Tootfinder

Size of bipartite graphs with given diameter and connectivity constraints
Sonwabile Mafunda
https://arxiv.org/abs/2509.01825 https://arxiv.org/pdf/2509.018…

Size of bipartite graphs with given diameter and connectivity constraints
In the first part of this paper we determine the maximum size of a (finite, simple, connected) bipartite graph of given order, diameter $d$, and connectivity $κ$. It was shown by Ali, Mazorodze, Mukwembi and Vetrík [On size, order, diameter and edge-connectivity of graphs. Acta Math. Hungar. {\bf 152}, (2017)] that for a connected triangle-free graph of order $n$, diameter $d$ and edge-connectivity $λ$, the size is bounded from above by about $\frac{1}{4}\left(n-\frac{(λ+c) d}{2}\right)^2…

Kcmil has to be one of the most cursed units for area.
If you're not familiar with North American wire sizes, heavy gauge wire like power lines are often sized in kcmil (sometimes abbreviated MCM because M = roman numeral 1000, not SI "mega").
As in kilo circular mils, where a circular mil is the area of an 0.001 inch diameter circle.
Not even *square* mils. Circular mils. Because irrational units and conversion factors for area are the best

Oriented diameter of graphs with diameter $4$ and given maximum edge girth
Jifu Lin, Lihua You
https://arxiv.org/abs/2507.23517 https://arxiv.org/pdf/2507.…

Oriented diameter of graphs with diameter $4$ and given maximum edge girth
Let $G$ be a bridgeless graph. We introduce the maximum edge girth of $G$, denoted by $g^*(G)=\max\{l_G(e)\mid e\in E(G)\}$, where $l_G(e)$ is the edge girth of $e$, defined as the length of the shortest cycle containing $e$. Let $F(d,A)$ be the smallest value for which every bridgeless graph $G$ with diameter $d$ and $g^*(G)\in A$ admits a strong orientation $\overrightarrow{G}$ such that the diameter of $\overrightarrow{G}$ is at most $F(d,A)$. Let $f(d)=F(d,A)$, where $A=\{a\in \mathbb{N}\mi…

A Model-Based Dictionary Approach for Magnetic Nanoparticle Signal Prediction
Asli Alpman, Mustafa Utkur, Emine Ulku Saritas
https://arxiv.org/abs/2509.01127 https://

A Model-Based Dictionary Approach for Magnetic Nanoparticle Signal Prediction
Magnetic particle imaging (MPI) is a tracer-based medical imaging modality that enables quantification and spatial mapping of magnetic nanoparticle (MNP) distribution. The magnetization response of MNPs depends on experimental conditions such as drive field (DF) settings and medium viscosity, as well as on magnetic parameters of MNPs such as magnetic core diameter, hydrodynamic diameter, and magnetic anisotropy constant. A comprehensive understanding of the magnetization response of MNPs can fa…

Extensions of the Bonnet-Myers Theorem
Ronggang Li, Shaoqing Wang
https://arxiv.org/abs/2509.02126 https://arxiv.org/pdf/2509.02126

Extensions of the Bonnet-Myers Theorem
In this paper, we present extensions of the classical Bonnet-Myers theorem for Riemannian manifolds with nonnegative Ricci curvature. Our results provide criteria for compactness and a method for estimating the diameter of such manifolds under general curvature conditions. As applications, we establish compactness theorems for manifolds whose Ricci curvature decays at polynomial or exponential rates.

Estimate of the exit time for the Long Range Ising model on random regular graphs
Vanessa Jacquier
https://arxiv.org/abs/2509.02188 https://arxiv.org/pdf/2…

Estimate of the exit time for the Long Range Ising model on random regular graphs
We investigate the metastable behavior of the long-range Ising model on random regular graphs under Glauber dynamics at low-temperature. We estimate the energy barrier and exit time from the metastable state using a nontrivial path-wise approach that explicitly accounts for the spatial decay of the interactions and the structural properties of the graph, such as the Cheeger constant and known estimates of the diameter. Our results generalize those of Dommers \cite{dommers2017metastability} for …

Microscale architected materials for elastic wave guiding: Fabrication and dynamic characterization across length and time scales
Vignesh Kannan, Charles Dorn, Ute Drechsler, Dennis M. Kochmann
https://arxiv.org/abs/2507.01757

Microscale architected materials for elastic wave guiding: Fabrication and dynamic characterization across length and time scales
We present an experimental protocol for the fabrication and characterization of scalable microarchitected elastic waveguides. Using silicon microfabrication techniques, we develop free-standing 2D truss-based architected waveguides with a maximum diameter of 80 mm, unit cells size of 100 micrometer, and minimum beam width of 5 micrometer, thus achieving scale separation. To characterize elastic wave propagation, we introduce a custom-built scanning optical pump-probe experiment that enables con…

On the fault diameter and wide diameter of the exchanged 3-ary $n$-cube
Rongshuan Geng, Wantao Ning
https://arxiv.org/abs/2508.07174 https://arxiv.org/pdf/…

On the fault diameter and wide diameter of the exchanged 3-ary $n$-cube
Fault diameter and wide diameter are two critical parameters for evaluating communication performance in interconnection networks. They measure the fault tolerance and transmission efficiency of networks. The exchanged 3-ary $n$-cube is a recently proposed variant of the hypercube, denoted by $E3C(r, s, t)$. In this work, we obtain that the $(2r + 1)$-fault diameter and $(2r + 2)$-wide diameter of $E3C(r, s, t)$ are bounded between $n + 3$ and $n + 5$ for $1 \leq r \leq s \leq t$.

Asteroid Rotation Periods: Statistical Analysis in the Diameter-Spin Distribution
Maryam Nastaran, Atila Poro, Raziyeh Hosseini, Matin Najarzadeh
https://arxiv.org/abs/2508.17415

Asteroid Rotation Periods: Statistical Analysis in the Diameter-Spin Distribution
This study examines the rotational characteristics of asteroids through statistical modeling of the diameter-period relationship. A statistical evaluation of the diameter-period relationship was conducted using a dataset of 34,326 asteroids. Clustering identified three main groups, including a dense cluster below the spin barrier, a population of small, fast-rotating asteroids, and a more diffuse group. Geometric and density-based analyses showed that the densest region consists of objects with…

Largest planar graphs of diameter $3$ and fixed maximum degree -- connection with fractional matchings
Antoine Dailly, Sasha Darmon, Ugo Giocanti, Claire Hilaire, Petru Valicov
https://arxiv.org/abs/2507.18797

Largest planar graphs of diameter $3$ and fixed maximum degree -- connection with fractional matchings
The degree diameter problem asks for the maximum possible number of vertices in a graph of maximum degree $Δ$ and diameter $D$. In this paper, we focus on planar graphs of diameter $3$. Fellows, Hell and Seyffarth (1995) proved that for all $Δ\geq 8$, the maximum number $\mathrm{np}_{Δ, D}$ of vertices of a planar graph with maximum degree at most $Δ$ and diameter at most 3 satisfies $\frac{9}{2}Δ- 3 \leq \mathrm{np}_{Δ,3} \leq 8 Δ+ 12$. We show that the lower bound they gave is optimal,…

Effect of freestream turbulence on the coherent dynamics of a wind turbine wake
Neelakash Biswas, Oliver R. H. Buxton
https://arxiv.org/abs/2506.23728 http…

Effect of freestream turbulence on the coherent dynamics of a wind turbine wake
The wake of a model wind turbine exposed to freestream turbulence (FST) with a variety of turbulent characteristics is studied through Particle Image Velocimetry experiments. The FST cases spanned turbulent intensities (T_i) in the range 1% < T_i < 13.1 % and integral length scales (L_v) in the range 0.01D < L_v < 0.11D (where D is the diameter of the turbine model)}. Increasing T_i and L_v in this range resulted in an earlier breakdow…

Understanding the atomically precise evolution of the miscibility of newly prepared face-centered cubic W-Cu nanoalloys and its asymmetry
Yongxin Zhang, Weihan Zhang, Luneng Zhao, Zixiang Zhao, Siqi Lu, Yangrui Liu, Dongsheng Song, Changzheng Wei, Zhentao Pang, Yifeng Ren, Junfeng Gao, Weiwei Gao, Di Wu, Jijun Zhao, Kuo-Juei Hu, Wei Ji, Yu Deng, Binghui Ge, Fengqi Song

Understanding the atomically precise evolution of the miscibility of newly prepared face-centered cubic W-Cu nanoalloys and its asymmetry
According to classical Miedema theory, reducing crystals to the order of nanometer sizes might greatly modulate the mixing enthalpy of elements, thus enabling the invention of a lot of new bulk-immiscible alloys. Although numerous alloys with higher mixing enthalpies remain unexplored, this strategy is approaching its limit, as reflected by the critical diameter of recent alloys of 1.8 nm, which corresponds to ~150 atoms and hardly provides a crystalline order. Future development requires not o…

On the duality between Diameter Two Properties and Ideals in Banach Spaces
Sudeshna Basu
https://arxiv.org/abs/2507.18981 https://arxiv.org/pdf/2507.18981

On the duality between Diameter Two Properties and Ideals in Banach Spaces
We prove that the dual of an M ideal of a Banach space inherits all the versions of $w^*$ diameter two properties. We give a counter example to show that the converse is not true. We use these results to explore these properties in $C(K)$ spaces and its duals.

2D Ultrasound Elasticity Imaging of Abdominal Aortic Aneurysms Using Deep Neural Networks
Utsav Ratna Tuladhar, Richard Simon, Doran Mix, Michael Richards
https://arxiv.org/abs/2508.19303

2D Ultrasound Elasticity Imaging of Abdominal Aortic Aneurysms Using Deep Neural Networks
Abdominal aortic aneurysms (AAA) pose a significant clinical risk due to their potential for rupture, which is often asymptomatic but can be fatal. Although maximum diameter is commonly used for risk assessment, diameter alone is insufficient as it does not capture the properties of the underlying material of the vessel wall, which play a critical role in determining the risk of rupture. To overcome this limitation, we propose a deep learning-based framework for elasticity imaging of AAAs with …

@… wanted to sanity check something here.
The H7 series UFBGA176 25 package is 0.65mm pitch, 0.29mm diameter solder balls. Their recommended pad diameter is 0.3mm which is odd, per IPC I think you'd normally want an 0.25mm land.
But where things get weird is the 0.8mm TFBGA240 25. It's 0.4mm diameter balls, so I would expect 0.3mm lands but…

On the Structure of Carbon Nanotubes: Results from Computer-Assisted Proofs
Miguel Ayala, Rustum Choksi, Benedikt Wirth
https://arxiv.org/abs/2506.22614 ht…

On the Structure of Carbon Nanotubes: Results from Computer-Assisted Proofs
We present a toolbox based on computer-assisted proofs to rigorously study the structure of capped carbon nanotubes. We model nanotubes as minimizers of an interatomic potential. Numerical simulations and validated computations produce rigorous mathematical results about atomic distances and structural variations. In particular, we rigorously measure the diameter, bond lengths, and bond angles of nanotubes and thereby precisely quantify oscillations near the caps, differences between interactio…

Data-Driven Multi-Objective Optimization of Large-Diameter Si Floating-Zone Crystal Growth
Lucas Vieira, Milena Petkovic, Robert Menzel, Natasha Dropka
https://arxiv.org/abs/2508.16111

Data-Driven Multi-Objective Optimization of Large-Diameter Si Floating-Zone Crystal Growth
Floating Zone (FZ) silicon crystal growth is essential for high-power electronics and advanced detection systems. The increasing pressure to scale up the process is challenging due to competing objectives. This study presents a surrogate-based optimization framework to address Multi-Objective Optimization (MOO) in FZ growth, considering eight relevant objectives related to productivity, geometrical and growth parameters, and crystal quality. A Deep Ensemble (DE) of Neural Networks serves as a s…

On Lattice Diameter Segments and A Discrete Borsuk Partition Problem
Anouk E. Brose, Jes\'us A. De Loera, Gyivan Lopez-Campos, Antonio J. Torres
https://arxiv.org/abs/2508.20009

On Lattice Diameter Segments and A Discrete Borsuk Partition Problem
The lattice diameter of a bounded set $S \subset \mathbb{R}^d$ measures the maximal number of lattice points in a segment whose endpoints are lattice points in $S$. Such a segment is called a lattice diameter segment of $S$. This simple invariant yields interesting applications and challenges. We describe a polynomial-time algorithm that computes lattice diameter segments of lattice polygons and show that computing lattice diameters of semi-algebraic sets in dimensions three and higher is NP-ha…

Twisted embeddings of tori have small extrinsic systole
Sahana Vasudevan
https://arxiv.org/abs/2507.23766 https://arxiv.org/pdf/2507.23766

Twisted embeddings of tori have small extrinsic systole
We prove a type of systolic inequality for embeddings of $T^2$ in $\mathbb{R}^3$. In particular, a highly twisted $T^2$ embedded in $\mathbb{R}^3$ must contain a non-contractible loop of small $\mathbb{R}^3$-diameter.

A Fast Parallel Median Filtering Algorithm Using Hierarchical Tiling
Louis Sugy (NVIDIA)
https://arxiv.org/abs/2507.19926 https://arxiv.org/pdf/2507.19926

A Fast Parallel Median Filtering Algorithm Using Hierarchical Tiling
Median filtering is a non-linear smoothing technique widely used in digital image processing to remove noise while retaining sharp edges. It is particularly well suited to removing outliers (impulse noise) or granular artifacts (speckle noise). However, the high computational cost of median filtering can be prohibitive. Sorting-based algorithms excel with small kernels but scale poorly with increasing kernel diameter, in contrast to constant-time methods characterized by higher constant factors…

Learning-Based Modeling of a Magnetically Steerable Soft Suction Device for Endoscopic Endonasal Interventions
Majid Roshanfar, Alex Zhang, Changyan He, Amir Hooshiar, Dale J. Podolsky, Thomas Looi, Eric Diller
https://arxiv.org/abs/2507.15155

Learning-Based Modeling of a Magnetically Steerable Soft Suction Device for Endoscopic Endonasal Interventions
This letter introduces a novel learning-based modeling framework for a magnetically steerable soft suction device designed for endoscopic endonasal brain tumor resection. The device is miniaturized (4 mm outer diameter, 2 mm inner diameter, 40 mm length), 3D printed using biocompatible SIL 30 material, and integrates embedded Fiber Bragg Grating (FBG) sensors for real-time shape feedback. Shape reconstruction is represented using four Bezier control points, enabling a compact and smooth model o…

Victoria Shynkar and her colleagues, who work for the demining charity the Halo Trust,
uncovered 243 TM-62 Soviet-designed anti-tank mines left by the Russian army in a neighbouring field.
A chunky and intimidating 32-centimetres in diameter and 13-cm-wide,
the TM-62 contains 7.5 kilos of TNT and can puncture a tank if triggered. 
The presence of landmines and other unexploded ordnance is a significant issue in Ukraine,
impacting civilians and Ukraine’s agricultu…

Ukraine’s Contaminated Land: Clearing Landmines With Rakes, Tractors and Drones - bellingcat
This story was produced in partnership with Agence France-Presse (AFP). In a field near the small town of Bezymenne in southern Ukraine, Viktoria Shynkar carefully picks out a narrow path through the overgrown grass in front of her.  This small corridor of farmland in Mykolaiv Oblast will be checked for the presence of landmines and […]

Predictive Analysis of Gmelina arborea (Melina) Growth in Plantations of Esmeraldas: A Perspective for Silvicultural Management in Tropical Ecuador
Jos\'e Gabriel Carvajal Benavides, Hugo Orlando Paredes Rodr\'iguez, Oscar Armando Rosales Enr\'iquez, Eduardo Jaime Chagna Avila, Xavier Germ\'an Valencia Valenzuela, Guillermo David Varela J\'acome

Predictive Analysis of Gmelina arborea (Melina) Growth in Plantations of Esmeraldas: A Perspective for Silvicultural Management in Tropical Ecuador
This study presents a rigorous assessment of the growth performance of Gmelina arborea (melina) in a 67-hectare plantation located in Chontaduro, Tabiazo Parish, Esmeraldas, Ecuador. The plantation was established in 2017 under a high-density planting system (650 trees/ha). Permanent monitoring techniques were applied in 16 one-hectare plots to analyze structural growth variables, including survival rate, diameter at breast height (DBH), total height, commercial height, basal area, volume, and …

Lensing and Photon Rings in a Magnetized Black Hole Spacetime
Muhammad Haider Khan, Volker Perlick
https://arxiv.org/abs/2508.20575 https://arxiv.org/pdf/2…

Lensing and Photon Rings in a Magnetized Black Hole Spacetime
We analyze gravitational lensing, in particular the shadow and photon rings, in the Ernst spacetime, also known as the Schwarzschild-Melvin spacetime, which describes a Schwarzschild black hole immersed in a homogenous magnetic field. Although the geodesic equation in this spacetime is chaotic, there are some relevant features that can be determined analytically. Among other things, we give analytic formulas for the vertical diameter of the shadow for an observer at arbitrary inclination and fo…

So...those bendicks 🍫 mints I bought in May seem to have gone 🙂 Hmm, this ball weighs 42g and measures ~64mm diameter; For that diameter of solid aluminium I reckon it would be 370g, so much less dense than I guessed

Oriented diameter of graphs with given domination number
Xiaolin Wang, Yaojun Chen
https://arxiv.org/abs/2506.15997 https://arxiv.org…

Oriented diameter of graphs with given domination number
Let $G$ be a connected bridgeless graph with domination number $γ$. The oriented diameter (strong diameter) of $G$ is the smallest integer $d$ for which $G$ admits a strong orientation with diameter (strong diameter) $d$. Kurz and Lätsch (2012) conjectured the oriented diameter of $G$ is at most $\lceil \frac{7γ+1}{2}\rceil$ and the bound is sharp. In this paper, we confirm the conjecture by induction on $γ$ through contracting an unavoidable alternative subgraph, which holds potential for …

Cocoon-to-Butterfly Transformation in Protoplanetary Nebula: Detection of a Spherical Halo and a Barrel-shaped Torus in IRAS 06530$-$0213
Hao-Min Sun, Yong Zhang, Sheng-Li Qin
https://arxiv.org/abs/2508.19666

Cocoon-to-Butterfly Transformation in Protoplanetary Nebula: Detection of a Spherical Halo and a Barrel-shaped Torus in IRAS 06530$-$0213
Protoplanetary nebulae (PPNs) represent a critical evolutionary bridging stage between the asymptotic giant branch (AGB) and planetary nebula (PN) stages. Their dynamical structures provide key insights into late stellar evolution. Here, we report CO and $^{13}$CO imaging observations of the carbon-rich PPN IRAS 06530$-$0213, a source exhibiting the unidentified 21 micron emission band, conducted with the Northern Extended Millimeter Array (NOEMA). The CO maps reveal a spherical halo (diameter …

Linear Bound for Kakimizu Complex Diameter of Hyperbolic Knots
Xiao Chen, Wujie Shen
https://arxiv.org/abs/2508.03353 https://arxiv.org/pdf/2508.03353

Linear Bound for Kakimizu Complex Diameter of Hyperbolic Knots
We show that the upper bound of the diameter of the Kakimizu complex of an atoroidal knot grows linearly with the knot genus $g$. Specifically, the diameter is at most $2$ when $g = 1$, at most $6$ when $g = 2$, and at most $4g - 3$ for $g \geq 3$. This confirms a conjecture of Sakuma--Shackleton.

Computing Largest Subsets of Points Whose Convex Hulls have Bounded Area and Diameter
Gianmarco Picarella, Marc van Kreveld, Frank Staals, Sjoerd de Vries
https://arxiv.org/abs/2507.04933

Computing Largest Subsets of Points Whose Convex Hulls have Bounded Area and Diameter
We study the problem of computing a convex region with bounded area and diameter that contains the maximum number of points from a given point set $P$. We show that this problem can be solved in $O(n^6k)$ time and $O(n^3k)$ space, where $n$ is the size of $P$ and $k$ is the maximum number of points in the found region. We experimentally compare this new algorithm with an existing algorithm that does the same but without the diameter constraint, which runs in $O(n^3k)$ time. For the new algorith…

Scaling of thin wire cylindrical compression after 100 fs Joule surface heating with material, diameter and laser energy
L. Yang, M. -L. Herbert, C. B\"ahtz, V. Bouffetier, E. Brambrink, T. Dornheim, N. Fefeu, T. Gawne, S. G\"ode, J. Hagemann, H. H\"oeppner, L. G. Huang, O. S. Humphries, T. Kluge, D. Kraus, J. L\"utgert, J. -P. Naedler, M. Nakatsutsumi, A. Pelka, T. R. Preston, C. Qu, S. V. Rahul, R. Redmer, M. Rehwald, L. Randolph, J. J. Santos, M. \v{S}m\'id, …

Scaling of thin wire cylindrical compression after 100 fs Joule surface heating with material, diameter and laser energy
We present the first systematic experimental validation of return-current-driven implosion scaling in micrometer-sized wires irradiated by femtosecond laser pulses. Employing XFEL-based imaging with sub-micrometer spatial and femtosecond temporal resolution, supported by hydrodynamic and particle-in-cell simulations, we reveal how return current density depends precisely on wire diameter, material properties, and incident laser energy. We identify deviations from simple theoretical predictions …

Careful synchronisation and the diameter of transformation semigroups with few generators
Andrew Ryzhikov
https://arxiv.org/abs/2506.13962 https://

Careful synchronisation and the diameter of transformation semigroups with few generators
A word is called carefully synchronising for a partial deterministic finite semi-automaton if it maps all states to the same state. Equivalently, it is a composition of partial transformations equal to a constant total transformation. There is a sequence of several papers providing stronger and stronger lower bounds on the length of shortest carefully synchronising words for $n$-state partial DFAs over small alphabets. It resulted in the lower bounds of $Ω(\frac{2^{n/3}}{n\sqrt{n}})$ and $Ω(\…

Going Beyond Surfaces in Diameter Approximation
Micha{\l} W{\l}odarczyk
https://arxiv.org/abs/2507.03447 https://arxiv.org/pdf/2507.0…

Going Beyond Surfaces in Diameter Approximation
Calculating the diameter of an undirected graph requires quadratic running time under the Strong Exponential Time Hypothesis and this barrier works even against any approximation better than 3/2. For planar graphs with positive edge weights, there are known $(1+\varepsilon)$-approximation algorithms with running time $poly(1/ε, \log n) \cdot n$. However, these algorithms rely on shortest path separators and this technique falls short to yield efficient algorithms beyond graphs of bounded genus…

Associated primes of the second power of closed neighborhood ideals of graphs
Ha Thi Thu Hien, Thanh Vu
https://arxiv.org/abs/2507.08777 https://

Associated primes of the second power of closed neighborhood ideals of graphs
We study simple graphs for which the maximal homogeneous ideal is an associated prime of the second power of their closed neighborhood ideals. In particular, we show that such graphs must have diameter at most $6$, and that those with diameter $2$ must be vertex diameter-$2$-critical.

Can you guess what this is? 😉

Curvature operator and Euler number
Huang Teng, Tan Qiang
https://arxiv.org/abs/2507.22091 https://arxiv.org/pdf/2507.22091

Curvature operator and Euler number
Let $(X,g)$ be a compact $n$-dimensional smooth Riemannian manifold with a lower bound on the average of the lowest $n-p$ eigenvalues of the curvature operator and the diameter of $X$ is bounded above by $D>0$. In this article, we investigate the relationship between the curvature operator and the Euler number of $X$. Our analysis is based on more general vanishing theorems for a Dirac operator associated with a smooth $1$-form on $X$. As a consequence, we obtain partial affirmative answers to …

Examples of diameter-2 graphs with no triangle or $K_{2,t}$
Sean Eberhard, Vladislav Taranchuk, Craig Timmons
https://arxiv.org/abs/2508.19646 https://arxi…

Examples of diameter-2 graphs with no triangle or $K_{2,t}$
For each $t \ge 1$ let $W_t$ denote the class of graphs other than stars that have diameter $2$ and contain neither a triangle nor a $K_{2,t}$. The famous Hoffman--Singleton Theorem implies that $W_2$ is finite. Recently Wood suggested the study of $W_t$ for $t > 2$ and conjectured that $W_t$ is finite for all $t \ge 2$. In this note we show that (1) $W_3$ is infinite, (2) $W_5$ contains infinitely many regular graphs, and (3) $W_7$ contains infinitely many Cayley graphs. Our $W_3$ and $W_5$ ex…

Cosmic Distance Duality Relation with DESI DR2 and Transparency
Xuwei Zhang, Xiaofeng Yang, Yunliang Ren, Shuangnan Chen, Yangjun Shi, Cheng Cheng, Xiaolong He
https://arxiv.org/abs/2506.17926

Cosmic Distance Duality Relation with DESI DR2 and Transparency
The Cosmic Distance Duality Relation (CDDR), a fundamental assumption in modern cosmology, posits a direct link between angular diameter distance and luminosity distance. This study presents a comprehensive, model-independent, and data-driven test of the CDDR using a combination of cosmological observations, including Supernovae (SN), Baryon Acoustic Oscillations (BAO), and Hubble parameter ($H(z)$) measurements. We employ both Gaussian Process Regression (GPR) and a novel Compressed Point (CPI…

Impacts and Ejecta in Natural Granular Material
Esteban Wright, Emau Argueta, Wolfgang Losert
https://arxiv.org/abs/2507.11691 https://

Impacts and Ejecta in Natural Granular Material
With laboratory experiments we investigate the ejecta of low-velocity (~m/s) impacts into multi-scale granular media and compare them against ejecta from impacts into mono-scale media. Impacts are into a 50 cm diameter galvanized washtub filled with fine sand that has larger diameter gravel buried below the surface is filmed with two high-speed cameras. The resulting ejecta curtain consists mainly of fine sand, and has a complex asymmetric structure that depends on the location and interaction …

Hey, Jörg Schoppmeyer opened his talk at the #SolarEclipse Conference in Leuven on imaging annular eclipses without filters with one of my Australian pictures from 1999 (upper right): see https://geocities.restorativland.org/CapeCanaveral/5599/aus99/story.html for how they originated. Schoppmeyer's video https://www.youtube.com/watch?v=lbtQrHdl5Og of the 2023 ASE actually found scientific use: https://www.iota-es.de/JOA/JOA2024_2.pdf#page=3 (once again confirming the larger solar diameter https://scicomm.xyz/@cosmos4u/114681336115327260 had determined by an entirely different technique). 6/n

Seven-Probe Fiber Detector for Time-Resolved Source Tracking in HDR-Brachytherapy: Experimental Evaluation
Mathieu Gonod, Miguel Angel Suarez, Samir Laskri, Gwenael Rolin, Karine Charriere, Emmanuel Dordor, Julien Crouzilles, Thomas Lihoreau, Lionel Pazart, Jean-Francois Vinchant, Leone Aubignac, Thierry Grosjean
https://arxiv.o…

Seven-Probe Fiber Detector for Time-Resolved Source Tracking in HDR-Brachytherapy: Experimental Evaluation
{\bf Purpose:} This study evaluates a compact biocompatible Seven-probe Scintillator Detector (7SD) for monitoring HDR-BT treatment sequences across a range of dwell times and source-probe spacings representative of most HDR-BT techniques. {\bf Methods:} The SSD comprises seven detection cells made of Gd$_2$O$_2$S:Tb, each measuring 0.28 $\pm$ 0.02 mm in diameter and 0.43 $\pm$ 0.02 mm in length, coupled to the microstructured tips of silica optical fibers (110-micron diameter). The probes, s…

Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3
Avery Carr
https://arxiv.org/abs/2508.19302 https://arxiv.org/pdf/2508.1930…

Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3
In this short note it is shown that every graph of diameter 2 and minimum degree at least 3 contains a cycle of length 4 or 8. This result contributes to the study of the Erdős--Gyárfás Conjecture.

Hyperfine interaction of electrons confined in CsPbI$_3$ nanocrystals with nuclear spin fluctuations
Sergey R. Meliakov, Evgeny A. Zhukov, Vasilii V. Belykh, Kirill V. Kavokin, Mikhail O. Nestoklon, Elena V. Kolobkova, Maria S. Kuznetsova, Manfred Bayer, Dmitri R. Yakovlev
https://arxiv.org/abs/2508.17881

Hyperfine interaction of electrons confined in CsPbI$_3$ nanocrystals with nuclear spin fluctuations
The coherent spin dynamics of electrons are investigated for CsPbI$_3$ perovskite nanocrystals in a glass matrix using time-resolved Faraday ellipticity. In nanocrystals with a diameter of about 11 nm, the Larmor precession frequency has a linear dependence on magnetic field corresponding to the electron Landé $g$-factor of 2.07. We find a finite Larmor precession frequency at zero magnetic field, corresponding to the electron spin splitting of $0.8$ $μ$eV. This splitting is explained by the …

Good Morning #Canada
In the Ojibwe culture, a dreamcatcher is made with willow hoop, on which is woven a net or web and decorated with sacred items such as feathers or beads. Traditionally, dreamcatchers are hung over a cradle or bed as protection during sleep as Native Americans believed that at night the air was filled with dreams, both good and bad. Today, based on current events, we need numerous and bigger #Dreamcatchers to filter out the crap. I'm fortunate that the world's largest dreamcatcher, measuring 12.93 metres (over 42 feet) in diameter, is in my backyard, only 45 minutes north of where I live. It was created by Dale (Bobbie) Williams and located in Rama First Nation, Ontario, Canada, near Orillia. Williams was inspired to create it after learning the Guinness World Record holder for a dreamcatcher was in Europe and he felt it didn't meet the traditional definition. I think it had sausages hanging from it.
#CanadaIsAwesome #BigStuffInSmallTowns #RoadTrip
https://www.orilliamatters.com/local-news/worlds-largest-dream-catcher-aims-to-provide-powerful-energy-in-rama-8721002

Circular Mystery: Exploring Diffuse Emission Surrounding a Radio Galaxy with uGMRT and VLA Multiwavelength Observations
Shobha Kumari, Sabyasachi Pal, Souvik Manik
https://arxiv.org/abs/2506.18556

Circular Mystery: Exploring Diffuse Emission Surrounding a Radio Galaxy with uGMRT and VLA Multiwavelength Observations
We report the discovery of J1218+1813, a circular diffuse radio source detected in the Very Large Array (VLA) FIRST survey at 1400 MHz. The source has an angular diameter of approximately one arcminute, corresponding to a physical size of ~180 kpc, and is associated with an elliptical galaxy with a redshift of z = 0.139635. To investigate its nature, we conducted a comprehensive multiwavelength analysis spanning both high and low radio frequencies, utilizing the VLA in C-configuration at L, C a…

I got bored so here's some ideas I had about ways to make non-digital AI models which anyone can try if you're bored enough!
- gear ratios for weights
- pulleys for weights
- probs could get pipe diameter haha
- sunglasses (shine light through and brightest is the result)
And there's one analog one I'm trying myself which I can keep posting on if anyone cares!
#ai

On the diameter and girth of zero-divisor graphs of inverse semigroups
Yanhui Wang, Xinyi Zhu, Pei Gao
https://arxiv.org/abs/2508.03632 https://arxiv.org/p…

On the diameter and girth of zero-divisor graphs of inverse semigroups
Let $S$ be an inverse semigroup with zero and let $Z(S)^\times$ be its set of non-zero divisors with respect to the natural partial order $\le $ on $S$, that is, $a \in Z(S)^\times $ if there exists $b\in S\setminus\{0\}$ with $ω(a, b) = \{c \in S: c \leq a\ \mbox{and}\ c \leq b\}=\{0\}$. The set $Z(S)^\times$ makes up the vertices of the corresponding {\it zero-divisor graph} $Γ(S)$, with two distinct vertices $a, b$ forming an edge if $ω(a, b)=\{0\}$. We characterize {\it zero-divisor grap…

Geometric Optimization and IPA-Induced Dispersion Tuning in Solid-Core Photonic Crystal Fibers
Zekeriya Mehmet Yuksel, Hasan Oguz, Ozgur Onder Karakilinc, Halil Berberoglu, Mirbek Turduev, Muzaffer Adak, Sevgi Ozdemir Kart
https://arxiv.org/abs/2507.10815

Geometric Optimization and IPA-Induced Dispersion Tuning in Solid-Core Photonic Crystal Fibers
This study presents a numerical investigation of solid-core photonic crystal fibers with circular and hexagonal cladding geometries. The goal is to optimize optical parameters for nonlinear photonics and environmental sensing. Full-vectorial simulations using FDTD, PWE, and FDE are used to analyze the effects of core diameter, pitch, and air filling fraction on the zero-dispersion wavelength, nonlinear coefficient, effective mode area, and confinement loss. Reducing the core diameter from 2.4 t…

Synthesis of nanoparticles from carboxymethyl cellulose using one-pot hydrothermal carbonization for Drug Entrapment Studies
Mohaddeseh Sharifi, S. Hajir Bahrami
https://arxiv.org/abs/2507.18299

Synthesis of nanoparticles from carboxymethyl cellulose using one-pot hydrothermal carbonization for Drug Entrapment Studies
Porous nanomaterials have recently attracted a lot of attention due to various properties and potential applications. In this study, carbon nanoparticles (CNPs) were synthesized by the one-pot hydrothermal carbonization (HTC) using carboxymethyl cellulose (CMC). Urea was used as the nitrogen source for carbonization. The presence of urea in CMC solution for carbonization resulted in CNPsu reduction in the diameter of particles from 4 micrometer to 1 micrometer. Activation process at high temper…

On the Particle Image Overlap in Single Camera Defocusing Approaches
Christian Sax, Jochen Kriegseis
https://arxiv.org/abs/2506.18170 https://

On the Particle Image Overlap in Single Camera Defocusing Approaches
Particle image (PI) overlap presents a significant challenge in single-camera particle tracking and sizing techniques such as Defocusing Particle Tracking Velocimetry (DPTV) and Interferometric Particle Imaging (IPI). In DPTV, overlap obscures PI boundaries, complicating the detection and accurate estimation of PI diameter and center position, which increases uncertainty in the reconstructed particle positions. In IPI, overlap reduces the usable area of the interference pattern, limiting the ac…

A Size Condition for Small Diameter Orientable Graphs
Sopon Boriboon, Teeradej Kittipassorn
https://arxiv.org/abs/2508.17569 https://arxiv.org/pdf/2508.175…

A Size Condition for Small Diameter Orientable Graphs
In 2002, Koh and Tay conjectured that every bridgeless graph of order $n\geq 5$ and size at least ${n\choose 2}-n+5$ has an orientation of diameter two. Later, Cochran, Czabarka, Dankelmann and Székely proved this conjecture and asked what is the minimum number of edges required in a bridgeless graph of order $n$ to guarantee the existence of an orientation of diameter at most $d$? We conjecture that the answer is ${n-d \choose 2}+n+2$. We prove this conjecture for the case $d=n-2$ and prove t…

The SST-1M stereoscopic system
C. Alispach, A. Araudo, M. Balbo, V. Beshley, J. Bla\v{z}ek, J. Borkowski, S. Boula, T. Bulik, F. Cadoux, S. Casanova, A. Christov, J. Chudoba, L. Chytka, P. \v{C}echvala, P. D\v{e}dic, D. della Volpe, Y. Favre, M. Garczarczyk, L. Gibaud, T. Gieras, E. G{\l}owacki, P. Hamal, M. Heller, M. Hrabovsk\'y, P. Jane\v{c}ek, M. Jel\'inek, V. J\'ilek, J. Jury\v{s}ek, V. Karas, B. Lacave, E. Lyard, E. Mach, D. Mand\'at, W. Marek, S. Michal, J. Micha…

The SST-1M stereoscopic system
The Single-Mirror Small-Size Telescope (SST-1M) is an Imaging Atmospheric Cherenkov Telescope designed for detecting very high-energy gamma rays. With a compact design achieved through the adoption of silicon-photomultiplier pixels and a lightweight structure, SST-1M offers a large field of view of about 9° and features a mirror system of 4 m diameter with an optical PSF (at 80% of photon inclusion) of 0.08° on axis and 0.21° at 4° off-axis, and a fully digitizing readout almost deadtime fr…

JWST Near Infrared Spectroscopy of High Albedo Jupiter Trojans: A New Surface Type in the Trojan Belt
Michael E. Brown, Ian Wong, Matthew Belyakov
https://arxiv.org/abs/2506.19922

JWST Near Infrared Spectroscopy of High Albedo Jupiter Trojans: A New Surface Type in the Trojan Belt
We present 0.8 to 5 $μ$m JWST spectra of four $\sim$20 km diameter Jupiter Trojans known to have albedos elevated above the values typical in the remaining Trojan population. The spectra of these four high albedo Jupiter Trojans are all similar, with red slopes in the optical-IR transition region, a break to lower slopes at 1.3 $μ$m, and a broad absorptions from 2.8 to 4 $μ$m. The 0.8 to 2.5 $μ$m spectra of these objects match the spectra of neither the well-known "red" and "less-red" Jupit…

Modified Distance Ratio Metrics via Domain Diameter and their geometric implications
Bibekananda Maji, Pritam Naskar, Swadesh Kumar Sahoo
https://arxiv.org/abs/2508.01607 https:…

Modified Distance Ratio Metrics via Domain Diameter and their geometric implications
Let $D\subsetneq\mathbb{R}^n,~n\ge 2$, be a domain. In this manuscript, a new version of the Vuorinen's distance ratio metric $j_D$ [{\tt J. Analyse Math.} {\bf 45} (1985), 69--115], denoted by $ζ_D$, and a version of Gehring-Osgood's distance ratio metric $j_D'$ [{\tt J. Analyse Math.} {\bf 36} (1979), 50--74], denoted by $ζ_D'$, are introduced to better understand how quasihyperbolic geometry interacts with bounded uniform domains in $\mathbb{R}^n$. We show that the metric $m_D$, introduced…

An optimal two-side Robin-Robin domain decomposition method for H(div)-elliptic problem
Na Xuyang
https://arxiv.org/abs/2506.12485 https://

An optimal two-side Robin-Robin domain decomposition method for H(div)-elliptic problem
In this paper, we develop a new two-side Robin-Robin domain decomposition method for H(div)-elliptic problem. Numerical results show that the convergence rate of the new algorithm only depends on $H/h$, where $H$ is diameter of subdomains and $h$ is the mesh size. Besides, an algebraic system of Robin boundary conditions is derived from the iterative method. We solve it by MINRES and get asymptotically stable iteration numbers as well.

Universal diameter bounds for random graphs with given degrees
Louigi Addario-Berry, Gabriel Crudele
https://arxiv.org/abs/2507.10759 https://

Universal diameter bounds for random graphs with given degrees
Given a graph $G$, let $\mathrm{diam}(G)$ be the greatest distance between any two vertices of $G$ which lie in the same connected component, and let $\mathrm{diam}^+(G)$ be the greatest distance between any two vertices of $G$; so $\mathrm{diam}^+(G)=\infty$ if $G$ is not connected. Fix a sequence $(d_1,\ldots,d_n)$ of positive integers, and let $\mathbf{G}$ be a uniformly random connected simple graph with $V(\mathbf{G})=[n]:=\{1,\ldots,n\}$ such that $\mathrm{deg}_{\mathbf{G}}(v)=d_v$ for …

On upper bounds on the number of parts in the problem of partitioning sets into parts of smaller diameter
Arthur Igorevich Bikeev, Andrei Mikhailovich Raigorodskii
https://arxiv.org/abs/2508.14578

On upper bounds on the number of parts in the problem of partitioning sets into parts of smaller diameter
In the present paper, we study problems related to the classical Borsuk's problem. Recall that the Borsuk's problem consists in finding the smallest number $ f(n) $ of parts of smaller diameter into which an arbitrary set of diameter 1 in Euclidean space $ {\mathbb R}^n $ can be divided. Here we will discuss the quantity $ χ(n,b) $ which differs from the quantity $ f(n) $ in that in its definition an arbitrary set of diameter 1 in $ {\mathbb R}^n $ must be partitioned into parts whose diameter…

Short-range and long-range correlations in driven dense colloidal mixtures in narrow pores
Frantisek Slanina, Miroslav Kotrla, Karel Netocny
https://arxiv.org/abs/2508.09718 htt…

Short-range and long-range correlations in driven dense colloidal mixtures in narrow pores
The system of driven dense colloid mixture in a tube with diameter comparable with particle size is modeled by a generalization of asymmetric simple exclusion (ASEP) model. The generalization goes in two directions: relaxing the exclusion constraint by allowing several (but few) particles on a site, and by considering two species of particles, which differ by size and transport coefficients. We calculate the nearest-neighbor correlations using a variant of Kirkwood approximation and show by com…

Most Fatou and Julia components are small for polynomials
Jinsong Zeng
https://arxiv.org/abs/2507.08471 https://arxiv.org/pdf/2507.08…

Most Fatou and Julia components are small for polynomials
We prove that Julia components of polynomials are generally small in diameter. For polynomials without irrationally neutral cycles, Fatou components are also typically small, even when the Julia set is not locally connected.

Quantifying the Impact of 2D and 3D BAO Measurements on the Cosmic Distance Duality Relation with HII Galaxy observation
Jie Zheng (HNAS), Da-Chun Qiang (HNAS), Zhi-Qiang You (HNAS), Darshan Kumar (HNAS)
https://arxiv.org/abs/2507.17113

Quantifying the Impact of 2D and 3D BAO Measurements on the Cosmic Distance Duality Relation with HII Galaxy observation
The cosmic distance duality relation (CDDR) is a fundamental and practical condition in observational cosmology that connects the luminosity distance and angular diameter distance. Testing its validity offers a powerful tool to probe new physics beyond the standard cosmological model. In this work, for the first time, we present a novel consistency test of CDDR by combining HII galaxy data with a comprehensive set of Baryon Acoustic Oscillations (BAO) measurements. The BAO measurements include …

Preferred Synthesis of Armchair SnS2 Nanotubes
Abid, Luneng Zhao, Ju Huang, Yongjia Zheng, Yuta Sato, Qingyun Lin, Zhen Han, Chunxia Yang, Tianyu Wang, Bill Herve Nduwarugira, Yicheng Ma, Lingfeng Wang, Yige Zheng, Hang Wang, Salman Ullah, Afzal Khan, Qi Zhang, Wenbin Li, Junfeng Gao, Bingfeng Ju, Feng Ding, Yan Li, Kazu Suenaga, Shigeo Maruyama, Huayong Yang, Rong Xiang

Preferred Synthesis of Armchair SnS2 Nanotubes
In this work, we present the synthesis of tin disulfide (SnS2) nanotubes (NTs) with preferred chiral angle. A sacrificial template is used to create channels of boron nitride nanotubes (BNNTs) with an optimized diameter of 4-5 nm, inside of which SnS2 NTs are formed with the high yield and structural purity. Atomic resolution imaging and nano-area electron diffraction reveal that these synthesized SnS2 NTs prefer to have an armchair configuration with a probability of approximately 85%. Calcula…

High-Speed Thermal Imaging of Disk-shaped Firebrands in a Wind Tunnel
Charles Callahan, Erick Gatica, Sean Coburn, Sam Simons-Wellin, Luke Heinzen, Laura Shannon, John Farnsworth, Peter E. Hamlington, Gregory B. Rieker
https://arxiv.org/abs/2506.15891

High-Speed Thermal Imaging of Disk-shaped Firebrands in a Wind Tunnel
The transport and temperature-time history of disk-shaped firebrands was studied with high-speed thermal imaging in a wind tunnel. One millimeter diameter wooden disks were ignited using a novel firebrand generator. The firebrands dropped vertically into a wind tunnel crossflow. Optical images of the firebrands were recorded at 960 frames/second during their transport in the wind tunnel test section at three different wind speeds. The resulting high speed color videos were processed using a par…

Ultrastable jammed sphere packings with a wide range of particle dispersities
Robert S. Hoy
https://arxiv.org/abs/2506.16521 https://…

Ultrastable jammed sphere packings with a wide range of particle dispersities
We show that for a standard continuously-polydisperse model with particle-diameter distribution $P(σ) \propto σ^{-3}$ and polydispersity index $Δ$, employing a combination of standard SWAP moves and transient degree of freedom (TDOF) moves during a Lubachevsky-Stillinger-like particle-growth process dramatically increases the generated packings' jamming densities $ϕ_{\rm J}(Δ)$ and coordination numbers $Z_{\rm J}(Δ)$, for a wide range of $Δ$. We find that the fractional increase in $ϕ_{…

Parameterized complexity of isometric path partition: treewidth and diameter
Dibyayan Chakraborty, Oscar Defrain, Florent Foucaud, Mathieu Mari, Prafullkumar Tale
https://arxiv.org/abs/2508.05448

Parameterized complexity of isometric path partition: treewidth and diameter
We investigate the parameterized complexity of the Isometric Path Partition problem when parameterized by the treewidth ($\mathrm{tw}$) of the input graph, arguably one of the most widely studied parameters. Courcelle's theorem shows that graph problems that are expressible as MSO formulas of constant size admit FPT algorithms parameterized by the treewidth of the input graph. This encompasses many natural graph problems. However, many metric-based graph problems, where the solution is defined …

RS-Coded Adaptive Dynamic Network for Reliable Long-Term Information Transmission in Disturbed Multimode Fiber
Yang Hu, Minyu Fan, Kun Liu, Songsong Zhu, Nan Jiang, Sha Wang
https://arxiv.org/abs/2506.16859

RS-Coded Adaptive Dynamic Network for Reliable Long-Term Information Transmission in Disturbed Multimode Fiber
Multimode fiber (MMF), due to its large core diameter and high mode capacity, holds potential in high-speed communications. However, inherent modal dispersion causes output speckle distortion, and transmission characteristics are sensitive to environmental disturbances, limiting its reliable application. Conventional transmission matrix (TM) methods face challenges such as complex calibration and environmental sensitivity. Although current deep learning approaches demonstrate reconstruction pot…

Constrained Flips in Plane Spanning Trees
Oswin Aichholzer, Joseph Dorfer, Birgit Vogtenhuber
https://arxiv.org/abs/2508.15520 https://arxiv.org/pdf/2508.1…

Constrained Flips in Plane Spanning Trees
A flip in a plane spanning tree $T$ is the operation of removing one edge from $T$ and adding another edge such that the resulting structure is again a plane spanning tree. For trees on a set of points in convex position we study two classic types of constrained flips: (1)~Compatible flips are flips in which the removed and inserted edge do not cross each other. We relevantly improve the previous upper bound of $2n-O(\sqrt{n})$ on the diameter of the compatible flip graph to~$\frac{5n}{3}-O(1)$…

The Potential Danger to Satellites due to Ejecta from a 2032 Lunar Impact by Asteroid 2024 YR4
Paul Wiegert, Peter Brown, Jack Lopes, Martin Connors
https://arxiv.org/abs/2506.11217

The Potential Danger to Satellites due to Ejecta from a 2032 Lunar Impact by Asteroid 2024 YR4
On 2032 December 22 the 60 m diameter asteroid 2024 YR4 has a 4% chance of impacting the Moon. Such an impact would release 6.5 MT TNT equivalent energy and produce a ~1 km diameter crater. We estimate that up to 10^8 kg of lunar material could be liberated in such an impact by exceeding lunar escape speed. Depending on the actual impact location on the Moon as much as 10% of this material may accrete to the Earth on timescales of a few days. The lunar ejecta-associated particle fluence at 0.1 …

Hubble Space Telescope Observations of the Interstellar Interloper 3I/ATLAS: #Interstellar Comet, Hubble Makes Size Estimate: https://science.nasa.gov/missions/hubble/as-nasa-missions-study-interstellar-comet-hubble-makes-size-estimate/ and https://www.esa.int/ESA_Multimedia/Images/2025/08/Hubble_sizes_up_rare_interstellar_comet (which is 5.6 km > nucleus diameter > 320 m, so we still don't know much here).

Thermodynamics and Shadows of Kerr black holes endowed with a global monopole charge
Balendra Pratap Singh, Md Sabir Ali
https://arxiv.org/abs/2506.02653 h…

Thermodynamics and Shadows of Kerr black holes endowed with a global monopole charge
In this article, we present the thermodynamic and shadow properties of rotating black holes with global monopole charge. The angular diameter of Sgr A$^{*}$ black hole is 48.7 $\pm$ 7 $μas$, which is 8 $kps$ far away having a mass of $M = 4.0_{-0.6}^{+1.1} \times 10^6 M\odot$ as observed by Event Horizon Telescope and for the M87 black hole, the observed angular diameter is $θ_d = 42 \pm 3 μ$as, which is almost $16$ $Mpc$ far away with a mass of $M = (6.5 \pm 0.7) \times 10^9 M_\odot$. The g…

Scanning Tunneling Microscope Tip-Induced Formation of Bi Bilayers on Bi$_2$Te$_3$
Duy Nguyen, Jay A. Gupta
https://arxiv.org/abs/2507.16081 https://

Scanning Tunneling Microscope Tip-Induced Formation of Bi Bilayers on Bi$_2$Te$_3$
We report the formation of Bi(111) bilayer (BL) islands and crater structures on Bi$_2$Te$_3$(111) surfaces induced by voltage pulses from an STM tip. Pulses above a threshold voltage ($+3$ V) produce craters $\sim 0.5$ microns in diameter, similar to the size of the tip. Redeposited material self-assembles into a network of atomically ordered islands with a lattice constant identical to the underlying Bi$_2$Te$_3$ surface. The island size monotonically decreases over several microns from the p…

Maximal sets of a given diameter in Hamming cubes
Boris Bukh, Aleksandre Saatashvili
https://arxiv.org/abs/2507.10828 https://arxiv.o…

Maximal sets of a given diameter in Hamming cubes
A subset of the Hamming cube over $n$-letter alphabet is said to be $d$-maximal if its diameter is $d$, and adding any point increases the diameter. Our main result shows that each $d$-maximal set is either of size at most $(n+o(n))^d$ or contains a non-trivial Hamming ball. The bound of $(n+o(n))^d$ is asymptotically tight. Additionally, we give a non-trivial lower bound on the size of any $d$-maximal set and show that the number of essentially different $d$-maximal sets is finite.

Laser ablated sub-wavelength structure anti-reflection coating on an alumina lens
Shaul Hanany, Scott Cray, Samuel Dietterich, Jan Dusing, Calvin Firth, Jurgen Koch, Rex Lam, Tomotake Matsumura, Haruyuki Sakurai, Yuki Sakurai, Aritoki Suzuki, Ryota Takaku, Qi Wen, Alexander Wienke, Andrew Y. Yan
https://arxiv.org/abs/2506.13042

Laser ablated sub-wavelength structure anti-reflection coating on an alumina lens
We used laser ablation to fabricate sub-wavelength structure anti-reflection coating (SWS-ARC) on a 5 cm diameter alumina lens. With an aspect ratio of 2.5, the SWS-ARC are designed to give a broad-band low reflectance response between 110 and 290 GHz. SWS shape measurements conducted on both sides of the lens give 303 $μ$m pitch and total height between 750 and 790 $μ$m, matching or exceeding the aspect ratio design values. Millimeter-wave transmittance measurements in a band between 140 and…

Forecast constraints on null tests of the $\Lambda$CDM model with SPHEREx
Alejandro Mata Rom\'an, Indira Ocampo, Savvas Nesseris
https://arxiv.org/abs/2507.16604

Forecast constraints on null tests of the $Λ$CDM model with SPHEREx
In this work we quantify the ability of the upcoming SPHEREx survey to constrain cosmological observables and test the internal consistency of the cosmological constant and cold dark matter ($Λ$CDM) model. Using Fisher matrix forecasting, we assess the expected precision on Baryon Acoustic Oscillations (BAO) observables, such as the angular diameter distance $D_\mathrm{A}(z)$ and the Hubble parameter $H(z)$. We further explore SPHEREx's potential to probe some of the fundamental assumptions of…

Euclidean lengths and the Culler-Shalen norms of slopes
Kazuhiro Ichihara
https://arxiv.org/abs/2507.09986 https://arxiv.org/pdf/2507…

Euclidean lengths and the Culler-Shalen norms of slopes
In the study of exceptional Dehn fillings, two functions on slopes, called the Euclidean length on a horotorus and the Culler-Shalen norm, play important roles. In this paper, we investigate their relationship and establish two inequalities between them. As a byproduct, some bounds on the boundary slope diameter are given.

Beam Cross Sections Create Mixtures: Improving Feature Localization in Secondary Electron Imaging
Vaibhav Choudhary, Akshay Agarwal, Vivek K Goyal
https://arxiv.org/abs/2508.09942

Beam Cross Sections Create Mixtures: Improving Feature Localization in Secondary Electron Imaging
Secondary electron (SE) imaging techniques, such as scanning electron microscopy and helium ion microscopy (HIM), use electrons emitted by a sample in response to a focused beam of charged particles incident at a grid of raster scan positions. Spot size -- the diameter of the incident beam's spatial profile -- is one of the limiting factors for resolution, along with various sources of noise in the SE signal. The effect of the beam spatial profile is commonly understood as convolutional. We sho…

Density and Particle Sourcing Optimization in a Helicon Plasma Source Prototype For Wakefield Accelerator Applications
Michael Zepp, Marcel Granetzny, Oliver Schmitz
https://arxiv.org/abs/2508.12929

Density and Particle Sourcing Optimization in a Helicon Plasma Source Prototype For Wakefield Accelerator Applications
Helicon plasmas are being considered as plasma sources for wakefield accelerators, subject to strict density requirements. We present various mechanisms to increase axial density homogeneity in a helicon plasma for implementation in such an accelerator. We consider various background neutral flow configurations for helicons generated with first one antenna and then two identical antennas in a 2 meter long, 52 mm diameter plasma chamber with homogeneous magnetic field. In the case of a single an…

Submillimeter galaxy overdensities around physically associated quasar pairs
Eileen Herwig, Fabrizio Arrigoni Battaia, Chian-Chou Chen, Aura Obreja, Marta Nowotka, Rhea-Silvia Remus, Hidenobu Yajima
https://arxiv.org/abs/2506.11193

Submillimeter galaxy overdensities around physically associated quasar pairs
A commonly employed method to detect protoclusters in the young universe is the search for overdensities of massive star forming galaxies, such as submillimeter galaxies (SMGs), around high-mass halos, including those hosting quasars. In this work, we study the Megaparsec environment surrounding nine physically associated quasar pairs between $z=2.45$ and $z=3.82$ with JCMT/SCUBA-2 observations at 450 $μ$m and 850 $μ$m covering a field of view of roughly 13.7 arcmin in diameter (or 32 Mpc$^2$…

Fully-Distributed Construction of Byzantine-Resilient Dynamic Peer-to-Peer Networks
Aayush Gupta, Gopal Pandurangan
https://arxiv.org/abs/2506.04368 https:…

Fully-Distributed Construction of Byzantine-Resilient Dynamic Peer-to-Peer Networks
We address a fundamental problem in Peer-to-Peer (P2P) networks, namely, constructing and maintaining dynamic P2P overlay network topologies with essential properties such as connectivity, low diameter, and high expansion, that are resilient to continuous high churn and the presence of a large number of malicious (Byzantine) nodes. Our main goal is to construct and maintain a sparse (bounded degree) expander topology despite high churn and a large number of Byzantine nodes. Such an expander top…

Weakly distance-regular digraphs of diameter 2
Xiangli Wang, Yuefeng Yang
https://arxiv.org/abs/2507.11298 https://arxiv.org/pdf/2507…

Weakly distance-regular digraphs of diameter 2
Weakly distance-regular digraphs is a directed version of distance-regular graphs. In this paper, we characterize all weakly distance-regular digraphs of diameter 2.

An effective microscopic model for plasmonic sensing of malaria
A. S. Kiyumbi, M. S. Tame
https://arxiv.org/abs/2506.15391 https://ar…

An effective microscopic model for plasmonic sensing of malaria
An effective microscopic model for plasmonic sensing is developed and studied in this work. The model is applied to a reference sensor made from a plasmonic metasurface comprised of an array of nanoholes 150 nm in diameter patterned in a 150 nm thick gold film. The sensor is functionalized to detect plasmodium lactate dehydrogenase (pLDH), a malaria biomarker. The biochemistry above the sensor's metasurface is modelled as stacks of closely packed adlayers. Using the Maxwell Garnett effective me…

Testing the cosmic distance duality relation with baryon acoustic oscillations and supernovae data
Tian-Nuo Li, Guo-Hong Du, Peng-Ju Wu, Jing-Zhao Qi, Jing-Fei Zhang, Xin Zhang
https://arxiv.org/abs/2507.13811

Testing the cosmic distance duality relation with baryon acoustic oscillations and supernovae data
One of the most fundamental relationships in modern cosmology is the cosmic distance duality relation (CDDR), which describes the relationship between the angular diameter distance ($D_{\rm A}$) and the luminosity distance ($D_{\rm L}$), and is expressed as: $η(z)=D_{\rm L}(z)(1+z)^{-2}/D_{\rm A}(z)=1$. In this work, we conduct a comprehensive test of the CDDR by combining baryon acoustic oscillation (BAO) data from the SDSS and DESI surveys with type Ia supernova (SN) data from PantheonPlus a…

On Dust Devil Diameters, Occurrence Rates, and Activity
Brian Jackson, Lori Fenton, Ralph Lorenz, Chelle Szurgot, Joshua Gambill, Gwendolyn Arzaga
https://arxiv.org/abs/2507.03643

On Dust Devil Diameters, Occurrence Rates, and Activity
As a phenomenon that occurs on Earth and on Mars, the diameter of a dust devil helps determine the amount of dust the devil injects into the atmosphere for both worlds -- for a given dust flux density (dust lifted per area per time), a wider devil will lift more dust into the air. However, the factors that determine a dust devil's diameter $D$ and how it might relate to ambient conditions have remained unclear. Moreover, estimating the contribution to an atmospheric dust budget from a populatio…

On physical considerations regarding development and validation of Heat Flux Partitioning models: application to vertical boiling flows simulations
Luc Favre (IMFT, EDF R&D MFEE), Catherine Colin (IMFT), S. Pujet (EDF R&D MFEE), St\'ephane Mimouni (EDF R&D MFEE)
https://arxiv.org/abs/2507.12478

On physical considerations regarding development and validation of Heat Flux Partitioning models: application to vertical boiling flows simulations
As part of a critical assessment of wall boiling modeling through Heat Flux Partitioning approach, a new model dedicated to vertical boiling flows is proposed, with a revisited partitioning including a boiling heat flux related to bubble coalescence. Closure laws include a recent model for bubble dynamics, a new correlation for the bubble maximum lift-off diameter, and comprehensive selection of existing models for nucleation site density and bubble wait time. Each formulation are compared to r…

Liquid-gas state regularities as a manifestation of global isomorphism with the Ising model
L. A. Bulavin, V. L. Kulinskii, A. M. Katts, A. M. Maslechko
https://arxiv.org/abs/2506.14622

Liquid-gas state regularities as a manifestation of global isomorphism with the Ising model
Liquid-gas equilibrium is considered using the global isomorphism with the Ising-like (lattice gas) model. Such an approach assumes the existence of the order parameter in terms of which the symmetry of binodal is restored not only in the vicinity of the critical point (critical isomorphism) but also globally in the whole coexistence region. We show how the empirical law of the rectilinear density diameter of the liquid-gas binodal allows us to derive a rather simple form of the isomorphism tra…

Bounded diameter monochromatic component covers
Alexey Pokrovskiy
https://arxiv.org/abs/2507.05842 https://arxiv.org/pdf/2507.05842…

Bounded diameter monochromatic component covers
Ryser conjectured that every $r$-edge-coloured complete graph can be covered by $r-1$ monochromatic trees. Motivated by a question of Austin in analysis, Milićević predicted something stronger -- that every $r$-edge-coloured complete graph can be covered by $r-1$ monochromatic trees \emph{of bounded diameter}. Here we show that the two conjectures are equivalent. As immediate corollaries we obtain new results about Milićević's Conjecture, most notably that it is true for $r=5$. We also obta…

A dynamical dichotomy in large binary asteroids
K. Minker, B. Carry, F. Vachier, M. Marsset, J. \v{D}urech, J. Hanu\v{s}, L. Liberato, W. J. Merline, J. L. Margot, C. Dumas, L. M. Close, A. Conrad, W. M. Grundy, R. Behrend, R. Roy, J. Berthier, I. Sokova, E. Sokov, D. Gorshanov, M. Ferrais, E. Jehin, A. Martin, K. B. Alton
https://

A dynamical dichotomy in large binary asteroids
No less than 15% of large (diameter greater than 140 km) asteroids have satellites. The commonly accepted mechanism for their formation is post-impact reaccumulation. However, the detailed physical and dynamical properties of these systems are not well understood, and many of them have not been studied in detail. We aim to study the population of large binary asteroid systems. To do so, we compare the gravitational fields predicted from the shape of the primary body with the non-Keplerian gravi…

The dynamics of background evolution and structure formation in phase space: a semi-cosmographic reconstruction
Pankaj Chavan, Tapomoy Guha Sarkar, Anjan A Sen
https://arxiv.org/abs/2506.14275

The dynamics of background evolution and structure formation in phase space: a semi-cosmographic reconstruction
The Baryon Acoustic Oscillation (BAO) feature, imprinted in the transverse and radial clustering of dark matter tracers, enables the simultaneous measurement of the angular diameter distance $D_A(z)$ and the Hubble parameter $H(z)$ at a given redshift. Further, measuring the redshift space anisotropy (RSD) allows us to measure the combination $f_8\equiv fσ_8(z)$. Motivated by this, we simultaneously study the dynamics of background evolution and structure formation in an abstract phase space o…

A Parametric Study on the Pulsation of Burner-Stabilized CH4-O2 Flames Moderated by CO2 Addition -- Frequencies, Modes and Regime Diagrams
Xiangyu Nie, Shuoxun Zhang, Shengkai Wang
https://arxiv.org/abs/2507.10905

A Parametric Study on the Pulsation of Burner-Stabilized CH4-O2 Flames Moderated by CO2 Addition -- Frequencies, Modes and Regime Diagrams
This study investigated the pulsating instability of burner-stabilized premixed CH4-O2 flames at various levels of CO2 dilution. Experiments were conducted using a water-cooled porous-plug burner of 18 mm diameter over a wide range of mixture compositions and flow rates, during which time-resolved measurements of flame chemiluminescence and gas temperature were obtained. The primary oscillation frequencies of the pulsating flames were determined using fast Fourier transform and harmonic power a…

Short Simple Orthogonal Geodesic Chords on a 2-Disk with Convex Boundary
Isabel Beach
https://arxiv.org/abs/2507.07797 https://arxiv.…

Short Simple Orthogonal Geodesic Chords on a 2-Disk with Convex Boundary
We prove the existence of at least two distinct short, simple orthogonal geodesic chords on a Riemannian 2-disk $M$ with convex boundary. The lengths of these curves are bounded in terms of the length of $\partial M$, the diameter of $M$, and the area of $M$. We also prove the existence of a short, simple geodesic chord on any Riemannian 2-disk.

Oriented Diameter of Mixed Graphs with Given Maximum Undirected Degree
Ran An, Hengzhe Li, Jianbing Liu, Gaoxing Sun
https://arxiv.org/abs/2507.02277 https…

Oriented Diameter of Mixed Graphs with Given Maximum Undirected Degree
In 2018, Dankelmann, Gao, and Surmacs [J. Graph Theory, 88(1): 5--17, 2018] established sharp bounds on the oriented diameter of a bridgeless undirected graph and a bridgeless undirected bipartite graph in terms of vertex degree. In this paper, we extend these results to \emph{mixed graphs}, which contain both directed and undirected edges. Let the \emph{undirected degree} $d^*_G(x)$ of a vertex $x \in V(G)$ be the number of its incident undirected edges in a mixed graph $G$ of order $n$, and…

New tests of cosmic distance duality relation with DESI 2024 BAO observations
Qiumin Wang, Shuo Cao, Jianyong Jiang, Kaituo Zhang, Xinyue Jiang, Tonghua Liu, Chengsheng Mu, Dadian Cheng
https://arxiv.org/abs/2506.12759

New tests of cosmic distance duality relation with DESI 2024 BAO observations
In this paper, we test the cosmic distance duality relation (CDDR), as required by the Etherington reciprocity theorem, which connects the angular diameter distance and the luminosity distance via the relation \( D_{\rm L}(z) = D_{\rm A}(z)(1+z)^2 \). Our analysis is based on the latest baryon acoustic oscillation (BAO) measurements provided by the Dark Energy Survey (DES), the Baryon Oscillation Spectroscopic Survey (BOSS)/Extended BOSS (eBOSS), and the Dark Energy Spectroscopic Instrument (DE…

Some sharp bounds on the average Steiner (k, l)-eccentricity for trees
Cheng Zeng, Gengji Li
https://arxiv.org/abs/2506.17915 https://

Some sharp bounds on the average Steiner (k, l)-eccentricity for trees
In this paper we introduce some transformations for trees that do not increase the average Steiner $(k,l)$-eccentricity for all $0\leq l\leq k\leq n$. Using these transformations, we obtain some sharp bounds on the average Steiner $(k,l)$-eccentricity for trees with some certain conditions, including given nodes, given diameter, given max degree and given leaves, and get the corresponding extremal trees as well.

Matroids, intersecting bases, and Borsuk property
Gyivan L\'opez-Campos, Fr\'ed\'eric Meunier, Jorge L. Ram\'irez Alfons\'in
https://arxiv.org/abs/2506.17082

Matroids, intersecting bases, and Borsuk property
A subset $S$ of $\mathbb R^d$ has the Borsuk property if it can be decomposed into at most $d+1$ parts of diameter smaller than $S$. This is an important geometric property, inspired by a conjecture of Borsuk from the 1930s, which has attracted considerable attention over the years. In this paper, we define and investigate the Borsuk property for matroids, providing a purely combinatorial approach to the Borsuk property for matroid polytopes, a well-studied family of $(0,1)$-polytopes associate…

Revisiting Cosmic Distance Duality with Megamasers and DESI DR2: Model Independent Constraints on Early-Late Calibration
Brijesh Kanodia, Ujjwal Upadhyay, Yashi Tiwari
https://arxiv.org/abs/2507.11518

Revisiting Cosmic Distance Duality with Megamasers and DESI DR2: Model Independent Constraints on Early-Late Calibration
The Cosmic Distance Duality Relation (CDDR) connects the angular diameter distance ($d_A$) and the luminosity distance ($d_L$) at a given redshift. This fundamental relation holds in any metric theory of gravity, provided that photon number is conserved and light propagates along null geodesics. A deviation from this relation could indicate new physics beyond the standard cosmological model. In this work, we test the validity of the CDDR at very low redshifts ($z < 0.04$) by combining $d_A$ fro…

On the generator graph of a cyclic group
Zekhaya B. Shozi, Teresa L. Tacbobo
https://arxiv.org/abs/2508.14865 https://arxiv.org/pdf/2508.14865

On the generator graph of a cyclic group
In this paper, we continue the study of the generator graph of a group. In 2023, Tacbobo [9] defined the generator graph of a nontrivial group to be the graph whose vertices are the elements of the group, with two vertices being adjacent if at least one of them is a generator of the group. Building on the properties established in [9], we prove that the diameter of the generator graph of a cyclic group is at most $2$. Furthermore, we present explicit formulas for some topological indices of the…

Improved Decomposition Bounds for Partition Polytopes and Odd-Covers
Steffen Borgwardt, Zden\v{e}k Dvo\v{r}\'ak, Bryce Frederickson, Abigail Nix, Youngho Yoo
https://arxiv.org/abs/2507.12748

Improved Decomposition Bounds for Partition Polytopes and Odd-Covers
The assignments of a set of $m$ items into $n$ clusters of prescribed sizes $κ_1,\dots,κ_n$ can be encoded as the vertices of the \emph{partition polytope} $\mathrm{PP}(κ_1,\dots,κ_n)$. We prove that, if $K = \max\{κ_1,\dots,κ_n\}$, then the combinatorial diameter of $\mathrm{PP}(κ_1,\dots,κ_n)$ is at most $\lceil 3K/2\rceil$. This improves the previously known upper bound of $2K$. A \emph{cycle} (resp.~\emph{path}) \emph{odd-cover} of a graph $G$ is a set $\mathcal{H}$ of cycles (res…

A characterization of all graphs cospectral to the double star $P_2(1,n)$
Emily Barranca, Michael D. Barrus
https://arxiv.org/abs/2506.06934 https://

A characterization of all graphs cospectral to the double star $P_2(1,n)$
We examine the adjacency spectrum of trees with diameter three, also referred to as double stars. Using $P_2(a,b)$ to denote a double star with $ a$ and $b$ leaves at its respective endpoints, we discuss graphs which are cospectral to double stars for various parameters $a$ and $b$. In particular, we give constructions for graphs cospectral to $P_2(1,2k)$ for integers $k$. Lastly, we show that the double star $P_2(1,n)$ is determined by its spectrum when $n$ is odd. That is, if a graph $G$ cosp…

The Moore Bound for Regular Simplicial Complexes
Sukrit Chakraborty
https://arxiv.org/abs/2508.04741 https://arxiv.org/pdf/2508.04741

The Moore Bound for Regular Simplicial Complexes
We derive Moore-type upper bounds for regular simplicial complexes and present logarithmic lower bounds on their diameter based on minimum degree.

Majority dynamics on finite trees
Itai Benjamini, Georgii Zakharov, Maksim Zhukovskii
https://arxiv.org/abs/2507.04714 https://arxiv.…

Majority dynamics on finite trees
For an arbitrary finite tree $T$, we find the exact value of the wort-case stabilisation time of majority dynamics on $T$. We also prove that for a perfect rooted cubic tree $T$ with diameter $D$ and uniformly random initial opinions, the dynamics stabilises in time $τ\in(D/4,D/3)$ with high probability.

Geodesic transitive graphs of small valency
Jun-Jie Huang
https://arxiv.org/abs/2506.04670 https://arxiv.org/pdf/2506.04670

Geodesic transitive graphs of small valency
For a graph $Γ$, the {\em distance} $d_Γ(u,v)$ between two distinct vertices $u$ and $v$ in $Γ$ is defined as the length of the shortest path from $u$ to $v$, and the {\em diameter} $\mathrm{diam}(Γ)$ of $Γ$ is the maximum distance between $u$ and $v$ for all vertices $u$ and $v$ in the vertex set of $Γ$. For a positive integer $s$, a path $(u_0,u_1,\ldots,u_{s})$ is called an {\em $s$-geodesic} if the distance of $u_0$ and $u_s$ is $s$. The graph $Γ$ is said to be {\em distance transiti…