Tootfinder

Non-local Metric-Affine Gravity
Salvatore Capozziello, Damianos Iosifidis
https://arxiv.org/abs/2510.01777 https://arxiv.org/pdf/2510.01777

Non-local Metric-Affine Gravity
Non-local gravity can potentially solve several problems of gravitational field both at Ultra-Violet and Infra-Red scales. However, such an approach has been formulated mainly in metric formalism. In this paper, we discuss non-local theories of gravity in the metric-affine framework. In particular, we study the dynamics of metric-affine analogue of some well-studied non-local theories, by treating the metric and the connection as independent fields. The approach gives the opportunity to deal wi…

Metric Convergence of Sequences of Static Spacetimes with the Null Distance
Brian Allen
https://arxiv.org/abs/2510.02237 https://arxiv.org/pdf/2510.02237…

Metric Convergence of Sequences of Static Spacetimes with the Null Distance
How should one define metric space notions of convergence for sequences of spacetimes? Since a Lorentzian manifold does not define a metric space directly, the uniform convergence, Gromov-Hausdorff (GH) convergence, and Sormani-Wenger Intrinsic Flat (SWIF) convergence does not extend automatically. One approach is to define a metric space structure, which is compatible with the Lorentzian structure, so that the usual notions of convergence apply. This approach was taken by C. Sormani and C. Veg…

Evaluation of Stress Detection as Time Series Events -- A Novel Window-Based F1-Metric
Harald Vilhelm Skat-R{\o}rdam, Sneha Das, Kathrine Sofie Rasmussen, Nicole Nadine L{\o}nfeldt, Line Clemmensen
https://arxiv.org/abs/2509.03240

Evaluation of Stress Detection as Time Series Events -- A Novel Window-Based F1-Metric
Accurate evaluation of event detection in time series is essential for applications such as stress monitoring with wearable devices, where ground truth is typically annotated as single-point events, even though the underlying phenomena are gradual and temporally diffused. Standard metrics like F1 and point-adjusted F1 (F1$_{pa}$) often misrepresent model performance in such real-world, imbalanced datasets. We introduce a window-based F1 metric (F1$_w$) that incorporates temporal tolerance, enab…

Throttling for metric dimension and its variants
Boris Brimkov, Peter Diao, Jesse Geneson, Carolyn Reinhart, Shen-Fu Tsai, William Wang, Kyle Worley
https://arxiv.org/abs/2510.00530

Throttling for metric dimension and its variants
Metric dimension is a graph parameter that has been applied to robot navigation and finding low-dimensional vector embeddings. Throttling entails minimizing the sum of two available resources when solving certain graph problems. In this paper, we introduce throttling for metric dimension, edge metric dimension, and mixed metric dimension. In the context of vector embeddings, metric dimension throttling finds a low-dimensional, low-magnitude embedding with integer coordinates. We show that compu…

Product-State Manifolds for M Quantum Systems with N Levels using the Fano form and the Induced Euclidean Metric
Fotios D. Oikonomou
https://arxiv.org/abs/2509.02891 https://

Product-State Manifolds for M Quantum Systems with N Levels using the Fano form and the Induced Euclidean Metric
In quantum mechanics separable states can be characterized as convex combinations of product states whereas non-separable states exhibit entanglement. Quantum entanglement has played a pivotal role in both theoretical investigations and practical applications within quantum information science. In this study, we explore the connection between product states and geometric structures, specifically manifolds and their associated geometric properties such as the first fundamental form (metric). We …

The set of distances in a Polish metric space
John D. Clemens
https://arxiv.org/abs/2509.01027 https://arxiv.org/pdf/2509.01027

The set of distances in a Polish metric space
We show that a set of non-negative reals is the distance set of a separable complete metric space if and only if it is either countable or is an analytic set which has 0 as a limit point. We also consider spaces with simpler distance sets.

An Efficient Quality Metric for Video Frame Interpolation Based on Motion-Field Divergence
Conall Daly, Darren Ramsook, Anil Kokaram
https://arxiv.org/abs/2510.01361 https://

An Efficient Quality Metric for Video Frame Interpolation Based on Motion-Field Divergence
Video frame interpolation is a fundamental tool for temporal video enhancement, but existing quality metrics struggle to evaluate the perceptual impact of interpolation artefacts effectively. Metrics like PSNR, SSIM and LPIPS ignore temporal coherence. State-of-the-art quality metrics tailored towards video frame interpolation, like FloLPIPS, have been developed but suffer from computational inefficiency that limits their practical application. We present $\text{PSNR}_{\text{DIV}}$, a novel ful…

Metric version of the Zariski Multiplicity Conjecture is true for multiplicity two
A. Fernandes, Z. Jelonek, J. E. Sampaio
https://arxiv.org/abs/2509.03447 https://

Metric version of the Zariski Multiplicity Conjecture is true for multiplicity two
We prove that if two algebraic $(n-1)$-dimensional cones $P, R\subset\mathbb C^n$ are ambient homeomorphic, then their bases $B_P$ and $B_R$ have the same Euler characteristic. As an application, we show our main result: if $(X,0),(Y,0)\subset (\C^n,0)$ are germs of analytic hypersurfaces, which are ambient bi-Lipschitz equivalent and $m_0(X)=2$, then also $m_0(Y)=2.$. As another application, we also obtain a complete positive answer to the Metric Arnold-Vassiliev Problem, which says that if tw…

Trace and Extension Theorems for Besov Functions in Doubling Metric Measure Spaces
Iv\'an Caama\~no, Josh Kline
https://arxiv.org/abs/2510.01385 https://

Trace and Extension Theorems for Besov Functions in Doubling Metric Measure Spaces
In the setting of a non-complete doubling metric measure space $(Ω,d,μ)$, we construct various bounded linear trace and extension operators for homogeneous and inhomogeneous Besov spaces $B^α_{p,q}$. Equipping the boundary $\partialΩ:=\overlineΩ\setminusΩ$ with a measure which is codimension $θ$ Ahlfors regular with respect to $μ$, these operators take the form \[ T:B^α_{p,q}(Ω)\to B^{α-θ/p}_{p,q}(\partialΩ),\quad E:B^α_{p,q}(\partialΩ)\to B^{α+θ/p}_{p,q}(Ω). \] The trac…

MightyPPL: Verification of MITL with Past and Pnueli Modalities
Hsi-Ming Ho, Shankara Narayanan Krishna, Khushraj Madnani, Rupak Majumdar, Paritosh Pandya
https://arxiv.org/abs/2510.01490

MightyPPL: Verification of MITL with Past and Pnueli Modalities
Metric Interval Temporal Logic (MITL) is a popular formalism for specifying properties of reactive systems with timing constraints. Existing approaches to using MITL in verification tasks, however, have notable drawbacks: they either support only limited fragments of the logic or allow for only incomplete verification. This paper introduces MightyPPL, a new tool for translating formulae in Metric Interval Temporal Logic with Past and Pnueli modalities (MITPPL) over the pointwise semantics into …

Scalar Curvature And Transfer Maps In Spin And Spin^c Bordism
Elliot Granath
https://arxiv.org/abs/2509.02793 https://arxiv.org/pdf/2509.02793

Scalar Curvature And Transfer Maps In Spin And Spin^c Bordism
In 1992, Stolz proved that, among simply connected Spin-manifolds of dimension 5 or greater, the vanishing of a particular invariant $α$ is necessary and sufficient for the existence of a metric of positive scalar curvature. More precisely, there is a map $α\colonΩ_*^{\rm Spin}\to {\rm ko}$ (which may be realized as the index of a Dirac operator) which Hitchin established vanishes on bordism classes containing a manifold with a metric of positive scalar curvature. Stolz showed $\kerα$ is th…

Analysis on asymmetric metric measure spaces: $q$-heat flow, $q$-Laplacian and Sobolev spaces
Alexandru Krist\'aly, Shin-ichi Ohta, Wei Zhao
https://arxiv.org/abs/2509.03268

Analysis on asymmetric metric measure spaces: $q$-heat flow, $q$-Laplacian and Sobolev spaces
We investigate geometric analysis on metric measure spaces equipped with asymmetric distance functions. Extending concepts from the symmetric case, we introduce upper gradients and corresponding $L^q$-energy functionals as well as $q$-Laplacian in the asymmetric setting. Along the lines of gradient flow theory, we then study $q$-heat flow as the $L^2$-gradient flow for $L^q$-energy. We also study the Sobolev spaces over asymmetric metric measure spaces, extending some results of Ambrosio--Gigli…

The trace-free Einstein tensor is not variational for the metric as field variable
Arian L. von Blanckenburg, Domenico Giulini, Philip K. Schwartz
https://arxiv.org/abs/2509.02490

The trace-free Einstein tensor is not variational for the metric as field variable
It is well-known that the trace-free Einstein tensor of a pseudo-Riemannian metric cannot arise by variation of a local diffeomorphism-invariant action functional with the (inverse) metric as field variable. We show that this statement remains true even for general local actions, without the assumption of diffeomorphism invariance.

Lipschitz-free spaces and Bossard's reduction argument
Richard J. Smith
https://arxiv.org/abs/2509.00722 https://arxiv.org/pdf/2509.00722

Lipschitz-free spaces and Bossard's reduction argument
Motivated by recent work of E. Basset, G. Lancien and A. Procházka, we use the reduction argument of Bossard to prove two results: if a separable Banach space is isomorphically universal for the class of Lipschitz-free spaces over the countable complete discrete metric spaces then it is isomorphically universal for the class of separable Banach spaces, and if a complete separable metric space is Lipschitz universal for the same class of metric spaces then it is Lipschitz universal for all sepa…

Geometric properties of unit groups of von Neumann's continuous rings
Friedrich Martin Schneider
https://arxiv.org/abs/2509.01556 https://arxiv.org/pdf…

Geometric properties of unit groups of von Neumann's continuous rings
We prove that, if $R$ is an irreducible, continuous ring, then its unit group $\mathrm{GL}(R)$, equipped with the topology generated by the rank metric, is topologically simple modulo its center, path-connected, locally path-connected, bounded in the sense of Bourbaki, and not admitting any non-zero escape function. All these topological insights are consequences of more refined geometric results concerning the rank metric, in particular with regard to the set of algebraic elements. Thanks to t…

TREE:Token-Responsive Energy Efficiency Framework For Green AI-Integrated 6G Networks
Tao Yu, Kaixuan Huang, Tengsheng Wang, Jihong Li, Shunqing Zhang, Shuangfeng Han, Xiaoyun Wang, Qunsong Zeng, Kaibin Huang, Vincent K. N. Lau
https://arxiv.org/abs/2509.02250

TREE:Token-Responsive Energy Efficiency Framework For Green AI-Integrated 6G Networks
As wireless networks evolve toward AI-integrated intelligence, conventional energy-efficiency metrics fail to capture the value of AI tasks. In this paper, we propose a novel EE metric called Token-Responsive Energy Efficiency (TREE), which incorporates the token throughput of large models as network utility carriers into the system utility. Based on this metric, we analyze the design principles of AI-integrated 6G networks from the perspective of three critical AI elements, namely computing po…

End-to-End Deep Learning for Predicting Metric Space-Valued Outputs
Yidong Zhou, Su I Iao, Hans-Georg M\"uller
https://arxiv.org/abs/2509.23544 https://

End-to-End Deep Learning for Predicting Metric Space-Valued Outputs
Many modern applications involve predicting structured, non-Euclidean outputs such as probability distributions, networks, and symmetric positive-definite matrices. These outputs are naturally modeled as elements of general metric spaces, where classical regression techniques that rely on vector space structure no longer apply. We introduce E2M (End-to-End Metric regression), a deep learning framework for predicting metric space-valued outputs. E2M performs prediction via a weighted Fréchet me…

Spectral bounds and heat kernel upper estimates for Dirichlet forms
Aobo Chen, Zhenyu Yu
https://arxiv.org/abs/2509.01115 https://arxiv.org/pdf/2509.01115

Spectral bounds and heat kernel upper estimates for Dirichlet forms
We use a Harnack-type inequality on exit times and spectral bounds to characterize upper bounds of the heat kernel associated with any regular Dirichlet form without killing part, where the scale function may vary with position. We further show that this Harnack-type inequality is preserved under quasi-symmetric changes of metric on uniformly perfect metric spaces. This generalised the work of Mariano and Wang [Stochastic Process. Appl. 189 (2025) 104707)].

Introducing LCOAI: A Standardized Economic Metric for Evaluating AI Deployment Costs
Eliseo Curcio
https://arxiv.org/abs/2509.02596 https://arxiv.org/pdf/2…

Introducing LCOAI: A Standardized Economic Metric for Evaluating AI Deployment Costs
As artificial intelligence (AI) becomes foundational to enterprise infrastructure, organizations face growing challenges in accurately assessing the full economic implications of AI deployment. Existing metrics such as API token costs, GPU-hour billing, or Total Cost of Ownership (TCO) fail to capture the complete lifecycle costs of AI systems and provide limited comparability across deployment models. This paper introduces the Levelized Cost of Artificial Intelligence (LCOAI), a standardized e…

Crosslisted article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[2/10]:
- AutoPK: Leveraging LLMs and a Hybrid Similarity Metric for Advanced Retrieval of Pharmacokinetic ...
Sholehrasa, Ghanaatian, Caragea, Tell, Riviere, Jaberi-Douraki

Calibrating the Full Predictive Class Distribution of 3D Object Detectors for Autonomous Driving
Cornelius Schr\"oder, Marius-Raphael Schl\"uter, Markus Lienkamp
https://arxiv.org/abs/2510.01829

Calibrating the Full Predictive Class Distribution of 3D Object Detectors for Autonomous Driving
In autonomous systems, precise object detection and uncertainty estimation are critical for self-aware and safe operation. This work addresses confidence calibration for the classification task of 3D object detectors. We argue that it is necessary to regard the calibration of the full predictive confidence distribution over all classes and deduce a metric which captures the calibration of dominant and secondary class predictions. We propose two auxiliary regularizing loss terms which introduce …

Evaluating Spatiotemporal Consistency in Automatically Generated Sewing Instructions
Luisa Geiger, Mareike Hartmann, Michael Sullivan, Alexander Koller
https://arxiv.org/abs/2509.24792

Evaluating Spatiotemporal Consistency in Automatically Generated Sewing Instructions
In this paper, we propose a novel, automatic tree-based evaluation metric for LLM-generated step-by-step assembly instructions, that more accurately reflects spatiotemporal aspects of construction than traditional metrics such as BLEU and BERT similarity scores. We apply our proposed metric to the domain of sewing instructions, and show that our metric better correlates with manually-annotated error counts as well as human quality ratings, demonstrating our metric's superiority for evaluating t…

Towards Data-Driven Metrics for Social Robot Navigation Benchmarking
Pilar Bachiller-Burgos, Ulysses Bernardet, Luis V. Calderita, Pranup Chhetri, Anthony Francis, Noriaki Hirose, No\'e P\'erez, Dhruv Shah, Phani T. Singamaneni, Xuesu Xiao, Luis J. Manso
https://arxiv.org/abs/2509.01251

Towards Data-Driven Metrics for Social Robot Navigation Benchmarking
This paper presents a joint effort towards the development of a data-driven Social Robot Navigation metric to facilitate benchmarking and policy optimization. We provide our motivations for our approach and describe our proposal for storing rated social navigation trajectory datasets. Following these guidelines, we compiled a dataset with 4427 trajectories -- 182 real and 4245 simulated -- and presented it to human raters, yielding a total of 4402 rated trajectories after data quality assurance…

AutoPK: Leveraging LLMs and a Hybrid Similarity Metric for Advanced Retrieval of Pharmacokinetic Data from Complex Tables and Documents
Hossein Sholehrasa, Amirhossein Ghanaatian, Doina Caragea, Lisa A. Tell, Jim E. Riviere, Majid Jaberi-Douraki
https://arxiv.org/abs/2510.00039

AutoPK: Leveraging LLMs and a Hybrid Similarity Metric for Advanced Retrieval of Pharmacokinetic Data from Complex Tables and Documents
Pharmacokinetics (PK) plays a critical role in drug development and regulatory decision-making for human and veterinary medicine, directly affecting public health through drug safety and efficacy assessments. However, PK data are often embedded in complex, heterogeneous tables with variable structures and inconsistent terminologies, posing significant challenges for automated PK data retrieval and standardization. AutoPK, a novel two-stage framework for accurate and scalable extraction of PK da…

Tilted Dirac cones and their topology in Holographic Materials
Jeong-Won Seo, Taewon Yuk, Sang-Jin Sin
https://arxiv.org/abs/2509.03033 https://arxiv.org/p…

Tilted Dirac cones and their topology in Holographic Materials
We explore strongly correlated materials with tilted Dirac cone by introducing a method to realize this spectral feature within a holographic setup. Following the work by Moradpouri et al., we construct an asymptotically AdS spacetime by uplifting the vielbein of Volovik et al to tilt the flat spacetime light cone. We then couple the resulting metric to holographic fermions and compute their spectral functions, confirming the presence of a tilted Dirac cone in momentum space. We also calculate …

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Left K-Cauchy regular maps between quasi-metric spaces
Om Dev Singh, Anubha Jindal
https://arxiv.org/abs/2509.24619 https://arxiv.org/pdf/2509.24619…

Left K-Cauchy regular maps between quasi-metric spaces
This article presents a systematic study of a class of maps between quasi-metric spaces that preserve left K-Cauchy sequences. We call such maps left K-Cauchy regular maps. Several characterizations of these maps have been given in terms of the structural properties of the underlying quasi-metric spaces. In particular, we characterize left K-Cauchy regular maps in terms of hereditarily precompact sets by using a suitable version of the classical Efremovic Lemma in the setting of quasi-metric sp…

A semi-symmetric metric connection, perfect fluid space-time and phantom barrier
Miroslav Maksimovi\'c, Milan Zlatanovi\'c, Marija Najdanovi\'c
https://arxiv.org/abs/2510.00849

A semi-symmetric metric connection, perfect fluid space-time and phantom barrier
We consider a concircularly semi-symmetric metric connection and its application. The Ricci tensors with respect to the concircularly semi-symmetric metric connection are symmetric, and they are used to define Einstein type manifolds. In this way, conditions under which a pseudo-Riemannian manifold is quasi-Einstein are obtained. On a Lorentzian manifold, a concircularly semi-symmetric metric connection with a unit timelike generator becomes a semi-symmetric metric $P$-connection, and a Lorentz…

Contrastive Retrieval Heads Improve Attention-Based Re-Ranking
Linh Tran, Yulong Li, Radu Florian, Wei Sun
https://arxiv.org/abs/2510.02219 https://arxiv.o…

Contrastive Retrieval Heads Improve Attention-Based Re-Ranking
The strong zero-shot and long-context capabilities of recent Large Language Models (LLMs) have paved the way for highly effective re-ranking systems. Attention-based re-rankers leverage attention weights from transformer heads to produce relevance scores, but not all heads are created equally: many contribute noise and redundancy, thus limiting performance. To address this, we introduce CoRe heads, a small set of retrieval heads identified via a contrastive scoring metric that explicitly reward…

Credible Uncertainty Quantification under Noise and System Model Mismatch
Penggao Yan, Li-Ta Hsu
https://arxiv.org/abs/2509.03311 https://arxiv.org/pdf/250…

Credible Uncertainty Quantification under Noise and System Model Mismatch
State estimators often provide self-assessed uncertainty metrics, such as covariance matrices, whose reliability is critical for downstream tasks. However, these self-assessments can be misleading due to underlying modeling violations like noise or system model mismatch. This letter addresses the problem of estimator credibility by introducing a unified, multi-metric evaluation framework. We construct a compact credibility portfolio that synergistically combines traditional metrics like the Nor…

On the non-existence of perfect codes in the sum-rank metric
Giuseppe Del Prete, Antonio Roccolano, Ferdinando Zullo
https://arxiv.org/abs/2508.20940 https://

On the non-existence of perfect codes in the sum-rank metric
We study perfect codes in the sum-rank metric, a generalization of both the Hamming and rank metrics relevant in multishot network coding and space-time coding. A perfect code attains equality in the sphere-packing bound, corresponding to a partition of the ambient space into disjoint metric balls. While perfect codes in the Hamming and rank metrics are completely classified, the existence of nontrivial perfect codes in the sum-rank metric remains largely open. In this paper, we investigate lin…

Multi-AAV-enabled Distributed Beamforming in Low-Altitude Wireless Networking for AoI-Sensitive IoT Data Forwarding
Zifan Lang, Guixia Liu, Jiahui Li, Geng Sun, Zemin Sun, Jiacheng Wang, Dusit Niyato, Victor C. M. Leung
https://arxiv.org/abs/2509.01427

Multi-AAV-enabled Distributed Beamforming in Low-Altitude Wireless Networking for AoI-Sensitive IoT Data Forwarding
With the rapid development of low-altitude wireless networking, autonomous aerial vehicles (AAVs) have emerged as critical enablers for timely and reliable data delivery, particularly in remote or underserved areas. In this context, the age of information (AoI) has emerged as a critical performance metric for evaluating the freshness and timeliness of transmitted information in Internet of things (IoT) networks. However, conventional AAV-assisted data transmission is fundamentally limited by fi…

Quantifying the noise sensitivity of the Wasserstein metric for images
Erik Lager, Gilles Mordant, Amit Moscovich
https://arxiv.org/abs/2510.01015 https://…

Quantifying the noise sensitivity of the Wasserstein metric for images
Wasserstein metrics are increasingly being used as similarity scores for images treated as discrete measures on a grid, yet their behavior under noise remains poorly understood. In this work, we consider the sensitivity of the signed Wasserstein distance with respect to pixel-wise additive noise and derive non-asymptotic upper bounds. Among other results, we prove that the error in the signed 2-Wasserstein distance scales with the square root of the noise standard deviation, whereas the Euclide…

Basic scientists' disproportionate impact amid applied drift reveals structural asymmetry in science
Rikuei Kaku, Mikako Bito, Keita Nishimoto, Ichiro Sakata, Kimitaka Asatani
https://arxiv.org/abs/2509.01530

Basic scientists' disproportionate impact amid applied drift reveals structural asymmetry in science
Despite broad acclaim for basic research, science is undergoing an applied shift that marginalizes basic scientists. This gap reflects an incomplete understanding of their distinctive roles, which prevents translating philosophical appreciation into effective support. We introduce a scalable metric--the application score--to position research along the basic-applied spectrum and apply it to 62 million publications (1970-2023) to reveal the distinctive contributions of basic scientists. We find …

Distance-based (and path-based) covering problems for graphs of given cyclomatic number
Dibyayan Chakraborty, Florent Foucaud, Anni Hakanen
https://arxiv.org/abs/2509.00383 http…

Distance-based (and path-based) covering problems for graphs of given cyclomatic number
We study a large family of graph covering problems, whose definitions rely on distances, for graphs of bounded cyclomatic number (that is, the minimum number of edges that need to be removed from the graph to destroy all cycles). These problems include (but are not restricted to) three families of problems: (i) variants of metric dimension, where one wants to choose a small set $S$ of vertices of the graph such that every vertex is uniquely determined by its ordered vector of distances to the v…

Comparing Contrastive and Triplet Loss in Audio-Visual Embedding: Intra-Class Variance and Greediness Analysis
Donghuo Zeng
https://arxiv.org/abs/2510.02161 https://

Comparing Contrastive and Triplet Loss in Audio-Visual Embedding: Intra-Class Variance and Greediness Analysis
Contrastive loss and triplet loss are widely used objectives in deep metric learning, yet their effects on representation quality remain insufficiently understood. We present a theoretical and empirical comparison of these losses, focusing on intra- and inter-class variance and optimization behavior (e.g., greedy updates). Through task-specific experiments with consistent settings on synthetic data and real datasets-MNIST, CIFAR-10-it is shown that triplet loss preserves greater variance within…

ORACLE: A rigorous metric and method to explore all near-optimal designs for energy systems
E. M. Turan, S. Moret, A. Bardow
https://arxiv.org/abs/2509.26452 https://

ORACLE: A rigorous metric and method to explore all near-optimal designs for energy systems
Optimization models are fundamental tools for providing quantitative insights to decision-makers. However, models, objectives, and constraints do not capture all real-world factors accurately. Thus, instead of the single optimal solution, real-world stakeholders are often interested in the near-optimal space -- solutions that lie within a specified margin of the optimal objective value. Solutions in the near-optimal space can then be assessed regarding desirable non-modeled or qualitative aspec…

Local asymmetry in spatial interactions: A generalized slide-vector approach
Bin Liu, Zhaoya Gong, Jean-Claude Thill
https://arxiv.org/abs/2509.01131 https://

Local asymmetry in spatial interactions: A generalized slide-vector approach
The conceptualization of space is crucial for comprehending the processes that shape geographic phenomena. Functional space exhibits asymmetric spatial separations, which deviate from the symmetry axiom of metric space commonly adopted as a representation of the geographical space. However, existing literature has paid scant attention to the issue of asymmetry of spatial separation. Technically, spatial models and analysis methods grounded in a Euclidean representation of the geographical space…

Zimtohrli: An Efficient Psychoacoustic Audio Similarity Metric
Jyrki Alakuijala, Martin Bruse, Sami Boukortt, Jozef Marus Coldenhoff, Milos Cernak
https://arxiv.org/abs/2509.26133

Zimtohrli: An Efficient Psychoacoustic Audio Similarity Metric
This paper introduces Zimtohrli, a novel, full-reference audio similarity metric designed for efficient and perceptually accurate quality assessment. In an era dominated by computationally intensive deep learning models and proprietary legacy standards, there is a pressing need for an interpretable, psychoacoustically-grounded metric that balances performance with practicality. Zimtohrli addresses this gap by combining a 128-bin gammatone filterbank front-end, which models the frequency resolut…

Metric response of relative entropy: a universal indicator of quantum criticality
Pritam Sarkar, Diptiman Sen, Arnab Sen
https://arxiv.org/abs/2509.22515 https://

Metric response of relative entropy: a universal indicator of quantum criticality
The information-geometric origin of fidelity susceptibility and its utility as a universal probe of quantum criticality in many-body settings have been widely discussed. Here we explore the metric response of quantum relative entropy (QRE), by tracing out all but $n$ adjacent sites from the ground state of spin chains of finite length $N$, as a parameter of the corresponding Hamiltonian is varied. The diagonal component of this metric defines a susceptibility of the QRE that diverges at quantum…

Global existence of the irrotational Euler-Norstrom equations with a positive cosmological constant: The gravitational field equation
Uwe Brauer, Lavi Karp
https://arxiv.org/abs/2509.02023

Global existence of the irrotational Euler-Norstrom equations with a positive cosmological constant: The gravitational field equation
Our objective is to demonstrate the global existence of classical solutions for the nonlinear irrotational Euler-Nordstroem system, which includes a linear equation of state and a cosmological constant. In this framework, the gravitational field is represented by a single scalar function that satisfies a specific semi-linear wave equation. We focus on spatially periodic deviations from the background metric, which is why we study the semi-linear wave equation on the three-dimensional torus $\ma…

Infinity thick quasiconvexity and applications
Miguel Garc\'ia-Bravo, Toni Ikonen, Zheng Zhu
https://arxiv.org/abs/2509.01194 https://arxiv.org/pdf/250…

Infinity thick quasiconvexity and applications
We investigate geometric properties of a metric measure space where every function in the Newton--Sobolev space $N^{1,\infty}(Z)$ has a Lipschitz representative. We prove that when the metric space is locally complete and the reference measure is infinitesimally doubling, the above property is equivalent to the space being very $\infty$-thick quasiconvex up to a scale. That is, up to some scale, every pair of points can be joined by a family of quasiconvex curves that is not negligible for the …

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Notions of Cauchy completeness for normed categories
Dirk Hofmann, Walter Tholen
https://arxiv.org/abs/2510.00912 https://arxiv.org/pdf/2510.00912

Notions of Cauchy completeness for normed categories
As already mentioned by Lawvere in his 1973 paper, the characterisation of Cauchy completeness of metric spaces in terms of representability of adjoint distributors amounts to the idempotent-split property of an ordinary category when the governing symmetric monoidal-closed category is changed from the extended real half-line to the category of sets. In this paper, for any commutative quantale \(\mathcal{V}\), we extend these two characterisations of Lawvere-style completeness to \(\mathcal{V}\…

Path--Averaged Contractions: A New Generalization of the Banach Contraction Principle
Nicola Fabiano
https://arxiv.org/abs/2510.01496 https://arxiv.org/pdf…

Path--Averaged Contractions: A New Generalization of the Banach Contraction Principle
We introduce a novel class of self-mappings on metric spaces, called \textbf{PA-contractions} (Path-Averaged Contractions), defined by an averaging condition over iterated distances. We prove that every continuous PA-contraction on a complete metric space has a unique fixed point, and the Picard iterates converge to it. This condition strictly generalizes the classical Banach contraction principle. We provide examples showing that PA-contractions are independent of F-contractions, Kannan, Chatt…

Multi Scale Analysis of Nifty 50 Return Characteristics Valuation Dynamics and Market Complexity 1990 to 2024
Chandradew Sharma
https://arxiv.org/abs/2509.00697 https://

Multi Scale Analysis of Nifty 50 Return Characteristics Valuation Dynamics and Market Complexity 1990 to 2024
This study presents a unified, distribution-aware, and complexity-informed framework for understanding equity return dynamics in the Indian market, using 34 years (1990 to 2024) of Nifty 50 index data. Addressing a key gap in the literature, we demonstrate that the price to earnings ratio, as a valuation metric, may probabilistically map return distributions across investment horizons spanning from days to decades. Return profiles exhibit strong asymmetry. One-year returns show a 74 percent p…

On Topology and Geometry of Hessian Manifolds
Hanwen Liu
https://arxiv.org/abs/2509.01176 https://arxiv.org/pdf/2509.01176…

On Topology and Geometry of Hessian Manifolds
For a differentiable manifold $M$, a pair $(M, \nabla)$ is termed an affine manifold, if $\nabla$ is a flat and torsion-free connection on the tangent bundle $TM\rightarrow M$. A Riemannian metric $g$ on $M$ is called a Hessian metric on affine manifold $(M, \nabla)$, if $g$ can be expressed locally as the Hessian quadratic form of some smooth potential $f$. An affine manifold equipped with a Hessian metric is termed a Hessian manifold. We study the topology and geometry of Hessian manifolds. …

"Scientists shocked to find marine life thriving on World War II explosives in the Baltic Sea"
#BalticSea #Oceans #Environment

Marine life found thriving on WWII explosives in the Baltic Sea
German waters alone contain about 1.5 million metric tonnes of dumped weapons, mostly from the two world wars in the 20th century.

Intrinsic nonlinear valley Nernst effect in the strained bilayer graphene
Ying-Li Wu, Jia-Liang Wan, Xiao-Qin Yu
https://arxiv.org/abs/2509.01961 https://a…

Intrinsic nonlinear valley Nernst effect in the strained bilayer graphene
We theoretically analyze the nonlinear valley Nernst effect (NVNE) as the second-order response of temperature gradient through the semiclassical framework of electron dynamics up to second order. Our study shows that an intrinsic nonlinear pure valley current can be generated vertically to the applied temperature in the materials with both inversion and time-reversal symmetries. This intrinsic NVNE has a quantum origin from the quantum metric and shows independence from the relaxation time. It…

Stability of the inverse Sturm-Liouville problem on a quantum tree
Natalia P. Bondarenko
https://arxiv.org/abs/2510.01920 https://arxiv.org/pdf/2510.01920

Stability of the inverse Sturm-Liouville problem on a quantum tree
This paper deals with the Sturm-Liouville operators with distribution potentials of the space $W_2^{-1}$ on a metric tree. We study an inverse spectral problem that consists in the recovery of the potentials from the characteristic functions related to various boundary conditions. We prove the uniform stability of this inverse problem for potentials in a ball of any fixed radius, as well as the local stability under small perturbations of the spectral data. Our approach is based on a stable alg…

How Instruction-Tuning Imparts Length Control: A Cross-Lingual Mechanistic Analysis
Elisabetta Rocchetti, Alfio Ferrara
https://arxiv.org/abs/2509.02075 https://

How Instruction-Tuning Imparts Length Control: A Cross-Lingual Mechanistic Analysis
Adhering to explicit length constraints, such as generating text with a precise word count, remains a significant challenge for Large Language Models (LLMs). This study aims at investigating the differences between foundation models and their instruction-tuned counterparts, on length-controlled text generation in English and Italian. We analyze both performance and internal component contributions using Cumulative Weighted Attribution, a metric derived from Direct Logit Attribution. Our finding…

Local rigidity of covering constructions and Weil--Petersson subvarieties of the moduli space of curves
Carlos A. Serv\'an
https://arxiv.org/abs/2509.25523 https://

Local rigidity of covering constructions and Weil--Petersson subvarieties of the moduli space of curves
We show that totally geodesic subvarieties of the moduli space $\mathcal M_{g,n}$ of genus $g$ curves with $n$ marked points, endowed with the Weil--Petersson metric, are locally rigid. This implies that covering constructions -- examples of totally geodesic subvarieties of $\mathcal M_{g,n}$ endowed with the Teichmüller metric -- are locally rigid. We deduce the local rigidity statement from a more general rigidity result for a class of orbifold maps to $\mathcal M_{g,n}$.

Observer-Usable Information as a Task-specific Image Quality Metric
Changjie Lu, Sourya Sengupta, Hua Li, Mark A. Anastasio
https://arxiv.org/abs/2510.00298 https://

Observer-Usable Information as a Task-specific Image Quality Metric
Objective, task-based, measures of image quality (IQ) have been widely advocated for assessing and optimizing medical imaging technologies. Besides signal detection theory-based measures, information-theoretic quantities have been proposed to quantify task-based IQ. For example, task-specific information (TSI), defined as the mutual information between an image and task variable, represents an optimal measure of how informative an image is for performing a specified task. However, like the idea…

General approach to vacuum nonsingular black holes: exact solutions from equation of state
O. B. Zaslavskii
https://arxiv.org/abs/2509.00899 https://arxiv.…

General approach to vacuum nonsingular black holes: exact solutions from equation of state
We consider spherically symmetric static black hole configurations that obey the vacuum equation of state: $p_{r}=-ρ$, where $p_{r}$ is the radial pressure, $ρ$ being energy density. We find in a closed form the metric for an arbitrary equation of state for tangential pressure $p_{θ}(ρ)$. The corresponding formulas enable us to embrace compact Schwarzschild-like configurations and dispersed systems. They include metrics with a regular center and singular ones. In a particular case, the metr…

A Spectral-Grassmann Wasserstein metric for operator representations of dynamical systems
Thibaut Germain, R\'emi Flamary, Vladimir R. Kostic, Karim Lounici
https://arxiv.org/abs/2509.24920

A Spectral-Grassmann Wasserstein metric for operator representations of dynamical systems
The geometry of dynamical systems estimated from trajectory data is a major challenge for machine learning applications. Koopman and transfer operators provide a linear representation of nonlinear dynamics through their spectral decomposition, offering a natural framework for comparison. We propose a novel approach representing each system as a distribution of its joint operator eigenvalues and spectral projectors and defining a metric between systems leveraging optimal transport. The proposed …

On the connectedness of the boundary of hierarchically hyperbolic spaces
Ravi Tomar
https://arxiv.org/abs/2509.00321 https://arxiv.org/pdf/2509.00321

On the connectedness of the boundary of hierarchically hyperbolic spaces
We prove that, under a mild assumption, any metrizable compactification of a one-ended proper geodesic metric space is connected. As a consequence, we deduce that the boundary, introduced by Durham--Hagen--Sisto, of a one-ended hierarchically hyperbolic space is connected. Moreover, we prove that the connectedness of the boundary of a hierarchically hyperbolic group is equivalent to the one-endedness of the group. As an application, we show that if, for $n\geq 2$, $G_1=A_1\ast\dots\ast A_n$ and…

A Robust Neural Control Design for Multi-drone Slung Payload Manipulation with Control Contraction Metrics
Xinyuan Liang, Longhao Qian, Yi Lok Lo, Hugh H. T. Liu
https://arxiv.org/abs/2510.01489

A Robust Neural Control Design for Multi-drone Slung Payload Manipulation with Control Contraction Metrics
This paper presents a robust neural control design for a three-drone slung payload transportation system to track a reference path under external disturbances. The control contraction metric (CCM) is used to generate a neural exponentially converging baseline controller while complying with control input saturation constraints. We also incorporate the uncertainty and disturbance estimator (UDE) technique to dynamically compensate for persistent disturbances. The proposed framework yields a modu…

Strong gravitational lensing by compact objects with magnetic dipole
Jin Young Kim
https://arxiv.org/abs/2509.01040 https://arxiv.org/pdf/2509.01040…

Strong gravitational lensing by compact objects with magnetic dipole
Compact objects with magnetic dipole are considered as gravitational lenses. The presence of strong magnetic field near the photon sphere can affect the trajectory of light. We compute the deflection angle near the photon sphere on the equatorial plane of the magnetic dipole. In the Einstein-Maxwell gravity we use the asymptotic metric when a massive object has a magnetic dipole moment. In the Einstein-Born-Infeld gravity we use the effective metric accomodating the nonlinear electrodynamic eff…

Metric Poincar\'e inequalities for graphs
Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov, Konstantinos Tyros
https://arxiv.org/abs/2509.25489 https://

Metric Poincaré inequalities for graphs
This article considers embeddings of bounded degree graphs into general metric spaces. Our first main result is a metric analogue of Matoušek's extrapolation that relates the Poincaré constants $γ(G,\varrho^p)$ and $γ(G,\varrho^q)$ for any pair of exponents $0 < p,q < \infty$, any bounded degree expander graph $G$, and any metric space $\mathcal{M}=(M,\varrho)$. Our second main result provides a sharp estimate of the Poincaré constant $γ(G,\varrho)$ in terms of the cardinalities of the ve…

Explore Briefly, Then Decide: Mitigating LLM Overthinking via Cumulative Entropy Regulation
Tianyi Jiang, Yi Bin, Yujuan Ding, Kainian Zhu, Fei Ma, Jingkuan Song, Heng Tao Shen
https://arxiv.org/abs/2510.02249

Explore Briefly, Then Decide: Mitigating LLM Overthinking via Cumulative Entropy Regulation
Large Language Models (LLMs) have demonstrated remarkable reasoning abilities on complex problems using long Chain-of-Thought (CoT) reasoning. However, they often suffer from overthinking, meaning generating unnecessarily lengthy reasoning steps for simpler problems. This issue may degrade the efficiency of the models and make them difficult to adapt the reasoning depth to the complexity of problems. To address this, we introduce a novel metric Token Entropy Cumulative Average (TECA), which mea…

AoI-based Scheduling of Correlated Sources for Timely Inference
Md Kamran Chowdhury Shisher, Vishrant Tripathi, Mung Chiang, Christopher G. Brinton
https://arxiv.org/abs/2509.01926

AoI-based Scheduling of Correlated Sources for Timely Inference
We investigate a real-time remote inference system where multiple correlated sources transmit observations over a communication channel to a receiver. The receiver utilizes these observations to infer multiple time-varying targets. Due to limited communication resources, the delivered observations may not be fresh. To quantify data freshness, we employ the Age of Information (AoI) metric. To minimize the inference error, we aim to design a signal-agnostic scheduling policy that leverages AoI wi…

Survival probability for jump processes in unbounded domains on metric measure spaces
Phanuel Mariano, Jing Wang
https://arxiv.org/abs/2508.21158 https://a…

Survival probability for jump processes in unbounded domains on metric measure spaces
We study the large time behavior of the survival probability $\mathbb{P}_x\left(τ_D>t\right)$ for symmetric jump processes in unbounded domains with a positive bottom of the spectrum. We prove asymptotic upper and lower bounds with explicit constants in terms of the bottom of the spectrum $λ(D)$. Our main result applies to symmetric jump processes in general metric measure spaces. For $α$-stable processes in unbounded uniformly $C^{1,1}$ domains, our results provide a probabilistic interpret…

Crosslisted article(s) found for cs.MM. https://arxiv.org/list/cs.MM/new
[1/1]:
- An Efficient Quality Metric for Video Frame Interpolation Based on Motion-Field Divergence
Conall Daly, Darren Ramsook, Anil Kokaram

Uncertainty Under the Curve: A Sequence-Level Entropy Area Metric for Reasoning LLM
Yongfu Zhu, Lin Sun, Guangxiang Zhao, Weihong Lin, Xiangzheng Zhang
https://arxiv.org/abs/2508.20384

Uncertainty Under the Curve: A Sequence-Level Entropy Area Metric for Reasoning LLM
In this work, we introduce Entropy Area Score (EAS), a simple yet effective metric to quantify uncertainty in the answer generation process of reasoning large language models (LLMs). EAS requires neither external models nor repeated sampling, it integrates token-level predictive entropy from the model itself to capture the evolution of uncertainty during generation. Empirical results show that EAS is strongly correlated with answer entropy across models and datasets. In training data selection,…

On the stability of Ricci flow on hyperbolic 3-manifolds of finite volume
Ruojing Jiang, Franco Vargas Pallete
https://arxiv.org/abs/2509.00188 https://arx…

On the stability of Ricci flow on hyperbolic 3-manifolds of finite volume
On a hyperbolic 3-manifold of finite volume, we prove that if the initial metric is sufficiently close to the hyperbolic metric $h_0$, then the normalized Ricci-DeTurck flow exists for all time and converges exponentially fast to $h_0$ in a weighted Hölder norm. A key ingredient of our approach is the application of interpolation theory. Furthermore, this result is a valuable tool for investigating minimal surface entropy, which quantifies the growth rate of the number of closed minimal surf…

Asymptotic behavior of the Bergman kernel and associated invariants in weakly pseudoconvex domains
Ninh Van Thu
https://arxiv.org/abs/2509.00301 https://ar…

Asymptotic behavior of the Bergman kernel and associated invariants in weakly pseudoconvex domains
In this paper, we present an explicit description for the boundary behavior of the Bergman kernel function, the Bergman metric, and the associated curvatures along certain sequences converging to an $h$-extendible boundary point.

Polynomial Invariants of q-Matroids and Rank-Metric Codes
Heide Gluesing-Luerssen, Benjamin Jany
https://arxiv.org/abs/2509.21618 https://arxiv.org/pdf/250…

Polynomial Invariants of q-Matroids and Rank-Metric Codes
It is shown that the Whitney function of a representable q-matroid and the collection of all higher weight enumerators of any representing rank-metric code determine each other via a monomial substitution. Moreover, the q-matroid itself and the collection of all higher support enumerators of the code determine each other. Next, it is proven that the Whitney function of a q-matroid and the Whitney function of its projectivization determine each other via a monomial substitution. Finally, q-matro…

GM-Skip: Metric-Guided Transformer Block Skipping for Efficient Vision-Language Models
Lianming Huang, Haibo Hu, Qiao Li, Xin He, Nan Guan, Chun Jason Xue
https://arxiv.org/abs/2508.18227

GM-Skip: Metric-Guided Transformer Block Skipping for Efficient Vision-Language Models
Transformer-based Vision-Language Models (VLMs) have achieved impressive performance on tasks such as image captioning, object recognition, and visual reasoning, but their high computational cost hinders deployment in latency-sensitive applications like autonomous driving. We introduce GM-Skip, a flexible and metric-adaptive framework for Transformer block skipping that accelerates VLM inference while preserving output quality. GM-Skip features a greedy, metric-guided block selection strategy t…

Tunable quantum metric and band topology in bilayer Dirac model
Xun-Jiang Luo, Xing-Lei Ma, K. T. Law
https://arxiv.org/abs/2509.23622 https://arxiv.org/pd…

Tunable quantum metric and band topology in bilayer Dirac model
Quantum metric, a fundamental component of quantum geometry, has attracted broad interest in recent years due to its critical role in various quantum phenomena. Meanwhile, band topology, which serves as an important framework in condensed matter physics, has led to the discovery of various topological phases. In this work, we introduce a bilayer Dirac model that allows precise tuning of both properties. Our approach combines two Dirac Hamiltonians with distinct energy scales; one producing rela…

Crosslisted article(s) found for eess.SY. https://arxiv.org/list/eess.SY/new
[1/1]:
- Introducing LCOAI: A Standardized Economic Metric for Evaluating AI Deployment Costs
Eliseo Curcio

Crosslisted article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Constructions of Large m-Distance Sets on Triangular Lattice
Li-Ren Bao, Wei-Hsuan Yu

Crosslisted article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[2/10]:
- AutoPK: Leveraging LLMs and a Hybrid Similarity Metric for Advanced Retrieval of Pharmacokinetic ...
Sholehrasa, Ghanaatian, Caragea, Tell, Riviere, Jaberi-Douraki

Replaced article(s) found for math.FA. https://arxiv.org/list/math.FA/new
[1/1]:
- On nonexpansiveness of metric projection operators on Wasserstein spaces
Anshul Adve, Alp\'ar M\'esz\'aros

Computation of Feasible Assume-Guarantee Contracts: A Resilience-based Approach
Negar Monir, Youssef Ait Si, Ratnangshu Das, Pushpak Jagtap, Adnane Saoud, Sadegh Soudjani
https://arxiv.org/abs/2509.01832

Computation of Feasible Assume-Guarantee Contracts: A Resilience-based Approach
We propose a resilience-based framework for computing feasible assume-guarantee contracts that ensure the satisfaction of temporal specifications in interconnected discrete-time systems. Interconnection effects are modeled as structured disturbances. We use a resilience metric, the maximum disturbance under which local specifications hold, to refine assumptions and guarantees across subsystems iteratively. For two subsystems, we demonstrate correctness, monotone refinement of guarantees, and th…

Death of the Novel(ty): Beyond n-Gram Novelty as a Metric for Textual Creativity
Arkadiy Saakyan, Najoung Kim, Smaranda Muresan, Tuhin Chakrabarty
https://arxiv.org/abs/2509.22641

Death of the Novel(ty): Beyond n-Gram Novelty as a Metric for Textual Creativity
N-gram novelty is widely used to evaluate language models' ability to generate text outside of their training data. More recently, it has also been adopted as a metric for measuring textual creativity. However, theoretical work on creativity suggests that this approach may be inadequate, as it does not account for creativity's dual nature: novelty (how original the text is) and appropriateness (how sensical and pragmatic it is). We investigate the relationship between this notion of creativity …

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Geodesic complexity of the octahedron, and an algorithm for cut loci on convex polyhedra
Florian Frick, Pranav Rajbhandari

Delsarte duality on subspaces and applications to rank-metric codes and q-matroids
Martino Borello, Olga Polverino, Ferdinando Zullo
https://arxiv.org/abs/2509.24409 https://

Delsarte duality on subspaces and applications to rank-metric codes and q-matroids
We study the interplay between the lattice of F_{q^m}-subspaces and the lattice of F_{q^m}-subspaces of an F_{q^m}-vector space. Introducing notions of weight and defect relative to an F_q-subspace, we analyze the sequence of maximum non-zero defects. We establish a correspondence between subspaces of positive defect and their Delsarte duals, enabling explicit characterizations of the associated sequences of maximum non-zero defects. Our framework unifies several classes of subspaces studied in…

First-Order Axial Perturbation of the Reissner-Nordstr\"om Metric In a Possible Chern-Simons Gravity Background
Abhishek Rout, Brett Altschul
https://arxiv.org/abs/2510.01106

First-Order Axial Perturbation of the Reissner-Nordström Metric In a Possible Chern-Simons Gravity Background
We axial perturbations of Reissner-Nordström black holes within the framework of Chern-Simons modified gravity, a theory with includes parity violation. We derive the governing equations for the perturbations, focusing on the radial function $R(r)$ and its behavior across distinct regions: near the singularity ($r \rightarrow 0$), between the inner and outer Reissner-Nordström horizons ($r_-< r< r_+$), and in the asymptotic regime ($r \rightarrow \infty$). Using a combination of analytical an…

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Rigidity of Circle Packings with Flexible Radii
Robert Connelly, Zhen Zhang
h…

How Does Cognitive Bias Affect Large Language Models? A Case Study on the Anchoring Effect in Price Negotiation Simulations
Yoshiki Takenami, Yin Jou Huang, Yugo Murawaki, Chenhui Chu
https://arxiv.org/abs/2508.21137

How Does Cognitive Bias Affect Large Language Models? A Case Study on the Anchoring Effect in Price Negotiation Simulations
Cognitive biases, well-studied in humans, can also be observed in LLMs, affecting their reliability in real-world applications. This paper investigates the anchoring effect in LLM-driven price negotiations. To this end, we instructed seller LLM agents to apply the anchoring effect and evaluated negotiations using not only an objective metric but also a subjective metric. Experimental results show that LLMs are influenced by the anchoring effect like humans. Additionally, we investigated the rel…

Crosslisted article(s) found for math.FA. https://arxiv.org/list/math.FA/new
[1/1]:
- On the Incompatibility of Quantum State Geometry and Fuzzy Metric Spaces: Three No-Go Theorems
Nicola Fabiano

Almost paracontact metric 3-dimensional Walker manifolds
Galia Nakova, Cornelia-Livia Bejan
https://arxiv.org/abs/2509.21809 https://arxiv.org/pdf/2509.218…

Almost paracontact metric 3-dimensional Walker manifolds
In this paper we construct and study almost paracontact metric structures $(φ,ξ,η,g)$ on a 3-dimensional Walker manifold $(M,g)$ with respect to a local basis only by the coordinate functions of a unit space-like vector field $ξ$, globally defined on $M$ and a function $f$ on $M$, characterizing the Lorentzian metric $g$. Necessary and sufficient conditions are obtained for $M$, endowed with these structures, to fall in one of the following classes of 3-dimensional almost paracontact metric…

Conformal Geometry and Regularization of Disclinations by a Cosmological Constant in $(2 1)$ Dimensions
A. Carvalho, C. Furtado
https://arxiv.org/abs/2509.01635 https://

Conformal Geometry and Regularization of Disclinations by a Cosmological Constant in $(2+1)$ Dimensions
We investigate the effect of a cosmological constant $Λ$ on the geometry generated by a two-dimensional disclination in a conformal metric framework. For $Λ>0$, we obtain an exact analytic solution of the Liouville-type equation, which regularizes the defect core, preserves the topological charge, and yields a compact space with finite volume and positive curvature. For $Λ<0$, the solution must be obtained numerically and asymptotically approaches $R \to 3Λ< 0$, producing an open hyperbolic…

Crosslisted article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Intrinsic Bottleneck Distance for Merge Trees
David Beers, Gillian Grindstaff

Ricci-Yamabe solitons on a Walker 3-manifold
Abdou Bousso, Ameth Ndiaye
https://arxiv.org/abs/2509.01764 https://arxiv.org/pdf/2509.01764

Ricci-Yamabe solitons on a Walker 3-manifold
This paper is devoted to the study of Ricci-Yamabe solitons on a particular class of Walker manifolds in dimension 3. We consider a Walker metric where the function f depends on the three coordinates. The novelty of our research lies in the fact that the soliton field is found from the Hodge decomposition of De-Rham with the potential function. We classify all Ricci Yamabe and gradient Ricci-Yamabe soliton in a given Walker 3-manifold by using this decomposition. Many examples are given in th…

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Cohomogeneity one RCD-spaces
Diego Corro, Jes\'us N\'u\~nez-Zimbr\'on, Jaime Santos-Rodr\'iguez

Viability Constraints on Baryogenesis in f (R, Lm, T) Gravity
Kalyan Malakar, Rajdeep Mazumdar, Mrinnoy M Gohain, Kalyan Bhuyan
https://arxiv.org/abs/2509.03053 https://

Viability Constraints on Baryogenesis in f (R, Lm, T) Gravity
Our study explores gravitational baryogenesis in the context of f(R, Lm, T) gravity, where R denotes the Ricci scalar, Lm represents the Lagrangian density of the matter field, and T stands for the metric contraction of T_{mu nu}. We focus on a linear model: f(R, Lm, T) = alpha R + beta Lm + gamma T, and examine the parameter constraints for a successful baryon asymmetry generation in four different eras of the cosmos under the assumption of a power-law cosmic expansion. The computed baryon-to-…

Totally convex functions, $L^2$-Optimal transport for laws of random measures, and solution to the Monge problem
Alessandro Pinzi, Giuseppe Savar\'e
https://arxiv.org/abs/2509.01768

Totally convex functions, $L^2$-Optimal transport for laws of random measures, and solution to the Monge problem
We study the Optimal Transport problem for laws of random measures in the Kantorovich-Wasserstein space $\mathcal{P}_2(\mathcal{P}_2(\mathrm{H}))$, associated with a Hilbert space $\mathrm{H}$ (with finite or infinite dimension) and for the corresponding quadratic cost induced by the squared Wasserstein metric in $\\mathcal{P}_2(\mathrm{H}).$ Despite the lack of smoothness of the cost, the fact that the space $\mathcal{P}_2(\mathrm{H})$ is not Hilbertian, and the curvature distortion induced …

Crosslisted article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Quantum-inspired Benchmark for Estimating Intrinsic Dimension
Aritra Das, Joseph T. Iosue, Victor V. Albert

Weyl double copy in bimetric massive gravity
Hugo Garc\'ia-Compe\'an, C\'esar I. Ramos
https://arxiv.org/abs/2510.01550 https://arxiv.org/pdf/2…

Weyl double copy in bimetric massive gravity
The Weyl double copy formalism, which relates the Weyl spinor with the square of the field strength, is studied in the context of Hassan-Rosen bigravity for stationary and time-dependent solutions. We consider the dyonic Kerr-Newman-(A)dS solution and the Plebański-Demiański metric in the context of bigravity. These solutions are studied in the Weyl double copy both with matter independently coupled and show that no massive modes are present in the Weyl spinor. The equations of motion for the…

Minimal surface entropy and applications of Ricci flow on finite-volume hyperbolic 3-manifolds
Ruojing Jiang, Franco Vargas Pallete
https://arxiv.org/abs/2509.00197 https://

Minimal surface entropy and applications of Ricci flow on finite-volume hyperbolic 3-manifolds
This paper studies minimal surface entropy (the exponential asymptotic growth of the number of minimal surfaces up to a given value of area) for negatively curved metrics on hyperbolic $3$-manifolds of finite volume, particularly its comparison to the hyperbolic minimal surface entropy in terms of sectional and scalar curvature. On one hand, for metrics that are bilipschitz equivalent to the hyperbolic metric and have sectional curvature bounded above by $-1$ and uniformly bounded below, we s…

The Teukolsky scalar as a gateway for quantizing gravity on rotating black holes
Christiane K. M. Klein
https://arxiv.org/abs/2509.00978 https://arxiv.org/…

The Teukolsky scalar as a gateway for quantizing gravity on rotating black holes
The quantization of linearized gravity on black hole spacetimes and the construction of states for that theory is a sought-after, yet difficult achievement. One of the main reasons is the difficulty of reconciling the positivity and gauge invariance of potential states. On Kerr spacetimes, the spin-2 Teukolsky scalars express the same degrees of freedom as the metric perturbations, up to pure gauge and radiative solutions, while avoiding the issue of gauge. In this work, we therefore explore th…

Impact of Pulsar SAX J1748.9-2021 Observations on $f(\mathcal{Q}, \mathbb{T})$ Gravity
M. Sharif, Iqra Ibrar
https://arxiv.org/abs/2509.02641 https://arxiv…

Impact of Pulsar SAX J1748.9-2021 Observations on $f(\mathcal{Q}, \mathbb{T})$ Gravity
The main objective of this study is to investigate the viability and stability of a pulsar filled with anisotropic matter in $f(\mathcal{Q}, \mathbb{T})$ gravity, where $\mathcal{Q}$ represents non-metricity and $\mathbb{T}$ is the trace of the energy-momentum tensor. In this context, we employ non-singular solution and a particular model of this gravity. We use junction conditions to evaluate unknown constants in the metric coefficients. Observations from the pulsar SAX J1748.9-2021 star are e…

[2025-09-04 Thu (UTC), 1 new article found for math.MG Metric Geometry]
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Local Well-Posedness for the Bartnik Stationary Extension Problem near Schwarzschild Spheres
Ahmed Ellithy
https://arxiv.org/abs/2509.03478 https://arxiv.o…

Local Well-Posedness for the Bartnik Stationary Extension Problem near Schwarzschild Spheres
We investigate the Bartnik stationary extension conjecture, which arises from the definition of the spacetime Bartnik mass for a compact region in a general initial data set satisfying the dominant energy condition. This conjecture posits the existence and uniqueness (up to isometry) of an asymptotically flat stationary vacuum spacetime containing an initial data set $(M, \mathfrak{g}, Π)$ that realizes prescribed Bartnik boundary data on $\partial M$, consisting of the induced metric, mean cu…

[2025-10-03 Fri (UTC), 1 new article found for math.MG Metric Geometry]
toXiv_bot_toot

First eigenvalue and nodal domains of the drift Laplacian on symmetric self-shrinkers in $\mathbb{R}^3$
Elham Matinpour
https://arxiv.org/abs/2509.25617 https://

First eigenvalue and nodal domains of the drift Laplacian on symmetric self-shrinkers in $\mathbb{R}^3$
Consider $\mathbb{R}^3$ equipped with the Euclidean metric and the Gaussian measure. Let $Σ$ be a complete embedded self-shrinker in $\mathbb{R}^3$ with the induced metric and weighted measure, and let $λ_1$ denote the first eigenvalue of the drift Laplacian in the weighted $L^2$ space. Inspired by Choe and Soret's estimate of the first eigenvalue of the Laplacian on symmetric minimal surfaces in $\mathbb{S}^3$, we prove that $λ_1$= 1/2 for self-shrinkers invariant under the dihedral group $…

[2025-09-03 Wed (UTC), 2 new articles found for math.MG Metric Geometry]
toXiv_bot_toot

Symmetric Killing tensors on almost abelian Lie groups
Renan Berto-Cuevas, Viviana del Barco, Andrei Moroianu
https://arxiv.org/abs/2509.26195 https://arxi…

Symmetric Killing tensors on almost abelian Lie groups
In this work we provide a complete characterization of left-invariant symmetric Killing tensors on almost abelian Lie groups endowed with a left-invariant Riemannian metric. We show in particular that all such tensors are decomposable, in the sense that they can be expressed as a polynomial in the Killing vector fields and the Riemannian metric.

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Two nearly equal distances in $R^d$
P. Erd\H{o}s, E. Makai, Jr., J. Pach
http…