Tootfinder

Metric weak proper discontinuity for pseudo-Anosov maps
Inhyeok Choi
https://arxiv.org/abs/2506.21214 https://arxiv.org/pdf/2506.2121…

Metric weak proper discontinuity for pseudo-Anosov maps
We present a metric version of weak proper discontinuity (WPD) for pseudo-Anosov maps on surfaces. As an application, we show that there are plenty of quasi-morphisms on the homeomorphism group of a torus or a hyperbolic surface that are unbounded on certain homeomorphisms with large fixed set.

On geometry of $Q^{(2k)}_g$-curvature
Mingxiang Li, Juncheng Wei, Xingwang Xu
https://arxiv.org/abs/2506.20165 https://arxiv.org/pdf/…

On geometry of $Q^{(2k)}_g$-curvature
The main purpose of current article is to study the geometry of $Q$-curvature. For simplicity, we start with a very simple model: a complete and conformal metric $g=e^{2u}|dx|^2$ on $\mathbb{R}^n$. We assume the metric $g$ has non-negative $nth$-order $Q$-curvature and non-negative scalar curvature. We show that the Ricci curvature is non-negative. We further assume that the metric $g$ is not degenerate in the sense that the isoperimetric ratio near the end is positive. With this extr…

On gradient descent-ascent flows in metric spaces
Noboru Isobe, Sho Shimoyama
https://arxiv.org/abs/2506.20258 https://arxiv.org/pdf/…

On gradient descent-ascent flows in metric spaces
Gradient descent-ascent (GDA) flows play a central role in finding saddle points of bivariate functionals, with applications in optimization, game theory, and robust control. While they are well-understood in Hilbert and Banach spaces via maximal monotone operator theory, their extension to general metric spaces, particularly Wasserstein spaces, has remained largely unexplored. In this paper, we develop a mathematical theory of GDA flows on the product of two complete metric spaces, formulating…

Leveraging Correlation Across Test Platforms for Variance-Reduced Metric Estimation
Rachel Luo, Heng Yang, Michael Watson, Apoorva Sharma, Sushant Veer, Edward Schmerling, Marco Pavone
https://arxiv.org/abs/2506.20553

Leveraging Correlation Across Test Platforms for Variance-Reduced Metric Estimation
Learning-based robotic systems demand rigorous validation to assure reliable performance, but extensive real-world testing is often prohibitively expensive, and if conducted may still yield insufficient data for high-confidence guarantees. In this work, we introduce a general estimation framework that leverages paired data across test platforms, e.g., paired simulation and real-world observations, to achieve better estimates of real-world metrics via the method of control variates. By incorpora…

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…

Geological resources may be able to provide billions—or even trillions—of metric tons of clean hydrogen,
according to estimates from US government researchers.
By tapping into existing hydrogen accumulations and stimulating underground rocks to make more of the electron-rich gas,
a new crop of energy entrepreneurs think they can put low-carbon hydrogen on the market for as little as $1 per kilogram.
The concept is proven at just one site today -- But if it works as w…

Trillions of tons of hydrogen may be waiting under our feet
A new energy industry is emerging around hydrogen made by rocks instead of renewables

Gromov-Hausdorff distance between chromatic metric pairs and stability of the six-pack
Ond\v{r}ej Draganov, Sophie Rosenmeier, Nicol\`o Zava
https://arxiv.org/abs/2507.17994 htt…

Gromov-Hausdorff distance between chromatic metric pairs and stability of the six-pack
Chromatic metric pairs consist of a metric space and a coloring function partitioning a subset thereof into various colors. It is a natural extension of the notion of chromatic point sets studied in chromatic topological data analysis. A useful tool in the field is the six-pack, a collection of six persistence diagrams, summarizing homological information about how the colored subsets interact. We introduce a suitable generalization of the Gromov-Hausdorff distance to compare chromatic metric p…

Generalised state space geometry in Hermitian and non-Hermitian quantum systems
Kunal Pal
https://arxiv.org/abs/2507.18486 https://arxiv.org/pdf/2507.18486…

Generalised state space geometry in Hermitian and non-Hermitian quantum systems
One of the key features of information geometry in the classical setting is the existence of a metric structure and a family of connections on the space of probability distributions. The uniqueness of the Fisher--Rao metric and the duality of these connections is at the heart of classical information geometry. However, these features do not carry over straightforwardly to quantum systems, where a Hermitian inner product structure on the Hilbert space induces a metric on the complex projective s…

Formation of Bound States in Quintessence Alternative Theories
George Koutsoumbas, Andri Machattou, Eleftherios Papantonopoulos
https://arxiv.org/abs/2506.21097

Formation of Bound States in Quintessence Alternative Theories
We study the formation and behaviour of bound states formed outside the horizon of a black hole in the presence of quintessence matter. Calculating the Regge and Wheeler potential for general metric function, we find that the presence of quintessence influences significantly the metric function and the Hawking temperature. We show that large black holes radiate less in the presence of large quintessence matter and it seems to live longer, while small black holes radiate more.

Prokhorov Metric Convergence of the Partial Sum Process for Reconstructed Functional Data
Tim Kutta, Piotr Kokoszka
https://arxiv.org/abs/2506.21172 https:…

Prokhorov Metric Convergence of the Partial Sum Process for Reconstructed Functional Data
Motivated by applications in functional data analysis, we study the partial sum process of sparsely observed, random functions. A key novelty of our analysis are bounds for the distributional distance between the limit Brownian motion and the entire partial sum process in the function space. To measure the distance between distributions, we employ the Prokhorov and Wasserstein metrics. We show that these bounds have important probabilistic implications, including strong invariance principles an…

Smoothed Analysis of Online Metric Problems
Christian Coester, Jack Umenberger
https://arxiv.org/abs/2507.17834 https://arxiv.org/pdf/2507.17834

Smoothed Analysis of Online Metric Problems
We study three classical online problems -- $k$-server, $k$-taxi, and chasing size $k$ sets -- through a lens of smoothed analysis. Our setting allows request locations to be adversarial up to small perturbations, interpolating between worst-case and average-case models. Specifically, we show that if the metric space is contained in a ball in any normed space and requests are drawn from distributions whose density functions are upper bounded by $1/σ$ times the uniform density over the ball, th…

$k$-Approval Veto: A Spectrum of Voting Rules Balancing Metric Distortion and Minority Protection
Fatih Erdem Kizilkaya, David Kempe
https://arxiv.org/abs/2507.17981 https://

$k$-Approval Veto: A Spectrum of Voting Rules Balancing Metric Distortion and Minority Protection
In the context of single-winner ranked-choice elections between $m$ candidates, we explore the tradeoff between two competing goals in every democratic system: the majority principle (maximizing the social welfare) and the minority principle (safeguarding minority groups from overly bad outcomes).To measure the social welfare, we use the well-established framework of metric distortion subject to various objectives: utilitarian (i.e., total cost), $α$-percentile (e.g., median cost for $α= 1/2$…

Explicit Constructions of Sum-Rank Metric Codes from Quadratic Kummer Extensions
Zhu Yunlong, Zhao Chang-An
https://arxiv.org/abs/2506.18653 https://

Explicit Constructions of Sum-Rank Metric Codes from Quadratic Kummer Extensions
This paper presents new constructions of sum-rank metric codes derived from algebraic function fields, while the existing results about such codes remain limited. A central challenge in this field involves the determination of parameters. We address this challenge through quadratic Kummer extensions, and propose two general constructions of $2\times2$ sum-rank codes. The novel sum-rank metric code constructions derived from algebraic function fields demonstrate superior code lengths compared to…

Quantum Wasserstein distances for quantum permutation groups
Anshu, David Jekel, Therese Basa Landry
https://arxiv.org/abs/2505.19269 https://

Quantum Wasserstein distances for quantum permutation groups
We seek an analog for the quantum permutation group $S_n^+$ of the normalized Hamming distance for permutations. We define three distances on the tracial state space of $C(S_n^+)$ that generalize the $L^1$-Wasserstein distance of probability measures on $S_n$ equipped with the normalized Hamming metric, for which we demonstrate basic metric properties, subadditivity under convolution, and density of the Lipschitz elements in the $\mathrm{C}^{\ast}$-algebra.

A family of graph GOSPA metrics for graphs with different sizes
Jinhao Gu, \'Angel F. Garc\'ia-Fern\'andez, Robert E. Firth, Lennart Svensson
https://arxiv.org/abs/2506.17316

A family of graph GOSPA metrics for graphs with different sizes
This paper proposes a family of graph metrics for measuring distances between graphs of different sizes. The proposed metric family defines a general form of the graph generalised optimal sub-pattern assignment (GOSPA) metric and is also proved to satisfy the metric properties. Similarly to the graph GOSPA metric, the proposed graph GOSPA metric family also penalises the node attribute costs for assigned nodes between the two graphs, and the number of unassigned nodes. However, the proposed fam…

Quantum ergodicity for contact metric structures
Lino Benedetto
https://arxiv.org/abs/2507.18216 https://arxiv.org/pdf/2507.18216

Quantum ergodicity for contact metric structures
This paper is dedicated to the proof of a Quantum Ergodicity (QE) theorem for the eigenfunctions of subLaplacians on contact metric manifolds, under the assumption that the Reeb flow is ergodic. To do so, we rely on a semiclassical pseudodifferential calculus developed for general filtered manifolds that we specialize to the setting of contact manifolds. Our strategy is then reminiscent of an implementation of the Born-Oppenheimer approximation as we rely on the construction of microlocal proje…

The metric compactification of a Kobayashi hyperbolic complex manifold and a Denjoy--Wolff Theorem
Vikramjeet Singh Chandel, Nishith Mandal
https://arxiv.org/abs/2507.18156 http…

The metric compactification of a Kobayashi hyperbolic complex manifold and a Denjoy--Wolff Theorem
We study the metric compactification of a Kobayashi hyperbolic complex manifold \(\mathcal{X} \) equipped with the Kobayashi distance \( \mathsf{k}_{\mathcal{X}} \). We show that this compactification is genuine -- i.e., \( \mathcal{X} \) embeds as a dense open subset -- even without completeness of \( \mathsf{k}_{\mathcal{X}} \), and that it becomes a \emph{good compactification} in the sense of Bharali--Zimmer when \((\mathcal{X}, \mathsf{k}_{\mathcal{X}}) \) is complete. As an application, w…

Metric Poissonian pair correlation for real sequences and energy estimates
Bryce Kerr, Hongliang Wang
https://arxiv.org/abs/2506.17031 https://

Metric Poissonian pair correlation for real sequences and energy estimates
In this paper, we establish new conditions under which a sequence of real numbers has metric Poissonian pair correlation. Our conditions improve upon results of Aistleitner, El-Baz and Munsch, and resolve one of their open problems for sequences that grow faster than a quadratic polynomial. As applications, we show that quantitatively convex and polynomial sequences are metric Poissonian.

This https://arxiv.org/abs/2409.16556 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Twisted Roe algebras and their $K$-theory
In this paper, we introduce a notion of twisted Roe algebra and a twisted coarse Baum-Connes conjecture with coefficients. We will study the basic properties of twisted Roe algebras, including a coarse analogue of the imprimitivity theorem for metric spaces with a structure of coarse fibrations. We show that the twisted coarse Baum-Connes conjecture with coefficients holds for a metric space with a coarse fibration structure when the base space and the fiber satisfy the twisted coarse Baum-Conn…

Communication-Aware Map Compression for Online Path-Planning: A Rate-Distortion Approach
Ali Reza Pedram, Evangelos Psomiadis, Dipankar Maity, Panagiotis Tsiotras
https://arxiv.org/abs/2506.20579

Communication-Aware Map Compression for Online Path-Planning: A Rate-Distortion Approach
This paper addresses the problem of collaborative navigation in an unknown environment, where two robots, referred to in the sequel as the Seeker and the Supporter, traverse the space simultaneously. The Supporter assists the Seeker by transmitting a compressed representation of its local map under bandwidth constraints to support the Seeker's path-planning task. We introduce a bit-rate metric based on the expected binary codeword length to quantify communication cost. Using this metric, we for…

Charged rotating quantum black holes
Dyuman Bhattacharya, Robie A. Hennigar, Robert B. Mann, Ming Zhanga
https://arxiv.org/abs/2506.19941 https://

Charged rotating quantum black holes
We investigate the thermodynamic and holographic properties of charged and rotating quantum black holes in a doubly holographic braneworld setup. These quantum black holes are derived from the anti-de Sitter C-metric and are exact solutions to a semi-classical gravitational theory which incorporates all orders of the backreaction of quantum fields on spacetime. The inclusion of both charge and rotation extends and generalizes previous studies. The thermodynamics and critical behavior of the bla…

WattsOnAI: Measuring, Analyzing, and Visualizing Energy and Carbon Footprint of AI Workloads
Hongzhen Huang, Kunming Zhang, Hanlong Liao, Kui Wu, Guoming Tang
https://arxiv.org/abs/2506.20535

WattsOnAI: Measuring, Analyzing, and Visualizing Energy and Carbon Footprint of AI Workloads
The rapid advancement of AI, particularly large language models (LLMs), has raised significant concerns about the energy use and carbon emissions associated with model training and inference. However, existing tools for measuring and reporting such impacts are often fragmented, lacking systematic metric integration and offering limited support for correlation analysis among them. This paper presents WattsOnAI, a comprehensive software toolkit for the measurement, analysis, and visualization of …

General Proximal Quasi-Newton Methods based on model functions for nonsmooth nonconvex problems
Xiaoxi Jia, Peter Ochs
https://arxiv.org/abs/2507.18363 https://

General Proximal Quasi-Newton Methods based on model functions for nonsmooth nonconvex problems
In this manuscript, we propose a general proximal quasi-Newton method tailored for nonconvex and nonsmooth optimization problems, where we do not require the sequence of the variable metric (or Hessian approximation) to be uniformly bounded as a prerequisite, instead, the variable metric is updated by a continuous matrix generator. From the respective of the algorithm, the objective function is approximated by the so-called local model function and subproblems aim to exploit the proximal point(…

The metric system is 150 years old. The metre originated in the French Revolution, but its definition has changed many times since - ABC News https://www.abc.net.au/news/science/2025-05-20/metre-treaty-anniversary-met…

The metre originated in the French Revolution, but its definition has changed many times since
The next time you pick up a bag of spuds from the supermarket or fill up the car with petrol, you can thank a treaty signed in 1875 for the metric system that underpins daily life.

On the space of metrics with non-positive curvature
Yasha Savelyev
https://arxiv.org/abs/2506.19983 https://arxiv.org/pdf/2506.19983

On the space of metrics with non-positive curvature
Let $\mathcal{M} (X)$ denote the space of complete Riemannian metrics with non-positive sectional curvature and with negatively curved ends, on a manifold $X$. We show that $\mathcal{M} (\mathbb{R} \times S ^{1}) $ and $\mathcal{M} (\mathbb{R} ^{} \times Y)$ are path disconnected, where $Y$ is compact and admits a negative curvature metric. The proof is very concise, using as the main ingredient Fuller index theory. Furthermore, we get a new metric deformation invariant based on geodesic string…

On the Invariance of Expansive Measures for Flows
Eduardo Pedrosa, Elias Rego, Alexandre Trilles
https://arxiv.org/abs/2506.21533 https://

On the Invariance of Expansive Measures for Flows
We study expansive measures for continuous flows without fixed points on compact metric spaces, as introduced in [6]. We provide a new characterization of expansive measures through dynamical balls that, in contrast to the dynamical balls considered in [6], are actually Borel sets. This makes the theory more amenable to measure-theoretic analysis. We then establish a version of the Brin-Katok local entropy formula for flows using these generalized dynamical balls. As an application, we prove th…

This https://arxiv.org/abs/2505.06448 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDL_…

Gaming the Metrics? Bibliometric Anomalies and the Integrity Crisis in Global University Rankings
Global university rankings have transformed how certain institutions define success, often elevating metrics over meaning. This study examines universities with rapid research growth suggestive of metric-driven behaviors. Among the 1,000 most publishing institutions, 98 showed extreme output increases between 2018-2019 and 2023-2024. Of these, eighteen were selected for exhibiting sharp declines in first and corresponding authorship. Compared to national, regional, and international norms, thes…

On the local metric dimension of $K_5$-free graphs
Ali Ghalavand, Xueliang Li
https://arxiv.org/abs/2507.13752 https://arxiv.org/pdf/…

On the local metric dimension of $K_5$-free graphs
Let \( G \) be a graph with order \( n(G) \geq 5 \), local metric dimension \( \dim_l(G) \), and clique number \( ω(G) \). In this paper, we investigate the local metric dimension of \( K_5 \)-free graphs and prove that \( \dim_l(G) \leq \lfloor\frac{2}{3}n(G)\rfloor \) when \( ω(G) = 4 \). As a consequence of this finding, along with previous publications, we establish that if \( G \) is a \( K_5 \)-free graph, then \( \dim_l(G) \leq \lfloor\frac{2}{5}n(G)\rfloor \) when \( ω(G) = 2 \), \( …

Atomic Density Distributions in Proteins: Structural and Functional Implications
Sotirios Touliopoulos, Nicholas M. Glykos
https://arxiv.org/abs/2505.18566

Atomic Density Distributions in Proteins: Structural and Functional Implications
Atomic packing is an important metric for characterizing protein structures, as it significantly influences various features including the stability, the rate of evolution and the functional roles of proteins. Packing in protein structures is a measure of the overall proximity between the proteins' atoms and it can vary notably among different structures. However, even single domain proteins do not exhibit uniform packing throughout their structure. Many different methods have been used to me…

Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces
G\'abor Lugosi, Marcos Matabuena
https://arxiv.org/abs/2507.15741 h…

Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces
This paper introduces a framework for uncertainty quantification in regression models defined in metric spaces. Leveraging a newly defined notion of homoscedasticity, we develop a conformal prediction algorithm that offers finite-sample coverage guarantees and fast convergence rates of the oracle estimator. In heteroscedastic settings, we forgo these non-asymptotic guarantees to gain statistical efficiency, proposing a local $k$--nearest--neighbor method without conformal calibration that is ad…

Probing metric fluctuations with the spin of a particle: a quantum simulation with bimodal optical cavities
Jiannis K. Pachos, Patricio Salgado-Rebolledo, Martine Schut
https://arxiv.org/abs/2507.18351

Probing metric fluctuations with the spin of a particle: a quantum simulation with bimodal optical cavities
Exploring potential empirical manifestations of quantum gravity is a challenging pursuit. In this study, we utilise a lattice representation of a (2+1)D massive gravity toy model interacting with Dirac fermions that can support specific spacetime fluctuations. We focus on the evolution of the fermion's spin due to its coupling to spacetime fluctuations. To monitor their dynamics a minimal model is required that comprises two bosonic modes describing spacetime geometry fluctuations coupled with …

Replaced article(s) found for math.PR. https://arxiv.org/list/math.PR/new
[1/1]:
- Kesten's incipient infinite cluster for the three-dimensional, metric-graph Gaussian free field, ...
Pete Rigas

On Function-Correcting Codes in the Lee Metric
Gyanendra K. Verma, Abhay Kumar Singh
https://arxiv.org/abs/2507.17654 https://arxiv.org/pdf/2507.17654

On Function-Correcting Codes in the Lee Metric
Function-correcting codes are a coding framework designed to minimize redundancy while ensuring that specific functions or computations of encoded data can be reliably recovered, even in the presence of errors. The choice of metric is crucial in designing such codes, as it determines which computations must be protected and how errors are measured and corrected. Previous work by Liu and Liu [6] studied function-correcting codes over $\mathbb{Z}_{2^l},\ l\geq 2$ using the homogeneous metric, whi…

Replaced article(s) found for cs.PF. https://arxiv.org/list/cs.PF/new
[1/1]:
- Power-Capping Metric Evaluation for Improving Energy Efficiency in HPC Applications
Patrou, Wang, Elwasif, Eisenbach, Miller, Godoy, Hernandez

Subgraph Entropy
Tawfiq Ahmed, Tarik Aougab, Matt Clay
https://arxiv.org/abs/2506.18838 https://arxiv.org/pdf/2506.18838

Subgraph Entropy
Given $r \geq 3$, we prove that there exists $λ>0$ depending only on $r$ so that if $G$ is a metric graph of rank $r$ with metric entropy $1$, then there exists a proper subgraph $H$ of $G$ with metric entropy at least $λ$. This answers a question of the second two authors together with Rieck. We interpret this as a graph theoretic version of the Bers Lemma from hyperbolic geometry, and explain some connections to the pressure metric on the Culler-Vogtmann Outer Space.

Probabilistic Trajectory GOSPA: A Metric for Uncertainty-Aware Multi-Object Tracking Performance Evaluation
Yuxuan Xia, \'Angel F. Garc\'ia-Fern\'andez, Johan Karlsson, Yu Ge, Lennart Svensson, Ting Yuan
https://arxiv.org/abs/2506.15148

Probabilistic Trajectory GOSPA: A Metric for Uncertainty-Aware Multi-Object Tracking Performance Evaluation
This paper presents a generalization of the trajectory general optimal sub-pattern assignment (GOSPA) metric for evaluating multi-object tracking algorithms that provide trajectory estimates with track-level uncertainties. This metric builds on the recently introduced probabilistic GOSPA metric to account for both the existence and state estimation uncertainties of individual object states. Similar to trajectory GOSPA (TGOSPA), it can be formulated as a multidimensional assignment problem, and …

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Positive mass and isoperimetry for continuous metrics with nonnegative scalar curvature
Gioacchino Antonelli, Mattia Fogagnolo, Stefano Nardulli, Marco Pozzetta

$\mathbf{O}(D,D)$-Symmetric Box Operator and $\alpha^{\prime}$-Corrections with Riemann Curvature
Kawon Lee, Jeong-Hyuck Park
https://arxiv.org/abs/2506.21143

$\mathbf{O}(D,D)$-Symmetric Box Operator and $α^{\prime}$-Corrections with Riemann Curvature
Within the framework of Double Field Theory, we construct an $\mathbf{O}(D,D)$-symmetric d'Alembertian, or box operator, that is applicable to tensors of arbitrary rank. Parameterized by the Riemannian metric and the $B$-field, the operator naturally incorporates the Riemann curvature tensor and the $H$-flux. When applied to the massless string sector, it produces a consistent stringy wave equation under an $\mathbf{O}(D,D)$-symmetric harmonic gauge condition. Furthermore, the one-loop integral…

Quantum metric and localization in a quasicrystal
Quentin Marsal, Patric Holmvall, Annica M. Black-Schaffer
https://arxiv.org/abs/2506.15575 https://

Quantum metric and localization in a quasicrystal
We use the quantum metric to understand the properties of quasicrystals, represented by the one-dimensional (1D) Fibonacci chain. We show that the quantum metric can relate the localization properties of the eigenstates to the scale-invariance of both the chain and its energy spectrum. In particular, the quantum metric incorporates information about distances between the local symmetry centers of each eigenstate, making it much more sensitive to the localization properties of quasicrystals than…

Some Fixed Point Theorems in $(\alpha,\beta)$- Metric Spaces with applications to Fredholm integral and non-linear differential equations
Irfan Ahmed, Shallu Sharma, Sahil Billawria
https://arxiv.org/abs/2506.17225

Some Fixed Point Theorems in $(α,β)$- Metric Spaces with applications to Fredholm integral and non-linear differential equations
In this paper, we presented a new type of metric space called $(α,β)$-metric space along with some novel contraction mappings named $(α,β)$-contraction and weak $(α,β)$-contraction mapping. We established some fixed point theorem for these newly introduced contractive mappings. Our results extended some fixed point results in the existing literature. We also provide an example which holds for the weak $(α,β)$-contraction. Furthermore, we proved Kannan's fixed point theorem and Reich's f…

A real-time metric of online engagement monitoring
Laura J. Johnston, Jim E. Griffin, Ioanna Manolopoulou, Takoua Jendoubi
https://arxiv.org/abs/2507.12162

A real-time metric of online engagement monitoring
Measuring online behavioural student engagement often relies on simple count indicators or retrospective, predictive methods, which present challenges for real-time application. To address these limitations, we reconceptualise an existing course-wide engagement metric to create a chapter-based version that aligns with the weekly structure of online courses. Derived directly from virtual learning environment log data, the new metric allows for cumulative, real-time tracking of student activity w…

On the Dark-Energy Enigma
Ali H. Chamseddine, J\"urg Fr\"ohlich
https://arxiv.org/abs/2506.21099 https://arxiv.org/pdf/2506…

On the Dark-Energy Enigma
We present a model that offers an explanation for the presence of (Dark Matter and) Dark Energy in the universe. A key idea is to express the volume form of the Lorentzian metric on space-time in terms of a positive function of a new scalar field multiplying a certain four-form given by the wedge product of the differential of the mimetic scalar field and a certain closed three-form. An ansatz for this three-form related to one commonly used to determine the winding number of a map from a three…

Constructions and List Decoding of Sum-Rank Metric Codes Based on Orthogonal Spaces over Finite Fields
Xuemei Liu, Jiarong Zhang, Gang Wang
https://arxiv.org/abs/2507.16377 http…

Constructions and List Decoding of Sum-Rank Metric Codes Based on Orthogonal Spaces over Finite Fields
Sum-rank metric codes, as a generalization of Hamming codes and rank metric codes, have important applications in fields such as multi-shot linear network coding, space-time coding and distributed storage systems. The purpose of this study is to construct sum-rank metric codes based on orthogonal spaces over finite fields, and calculate the list sizes outputted by different decoding algorithms. The following achievements have been obtained. In this study, we construct a cyclic orthogonal grou…

DMOSpeech 2: Reinforcement Learning for Duration Prediction in Metric-Optimized Speech Synthesis
Yinghao Aaron Li, Xilin Jiang, Fei Tao, Cheng Niu, Kaifeng Xu, Juntong Song, Nima Mesgarani
https://arxiv.org/abs/2507.14988

DMOSpeech 2: Reinforcement Learning for Duration Prediction in Metric-Optimized Speech Synthesis
Diffusion-based text-to-speech (TTS) systems have made remarkable progress in zero-shot speech synthesis, yet optimizing all components for perceptual metrics remains challenging. Prior work with DMOSpeech demonstrated direct metric optimization for speech generation components, but duration prediction remained unoptimized. This paper presents DMOSpeech 2, which extends metric optimization to the duration predictor through a reinforcement learning approach. The proposed system implements a nove…

DESIgning concordant distances in the age of precision cosmology: the impact of density fluctuations
David Camarena, Kylar Greene, John Houghteling, Francis-Yan Cyr-Racine
https://arxiv.org/abs/2507.17969

DESIgning concordant distances in the age of precision cosmology: the impact of density fluctuations
Discrepancies between distance measurements and $Λ$CDM predictions reveal notable features in the distance-redshift relation, possibly suggesting the presence of an evolving dark energy component. Given the central role of the Friedmann-Lemaître-Robertson-Walker (FLRW) metric in modeling cosmological distances, we investigate here whether these features instead point to a possible departure from the fundamental FLRW symmetries. Exploiting the transverse and line-of-sight distances provided by…

Inexact Levenberg-Marquardt methods under H\"{o}lder metric subregularity
Bas Symoens, Morteza Rahimi, Masoud Ahookhosh
https://arxiv.org/abs/2507.16461

Inexact Levenberg-Marquardt methods under Hölder metric subregularity
This paper investigates two inexact Levenberg-Marquardt (LM) methods for solving systems of nonlinear equations. Both approaches compute approximate search directions by solving the LM linear system inexactly, subject to specific residual-based conditions. The first method uses an adaptive scheme to update the LM parameter, and we establish its local superlinear convergence under Hölder metric subregularity and local Hölder continuity of the gradient. The second method combines an inexact LM …

Characterisation of the signal to noise ratio of 2-photon microscopes
Radek Mach\'a\v{n}, Shau Poh Chong, Khee Leong Lee, Peter T\"or\"ok
https://arxiv.org/abs/2507.18191

Characterisation of the signal to noise ratio of 2-photon microscopes
Signal to noise ratio (SNR) is a key performance metric of an imaging instrument. Here we describe characterisation of SNR of a custom 2-photon microscope and compare the SNR performance of our microscope with selected commercial 2-photon microscopes. The methodology described in this paper can serve as guidance for others wishing to characterise and benchmark their 2-photon or other point-scanning microscopes.

Intertwining local (adjacency) metric dimension with the clique number of a graph
Ali Ghalavand, Sandi Klav\v{z}ar, Xueliang Li
https://arxiv.org/abs/2507.13777

Intertwining local (adjacency) metric dimension with the clique number of a graph
Let $G$ be a simple connected graph with order $ n(G)$, local metric dimension $ {\rm dim}_l(G)$, local adjacency metric dimension $ {\rm dim}_{A,l}(G)$, and clique number $ ω(G)$, where $G\not\cong K_{n(G)}$ and $ω(G)\geq3$. It is proved that $ {\rm dim}_{A,l}(G) \leq \left\lfloor \left(\frac{ω(G) - 2}{ω(G) - 1}\right)n(G)\right\rfloor$. Consequently, the conjecture asserting that the latter expression is an upper bound for ${\rm dim}_l(G)$ is confirmed. It is important to note that there …

An ergodic Lebesgue differentiation theorem
Aidan Young
https://arxiv.org/abs/2506.21421 https://arxiv.org/pdf/2506.21421

An ergodic Lebesgue differentiation theorem
We show that if $(X, μ, T)$ is a probability measure-preserving dynamical system, and $\mathscr{P}$ is a countable partition of $(X, μ)$, then the limit $$ \lim_{n, k \to \infty} \mathbb{E} \left[ \frac{1}{k} \sum_{j = 0}^{k - 1} f \circ T^j \mid \bigvee_{i = 0}^{n - 1} T^{-i} \mathscr{P} \right] $$ exists almost surely for all $f \in L^p(μ), p > 1$. We prove this as a corollary of a geometric result: that if $(X, μ)$ is a metric measure space on which the Hardy-Littlewood maximal inequalit…

Eigenfunction asymptotics in the complex domain for a compact Lie group
Simone Gallivanone, Roberto Paoletti
https://arxiv.org/abs/2507.18285 https://arxiv…

Eigenfunction asymptotics in the complex domain for a compact Lie group
Let $(G,κ)$ be a compact connected Lie group endowed with a biinvariant Riemannian metric, and let $\tilde{G}$ be the complexification of $G$. We apply Grauert tube techniques to the near-diagonal scaling asymptotics of certain operator kernels, which are defined in terms of the matrix elements of an irreducuble representation drifting to infinity along a ray in weight space. These kernels are the equivariant components of Poisson and Szegő kernels on a fixed sphere bundle in $\tilde{G}$, whe…

A Computationally Aware Multi Objective Framework for Camera LiDAR Calibration
Venkat Karramreddy, Rangarajan Ramanujam
https://arxiv.org/abs/2506.20636 ht…

A Computationally Aware Multi Objective Framework for Camera LiDAR Calibration
Accurate extrinsic calibration between LiDAR and camera sensors is important for reliable perception in autonomous systems. In this paper, we present a novel multi-objective optimization framework that jointly minimizes the geometric alignment error and computational cost associated with camera-LiDAR calibration. We optimize two objectives: (1) error between projected LiDAR points and ground-truth image edges, and (2) a composite metric for computational cost reflecting runtime and resource usa…

Understanding the Theoretical Guarantees of DPM
Yara Sch\"utt, Esfandiar Mohammadi
https://arxiv.org/abs/2506.18685 https://arxi…

Understanding the Theoretical Guarantees of DPM
In this study, we conducted an in-depth examination of the utility analysis of the differentially private mechanism (DPM). The authors of DPM have already established the probability of a good split being selected and of DPM halting. In this study, we expanded the analysis of the stopping criterion and provided an interpretation of these guarantees in the context of realistic input distributions. Our findings revealed constraints on the minimum cluster size and the metric weight for the scoring…

The Combinatorial Rank of Subsets: Metric Density in Finite Hamming Spaces
Jamolidin K. Abdurakhmanov
https://arxiv.org/abs/2506.13081 https://

The Combinatorial Rank of Subsets: Metric Density in Finite Hamming Spaces
We introduce a novel concept of rank for subsets of finite metric spaces E^n_q (the set of all n-dimensional vectors over an alphabet of size q) equipped with the Hamming distance, where the rank R(A) of a subset A is defined as the number of non-constant columns in the matrix formed by the vectors of A. This purely combinatorial definition provides a new perspective on the structure of finite metric spaces, distinct from traditional linear-algebraic notions of rank. We establish tight bounds f…

L-CLIPScore: a Lightweight Embedding-based Captioning Metric for Evaluating and Training
Li Li, Yingzhe Peng, Xu Yang, Ruoxi Cheng, Haiyang Xu, Ming Yan, Fei Huang
https://arxiv.org/abs/2507.08710

L-CLIPScore: a Lightweight Embedding-based Captioning Metric for Evaluating and Training
We propose a novel embedding-based captioning metric termed as L-CLIPScore that can be used for efficiently evaluating caption quality and training captioning model. L-CLIPScore is calculated from a lightweight CLIP (L-CLIP), which is a dual-encoder architecture compressed and distilled from CLIP. To compress, we apply two powerful techniques which are weight multiplexing and matrix decomposition for reducing the parameters of encoders and word embedding matrix, respectively. To distill, we des…

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- On the geometry of synthetic null hypersurfaces
Fabio Cavalletti, Davide Manini, Andrea Mondino

Holomorphic Unified Field Theory of Gravity and the Standard Model
John. W. Moffat, Ethan. J. Thompson
https://arxiv.org/abs/2506.19161 https://

Holomorphic Unified Field Theory of Gravity and the Standard Model
We present a holomorphic framework in which gravity, gauge interactions, and their couplings to charges and currents emerge from a single geometric action on a four-complex-dimensional manifold. The Hermitian metric yields on the real slice $y^μ= 0$, a real symmetric metric $g_{(μν)}$ giving the vacuum Einstein equations, and an antisymmetric part $g_{[μν]}$ that reproduces Maxwell's equations with sources. A single holomorphic gauge connection for $G_{\text{GUT}}$, such as $SU(5)$ or $SO(…

The Alpha Group Tensorial Metric
Cleber Souza Correa, Thiago Braido Nogueira de Melo, Diogo Machado Cust\'odio
https://arxiv.org/abs/2507.16954 https://

The Alpha Group Tensorial Metric
The Alpha Group is an abstract geometry group in $\mathbb{R}^4$. The way it was conceived allows a new interpretation of the structure of hypercomplex space, with a new geometry and spatial topology, and a meaning for the geometric representation of $\mathbb{R}^4$ space to infinity. Therefore, it has been described as the tensorial metric formula in the Alpha Group. It will be shown that the Riemannian and Euclidean distance metrics between infinitesimal surfaces are represented as special case…

Compatibility of Max and Sum Objectives for Committee Selection and $k$-Facility Location
Yue Han, Elliot Anshelevich
https://arxiv.org/abs/2507.17063 https://

Compatibility of Max and Sum Objectives for Committee Selection and $k$-Facility Location
We study a version of the metric facility location problem (or, equivalently, variants of the committee selection problem) in which we must choose $k$ facilities in an arbitrary metric space to serve some set of clients $C$. We consider four different objectives, where each client $i\in C$ attempts to minimize either the sum or the maximum of its distance to the chosen facilities, and where the overall objective either considers the sum or the maximum of the individual client costs. Rather than…

Exact vacuum solution with Hopf structure in general relativity
Junpei Harada
https://arxiv.org/abs/2506.20878 https://arxiv.org/pdf/…

Exact vacuum solution with Hopf structure in general relativity
An exact solution to the vacuum Einstein equations is presented, whose structure is based on the Hopf fibration. The solution employs a geodesic null vector field that defines a twisting congruence and appears in the metric in Kerr-Schild form. This solution is of Petrov type D and involves two parameters. Remarkably, the resulting spacetime is regular, with no curvature singularities. Both the Kretschmann scalar and the Chern-Pontryagin scalar are nonzero and remain finite throughout the space…

Parallel Ray Tracing of Black Hole Images Using the Schwarzschild Metric
Liam Naddell, Marcelo Ponce
https://arxiv.org/abs/2507.16165 https://

Parallel Ray Tracing of Black Hole Images Using the Schwarzschild Metric
Rendering images of black holes by utilizing ray tracing techniques is a common methodology employed in many aspects of scientific and astrophysical visualizations. Similarly, general ray tracing techniques are widely used in areas related to computer graphics. In this work we describe the implementation of a parallel open-source program that can ray trace images in the presence of a black hole geometry. We do this by combining a couple of different techniques usually present in parallel scient…

AbRank: A Benchmark Dataset and Metric-Learning Framework for Antibody-Antigen Affinity Ranking
Chunan Liu, Aurelien Pelissier, Yanjun Shao, Lilian Denzler, Andrew C. R. Martin, Brooks Paige, Mariia Rodriguez Martinez
https://arxiv.org/abs/2506.17857

AbRank: A Benchmark Dataset and Metric-Learning Framework for Antibody-Antigen Affinity Ranking
Accurate prediction of antibody-antigen (Ab-Ag) binding affinity is essential for therapeutic design and vaccine development, yet the performance of current models is limited by noisy experimental labels, heterogeneous assay conditions, and poor generalization across the vast antibody and antigen sequence space. We introduce AbRank, a large-scale benchmark and evaluation framework that reframes affinity prediction as a pairwise ranking problem. AbRank aggregates over 380,000 binding assays from…

Embedding $\mathrm{SL}(2,\mathbb{C})/\mathbb{Z}_2$ in Complex Riemannian Geometry
John. W. Moffat, Ethan. J. Thompson
https://arxiv.org/abs/2506.19158 http…

Embedding $\mathrm{SL}(2,\mathbb{C})/\mathbb{Z}_2$ in Complex Riemannian Geometry
We present a unified framework demonstrating how the spinor complex Lorentz group SL(2,C)/Z\_2 is realized as a canonical subgroup within a four-dimensional complex Riemannian manifold. Building on the complex, holomorphic metric extension and contour-integration regularization of classical singularities, we show that promoting the metric to a complex-valued tensor on a complex 4-fold enlarges the frame bundle to SO(4,C). Its spin double cover factorizes as a product of two independent SL(2,C) …

Maximal inequalities for square functions associated to group metric measure spaces
Panchugopal Bikram, Diptesh Saha
https://arxiv.org/abs/2506.18589 https…

Maximal inequalities for square functions associated to group metric measure spaces
In this article, we establish weighted strong and weak type inequalities for non-commutative square functions associated with the differences of ball averages and martingales over group metric measure spaces. These results generalise the main outcome of \cite{saha-rayweighted}.

The distance function and Lipschitz classes of mappings between metric spaces
Marijan Markovic
https://arxiv.org/abs/2507.14508 https://

The distance function and Lipschitz classes of mappings between metric spaces
We investigate when the local Lipschitz property of the real-valued function $g(z) = d_Y (f(z),A)$ implies the global Lipschitz property of the mapping $f:X\to Y$ between the metric spaces $(X,d_X)$ and $(Y,d_Y)$. Here, $d_Y(y,A)$ denotes the distance of $y\in Y$ from the non-empty set $\subseteq Y$. As a consequence, we find that an analytic function on a uniform domain of a normed space belongs to the Lipschitz class if and only if its modulus satisfies the same condition; in the case of the …

Hair imprints of the gravitational decoupling and hairy black hole spectroscopy
V. F. Guimar\~aes, R. T. Cavalcanti, R. da Rocha
https://arxiv.org/abs/2506.20044

Hair imprints of the gravitational decoupling and hairy black hole spectroscopy
Hairy black holes by gravitational decoupling (GD) are probed to derive the gravitational waveform produced by perturbation theory applied to these compact objects. Using the Regge-Wheeler and Zerilli equations governing the metric perturbations and applying a higher-order WKB method, the quasinormal modes (QNMs) are computed and discussed. Compared to the QNMs produced in the ringdown phase of Reissner-Nordström black hole solutions, it yields a clear physical signature of primary hair imprin…

Asymptotic analysis and design of linear elastic shell lattice metamaterials
Di Zhang, Ligang Liu
https://arxiv.org/abs/2506.18910 https://

Asymptotic analysis and design of linear elastic shell lattice metamaterials
We present an asymptotic analysis of shell lattice metamaterials based on Ciarlet's shell theory, introducing a new metric--asymptotic directional stiffness (ADS)--to quantify how the geometry of the middle surface governs the effective stiffness. We prove a convergence theorem that rigorously characterizes ADS and establishes its upper bound, along with necessary and sufficient condition for achieving it. As a key result, our theory provides the first rigorous explanation for the high bulk mod…

Hybrid thermalization in the large $N$ limit
Toshali Mitra, Sukrut Mondkar, Ayan Mukhopadhyay, Alexander Soloviev
https://arxiv.org/abs/2506.20715 https://…

Hybrid thermalization in the large $N$ limit
Semi-holography provides a formulation of dynamics in gauge theories involving both weakly self-interacting (perturbative) and strongly self-interacting (non-perturbative) degrees of freedom. These two subsectors interact via their effective metrics and sources, while the full local energy-momentum tensor is conserved in the physical background metric. In the large $N$ limit, the subsectors have their individual entropy currents, and so the full system can reach a pseudo-equilibrium state in wh…

Analytic Theory on the Space of Blaschke Products: Simultaneous Uniformization and Pressure Metric
Yan Mary He, Homin Lee, Insung Park
https://arxiv.org/abs/2507.17077 https://

Analytic Theory on the Space of Blaschke Products: Simultaneous Uniformization and Pressure Metric
In this paper, we study complex analytic aspects of the moduli space $\Bcal_d^{fm}$ of degree $d\ge2$ fixed-point-marked Blaschke products. We define a complex structure on $\Bcal_d^{fm}$ and prove the simultaneous uniformization theorem for fixed-point-marked quasi-Blaschke products. As an application, we show that the pressure semi-norms on the space of Blaschke products are non-degenerate outside of the super-attracting locus $\mathcal{SA}^{fm}_d$, which is a codimension-1 subspace of $\Bcal…

[2025-06-27 Fri (UTC), 3 new articles found for math.MG Metric Geometry]
toXiv_bot_toot

Monocular One-Shot Metric-Depth Alignment for RGB-Based Robot Grasping
Teng Guo, Baichuan Huang, Jingjin Yu
https://arxiv.org/abs/2506.17110 https://

Monocular One-Shot Metric-Depth Alignment for RGB-Based Robot Grasping
Accurate 6D object pose estimation is a prerequisite for successfully completing robotic prehensile and non-prehensile manipulation tasks. At present, 6D pose estimation for robotic manipulation generally relies on depth sensors based on, e.g., structured light, time-of-flight, and stereo-vision, which can be expensive, produce noisy output (as compared with RGB cameras), and fail to handle transparent objects. On the other hand, state-of-the-art monocular depth estimation models (MDEMs) provid…

Laboratory Frame Representation for General High-Frequency Gravitational Waveforms
Lars Fischer, Tom Krokotsch, Gudrid Moortgat-Pick
https://arxiv.org/abs/2506.20198

Laboratory Frame Representation for General High-Frequency Gravitational Waveforms
Next-generation gravitational wave (GW) experiments will explore higher frequency ranges, where GW wavelengths approach the size of the detector itself. In this regime, GWs may be detected not just through the well-known mechanical deformation by tidal forces but also via induced effective currents in electromagnetic background fields. However, the calculation of this signal requires the GW metric in laboratory coordinates of the detector, and an accurate transformation to all orders into this …

[2025-06-26 Thu (UTC), no new articles found for math.MG Metric Geometry]
toXiv_bot_toot

Notes on the uniqueness of Type II Yamabe metrics
Shota Hamanaka, Pak Tung Ho
https://arxiv.org/abs/2506.17876 https://arxiv.org/pdf/…

Notes on the uniqueness of Type II Yamabe metrics
In this paper, we study the uniqueness of type II Yamabe metrics in conformal classes on a compact connected manifold with boundary, and we investigate Obata-type theorems for type II Yamabe metrics. In particular, we establish a theorem which gives a sufficient condition for a metric to be the unique Type II Yamabe metric in its conformal class. We also prove the corresponding theorem for the CR Yamabe problem on closed manifolds.

The model theory of metric lattices: pseudofinite partition lattices
Jos\'e Contreras Mantilla, Thomas Sinclair
https://arxiv.org/abs/2507.10932 https:…

The model theory of metric lattices: pseudofinite partition lattices
We initiate the study of general metric lattices in the context of the model theory of metric structures. As an application we develop a theory of pseudo-finite limits of partition lattices and connect this theory with the theory of continuous limits of partition lattices due to Björner and Lovász.

On the Age of Information in Single-Server Queues with Aged Updates
Fernando Miguelez, Urtzi Ayesta, Josu Doncel, Maria Dolores Ugarte
https://arxiv.org/abs/2506.19648

On the Age of Information in Single-Server Queues with Aged Updates
The Age of Information (AoI) is a performance metric that quantifies the freshness of data in systems where timely updates are critical. Most state-of-the-art methods typically assume that packets enter the monitored system with zero age, neglecting situations, such as those prevalent in multi-hop networks or distributed sensing, where packets experience prior delays. In this paper, the AoI is investigated when packets have a non-zero initial age. We derive an expression for the average AoI in …

DRIVE Through the Unpredictability:From a Protocol Investigating Slip to a Metric Estimating Command Uncertainty
Nicolas Samson, William Larriv\'ee-Hardy, William Dubois, \'Elie Roy-Brouard, Edith Brotherton, Dominic Baril, Julien L\'epine, Fran\c{c}ois Pomerleau
https://arxiv.org/abs/2506.16593

DRIVE Through the Unpredictability:From a Protocol Investigating Slip to a Metric Estimating Command Uncertainty
Off-road autonomous navigation is a challenging task as it is mainly dependent on the accuracy of the motion model. Motion model performances are limited by their ability to predict the interaction between the terrain and the UGV, which an onboard sensor can not directly measure. In this work, we propose using the DRIVE protocol to standardize the collection of data for system identification and characterization of the slip state space. We validated this protocol by acquiring a dataset with two…

Quantum optical model of an artificial neuron
Vivek Mehta, Utpal Roy
https://arxiv.org/abs/2507.17349 https://arxiv.org/pdf/2507.17349

Quantum optical model of an artificial neuron
Magnini \emph{et al.} [\emph{Mach. Learn.: Sci. Technol. 1 (2020) 045008}] recently introduced a qubit-based model of an artificial neuron, along with its applications. The design of its quantum circuit is pivotal for effective implementation. In this context, we present two quantum circuit synthesis algorithms tailored for the realisation of the quantum neuron. Comprehensive circuit simulations are conducted, and the resulting performance is assessed using the circuit cost metric. Additionally…

Coarse Separation of Coarse PD(n) spaces
Harsh Patil
https://arxiv.org/abs/2506.21492 https://arxiv.org/pdf/2506.21492

Coarse Separation of Coarse PD(n) spaces
We show that if a subspace $A$ of a coarse $PD(n)$ metric space $X$ coarsely separates it, then it must have asymptotic dimension at least $n-1$.

Unsupervised Ground Metric Learning
Janis Auffenberg, Jonas Bresch, Oleh Melnyk, Gabriele Steidl
https://arxiv.org/abs/2507.13094 https://

Unsupervised Ground Metric Learning
Data classification without access to labeled samples remains a challenging problem. It usually depends on an appropriately chosen distance between features, a topic addressed in metric learning. Recently, Huizing, Cantini and Peyré proposed to simultaneously learn optimal transport (OT) cost matrices between samples and features of the dataset. This leads to the task of finding positive eigenvectors of a certain nonlinear function that maps cost matrices to OT distances. Having this basic ide…

On the relation between distances and seminorms on Fr\'echet spaces, with application to isometries
Isabelle Chalendar, Lucas Oger, Jonathan R. Partington
https://arxiv.org/abs/2506.16801

On the relation between distances and seminorms on Fréchet spaces, with application to isometries
A study is made of linear isometries on Fréchet spaces for which the metric is given in terms of a sequence of seminorms. This establishes sufficient conditions on the growth of the function that defines the metric in terms of the seminorms to ensure that a linear operator preserving the metric also preserves each of these seminorms. As an application, characterizations are given of the isometries on various spaces including those of holomorphic functions on complex domains and continuous func…

Optical Billiards
Sylvie Oliffson Kamphorst, S\^onia Pinto-de-Carvalho, C\'assio Henrique Vieira Morais
https://arxiv.org/abs/2507.18367 https://arxiv.…

Optical Billiards
This paper investigates the dynamics of optical billiards, a generalization of classic billiards, where light rays travel within a refractive medium and reflect elastically at the boundary. Inspired by studies of acoustic modes in rapidly rotating stars, optical billiards are approached using Riemannian geometry, treating the refractive index as a metric. The discrete dynamics is explored through geodesics, curvature properties, highlighting similarities and differences with classical billiards…

Multiset Metric Dimension of Binomial Random Graphs
Austin Eide, Pawel Pralat
https://arxiv.org/abs/2507.11686 https://arxiv.org/pdf/…

Multiset Metric Dimension of Binomial Random Graphs
For a graph $G = (V,E)$ and a subset $R \subseteq V$, we say that $R$ is \textit{multiset resolving} for $G$ if for every pair of vertices $v,w$, the \textit{multisets} $\{d(v,r): r \in R\}$ and $\{d(w,r):r \in R\}$ are distinct, where $d(x,y)$ is the graph distance between vertices $x$ and $y$. The \textit{multiset metric dimension} of $G$ is the size of a smallest set $R \subseteq V$ that is multiset resolving (or $\infty$ if no such set exists). This graph parameter was introduced by Simanju…

Positive intermediate Ricci curvature on cohomogeneity one manifolds in low dimensions
Elahe Khalili Samani, Lawrence Mouill\'e
https://arxiv.org/abs/2507.17920 https://

Positive intermediate Ricci curvature on cohomogeneity one manifolds in low dimensions
We explore existence of invariant metrics with positive intermediate Ricci curvature on closed, low-dimensional cohomogeneity one manifolds. For a certain cohomogeneity one $\mathsf{Spin}(4)$-action on $S^3 \times \mathbb{C}\mathrm{P}^2$, we construct an invariant metric with positive $4$-intermediate Ricci curvature and show it cannot admit one with positive $3$-intermediate Ricci curvature. We establish similar obstructions for several other cohomogeneity one manifolds.

Effective action of bosonic string theory at order $\alpha'^3$
Mehdi Ameri, Alireza Pahlavan, Mohammad R. Garousi
https://arxiv.org/abs/2506.19471 http…

Effective action of bosonic string theory at order $α'^3$
In this work, we derive the classical effective action of bosonic string theory at order $α'^{3}$ for the metric, Kalb-Ramond field, and dilaton by imposing a higher-derivative extension of the Buscher rules on the circular reduction of the minimal basis at this order, in the schemes where their corresponding actions at order $α'$ are the Meissner and the Metsaev-Tseytlin schemes. We find that T-duality fixes all coupling constants in terms of the known overall factor at order $α'$ and a sin…

Well-posed geometric boundary data in General Relativity, III: conformal-volume boundary data
Zhongshan An, Michael T. Anderson
https://arxiv.org/abs/2507.15567

Well-posed geometric boundary data in General Relativity, III: conformal-volume boundary data
In this third work in a series, we prove the local-in-time well-posedness of the IBVP for the vacuum Einstein equations in general relativity with twisted DIrichlet boundary conditions on a finite timelike boundary. The boundary conditions consist of specification of the pointwise conformal class of the boundary metric, together with a scalar density involving a combination of the volume form of the bulk metric restricted to the boundary together with the volume form of the boundary metric itse…

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- The $m$th order Orlicz projection bodies
Xia Zhou, Deping Ye, Zengle Zhang

Supersymmetry and integrability of the elliptic $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{T}^4$ superstring
Ben Hoare, Fiona K. Seibold
https://arxiv.org/abs/2507.18548

Supersymmetry and integrability of the elliptic $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{T}^4$ superstring
We construct a 1-parameter family of Ramond-Ramond fluxes supporting the elliptic $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{T}^4$ metric with constant dilaton and preserving 8 of the 16 supercharges of the undeformed background. On the supersymmetric locus, we compute the tree-level worldsheet S-matrix in uniform light-cone gauge up to quadratic order in fermions and find that it non-trivially satisfies the classical Yang-Baxter equation. Moreover, imposing classical integrability and …

Discrimination of metric theories
F. J. Lobo, M. Rivera-Tapia, G. Rubilar, O. Jim\'enez, A. Delgado
https://arxiv.org/abs/2506.12243 https://

Discrimination of metric theories
We study the possibility of discriminating between metric theories within the Parametrized Post-Newtonian formalism. In this approach, the two-dimensional quantum state of a massive quantum clock becomes, after propagating at low speed and in a weak gravitational field, a function of the post-Newtonian parameters and thus a signature of a metric theory. To discriminate among metric theories, we resort to quantum-state discrimination strategies such as minimum error and unambiguous state discrim…

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Discrete Laplacians -- spherical and hyperbolic
Ivan Izmestiev, Wai Yeung Lam

Integral gradient estimates on a closed surface
Yuxiang Li, Rongze Sun
https://arxiv.org/abs/2507.12790 https://arxiv.org/pdf/2507.12…

Integral gradient estimates on a closed surface
Let $(Σ, g)$ be a closed Riemann surface, and let $u$ be a weak solution to equation \[ - Δ_g u = μ, \] where $μ$ is a signed Radon measure. We aim to establish $L^p$ estimates for the gradient of $u$ that are independent of the choice of the metric $g$. This is particularly relevant when the complex structure approaches the boundary of the moduli space. To this end, we consider the metric $g' = e^{2u} g$ as a metric of bounded integral curvature. This metric satisfies a so-called quadratic…

Graviton scattering on self-dual black holes
Tim Adamo, Giuseppe Bogna, Lionel Mason, Atul Sharma
https://arxiv.org/abs/2507.18605 https://arxiv.org/pdf/25…

Graviton scattering on self-dual black holes
The computation of gravitational wave scattering on black hole spacetimes is an extremely hard problem, typically requiring approximation schemes which either treat the black hole perturbatively or are only amenable to numerical techniques. In this paper, we consider linearised gravitational waves (or gravitons) scattering on the self-dual analogue of a black hole: namely, the self-dual Taub-NUT metric. Using the hidden integrability of the self-dual sector, we can solve the linearised Einstein…

LQG inspired spacetimes as solutions of the Einstein equations
Marcos V. de S. Silva, Carlos F. S. Pereira, G. Alencar, Celio R. Muniz
https://arxiv.org/abs/2506.19818

LQG inspired spacetimes as solutions of the Einstein equations
Black bounces are compact objects with a wormhole structure hidden behind an event horizon. This type of metric can be obtained through general relativity by considering the presence of exotic matter. Such spacetimes can also arise within the framework of effective theories inspired by loop quantum gravity. In this work, we verify the possibility of obtaining black bounce models inspired by loop quantum gravity as solutions of general relativity. For this, we examine which sources can generate …

The infinitesimal structure of manifolds with non-continuous Riemannian metrics
Vanessa Ryborz
https://arxiv.org/abs/2507.14726 https://

The infinitesimal structure of manifolds with non-continuous Riemannian metrics
This paper investigates the failure of certain metric measure spaces to be infinitesimally Hilbertian or quasi-Riemannian manifolds, by constructing examples arising from a manifold $M$ endowed with a Riemannian metric $g$ that is possibly discontinuous, with $g, g^{-1} \in L^\infty_{\mathrm{loc}} $ and $ g \in W^{1,p}_{\mathrm{loc}}$ for $ p < \mathrm{dim} M - 1 $.

Gravitational wave propagation in hybrid metric-Palatini gravity
Cl\'audio Gomes, Jo\~ao Lu\'is Rosa, Miguel A. S. Pinto
https://arxiv.org/abs/2506.12870

Gravitational wave propagation in hybrid metric-Palatini gravity
In this work we analyze the propagation properties of gravitational waves in the hybrid metric-Palatini gravity theory. We introduce the scalar-tensor representation of the theory to make explicit the scalar degrees of freedom of the theory and obtain their equations of motion in a form decoupled from the metric tensor. Then, we introduce linear perturbations for the metric tensor and for the two scalar fields and obtain the propagation equations for these three quantities. We analyzed the theo…

Vanishing Metric Commutation Relation and Higher-derivative De Donder Gauge in Quadratic Gravity
Ichiro Oda
https://arxiv.org/abs/2507.10712 https://

Vanishing Metric Commutation Relation and Higher-derivative De Donder Gauge in Quadratic Gravity
We show that the equal-time commutation relations (ETCRs) among the time derivatives of the metric tensor identically vanish in the higher-derivative de Donder gauge as well as the conventional de Donder gauge (or harmonic gauge) for general coordinate invariance in the manifestly covariant canonical operator formalism of quadratic gravity. These ETCRs provide us with the vanishing four-dimensional commutation relation, which implies that the metric tensor behaves as if it were not a quantum op…

Emergent field theory
Erick I. Duque
https://arxiv.org/abs/2507.16163 https://arxiv.org/pdf/2507.16163…

Emergent field theory
The uniqueness theorems for general relativity and Yang-Mills theories can be circumvented by dropping the ubiquitous, yet often implicit, assumption that physical fields, such as the spacetime metric, are fundamental. The novel concept of emergent fields makes it possible to construct modified theories of gravity and forces where the spacetime metric and strength tensor fields emerge from a covariance analysis in the canonical formulation with nontrivial relations to the fundamental phase spac…

[2025-07-25 Fri (UTC), 1 new article found for math.MG Metric Geometry]
toXiv_bot_toot

[2025-06-25 Wed (UTC), 4 new articles found for math.MG Metric Geometry]
toXiv_bot_toot

Exploring Entanglement Entropy for a Particle on a Torus with constant Metric and constant $U(1)$-Gauge Field
Helmuth Huffel, Gerald Kelnhofer
https://arxiv.org/abs/2506.11292

Exploring Entanglement Entropy for a Particle on a Torus with constant Metric and constant $U(1)$-Gauge Field
In this paper, we focus on the entanglement entropy associated with a particle confined to a torus with constant metric and $θ$-terms related to a constant external $U(1)$-gauge field. Through this investigation, we aim to elucidate the interplay between geometric properties, topological terms, and entanglement entropy. Remarkably, we find that the presence of non-vanishing entanglement entropy is closely tied to fixing the metric. This insight highlights the significant influence of quantum e…

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Non-collapsed spaces with Ricci curvature bounded from below
Guido De Philippis, Nicola Gigli