Tootfinder

Reframing Pattern: A Comprehensive Approach to a Composite Visual Variable
Tingying He, Jason Dykes, Petra Isenberg, Tobias Isenberg
https://arxiv.org/abs/2508.02639 https://

Reframing Pattern: A Comprehensive Approach to a Composite Visual Variable
We present a new comprehensive theory for explaining, exploring, and using pattern as a visual variable in visualization. Although patterns have long been used for data encoding and continue to be valuable today, their conceptual foundations are precarious: the concepts and terminology used across the research literature and in practice are inconsistent, making it challenging to use patterns effectively and to conduct research to inform their use. To address this problem, we conduct a comprehen…

Dynamic Coupling of Infiltration-Soil Moisture Feedback:Emergent Vegetation Patterns in a Water-Vegetation Model
Juan Yan, Xiaoli Wang, Guohong Zhang, Yuan Yuan
https://arxiv.org/abs/2508.01755

Dynamic Coupling of Infiltration-Soil Moisture Feedback:Emergent Vegetation Patterns in a Water-Vegetation Model
We present a modified water-vegetation model to investigate the mechanistic relationship between infiltration-soil moisture feedback and vegetation pattern in arid/semi-arid ecosystems. Employing Turing pattern formation theory, we drive conditions for diffusion-induced instability and analyze spatiotemporal dynamics near Turing-Hopf bifurcation points. Our key findings include: (i) The system exhibits rich dynamics including multiple stable equilibria, supercritical/subcritical Hopf bifurcatio…

Pattern formation in a coupled driven diffusive system
G. E. Freire Oliveira, R. Dickman, M. O. Lavrentovich, R. K. P. Zia
https://arxiv.org/abs/2509.00220 https://

Pattern formation in a coupled driven diffusive system
We investigate pattern formation in a driven mixture of two repulsive particles by introducing a Field-based Lattice Model (FLM), a hybrid model that combines aspects of the driven Widom-Rowlison lattice gas (DWRLG) and its statistical field theory \cite{DWRLG1,DWRLG2}. We find that the FLM effectively captures the bulk behavior of the DWRLG in both low- and high-density phases, suggesting that phase transitions in these models may share a universality class. Under the effect of the drive, the …

Exploring the Theory and Practice of Concurrency in the Entity-Component-System Pattern
Patrick Redmond, Jonathan Castello, Jos\'e Manuel Calder\'on Trilla, Lindsey Kuper
https://arxiv.org/abs/2508.15264

Exploring the Theory and Practice of Concurrency in the Entity-Component-System Pattern
The Entity-Component-System (ECS) software design pattern, long used in game development, encourages a clean separation of identity (entities), data properties (components), and computational behaviors (systems). Programs written using the ECS pattern are naturally concurrent, and the pattern offers modularity, flexibility, and performance benefits that have led to a proliferation of ECS frameworks. Nevertheless, the ECS pattern is little-known and not well understood outside of a few domains. …

The Pattern of Exotic Hidden-Heavy Hadrons Revealed
Roberto Bruschini
https://arxiv.org/abs/2507.20821 https://arxiv.org/pdf/2507.20821

The Pattern of Exotic Hidden-Heavy Hadrons Revealed
For more than twenty years, theory has failed to explain the pattern of the exotic heavy hadrons. We illustrate a simple solution to this longstanding puzzle using the Born-Oppenheimer approximation for QCD. Exotic hidden-heavy hadrons are bound states and resonances in potentials that are repulsive at short range and cross a heavy-hadron--pair threshold before approaching it. This explains the proximity of the exotic hidden-heavy hadrons to heavy-hadron--pair thresholds, identifies the thresho…

Tutorial on the Probabilistic Unification of Estimation Theory, Machine Learning, and Generative AI
Mohammed Elmusrati
https://arxiv.org/abs/2508.15719 https://

Tutorial on the Probabilistic Unification of Estimation Theory, Machine Learning, and Generative AI
Extracting meaning from uncertain, noisy data is a fundamental problem across time series analysis, pattern recognition, and language modeling. This survey presents a unified mathematical framework that connects classical estimation theory, statistical inference, and modern machine learning, including deep learning and large language models. By analyzing how techniques such as maximum likelihood estimation, Bayesian inference, and attention mechanisms address uncertainty, the paper illustrates …

The Phases of Chaos
Tarek Anous, Diego M. Hofman
https://arxiv.org/abs/2506.20542 https://arxiv.org/pdf/2506.20542

The Phases of Chaos
We develop a novel physical picture to understand certain universal properties of the GUE matrix model which are typically ascribed to quantum chaos, i.e. the ramp and the plateau. We argue that these features should instead be associated with a pattern of spontaneous (or weak explicit) symmetry breaking. In this language, the GUE matrix model corresponds to an effective theory that describes the symmetry-broken phase, and where the Hermitian matrix of the GUE should be understood as a massive …

Triangular and tetrahedral number differences of sumset sizes in additive number theory
Melvyn B. Nathanson
https://arxiv.org/abs/2506.15015 https://

Triangular and tetrahedral number differences of sumset sizes in additive number theory
The study of sums of finite sets of integers has mostly concentrated on sets with very small sumsets (Freiman's theorem and related work) and on sets with very large sumsets (Sidon sets and $B_h$-sets). This paper considers the full range of sumset sizes of finite sets of integers and an unexpected pattern (related to the triangular and tetrahedral numbers) that appears in the distribution of popular sumset sizes of sets of size 4.

Amorphous Solid Model of Vectorial Hopfield Neural Networks
F. Gallavotti, A. Zaccone
https://arxiv.org/abs/2507.22787 https://arxiv.org/pdf/2507.22787

Amorphous Solid Model of Vectorial Hopfield Neural Networks
We present a vectorial extension of the Hopfield associative memory model inspired by the theory of amorphous solids, where binary neural states are replaced by unit vectors $\mathbf{s}_i \in \mathbb{R}^3$ on the sphere $S^2$. The generalized Hebbian learning rule creates a block-structured weight matrix through outer products of stored pattern vectors, analogous to the Hessian matrix structure in amorphous solids. We demonstrate that this model exhibits quantifiable structural properties chara…

Citation Issues in Wave Mechanics Theory of Microwave Absorption
Yue Liu, Ying Liu, Michael G. B. Drew
https://arxiv.org/abs/2508.06522 https://arxiv.org/p…

Citation Issues in Wave Mechanics Theory of Microwave Absorption
The wave mechanics theory of microwave absorption challenges the long-standing impedance-matching and quarter-wavelength paradigms by demonstrating that conventional models mistakenly conflate bulk material parameters with thin-film phenomena. Drawing on a corpus of 35 peer-reviewed papers and preprints, the study performs a citation-pattern analysis and a logical audit of established theory. Results reveal a striking asymmetry in scholarly engagement, only a handful of supportive or neutral ci…

Aufbau suppressed coupled cluster as a post-linear-response method
Trine Kay Quady, Harrison Tuckman, Eric Neuscamman
https://arxiv.org/abs/2506.16680 http…

Aufbau suppressed coupled cluster as a post-linear-response method
We investigate the ability of Aufbau suppressed coupled cluster theory to act as a post-linear-response correction to widely used linear response methods for electronically excited states. We find that the theory is highly resilient to shortcomings in the underlying linear response method, with final results from less accurate starting points nearly as good as those from the best starting points. This pattern is especially stark in charge transfer states, where the approach converts starting po…

Urban-STA4CLC: Urban Theory-Informed Spatio-Temporal Attention Model for Predicting Post-Disaster Commercial Land Use Change
Ziyi Guo, Yan Wang
https://arxiv.org/abs/2508.08976 …

Urban-STA4CLC: Urban Theory-Informed Spatio-Temporal Attention Model for Predicting Post-Disaster Commercial Land Use Change
Natural disasters such as hurricanes and wildfires increasingly introduce unusual disturbance on economic activities, which are especially likely to reshape commercial land use pattern given their sensitive to customer visitation. However, current modeling approaches are limited in capturing such complex interplay between human activities and commercial land use change under and following disturbances. Such interactions have been more effectively captured in current resilient urban planning the…

In Reverie Together: Ten Years of Mathematical Discovery with a Machine Collaborator
Randy Davila, Boris Brimkov, Ryan Pepper
https://arxiv.org/abs/2507.17780 https://

In Reverie Together: Ten Years of Mathematical Discovery with a Machine Collaborator
We present four open conjectures in graph theory generated by the automated conjecturing system \texttt{TxGraffiti}. Each conjecture is concise, grounded in natural graph invariants, and empirically validated across hundreds of graphs. Despite extensive effort, these statements remain unresolved--defying both proof and counterexample. They are not only mathematical challenges but creative expressions--born of symbolic pattern recognition and mathematician-defined heuristics, refined through yea…

Spectral density estimates of surface-localized eigenmodes for transmission eigenvalue problems
Yan Jiang, Hongyu Liu, Kai Zhang, Haoran Zheng
https://arxiv.org/abs/2508.16203 h…

Spectral density estimates of surface-localized eigenmodes for transmission eigenvalue problems
This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp spectral density estimates--establishing both lower and upper bounds--to demonstrate that a significant proportion of transmission eigenfunctions manifest this surface-localizing behavior. Our analysis elucidates the connection between the geometric rigidity of…

Multipath-Enhanced Measurement of Antenna Patterns: Theory
Daniel D. Stancil
https://arxiv.org/abs/2507.03639 https://arxiv.org/pdf/2…

Multipath-Enhanced Measurement of Antenna Patterns: Theory
Traditional antenna pattern measurements involve minimizing the impact of multipath propagation in the measurement environment. In contrast, this work introduces a measurement approach that uses rather than mitigates multipath propagation. This is referred to as the Multipath-Enhanced Antenna Pattern (MEAP) Measurement technique. In this respect the approach has some kinship with Multiple-Input Multiple-Output (MIMO) systems. The advantage in the case of MIMO systems is increased capacity; in t…

Improved nuclear-structure corrections to the hyperfine splitting of electronic and muonic deuterium
Jose Bonilla, Thomas R. Richardson, Sonia Bacca, Chen Ji, Lucas Platter
https://arxiv.org/abs/2508.18776

Improved nuclear-structure corrections to the hyperfine splitting of electronic and muonic deuterium
We calculate the nuclear-structure correction to the hyperfine splitting in both electronic and muonic deuterium using interactions from chiral effective field theory. We explore the sensitivity to different parameterizations of the nucleon-nucleon force, study the convergence pattern in the order-by-order chiral expansion, and estimate remaining uncertainties. Our results are consistent with earlier calculations from pionless effective field theory, offering new insights for a robust uncertain…

The non-maximal symmetry breaking patterns in the supersymmetric $\widehat {\mathfrak{s} \mathfrak{u}}(8)_{k_U =1}$ theory
Ning Chen, Jianan Tian, Bin Wang
https://arxiv.org/abs/2508.11160

The non-maximal symmetry breaking patterns in the supersymmetric $\widehat {\mathfrak{s} \mathfrak{u}}(8)_{k_U =1}$ theory
We study the non-maximal symmetry breaking patterns of ${\mathfrak{s} \mathfrak{u}}(8) \to \mathfrak{g}_{531}/\mathfrak{g}_{351}$ allowed in a supersymmetric theory with the affine Lie algebra of $\widehat {\mathfrak{s} \mathfrak{u}}(8)_{k_U=1}$, which was recently proposed to explain the three-generational standard model quark/lepton mass hierarchies as well as the Cabbibo-Kobayashi-Maskawa mixing pattern. Three gauge couplings are found to achieve the unification below the Planck scales, acco…

Replaced article(s) found for cs.FL. https://arxiv.org/list/cs.FL/new
[1/1]:
- A Myhill-Nerode Theorem for Generalized Automata, with Applications to Pattern Matching and Compr...
Nicola Cotumaccio

Replaced article(s) found for hep-th. https://arxiv.org/list/hep-th/new
[1/2]:
- The Laue pattern and the Rydberg formula in classical soliton models
Shinichiro Yamato

Quantum fluctuations in two-dimensional altermagnets
Niklas Cichutek, Peter Kopietz, Andreas R\"uckriegel
https://arxiv.org/abs/2507.11218 https://

Quantum fluctuations in two-dimensional altermagnets
The magnetic properties of two-dimensional altermagnets can be obtained from a square lattice Heisenberg model with antiferromagetic nearest neighbor interaction and two types of next-nearest neighbor interactions arranged in a checkerboard pattern. Using nonlinear spin-wave theory we calculate for this model the corrections to the renormalized magnon spectrum and the staggered magnetization to first order in the inverse spin quantum number $1/S$. We also show that to order $1/S^2$ the ground s…

From heteroclinic loops to homoclinic snaking in reversible systems: rigorous forcing through computer-assisted proofs
Jan Bouwe van den Berg, Gabriel William Duchesne, Jean-Philippe Lessard
https://arxiv.org/abs/2507.16798

From heteroclinic loops to homoclinic snaking in reversible systems: rigorous forcing through computer-assisted proofs
Homoclinic snaking is a widespread phenomenon observed in many pattern-forming systems. Demonstrating its occurrence in non-perturbative regimes has proven difficult, although a forcing theory has been developed based on the identification of patterned front solutions. These heteroclinic solutions are themselves challenging to analyze due to the nonlinear nature of the problem. In this paper, we use computer-assisted proofs to find parameterized loops of heteroclinic connections between equilib…

Assessing Convergence Patterns Across Modern Nucleon-Nucleon Potentials
P. J. Millican, R. J. Furnstahl, J. A. Melendez, D. R. Phillips
https://arxiv.org/abs/2508.17558 https://…

Assessing Convergence Patterns Across Modern Nucleon-Nucleon Potentials
The BUQEYE model for correlated effective field theory (EFT) truncation errors assumes a regular pattern of dimensionless coefficients extracted from order-by-order observable calculations. This enables results from lower orders to inform statistical predictions for error estimates of omitted higher orders. We test the model for multiple chiral EFT ($χ$EFT) nucleon-nucleon (NN) potentials using a suite of six common NN scattering observables represented as functions of relative momentum and sc…

Replaced article(s) found for nlin.PS. https://arxiv.org/list/nlin.PS/new
[1/1]:
- Theory of dispersive shock waves induced by the Raman effect in optical fibers
D. V. Shaykin, A. M. Kamchatnov