), leads to closed-form expressions for the square-root mass ratios of all three charged families. The u…

Gaussian Sequence Model: Sample Complexities of Testing, Estimation and LFHT
Zeyu Jia, Yury Polyanskiy
https://arxiv.org/abs/2507.16734 https://

Gaussian Sequence Model: Sample Complexities of Testing, Estimation and LFHT
We study the Gaussian sequence model, i.e. $X \sim N(\mathbfθ, I_\infty)$, where $\mathbfθ \in Γ\subset \ell_2$ is assumed to be convex and compact. We show that goodness-of-fit testing sample complexity is lower bounded by the square-root of the estimation complexity, whenever $Γ$ is orthosymmetric. We show that the lower bound is tight when $Γ$ is also quadratically convex, thus significantly extending validity of the testing-estimation relationship from [GP24]. Using similar methods, we…

Simultaneous improved predictions of nuclear mass and charge radius via multi-task Gaussian process machine learning approach
Weihu Ye, Niu Wan
https://arxiv.org/abs/2507.17357 …

Simultaneous improved predictions of nuclear mass and charge radius via multi-task Gaussian process machine learning approach
We introduce a multi-task Gaussian process (GP) machine learning model to simultaneously predict nuclear masses and charge radii across the nuclear chart. Utilizing 12 physical input features, our multi-task GP consistently outperforms single-task learning, achieving root-mean-square deviations of 0.09 MeV for masses and 0.004 fm for charge radii. The model explicitly incorporates correlations between these observables. By employing the SHapley Additive exPlanations (SHAP) method, we interpret …

On balancing and Lucas-balancing numbers expressible as product of two $k$-Fibonacci numbers
Bibhu Prasad Tripathy, Bijan Kumar Patel
https://arxiv.org/abs/2508.12238 https://…

On balancing and Lucas-balancing numbers expressible as product of two $k$-Fibonacci numbers
A positive integer $n$ is called a balancing number if there exists a positive integer $r$ such that $1 + 2 + \cdots + (n-1) = (n+1) + (n+2) + \cdots + (n+r)$. The corresponding value $r$ is known as the balancer of $n$. If $n$ is a balancing number, then $8n^{2}+1$ is a perfect square, and its positive square root is called a Lucas-balancing number. For any integer $k \geq 2$, let $\{F_{n}^{(k)} \}_{n \geq -(k-2)}$ denote $k$-generalized Fibonacci sequence which starts with $0, \dots ,1$($k$ t…

Dynamical correlation functions for the one-dimensional Bose-Hubbard insulator
Kevin zu M\"unster, Florian Gebhard, Satoshi Ejima, Holger Fehske
https://arxiv.org/abs/2507.03125

Dynamical correlation functions for the one-dimensional Bose-Hubbard insulator
We calculate the dynamical current and kinetic-energy correlation functions for the first Mott lobe of the one-dimensional Bose-Hubbard model. We employ the strong-coupling expansion up to sixth order in $x=t/U$, and the dynamical density-matrix renormalization group method on rings with 64 sites. The correlation functions are finite above the single-particle gap with a square-root onset, as is also found from field theory close to the Mott transition. The correlation functions display a featur…

Wigner Phase-Space Densities of Nuclear Clusters and Hypernuclei
Jiaxing Zhao, Joerg Aichelin, Elena Bratkovskaya
https://arxiv.org/abs/2508.05814 https://…

Wigner Phase-Space Densities of Nuclear Clusters and Hypernuclei
We solve the Schrödinger equation for few-body systems to obtain the wave function for light nuclear clusters and hypernuclei from d to $\rm ^5_{ΛΛ}He$ employing realistic nucleon-nucleon and nucleon-$Λ$ potentials. We project the solution to the hyperspherical harmonic basis states to obtain the corresponding density matrices and the Wigner densities. The experimental root mean square (rms) radii and binding energies of the different clusters are well reproduced. The Wigner densities obtai…