Tootfinder

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.

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…

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…

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…

Moving Beyond Marginal Carbon Intensity: A Poor Metric for Both Carbon Accounting and Grid Flexibility
Philipp Wiesner, Odej Kao
https://arxiv.org/abs/2507.11377

Moving Beyond Marginal Carbon Intensity: A Poor Metric for Both Carbon Accounting and Grid Flexibility
Marginal Carbon Intensity (MCI) has been promoted as an effective metric for carbon-aware computing. Although it is already considered as impractical for carbon accounting purposes, many still view it as valuable when optimizing for grid flexibility by incentivizing electricity usage during curtailment periods. In this statement paper, we argue that MCI is neither reliable nor actionable for either purpose. We outline its fundamental limitations, including non-observability, reliance on opaque …

Amazon's 2024 sustainability report says it emitted 68.25M metric tons of carbon dioxide equivalent, up 6% from 2023 and the first rise in three years (Matt Day/Bloomberg)
https://www.bloomberg.com/news/articles/2025-07-16/a…

Amazon’s (AMZN) Carbon Emissions Climbed 6% in 2024 on Data Center Buildout
Amazon.com Inc.’s carbon emissions rose for the first time in three years in 2024, driven by data center construction and fuel consumption by its delivery providers.

Decay of dark energy into dark matter in a metric $f(R)$ gravity: effective running Hubble constant
Giovanni Montani, Mariaveronica De Angelis, Maria Giovanna Dainotti
https://arxiv.org/abs/2506.13288

Decay of dark energy into dark matter in a metric $f(R)$ gravity: effective running Hubble constant
We examine a modified late-Universe dynamics where dark energy decays into dark matter, within the framework of metric $f(R)$-gravity in the Jordan frame. After a detailed analysis of the modified $Λ\text{CDM}$ model, we introduce a theoretical diagnostic tool to capture the emergence of an effective running Hubble constant as a function of redshift. We then compare this theoretical model with the 40-bin analysis of the Supernova Pantheon sample. This comparison allows us to determine the valu…

Rank metric isometries and determinant-preserving mappings on II$_1$-factors
Jinghao Huang, Karimbergen Kudaybergenov, Fedor Sukochev
https://arxiv.org/abs/2506.11428

Rank metric isometries and determinant-preserving mappings on II$_1$-factors
We fully describe the general form of a linear (or conjugate-linear) rank metric isometry on the Murray--von Neumann algebra associated with a II$_1$-factor. As an application, we establish Frobenius' theorem in the setting of II$_1$-factors, by showing that every determinant-preserving linear bijection between two II$_1$-factors is necessarily an isomorphism or an anti-isomorphism. This confirms the Harris--Kadison conjecture (1996).

Poisson-type problems with transmission conditions at boundaries of infinite metric trees
Maryna Kachanovska, Kiyan Naderi, Konstantin Pankrashkin
https://arxiv.org/abs/2506.11218

Poisson-type problems with transmission conditions at boundaries of infinite metric trees
The paper introduces a Poisson-type problem on a mixed-dimensional structure combining a Euclidean domain and a lower-dimensional self-similar component touching a compact surface (interface). The lower-dimensional piece is a so-called infinite metric tree (one-dimensional branching structure), and the key ingredient of the study is a rigorous definition of the gluing conditions between the two components. These constructions are based on the recent concept of embedded trace maps and some abstr…

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…

Five months into its unprecedented dismantling of foreign-aid programs,
the Trump administration has given the order to incinerate food instead of sending it to people abroad who need it.
Nearly 500 metric tons of emergency food
—enough to feed about 1.5 million children for a week
—are set to expire tomorrow, according to current and former government employees with direct knowledge of the rations.
Within weeks, two of those sources told me, the food, meant for c…

The U.S. Will Incinerate 500 Tons of Emergency Food Aid
Federal workers warned for months that the high-energy biscuits would go to waste.

Improving Speech Enhancement with Multi-Metric Supervision from Learned Quality Assessment
Wei Wang, Wangyou Zhang, Chenda Li, Jiatong Shi, Shinji Watanabe, Yanmin Qian
https://arxiv.org/abs/2506.12260

Improving Speech Enhancement with Multi-Metric Supervision from Learned Quality Assessment
Speech quality assessment (SQA) aims to predict the perceived quality of speech signals under a wide range of distortions. It is inherently connected to speech enhancement (SE), which seeks to improve speech quality by removing unwanted signal components. While SQA models are widely used to evaluate SE performance, their potential to guide SE training remains underexplored. In this work, we investigate a training framework that leverages a SQA model, trained to predict multiple evaluation metri…

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…

A Halpha metric for identifying dormant black holes in X-ray transients
J. Casares, M. A. P. Torres, S. Navarro Umpi\'errez
https://arxiv.org/abs/2506.13765

A Halpha metric for identifying dormant black holes in X-ray transients
Dormant black holes (BHs) in X-ray transients can be identified by the presence of broad Ha emission lines from quiescent accretion discs. Unfortunately, short-period cataclysmic variables (CVs) can also produce broad Ha lines, especially when viewed at high inclinations, and are thus a major source of contamination. Here we compare the full width at half maximum (FWHM) and equivalent width (EW) of the Ha line in a sample of 20 quiescent BH transients and 354 CVs (305 from SDSS I to IV) with se…

Interpolative Metrics Are Not New: A Study of Generalized Contractions in b-Suprametric Spaces
Hassan Khandani
https://arxiv.org/abs/2506.11205 https://

Interpolative Metrics Are Not New: A Study of Generalized Contractions in b-Suprametric Spaces
{Researchers recently introduced interpolative metric spaces and established fixed-point theorems in this setting. We demonstrate that these metrics are a special case of b-metrics. On the other hand, suprametrics and b-suprametrics have also been introduced, and we show that b-suprametric spaces generalize b-metric spaces. We establish corresponding results previously presented in interpolative metric spaces in the framework of b-suprametric spaces with weaker conditions.

Composition operators in Sobolev spaces with a metric measure space as a domain. II
Danil A. Sboev, Sergey K. Vodopyanov
https://arxiv.org/abs/2507.11455 h…

Composition operators in Sobolev spaces with a metric measure space as a domain. II
We obtain a description of the homeomorphisms which induce bounded composition operators in Sobolev spaces of functions on metric measure spaces.

On Tight Robust Coresets for $k$-Medians Clustering
Lingxiao Huang, Zhenyu Jiang, Yi Li, Xuan Wu
https://arxiv.org/abs/2507.11260 https://

On Tight Robust Coresets for $k$-Medians Clustering
This paper considers coresets for the robust $k$-medians problem with $m$ outliers, and new constructions in various metric spaces are obtained. Specifically, for metric spaces with a bounded VC or doubling dimension $d$, the coreset size is $O(m) + \tilde{O}(kd\varepsilon^{-2})$, which is optimal up to logarithmic factors. For Euclidean spaces, the coreset size is $O(m\varepsilon^{-1}) + \tilde{O}(\min\{k^{4/3}\varepsilon^{-2},k\varepsilon^{-3}\})$, improving upon a recent result by Jiang and …

Metric Framework of Coherent Activity Patterns Identification in Spiking Neuronal Networks
Daniil Radushev, Olesia Dogonasheva, Boris Gutkin, Denis Zakharov
https://arxiv.org/abs/2506.12291

Metric Framework of Coherent Activity Patterns Identification in Spiking Neuronal Networks
Partial synchronization plays a crucial role in the functioning of neuronal networks: selective, coordinated activation of neurons enables information processing that flexibly adapts to a changing computational context. Since the structure of coherent activity patterns reflects the network's current state, developing automated tools to identify them is a key challenge in neurodynamics. Existing methods for analyzing neuronal dynamics tend to focus on global characteristics of the network, such …

A Holomorphic Splitting Theorem
Miao Song
https://arxiv.org/abs/2506.13517 https://arxiv.org/pdf/2506.13517

A Holomorphic Splitting Theorem
A long-term project is to construct a complete Calabi-Yau metric on the complement of the anticanonical divisor in a compact Kähler manifold $\oM$. We focus on the case where this smooth divisor has multiplicity 2 and is itself a compact Calabi-Yau manifold. Firstly we solved the Monge-Ampère equation when the Ricci potiential is of $O(r^{-1})$ decay on the generalized $ALG$ manifolds. Then we used the solution to this Kähler Ricci flat metric to prove a holomorphic splitting theorem: If $K_…

By Israel’s own metric, it has wounded over 2 million Palestinians in Gaza alone.
#israel #genocide #ethnicCleansing

Κάποιος Ταδόπουλος (@_Wiesenthal_S_@todon.nl)
Attached: 1 image "Israel includes those treated for anxiety in the injury count" 🙄

CGVQM D: Computer Graphics Video Quality Metric and Dataset
Akshay Jindal, Nabil Sadaka, Manu Mathew Thomas, Anton Sochenov, Anton Kaplanyan
https://arxiv.org/abs/2506.11546

CGVQM+D: Computer Graphics Video Quality Metric and Dataset
While existing video and image quality datasets have extensively studied natural videos and traditional distortions, the perception of synthetic content and modern rendering artifacts remains underexplored. We present a novel video quality dataset focused on distortions introduced by advanced rendering techniques, including neural supersampling, novel-view synthesis, path tracing, neural denoising, frame interpolation, and variable rate shading. Our evaluations show that existing full-reference…

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…

Fine-grained Timing Analysis of Digital Integrated Circuits in Answer Set Programming
Alessandro Bertagnon, Marcello Dalpasso, Michele Favalli, Marco Gavanelli
https://arxiv.org/abs/2507.11150

Fine-grained Timing Analysis of Digital Integrated Circuits in Answer Set Programming
In the design of integrated circuits, one critical metric is the maximum delay introduced by combinational modules within the circuit. This delay is crucial because it represents the time required to perform a computation: in an Arithmetic-Logic Unit it represents the maximum time taken by the circuit to perform an arithmetic operation. When such a circuit is part of a larger, synchronous system, like a CPU, the maximum delay directly impacts the maximum clock frequency of the entire system. Ty…

On the existence of consistent adversarial attacks in high-dimensional linear classification
Matteo Vilucchio, Lenka Zdeborov\'a, Bruno Loureiro
https://arxiv.org/abs/2506.12454

On the existence of consistent adversarial attacks in high-dimensional linear classification
What fundamentally distinguishes an adversarial attack from a misclassification due to limited model expressivity or finite data? In this work, we investigate this question in the setting of high-dimensional binary classification, where statistical effects due to limited data availability play a central role. We introduce a new error metric that precisely capture this distinction, quantifying model vulnerability to consistent adversarial attacks -- perturbations that preserve the ground-truth l…

Sensor Model Identification via Simultaneous Model Selection and State Variable Determination
Christian Brommer, Alessandro Fornasier, Jan Steinbrener, Stephan Weiss
https://arxiv.org/abs/2506.11263

Sensor Model Identification via Simultaneous Model Selection and State Variable Determination
We present a method for the unattended gray-box identification of sensor models commonly used by localization algorithms in the field of robotics. The objective is to determine the most likely sensor model for a time series of unknown measurement data, given an extendable catalog of predefined sensor models. Sensor model definitions may require states for rigid-body calibrations and dedicated reference frames to replicate a measurement based on the robot's localization state. A health metric is…

The metric from energy-momentum non-conservation: Generalizing Noether and completing spectral geometry
Achim Kempf
https://arxiv.org/abs/2506.11186 https:…

The metric from energy-momentum non-conservation: Generalizing Noether and completing spectral geometry
We complete the program of spectral geometry, in the sense that we show that a manifold's shape, i.e., its metric, can be reconstructed from its resonant sound when tapped lightly, i.e., from its spectrum, -- if in addition we also record the resonances' mutual excitation pattern when the driving is strong enough to reach the nonlinear regime. Applied to spacetime, this finding yields a generalization of Noether's theorem: the specific pattern of energy-momentum non-conservation on a generic cu…

Homeomorphic Sobolev extensions and integrability of hyperbolic metric
Xilin Zhou
https://arxiv.org/abs/2506.10216 https://arxiv.org/…

Homeomorphic Sobolev extensions and integrability of hyperbolic metric
Very recently, it was proved that if the hyperbolic metric of a planar Jordan domain is $L^q$-integrable for some $q\in (1,\infty)$, then every homeomorphic parametrization of the boundary Jordan curve via the unit circle can be extended to a Sobolev homeomorphism of the entire disk. This naturally raises the question of whether the extension holds under more general integrability conditions on the hyperbolic metric. In this work, we examine the case where the hyperbolic metric is $ϕ$-inte…

Dark energy and QCD instanton vacuum in Friedmann-Lemaitre-Robertson-Walker universe
M. M. Musakhanov
https://arxiv.org/abs/2506.13128 https://

Dark energy and QCD instanton vacuum in Friedmann-Lemaitre-Robertson-Walker universe
The standard model of the universe, lambdaCDM, is based on the Friedmann-Lemaitre-Robertson-Walker metric with flat 3-dim coordinate space and Friedmann equations. The cosmological constant lambda is providing the cancellations of the matter fields contributions in the flat space. The dynamical dark energy is appearing on over of the vacuum energy of matter fields at the flat space. Within the Standard Model the gluon Yang-Mills (YM) fields are playing the special role since specific properties…

Second-Order Characterizations of Tilt Stability in Composite Optimization
Boris S. Mordukhovich, Peipei Tang, Chengjing Wang
https://arxiv.org/abs/2507.11253

Second-Order Characterizations of Tilt Stability in Composite Optimization
Tilt stability is a fundamental concept of variational analysis and optimization that plays a pivotal role in both theoretical issues and numerical computations. This paper investigates tilt stability of local minimizers for a general class of composite optimization problems in finite dimensions, where extended-real-valued objectives are compositions of parabolically regular and smooth functions. Under the weakest metric subregularity constraint qualification and other verifiable conditions, we…

Topological Conservation Laws in Magnetohydrodynamics on Higher-Dimensional Riemannian Manifolds
Naoki Sato, Ken Abe, Michio Yamada
https://arxiv.org/abs/2506.13251

Topological Conservation Laws in Magnetohydrodynamics on Higher-Dimensional Riemannian Manifolds
Are conservation laws such as fluid enstrophy, fluid helicity, or magnetic helicity inherently tied to the geometry of Euclidean space or the dimensionality of a fluid system? In this work, we first derive the equations of ideal magnetohydrodynamics (MHD) on a general Riemannian manifold. We then demonstrate that the associated conservation laws arise not from the flatness of the metric, but rather from the intrinsic mathematical structure of the governing equations. Moreover, we demonstrate th…

Persistent Homology of Music Network with Three Different Distances
Eunwoo Heo, Byeongchan Choi, Myung ock Kim, Mai Lan Tran, Jae-Hun Jung
https://arxiv.org/abs/2506.13595

Persistent Homology of Music Network with Three Different Distances
Persistent homology has been widely used to discover hidden topological structures in data across various applications, including music data. To apply persistent homology, a distance or metric must be defined between points in a point cloud or between nodes in a graph network. These definitions are not unique and depend on the specific objectives of a given problem. In other words, selecting different metric definitions allows for multiple topological inferences. In this work, we focus on apply…

An Isomorphism Theorem for Some Linear Elliptic Differential Operators on Quasi-Asymptotically Conical Manifolds
Mohamed Nouidha
https://arxiv.org/abs/2506.13069

An Isomorphism Theorem for Some Linear Elliptic Differential Operators on Quasi-Asymptotically Conical Manifolds
We study a linear elliptic differential operator of the form $\mathcal{P}=Δ+ V - λ$ on a quasi-asymptotically conical (\textbf{QAC}) manifold $(M, g)$, where $g$ is a polyhomogeneous metric and $V$ is a $b$-vector field that is unbounded with respect to the metric $g$.

Fairness-Aware Secure Integrated Sensing and Communications with Fractional Programming
Ali Khandan Boroujeni, Kuranage Roche Rayan Ranasinghe, Giuseppe Thadeu Freitas de Abreu, Stefan K\"opsell, Ghazal Bagheri, Rafael F. Schaefer
https://arxiv.org/abs/2507.11224

Fairness-Aware Secure Integrated Sensing and Communications with Fractional Programming
We propose a novel secure integrated sensing and communications (ISAC) system designed to serve multiple communication users (CUs) and targets. To that end, we formulate an optimization problem that maximizes the secrecy rate under constraints balancing both communication and sensing requirements. To enhance fairness among users, an entropy-regularized fairness metric is introduced within the problem framework. We then propose a solution employing an accelerated quadratic transform (QT) with a …

Replaced article(s) found for cs.CG. https://arxiv.org/list/cs.CG/new
[1/1]:
- Multipacking in Euclidean Metric Space
Arun Kumar Das, Sandip Das, Sk Samim Islam, Ritam M Mitra, Bodhayan Roy

Metrics on Permutation Families Defined by a Restriction Graph
Danylo Tymoshenko, Leonhard Nagel
https://arxiv.org/abs/2507.10569 https://

Metrics on Permutation Families Defined by a Restriction Graph
Understanding the metric structure of permutation families is fundamental to combinatorics and has applications in social choice theory, bioinformatics, and coding theory. We study permutation families defined by restriction graphs--oriented graphs that constrain the relative order of elements in valid permutations. For any restriction graph $G$, we determine the maximum distance achievable by two permutations under the $\ell_\infty$-metric and provide an explicit algorithm that constructs opti…

On QoE-Aware Traffic Management for Real-time, Interactive Video with Time-variant Spatial Complexity
Szilveszter N\'adas, Lars Ernstr\"om, David Lindero, Jonathan Lynam
https://arxiv.org/abs/2507.11798

On QoE-Aware Traffic Management for Real-time, Interactive Video with Time-variant Spatial Complexity
We analyzed spatial complexity, defined as the relationship between the required bitrate and a corresponding picture Quality of Experience (QoE) metric, for realistic, long, real-time, interactive video clips. Apart from variation across different content types, e.g., game genres, we discovered time-variability within a clip from second to second, and explored the ramifications for traffic management. We introduced utility as an elegant way to manage resource sharing preferences. Our analysis o…

Intermediate Interaction Strategies for Collective Behavior
Y. Kikuchi, M. Iwamoto
https://arxiv.org/abs/2507.09457 https://arxiv.org…

Intermediate Interaction Strategies for Collective Behavior
From bird flocks and fish schools to migrating cell sheets, collective motion is a ubiquitous biological phenomenon that inspires quantitative modeling through self-propelled particle (SPP) frameworks. Conventional SPP models prescribe either distance-based (metric) or rank-based (topological) interactions; however, empirical studies indicate that real groups may blend both types of interaction. Motivated by this graded perception, we introduce a new three-dimensional SPP model in which metric …

An Introductory Survey of Recursions in the Computation of Resistance Distance
Emily J. Evans, Russell Jay Hendel
https://arxiv.org/abs/2506.12048 https://…

An Introductory Survey of Recursions in the Computation of Resistance Distance
This paper presents an introduction and expository account of a beautiful, current, and active application of recursions to the computation of resistance distance. Resistance distance, also referred to as effective resistance, is a well-known graph metric that arises naturally by considering a graph as an electrical circuit; heuristically resistance distance measures both the number of paths between two vertices in a graph and the cost of each path. This topic finds applications in a rich array…

R\'enyi-Induced Information Geometry and Hartigan's Prior Family
Rebecca Maria Kuntz, Heinrich von Campe, Bj\"orn Malte Sch\"afer
https://arxiv.org/abs/2506.12028

Rényi-Induced Information Geometry and Hartigan's Prior Family
We derive the information geometry induced by the statistical Rényi divergence, namely its metric tensor, its dual parametrized connections, as well as its dual Laplacians. Based on these results, we demonstrate that the Rényi-geometry, though closely related, differs in structure from Amari's well-known $α$-geometry. Subsequently, we derive the canonical uniform prior distributions for a statistical manifold endowed with a Rényi-geometry, namely the dual Rényi-covolumes. We find that the …

Impact of Buchdahl metric potential on thin-shell gravastar framework in de Rham-Gabadadze-Tolley like massive gravity
Meghanil Sinha, S. Surendra Singh
https://arxiv.org/abs/2506.11171

Impact of Buchdahl metric potential on thin-shell gravastar framework in de Rham-Gabadadze-Tolley like massive gravity
This paper presents a study on gravitational vacuum stars (gravastars) with an isotropic matter distribution in de Rham-Gabadadze-Tolley (dRGT) massive gravity incorporating Buchdahl metric function. Here we have conducted an analysis on thin-shell singularity-free gravastar configuration. The study demonstrates the viability of gravastars as alternatives to black holes (BHs) in this massive gravity. Our research yields singularity free analytical solutions for gravastar interior and without ev…

Infinity Search: Approximate Vector Search with Projections on q-Metric Spaces
Antonio Pariente, Ignacio Hounie, Santiago Segarra, Alejandro Ribeiro
https://arxiv.org/abs/2506.06557

Infinity Search: Approximate Vector Search with Projections on q-Metric Spaces
Despite the ubiquity of vector search applications, prevailing search algorithms overlook the metric structure of vector embeddings, treating it as a constraint rather than exploiting its underlying properties. In this paper, we demonstrate that in $q$-metric spaces, metric trees can leverage a stronger version of the triangle inequality to reduce comparisons for exact search. Notably, as $q$ approaches infinity, the search complexity becomes logarithmic. Therefore, we propose a novel projectio…

Convergence to equilibrium for a class of exchange economies
R. S. MacKay
https://arxiv.org/abs/2506.11770 https://arxiv.org/pdf/2506…

Convergence to equilibrium for a class of exchange economies
For a class of stochastic dynamical models of exchange economies that we call ``fully connected Cobb-Douglas'', the paper proves convergence of the probability distribution to an equilibrium, in total variation metric as time goes to infinity. The convergence is exponential and the equilibrium is determined uniquely by the number of agents, their ``exponents'', and the initial amounts of money and goods in the economy.

The impact of economic policies on housing prices. Approximations and predictions in the UK, the US, France, and Switzerland from the 1980s to today
Nicolas Houli\'e
https://arxiv.org/abs/2505.09620

The impact of economic policies on housing prices. Approximations and predictions in the UK, the US, France, and Switzerland from the 1980s to today
I show that house prices can be modeled using machine learning (kNN and tree-bagging) and a small dataset composed of macro-economic factors (MEF), including an inflation metric (CPI), US treasury rates (10-yr), Gross Domestic Product (GDP), and portfolio size of central banks (ECB, FED). This set of parameters covers all the parties involved in a transaction (buyer, seller, and financing facility) while ignoring the intrinsic properties of each asset and encompassing local (inflation) and liqu…

Momentum-space Metric Tensor from Nonadiabatic Evolution of Bloch Electrons
Yafei Ren
https://arxiv.org/abs/2506.06439 https://arxiv.…

Momentum-space Metric Tensor from Nonadiabatic Evolution of Bloch Electrons
We reveal a fundamental geometric structure of momentum space arising from the nonadiabatic evolution of Bloch electrons. By extending semiclassical wave packet theory to incorporate nonadiabatic effects, we introduce a momentum-space metric tensor -- the nonadiabatic metric. This metric gives rise to two velocity corrections, dubbed geometric and geodesic velocities, providing a unified and intuitive framework for understanding nonlinear and nonadiabatic transport phenomena beyond Berry phase …

Replaced article(s) found for math.SP. https://arxiv.org/list/math.SP/new
[1/1]:
Spectral bounds for exit times on metric measure Dirichlet spaces and applications

Surjectivity of the Cannon--Thurston map in metric (graph) bundles
Rakesh Halder
https://arxiv.org/abs/2507.07076 https://arxiv.org/p…

Surjectivity of the Cannon--Thurston map in metric (graph) bundles
Metric (graph) bundles generalize the notion of fiber bundles to the context of geometric group theory and were introduced by Mj and Sardar. Suppose $X$ is a metric (graph) bundle over $B$ such that the fibers are (uniformly) hyperbolic, and the total space $X$ is also hyperbolic. In this generality, Mj--Sardar proved that the inclusion of a fiber into $X$ admits a continuous extension to the (Gromov) boundary. In this article, we prove that such a continuous extension map between boundaries …

Regular Spacetimes in the Effective Metric Description
Mattia Damia Paciarini, Miko{\l}aj Myszkowski, Francesco Sannino, Vania Vellucci
https://arxiv.org/abs/2506.12620

Regular Spacetimes in the Effective Metric Description
Over the past few decades, significant effort has been directed towards developing various regularized models for compact objects. Recently, a new observable-based parametrization was introduced to account for black hole deformations in a model-independent fashion, referred to as the Effective Metric Description (EMD) \cite{Binetti:2022xdi, DelPiano:2023fiw, DelPiano:2024gvw, DelPiano:2024nrl}. In this paper, we carry out a systematic investigation of the regularity of static and spherically sy…

Robust Multi-Manifold Clustering via Simplex Paths
Haoyu Chen, Anna Little, Akin Narayan
https://arxiv.org/abs/2507.10710 https://arx…

Robust Multi-Manifold Clustering via Simplex Paths
This article introduces a novel, geometric approach for multi-manifold clustering (MMC), i.e. for clustering a collection of potentially intersecting, d-dimensional manifolds into the individual manifold components. We first compute a locality graph on d-simplices, using the dihedral angle in between adjacent simplices as the graph weights, and then compute infinity path distances in this simplex graph. This procedure gives a metric on simplices which we refer to as the largest angle path dista…

Mind the Gap: A Readability-Aware Metric for Test Code Complexity
Wendk\^uuni C. Ou\'edraogo, Yinghua Li, Xueqi Dang, Xin Zhou, Anil Koyuncu, Jacques Klein, David Lo, Tegawend\'e F. Bissyand\'e
https://arxiv.org/abs/2506.06764

Mind the Gap: A Readability-Aware Metric for Test Code Complexity
Automatically generated unit tests-from search-based tools like EvoSuite or LLMs-vary significantly in structure and readability. Yet most evaluations rely on metrics like Cyclomatic Complexity and Cognitive Complexity, designed for functional code rather than test code. Recent studies have shown that SonarSource's Cognitive Complexity metric assigns near-zero scores to LLM-generated tests, yet its behavior on EvoSuite-generated tests and its applicability to test-specific code structures remai…

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
Characterization of the sphere by means of congruent support cones

Linear codes for $b$-symbol read channels attaining the Griesmer bound
Sascha Kurz
https://arxiv.org/abs/2507.07728 https://arxiv.org…

Linear codes for $b$-symbol read channels attaining the Griesmer bound
Reading channels where $b$-tuples of adjacent symbols are read at every step have e.g.\ applications in storage. Corresponding bounds and constructions of codes for the $b$-symbol metric, especially the pair-symbol metric where $b=2$, were intensively studied in the last fifteen years. Here we determine the optimal code parameters of linear codes in the $b$-symbol metric assuming that the minimum distance is sufficiently large. We also determine the optimal parameters of linear binary codes in …

Efficacy of Image Similarity as a Metric for Augmenting Small Dataset Retinal Image Segmentation
Thomas Wallace, Ik Siong Heng, Senad Subasic, Chris Messenger
https://arxiv.org/abs/2507.04862

Efficacy of Image Similarity as a Metric for Augmenting Small Dataset Retinal Image Segmentation
Synthetic images are an option for augmenting limited medical imaging datasets to improve the performance of various machine learning models. A common metric for evaluating synthetic image quality is the Fréchet Inception Distance (FID) which measures the similarity of two image datasets. In this study we evaluate the relationship between this metric and the improvement which synthetic images, generated by a Progressively Growing Generative Adversarial Network (PGGAN), grant when augmenting Di…

A Test for Jumps in Metric-Space Conditional Means
David Van Dijcke
https://arxiv.org/abs/2507.04560 https://arxiv.org/pdf/2507.04560…

A Test for Jumps in Metric-Space Conditional Means
Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for jumps in conditional means when outcomes lie in a non-Euclidean metric space. Using local Fréchet regression$\unicode{x2014}$which generalizes standard regression to metric-space valued data$\unicode{x2014}$the method estimates a mean path on either side of …

Numerical analysis of quasiperiodic oscillations in the Hartle-Thorne spacetime
K. Boshkayev, T. Konysbayev, Ye. Kurmanov, M. Muccino, H. Quevedo
https://arxiv.org/abs/2506.11581 …

Numerical analysis of quasiperiodic oscillations in the Hartle-Thorne spacetime
We numerically analyze quasiperiodic oscillations (QPOs) using a well-established spacetime model with neutron star sources. Within the framework of general relativity, we present expressions for the fundamental frequencies of test particles in the gravitational field of a slowly rotating and slightly deformed compact object defined by the Hartle-Thorne (HT) metric. Using the Relativistic Precession Model (RPM) formulated by Stella and Morinsk, we examine quasiperiodic oscillation data from eig…

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

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

The Multi-marginal Monge Problem and an Application to Metasurfaces
Irem Altiner, Cristian E. Guti\'errez
https://arxiv.org/abs/2507.11440 https://

The Multi-marginal Monge Problem and an Application to Metasurfaces
This paper studies the multi-marginal Monge problem in the setting of compact metric spaces proving existence and uniqueness of solutions when the cost function is Lipschitz. We apply the results obtained to solve an optics problem involving metalenses, that is, we design a refracting-reflecting metalens that preserves given energy distributions.

Canadians, please confirm this is valid
EDIT: Added in better alt text

Regionalized Metric Framework: A Novel Approach for Evaluating Multimodal Multi-Objective Optimization Algorithms
Jintai Chen, Fangqing Liu, Xueming Yan, Han Huang
https://arxiv.org/abs/2506.00468

Regionalized Metric Framework: A Novel Approach for Evaluating Multimodal Multi-Objective Optimization Algorithms
This study aims to optimize the evaluation metric of multimodal multi-objective optimization problems using a Regionalized Metric Framework, which provides a certain boost to research in this field. Existing evaluation metrics usually use the reference set as the evaluation basis, which inevitably leads to reference set dependence. To optimize this problem, this study proposes an evaluation metric based on a Regionalized Metric Framework. The algorithm divides the set of solutions to be evaluat…

Simulated non-Markovian Noise Resilience of Silicon-Based Spin Qubits with Surface Code Error Correction
Oscar Gravier, Thomas Ayral, Beno\^it Vermersch, Tristan Meunier, Valentin Savin
https://arxiv.org/abs/2507.08713

Simulated non-Markovian Noise Resilience of Silicon-Based Spin Qubits with Surface Code Error Correction
We investigate the resilience of silicon-based spin qubits against non-Markovian noise within the framework of quantum error correction. We consider a realistic non-Markovian noise model that affects both the Larmor frequency and exchange energy of qubits, allowing accurate simulations of noisy quantum circuits. We employ numerical emulation to assess the performance of the distance-3 rotated surface code and its XZZX variant, using a logical qubit coherence time metric based on Ramsey-like exp…

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
The Stepanov theorem for Q-valued functions
https://

Common Fixed Point Theorems on LR-$(\delta,\phi)$ Quasi Partial $b$-Metric Spaces
Anuradha Gupta, Rahul Mansotra
https://arxiv.org/abs/2506.10581 https://

Common Fixed Point Theorems on LR-$(δ,ϕ)$ Quasi Partial $b$-Metric Spaces
In this article, we introduce the LR-$(δ,ϕ)$ quasi partial $b$-metric space. Also, the common fixed point theorem on complete LR-$(δ,ϕ)$ quasi partial $b$-metric space has been proved. A non-trivial example is also given.

Isoperimetric inequality on Finsler metric measure manifolds with non-negative weighted Ricci curvature
Xinyue Cheng, Yalu Feng, Liulin Liu
https://arxiv.org/abs/2507.08571

Isoperimetric inequality on Finsler metric measure manifolds with non-negative weighted Ricci curvature
In this paper, we define the volume entropy and the second Cheeger constant and prove a sharp isoperimetric inequality involving the volume entropy on Finsler metric measure manifolds with non-negative weighted Ricci curvature ${\rm Ric}_{\infty}$. As an application, we prove a Cheeger-Buser type inequality for the first eigenvalue of Finsler Laplacian by using the volume entropy and the second Cheeger constant.

This https://arxiv.org/abs/2308.09696 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Exploring Metric and Strong Metric Dimensions in Inclusion Ideal Graphs of Commutative Rings
The inclusion ideal graph of a commutative unitary ring $R$ is the (undirected) graph $In(R)$ whose vertices all non-trivial ideals of $R$ and two distinct vertices are adjacent if and only if one of them is a proper subset of the other one. In this paper, the metric dimension of $In(R)$ is discussed. Moreover, the structure of the resolving graph of $In(R)$ is characterized and as an application, we compute the strong metric dimension of $In(R)$.

Charged Particle Oscillations around a Black Hole Surrounded by CDM Halos
Zakaria Ahal, Hasan El Moumni, Karima Masmar
https://arxiv.org/abs/2507.11139 htt…

Charged Particle Oscillations around a Black Hole Surrounded by CDM Halos
HF QPOs are among the most intriguing phenomena observed in LMXBs containing BHs or neutron stars. In this work, we investigate charged particles' dynamics in the nearby of a Schwarzschild-like BH embedded in a uniform magnetic field and surrounded on all sides by CDM. Thereby gaining deeper insight into the influence of magnetic and DM distributions on observable phenomena near compact objects. We first present a modified metric, which incorporates the effects of a CDM ... We compute the fun…

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Affine Hardy--Littlewood--Sobolev inequalities
Juli\'an Haddad, Monika Ludwig

Self-adjoint extensions for the Laplacian operator on non-compacts graphs and the existence and stability of standing waves for NLS models
Jaime Angulo Pava, Alexander Munoz
https://arxiv.org/abs/2507.10821

Self-adjoint extensions for the Laplacian operator on non-compacts graphs and the existence and stability of standing waves for NLS models
In this work we first study a systematic way to describe the unitary dynamics of the Schrödinger operator on a looping-edge graphs $\mathcal{G}$ (a graph consisting of a circle and a finite amount $N$ of infinite half-lines attached to a common vertex). We also apply our approach on $\mathcal T$-shaped graphs (metric graphs that consists of a pendant edge and a finite amount of half-lines attached to the common vertex). In both cases we obtain novel boundary conditions on the unique vertex tha…

Invariants for sum-rank metric codes
Paolo Santonastaso, Ferdinando Zullo
https://arxiv.org/abs/2507.04158 https://arxiv.org/pdf/2507…

Invariants for sum-rank metric codes
The code equivalence problem is central in coding theory and cryptography. While classical invariants are effective for Hamming and rank metrics, the sum-rank metric, which unifies both, introduces new challenges. This paper introduces new invariants for sum-rank metric codes: generalised idealisers, the centraliser, the center, and a refined notion of linearity. These lead to the definition of nuclear parameters, inspired by those used in division algebra theory, where they are crucial for pro…

A topological rigidity theorem on noncompact Hessian manifolds
Hanzhang Yin, Bin Zhou
https://arxiv.org/abs/2507.11111 https://arxiv.…

A topological rigidity theorem on noncompact Hessian manifolds
In this work, we obtain a short time solution for a geometric flow on noncompact affine Riemannian manifolds. Using this result, we can construct a Hessian metric with nonnegative bounded Hessian sectional curvature on some Hessian manifolds with nonnegative Hessian sectional curvature. Our results can be regarded as a real version of Lee-Tam \cite{LT20}. As an application, we prove that a complete noncompact Hessian manifold with nonnegative Hessian sectional curvature is diffeomorphic to $\ma…

Energy inequalities for cutoff functions of $p$-energies on metric measures spaces
Meng Yang
https://arxiv.org/abs/2507.08577 https://

Energy inequalities for cutoff functions of $p$-energies on metric measures spaces
For $p\in(1,+\infty)$, and for a $p$-energy on a metric measure space, we establish equivalent conditions for the conjunction of the Poincaré inequality and the cutoff Sobolev inequality. In particular, we employ a technique of Trudinger and Wang [Amer. J. Math. 124 (2002), no. 2, 369--410] to derive a Wolff potential estimate for superharmonic functions, and a method of Holopainen [Contemp. Math. 338 (2003), 219--239] to prove the elliptic Harnack inequality for harmonic functions. As applica…

Balanced quasistatic evolutions of critical points in metric spaces
Stefano Almi, Massimo Fornasier, Jona Klemenc, Alessandro Scagliotti
https://arxiv.org/abs/2506.09812

Balanced quasistatic evolutions of critical points in metric spaces
Quasistatic evolutions of critical points of time-dependent energies exhibit piecewise smooth behavior, making them useful for modeling continuum mechanics phenomena like elastic-plasticity and fracture. Traditionally, such evolutions have been derived as vanishing viscosity and inertia limits, leading to balanced viscosity solutions. However, for nonconvex energies, these constructions have been realized in Euclidean spaces and assume non-degenerate critical points. In this paper, we take a di…

Improving the average dilation of a metric graph by adding edges
Sariel Har-Peled, Eliot W. Robson
https://arxiv.org/abs/2506.04246 https://

Improving the average dilation of a metric graph by adding edges
For a graph $G$ spanning a metric space, the dilation of a pair of points is the ratio of their distance in the shortest path graph metric to their distance in the metric space. Given a graph $G$ and a budget $k$, a classic problem is to augment $G$ with $k$ additional edges to reduce the maximum dilation. In this note, we consider a variant of this problem where the goal is to reduce the average dilation for pairs of points in $G$. We provide an $O(k)$ approximation algorithm for this proble…

Linear rank-metric intersecting codes
Daniele Bartoli, Martino Borello, Giuseppe Marino, Martin Scotti
https://arxiv.org/abs/2507.00569 https://

Linear rank-metric intersecting codes
In this paper we introduce and investigate rank-metric intersecting codes, a new class of linear codes in the rank-metric context, inspired by the well-studied notion of intersecting codes in the Hamming metric. A rank-metric code is said to be intersecting if any two nonzero codewords have supports intersecting non trivially. We explore this class from both a coding-theoretic and geometric perspective, highlighting its relationship with minimal codes, MRD codes, and Hamming-metric intersecting…

Depth-Sequence Transformer (DST) for Segment-Specific ICA Calcification Mapping on Non-Contrast CT
Xiangjian Hou, Ebru Yaman Akcicek, Xin Wang, Kazem Hashemizadeh, Scott Mcnally, Chun Yuan, Xiaodong Ma
https://arxiv.org/abs/2507.08214

Depth-Sequence Transformer (DST) for Segment-Specific ICA Calcification Mapping on Non-Contrast CT
While total intracranial carotid artery calcification (ICAC) volume is an established stroke biomarker, growing evidence shows this aggregate metric ignores the critical influence of plaque location, since calcification in different segments carries distinct prognostic and procedural risks. However, a finer-grained, segment-specific quantification has remained technically infeasible. Conventional 3D models are forced to process downsampled volumes or isolated patches, sacrificing the global con…

Generic regularity for minimizing hypersurfaces in dimension 11
Otis Chodosh, Christos Mantoulidis, Felix Schulze, Zhihan Wang
https://arxiv.org/abs/2506.12852

Generic regularity for minimizing hypersurfaces in dimension 11
We prove that area-minimizing hypersurfaces are generically smooth in ambient dimension $11$ in the context of the Plateau problem and of area minimization in integral homology. For higher ambient dimensions, $n+1 \geq 12$, we prove in the same two contexts that area-minimizing hypersurfaces have at most an $n-10-ε_n$ dimensional singular set after an arbitrarily $C^\infty$-small perturbation of the Plateau boundary or the ambient Riemannian metric, respectively.

Failure of the Flat Chain Conjecture and non-regularity of the prescribed Jacobian equation
Jakub Tak\'a\v{c}
https://arxiv.org/abs/2506.13718 https://…

Failure of the Flat Chain Conjecture and non-regularity of the prescribed Jacobian equation
We show that the Flat Chain Conjecture in Lang's formulation (that is, without requiring finite mass of the underlying currents) fails for metric $k$-currents in $\mathbb{R}^d$ whenever $d\geq 2$ and $k\in\{1, \dots, d\}$. In all other cases, it holds. We first connect the conjecture to a regularity statement concerning the prescribed Jacobian equation near $L^\infty$. We then show that the equation does not have the required regularity. For a Lipschitz vector field $π$, its derivative $\mathr…

[2025-06-17 Tue (UTC), 1 new article found for math.MG Metric Geometry]
toXiv_bot_toot

Kernel Trace Distance: Quantum Statistical Metric between Measures through RKHS Density Operators
Arturo Castellanos, Anna Korba, Pavlo Mozharovskyi, Hicham Janati
https://arxiv.org/abs/2507.06055

Kernel Trace Distance: Quantum Statistical Metric between Measures through RKHS Density Operators
Distances between probability distributions are a key component of many statistical machine learning tasks, from two-sample testing to generative modeling, among others. We introduce a novel distance between measures that compares them through a Schatten norm of their kernel covariance operators. We show that this new distance is an integral probability metric that can be framed between a Maximum Mean Discrepancy (MMD) and a Wasserstein distance. In particular, we show that it avoids some pitfa…

On the Maximum Size of Codes Under the Damerau-Levenshtein Metric
Zuo Ye, Gennian Ge
https://arxiv.org/abs/2507.04806 https://arxiv.o…

On the Maximum Size of Codes Under the Damerau-Levenshtein Metric
The Damerau-Levenshtein distance between two sequences is the minimum number of operations (deletions, insertions, substitutions, and adjacent transpositions) required to convert one sequence into another. Notwithstanding a long history of this metric, research on error-correcting codes under this distance has remained limited. Recently, motivated by applications in DNA-based storage systems, Gabrys \textit{et al} and Wang \texit{et al} reinvigorated interest in this metric. In their works, som…

Replaced article(s) found for gr-qc. https://arxiv.org/list/gr-qc/new
[1/2]:
Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II:...

[2025-06-16 Mon (UTC), 2 new articles found for math.MG Metric Geometry]
toXiv_bot_toot

Curvature-Enhanced Inertia in Curved Spacetimes: An ADM-Based Formalism with Multipole Connections
Ilias Kynigalakis
https://arxiv.org/abs/2506.12983 https…

Curvature-Enhanced Inertia in Curved Spacetimes: An ADM-Based Formalism with Multipole Connections
We propose a covariant definition of an inertia tensor on spatial hypersurfaces in general relativity, constructed via integrals of geodesic distance functions using the exponential map. In the ADM 3+1 decomposition, we consider a spacelike slice (Sigma, gamma_ij) with induced metric gamma_ij, lapse N, shift N^i, and a mass-energy density rho(x) on Sigma. At each point p in Sigma, we define a Riemannian inertia tensor I_p(u,v) as an integral over Sigma involving geodesic distances and the expon…

[2025-07-16 Wed (UTC), 1 new article found for math.MG Metric Geometry]
toXiv_bot_toot

This https://arxiv.org/abs/2410.06864 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Rigidity in fixed angle inverse scattering for Riemannian metrics
The fixed angle inverse scattering problem for a velocity consists in determining a sound speed, or a Riemannian metric up to diffeomorphism, from measurements obtained by probing the medium with a single plane wave. This is a formally determined inverse problem that is open in general. In this article we consider the rigidity question of distinguishing a sound speed or a Riemannian metric from the Euclidean metric. We prove that a general smooth metric that is Euclidean outside a ball can be d…

Cosmological Analysis of $f(R,\Sigma, T)$ Gravity via $O_m(z)$ Reconstruction: Implications into Dark Energy Dynamics
S. H. Shekh, Anil Kumar Yadav, Anirudh Pradhan, N. Myrzakulov
https://arxiv.org/abs/2506.13446

Cosmological Analysis of $f(R,Σ, T)$ Gravity via $O_m(z)$ Reconstruction: Implications into Dark Energy Dynamics
This study investigates the cosmological implications of $f(R,Σ,T)$ gravity by reconstructing the Hubble parameter from a logarithmic parameterization of the $O_m(z)$ diagnostic. Our approach offers a model-independent way to probe the nature of dark energy and differentiate it from a cosmological constant. We derive the field equations for $f(R,Σ,T) = R + Σ+ 2πηT$ within the homogeneous, isotropic, and spatially flat Friedmann-Robertson-Walker (FRW) metric. A comprehensive analysis of key…

Metric reconstruction and the Hamiltonian for eccentric, precessing binaries in the small-mass-ratio limit
Zachary Nasipak
https://arxiv.org/abs/2507.07746

Metric reconstruction and the Hamiltonian for eccentric, precessing binaries in the small-mass-ratio limit
We calculate the first-order (in the mass-ratio) metric perturbation produced by a small body on an eccentric, precessing bound orbit about a Kerr black hole. We reconstruct the metric perturbation from the maximal spin-weight Weyl scalars, $ψ_0$ and $ψ_4$, using four different methods. The first two follow the work of Chrzanowski, Cohen, Kegeles, and Wald and reconstruct the metric perturbation from either $ψ_0$ or $ψ_4$, leading to perturbations in the ingoing or outgoing radiation gauges…

On the local metric dimension of $K_4$-free graphs
Ali Ghalavand, Sandi Klav\v{z}ar, Xueliang Li
https://arxiv.org/abs/2506.00414 https://

On the local metric dimension of $K_4$-free graphs
Let $G$ be a graph of order $ n(G) $, local metric dimension $ \dim_l(G) $, and clique number $ ω(G) $. It has been conjectured that if $ n(G) \geq ω(G) + 1 \geq 4 $, then $ \dim_l(G) \leq \left( \frac{ω(G) - 2}{ω(G) - 1} \right) n(G) $. In this paper the conjecture is confirmed for the case $ ω(G) = 3 $. Consequently, a problem regarding the local metric dimension of planar graphs is also resolved.

Geometric Convergence to an Extreme Limit Space with nonnegative scalar curvature
Christina Sormani, Wenchuan Tian, Wai-Ho Yeung
https://arxiv.org/abs/2506.12491

Geometric Convergence to an Extreme Limit Space with nonnegative scalar curvature
In 2014, Gromov conjectured that sequences of manifolds with nonnegative scalar curvature should have subsequences which converge in some geometric sense to limit spaces with some notion of generalized nonnegative scalar curvature. In recent joint work with Changliang Wang, the authors found a sequence of warped product Riemannian metrics on $\Sph^2\times \Sph^1$ with nonnegative scalar curvature whose metric tensors converge in the $W^{1,p}$ sense for $p<2$ to an extreme warped product limit s…

Null Distance and Temporal Functions
Andrea Nigri
https://arxiv.org/abs/2507.07158 https://arxiv.org/pdf/2507.07158

Null Distance and Temporal Functions
The notion of null distance was introduced by Sormani and Vega as part of a broader program to develop a theory of metric convergence adapted to Lorentzian geometry. Given a time function $τ$ on a spacetime $(M,g)$, the associated null distance $\hat{d}_τ$ is constructed from and closely related to the causal structure of $M$. While generally only a semi-metric, $\hat{d}_τ$ becomes a metric when $τ$ satisfies the local anti-Lipschitz condition. In this work, we focus on temporal functions…

Metric functionals and weak convergence
Armando W. Guti\'errez, Olavi Nevanlinna
https://arxiv.org/abs/2506.04154 https://arxiv.o…

Metric functionals and weak convergence
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When restricted to bounded sequences in normed linear spaces, we prove that our notion of weak convergence agrees with the standard one.

On the Gromov--Hausdorff stability of metric viscosity solutions
Shimpei Makida
https://arxiv.org/abs/2507.06495 https://arxiv.org/pdf/2507.06495 https://arxiv.org/html/2507.06495
arXiv:2507.06495v1 Announce Type: new
Abstract: We establish the stability of metric viscosity solutions to first-order Hamilton--Jacobi equations under Gromov--Hausdorff convergence. Our proof combines a characterization of metric viscosity solutions via quadratic distance functions with a doubling variable method adapted to epsilon-isometries, which allows us to pass to the Gromov--Hausdorff limit without embedding the spaces into a common ambient space. As a byproduct, we give a PDE-based proof of the stability of the dual Kantorovich problems under measured-Gromov--Hausdorff convergence.
toXiv_bot_toot

Enumeration of geometric Weierstrass points of metric graphs
Diego A. Robayo Bargans
https://arxiv.org/abs/2506.22130 https://arxiv.o…

Enumeration of geometric Weierstrass points of metric graphs
A classical result states that on a smooth algebraic curve of genus $g$ the number of Weierstrass points, counted with multiplicity, is $g^3-g$. In this paper, we introduce the notion of geometric Weierstrass points of metric graphs and show that a generic metric graph of genus $g$ has $g^3-g$ geometric Weierstrass points counted with multiplicity. Our methods also provide a new proof of the existence of Weierstrass points on metric graphs of genus bigger than or equal to $2$.

A Metric Framework for Triangle Inequalities via Barycentric Coordinates
Xi Feng
https://arxiv.org/abs/2506.10050 https://arxiv.org/p…

A Metric Framework for Triangle Inequalities via Barycentric Coordinates
This paper presents a unified metric-based framework for triangle geometric inequalities using barycentric coordinates. By interpreting classical inequalities as squared distances between points(a process termed metricization)we derive and refine numerous well-known inequalities. Furthermore, the squared-distance function ELD_I, measures distances from the incenter to points on the Euler line, also yielding generalized inequalities. The method offers geometric clarity and extends naturally to h…

A hyperk\"ahler metric on twisted cotangent bundles of the complex projective space
Takashi Hashimoto
https://arxiv.org/abs/2507.06604 https://…

A hyperkähler metric on twisted cotangent bundles of the complex projective space
We construct a hyperkähler metric on twisted cotangent bundles of the complex projective space $\mathbb{CP}^n$ explicitly in terms of local coordinates. Note that the twisted cotangent bundles of $\mathbb{CP}^n$ are holomorphically isomorphic to complex semisimple coadjoint orbits of $\mathrm{SL}_{n+1}(\mathbb{C})$.

Fixed Points of Meir-Keeler and Leader Contractions with bounded orbits in b-Metric Spaces
Hassan Khandani
https://arxiv.org/abs/2506.09074 https://…

Fixed Points of Meir-Keeler and Leader Contractions with bounded orbits in b-Metric Spaces
We establish fixed-point theorems for Meir-Keeler-type contractions in b-metric spaces. While Lu et al. demonstrated via an explicit counterexample that classical Meir-Keeler contractions may fail to admit fixed points in this setting, we prove that a natural strengthening of the conditions yields existence results. Specifically, we show that every non-expansive Leader contraction with bounded orbits in a b-metric space possesses a fixed point. To contextualize our findings, we present a hier…

Gromov's reconstruction theorem and measured Gromov-Hausdorff convergence in Lorentzian geometry
Mathias Braun, Clemens S\"amann
https://arxiv.org/abs/2506.10852

Gromov's reconstruction theorem and measured Gromov-Hausdorff convergence in Lorentzian geometry
We establish Gromov's celebrated reconstruction theorem in Lorentzian geometry. Alongside this result, we introduce and study a natural concept of isomorphy of normalized bounded Lorentzian metric measure spaces. We outline applications to the spacetime reconstruction problem from causal set theory. Lastly, we propose three notions of convergence of (isomorphism classes of) normalized bounded Lorentzian metric measure spaces, for which we prove several fundamental properties.

Vacuum Homogeneous and Nonhomogeneous Metrics with Conventional and Quantized Metric Tensor: Singular or Nonsingular Solution
A. Tawfik (Egyptian Ctr. Theor. Phys., Cairo,Future U. in Egypt), S. G. Elgendi (Islamic U. in Madinah), M. Hanafy (Benha U.)
https://arxiv.org/abs/2506.08254

Vacuum Homogeneous and Nonhomogeneous Metrics with Conventional and Quantized Metric Tensor: Singular or Nonsingular Solution
To investigate whether the Universe underwent a singularity or maintained a nonsingular state, we carry out analytical and numerical analyses of the evolution of the Raychaudhuri equations in vacuum, alongside homogeneous and nonhomogeneous cosmic backgrounds. The results obtained from the Schwarzschild, Friedmann--Lemaitre--Robertson--Walker (FLRW), and Einstein--Gilbert--Straus (EGS) metrics are systematically compared. Analyzing the results from both, conventional and quantized metric tensor…

Renormalization group flows in area-metric gravity
Johanna Borissova, Bianca Dittrich, Astrid Eichhorn, Marc Schiffer
https://arxiv.org/abs/2507.02034 http…

Renormalization group flows in area-metric gravity
We put forward the first analysis of renormalization group flows in an area-metric theory, motivated by spin-foam quantum gravity. Area-metric gravity contains the well-known length-metric degrees of freedom of standard gravity as well as additional shape-mismatching degrees of freedom. To be phenomenologically viable, the shape-mismatching degrees of freedom have to decouple under the renormalization group flow towards lower scales. We test this scenario by calculating the renormalization grou…

A sequence of compact metric spaces and an isometric embedding into the Gromov-Hausdorff space
Takuma Byakuno
https://arxiv.org/abs/2507.07449 https://

A sequence of compact metric spaces and an isometric embedding into the Gromov-Hausdorff space
For a convergent series with positive terms, we prove that the $\ell^\infty$ product space of bounded subspaces of the Gromov-Hausdorff space can be isometrically embedded into the Gromov-Hausdorff space, where each subspace consists of compact metric spaces with the diameter less than or equal to the term.

New Solutions for Topological Defects with Continuous Distributions:A Conformal Metric Perspective
A. M. de M. Carvalho, G. Q. Garcia, C. Furtado
https://arxiv.org/abs/2507.06117 …

New Solutions for Topological Defects with Continuous Distributions:A Conformal Metric Perspective
We present new exact solutions for two-dimensional geometries generated by continuous distributions of topological defects within a conformal metric framework. By reformulating Einstein's equations in two dimensions as a Poisson equation for the conformal factor, we analyze how smooth defect densities -- such as Gaussian, exponential, and power-law profiles -- regularize curvature singularities and encode nontrivial topological information. Each distribution yields a well-defined geometry that …

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- A link condition for simplicial complexes, and CUB spaces
Thomas Haettel