Tootfinder

Fractal Flow: Hierarchical and Interpretable Normalizing Flow via Topic Modeling and Recursive Strategy
Binhui Zhang, Jianwei Ma
https://arxiv.org/abs/2508.19750 https://…

Fractal Flow: Hierarchical and Interpretable Normalizing Flow via Topic Modeling and Recursive Strategy
Normalizing Flows provide a principled framework for high-dimensional density estimation and generative modeling by constructing invertible transformations with tractable Jacobian determinants. We propose Fractal Flow, a novel normalizing flow architecture that enhances both expressiveness and interpretability through two key innovations. First, we integrate Kolmogorov-Arnold Networks and incorporate Latent Dirichlet Allocation into normalizing flows to construct a structured, interpretable lat…

Fractal analysis of slow-fast and regular systems: A survey of recent results and future perspectives
Renato Huzak (Hasselt University), Goran Radunovi\'c (University of Zagreb, Faculty of Science), Vesna \v{Z}upanovi\'c (University of Zagreb, Faculty of Electrical Engineering and Computing)
https://arxiv.org/abs/2508.19859

Fractal analysis of slow-fast and regular systems: A survey of recent results and future perspectives
We survey recent developments in fractal analysis of regular and slow-fast dynamical systems using Minkowski dimension. Our focus is on spiral trajectories near monodromic limit periodic sets in regular systems and entry-exit sequences in slow-fast systems with degenerate singularities. For regular systems, we recall connections between Minkowski dimension and cyclicity. Key results include fractal classifications of weak foci, degenerate foci, and polycycles, where dimensional relationships pr…

This https://arxiv.org/abs/2505.22166 has been replaced.
initial toot: https://mastoxiv.page/@…

Critical and Nonpercolating Phases in Bond Percolation on the Song-Havlin-Makse Network
We investigate bond percolation on the Song-Havlin-Makse (SHM) network, a scale-free tree with a tunable degree exponent and dimensionality. Using a generating function approach, we analytically derive the average size and the fractal exponent of the root cluster for deterministic cases. Our analysis reveals that bond percolation on the SHM network remains in a nonpercolating phase for all $p < 1$ when the network is fractal (i.e., finite-dimensional), whereas it exhibits a critical phase, wher…

An Approach to Estimating Quadratic Logistic Model Parameters of Fractal Dimension Curves
Yanguang Chen
https://arxiv.org/abs/2508.19917 https://arxiv.org/…

An Approach to Estimating Quadratic Logistic Model Parameters of Fractal Dimension Curves
The fractal dimension curves of urban form and growth fall into two categories: One can be described by common logistic function, and the other can be described with quadratic logistic function. The approach to estimating the parameter of the ordinary logistic model has been developed. However, how to estimate the parameter of quadratic logistic model is still a problem. This paper is devoted to finding a nonlinear regressive approach for estimating parameter values of quadratic logistic model …

Quantum-Circuit-Based Visual Fractal Image Generation in Qiskit and Analytics
Hillol Biswas
https://arxiv.org/abs/2508.18835 https://arxiv.org/pdf/2508.188…

Quantum-Circuit-Based Visual Fractal Image Generation in Qiskit and Analytics
As nature is ascribed as quantum, the fractals also pose some intriguing appearance which is found in many micro and macro observable entities or phenomena. Fractals show self-similarity across sizes; structures that resemble the entire are revealed when zoomed in. In Quantum systems, the probability density or wavefunction may exhibit recurring interference patterns at various energy or length scales. Fractals are produced by basic iterative rules (such as Mandelbrot or Julia sets), and they p…

Fractal Rhetorics: Scaling Small and Subtle Feminist Rhetorical Actions
https://ift.tt/rkcwdGj
updated: Thursday, August 28, 2025 - 8:05amfull name / name of organization: Jessi Thomsen, Western…
via Input 4 RELCFP

Observation of Magnetic Devil's Staircase-Like Behavior in Quasiperiodic Qubit Lattices
Alejandro Lopez-Bezanilla
https://arxiv.org/abs/2507.18818 https://

Observation of Magnetic Devil's Staircase-Like Behavior in Quasiperiodic Qubit Lattices
The devil's staircase (DS) phenomenon is a fractal response of magnetization to external fields, traditionally observed in periodic ferromagnetic systems, where the commensurability between spin arrangements, lattice parameters, and external magnetic fields governs abrupt changes in magnetization. Its occurrence in aperiodic, fractal-type systems has remained largely unexplored, despite their natural compatibility with such phenomena. Using a quantum annealing device, we uncover a wealth of abr…

Measuring Fractal Dimension using Discrete Global Grid Systems
Pramit Ghosh
https://arxiv.org/abs/2506.18175 https://arxiv.org/pdf/25…

Measuring Fractal Dimension using Discrete Global Grid Systems
This study builds a bridge between two well-studied but distant topics: fractal dimension and Discrete Global Grid System (DGGS). DGGSs are used as covering sets for geospatial vector data to calculate the Minkowski-Bouligand dimension. Using the method on synthetic data yields results within 1% of their theoretical fractal dimensions. A case study on opaque cloud fields obtained from satellite images gives fractal dimension in agreement with that available in the literature. The proposed metho…

Strichartz estimates for a Schr\"odinger equation on the half-line with a Neumann boundary condition
Nicola Garofalo, Gigliola Staffilani
https://arxiv.org/abs/2507.19998 h…

Strichartz estimates for a Schrödinger equation on the half-line with a Neumann boundary condition
In this paper we prove some new Strichartz estimates related to the Cauchy problem for the Bessel operator on the half-line and we establish a fractal version of the Tomas-Stein restriction theorem for the Hankel transform. Then we use the proved Strichartz estimates to show global in time well-posedness for a class of nonlinear $L^2_a$-critical problems, and local in time well-posedness in the sub-critical case.

Endpoint estimates for the fractal circular maximal function and related local smoothing
Sanghyuk Lee, Luz Roncal, Feng Zhang, Shuijiang Zhao
https://arxiv.org/abs/2506.20390

Endpoint estimates for the fractal circular maximal function and related local smoothing
Sharp $L^p$--$L^q$ estimates for the spherical maximal function over dilation sets of fractal dimensions, including the endpoint estimates, were recently proved by Anderson--Hughes--Roos--Seeger. More intricate $L^p$--$L^q$ estimates for the fractal circular maximal function were later established in the sharp range by Roos--Seeger, but the endpoint estimates have been left open, particularly when the fractal dimension of the dilation set lies in $[1/2, 1)$. In this work, we prove these missing…

Moderately Heavy Extremes under Long Range Dependence
Zao-Li Chen
https://arxiv.org/abs/2505.23103 https://arxiv.org/pdf/2505.23103…

Moderately Heavy Extremes under Long Range Dependence
We consider stationary sequences whose marginal tail is subexponential and lies in the Gumbel Maximum domain of attraction. Due to the extremely strong dependence, their extreme values are caused by multiple big values and are clustered in the large scale with fractal features. We establish functional extremal limit theorems with non-Gumbel limit objects to characterize these delicate phenomena.

Replaced article(s) found for math.CV. https://arxiv.org/list/math.CV/new
[1/1]:
- Fractal zeta functions at infinity and the $\phi$-shell Minkowski content
Goran Radunovi\'c (University of Zagreb)

This https://arxiv.org/abs/2505.14788 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Global properties, fractality, and mass segregation in single, paired, and grouped open clusters
We investigate the structural and dynamical properties of Open Clusters (OCs) classified as single, in pairs, or in groups. By analysing their mass, size, age, fractality, and mass segregation, we aim to identify systematic differences among these categories and evaluate the role of the Galactic environment in their evolution. Our sample comprises 420 single OCs, 415 in pairs, and 317 in groups. To characterise their structure, we apply the Q-parameter, which distinguishes fractal from radial d…

from my link log —
That fractal that's been up on my wall for 12 years.
https://chriskw.xyz/2025/05/21/Fractal/
saved 2025-05-23 htt…

Compact broadband thermal absorbers based on plasmonic fractal metasurfaces
Romil Audhkhasi, Virat Tara, Raymond Yu, Michelle L. Povinelli, Arka Majumdar
https://arxiv.org/abs/2506.20905

Compact broadband thermal absorbers based on plasmonic fractal metasurfaces
The ability to efficiently absorb thermal radiation within a small material volume is crucial for the realization of compact and high spatial resolution thermal imagers. Here we propose and experimentally demonstrate a compact plasmonic metasurface for broadband absorption in the 6 to 14 microns wavelength range. As opposed to previous works, our metasurface leverages strongly localized electromagnetic modes to achieve high absorption within a compact form factor. We numerically investigate the…

The Doeblin-Lenstra conjecture: effective results and central limit theorems
Gaurav Aggarwal, Anish Ghosh
https://arxiv.org/abs/2507.19084 https://arxiv.or…

The Doeblin-Lenstra conjecture: effective results and central limit theorems
We establish effective convergence rates in the Doeblin-Lenstra law, describing the limiting distribution of approximation coefficients arising from continued fraction convergents of a typical real number. More generally, we prove quantitative versions of the Doeblin-Lenstra law for best approximates in higher dimensions, as well as for points sampled from fractal measures on the real line, including the middle-third Cantor measure. Our method reduces the problem to proving effective converge…

Random subgroups of branch groups
Jorge Fari\~na-Asategui, Santiago Radi
https://arxiv.org/abs/2508.20082 https://arxiv.org/pdf/2508.20082

Random subgroups of branch groups
We show that independent Haar-random elements in a super strongly fractal branch profinite group generate a free subgroup acting freely on the boundary of the tree. This improves a previous result of Abért (2005) for weakly branch profinite groups, where independent random elements were shown to generate free subgroups acting only almost freely on the boundary. Our result also generalizes the analogous result of Abért and Virág (2005) for iterated wreath products.

Co-existence of alternative Generalized Chaplygin Gas and other Dark Energies in the Framework of Fractal Universe
Mahasweta Biswas, Rikpratik Sengupta, Ujjal Debnath
https://arxiv.org/abs/2508.14590

Co-existence of alternative Generalized Chaplygin Gas and other Dark Energies in the Framework of Fractal Universe
We have explored the possibility of the co-existence of two forms of dark energy in the form of an alternative Generalized Chaplygin Gas (GCG) along with a scalar field of field theoretic or extra dimensional origin in the background of a fractal universe. The essential physical model parameters have been computed and their variations have been plotted. Fractal cosmology in an universe dominated by the alternative GCG (overcoming the drawbacks of the conventional form of GCG) has also been stud…

Reducible Iterated Graph Systems: multiscale-freeness and multifractals
Nero Ziyu Li, Frank Xin Hu, Thomas Britz
https://arxiv.org/abs/2506.18073 https://

Reducible Iterated Graph Systems: multiscale-freeness and multifractals
Iterated Graph Systems (IGS) aims to transplant ideas from fractal geometry into graph theory. Building on this framework, we extend Edge IGS from the primitive to the reducible setting. Within this broader context, we formulate rigorous definitions of multifractality and multiscale-freeness for graph fractals, and we establish conditions that are equivalent to the occurrence of these two phenomena. We further determine the corresponding fractal and degree spectra, proving that both are finite …

Tunable lower critical fractal dimension for a non-equilibrium phase transition
Mattheus Burkhard, Luca Giacomelli, Cristiano Ciuti
https://arxiv.org/abs/2506.20617

Tunable lower critical fractal dimension for a non-equilibrium phase transition
We theoretically investigate the role of spatial dimension and driving frequency in a non-equilibrium phase transition of a driven-dissipative interacting bosonic system. In this setting, spatial dimension is dictated by the shape of the external driving field. We consider both homogeneous driving configurations, which correspond to standard integer-dimensional systems, and fractal driving patterns, which give rise to a non-integer Hausdorff dimension for the spatial density. The onset of criti…

Fractal Illusions: An Experimental Study of Long-Range Sentence-Length Correlations in Randomly Generated Natural Language Texts
Ying Zeng, Junying Cui, Lejun Li
https://arxiv.org/abs/2508.19782

Fractal Illusions: An Experimental Study of Long-Range Sentence-Length Correlations in Randomly Generated Natural Language Texts
This study re-evaluates the assumption that long-range correlations in sentence length are a fundamental feature of natural language and a marker of literary style. While previous research has suggested that punctuation marks--particularly full stops--generate structural regularities in narrative texts, our experiments challenge this view. Using Chinese as the primary language, supplemented with English, we constructed randomized linguistic sequences through three distinct methods. Surprisingly…

Nonlinear oscillations of strings and beams
Filip Ficek, Maciej Maliborski
https://arxiv.org/abs/2508.19091 https://arxiv.org/pdf/2508.19091

Nonlinear oscillations of strings and beams
We investigate the time-periodic solutions to the nonlinear wave and beam equations and uncover their intricate, fractal-like structure. In particular, we identify a new class of large-energy solutions with complex mode compositions and propose a systematic framework for their analysis. A Floquet stability study reveals that this class contains solutions that are linearly stable, suggesting that they may play a significant role in the nonlinear dynamics of the systems.

Strichartz and local smoothing estimates for the fractional Schr\"odinger equations over fractal time
Jin Bong Lee, Sanghyuk Lee, Luz Roncal
https://arxiv.org/abs/2508.16102

Strichartz and local smoothing estimates for the fractional Schrödinger equations over fractal time
We obtain Strichartz-type estimates for the fractional Schrödinger operator $f \mapsto e^{it(-Δ)^{γ/2}} f$ over a time set $E$ of fractal dimension. To obtain those estimates capturing fractal nature of $E$, we employ the notions in the spirit of the Assouad dimension, such as, bounded Assouad characteristic and Assouad specturm. We also prove the estimate $$ \| e^{it(-Δ)^{γ/2}} f \|_{L_t^q(\mathrm{d}μ; L_x^r(\mathbb{R}^d))} \le C \|f\|_{H^s}, $$ where $μ$ is a measur…

Fractal Analytics, which became India's first AI unicorn in 2022, files for an IPO in Mumbai to raise about $560M, and could value the company at over $3.5B (Saritha Rai/Bloomberg)
https://www.bloomberg.com/news/articles/2025-…

Barnsley-Navascu\'es fractal operators on Banach spaces on the Sierpi\'nski gasket
Asheesh Kumar Yadav, Himanshu Kumar, Saurabh Verma, Bilel Selmi
https://arxiv.org/abs/2508.14436

Barnsley-Navascués fractal operators on Banach spaces on the Sierpiński gasket
In this article, we define fractal operators motivated by the works of Barnsley and Navascués on various function spaces such as energy space, Lebesgue space, and oscillation space on the well-known fractal domain Sierpiński gasket. We further explore the properties of these operators from the perspectives of operator and approximation theory.

Fractal dimensions of complex networks: advocating for a topological approach
Rayna Andreeva, Hayde\'e Contreras-Peruyero, Sanjukta Krishnagopal, Nina Otter, Maria Antonietta Pascali, Elizabeth Thompson
https://arxiv.org/abs/2506.15236

Fractal dimensions of complex networks: advocating for a topological approach
Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal dimensions for metric spaces that have been shown to outperform existing techniques. In a parallel line of work, networks are ubiquitously used to model a variety of complex systems. Higher-order interactions, i.e., simultaneous interactions between more than …

Phase Transition of the Ising Model on a 3-Dimensional Fractal Lattice
Jozef Genzor, Roman Kr\v{c}m\'ar, Hiroshi Ueda, Denis Kochan, Andrej Gendiar, Tomotoshi Nishino
https://arxiv.org/abs/2506.17053

Phase Transition of the Ising Model on a 3-Dimensional Fractal Lattice
The critical behavior of the classical Ising model on a three-dimensional fractal lattice with Hausdorff dimension $d_H = \ln32 / \ln4 = 2.5$ is investigated using the higher-order tensor renormalization group (HOTRG) method. We determine the critical temperature $T_c \approx 2.65231$ and the critical exponents for magnetization $β\approx 0.059$ and field response $δ\approx 35$. Unlike a previously studied 2D fractal with $d_H \approx 1.792$, the specific heat for this 3D fractal exhibits a d…

The fractal Goodstein principle
David Fern\'andez-Duque, Andreas Weiermann
https://arxiv.org/abs/2508.14768 https://arxiv.org/pdf/2508.14768

The fractal Goodstein principle
The original Goodstein process is based on writing numbers in hereditary $b$-exponential normal form: that is, each number $n$ is written in some base $b\geq 2$ as $n=b^ea+r$, with $e$ and $r$ iteratively being written in hereditary $b$-exponential normal form. We define a new process which generalises the original by writing expressions in terms of a hierarchy of bases $B$, instead of a single base $b$. In particular, the `digit' $a$ may itself be written with respect to a smaller base $b'$. W…

Tractable Metric Spaces and the Continuity of Magnitude
Sara Kali\v{s}nik, Davorin Le\v{s}nik
https://arxiv.org/abs/2506.21128 https://

Tractable Metric Spaces and the Continuity of Magnitude
Magnitude is an isometric invariant of metric spaces introduced by Leinster. Since its inception, it has inspired active research into its connections with integral geometry, geometric measure theory, fractal dimensions, persistent homology, and applications in machine learning. In particular, when it comes to applications, continuity and stability of invariants play an important role. Although it has been shown that magnitude is nowhere continuous on the Gromov--Hausdorff space of finite metri…

Optimization of Fractal Image Compression
Nastaran Pourshab
https://arxiv.org/abs/2507.06325 https://arxiv.org/pdf/2507.06325

Optimization of Fractal Image Compression
Fractal Image Compression (FIC) is a lossy image compression technique that leverages self-similarity within an image to achieve high compression ratios. However, the process of compressing the image is computationally expensive. This paper investigates optimization techniques to improve the efficiency of FIC, focusing on increasing compression ratio and reducing computational time. The paper explores a novel approach named the Box Counting Method for estimating fractal dimensions, which is ver…

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory
Indubala Satija
https://arxiv.org/abs/2507.13418 https://

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory
Celebrating its golden jubilee, the Hofstadter butterfly fractal emerges as a remarkable fusion of art and science. This iconic X shaped fractal captivates physicists, mathematicians, and enthusiasts alike by elegantly illustrating the energy spectrum of electrons within a two dimensional crystal lattice influenced by a magnetic field. Enriched with integers of topological origin that serve as quanta of Hall conductivity, this quantum fractal and its variations have become paradigm models for t…

@… At work, probably at the last mozilla all-hands we attended.

MnBr$_2$ on the graphene on Ir(110) substrate: growth, structure, and super-moir\'e
Affan Safeer, Oktay G\"ulery\"uz, Nicolae Atodiresei, Wouter Jolie, Thomas Michely, Jeison Fischer
https://arxiv.org/abs/2508.19694

MnBr$_2$ on the graphene on Ir(110) substrate: growth, structure, and super-moiré
Single-layer MnBr$_2$ is grown on graphene (Gr) supported by Ir(110) and investigated using low-energy electron diffraction, scanning tunneling microscopy, and spectroscopy. The structure and epitaxial relationship with the substrate are systematically characterized. The growth morphology strongly depends on the growth temperature, evolving from fractal to dendritic and eventually to compact dendritic skeletal islands, reflecting changes in the underlying surface diffusion processes. MnBr$_2$ o…

Replaced article(s) found for physics.soc-ph. https://arxiv.org/list/physics.soc-ph/new
[1/1]:
- A Study on the Curves of Scaling Behavior of Fractal Cities
Yanguang Chen

Replaced article(s) found for math.CO. https://arxiv.org/list/math.CO/new
[1/2]:
- On some explicit integrals related to "fractal foothills"
Anton A Kutsenko

Support measures in fractal geometry
Goran Radunovi\'c (University of Zagreb), Steffen Winter (Karlsruhe Institute of Technology)
https://arxiv.org/abs/2508.08780 https://…

Support measures in fractal geometry
We introduce two novel families of geometric functionals-basic contents and support contents-for investigating the fractal properties of compact subsets in Euclidean space. These functionals are derived from the support measures arising in connection with the general Steiner formula due to Hug, Last, and Weil, and offer new tools for extracting geometric information beyond classical fractal dimensions. The basic contents are constructed from the support measures of the set itself, while the sup…

The Hashed Fractal Key Recovery (HFKR) Problem: From Symbolic Path Inversion to Post-Quantum Cryptographic Keys
Mohamed Aly Bouke
https://arxiv.org/abs/2506.04383

The Hashed Fractal Key Recovery (HFKR) Problem: From Symbolic Path Inversion to Post-Quantum Cryptographic Keys
Classical cryptographic systems rely heavily on structured algebraic problems, such as factorization, discrete logarithms, or lattice-based assumptions, which are increasingly vulnerable to quantum attacks and structural cryptanalysis. In response, this work introduces the Hashed Fractal Key Recovery (HFKR) problem, a non-algebraic cryptographic construction grounded in symbolic dynamics and chaotic perturbations. HFKR builds on the Symbolic Path Inversion Problem (SPIP), leveraging symbolic tr…

Harmonic fractal transformation for modeling complex neuronal effects: from bursting and noise shaping to waveform sensitivity and noise-induced subthreshold spiking
Mariia Sorokina
https://arxiv.org/abs/2508.05341

Harmonic fractal transformation for modeling complex neuronal effects: from bursting and noise shaping to waveform sensitivity and noise-induced subthreshold spiking
We propose the first fractal frequency mapping, which in a simple form enables to replicate complex neuronal effects. Unlike the conventional filters, which suppress or amplify the input spectral components according to the filter weights, the transformation excites novel components by a fractal recomposition of the input spectra resulting in a formation of spikes at resonant frequencies that are optimal for sampling. This enables high sensitivity detection, robustness to noise and noise-induce…

Fractality of Wireless Mesh Networks: Dimensional Effects on Network Performance
Marat Zaidyn, Sayat Akhtanov, Dana Turlykozhayeva, Symbat Temesheva, Almat Akhmetali, Alisher Skabylov, Nurzhan Ussipov
https://arxiv.org/abs/2506.19366

Fractality of Wireless Mesh Networks: Dimensional Effects on Network Performance
Wireless mesh networks (WMNs) depend on the spatial distribution of nodes, which directly influences connectivity, routing efficiency, and overall network performance. Conventional models typically assume uniform or random node placement, which inadequately represent the complex, hierarchical spatial patterns observed in practical deployments. In this study, we present a novel algorithm that constructs WMN topologies with tunable fractal dimensions, allowing precise control over spatial self-si…

Unconventional Phase Separation and Fractal Interfaces of Colloids in Active Liquids
Pragya Kushwaha, Pratikshya Jena, Partha Sarathi Mondal, Sanjay Puri, Shradha Mishra, Vijayakumar Chikkadi
https://arxiv.org/abs/2508.11000

Unconventional Phase Separation and Fractal Interfaces of Colloids in Active Liquids
Phase separation driven by nonequilibrium fluctuations is a hallmark of both living and synthetic active matter. Unlike equilibrium systems, where ordered states arise from the minimization of free energy, active systems are fueled by a constant injection of energy at the microscopic scale. The emergence of ordered phases in such driven systems challenges our conventional views of domain growth and interfacial structure. In this study, we investigate the coarsening of colloidal clusters in acti…

Replaced article(s) found for nlin.SI. https://arxiv.org/list/nlin.SI/new
[1/1]:
- Fractal decompositions and tensor network representations of Bethe wavefunctions
Subhayan Sahu, Guifre Vidal

On the Sierpinski triangle and its generalizations
L. De Carli, A. Echezabal, I. Morell
https://arxiv.org/abs/2506.20456 https://arxi…

On the Sierpinski triangle and its generalizations
By examining arithmetic operations between decimal numbers in a given base m we uncover fractal structures that generalize the Sierpinski triangle

Note to self:
When you install a dozen HDDs in a server with drive trays without indicators, it might be a good idea to write down which drive with which serial number is installed in what slot.
I just had to unscrew 5 of 14 HDDs to find the right one to remove!!
I normally like my Fractal Design Define 7 XL, but today... 🤬
#learnfrommymistakes

Fractal Path Strategies for Efficient 2D DMRG Simulations
Oliver R. Bellwood, Heitor P. Casagrande, William J. Munro
https://arxiv.org/abs/2507.11820 https…

Fractal Path Strategies for Efficient 2D DMRG Simulations
Numerical simulations of quantum magnetism in two spatial dimensions are often constrained by the area law of entanglement entropy, which heavily limits the accessible system sizes in tensor network methods. In this work, we investigate how the choice of mapping from a two-dimensional lattice to a one-dimensional path affects the accuracy of the two-dimensional Density Matrix Renormalization Group algorithm. We systematically evaluate all mappings corresponding to a subset of the Hamiltonian pa…

Construction and properties of fuzzy-valued fractal interpolation function by using iterated function system
CholHui Yun, Hyang Choe, MiGyong Ri
https://arxiv.org/abs/2508.00861

Construction and properties of fuzzy-valued fractal interpolation function by using iterated function system
In nature, there are many phenomena with both irregularity and uncertainty. Therefore, a fuzzy-valued fractal interpolation is more useful for modeling them than fuzzy interpolation or fractal interpolation. We construct fractal interpolation functions that interpolate a given data set of fuzzy numbers using an iterated function system and study the Holder continuity of the constructed function. Firstly, we construct an iterated function system (IFS) using the given data set and construct a fuz…

Random punctured hyperbolic surfaces & the Brownian sphere
Timothy Budd, Nicolas Curien
https://arxiv.org/abs/2508.18792 https://arxiv.org/pdf/2508.187…

Random punctured hyperbolic surfaces & the Brownian sphere
We consider random genus-0 hyperbolic surfaces $\mathcal{S}_n$ with $n + 1$ punctures, sampled according to the Weil-Petersson measure. We show that, after rescaling the metric by $n^{-1/4}$, the surface $\mathcal{S}_n$ converges in distribution to the Brownian sphere - a random compact metric space homeomorphic to the 2-sphere, exhibiting fractal geometry and appearing as a universal scaling limit in various models of random planar maps. Without rescaling the metric, we establish a local Benja…

Furstenberg set theorem for transversal families of functions
Tuomas Orponen, Aleksi Py\"or\"al\"a, Guangzeng Yi
https://arxiv.org/abs/2508.19047 https://

Furstenberg set theorem for transversal families of functions
We prove an extension of the Furstenberg set theorem to families of graphs satisfying a transversality condition. We apply the result to derive bounds on $L^{p}$-norms of Fourier transforms of fractal measures supported on plane curves.

Four-body physics in low-dimensional bosons with three-body interaction
V. Polkanov, O. Hryhorchak, V. Pastukhov
https://arxiv.org/abs/2506.18043 https://

Four-body physics in low-dimensional bosons with three-body interaction
The two-channel model for bosons with the three-body interaction is proposed. Similar to the Hamiltonian describing narrow Feshbach resonance in the two-body sector, our model includes the finite-range effects of the three-body potential and is well-defined in the ultraviolet (UV). A detailed exploration of the Efimov-like effect in the fractal-dimension system of four bosons is carried out. Peculiarities of the four-body bound states and the low-energy atom-trimer scattering in one dimension a…

On slice regular fractal-fractional Dirichlet type spaces
Jos\'e Oscar Gonz\'alez-Cervantes, Carlos Alejandro Moreno-Mu\~noz, Juan Bory-Reyes
https://arxiv.org/abs/2506.14172

On slice regular fractal-fractional Dirichlet type spaces
In this paper, we study some families of right modules of quaternionic slice regular functions induced by a generalized fractal-fractional derivative with respect to a truncated quaternionic exponential function on slices. Important Banach spaces of slice regular functions, namely the Bergman and the Dirichlet modules, are two important elements of one of our families.

Fractal depth-first search paths in statistical physics models
Qiyuan Shi, Youjin Deng, Ming Li
https://arxiv.org/abs/2508.10502 https://arxiv.org/pdf/2508…

Fractal depth-first search paths in statistical physics models
We study the fractal properties of depth-first search (DFS) paths in critical configurations of statistical physics models, including the two-dimensional $O(n)$ loop model for various $n$, and bond percolation in dimensions $d = 2$ to $6$. In the $O(n)$ loop model, the fractal dimension of the DFS path consistently matches that of the external perimeter, suggesting DFS as a convenient alternative for probing interface geometry. For bond percolation, the DFS path exhibits nontrivial fractal scal…

Something organic for #AbstractAug -- tree bark spotted on last week's walkabout in Collegetown
#photo #photography

On Complex Dimensions and Heat Content of Self-Similar Fractals
William E. Hoffer, Michel L. Lapidus
https://arxiv.org/abs/2508.09512 https://arxiv.org/pdf…

On Complex Dimensions and Heat Content of Self-Similar Fractals
Complex fractal dimensions, defined as poles of appropriate fractal zeta functions, describe the geometric oscillations in fractal sets. In this work, we show that the same possible complex dimensions in the geometric setting also govern the asymptotics of the heat content on self-similar fractals. We consider the Dirichlet problem for the heat equation on bounded open regions whose boundaries are self-similar fractals. The class of self-similar domains we consider allow for non-disjoint over…

Regularity of random attractor and fractal dimension of fractional stochastic Navier-Stokes equations on three-dimensional torus
Hui Liu, Chengfeng Sun, Jie Xin
https://arxiv.org/abs/2506.18480

Regularity of random attractor and fractal dimension of fractional stochastic Navier-Stokes equations on three-dimensional torus
In this paper we will study the asymptotic dynamics of fractional Navier-Stokes (NS) equations with additive white noise on three-dimensional torus $\mathbb T^3$. Under the conditions that the external forces $f(x)$ belong to the phase space $ H$ and the noise intensity function $h(x)$ satisfies $\|\nabla h\|_{L^\infty} < \sqrt πνλ_1^\frac{5}{4}$, where $ ν$ is the kinematic viscosity of the fluid and $λ_1$ is the first eigenvalue of the Stokes operator, we shown that the random …

Fractal Social Dynamics as a Driver of Consensus and Inequality
Airton Deppman
https://arxiv.org/abs/2507.13849 https://arxiv.org/pdf…

Fractal Social Dynamics as a Driver of Consensus and Inequality
Human social behavior is organized in stratified, hierarchical networks, with a support group with about 5 members, expanding proportionally at each layer up to a maximum of approximately 150 frequent interactions per individual. This is known as Social Brain Hypothesis, and its findings are supported by psychological and neurological evidence. The fractal network framework provides valuable insights into social phenomena such as the spread of fake news and the development of technology. This s…

Took longer than it prob should have, but I now have a 4tb (3.6, really, but who's counting) "Fikwot" (aka Kikwot, according to my OS) NVME SSD installed in my PC. Also PC got some bonus cleaning with the 20gal air compressor.
This Meshify case from Fractal doing a great job. It's been a year since the build, but there was just some caked on surface dust. Little bit of brushing and blasts of air and the PC looks almost new again.
Reason it took longer than expe…

Good morning from Harlem
#Photography #GoodMorning #Sunrise #NYC

Hodge-de Rham Theory on Higher-Dimensional Level-L Sierpinski Gaskets
Sze-Man Ngai, Shui-Hong Zhou
https://arxiv.org/abs/2508.12319 https://arxiv.org/pdf/2…

Hodge-de Rham Theory on Higher-Dimensional Level-L Sierpinski Gaskets
This paper extends the Hodge-de Rham theory of Aaron \textit{et al.} [Commun. Pure Appl. Anal. {\bf 13} (2014)] to higher-dimensional level-$l$ Sierpinski gaskets $SG_{\ell}^{n},$ providing a framework for analyzing differential forms and Laplacians on these fractal structures. We construct a sequence of graphs approximating $SG_{\ell}^{n}$ and define $k$-forms, de Rham derivatives, and their duals on these graphs. We prove that the extension of a $1$-form on a generation-$m$ graph to a $1$-for…

I saw some interesting artefacts in the clouds while doing some #openstreetmap mapping last night.

Fractality of open clusters in singles, pairs, and groups
Almat Akhmetali
https://arxiv.org/abs/2508.13980 https://arxiv.org/pdf/2508.13980

Fractality of open clusters in singles, pairs, and groups
In this work, we investigate the global structural properties and fractality of 1,876 open clusters (OCs) in different environments, including 1,145 singles, 392 pairs, and 339 groups. We analyze cluster mass, age, size, concentration, and fractal structure using the Q parameter and the fractal dimension fdim, and examine their correlations with key physical parameters. Our results reveal systematic environmental trends: clusters in groups are generally younger, less massive, slightly larger, a…

🇺🇦 #NowPlaying on #BBC6Music's #StuartMaconiesFreakZone
Brian Eno:
🎵 Fractal Zoom
#BrianEno
https://brianenoallsaints.bandcamp.com/track/fractal-zoom
https://open.spotify.com/track/03CLq6GK4ZthtKkC965VAV

Establishment of global phase coherence in a highly disordered fractal MgO/MgB2 nanocomposite: Roles of interface, morphology and defect
Iku Nakaaki, Aoi Hashimoto, Shun Kondo, Yuichi Ikuhara, Shuuichi Ooi, Minoru Tachiki, Shunichi Arisawa, Akiko Nakamura, Taku Moronaga, Jun Chen, Hiroyo Segawa, Takahiro Sakurai, Hitoshi Ohta, Takashi Uchino
https://…

Establishment of global phase coherence in a highly disordered fractal MgO/MgB2 nanocomposite: Roles of interface, morphology and defect
Recently, we have reported that a highly disordered fractal MgO/MgB2 nanocomposite exhibits bulk-like superconducting properties with isotropic pinning, showing an excellent phase-coherent capability irrespective of the low volume fraction (~30 vol. %) of MgB2 [Uchino et al., Phys. Rev. B 101, 035146 (2020); Teramachi et al,, Phys. Rev. B 108, 155146 (2023)]. Hence, this nanocomposite provides a useful experimental system to investigate the relationship between the structural disorder and the e…

Fractional Schwarzschild-Tangherlini black hole with a fractal event horizon
S. Jalalzadeh, H. Moradpour, G. R. Jafari, P. V. Moniz
https://arxiv.org/abs/2506.06031

Fractional Schwarzschild-Tangherlini black hole with a fractal event horizon
We demonstrate that the implementation of the fractional and non-local Wheeler--DeWitt (WDW) equation within the context of Schwarzschild geometry leads to the emergence of a Schwarzschild--Tangherlini black hole (BH), which is uniquely characterized by an event horizon that exhibits fractal properties and is defined by a non-integer dimension that lies in the continuum between the values of 1 and 2. Our calculations further reveal that this intriguing fractional BH may potentially possess a te…

This https://arxiv.org/abs/2501.18032 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Fractal algorithm for multiple lens analyses
A microlensing exoplanet search is a unique method for finding planets orbiting distant stars. However, in the past, the method used to analyze microlensing data could not deal with complex lens systems. The number of lenses was limited three or less. Positions calculations of images and integration of them suffered from severe round-off errors because of singularities. We developed a new algorithm to calculate the light curves of multiple lens systems. In this algorithm, fractal-like consecuti…

Shape and Spectrum: On the Heat and Volume of Self-Similar Fractals
William Hoffer
https://arxiv.org/abs/2507.08596 https://arxiv.org…

Shape and Spectrum: On the Heat and Volume of Self-Similar Fractals
In this work, we examine the relationship between geometry and spectrum of regions with fractal boundary. The relationship is well-understood for fractal harps in one dimension, but largely open for fractal drums in larger dimensions. To that end, we study fractals arising as attractors of self-similar iterated function systems with some separation conditions. On the geometric side, we analyze the tube zeta functions and their poles, called complex dimensions, which govern the asymptotics of th…

Mobility edges and fractal states in quasiperiodic Gross-Pitaevskii chains
Oleg I. Utesov, Yeongjun Kim, Sergej Flach
https://arxiv.org/abs/2506.06642 http…

Mobility edges and fractal states in quasiperiodic Gross-Pitaevskii chains
We explore properties of a Gross-Pitaevskii chain subject to an incommensurate periodic potential, i.e., a nonlinear Aubry-Andre model. We show that the condensate crucially impacts the properties of the elementary excitations. In contrast to the conventional linear Aubry-Andre model, the boundary between localized and extended states (mobility edge) exhibits nontrivial branching. For instance, in the high-density regime, tongues of extended phases at intermediate energies penetrate the domain …

Programmable Anyon Mobility through Higher Order Cellular Automata
Jie-Yu Zhang, Peng Ye
https://arxiv.org/abs/2508.13961 https://arxiv.org/pdf/2508.13961

Programmable Anyon Mobility through Higher Order Cellular Automata
Controlling anyon mobility is critical for robust quantum memory and understanding symmetry-enriched topological (SET) phases with subsystem symmetries (e.g., line-like, fractal, chaotic, or mixed supports). However, a unified framework for anyon mobility in SET phases with such diverse geometric patterns of symmetry supports has remained a major challenge. In this Letter, by introducing higher-order cellular automata (HOCA) -- a powerful computer science tool -- to SET physics, we establish a …

Crosslisted article(s) found for physics.bio-ph. https://arxiv.org/list/physics.bio-ph/new
[1/1]:
- Unconventional Phase Separation and Fractal Interfaces of Colloids in Active Liquids
Kushwaha, Jena, Mondal, Puri, Mishra, Chikkadi

Pricing Fractal Derivatives under Sub-Mixed Fractional Brownian Motion with Jumps
Nader Karimi
https://arxiv.org/abs/2506.24111 https://arxiv.org/pdf/2506.…

#mosstodon Well, not actually moss. It's a slime mould. Fuligo septica I think.

Quantitative Hardy--Littlewood maximal inequalities and Wiener--Stein theorem on fractal sets
Long Huang, Jinjun Li, Xiaofeng Wang
https://arxiv.org/abs/2506.07382

Quantitative Hardy--Littlewood maximal inequalities and Wiener--Stein theorem on fractal sets
Let $K\subset \mathbb{R}^d$ be a self-similar set with Hausdorff dimension $s$, and $μ$ be a self-similar probability measure supported on $K$. Let $H^α_μ$, $0<α\le s$, be the Hausdorff content on $K$, and $M_{\mathcal{D}}^μ$ be the Hardy--Littlewood maximal operator defined on $K$ associated with its basic cubes $\mathcal{D}$. In this paper, we establish quantitative strong type and weak type Hardy--Littlewood maximal inequalities on fractal set $K$ with respect to $H^α_μ$ for all range…

Modified Cubic B-spline Based Differential Quadrature Methods for Time-fractional Black-Scholes Equation
Nizamudheen V, Riyasudheen TK, Noufal Asharaf, Shefeeq T
https://arxiv.org/abs/2508.06780

Modified Cubic B-spline Based Differential Quadrature Methods for Time-fractional Black-Scholes Equation
The time-fractional Black-Scholes equation (TFBSE) is intended to price the options for which the underlying price fluctuates within a correlated fractal transmission system. Although the TFBSE is an influential approach for grasping the long-term memory traits of financial markets, the non-local nature of fractional derivatives makes significant challenges in finding an accurate solution. We perform an efficient use of the differential quadrature method (DQM) based on modified cubic B-splines …

Recent Progress on Fractal Percolation
Istv\'an Kolossv\'ary, Sascha Troscheit
https://arxiv.org/abs/2508.08150 https://arxiv.org/pdf/2508.08150

Recent Progress on Fractal Percolation
This is a survey paper about the fractal percolation process, also known as Mandelbrot percolation. It is intended to give a general breadth overview of more recent research in the topic, but also includes some of the more classical results, for example related to the connectivity properties. Particular emphasis is put on the dimension theory of the limiting set and also on the geometry of the non-trivial connected components in the supercritical regime. In particular, we show that both the Ass…

Fractional Schwarzschild-Tangherlini black hole with a fractal event horizon
S. Jalalzadeh, H. Moradpour, G. R. Jafari, P. V. Moniz
https://arxiv.org/abs/2506.06031

Fractional Schwarzschild-Tangherlini black hole with a fractal event horizon
We demonstrate that the implementation of the fractional and non-local Wheeler--DeWitt (WDW) equation within the context of Schwarzschild geometry leads to the emergence of a Schwarzschild--Tangherlini black hole (BH), which is uniquely characterized by an event horizon that exhibits fractal properties and is defined by a non-integer dimension that lies in the continuum between the values of 1 and 2. Our calculations further reveal that this intriguing fractional BH may potentially possess a te…

Injective (edge) colorings of generalized Sierpi\'{n}ski graphs
C. K. Bhanupriya, Bo\v{s}tjan Bre\v{s}ar
https://arxiv.org/abs/2508.14479 https://arxiv…

Injective (edge) colorings of generalized Sierpiński graphs
Generalized Sierpiński graphs constitute a distinctive class of fractal-like networks, whose self-similar properties have attracted growing attention. In particular, a number of graph invariants have been studied in generalized Sierpiński graphs. In this paper, we focus on injective colorings of this class of graphs, both the vertex and the edge version. The vertex version of injective colorings in generalized Sierpiński graphs was initiated in [Injective colorings of Sierpiński-like graphs…

Diffusion over ramified domains: solvability and fine regularity
Kevin Silva-P\'erez, Alejandro V\'elez-Santiago
https://arxiv.org/abs/2507.17909 https://

Diffusion over ramified domains: solvability and fine regularity
We consider a domain $Ω\subseteq\mathbb{R\!}^{\,2}$ with branched fractal boundary $Γ^{\infty}$ and parameter $τ\in[1/2,τ^{\ast}]$ introduced by Achdou and Tchou \cite{ACH08}, for $τ^{\ast}\simeq 0.593465$, which acts as an idealization of the bronchial trees in the lungs systems. For each $τ\in[1/2,τ^{\ast}]$, the corresponding region $Ω$ is a non-Lipschitz domain, which attains its roughest structure at the critical value $τ=τ^{\ast}$ in such way that in this endpoint parameter the …

Replaced article(s) found for math.SP. https://arxiv.org/list/math.SP/new
[1/1]:
- Improved fractal Weyl bounds for convex cocompact hyperbolic surfaces and large resonance-free re...
Louis Soares

Metallization of leaf-derived lignocellulose scaffolds for high performance flexible electronics and oligodynamic disinfection
Rakesh Rajendran Nair, Mihai Nita-Lazar, Valeriu Robert Badescu, Cristina Iftode, Jakob Wolansky, Tobias Antrack, Hans Kleemann, Karl Leo
https://arxiv.org/abs/2506.11640…

Metallization of leaf-derived lignocellulose scaffolds for high performance flexible electronics and oligodynamic disinfection
Vascular tubules in natural leaves form quasi-fractal networks that can be metallized. Traditional metallization techniques for these lignocellulose structures are complex, involving metal sputtering, nanoparticle solutions, or multiple chemical pretreatments. Here we present a novel, facile, and reliable method for metallizing leaf-derived lignocellulose scaffolds using silver microparticles. The method achieves properties on-par with the state-of-the-art, such as broadband optical transmittan…

Construction of fuzzy valued recurrent fractal interpolation functions and their properties
Hyang Choe, MiGyong Ri, CholHui Yun
https://arxiv.org/abs/2508.00860 https://

Construction of fuzzy valued recurrent fractal interpolation functions and their properties
In the process of measuring objects with local self-similarity, such as satellite images or coastlines, we obtain a data set with both local self-similarity and uncertainty. To better interpolate such data sets, an interpolation function with both local self-similarity and uncertainty is necessary. In this paper, we propose a construction of fuzzy valued recurrent fractal interpolation function using recurrent iterated function system that interpolates the given data set of fuzzy numbers. And w…

Can fractal dimension distinguish between grand-design and flocculent spiral arms?
Biju Saha, Subhadip Dutta, Arunima Banerjee
https://arxiv.org/abs/2508.04411 https://

Can fractal dimension distinguish between grand-design and flocculent spiral arms?
About two-thirds of disk galaxies host spiral arms, ranging from well-delineated grand-design spirals to fragmented flocculent spiral galaxies. We introduce fractal dimension $D_B$ as a non-parametric measure to distinguish between grand-designs and flocculents. We calculate the $D_B$ of 197 grand-designs and 322 flocculents from SDSS DR18, using the samples of \citet{Buta..2015} and \citet{Sarkar..2023}. Our calculated median values of $D_B$ are $1.29^{+0.06}_{-0.04}$ and $1.38^{+0.05}_{-0.06}…

Escape and transport in chaotic motion of charged particles in a magnetized plasma under the influence of two and three modes of drift waves
P. Haerter, E. D. Leonel, R. L. Viana
https://arxiv.org/abs/2506.20013

Escape and transport in chaotic motion of charged particles in a magnetized plasma under the influence of two and three modes of drift waves
This study investigates how two- and three-wave configurations govern particle escape and transport in tokamak edge plasmas. Using a Hamiltonian model derived from drift-wave turbulence, we analyze test particle dynamics through Poincaré maps, fractal escape basins, and entropy metrics. Introducing a third wave increases basin entropy, enhancing particle escape rates while reducing basin boundary entropy, indicative of suppressed basin mixing. Escape time analyses reveal resonant scattering di…

Replaced article(s) found for physics.data-an. https://arxiv.org/list/physics.data-an/new
[1/1]:
- Beyond traditional box-covering: Determining the fractal dimension of complex networks using a fi...
Michal Lepek, Kordian Makulski, Agata Fronczak, Piotr Fronczak…

Fast synthesis of turbulence with multi-scale coherent vortices
Zishuo Han, Weiyu Shen, Yue Yang
https://arxiv.org/abs/2506.01022 https://

Fast synthesis of turbulence with multi-scale coherent vortices
Turbulence synthesis methods often struggle to reproduce coherent vortices while capturing key statistical features. We introduce a fast synthetic turbulence method to generate instantaneous turbulent fields (termed `woven turbulence') with multi-scale vortices, combining the advantages of fractal models and coherent structures. The method generates multi-scale Burgers vortex tubes based on stochastic centerlines constructed by the fractional Brownian bridge. The largest and smallest vortices g…

#mosstodon Well, not actually moss. It's a slime mould. Fuligo septica I think.

Fractal Dimension in Nonlinear Wave Dynamics Governed by a Nonlinear Partial Differential Equation
Saugata Dutta, Kajal Kumar Mondal, Prasanta Chatterjee
https://arxiv.org/abs/2508.01816

Fractal Dimension in Nonlinear Wave Dynamics Governed by a Nonlinear Partial Differential Equation
This work presents a detailed analytical and geometrical investigation of the (2+1)-dimensional Boiti-Leon-Pempinelli system, a nonlinear dispersive model arising in the context of fluid and plasma dynamics. By employing a projective Riccati-based ansatz, a new class of exact solutions is systematically derived. These solutions, when visualized, exhibit intricate geometrical features that evolve across multiple spatial scales. To quantify this complexity, a voxel-based box-counting dimension an…

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new/
[1/1]:
H\"older continuity and dimensions of fractal Fourier series

Crossover in growth law in the vapor-liquid phase separation inside complex porous medium
Preethi M, Bhaskar Sen Gupta
https://arxiv.org/abs/2506.09646 htt…

Crossover in growth law in the vapor-liquid phase separation inside complex porous medium
We employ molecular dynamics simulations to investigate the domain morphology and growth kinetics of a vapor-liquid system embedded within a complex porous medium. By systematically varying the pore structure, we analyze the scaling behavior of correlation functions, structure factors, and domain growth exponents. The structure factor confirms the breakdown of Porod law and the emergence of fractal-like domain boundaries. Our key finding is the clear crossover in the domain growth law, from the…

Dynamical detection of extended nonergodic states in many-body quantum systems
David A. Zarate-Herrada, Isa\'ias Vallejo-Fabila, Lea F. Santos, E. Jonathan Torres-Herrera
https://arxiv.org/abs/2505.23910

Dynamical detection of extended nonergodic states in many-body quantum systems
Fractal dimensions are tools for probing the structure of quantum states and identifying whether they are localized or delocalized in a given basis. These quantities are commonly extracted through finite-size scaling, which limits the analysis to relatively small system sizes. In this work, we demonstrate that the correlation fractal dimension $D_2$ can be directly obtained from the long-time dynamics of interacting many-body quantum systems. Specifically, we show that it coincides with the exp…

Scaling, Fractal Dynamics and Critical Exponents{: Application} in a non-integer dimensional Ising model
Henrique A. de Lima, Ismael S. S. Carrasco, Marcio Santos, Fernando A. Oliveira
https://arxiv.org/abs/2507.00956

Scaling, Fractal Dynamics and Critical Exponents{: Application} in a non-integer dimensional Ising model
Moving beyond simple associations, researchers need tools to quantify how variables influence each other in space and time. Correlation functions provide a mathematical framework for characterizing these essential dependencies, revealing insights into causality, structure, and hidden patterns within complex systems. In physical systems with many degrees of freedom, such as gases, liquids, and solids, a statistical analysis of these correlations is essential. For a field $Ψ(\vec{x},t)$ that dep…

High-performance neuromorphic computing architecture of brain
Jinxuan Ma, Wanlin Guo
https://arxiv.org/abs/2508.03191 https://arxiv.org/pdf/2508.03191

High-performance neuromorphic computing architecture of brain
Artificial intelligence can outperform humans in specific tasks but consumes substantial energy. How the human brain can work at just 20 watts with complex cognitive intelligence? Here we decode the fundamental information strategy unit of brain, neural sphere, which agglomerates neurons into sphere to achieve energy-efficient and exhibits many ultra-long period or random electrophysiological activities. Chaos dynamics and fractal theory demonstrated the mathematical principle of neural spheres…

Replaced article(s) found for nlin.CD. https://arxiv.org/list/nlin.CD/new
[1/1]:
- Matrix logistic map: fractal spectral distributions and transfer of chaos
{\L}ukasz Pawela, Karol \.Zyczkowski

Replaced article(s) found for math.CA. https://arxiv.org/list/math.CA/new/
[1/1]:
H\"older continuity and dimensions of fractal Fourier series

Replaced article(s) found for physics.soc-ph. https://arxiv.org/list/physics.soc-ph/new
[1/1]:
- Model-based reconstruction of real-world fractal complex networks
Kordian Makulski, Mateusz Samsel, Michal Lepek, Agata Fronczak, Piotr Fronczak

Replaced article(s) found for cond-mat.dis-nn. https://arxiv.org/list/cond-mat.dis-nn/new
[1/1]:
- Beyond traditional box-covering: Determining the fractal dimension of complex networks using a fi...
Michal Lepek, Kordian Makulski, Agata Fronczak, Piotr Fronczak…

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- The Wild, Elusive Singularities of the T-fractal Surface
Chris Johnson, Robert Niemeyer

Local persistence exponent and its log-periodic oscillations
Yilin Ye, Denis S. Grebenkov
https://arxiv.org/abs/2507.08628 https://ar…

Local persistence exponent and its log-periodic oscillations
We investigate the local persistence exponent of the survival probability of a particle diffusing near an absorbing self-similar boundary. We show by extensive Monte Carlo simulations that the local persistence exponent exhibits log-periodic oscillations over a broad range of timescales. We determine the period and mean value of these oscillations in a family of Koch snowflakes of different fractal dimensions. The effect of the starting point and its local environment on this behavior is analyz…

Replaced article(s) found for gr-qc. https://arxiv.org/list/gr-qc/new
[1/2]:
- Anti-Gravity from Vacancies in Fractal Space-Time: The Case of a Menger Sponge
Karl Svozil

Conformational properties of strictly two-dimensional equilibrium polymers
J. P. Wittmer, A. Cavallo, A. Johner
https://arxiv.org/abs/2507.00649 https://…

Conformational properties of strictly two-dimensional equilibrium polymers
Two-dimensional monodisperse linear polymer chains are known to adopt for sufficiently large chain lengths $N$ and surface fractions $ϕ$ compact configurations with fractal perimeters. We show here by means of Monte Carlo simulations of reversibly connected hard disks (without branching, ring formation and chain intersection) that polydisperse self-assembled equilibrium polymers with a finite scission energy $E$ are characterized by the same universal exponents as their monodisperse peers. Con…

A family of non Minkowski measurable fractals in $\mathbb{R}^2$
Uta Freiberg, Jonas Lippold
https://arxiv.org/abs/2506.02640 https://…

A family of non Minkowski measurable fractals in $\mathbb{R}^2$
A long-standing conjecture of Lapidus asserts that, under certain conditions, a self-similar fractal set is not Minkowski measurable if and only if it is of lattice-type. For self-similar sets in $\mathbb{R}$, the Lapidus conjecture has been confirmed. However, in higher dimensions, it remains unclear whether all lattice-type self-similar sets are not Minkowski measurable. This work presents a family of lattice-type subsets in $\mathbb{R}^2$ that are not Minkowski measurable, hence providing fu…

Constraints on Barrow and Tsallis Holographic Dark Energy from DESI DR2 BAO data
Giuseppe Gaetano Luciano, Andronikos Paliathanasis, Emmanuel N. Saridakis
https://arxiv.org/abs/2506.03019

Constraints on Barrow and Tsallis Holographic Dark Energy from DESI DR2 BAO data
Barrow and Tsallis Holographic Dark Energy (HDE) are two recently proposed extensions of the standard HDE framework, incorporating generalized corrections to horizon entropy through the use of Barrow and Tsallis entropies. Tsallis entropy arises from non-extensive statistical phenomena which account for long-range correlations and deviations from additivity, while Barrow entropy emerges from quantum-gravitational effects on the horizon geometry, associated with fractal modifications and deforma…

This https://arxiv.org/abs/2501.02131 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sum-product phenomena for Ahlfors-regular sets
We utilise the recent work of Orponen to yield a result of sum and product for Ahlfors-regular sets. The result is sharp up to constants. As a corollary, we obtain the fractal analogue of Solymosi's $4/3$-bound for finite subsets of $\mathbb{R}.$