Tootfinder

Gordian split links in the Gehring ropelength problem
Friedrich Bauermeister
https://arxiv.org/abs/2506.04644 https://arxiv.org/pdf/2…

Gordian split links in the Gehring ropelength problem
A thick link is a link in Euclidean three-space such that each component of the link lies at distance at least 1 from every other component. Strengthening the notion of thickness, we define a thickly embedded link to be a thick link whose open radius-1/2 normal disk bundles of all components are embedded. The Gehring ropelength problem asks how large the sum of the lengths of the components of a thick (respectively thickly embedded) link must be, given the link homotopy (respectively isotopy) c…

Structural stability of three dimensional steady Prandtl equation
Weiming Shen, Yue Wang, Tong Yang
https://arxiv.org/abs/2506.04578 https://

Structural stability of three dimensional steady Prandtl equation
The well-posedness of the three dimensional Prandtl equation is an outstanding open problem due to the appearance of the secondary flow even though there are studies on analytic and Gevrey function spaces. This problem is raised as the third open problem in the classical book by Oleinik and Samokhin [43]. This paper aims to address this open problem in the steady case by introducing a new approach to study the structural stability of background profile that includes the famous Blasius solutions…

This https://arxiv.org/abs/2405.10886 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Three-mode tunable coupler for superconducting two-qubit gates
Building a scalable universal high-performance quantum processor is a formidable challenge. In particular, the problem of realizing fast high-perfomance two-qubit gates of high-fidelity remains needful. Here we propose a building block for a scalable quantum processor consisting of two transmons and a tunable three-mode coupler allowing for a ZZ interaction control. We experimentally demonstrate the native CZ gate with the pulse duration of 60 ns achieving the two-qubit gate fidelity above 98%,…

Admissibility of Completely Randomized Trials: A Large-Deviation Approach
Guido Imbens, Chao Qin, Stefan Wager
https://arxiv.org/abs/2506.05329 https://

Admissibility of Completely Randomized Trials: A Large-Deviation Approach
When an experimenter has the option of running an adaptive trial, is it admissible to ignore this option and run a non-adaptive trial instead? We provide a negative answer to this question in the best-arm identification problem, where the experimenter aims to allocate measurement efforts judiciously to confidently deploy the most effective treatment arm. We find that, whenever there are at least three treatment arms, there exist simple adaptive designs that universally and strictly dominate non…

This https://arxiv.org/abs/2503.17838 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Analysis of pitchfork bifurcations and symmetry breaking in the elliptic restricted three-body problem
A unified framework is proposed to quantitatively characterize pitchfork bifurcations and associated symmetry breaking in the elliptic restricted three-body problem (ERTBP). It is known that planar/vertical Lyapunov orbits and Lissajous orbits near the collinear libration points undergo pitchfork bifurcations with varying orbital energy. These bifurcations induce symmetry breaking, generating bifurcated families including halo/quasi-halo orbits, axial/quasi-axial orbits, and their corresponding…

Constraining the Baryon Fraction in the Intergalactic Medium with 92 localized Fast Radio Bursts
Yang Liu, Yuchen Zhang, Hongwei Yu, Puxun Wu
https://arxiv.org/abs/2506.03536

Constraining the Baryon Fraction in the Intergalactic Medium with 92 localized Fast Radio Bursts
Fast radio bursts (FRBs) are emerging as powerful cosmological probes for constraining the baryon fraction in the intergalactic medium (IGM), offering a promising avenue to address the missing baryon problem. In this paper, we analyze constraints on the IGM baryon fraction ($f_\mathrm{IGM}$) using 92 localized FRBs, incorporating a corrected probability distribution function for the IGM dispersion measure within three different cosmological models. We find that variations in the underlying cosm…

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This https://arxiv.org/abs/2505.09708 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

The uncertainty of magnetic fields in 3D non-local thermodynamic equilibrium inversions
We describe our approach to solve the problem of ensuring the solenoidality of the magnetic field vector in three-dimensional (3D) inversions, as well as the estimation of the uncertainty in the inferred magnetic field. The solenoidality of the magnetic field vector is often disregarded in the inversion of spectropolarimetric data due to limitations in the traditional one-dimensional inversion techniques. We propose a method to ensure the solenoidal condition in 3D inversions based on our meshf…

This https://arxiv.org/abs/2412.17556 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Bekenstein bounds in maximally symmetric nonlinear electrodynamics
We explore dynamical features of the maximally symmetric nonlinear extension of classical electromagnetism, recently proposed in the literature as ``ModMax'' electrodynamics. This family of theories is the only one that preserves all the symmetries of Maxwell's theory, having applications in the study of regular black hole solutions and supersymmetry. The purpose of this article is three-fold. Firstly, we study the initial-value problem of ModMax and show, by means of a simple geometric criteri…

Deformation Due to Non-planar Fault Movement in Fractional Maxwell Medium
Pabita Mahato (Mondal), Seema Sarkar (Mondal), Subhash Chandra (Mondal)
https://arxiv.org/abs/2506.04257 …

Deformation Due to Non-planar Fault Movement in Fractional Maxwell Medium
In seismically active regions, the accumulation of geophysical stress during the aseismic period and its impact on faults is crucial for identifying which faults are more likely to undergo future fault movement. In this model, we consider an infinite non-planar fault located in a viscoelastic half-space of a fractional Maxwell medium representing the lithosphere-asthenosphere system comprising three interconnected planar sections. The problem is formulated as a two-dimensional boundary value pr…

This https://arxiv.org/abs/2306.11707 has been replaced.
link: https://scholar.google.com/scholar?q=a

Hexagonal circular 3-webs with reducible polar curves of degree three
The paper reports the progress with the classical problem, posed by Blaschke and Bol in 1938. We present new examples and new classifications of natural classes of hexagonal circular 3-webs. The main results is the classification of hexagonal circular 3-webs with reducible polar curves of degree 3 and description of hexagonal circular 3-webs admitting a one-parameter Möbius symmetry.

This https://arxiv.org/abs/2412.16671 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Bi-normal trajectories in the Circular Restricted Three-Body Problem
In this note, we show there exist infinitely many trajectories which are bi-normal (i.e. normal at initial and final times) to the xz-plane, in the Spatial Circular Restricted Three-Body Problem, for energies below or slightly above the first critical value and near the primaries, under the assumption of the twist condition as defined by Moreno-van-Koert in arXiv:2011.06562. This is an application of the relative Poincaré-Birkhoff theorem for Lagrangians in Liouville domains, as proven by the …

This https://arxiv.org/abs/2501.01817 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Distributed Framework Construction for Affine Formation Control
In affine formation control problems, the construction of the framework with universal rigidity and affine localizability is a critical prerequisite, but it has not yet been well addressed, especially when additional agents join the formation or link/agent failures emerge. Motivated by this observation, we investigate the problem of constructing affine frameworks in three scenarios, including vertex addition, edge deletion and vertex deletion. Our approach starts from the original affine format…

This https://arxiv.org/abs/2506.01837 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Inverse Microparticle Design for Enhanced Optical Trapping and Detection Efficiency in All Six Degrees of Freedom
Achieving quantum-limited motional control of optically trapped particles beyond the sub-micrometer scale is an outstanding problem in levitated optomechanics. A key obstacle is solving the light scattering problem and identifying particle geometries that allow stable trapping and efficient motional detection of their center of mass and rotational motion in three dimensions. Here, we present a computational framework that combines an efficient electromagnetic scattering solver with the adjoint …

This https://arxiv.org/abs/2501.00671 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sylvester's problem for beta-type distributions
Consider $d+2$ i.i.d. random points $X_1,\ldots, X_{d+2}$ in $\mathbb R^d$. In this note, we compute the probability that their convex hull is a simplex focusing on three specific distributional settings: (i) the distribution of $X_1$ is multivariate standard normal; (ii) the density of $X_1$ is proportional to $(1-\|x\|^2)^β$ on the unit ball (the beta distribution); (iii) the density of $X_1$ is proportional to $(1+\|x\|^2)^{-β}$ (the beta prime distribution). In the Gau…

Characterization of Infinite Ideal Polyhedra in Hyperbolic 3-Space via Combinatorial Ricci Flow
Huabin Ge, Bobo Hua, Hao Yu, Puchun Zhou
https://arxiv.org/abs/2506.05036

Characterization of Infinite Ideal Polyhedra in Hyperbolic 3-Space via Combinatorial Ricci Flow
In his seminal work \cite{Ri96}, Rivin characterized finite ideal polyhedra in three-dimensional hyperbolic space. However, the characterization of infinite ideal polyhedra, as proposed by Rivin, has remained a long-standing open problem. In this paper, we introduce the combinatorial Ricci flow for infinite ideal circle patterns, a discrete analogue of Ricci flow on non-compact Riemannian manifolds, and prove a characterization of such circle patterns under certain combinatorial conditions. Our…

Evaluation of LLMs for mathematical problem solving
Ruonan Wang, Runxi Wang, Yunwen Shen, Chengfeng Wu, Qinglin Zhou, Rohitash Chandra
https://arxiv.org/abs/2506.00309

Evaluation of LLMs for mathematical problem solving
Large Language Models (LLMs) have shown impressive performance on a range of educational tasks, but are still understudied for their potential to solve mathematical problems. In this study, we compare three prominent LLMs, including GPT-4o, DeepSeek-V3, and Gemini-2.0, on three mathematics datasets of varying complexities (GSM8K, MATH500, and UNSW datasets). We take a five-dimensional approach based on the Structured Chain-of-Thought (SCoT) framework to assess final answer correctness, step com…

This https://arxiv.org/abs/2501.02485 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Semi-analytic construction of global transfers between quasi-periodic orbits in the spatial R3BP
Consider the spatial restricted three-body problem, as a model for the motion of a spacecraft relative to the Sun-Earth system. We focus on the dynamics near the equilibrium point $L_1$, located between the Sun and the Earth. We show that we can transfer the spacecraft from a quasi-periodic orbit that is nearly planar relative to the ecliptic to a quasi-periodic orbit that has large vertical amplitude, at zero energy cost. (In fact, the final orbit has the maximum vertical amplitude that can be…

Asymptotic analysis of high-dimensional uniformity tests under heavy-tailed alternatives
Tiefeng Jiang, Tuan Pham
https://arxiv.org/abs/2506.00393 https://…

Asymptotic analysis of high-dimensional uniformity tests under heavy-tailed alternatives
We study the high-dimensional uniformity testing problem, which involves testing whether the underlying distribution is the uniform distribution, given $n$ data points on the $p$-dimensional unit hypersphere. While this problem has been extensively studied in scenarios with fixed $p$, only three testing procedures are known in high-dimensional settings: the Rayleigh test \cite{Cutting-P-V}, the Bingham test \cite{Cutting-P-V2}, and the packing test \cite{Jiang13}. Most existing research focuses…

Consecutive collision orbits in the restricted three-body problem above the first critical energy value
Jungsoo Kang, Kevin Ruck
https://arxiv.org/abs/2506.01735

Consecutive collision orbits in the restricted three-body problem above the first critical energy value
In this paper, we study the planar circular restricted three-body problem for energy levels slightly above the first critical value. We first observe that the energy hypersurfaces in the Birkhoff regularization corresponding to these energy levels are of contact type. Then, using a version of Rabinowitz Floer homology and an analytic continuation argument, we establish the existence of a symmetric consecutive collision orbit and, furthermore, prove the existence of infinitely many such orbits f…

This https://arxiv.org/abs/2404.10304 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSE_…

LLM-Powered Test Case Generation for Detecting Bugs in Plausible Programs
Detecting tricky bugs in plausible programs, those that pass existing test suites yet still contain bugs, remains a significant challenge in software testing. To address this problem, we propose TrickCatcher, an LLM-powered approach to generating test cases for uncovering bugs in plausible programs. TrickCatcher operates in three stages: First, it uses an LLM to generate program variants based on the program under test (PUT) and its specification. Second, it employs an LLM to construct an input…

Occlusion-Aware Ground Target Tracking by a Dubins Vehicle Using Visibility Volumes
Collin Hague, Artur Wolek
https://arxiv.org/abs/2506.03400 https://

Occlusion-Aware Ground Target Tracking by a Dubins Vehicle Using Visibility Volumes
This paper considers the problem of tracking a point of interest (POI) moving along a known trajectory on the ground with an uncrewed aerial vehicle (UAV) modeled as a Dubins vehicle using a line-of-sight (LOS) sensor through an urban environment that may occlude the POI. A visibility volume (VV) encodes a time-varying, three-dimensional representation of the sensing constraints for a particular POI position. A constant-altitude, translating, and radially time-varying circular standoff orbit is…

Some Properties of Twisted Chevalley Groups
Deep H. Makadiya
https://arxiv.org/abs/2505.24430 https://arxiv.org/pdf/2505.24430…

Some Properties of Twisted Chevalley Groups
This thesis investigates certain structural properties of twisted Chevalley groups over commutative rings, focusing on three key problems. Let $R$ be a commutative ring satisfying mild conditions. Let $G_{π,σ} (Φ, R)$ denote a twisted Chevalley group over $R$, and let $E'_{π, σ} (Φ, R)$ denote its elementary subgroup. The first problem concerns the normality of $E'_{π, σ} (Φ, R, J)$, the relative elementary subgroups at level $J$, in the group $G_{π, σ} (Φ, R)$. The second problem…

Improving statistical learning methods via features selection without replacement sampling and random projection
Sulaiman khan, Muhammad Ahmad, Fida Ullah, Carlos Aguilar Iba\~nez, Jos\'e Eduardo Valdez Rodriguez
https://arxiv.org/abs/2506.00053

Improving statistical learning methods via features selection without replacement sampling and random projection
Cancer is fundamentally a genetic disease characterized by genetic and epigenetic alterations that disrupt normal gene expression, leading to uncontrolled cell growth and metastasis. High-dimensional microarray datasets pose challenges for classification models due to the "small n, large p" problem, resulting in overfitting. This study makes three different key contributions: 1) we propose a machine learning-based approach integrating the Feature Selection Without Re-placement (FSWOR) technique…

This https://arxiv.org/abs/2407.10571 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

Spanning Trees Minimizing Branching Costs
The Minimum Branch Vertices Spanning Tree problem aims to find a spanning tree $T$ in a given graph $G$ with the fewest branch vertices, defined as vertices with a degree three or more in $T$. This problem, known to be NP-hard, has attracted significant attention due to its importance in network design and optimization. Extensive research has been conducted on the algorithmic and combinatorial aspects of this problem, with recent studies delving into its fixed-parameter tractability. In this …

Monolithic framework to simulate fluid-structure interaction problems using geometric volume-of-fluid method
Soham Prajapati (Department of Aerospace Engineering and Mechanics, University of Minnesota - Twin Cities, Minneapolis, Minnesota, USA), Ali Fakhreddine (Department of Aerospace Engineering and Mechanics, University of Minnesota - Twin Cities, Minneapolis, Minnesota, USA), Krishnan Mahesh (Department of Aerospace Engineering and Mechanics, University of Minnesota - Twin Cities, …

Monolithic framework to simulate fluid-structure interaction problems using geometric volume-of-fluid method
We develop a three-dimensional Eulerian framework to simulate fluid-structure interaction (FSI) problems on a fixed Cartesian grid using the geometric volume-of-fluid (VOF) method. The coupled problem involves incompressible flow and viscous hyperelastic solids. A VOF-based one-continuum formulation is used to describe the unified momentum conservation equations with incompressibility constraints that are solved using the finite volume method (FVM). In the geometric VOF interface-capturing (IC)…

@… is wondering how much trouble a skipped heading level is for screen reader users. Three users have replied but it'd be great to see more feedback. Anyone else willing to reply to Manuel's post? Here is the link:
h…

Inverse Microparticle Design for Enhanced Optical Trapping and Detection Efficiency in All Six Degrees of Freedom
Moosung Lee, Benjamin A. Stickler, Thomas Pertsch, Sungkun Hong
https://arxiv.org/abs/2506.01837

Inverse Microparticle Design for Enhanced Optical Trapping and Detection Efficiency in All Six Degrees of Freedom
Achieving quantum-limited motional control of optically trapped particles beyond the sub-micrometer scale is an outstanding problem in levitated optomechanics. A key obstacle is solving the light scattering problem and identifying particle geometries that allow stable trapping and efficient motional detection of their center of mass and rotational motion in three dimensions. Here, we present a computational framework that combines an efficient electromagnetic scattering solver with the adjoint …

Locating Extremal Periodic Orbits for the Planar Circular Restricted Three Body Problem using Polynomial Sum-of-Squares Optimization
Vinay Sharma, Sergei I Chernyshenko
https://arxiv.org/abs/2505.23430

Locating Extremal Periodic Orbits for the Planar Circular Restricted Three Body Problem using Polynomial Sum-of-Squares Optimization
With an increasing interest in the design of long and complex space missions, the search for orbits that require the least amount of fuel is of fundamental interest. This paper develops existing computational models for locating Unstable Periodic Orbits (UPOs) in polynomial dynamical systems using Sum-of-Squares (SOS) optimization technique and proposes a numerical framework to converge UPOs for the Planar Circular Restricted Three-Body Problem (PCR3BP) in astrodynamics. This is done by develop…

Modeling the Monty Hall Decision Problem with Reaction Kinetics
Oliver Steinbock, Wen Zhu
https://arxiv.org/abs/2505.15824 https://ar…

Modeling the Monty Hall Decision Problem with Reaction Kinetics
Using the Monty Hall probability problem as a model system, we ask whether simple chemical reaction mechanisms can implement optimal strategies for non-trivial decision making. In this puzzle, a contestant chooses one of three doors (only one hides a prize), the host, knowing the content, opens another door revealing no prize, and finally the contestant must decide whether to stay with the original choice or switch to the remaining closed door. Assigning distinct molecular species to the player…

Mapping between Spin-Glass Three-Dimensional (3D) Ising Model and Boolean Satisfiability Problem
Zhidong Zhang
https://arxiv.org/abs/2505.18460 https://

Mapping between Spin-Glass Three-Dimensional (3D) Ising Model and Boolean Satisfiability Problem
The common feature for a nontrivial hard problem is the existence of nontrivial topological structures, non-planarity graphs, nonlocalities, or long-range spin entanglements in a model system with randomness. For instance, the Boolean satisfiability (K-SAT) problems are nontrivial, due to the existence of non-planarity graphs, nonlocalities, and the randomness. In this work, the relation between a spin-glass three-dimensional (3D) Ising model with the lattice size N = mnl and the K-SAT problems…

Poincar\'e on Gibbs and on Probability in Statistical Mechanics
Bruce D. Popp
https://arxiv.org/abs/2505.12168 https://arxiv.org/…

Poincaré on Gibbs and on Probability in Statistical Mechanics
This paper reviews a paper from 1906 by J. Henri Poincaré on statistical mechanics with a background in his earlier work and notable connections to J. Willard Gibbs. Poincaré's paper presents important ideas that are still relevant for understanding the need for probability in statistical mechanics. Poincaré understands the foundations of statistical mechanics as a many-body problem in analytical mechanics (reflecting his 1890 monograph on The Three-Body Problem and the Equations of Dynamics…