Tootfinder

Timecube guy's getting hammered in a dive bar RN.
https://phys.org/news/2025-06-theory-dimensions-space-secondary-effect.amp

Unfolding Data Quality Dimensions in Practice: A Survey
Vasileios Papastergios, Lisa Ehrlinger, Anastasios Gounaris
https://arxiv.org/abs/2507.17507 https:…

Unfolding Data Quality Dimensions in Practice: A Survey
Data quality describes the degree to which data meet specific requirements and are fit for use by humans and/or downstream tasks (e.g., artificial intelligence). Data quality can be assessed across multiple high-level concepts called dimensions, such as accuracy, completeness, consistency, or timeliness. While extensive research and several attempts for standardization (e.g., ISO/IEC 25012) exist for data quality dimensions, their practical application often remains unclear. In parallel to rese…

Dimensions of compositions modulo a prime
Jia Huang
https://arxiv.org/abs/2506.16953 https://arxiv.org/pdf/2506.16953

Dimensions of compositions modulo a prime
The (ordinary) representation theory of the symmetric group is fascinating and has rich connections to combinatorics, including the Frobenius correspondence to the self-dual graded Hopf algebra of symmetric functions. The $0$-Hecke algebra (of type $A$) is a deformation of the group algebra of the symmetric group, and its representation theory has an analogous correspondence to the dual graded Hopf algebras of quasisymmetric functions and noncommutative symmetric functions. Macdonald used the h…

On Growth of Sobolev norms for cubic Schr\"odinger equation with harmonic potential in dimensions $d=2,3$
Yilin Song, Ruixiao Zhang, Jiqiang Zheng
https://arxiv.org/abs/2506.17731

On Growth of Sobolev norms for cubic Schrödinger equation with harmonic potential in dimensions $d=2,3$
In this article, we study the growth of higher-order Sobolev norms for solutions to the defocusing cubic nonlinear Schrödinger equation with harmonic potential in dimensions $d=2,3$, \begin{align}\label{PNLS} \begin{cases}\tag{PNLS} i\partial_tu-Hu=|u|^{2}u,&(t,x)\in\mathbb{R}\times\mathbb{R}^d,\\ u(0,x)=u_0(x), \end{cases} \end{align} where $H=-Δ+|x|^2$. Motivated by Planchon-Tzvetkov-Visciglia [Rev. Mat. Iberoam., 39 (2023), 1405-1436], we first establish the bilinear St…

The hyperbolic lattice counting problem in large dimensions
Christos Katsivelos
https://arxiv.org/abs/2506.17753 https://arxiv.org/pd…

The hyperbolic lattice counting problem in large dimensions
For $n\geq 3$ and $Γ$ a cocompact lattice acting on the hyperbolic space $\mathbb{H}^n$, we investigate the average behaviour of the error term in the circle problem. First, we explore the local average of the error term over compact sets of $Γ\backslash\mathbb{H}^n$. Our upper bound depends on the quantum variance and the spectral exponential sums appearing in the study of the Prime geodesic theorem. We also prove $Ω$-results for the mean value and the second moment of the error term.

The Hidden Symmetries of Yang-Mills Theory in (3 1)-dimensions
L. A. Ferreira, H. Malavazzi
https://arxiv.org/abs/2506.15832 https://…

The Hidden Symmetries of Yang-Mills Theory in (3+1)-dimensions
We show that classical, non-supersymmetric Yang-Mills theories coupled to spin-1/2 and spin-0 elementary matter fields, in (3+1)-dimensional Minkowski space-time, possess an exact integrability structure with an infinite number of conserved charges in involution. Such an integrability lives on the space of non-abelian electric and magnetic charges, and is based on flat connections in generalized loop spaces, presenting an R-matrix, and Sklyanin relation. We present two novel symmetries of Yang-…

New theory proposes time has three dimensions, with space as a secondary effect
https://phys.org/news/2025-06-theory-dimensions-space-secondary-effect.html#google_vignette

Quasibound states of massive charged scalars around dilaton black holes in $2 1$ dimensions: Exact frequencies
H. S. Vieira
https://arxiv.org/abs/2506.18740

Quasibound states of massive charged scalars around dilaton black holes in $2+1$ dimensions: Exact frequencies
In this work, we investigate massive charged scalar perturbations in the background of three-dimensional dilaton black holes with a cosmological constant. We demonstrate that the wave equations governing the dynamics of these perturbations are exactly solvable, with the radial part expressible in terms of confluent Heun functions. The quasibound state frequencies are computed analytically, and we examine their dependence on the scalar field's mass and charge, as well as on the black hole's mass…

Mean first passage time of active Brownian particles in two dimensions
Sarafa A. Iyaniwura, Zhiwei Peng
https://arxiv.org/abs/2506.15813 https://

Mean first passage time of active Brownian particles in two dimensions
The mean first passage time (MFPT) is a key metric for understanding transport, search, and escape processes in stochastic systems. While well characterized for passive Brownian particles, its behavior in active systems-such as active Brownian particles (ABPs)-remains less understood due to their self-propelled, nonequilibrium dynamics. In this paper, we formulate and analyze an elliptic partial differential equation (PDE) to characterize the MFPT of ABPs in two-dimensional domains, including c…

On the capacity dimensions of the Brjuno and Perez-Marco sets
Nurali Akramov, Abduvahhob Ashirov
https://arxiv.org/abs/2507.15980 https://

On the capacity dimensions of the Brjuno and Perez-Marco sets
In this work, we prove that the complement of the Brjuno set $\mathcal{B}$ has a zero capacity with respect to the kernel $k^1_σ(z,ξ)=\ln^2{|z-ξ|}\left|\ln{\ln{\left(e+\frac{1}{|z-ξ|}\right)}}\right|^σ$ for any $σ> 2$. Similarly, the complement of the Perez-Marco set $\mathcal{PM}$ has a zero capacity with respect to the kernel $k^2_σ(z,ξ) = \ln^{2}{\ln\left(e+\frac{1} {\left| {z - ξ}\right|}\right)} \cdot\ln^σ{\ln\ln\left(e^3+\frac{1} {\left
…

Novel insight into centre-vortex geometry in four dimensions
Jackson A. Mickley, Chris Allton, Ryan Bignell, Derek B. Leinweber
https://arxiv.org/abs/2507.17200 https://

Novel insight into centre-vortex geometry in four dimensions
Centre-vortex surfaces are mapped out in four dimensions within the framework of SU(3) lattice gauge theory to understand the role of secondary loops that develop in three-dimensional visualisations of centre-vortex structure, appearing separate from the percolating cluster. Loops that initially appear disconnected in three-dimensional slices can originate from the same connected surface in four dimensions depending on the surface's curvature. For the first time, these secondary loops are ident…

Quenched scaling limit for biased random walks on random, heavy tailed conductances: low dimensions
Umberto De Ambroggio, Carlo Scali
https://arxiv.org/abs/2507.17583 https://…

Quenched scaling limit for biased random walks on random, heavy tailed conductances: low dimensions
We consider a random walk amongst positive random conductances on $\mathbb{Z}^d, d \ge 2$, with directional bias. When the conductances have a stable distribution with parameter $γ\in (0, 1)$, the walk is sub-ballistic. In this regime Fribergh and Kious (Ann. Prob. 2018) derived an annealed scaling limit for the appropriately rescaled walk towards the Fractional Kinetics process. We prove the quenched version of this result for all $d \ge 2$.

The 4th Dimension for Scaling Model Size
Ruike Zhu, Hanwen Zhang, Tianyu Shi, Chi Wang, Tianyi Zhou, Zengyi Qin
https://arxiv.org/abs/2506.18233 https://…

The 4th Dimension for Scaling Model Size
Scaling the size of large language models typically involves three dimensions: depth, width, and the number of parameters. In this work, we explore a fourth dimension, virtual logical depth (VLD), which increases the effective algorithmic depth without changing the overall parameter count by reusing parameters within the model. Although parameter reuse is not a new concept, its potential and characteristics in model scaling have not been thoroughly studied. Through carefully designed controlled…

Improving the Generation of VAEs with High Dimensional Latent Spaces by the use of Hyperspherical Coordinates
Alejandro Ascarate, Leo Lebrat, Rodrigo Santa Cruz, Clinton Fookes, Olivier Salvado
https://arxiv.org/abs/2507.15900

Improving the Generation of VAEs with High Dimensional Latent Spaces by the use of Hyperspherical Coordinates
Variational autoencoders (VAE) encode data into lower-dimensional latent vectors before decoding those vectors back to data. Once trained, decoding a random latent vector from the prior usually does not produce meaningful data, at least when the latent space has more than a dozen dimensions. In this paper, we investigate this issue by drawing insight from high dimensional statistics: in these regimes, the latent vectors of a standard VAE are by construction distributed uniformly on a hyperspher…

Selective Densification for Rapid Motion Planning in High Dimensions with Narrow Passages
Lu Huang, Lingxiao Meng, Jiankun Wang, Xingjian Jing
https://arxiv.org/abs/2507.15710

Selective Densification for Rapid Motion Planning in High Dimensions with Narrow Passages
Sampling-based algorithms are widely used for motion planning in high-dimensional configuration spaces. However, due to low sampling efficiency, their performance often diminishes in complex configuration spaces with narrow corridors. Existing approaches address this issue using handcrafted or learned heuristics to guide sampling toward useful regions. Unfortunately, these strategies often lack generalizability to various problems or require extensive prior training. In this paper, we propose a…

Dimensions of toggleability spaces
Ben Adenbaum, Spencer Daugherty, Nicholas Mayers
https://arxiv.org/abs/2508.14974 https://arxiv.org/pdf/2508.14974

Dimensions of toggleability spaces
We establish a conjecture of Defant, Hopkins, Poznanović, and Propp concerning the dimensions of toggleability spaces for products of chains, shifted staircases, type-A root posets, and type-B posets. Generalizing this result, we show that for a larger family of posets defined by restricted diagrams, the dimensions of toggleability spaces are equal to the rank of the poset plus one. As part of our approach, we build upon the technique of rook statistics introduced by Chan, Haddadan, Hopkins, a…

The essential and the Cremona dimensions of a group
Igor Dolgachev
https://arxiv.org/abs/2507.15096 https://arxiv.org/pdf/2507.15096

The essential and the Cremona dimensions of a group
The Cremona dimension of a group $G$ is the minimal $n$ such that $G$ is isomorphic to a subgroup of the Cremona group of birational transformations of an $n$-dimensional rational variety. In this survey article, we give many examples that gives evidence to the conjecture that the Cremona dimension of a finite group over the field of complex numbers is less than or equal to the essential dimension of the group.

Trans-dimensional Hamiltonian model selection and parameter estimation from sparse, noisy data
Abigail N. Poteshman, Jiwon Yun, Tim H. Taminiau, Giulia Galli
https://arxiv.org/abs/2506.18802

Trans-dimensional Hamiltonian model selection and parameter estimation from sparse, noisy data
High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and model dimensions are consistent with available data. This ill-posed regime may render traditional machine learning and deterministic methods unreliable or intractable, particularly in high-dimensional, nonlinear, and mixed continuous and discrete parameter spac…

Ties, Tails and Spectra: On Rank-Based Dependency Measures in High Dimensions
Nina D\"ornemann, Michael Fleermann, Johannes Heiny
https://arxiv.org/abs/2508.14992 https://

Ties, Tails and Spectra: On Rank-Based Dependency Measures in High Dimensions
This work is concerned with the limiting spectral distribution of rank-based dependency measures in high dimensions. We provide distribution-free results for multivariate empirical versions of Kendall's $τ$ and Spearman's $ρ$ in a setting where the dimension $p$ grows at most proportionally to the sample size $n$. Although rank-based measures are known to be well suited for discrete and heavy-tailed data, previous works in the field focused mostly on the continuous and light-tailed case. We c…

Strategic Integration of AI Chatbots in Physics Teacher Preparation: A TPACK-SWOT Analysis of Pedagogical, Epistemic, and Cybersecurity Dimensions
N. Mohammadipour
https://arxiv.org/abs/2507.14860

Strategic Integration of AI Chatbots in Physics Teacher Preparation: A TPACK-SWOT Analysis of Pedagogical, Epistemic, and Cybersecurity Dimensions
This study investigates the strategic and epistemically responsible integration of AI-powered chatbots into physics teacher education by employing a TPACK-guided SWOT framework across three structured learning activities. Conducted within a university-level capstone course on innovative tools for physics instruction, the activities targeted key intersections of technological, pedagogical, and content knowledge (TPACK) through chatbot-assisted tasks: simplifying abstract physics concepts, constr…

PRISON: Unmasking the Criminal Potential of Large Language Models
Xinyi Wu, Geng Hong, Pei Chen, Yueyue Chen, Xudong Pan, Min Yang
https://arxiv.org/abs/2506.16150

PRISON: Unmasking the Criminal Potential of Large Language Models
As large language models (LLMs) advance, concerns about their misconduct in complex social contexts intensify. Existing research overlooked the systematic understanding and assessment of their criminal capability in realistic interactions. We propose a unified framework PRISON, to quantify LLMs' criminal potential across five dimensions: False Statements, Frame-Up, Psychological Manipulation, Emotional Disguise, and Moral Disengagement. Using structured crime scenarios adapted from classic film…

Rotating Quantum Droplets in Low Dimensions
Kevin Hern\'andez, El\'ias Castellanos
https://arxiv.org/abs/2506.16719 https://a…

Rotating Quantum Droplets in Low Dimensions
Quantum droplets formed by rubidium, lithium, and sodium atoms have been analyzed in this paper by using a logarithmic-type Gross-Pitaevskii equation. Variational methods and numerical techniques were employed to solve the corresponding nonlinear equations. A disk-shaped Bose-Einstein condensate was analyzed to assess its radial evolution. Additionally, free expansion under rotation of the BEC was studied. Compression and expansion around the equilibrium radius were observed in different scenar…

On the One-Loop Exactness of Gravity Partition Function
Andres Goya, Mauricio Leston, Mario Passaglia
https://arxiv.org/abs/2507.16141 https://

On the One-Loop Exactness of Gravity Partition Function
In a previous work, we showed that the two- and three-loop contributions to the partition function of three-dimensional gravity in flat space vanish. This is in agreement with the expected one-loop exactness dictated by the underlying symmetry at the quantum level. To highlight the distinctive nature of the $D=3$ case, we extend the three-loop computation to arbitrary spacetime dimensions $D$. In higher dimensions, the number of contributions increases substantially, reinforcing the view that o…

Pyramid Mixer: Multi-dimensional Multi-period Interest Modeling for Sequential Recommendation
Zhen Gong, Zhifang Fan, Hui Lu, Qiwei Chen, Chenbin Zhang, Lin Guan, Yuchao Zheng, Feng Zhang, Xiao Yang, Zuotao Liu
https://arxiv.org/abs/2506.16942

Pyramid Mixer: Multi-dimensional Multi-period Interest Modeling for Sequential Recommendation
Sequential recommendation, a critical task in recommendation systems, predicts the next user action based on the understanding of the user's historical behaviors. Conventional studies mainly focus on cross-behavior modeling with self-attention based methods while neglecting comprehensive user interest modeling for more dimensions. In this study, we propose a novel sequential recommendation model, Pyramid Mixer, which leverages the MLP-Mixer architecture to achieve efficient and complete modelin…

Quasi-homological dimensions with respect to semidualizing modules
Souvik Dey, Luigi Ferraro, Mohsen Gheibi
https://arxiv.org/abs/2508.15064 https://arxiv.…

Quasi-homological dimensions with respect to semidualizing modules
Gheibi, Jorgensen and Takahashi recently introduced the quasi-projective dimension of a module over commutative Noetherian rings, a homological invariant extending the classic projective dimension of a module, and Gheibi later developed the dual notion of quasi-injective dimension. Takahashi and White in 2010 introduced the projective and injective dimension of a module with respect to a semidualizing module, which likewise generalize their classic counterparts. In this paper we unify and exten…

Thermal modifications of mesons and energy-energy correlators from real-time simulations of a $U(1)$ lattice gauge theory
Jo\~ao Barata, David Frenklakh, Swagato Mukherjee
https://arxiv.org/abs/2507.16890

Thermal modifications of mesons and energy-energy correlators from real-time simulations of a $U(1)$ lattice gauge theory
We investigate thermal properties of a $U(1)$ lattice gauge theory in $1+1$-dimensions through real-time simulations. We extract the spectral functions directly coupling to the pseudoscalar and scalar mesons, demonstrating the thermal modifications of these states with increasing temperatures. Introducing the notion of energy-flow operators, we quantify the temporal build-up of correlations in the energy flows across the lattice. We demonstrate that energy-energy correlators fail to factorize t…

BoSS: Beyond-Semantic Speech
Qing Wang, Zehan Li, Hang Lv, Hongjie Chen, Yaodong Song, Jian Kang, Jie Lian, Jie Li, Yongxiang Li, Zhongjiang He, Xuelong Li
https://arxiv.org/abs/2507.17563

BoSS: Beyond-Semantic Speech
Human communication involves more than explicit semantics, with implicit signals and contextual cues playing a critical role in shaping meaning. However, modern speech technologies, such as Automatic Speech Recognition (ASR) and Text-to-Speech (TTS) often fail to capture these beyond-semantic dimensions. To better characterize and benchmark the progression of speech intelligence, we introduce Spoken Interaction System Capability Levels (L1-L5), a hierarchical framework illustrated the evolution…

A predictor-corrector scheme for approximating signed distances using finite element methods
Amina El Bachari, Johann Rannou, Vladislav A. Yastrebov, Pierre Kerfriden, Susanne Claus
https://arxiv.org/abs/2506.17830

A predictor-corrector scheme for approximating signed distances using finite element methods
In this article, we introduce a finite element method designed for the robust computation of approximate signed distance functions to arbitrary boundaries in two and three dimensions. Our method employs a novel prediction-correction approach, involving first the solution of a linear diffusion-based prediction problem, followed by a nonlinear minimization-based correction problem associated with the Eikonal equation. The prediction step efficiently generates a suitable initial guess, significant…

Some results on Lower Assouad and quantization dimensions
Saurabh Verma, Ekta Agrawal, Shivam Dubey
https://arxiv.org/abs/2508.15282 https://arxiv.org/pdf/…

Some results on Lower Assouad and quantization dimensions
In this paper, we first show that the collection of all subsets of \( \mathbb{R} \) having lower dimension \( γ\in [0,1] \) is dense in \( Π(\mathbb{R}) \), the space of compact subsets of \( \mathbb{R} \). Furthermore, we show that the set of Borel probability measures with lower dimension \( β\in [0, m] \) is dense in \( Ω(\mathbb{R}^m) \), the space of Borel probability measures on \( \mathbb{R}^m \). We also prove that the quantization and the lower dimension of a measure \( \vartheta \…

Exact solution of asymmetric gelation between three walks on the square lattice
Aleksander L Owczarek, Andrew Rechnitzer
https://arxiv.org/abs/2507.17111 https://

Exact solution of asymmetric gelation between three walks on the square lattice
We find and analyse the exact solution of a model of three different polymers with asymmetric contact interactions in two dimensions, modelling a scenario where there are different types of polymers involved. In particular, we find the generating function of three directed osculating walks in star configurations on the square lattice with two interaction Boltzmann weights, so that there is one type of contact interaction between the top pair of walks and a different interaction betw…

Bayesian Semiparametric Orthogonal Tucker Factorized Mixed Models for Multi-dimensional Longitudinal Functional Data
Arkaprava Roy, Abhra Sarkar
https://arxiv.org/abs/2506.16668

Bayesian Semiparametric Orthogonal Tucker Factorized Mixed Models for Multi-dimensional Longitudinal Functional Data
We introduce a novel longitudinal mixed model for analyzing complex multidimensional functional data, addressing challenges such as high-resolution, structural complexities, and computational demands. Our approach integrates dimension reduction techniques, including basis function representation and Tucker tensor decomposition, to model complex functional (e.g., spatial and temporal) variations, group differences, and individual heterogeneity while drastically reducing model dimensions. The mod…

Rough Fabry-Perot cavity: a vastly multi-scale numerical problem
Tetiana Slipchenko, Jaime Abad-arredondo, Antonio Consoli, Francisco J Garc\'ia Vidal, Antonio I Fern\'andez-dom\'inguez, Pedro David Garc\'ia, Cefe L\'opez
https://arxiv.org/abs/2507.16607

Rough Fabry-Perot cavity: a vastly multi-scale numerical problem
A commercial Fabry-Perot laser diode is characterized by highly disproportionate dimensions, which poses a significant numerical challenge, even for state-of-the-art tools. This challenge is exacerbated when one of the cavity mirrors is rough-ened, as is the case when fabricating random laser diodes. Such a system involves length scales from several hundred mi-crometres (length) to a few nanometres (roughness) all of which are relevant when studying optical properties in the visi-ble. While inv…

Fast solvers for the high-order FEM simplicial de Rham complex
Pablo D. Brubeck, Patrick E. Farrell, Robert C. Kirby, Charles Parker
https://arxiv.org/abs/2506.17406

Fast solvers for the high-order FEM simplicial de Rham complex
We present new finite elements for solving the Riesz maps of the de Rham complex on triangular and tetrahedral meshes at high order. The finite elements discretize the same spaces as usual, but with different basis functions, so that the resulting matrices have desirable properties. These properties mean that we can solve the Riesz maps to a given accuracy in a $p$-robust number of iterations with $\mathcal{O}(p^6)$ flops in three dimensions, rather than the naïve $\mathcal{O}(p^9)$ flops. T…

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues
M. Burak Erdogan, William R. Green, Kevin LaMaster
https://arxiv.org/abs/2506.16378

$L^p$ boundedness of wave operators for higher order schrödinger operators with threshold eigenvalues
We consider the higher order Schrödinger operator $H=(-Δ)^m+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2m$, $m\in \mathbb N$ when $H$ has a threshold eigenvalue. We adapt our recent results for $m\geq 1$ when $n>4m$ to lower dimensions $2m

Mapping the Evolution of Research Contributions using KnoVo
Sajratul Y. Rubaiat, Syed N. Sakib, Hasan M. Jamil
https://arxiv.org/abs/2506.17508 https://

Mapping the Evolution of Research Contributions using KnoVo
This paper presents KnoVo (Knowledge Evolution), an intelligent framework designed for quantifying and analyzing the evolution of research novelty in the scientific literature. Moving beyond traditional citation analysis, which primarily measures impact, KnoVo determines a paper's novelty relative to both prior and subsequent work within its multilayered citation network. Given a target paper's abstract, KnoVo utilizes Large Language Models (LLMs) to dynamically extract dimensions of comparison…

Current Galactic Chemical Evolution models fail to explain rising Na-abundances of young thick disc stars
E. K. Owusu (School of Science, University of New South Wales Canberra, Australia Defence Force Academy, Australia, ARC Centre of Excellence for All-Sky Astrophysics in 3 Dimensions, Max-Planck-Institut f\"ur Astronomie, Heidelberg, Germany, Heidelberger Institut f\"ur Theoretische Studien, Heidelberg, Germany), A. J. Ruiter (School of Science, University of New South Wal…

Current Galactic Chemical Evolution models fail to explain rising Na-abundances of young thick disc stars
We recently identified an upturn in [Na/Fe] for the population of Solar-type stars in the Galactic thick disc ($-0.3 < [\mathrm{Fe/H}] < +0.3$ dex) at super-Solar metallicity in GALactic Archaeology with HERMES (GALAH) data. Here, we investigate the cause of this unexplained Na enrichment between ([Fe/H] $\sim 0 - 0.6$ dex) using the OMEGA$+$ galactic chemical evolution code. We investigate the increase of [Na/Fe] with four combinations of nucleosynthetic yields from the literature, with source…

Static Analysis as a Feedback Loop: Enhancing LLM-Generated Code Beyond Correctness
Scott Blyth, Sherlock A. Licorish, Christoph Treude, Markus Wagner
https://arxiv.org/abs/2508.14419

Static Analysis as a Feedback Loop: Enhancing LLM-Generated Code Beyond Correctness
Large language models (LLMs) have demonstrated impressive capabilities in code generation, achieving high scores on benchmarks such as HumanEval and MBPP. However, these benchmarks primarily assess functional correctness and neglect broader dimensions of code quality, including security, reliability, readability, and maintainability. In this work, we systematically evaluate the ability of LLMs to generate high-quality code across multiple dimensions using the PythonSecurityEval benchmark. We in…

Generalized symmetry enriched criticality in (3 1)d
Benjamin Moy
https://arxiv.org/abs/2507.15925 https://arxiv.org/pdf/2507.15925

Generalized symmetry enriched criticality in (3+1)d
We construct two classes of continuous phase transitions in 3+1 dimensions between phases that break distinct generalized global symmetries. Our analysis focuses on $SU(N)/\mathbb{Z}_N$ gauge theory coupled to $N_f$ flavors of Majorana fermions in the adjoint representation. For $N$ even and sufficiently large odd $N_f$, upon imposing time-reversal symmetry and an $SO(N_f)$ flavor symmetry, the massless theory realizes a quantum critical point between two gapped phases: one in which a $\mathbb{…

Floer homotopy theory for monotone Lagrangians
Ciprian Mircea Bonciocat
https://arxiv.org/abs/2506.17431 https://arxiv.org/pdf/2506.1…

Floer homotopy theory for monotone Lagrangians
We circumvent one of the roadblocks in associating Floer homotopy types to monotone Lagrangians, namely the curvature phenomena occurring in high dimensions. Given $N \ge 3$ and $R$ a connective $\mathbb E_1$-ring spectrum, there is a notion of an $N$-truncated, $R$-oriented flow category, to which we associate a module prospectrum over the Postnikov truncation $τ_{\le N - 3}R$. This endows ordinary Floer cohomology with an action of the Steenrod algebra over $τ_{\le N-3}R$, and also induces …

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 …

Ground and low-lying excited state potential energy surfaces of diiodomethane in four dimensions
Yijue Ding
https://arxiv.org/abs/2508.14843 https://arxiv.…

Ground and low-lying excited state potential energy surfaces of diiodomethane in four dimensions
We report a set of adiabatic potential energy surfaces (PESs) for diiodomethane, including the ground electronic state and all excited states accessible via single-photon absorption near 260 nm. Although constrained to four dimensions, these PESs capture the essential photochemical processes following photoexcitation--namely, bond breaking and rearrangement among the methyl radical and the two iodine atoms. Constructed using an accurate and efficient spline interpolation algorithm, the PESs rep…

The Solid-state Physics of Rydberg-dressed Bosonic Mixtures
Yi-Ming Duan, Liang-Jun He, Fabian Maucher, Yong-Chang Zhang
https://arxiv.org/abs/2507.16277 h…

The Solid-state Physics of Rydberg-dressed Bosonic Mixtures
We explore phases of two-component Rydberg-dressed Bose-Einstein condensates in three spatial dimensions. The competition between the effective ranges of inter- and intra-component soft-core interactions leads to a rich variety of ground states. These include states resembling ionic compounds with face-centered cubic or simple cubic lattice structure. Upon increasing the scattering length, the dimensionality of the symmetry-breaking is lower due to the suppression of large densities, leading to…

Invertible exterior powers
Kevin Coulembier
https://arxiv.org/abs/2507.14803 https://arxiv.org/pdf/2507.14803

Invertible exterior powers
We show that in a symmetric monoidal category over a field of characteristic zero, objects with an invertible exterior power are rigid. As an application we prove some conjectures on dimensions in symmetric monoidal categories recently stated by Baez, Moeller and Trimble.

CFP> Special Issue on The Economics of Buddhism and Jainism: Journal of Economics, Management, and Religion (JEMAR)
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New Journal and CFP: Inaugural Issue of Central Europe Yearbook Now Available The…
via Input 4 RELCFP

DIO: Refining Mutual Information and Causal Chain to Enhance Machine Abstract Reasoning Ability
Ruizhuo Song, Beiming Yuan
https://arxiv.org/abs/2508.15387 https://

DIO: Refining Mutual Information and Causal Chain to Enhance Machine Abstract Reasoning Ability
Despite the outstanding performance of current deep learning models across various domains, their fundamental bottleneck in abstract reasoning remains unresolved. To address this challenge, the academic community has introduced Raven's Progressive Matrices (RPM) problems as an authoritative benchmark for evaluating the abstract reasoning capabilities of deep learning algorithms, with a focus on core intelligence dimensions such as abstract reasoning, pattern recognition, and complex problem-sol…

SLM-Bench: A Comprehensive Benchmark of Small Language Models on Environmental Impacts -- Extended Version
Nghiem Thanh Pham, Tung Kieu, Duc-Manh Nguyen, Son Ha Xuan, Nghia Duong-Trung, Danh Le-Phuoc
https://arxiv.org/abs/2508.15478

SLM-Bench: A Comprehensive Benchmark of Small Language Models on Environmental Impacts -- Extended Version
Small Language Models (SLMs) offer computational efficiency and accessibility, yet a systematic evaluation of their performance and environmental impact remains lacking. We introduce SLM-Bench, the first benchmark specifically designed to assess SLMs across multiple dimensions, including accuracy, computational efficiency, and sustainability metrics. SLM-Bench evaluates 15 SLMs on 9 NLP tasks using 23 datasets spanning 14 domains. The evaluation is conducted on 4 hardware configurations, provid…

A refined trilinear Kakeya estimate in $\mathbb{R}^3$
Javier Ramos
https://arxiv.org/abs/2506.18769 https://arxiv.org/pdf/2506.18769

A refined trilinear Kakeya estimate in $\mathbb{R}^3$
We prove a refined trilinear Kakeya estimate in three dimensions, valid for small values of the transversality parameter.

Time Deep Gradient Flow Method for pricing American options
Jasper Rou
https://arxiv.org/abs/2507.17606 https://arxiv.org/pdf/2507.17606

Time Deep Gradient Flow Method for pricing American options
In this research, we explore neural network-based methods for pricing multidimensional American put options under the BlackScholes and Heston model, extending up to five dimensions. We focus on two approaches: the Time Deep Gradient Flow (TDGF) method and the Deep Galerkin Method (DGM). We extend the TDGF method to handle the free-boundary partial differential equation inherent in American options. We carefully design the sampling strategy during training to enhance performance. Both TDGF and D…

An Observation on Lloyd's k-Means Algorithm in High Dimensions
David Silva-S\'anchez, Roy R. Lederman
https://arxiv.org/abs/2506.14952 https://

An Observation on Lloyd's k-Means Algorithm in High Dimensions
Clustering and estimating cluster means are core problems in statistics and machine learning, with k-means and Expectation Maximization (EM) being two widely used algorithms. In this work, we provide a theoretical explanation for the failure of k-means in high-dimensional settings with high noise and limited sample sizes, using a simple Gaussian Mixture Model (GMM). We identify regimes where, with high probability, almost every partition of the data becomes a fixed point of the k-means algorith…

The Dirac oscillator, generalised parastatistics and colour Lie superalgebras
Phillip S. Isaac, Mitchell Ryan
https://arxiv.org/abs/2507.14780 https://

The Dirac oscillator, generalised parastatistics and colour Lie superalgebras
We study the Dirac oscillator in one, two and three spatial dimensions, showing that the corresponding ladder operators realise the $ \mathbb{Z}_2\times\mathbb{Z}_2 $-graded Lie superalgebras $ \mathfrak{pso}(3|2) $, $ \mathfrak{pso}(3|4) $ and $ \mathfrak{osp}_{01}(1|2) \oplus \mathfrak{sl}_{10}(1|1)$. These algebraic structures are related to parastatistics and their Fock spaces. We demonstrate that these colour algebras and Fock spaces are useful for analysing the Dirac o…

Isotopy versus equivariant isotopy in dimensions three and higher
Trent Lucas
https://arxiv.org/abs/2508.11104 https://arxiv.org/pdf/2508.11104

Isotopy versus equivariant isotopy in dimensions three and higher
Given a finite group action on a smooth manifold, we study the following question: if two equivariant diffeomorphisms are isotopic, must they be equivariantly isotopic? Birman-Hilden and Maclachlan-Harvey proved the answer is "yes" for most surfaces. By contrast, we give a general criterion in higher dimensions under which there are many equivariant diffeomorphisms which are isotopic but not equivariantly isotopic. Examples satisfying this criterion include branched covers of split links and "s…

A Grassroots Network and Community Roadmap for Interconnected Autonomous Science Laboratories for Accelerated Discovery
Rafael Ferreira da Silva, Milad Abolhasani, Dionysios A. Antonopoulos, Laura Biven, Ryan Coffee, Ian T. Foster, Leslie Hamilton, Shantenu Jha, Theresa Mayer, Benjamin Mintz, Robert G. Moore, Salahudin Nimer, Noah Paulson, Woong Shin, Frederic Suter, Mitra Taheri, Michela Taufer, Newell R. Washburn

A Grassroots Network and Community Roadmap for Interconnected Autonomous Science Laboratories for Accelerated Discovery
Scientific discovery is being revolutionized by AI and autonomous systems, yet current autonomous laboratories remain isolated islands unable to collaborate across institutions. We present the Autonomous Interconnected Science Lab Ecosystem (AISLE), a grassroots network transforming fragmented capabilities into a unified system that shorten the path from ideation to innovation to impact and accelerates discovery from decades to months. AISLE addresses five critical dimensions: (1) cross-institu…

The nonisospectral integrable hierarchies associated with Lie algebra $\mathfrak{sp}(6)$
Yanhui Bi, Bo Yuan, Yuqi Ruan, Tao Zhang
https://arxiv.org/abs/2507.17278 https://

The nonisospectral integrable hierarchies associated with Lie algebra $\mathfrak{sp}(6)$
In this paper, we consider nonisospectral problems of two distinct dimensions on the loop algebra of the symplectic Lie algebra $\mathfrak{sp}(6)$, and construct two integrable systems. Furthermore, we derive their Hamiltonian structures using the Tu scheme. Additionally, we construct an integrable hierarchy on the generalized Lie algebra $\mathfrak{Gsp}(6)$ and establish its Hamiltonian structure as well.

Spatially tailored spin wave excitation for spurious-free, low-loss magnetostatic wave filters with ultra-wide frequency tunability
Shuxian Wu, Shun Yao, Xingyu Du, Chin-Yu Chang, Roy H. Olsson III
https://arxiv.org/abs/2507.14469

Spatially tailored spin wave excitation for spurious-free, low-loss magnetostatic wave filters with ultra-wide frequency tunability
Yttrium iron garnet magnetostatic wave (MSW) radio frequency (RF) cavity filters are promising for sixth-generation (6G) communication systems due to their wide frequency tunability. However, the presence of severe spurious modes arising from the finite cavity dimensions severely degrades the filter performance. We present a half-cone transducer that spatially tailors spin wave excitation to selectively enhance the primary cavity modes comprising the MSW filter passband, while strongly suppress…

A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits
Sarah Meng Li (University of Amsterdam, University of Waterloo), Michele Mosca (University of Waterloo), Neil J. Ross (Dalhousie University), John van de Wetering (University of Amsterdam), Yuming Zhao (University of Copenhagen, University of Waterloo)
https://arxiv.org/abs…

A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits
We present a complete set of rewrite rules for n-qutrit Clifford circuits where n is any non-negative integer. This is the first completeness result for any fragment of quantum circuits in odd prime dimensions. We first generalize Selinger's normal form for n-qubit Clifford circuits to the qutrit setting. Then, we present a rewrite system by which any Clifford circuit can be reduced to this normal form. We then simplify the rewrite rules in this procedure to a small natural set of rules, giving…

Analyzing Character Representation in Media Content using Multimodal Foundation Model: Effectiveness and Trust
Evdoxia Taka, Debadyuti Bhattacharya, Joanne Garde-Hansen, Sanjay Sharma, Tanaya Guha
https://arxiv.org/abs/2506.14799

Analyzing Character Representation in Media Content using Multimodal Foundation Model: Effectiveness and Trust
Recent advances in AI has enabled automated analysis of complex media content at scale and generate actionable insights regarding character representation along such dimensions as gender and age. Past work focused on quantifying representation from audio/video/text using various ML models, but without having the audience in the loop. We ask, even if character distribution along demographic dimensions are available, how useful are they to the general public? Do they actually trust the numbers ge…

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…

A Nash-Kuiper theorem for isometric immersions in a high codimension
Zhiwen Zhao
https://arxiv.org/abs/2507.15808 https://arxiv.org/p…

A Nash-Kuiper theorem for isometric immersions in a high codimension
This paper is devoted to investigating the isometric immersion problem of Riemannian manifolds in a high codimension. It has recently been demonstrated that any short immersion from an $n$-dimensional smooth compact manifold into $2n$-dimensional Euclidean space can be uniformly approximated by $C^{1,θ}$ isometric immersions with any $θ\in(0,1/(n+2))$ in dimensions $n\geq3$. In this paper, we improve the Hölder regularity of the constructed isometric immersions in the local setting, achievin…

Local (Outer) Multiset Dimensions of Graphs
Rinovia Simanjuntak, M. Ali Hasan, Muhung Anggarawan
https://arxiv.org/abs/2507.15071 https://

Local (Outer) Multiset Dimensions of Graphs
Let $G$ be a finite, connected, undirected, and simple graph and $W$ be a set of vertices in $G$. A representation multiset of a vertex $u$ in $V(G)$ with respect to $W$ is defined as the multiset of distances between $u$ and the vertices in $W$. If every two adjacent vertices in $V(G)$ have a distinct multiset representation, the set $W$ is called a local multiset resolving set of $G$. If $G$ has a local multiset resolving set, then this set with the smallest cardinality is called the local mu…

Comprehensive Privacy Risk Assessment in Social Networks Using User Attributes Social Graphs and Text Analysis
Md Jahangir Alam, Ismail Hossain, Sai Puppala, Sajedul Talukder
https://arxiv.org/abs/2507.15124

Comprehensive Privacy Risk Assessment in Social Networks Using User Attributes Social Graphs and Text Analysis
The rise of social networking platforms has amplified privacy threats as users increasingly share sensitive information across profiles, content, and social connections. We present a Comprehensive Privacy Risk Scoring (CPRS) framework that quantifies privacy risk by integrating user attributes, social graph structures, and user-generated content. Our framework computes risk scores across these dimensions using sensitivity, visibility, structural similarity, and entity-level analysis, then aggre…

Observation of Kardar-Parisi-Zhang universal scaling in two dimensions
Simon Widmann, Siddhartha Dam, Johannes D\"ureth, Christian G. Mayer, Romain Daviet, Carl Philipp Zelle, David Laibacher, Monika Emmerling, Martin Kamp, Sebastian Diehl, Simon Betzold, Sebastian Klembt, Sven H\"ofling
https://arxiv.org/abs/2506.1552…

Observation of Kardar-Parisi-Zhang universal scaling in two dimensions
Equilibrium and nonequilibrium states of matter can exhibit fundamentally different behavior. A key example is the Kardar-Parisi-Zhang universality class in two spatial dimensions (2D KPZ), where microscopic deviations from equilibrium give rise to macroscopic scaling laws without equilibrium counterparts. While extensively studied theoretically, direct experimental evidence of 2D KPZ scaling has remained limited to interface growth so far. Here, we report the observation of universal scaling c…

Preconditioning and Linearly Implicit Time Integration for the Serre-Green-Naghdi Equations
Linwan Feng, David Shirokoff, Wooyoung Choi
https://arxiv.org/abs/2506.16045

Preconditioning and Linearly Implicit Time Integration for the Serre-Green-Naghdi Equations
The treatment of the differential PDE constraint poses a key challenge in computing the numerical solution of the Serre-Green-Naghdi (SGN) equations. In this work, we introduce a constant coefficient preconditioner for the SGN constraint operator and prove rigorous bounds on the preconditioned conditioning number. The conditioning bounds incorporate the effects of bathymetry in two dimensions, are quasi-optimal within a class of constant coefficient operators, highlight fundamental scalings for…

Five-loop Anomalous Dimensions of Cubic Scalar Theory from Operator Product Expansion
Rijun Huang, Qingjun Jin, Yi Li
https://arxiv.org/abs/2508.13620 https://

Five-loop Anomalous Dimensions of Cubic Scalar Theory from Operator Product Expansion
Recently, an Operator Product Expansion method has been proposed for renormalization in quantum field theories. This method extracts UV divergences from two-point propagator-type integrals, and it is believed to be applicable to generic QFTs. In the present work, we apply the OPE method to the renormalization of scalar theory with cubic interactions in six-dimensions. We have successfully computed the 5-loop corrections to the anomalous dimensions of the $ϕ^Q$ operator, as well as the large $N…

Spatial mapping and tuning of terahertz modes in a silicon whispering gallery mode resonator
Anna R. Petersen, Pablo Paulsen, Florian Sedlmeir, Nicholas J. Lambert, Harald G. L. Schwefel, Mallika Irene Suresh
https://arxiv.org/abs/2506.17257

Spatial mapping and tuning of terahertz modes in a silicon whispering gallery mode resonator
Identification and subsequent manipulation of resonant modes typically relies on comparison with calculations which require precise knowledge of material parameters and dimensions. For millimetre-sized resonators that support millimetre-wave modes, this is particularly challenging due to the poorly determined physical parameters and additional perturbative effects of nearby dielectric or metallic substrates in experimental setups. Here, we use perturbation from a metal needle to experimentally …

Language-Guided Tuning: Enhancing Numeric Optimization with Textual Feedback
Yuxing Lu, Yucheng Hu, Nan Sun, Xukai Zhao
https://arxiv.org/abs/2508.15757 https://

Language-Guided Tuning: Enhancing Numeric Optimization with Textual Feedback
Configuration optimization remains a critical bottleneck in machine learning, requiring coordinated tuning across model architecture, training strategy, feature engineering, and hyperparameters. Traditional approaches treat these dimensions independently and lack interpretability, while recent automated methods struggle with dynamic adaptability and semantic reasoning about optimization decisions. We introduce Language-Guided Tuning (LGT), a novel framework that employs multi-agent Large Langua…

$La_3Pd_2NaO_9$: A High-Valent Insulating Palladate
Qingqing Yang, Ning Guo, Tieyan Chang, Zheng Guo, Xiaoli Wang, Chuanyan Fan, Chao Liu, Lu Han, Feiyu Li, Tao He, Qiang Zheng, Yu-Sheng Chen, Junjie Zhang
https://arxiv.org/abs/2506.15966

$La_3Pd_2NaO_9$: A High-Valent Insulating Palladate
A high-valent palladate, $La_3Pd_2NaO_9$, has been synthesized for the first time. Single crystals with dimensions of 20 $μ$m on edge were successfully grown using the flux method at 420 $^o$C and 70 bar oxygen pressure. Energy dispersive spectroscopy (EDS) and inductively coupled plasma mass spectroscopy (ICP) measurements show that the atomic ratio of La: (Pd+Na) is 3: 3 and Pd: Na is 2: 1. X-ray photoelectron spectroscopy (XPS) measurements show that the oxidation state of Pd is dominated b…

Neutrino Portal to Extra Dimensions: Unified Origin of Dark Radiation, Dark Matter, and Neutrino Decay
Arnab Chaudhuri
https://arxiv.org/abs/2506.15485 htt…

Neutrino Portal to Extra Dimensions: Unified Origin of Dark Radiation, Dark Matter, and Neutrino Decay
We propose a unified framework based on sterile neutrinos propagating in large extra dimensions (LED) and coupled to a pseudo-Nambu-Goldstone boson (Majoron) arising from spontaneous lepton number violation. In this setup, the lightest Kaluza-Klein (KK) sterile neutrino serves as warm dark matter, higher KK modes decay invisibly producing a relativistic Majoron contributing to the effective number of neutrino species (Delta Neff), and active neutrinos undergo invisible decay. This model address…

Lang2Lift: A Framework for Language-Guided Pallet Detection and Pose Estimation Integrated in Autonomous Outdoor Forklift Operation
Huy Hoang Nguyen, Johannes Huemer, Markus Murschitz, Tobias Glueck, Minh Nhat Vu, Andreas Kugi
https://arxiv.org/abs/2508.15427

Lang2Lift: A Framework for Language-Guided Pallet Detection and Pose Estimation Integrated in Autonomous Outdoor Forklift Operation
The logistics and construction industries face persistent challenges in automating pallet handling, especially in outdoor environments with variable payloads, inconsistencies in pallet quality and dimensions, and unstructured surroundings. In this paper, we tackle automation of a critical step in pallet transport: the pallet pick-up operation. Our work is motivated by labor shortages, safety concerns, and inefficiencies in manually locating and retrieving pallets under such conditions. We prese…

Well-posedness and long-time behavior of a bulk-surface Cahn--Hilliard model with non-degenerate mobility
Jonas Stange
https://arxiv.org/abs/2507.16508 htt…

Well-posedness and long-time behavior of a bulk-surface Cahn--Hilliard model with non-degenerate mobility
We study a bulk-surface Cahn--Hilliard model with non-degenerate mobility and singular potentials in two dimensions. Following the ideas of the recent work by Conti, Galimberti, Gatti, and Giorgini [Calc. Var. Partial Differential Equations, 64(3):Paper No. 87, 32, 2025] for the Cahn--Hilliard equation with homogeneous Neumann boundary conditions, we show the uniqueness of weak solutions together with a continuous dependence estimate for sufficiently regular mobility functions. Next, under weak…

Massless monopole-string-domain wall fermions and polyhedral vacuum fermions
Minoru Eto, Yuito Suzuki
https://arxiv.org/abs/2506.16765 https://

Massless monopole-string-domain wall fermions and polyhedral vacuum fermions
Fermion zero modes of Bogomol'nyi-Prasad-Sommerfield monopole-string-domain wall composites in three spatial dimensions are studied. We analytically solve the Dirac equation and prove the existence of one fermion zero mode. Depending on mass parameters of bosons/fermions in the model, the zero modes are localized either on the monopoles, strings or domain walls, which we call monopole-string-domain wall fermions. We also show that in special cases, the zero modes can be confined within a finite…

Soft-Clamped Perimeter Modes of Polygon Resonators
Zhihao Niu, Yuanyuan Zhao
https://arxiv.org/abs/2506.18109 https://arxiv.org/pdf/2…

Soft-Clamped Perimeter Modes of Polygon Resonators
Polygon resonators are known for their small size and high force sensitivity. We propose an analytical model to predict the mechanical quality factors (Q) of polygon perimeter modes by incorporating a stress term in the Timoshenko-Gere equation. We discuss the origin of losses and their relationship with polygon structure dimensions. Notably, we demonstrate that the torsion loss can be suppressed through the torsion angle of supporting tethers. These results offer new insights into optimizing h…

A Hybrid Mixture Approach for Clustering and Characterizing Cancer Data
Kazeem Kareem, Fan Dai
https://arxiv.org/abs/2507.14380 https://

A Hybrid Mixture Approach for Clustering and Characterizing Cancer Data
Model-based clustering is widely used for identifying and distinguishing types of diseases. However, modern biomedical data coming with high dimensions make it challenging to perform the model estimation in traditional cluster analysis. The incorporation of factor analyzer into the mixture model provides a way to characterize the large set of data features, but the current estimation method is computationally impractical for massive data due to the intrinsic slow convergence of the embedded alg…

On the distance between mean and geometric median in high dimensions
Richard Schwank, Mathias Drton
https://arxiv.org/abs/2508.12926 https://arxiv.org/pdf/…

On the distance between mean and geometric median in high dimensions
The geometric median, a notion of center for multivariate distributions, has gained recent attention in robust statistics and machine learning. Although conceptually distinct from the mean (i.e., expectation), we demonstrate that both are very close in high dimensions when the dependence between the distribution components is suitably controlled. Concretely, we find an upper bound on the distance that vanishes with the dimension asymptotically, and derive a rate-matching first order expansion o…

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…

Analytical Theory of Chiral Active Particle Transport in a Fluctuating Density Field
Jayam Joshi, Shradha Mishra
https://arxiv.org/abs/2508.15366 https://a…

Analytical Theory of Chiral Active Particle Transport in a Fluctuating Density Field
We develop a closed-form analytical theory for the transport of a chiral active Brownian particle (cABP) in three dimensions, moving through a fluctuating local density field that coarse-grains steric and dynamical interactions in a dense active medium. The density field is modeled as an Ornstein--Uhlenbeck process with finite correlation time $τ$ and fluctuation strength $σ_ρ^2$, capturing both spatial variations and temporal memory. Within this framework, we derive exact expressions for th…

Pseudocriticality in antiferromagnetic spin chains
Sankalp Kumar, Sumiran Pujari, Jonathan D'Emidio
https://arxiv.org/abs/2506.16424 https://

Pseudocriticality in antiferromagnetic spin chains
Weak first-order pseudocriticality with approximate scale invariance has been observed in a variety of settings, including the intriguing case of deconfined criticality in 2+1 dimensions. Recently, this has been interpreted as extremely slow flows ("walking behavior") for real-valued couplings in proximity to a bona fide critical point with complex-valued couplings, described by a complex conformal field theory (CFT). Here we study an SU($N$) generalization of the the Heisenberg antiferromagnet…

A geometry of cubic discriminants in 8 dimensions
Elitza Hristova, Ivan Minchev
https://arxiv.org/abs/2508.12014 https://arxiv.org/pdf/2508.12014

A geometry of cubic discriminants in 8 dimensions
This paper examines 8-dimensional Riemannian manifolds whose structure group reduces to ${SO(4)}_{ir}\subset GL(8,\mathbb R)$, the image of an irreducible representation of $SO(4)$ on $\mathbb R^8$. We demonstrate that such a reduction can be described by an almost quaternion-Hermitian structure and a special rank-4 tensor field, which we call a cubic discriminant. This tensor field is pointwise linearly equivalent to the formula for the discriminant of a cubic polynomial. We show that the only…

The spectrum of open confining strings in the large-Nc limit
Alireza Sharifian, Andreas Athenodorou, Pedro Bicudo
https://arxiv.org/abs/2506.16342 https://…

The spectrum of open confining strings in the large-Nc limit
In this study, we conduct a thorough examination of the spectrum of the open confining string in 3+1 dimensions, commonly referred to as the open flux-tube, across various gauge groups of $SU(N_c)$. Our primary objective is to explore its behaviour as we approach the large-$N_c$ limit and the identification of possible world-sheet axion states. Specifically, we undertake a detailed analysis of the associated spectrum for $N_c=3, 4, 5, 6$. This marks the first systematic investigation of the ope…

Higher symmetries, anomalies, and crossed squares in lattice gauge theory
Anton Kapustin, Lev Spodyneiko
https://arxiv.org/abs/2507.16966 https://arxiv.org…

Higher symmetries, anomalies, and crossed squares in lattice gauge theory
We examine higher-form symmetries of quantum lattice gauge theories through the lens of homotopy theory and operator algebras. We show that in the operator-algebraic approach both higher-form symmetries and 't Hooft anomalies arise from considering restrictions of symmetry transformations to spatial regions. The data of these restrictions are naturally packaged into a higher group. For example, for gauge theories in two spatial dimensions, this information is encoded in a crossed square of grou…

A Topic Modeling Analysis of Stigma Dimensions, Social, and Related Behavioral Circumstances in Clinical Notes Among Patients with HIV
Ziyi Chen, Yiyang Liu, Mattia Prosperi, Krishna Vaddiparti, Robert L Cook, Jiang Bian, Yi Guo, Yonghui Wu
https://arxiv.org/abs/2506.09279

A Topic Modeling Analysis of Stigma Dimensions, Social, and Related Behavioral Circumstances in Clinical Notes Among Patients with HIV
Objective: To characterize stigma dimensions, social, and related behavioral circumstances in people living with HIV (PLWHs) seeking care, using natural language processing methods applied to a large collection of electronic health record (EHR) clinical notes from a large integrated health system in the southeast United States. Methods: We identified 9,140 cohort of PLWHs from the UF Health IDR and performed topic modeling analysis using Latent Dirichlet Allocation (LDA) to uncover stigma dimen…

Finiteness of homological dimensions of Ext modules
Kaito Kimura
https://arxiv.org/abs/2508.12843 https://arxiv.org/pdf/2508.12843

Finiteness of homological dimensions of Ext modules
Let $R$ be a commutative Noetherian local ring and let $M$ and $N$ be nonzero finitely generated $R$-modules. In this paper, we investigate how the finiteness of the homological dimension of Ext modules between $M$ and $N$ affects that of $M$ and $N$. One of our main result states that if $\operatorname{Ext}^i_R(M,N)$ has finite projective dimension for any $0\le i\le \operatorname{Rfd}_R M$, where $\operatorname{Rfd}_R M$ is the (large) restricted flat dimension of $M$, then $M$ has finite pro…

Newfluence: Boosting Model interpretability and Understanding in High Dimensions
Haolin Zou, Arnab Auddy, Yongchan Kwon, Kamiar Rahnama Rad, Arian Maleki
https://arxiv.org/abs/2507.11895

Newfluence: Boosting Model interpretability and Understanding in High Dimensions
The increasing complexity of machine learning (ML) and artificial intelligence (AI) models has created a pressing need for tools that help scientists, engineers, and policymakers interpret and refine model decisions and predictions. Influence functions, originating from robust statistics, have emerged as a popular approach for this purpose. However, the heuristic foundations of influence functions rely on low-dimensional assumptions where the number of parameters $p$ is much smaller than the …

Higher dimensional Sacks-Uhlenbeck-type functionals and applications
Gianmichele Di Matteo, Tobias Lamm
https://arxiv.org/abs/2506.17166 https://

Higher dimensional Sacks-Uhlenbeck-type functionals and applications
In this work, we generalize Sacks-Uhlenbeck's existence result for harmonic spheres, constructing for $n \ge 2$, regular, non-trivial, $n$-harmonic $n$-spheres into suitable target manifolds. We obtain an infinite family of new null-homotopic such maps. The proof follows a similar perturbative argument, which in high dimensions leads to a degenerate and double-phase-type Euler-Lagrange system, making the uniform regularity needed to formalize the bubbling harder to achieve. Then, we develop a r…

Beyond Human Judgment: A Bayesian Evaluation of LLMs' Moral Values Understanding
Maciej Skorski, Alina Landowska
https://arxiv.org/abs/2508.13804 https://

Beyond Human Judgment: A Bayesian Evaluation of LLMs' Moral Values Understanding
How do large language models understand moral dimensions compared to humans? This first large-scale Bayesian evaluation of market-leading language models provides the answer. In contrast to prior work using deterministic ground truth (majority or inclusion rules), we model annotator disagreements to capture both aleatoric uncertainty (inherent human disagreement) and epistemic uncertainty (model domain sensitivity). We evaluate top language models (Claude Sonnet 4, DeepSeek-V3, Llama 4 Maveri…

The Supersymmetric Standard Model, combined with a special Exotic Invariant, yields a new kind of SUSY mass splitting (E6)
John A. Dixon
https://arxiv.org/abs/2507.14381

The Supersymmetric Standard Model, combined with a special Exotic Invariant, yields a new kind of SUSY mass splitting (E6)
Exotic Invariants, with Lorentz invariance, have been found in the BRS cohomology of SUSY in 3+1 dimensions. Until recently, it was generally accepted that no such objects could exist. It is shown here that the Supersymmetric Standard Model (``the SSM'') can be coupled to a special Exotic Invariant to form a new model, which we call the Exotic Model (``the XM'') . This Exotic Model continues to generate the usual Vacuum Expectation Value (``VEV'') that breaks gauge symmetry from SU(3) X SU(2) X…

Optimal Sobolev inequalities of high order with $L^2$-remainder
Lorenzo Carletti, Fr\'ed\'eric Robert
https://arxiv.org/abs/2506.17028 https://

Optimal Sobolev inequalities of high order with $L^2$-remainder
We investigate the validity of the optimal higher-order Sobolev inequality $H_k^2(M^n)\hookrightarrow L^{\frac{2n}{n-2k}}(M^n)$ on a closed Riemannian manifold when the remainder term is the $L^2-$norm. Unlike the case $k=1$, the optimal inequality does not hold in general for $k>1$. We prove conditions for the validity and non-validity that depend on the geometry of the manifold. Our conditions are sharp when $k=2$ and in small dimensions.

Exploring the Landscape of Non-Equilibrium Memories with Neural Cellular Automata
Ethan Lake, Ehsan Pajouheshgar
https://arxiv.org/abs/2508.15726 https://a…

Exploring the Landscape of Non-Equilibrium Memories with Neural Cellular Automata
We investigate the landscape of many-body memories: families of local non-equilibrium dynamics that retain information about their initial conditions for thermodynamically long time scales, even in the presence of arbitrary perturbations. In two dimensions, the only well-studied memory is Toom's rule. Using a combination of rigorous proofs and machine learning methods, we show that the landscape of 2D memories is in fact quite vast. We discover memories that correct errors in ways qualitatively…

Simulation of parametrized cardiac electrophysiology in three dimensions using physics-informed neural networks
Roshan Antony Gomez, Julien St\"ocker, Bar{\i}\c{s} Cans{\i}z, Michael Kaliske
https://arxiv.org/abs/2506.15405

Simulation of parametrized cardiac electrophysiology in three dimensions using physics-informed neural networks
Physics-informed neural networks (PINNs) are extensively used to represent various physical systems across multiple scientific domains. The same can be said for cardiac electrophysiology, wherein fully-connected neural networks (FCNNs) have been employed to predict the evolution of an action potential in a 2D space following the two-parameter phenomenological Aliev-Panfilov (AP) model. In this paper, the training behaviour of PINNs is investigated to determine optimal hyperparameters to predict…

DREAMS: Preserving both Local and Global Structure in Dimensionality Reduction
No\"el Kury, Dmitry Kobak, Sebastian Damrich
https://arxiv.org/abs/2508.13747 https://…

DREAMS: Preserving both Local and Global Structure in Dimensionality Reduction
Dimensionality reduction techniques are widely used for visualizing high-dimensional data in two dimensions. Existing methods are typically designed to preserve either local (e.g. $t$-SNE, UMAP) or global (e.g. MDS, PCA) structure of the data, but none of the established methods can represent both aspects well. In this paper, we present DREAMS (Dimensionality Reduction Enhanced Across Multiple Scales), a method that combines the local structure preservation of $t$-SNE with the global structure …

Quantum droplets in curved space
Antonino Flachi, Takahiro Tanaka
https://arxiv.org/abs/2507.13682 https://arxiv.org/pdf/2507.13682…

Quantum droplets in curved space
This paper investigates the formation of quantum droplets in curved spacetime, highlighting the significant influence of curvature on the formation and properties of these objects. While our computations encompass various dimensions, we primarily focus on 2-dimensions. Our findings reveal a novel class of curvature-driven quantum effects leading to the formation of quasi-stable liquid droplets, suggesting a feasible pathway for experimental observation, particularly in microgravity environments.

A hybrid-frequency on-chip programmable synthetic-dimension simulator with arbitrary couplings
Xiao-Dong Zeng, Zhao-An Wang, Jia-Ming Ren, Yi-Tao Wang, Chun Ao, Wei Liu, Nai-Jie Guo, Lin-Ke Xie, Jun-You Liu, Yu-Hang Ma, Ya-Qi Wu, Shuang Wang, Pei-Yun Li, Zong-Quan Zhou, Mu Yang, Jin-Shi Xu, Xi-Wang Luo, Jian-Shun Tang, Chuan-Feng Li, Guang-Can Guo
https://

A hybrid-frequency on-chip programmable synthetic-dimension simulator with arbitrary couplings
High-performance photonic chips provide a powerful platform for analog computing, enabling the simulation of high-dimensional physical systems using low-dimensional devices with additional synthetic dimensions. The realization of large-scale complex simulations necessitates an architecture capable of arbitrary coupling configurations (encompassing symmetric, asymmetric and long-range coupling schemes) which is also crucial for scaling up. Previous approaches rely on excessive physical component…

On the number of faces of marked order polytopes
Ekaterina V. Melikhova
https://arxiv.org/abs/2507.13596 https://arxiv.org/pdf/2507.1…

On the number of faces of marked order polytopes
In this paper, we present a new method for computing the f-vector of a marked order polytope. Namely, given an arbitrary (polyhedral) subdivision of an arbitrary convex polytope, we construct a cochain complex (over the two-element field Z_2) such that the dimensions of its cohomology groups equal the components of the f-vector of the original polytope. In the case of a marked order polytope and its well-known cubosimplicial subdivision, this cochain complex can be described purely combinatoria…

Dipole-Induced Transition in 3-Dimensions
Itamar Procaccia, Tuhin Samanta
https://arxiv.org/abs/2507.11179 https://arxiv.org/pdf/2507…

Dipole-Induced Transition in 3-Dimensions
The Kosterlitz-Thouless and the Hexatic phase transitions are celebrated examples of dipole (vortex, dislocation) induced transitions in condensed matter physics. For very clear reasons, these important ``topological" transitions are restricted to 2-dimensions. Here we present a genuine dipole-induced transition in the 3-dimensional response of (athermal) amorphous solids to applied strain. Similarly to the existence of a hexatic phase between normal solid and fluid, we identify an intermediate…

Holographic Timelike Entanglement Across Dimensions
Carlos Nunez, Dibakar Roychowdhury
https://arxiv.org/abs/2508.13266 https://arxiv.org/pdf/2508.13266

Holographic Timelike Entanglement Across Dimensions
We develop a holographic framework for computing timelike entanglement entropy (tEE) in quantum field theories, extending the Ryu-Takayanagi prescription into Lorentzian settings. Using three broad classes of supergravity backgrounds, we derive both exact and approximate tEE expressions for slab, spherical, and hyperbolic regions, and relate them to the central charges of the dual conformal field theories. The method is applied to infinite families of supersymmetric linear quivers in dimensions…

A Satellite $N=2$ Superparticle in Extra Dimensions
F. E. A. de Souza, M. O. Tahim, R. I. O. Junior, I. M. Macedo
https://arxiv.org/abs/2508.13970 https://…

A Satellite $N=2$ Superparticle in Extra Dimensions
In this work we discuss the issue of localization of $N=2$ spinning particles. More specifically, we show that we can not confine the spinning particle within the Randall-Sundrum scenario. We argue that this result directly affects studies related to localization of $p$-form fields. We show that, due to the non confinement of the superparticle, we can not localize $p$-forms on the membrane.

Prey-taxis VS a Shortwave External Signal in Multiple Dimensions
Andrey Morgulis, Karrar Malal
https://arxiv.org/abs/2508.12432 https://arxiv.org/pdf/2508.…

Prey-taxis VS a Shortwave External Signal in Multiple Dimensions
We consider a model of the predator--prey community with prey-taxis. By that we mean the capability of the predators to get moving in a certain direction on the macroscopic level in response to the prey density gradients. Additionally, we suppose the same kind of sensitivity with respect to one more signal, called external, the production of which goes on independently of the community state. Such a signal can be due to the spatiotemporal inhomogeneity of the environment that results from the n…

Universality of giant graviton correlators
Augustus Brown, Daniele Dorigoni, Francesco Galvagno, Congkao Wen
https://arxiv.org/abs/2508.15657 https://arxiv…

Universality of giant graviton correlators
We study a class of heavy-heavy-light-light (HHLL) integrated correlators of superconformal primary operators in $SU(N)$ $\mathcal{N}=4$ super Yang-Mills theory involving two light operators from the stress-tensor multiplet and two heavy operators whose conformal dimensions are proportional to the number of colours $N$. In the large-$N$ limit these heavy operators are dual to sphere and AdS giant gravitons, realised holographically as D3-branes wrapping an $S^3$ inside either the $S^5$ or the $…

Emergent classical gravity as stress-tensor deformed field theories
Yun-Ze Li, Yunfei Xie, Song He
https://arxiv.org/abs/2508.15461 https://arxiv.org/pdf/2…

Emergent classical gravity as stress-tensor deformed field theories
We introduce a framework in which classical gravity arises from stress-tensor deformations of quantum field theories (QFTs). By expressing the deformed partition function as a gravitational path integral, we propose an equivalent description between a seed QFT coupled to gravity and an effective field theory defined on a deformation-induced metric. This approach, which does not rely on holography or extra dimensions, applies to a variety of gravitational models, including Einstein and Palatini …

On Carrollian and Celestial Correlators in General Dimensions
Harshal Kulkarni, Romain Ruzziconi, Akshay Yelleshpur Srikant
https://arxiv.org/abs/2508.06602 https://

On Carrollian and Celestial Correlators in General Dimensions
Carrollian holography is a framework for flat space holography, suggesting that gravity in asymptotically flat spacetime in $D$ dimensions is dual to a conformal Carrollian field theory in $D - 1$ dimensions living at null infinity. In this work, we elaborate on the definition of Carrollian amplitudes for massless scalar fields in general dimensions and provide explicit expressions for the two-, three-, and four-point functions. We show that these amplitudes naturally arise from Lorentzian holo…

Vogel's universality and Macdonald dimensions
Liudmila Bishler
https://arxiv.org/abs/2507.11414 https://arxiv.org/pdf/2507.11414

Vogel's universality and Macdonald dimensions
We discuss algebraic universality in the sense of P. Vogel for the simplest refined quantity, the Macdonald dimensions. The main known source of universal quantities is given by Chern-Simons theory. Refinement of Chern-Simons theory means introducing additional parameters. At the level of symmetric functions, the refinement is the transition from the Schur functions to the Macdonald polynomials. We consider the Macdonald polynomials associated with the simple Lie algebras, define Macdonald dime…