Tootfinder

Matching 2D Images in 3D: Metric Relative Pose from Metric Correspondences
Axel Barroso-Laguna, Sowmya Munukutla, Victor Adrian Prisacariu, Eric Brachmann
https://arxiv.org/abs/2404.06337

Matching 2D Images in 3D: Metric Relative Pose from Metric Correspondences
Given two images, we can estimate the relative camera pose between them by establishing image-to-image correspondences. Usually, correspondences are 2D-to-2D and the pose we estimate is defined only up to scale. Some applications, aiming at instant augmented reality anywhere, require scale-metric pose estimates, and hence, they rely on external depth estimators to recover the scale. We present MicKey, a keypoint matching pipeline that is able to predict metric correspondences in 3D camera space…

A note on continuous functions on metric spaces
Sam Sanders
https://arxiv.org/abs/2404.06805 https://arxiv.org/pdf/2404.06805<…

A note on continuous functions on metric spaces
Continuous functions on the unit interval are relatively tame from the logical and computational point of view. A similar behaviour is exhibited by continuous functions on compact metric spaces equipped with a countable dense subset. It is then a natural question what happens if we omit the latter 'extra data', i.e. work with 'unrepresented' compact metric spaces. In this paper, we study basic third-order statements about continuous functions on such unrepresented compact metric spaces in Kohle…

Transverse expansion of the metric at null hypersurfaces I. Uniqueness and application to Killing horizons
Marc Mars, Gabriel S\'anchez-P\'erez
https://arxiv.org/abs/2405.05377

Transverse expansion of the metric at null hypersurfaces I. Uniqueness and application to Killing horizons
This is the first in a series of two papers where we analyze the transverse expansion of the metric on a general null hypersurface. In this paper we obtain general geometric identities relating the transverse derivatives of the ambient Ricci tensor and the transverse expansion of the metric at the null hypersurface. We also explore the case where the hypersurface exhibits a generalized symmetry generator, namely a privileged vector field in the ambient space which, at the hypersurface, is null …

"Economists have a metric known as the “four-firm concentration ratio,” sometimes deployed in shorthand as “CR4.” It is a measure of competitiveness in a market for goods or services. When four companies gain a combined market share that is greater than 40 percent, an oligopoly has formed." https://www.theatlantic.com/ideas/archive/2024/04/food-industry-monopoly-power/678005/

So basically every major consumer "market” in Canada is an oligopoly. Yup. Makes sense.
#CanPoli #CdnPoli #LateStageCapitalism

This https://arxiv.org/abs/2309.14543 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

T-duality/plurality of BTZ black hole metric coupled to two fermionic fields
We ask the question of classical super (non-)Abelian T-duality for BTZ black hole metric coupling to two fermionic fields. Our approach is based on super Poisson-Lie (PL) T-duality in the presence of spectator fields. In order to study the Abelian T-duality of the metric we dualize over the Abelian Lie supergroups of the types $(1|2)$ and $(2|2)$, in such a way that it is shown that both original and dual backgrounds of the models are conformally invariant up to one-loop order in the …

Age of Computing: A Metric of Computation Freshness in Communication and Computation Cooperative Networks
Xingran Chen, Yusha Liu, Yali Zheng, Kun Yang
https://arxiv.org/abs/2403.05007

Age of Computing: A Metric of Computation Freshness in Communication and Computation Cooperative Networks
In communication and computation cooperative networks (3CNs), timely computation is crucial but not always guaranteed. There is a strong demand for computational tasks to be processed at computational nodes as timely as possible. However, a measure of timeliness in computation is lacking. In this letter, we introduce the novel concept, Age of Computing, to capture computation freshness in 3CNs. We develop two methods for calculating this metric, applicable to a wide range of 3CNs. These calcula…

Encoder-Quantization-Motion-based Video Quality Metrics
Yixu Chen, Zaixi Shang, Hai Wei, Yongjun Wu, Sriram Sethuraman
https://arxiv.org/abs/2404.06620 htt…

Encoder-Quantization-Motion-based Video Quality Metrics
In an adaptive bitrate streaming application, the efficiency of video compression and the encoded video quality depend on both the video codec and the quality metric used to perform encoding optimization. The development of such a quality metric need large scale subjective datasets. In this work we merge several datasets into one to support the creation of a metric tailored for video compression and scaling. We proposed a set of HEVC lightweight features to boost performance of the metrics. Our…

On metric equivalence of the Brieskorn-Pham hypersurfaces
Alexandre Fernandes, Zbigniew Jelonek, Jos\'e Edson Sampaio
https://arxiv.org/abs/2404.06922 …

On metric equivalence of the Brieskorn-Pham hypersurfaces
We show that two bi-Lipschitz equivalent Brieskorn-Pham hypersurfaces have the same multiplicities at $0$. Moreover we show that if two algebraic $(n-1)$-dimensional cones $P, R\subset\mathbb C^n$ with isolated singularities are homeomorphic, then they have the same degree.

Modified extremal K\"{a}hler metrics and multiplier Hermitian-Einstein metrics
Yasuhiro Nakagawa, Satoshi Nakamura
https://arxiv.org/abs/2405.05604 ht…

Modified extremal Kähler metrics and multiplier Hermitian-Einstein metrics
Motivated by the notion of multiplier Hermitian-Einstein metric of type $σ$ introduced by Mabuchi, we introduce the notion of $σ$-extremal Kähler metrics on compact Kähler manifolds, which generalizes Calabi's extremal Kähler metrics. We characterize the existence of this metric in terms of the coercivity of a certain functional on the space of Kähler metrics to show that, on a Fano manifold, the existence of a $σ$-extremal Kähler metric implies the existence of a multiplier Hermitian-E…

Unbounded visibility domains: metric estimates and an application
Annapurna Banik, Gautam Bharali
https://arxiv.org/abs/2405.05704 https://

Unbounded visibility domains: metric estimates and an application
We give an explicit lower bound, in terms of the distance from the boundary, for the Kobayashi metric of a certain class of bounded pseudoconvex domains in $\mathbb{C}^n$ with $\mathcal{C}^2$-smooth boundary using the regularity theory for the complex Monge--Ampere equation. Using such an estimate, we construct a family of unbounded Kobayashi hyperbolic domains in $\mathbb{C}^n$ having a certain negative-curvature-type property with respect to the Kobayashi distance. As an application, we prove…

This https://arxiv.org/abs/2311.09072 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

From Trees to Polynomials and Back Again: New Capacity Bounds with Applications to TSP
We give simply exponential lower bounds on the probabilities of a given strongly Rayleigh distribution, depending only on its expectation. This resolves a weak version of a problem left open by Karlin-Klein-Oveis Gharan in their recent breakthrough work on metric TSP, and this resolution leads to a minor improvement of their approximation factor for metric TSP. Our results also allow for a more streamlined analysis of the algorithm. To achieve these new bounds, we build upon the work of Gurvi…

Bumpy metric theorem for co-rank 1 sub-Riemannian and reversible sub-Finsler metrics
Shahriar Aslani, Ke Zhang
https://arxiv.org/abs/2405.05450 https://

Bumpy metric theorem for co-rank 1 sub-Riemannian and reversible sub-Finsler metrics
We prove that for a generic sub-Riemannian and reversible sub-Finsler metrics defined on a fixed co-rank 1 distribution, all strictly normal periodic orbits are non-degenerate.

Exploring the Adversarial Frontier: Quantifying Robustness via Adversarial Hypervolume
Ping Guo, Cheng Gong, Xi Lin, Zhiyuan Yang, Qingfu Zhang
https://arxiv.org/abs/2403.05100

Exploring the Adversarial Frontier: Quantifying Robustness via Adversarial Hypervolume
The escalating threat of adversarial attacks on deep learning models, particularly in security-critical fields, has underscored the need for robust deep learning systems. Conventional robustness evaluations have relied on adversarial accuracy, which measures a model's performance under a specific perturbation intensity. However, this singular metric does not fully encapsulate the overall resilience of a model against varying degrees of perturbation. To address this gap, we propose a new metric …

Condition Monitoring with Incomplete Data: An Integrated Variational Autoencoder and Distance Metric Framework
Maryam Ahang, Mostafa Abbasi, Todd Charter, Homayoun Najjaran
https://arxiv.org/abs/2404.05891

Condition Monitoring with Incomplete Data: An Integrated Variational Autoencoder and Distance Metric Framework
Condition monitoring of industrial systems is crucial for ensuring safety and maintenance planning, yet notable challenges arise in real-world settings due to the limited or non-existent availability of fault samples. This paper introduces an innovative solution to this problem by proposing a new method for fault detection and condition monitoring for unseen data. Adopting an approach inspired by zero-shot learning, our method can identify faults and assign a relative health index to various op…

"the people reporting the metric are so interested in making the numbers look right that they lie. The metric becomes worse than noise—it’s outright disinformation. Things look like they’re getting better when they’re getting worse" -- Eric Normand
https://ericnormand.substack.com/p/mea<…

Measuring dev productivity
Are we being obtuse?

This https://arxiv.org/abs/2310.04052 has been replaced.
link: https://scholar.google.com/scholar?q=a

Spectral metrics on quantum projective spaces
We show that the noncommutative differential geometry of quantum projective spaces is compatible with Rieffel's theory of compact quantum metric spaces. This amounts to a detailed investigation of the Connes metric coming from the unital spectral triple introduced by D'Andrea and Dabrowski. In particular, we establish that the Connes metric metrizes the weak-* topology on the state space of quantum projective space. This generalizes previous work by the second author and Aguilar regarding spect…

This https://arxiv.org/abs/2202.00577 has been replaced.
link: https://scholar.google.com/scholar?q=a

Generic families of finite metric spaces with identical or trivial 1-dimensional persistence
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of persistent homology provides an upper bound for the change of persistence in the bottleneck distance under perturbations of points, but without giving a lower bound. This paper clarifies the possible limitations persistent homology may have in distinguishing f…

The Convergence of Prescribed Combinatorial Ricci Flows for Total Geodesic Curvatures in Spherical Background Geometry
Guangming Hu, Ziping Lei, Yu Sun, Puchun Zhou
https://arxiv.org/abs/2404.05982

The Convergence of Prescribed Combinatorial Ricci Flows for Total Geodesic Curvatures in Spherical Background Geometry
In this paper, we study the existence and rigidity of (degenerated) circle pattern metric with prescribed total geodesic curvatures in spherical background geometry. To find the (degenerated) circle pattern metric with prescribed total geodesic curvatures, we define some prescribed combinatorial Ricci flows and study the convergence of flows for (degenerated) circle pattern metrics. We solve the prescribed total geodesic curvature problem and provide two methods to find the degenerated circle p…

This https://arxiv.org/abs/2403.00226 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

A Semantic Distance Metric Learning approach for Lexical Semantic Change Detection
Detecting temporal semantic changes of words is an important task for various NLP applications that must make time-sensitive predictions. Lexical Semantic Change Detection (SCD) task involves predicting whether a given target word, $w$, changes its meaning between two different text corpora, $C_1$ and $C_2$. For this purpose, we propose a supervised two-staged SCD method that uses existing Word-in-Context (WiC) datasets. In the first stage, for a target word $w$, we learn two sense-aware encode…

A variety of co-quasivarieties
Maria Manuel Clementino, Carlos Fitas, Dirk Hofmann
https://arxiv.org/abs/2404.05017 https://arxiv.org…

A variety of co-quasivarieties
It is shown that the duals of several categories of topological flavour, like the categories of ordered sets, generalised metric spaces, probabilistic metric spaces, topological spaces, approach spaces, are quasivarieties, presenting a common proof for all such results.

This https://arxiv.org/abs/2310.17000 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Confinement from Distance in Metric Space and its Relation to Cosmological Constant
We argue that, in a theory of quantum gravity, the gauge coupling and the confinement scale of a gauge theory are related to distance in the space of metric configurations, and in turn to the cosmological constant. To support the argument, we compute the gauge kinetic functions in variuos supersymmetric Heterotic and type II string compactifications and show that they depend on distance. According to the swampland program, the distance between two (anti) de Sitter vacua in the space of metric c…

Metric Distortion of Line-up Elections: The Right Person for the Right Job
Christopher Jerrett, Yue Han, Elliot Anshelevich
https://arxiv.org/abs/2405.04020

Metric Distortion of Line-up Elections: The Right Person for the Right Job
We provide mechanisms and new metric distortion bounds for line-up elections. In such elections, a set of $n$ voters, $k$ candidates, and $\ell$ positions are all located in a metric space. The goal is to choose a set of candidates and assign them to different positions, so as to minimize the total cost of the voters. The cost of each voter consists of the distances from itself to the chosen candidates (measuring how much the voter likes the chosen candidates, or how similar it is to them), as …

This https://arxiv.org/abs/2211.15020 has been replaced.
link: https://scholar.google.com/scholar?q=a

Quasi-symmetries between metric spaces and rough quasi-isometries between their infinite hyperbolic cones
In this paper, we first prove that any power quasi-symmetry of two metric spaces induces a rough quasi-isometry between their infinite hyperbolic cones. Second, we prove that for a complete metric space $Z$, there exists a point $ω$ in the Gromov boundary of its infinite hyperbolic cone such that $Z$ can be seen as the Gromov boundary relative to $ω$ of its infinite hyperbolic cone. Third, we prove that for a visual Gromov hyperbolic metric space $X$ and a Gromov boundary point $ω$, $X$ is r…

The Riemannian geometry of Sinkhorn divergences
Hugo Lavenant, Jonas Luckhardt, Gilles Mordant, Bernhard Schmitzer, Luca Tamanini
https://arxiv.org/abs/2405.04987

The Riemannian geometry of Sinkhorn divergences
We propose a new metric between probability measures on a compact metric space that mirrors the Riemannian manifold-like structure of quadratic optimal transport but includes entropic regularization. Its metric tensor is given by the Hessian of the Sinkhorn divergence, a debiased variant of entropic optimal transport. We precisely identify the tangent space it induces, which turns out to be related to a Reproducing Kernel Hilbert Space (RKHS). As usual in Riemannian geometry, the distance is bu…

Metric bootstraps for limsup sets
Felipe A. Ramirez
https://arxiv.org/abs/2405.03811 https://arxiv.org/pdf/2405.03811

Metric bootstraps for limsup sets
In metric Diophantine approximation, one frequently encounters the problem of showing that a limsup set has positive or full measure. Often it is a set of points in $m$-dimensional Euclidean space, or a set of $n$-by-$m$ systems of linear forms, satisfying some approximation condition infinitely often. The main results of this paper are bootstraps: if one can establish positive measure for such a limsup set in $m$-dimensional Euclidean space, then one can establish positive or full measure for …

This https://arxiv.org/abs/2211.11974 has been replaced.
link: https://scholar.google.com/scholar?q=a

Green function in metric measure spaces
We study existence and uniqueness of Green functions for the Cheeger $Q$-Laplacian in metric measure spaces that are Ahlfors $Q$-regular and support a $Q$-Poincaré inequality with $Q>1$. We prove uniqueness of Green functions both in the case of relatively compact domains, and in the global (unbounded) case. We also prove existence of global Green functions in unbounded spaces, complementing the existing results in relatively compact domains proved recently in [BBL20].

A Graph-Theoretical Approach to Ring Analysis: An Exploration of Dominant Metric Dimension in Compressed Zero Divisor Graphs and Its Interplay with Ring Structures
Nasir Ali, Hafiz Muhammad Afzal Siddiqui, Muhammad Imran Qureshi
https://arxiv.org/abs/2405.04934

A Graph-Theoretical Approach to Ring Analysis: An Exploration of Dominant Metric Dimension in Compressed Zero Divisor Graphs and Its Interplay with Ring Structures
The paper systematically classifies rings based on the dominant metric dimensions (Ddim) of their associated CZDG, establishing consequential bounds for the Ddim of these compressed zero-divisor graphs. The authors investigate the interplay between the ring-theoretic properties of a ring ( R ) and associated CZDG. An undirected graph consisting of vertex set ( Z(R_E)\{[0]}\ =\ R_E\{[0],[1]}), where ( R_E=\{[x]:\ x\in R\} ) and ([x]=\{y\in R:\ \text{ann}(x)=\text{ann}(y)\} ) is called a compress…

Towards a generalized accessibility measure for transportation equity and efficiency
Rajat Verma, Mithun Debnath, Shagun Mittal, Satish V. Ukkusuri
https://arxiv.org/abs/2404.04985 https://arxiv.org/pdf/2404.04985
arXiv:2404.04985v1 Announce Type: new
Abstract: Locational measures of accessibility are widely used in urban and transportation planning to understand the impact of the transportation system on influencing people's access to places. However, there is a considerable lack of measurement standards and publicly available data. We propose a generalized measure of locational accessibility that has a comprehensible form for transportation planning analysis. This metric combines the cumulative opportunities approach with gravity-based measures and is capable of catering to multiple trip purposes, travel modes, cost thresholds, and scales of analysis. Using data from multiple publicly available datasets, this metric is computed by trip purpose and travel time threshold for all block groups in the United States, and the data is made publicly accessible. Further, case studies of three large metropolitan areas reveal substantial inefficiencies in transportation infrastructure, with the most inefficiency observed in sprawling and non-core urban areas, especially for bicycling. Subsequently, it is shown that targeted investment in facilities can contribute to a more equitable distribution of accessibility to essential shopping and service facilities. By assigning greater weights to socioeconomically disadvantaged neighborhoods, the proposed metric formally incorporates equity considerations into transportation planning, contributing to a more equitable distribution of accessibility to essential services and facilities.

RoboHop: Segment-based Topological Map Representation for Open-World Visual Navigation
Sourav Garg, Krishan Rana, Mehdi Hosseinzadeh, Lachlan Mares, Niko S\"underhauf, Feras Dayoub, Ian Reid
https://arxiv.org/abs/2405.05792

RoboHop: Segment-based Topological Map Representation for Open-World Visual Navigation
Mapping is crucial for spatial reasoning, planning and robot navigation. Existing approaches range from metric, which require precise geometry-based optimization, to purely topological, where image-as-node based graphs lack explicit object-level reasoning and interconnectivity. In this paper, we propose a novel topological representation of an environment based on "image segments", which are semantically meaningful and open-vocabulary queryable, conferring several advantages over previous works…

RMS asymmetry: a robust metric of galaxy shapes in images with varied depth and resolution
Elizaveta Sazonova, Cameron Morgan, Michael Balogh, Katherine Alatalo, Jose A. Benavides, Asa Bluck, Sarah Brough, Innocenza Busa, Ricardo Demarco, Darko Donevski, Miguel Figueira, Garreth Martin, Vicente Rodriguez-Gomez, Javier Rom\'an, Kate Rowlands
https…

RMS asymmetry: a robust metric of galaxy shapes in images with varied depth and resolution
Structural disturbances, such as galaxy mergers or instabilities, are key candidates for driving galaxy evolution, so it is important to detect and quantify galaxies hosting these disturbances spanning a range of masses, environments, and cosmic times. Traditionally, this is done by quantifying the asymmetry of a galaxy as part of the concentration-asymmetry-smoothness system, $A_{\rm{CAS}}$, and selecting galaxies above a certain threshold as merger candidates. However, in this work, we show t…

The G\"odel Universe as the Lie Group with left-invariant Lorentz metric
V. N. Berestovskii
https://arxiv.org/abs/2404.06866 https://

The Gödel Universe as the Lie Group with left-invariant Lorentz metric
The author studies the Gödel Universe as the Lie group with left-invariant Lorentz metric. The expressions for timelike and isotropic geodesics in elementary functions are found by methods of geometric theory of optimal control for the search of geodesics on Lie groups with left-invariant (sub-)Lorentz metrics. It is proved that the Gödel Universe has no closed timelike or isotropic geodesics.

This isn't really news. The key flaw in any Key Performance Indicator is that humans, given any metric they CAN influence, will game it. No exceptions.
https://www.chronicle.com/article/the-dark-world-of-citation-cartels

There doesn't seem to be customer reviews for the state-funded NGOs that I need to choose between, so I'm going by glassdoor/indeed employee reviews. We probably want to go with the org that has happier employees, rather than the ones complaining, "we're understaffed and overworked! Caseloads are ridiculous!"
Hopefully this metric works out..

Classical and quantum field theory in a box with moving boundaries: A numerical study of the Dynamical Casimir Effect
Alberto Garc\'ia Mart\'in-Caro, Gerardo Garc\'ia-Moreno, Javier Olmedo, Jose M. S\'anchez Vel\'azquez
https://arxiv.org/abs/2404.06166

Classical and quantum field theory in a box with moving boundaries: A numerical study of the Dynamical Casimir Effect
We present a detailed description of a quantum scalar field theory within a flat spacetime confined to a cavity with perfectly reflecting moving boundaries. Moreover, we establish an equivalence between this time-dependent setting and a field theory on an acoustic metric with static Dirichlet boundary conditions. We discuss the classical and quantum aspects of the theory from the latter perspective, accompanied by the introduction of novel numerical techniques designed for the (nonperturbative)…

Characterizing Lipschitz images of injective metric spaces
Judyta B\k{a}k, Taras Banakh, Joanna Garbuli\'nska-W\k{e}grzyn, Magdalena Nowak, Micha{\l} Pop{\l}awski
https://arxiv.org/abs/2405.01860

Characterizing Lipschitz images of injective metric spaces
A metric space $X$ is {\em injective} if every non-expanding map $f:B\to X$ defined on a subspace $B$ of a metric space $A$ can be extended to a non-expanding map $\bar f:A\to X$. We prove that a metric space $X$ is a Lipschitz image of an injective metric space if and only if $X$ is Lipschitz connected in the sense that for every points $x,y\in X$, there exists a Lipschitz map $f:[0,1]\to X$ such that $f(0)=x$ and $f(1)=y$. In this case the metric space $X$ carries a well-defined intrinsic met…

Three-Year Starting Offensive Lineman Signs Contract With Las Vegas Raiders https://www.yardbarker.com/nfl/articles/three_year_starting_offensive_lineman_signs_contract_with_las_vegas_raiders/s1_17198_…

Three-Year Starting Offensive Lineman Signs Contract With Las Vegas Raiders
Five-year veteran center Andre James signed a new contract with the Las Vegas Raiders. James, a former undrafted free agent, spent the entirety of his professional career with the Las Vegas/Oakland Raiders. James enters free agency following the best season of his professional career. Starting and appearing in 16 games, Andre James recorded a career-best 74.6 PFF grade during the final year of his contract. By that metric, he was the ninth-best center in the league out of 36 eligible players. T…

This https://arxiv.org/abs/2402.02731 has been replaced.
link: https://scholar.google.com/scholar?q=a

Computing Augustin Information via Hybrid Geodesically Convex Optimization
We propose a Riemannian gradient descent with the Poincaré metric to compute the order-$α$ Augustin information, a widely used quantity for characterizing exponential error behaviors in information theory. We prove that the algorithm converges to the optimum at a rate of $\mathcal{O}(1 / T)$. As far as we know, this is the first algorithm with a non-asymptotic optimization error guarantee for all positive orders. Numerical experimental results demonstrate the empirical efficiency of the algor…

Uncertainty quantification in metric spaces
G\'abor Lugosi, Marcos Matabuena
https://arxiv.org/abs/2405.05110 https://arxiv.org/p…

Uncertainty quantification in metric spaces
This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently handle large datasets and are agnostic to the predictive base model used. Furthermore, the algorithms possess asymptotic consistency guarantees and, in some special homoscedastic cases, we provide non-asymptotic guarantees. To illustrate the effectiveness of the p…

Exploring the Adversarial Frontier: Quantifying Robustness via Adversarial Hypervolume
Ping Guo, Cheng Gong, Xi Lin, Zhiyuan Yang, Qingfu Zhang
https://arxiv.org/abs/2403.05100

Exploring the Adversarial Frontier: Quantifying Robustness via Adversarial Hypervolume
The escalating threat of adversarial attacks on deep learning models, particularly in security-critical fields, has underscored the need for robust deep learning systems. Conventional robustness evaluations have relied on adversarial accuracy, which measures a model's performance under a specific perturbation intensity. However, this singular metric does not fully encapsulate the overall resilience of a model against varying degrees of perturbation. To address this gap, we propose a new metric …

Sobolev mappings on metric spaces and Minkowski dimension
Efstathios Konstantinos Chrontsios Garitsis
https://arxiv.org/abs/2405.05172 https://

Sobolev mappings on metric spaces and Minkowski dimension
We introduce the class of compactly Hölder mappings between metric spaces and determine the extent to which they distort the Minkowski dimension of a given set. These mappings are defined purely with metric notions and can be seen as a generalization of Sobolev mappings, without the requirement for a measure on the source space. In fact, we show that if $f:X\rightarrow Y$ is a continuous mapping lying in some super-critical Newtonian-Sobolev space $N^{1,p}(X,μ)$, under standard assumptions on…

Horizon-penetrating form of parametrized metrics for static and stationary black holes
Yixuan Ma, Luciano Rezzolla
https://arxiv.org/abs/2404.06509 https:/…

Horizon-penetrating form of parametrized metrics for static and stationary black holes
The Rezzolla-Zhidenko (RZ) and Konoplya-Rezzolla-Zhidenko (KRZ) frameworks provide an efficient approach to characterize agnostically spherically symmetric or stationary black-hole spacetimes in arbitrary metric theories. In their original construction, these metrics were defined only in the spacetime region outside of the event horizon, where they can reproduce any black-hole metric with with percent precision and a few parameters only. At the same time, numerical simulations of accreting blac…

This https://arxiv.org/abs/2008.01406 has been replaced.
link: https://scholar.google.com/scholar?q=a

Gromov hyperbolization of unbounded noncomplete spaces and Hamenstädt metric
In this paper, we investigate Gromov hyperbolizations of unbounded locally complete and incomplete metric spaces associated with three hyperbolic type metrics: the hyperbolization metric introduced by Ibragimov, the distance ratio metric, and the quasihyperbolic metric. As an application, we obtain a Gromov hyperbolic characterization of unbounded uniform domains in Banach spaces.

Age of Information and Energy Consumption in IoT: an Experimental Evaluation
Federico Cristofani, Valerio Luconi, Alessio Vecchio
https://arxiv.org/abs/2405.05849

Age of Information and Energy Consumption in IoT: an Experimental Evaluation
The Age of Information (AoI) is an end-to-end metric frequently used to understand how "fresh" the information about a remote system is. In this paper, we present an experimental study of the relationship between AoI and the energy spent by the device that produces information, e.g. an IoT device or a monitoring sensor. Such a relationship has been almost neglected so far, but it is particularly important whenever the sensing side is battery-operated. The study is carried out in a scenario wher…

A Clique-Based Separator for Intersection Graphs of Geodesic Disks in $\mathbb{R}^2$
Boris Aronov, Mark de Berg, Leonidas Theocharous
https://arxiv.org/abs/2403.04905

A Clique-Based Separator for Intersection Graphs of Geodesic Disks in $\mathbb{R}^2$
Let $d$ be a (well-behaved) shortest-path metric defined on a path-connected subset of $\mathbb{R}^2$ and let $\mathcal{D}=\{D_1,\ldots,D_n\}$ be a set of geodesic disks with respect to the metric $d$. We prove that $\mathcal{G}^{\times}(\mathcal{D})$, the intersection graph of the disks in $\mathcal{D}$, has a clique-based separator consisting of $O(n^{3/4+\varepsilon})$ cliques. This significantly extends the class of objects whose intersection graphs have small clique-based separators. Our…

Integrability of the sub-Riemannian geodesic flow of the left-invariant metric on the Heisenberg group
Milan Pavlovic, Tijana Sukilovic
https://arxiv.org/abs/2404.06586

Integrability of the sub-Riemannian geodesic flow of the left-invariant metric on the Heisenberg group
In this paper, we study two different classes of normal geodesic flows corresponding to the left-invariant sub-Riemannian metric on the $(2n+1)$-dimensional Heisenberg group. The first class corresponds to the left-invariant distribution, while the second corresponds to the right-invariant one. We prove that corresponding Hamiltonian L-L and L-R systems are completely integrable.

Data-Dependent LSH for the Earth Mover's Distance
Rajesh Jayaram, Erik Waingarten, Tian Zhang
https://arxiv.org/abs/2403.05041 https://

Data-Dependent LSH for the Earth Mover's Distance
We give new data-dependent locality sensitive hashing schemes (LSH) for the Earth Mover's Distance ($\mathsf{EMD}$), and as a result, improve the best approximation for nearest neighbor search under $\mathsf{EMD}$ by a quadratic factor. Here, the metric $\mathsf{EMD}_s(\mathbb{R}^d,\ell_p)$ consists of sets of $s$ vectors in $\mathbb{R}^d$, and for any two sets $x,y$ of $s$ vectors the distance $\mathsf{EMD}(x,y)$ is the minimum cost of a perfect matching between $x,y$, where the cost of matchi…

A goodness-of-fit diagnostic for count data derived from half-normal plots with a simulated envelope
Darshana Jayakumari, Jochen Einbeck, John Hinde, Julien Mainguy, Rafael de Andrade Moral
https://arxiv.org/abs/2405.05121

A goodness-of-fit diagnostic for count data derived from half-normal plots with a simulated envelope
Traditional methods of model diagnostics may include a plethora of graphical techniques based on residual analysis, as well as formal tests (e.g. Shapiro-Wilk test for normality and Bartlett test for homogeneity of variance). In this paper we derive a new distance metric based on the half-normal plot with a simulation envelope, a graphical model evaluation method, and investigate its properties through simulation studies. The proposed metric can help to assess the fit of a given model, and also…

The Riemannian geometry of Sinkhorn divergences
Hugo Lavenant, Jonas Luckhardt, Gilles Mordant, Bernhard Schmitzer, Luca Tamanini
https://arxiv.org/abs/2405.04987

The Riemannian geometry of Sinkhorn divergences
We propose a new metric between probability measures on a compact metric space that mirrors the Riemannian manifold-like structure of quadratic optimal transport but includes entropic regularization. Its metric tensor is given by the Hessian of the Sinkhorn divergence, a debiased variant of entropic optimal transport. We precisely identify the tangent space it induces, which turns out to be related to a Reproducing Kernel Hilbert Space (RKHS). As usual in Riemannian geometry, the distance is bu…

This https://arxiv.org/abs/2405.01582 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

Text Quality-Based Pruning for Efficient Training of Language Models
In recent times training Language Models (LMs) have relied on computationally heavy training over massive datasets which makes this training process extremely laborious. In this paper we propose a novel method for numerically evaluating text quality in large unlabelled NLP datasets in a model agnostic manner to assign the text instances a "quality score". By proposing the text quality metric, the paper establishes a framework to identify and eliminate low-quality text instances, leading to im…

Towards a generalized accessibility measure for transportation equity and efficiency
Rajat Verma, Mithun Debnath, Shagun Mittal, Satish V. Ukkusuri
https://arxiv.org/abs/2404.04985 https://arxiv.org/pdf/2404.04985
arXiv:2404.04985v1 Announce Type: new
Abstract: Locational measures of accessibility are widely used in urban and transportation planning to understand the impact of the transportation system on influencing people's access to places. However, there is a considerable lack of measurement standards and publicly available data. We propose a generalized measure of locational accessibility that has a comprehensible form for transportation planning analysis. This metric combines the cumulative opportunities approach with gravity-based measures and is capable of catering to multiple trip purposes, travel modes, cost thresholds, and scales of analysis. Using data from multiple publicly available datasets, this metric is computed by trip purpose and travel time threshold for all block groups in the United States, and the data is made publicly accessible. Further, case studies of three large metropolitan areas reveal substantial inefficiencies in transportation infrastructure, with the most inefficiency observed in sprawling and non-core urban areas, especially for bicycling. Subsequently, it is shown that targeted investment in facilities can contribute to a more equitable distribution of accessibility to essential shopping and service facilities. By assigning greater weights to socioeconomically disadvantaged neighborhoods, the proposed metric formally incorporates equity considerations into transportation planning, contributing to a more equitable distribution of accessibility to essential services and facilities.

A Goldstone Boson Equivalence for Inflation
Daniel Green, Kshitij Gupta, Yiwen Huang
https://arxiv.org/abs/2403.05274 https://arxiv.o…

A Goldstone Boson Equivalence for Inflation
The effective field theory of single-field inflation characterizes the inflationary epoch in terms of a pattern of symmetry breaking. An operator acquires a time-dependent vacuum expectation value, defining a preferred spatial slicing. In the absence of dynamical gravity, the fluctuations around the time-dependent background are described by the Goldstone boson associated with this symmetry breaking process. With gravity, the Goldstone is eaten by the metric, becoming the scalar metric fluctuat…

Log-Lipschitz and H\"older regularity imply smoothness for complex analytic sets
Jos\'e Edson Sampaio
https://arxiv.org/abs/2404.06943 https://

Log-Lipschitz and Hölder regularity imply smoothness for complex analytic sets
In this paper, we prove metric analogues, in any dimension and in any co-dimension, of the famous Theorem of Mumford on smoothness of normal surfaces and the beautiful Theorem of Ramanujam that gives a topological characterization of $\mathbb{C}^2$ as an algebraic surface. For instance, we prove that a complex analytic set that is log-Lipschitz regular at 0 (i.e., a complex analytic set that has a neighbourhood of the origin which bi-log-Lipschitz homeomorphic to an Euclidean ball) must be smoo…

Classical and quantum field theory in a box with moving boundaries: A numerical study of the Dynamical Casimir Effect
Alberto Garc\'ia Mart\'in-Caro, Gerardo Garc\'ia-Moreno, Javier Olmedo, Jose M. S\'anchez Vel\'azquez
https://arxiv.org/abs/2404.06166

Classical and quantum field theory in a box with moving boundaries: A numerical study of the Dynamical Casimir Effect
We present a detailed description of a quantum scalar field theory within a flat spacetime confined to a cavity with perfectly reflecting moving boundaries. Moreover, we establish an equivalence between this time-dependent setting and a field theory on an acoustic metric with static Dirichlet boundary conditions. We discuss the classical and quantum aspects of the theory from the latter perspective, accompanied by the introduction of novel numerical techniques designed for the (nonperturbative)…

Local limit theorem of Brownian motion on metric trees
Soonki Hong
https://arxiv.org/abs/2403.05089 https://arxiv.org/pdf/2403.05089<…

Local limit theorem of Brownian motion on metric trees
Let $\mathcal{T}$ be a locally finite tree whose geometric boundary has infinitely many points. Suppose that a non-amenable group $\G$ acts isometrically and geometrically on the tree $\mathcal{T}$. In this paper, we show that if the length spectrum is Diophantine, then there exists a continuous function $C$ on $\mathcal{T}^2$ such that the heat kernel $p(t,x,y)$ of $\mathcal{T}$ satisfies $$\lim_{t\rightarrow \infty}t^{3/2}e^{λ_0t}p(t,x,y)=C(x,y)$$ for any $x,y\in \mathcal{T}$. Here, $�…

Characterizing Lipschitz images of injective metric spaces
Judyta B\k{a}k, Taras Banakh, Joanna Garbuli\'nska-W\k{e}grzyn, Magdalena Nowak, Micha{\l} Pop{\l}awski
https://arxiv.org/abs/2405.01860

Characterizing Lipschitz images of injective metric spaces
A metric space $X$ is {\em injective} if every non-expanding map $f:B\to X$ defined on a subspace $B$ of a metric space $A$ can be extended to a non-expanding map $\bar f:A\to X$. We prove that a metric space $X$ is a Lipschitz image of an injective metric space if and only if $X$ is Lipschitz connected in the sense that for every points $x,y\in X$, there exists a Lipschitz map $f:[0,1]\to X$ such that $f(0)=x$ and $f(1)=y$. In this case the metric space $X$ carries a well-defined intrinsic met…

This https://arxiv.org/abs/2404.15523 has been replaced.
link: https://scholar.google.com/scholar?q=a

Understanding Hyperbolic Metric Learning through Hard Negative Sampling
In recent years, there has been a growing trend of incorporating hyperbolic geometry methods into computer vision. While these methods have achieved state-of-the-art performance on various metric learning tasks using hyperbolic distance measurements, the underlying theoretical analysis supporting this superior performance remains under-exploited. In this study, we investigate the effects of integrating hyperbolic space into metric learning, particularly when training with contrastive loss. We i…

This https://arxiv.org/abs/2212.00147 has been replaced.
link: https://scholar.google.com/scholar?q=a

Homotopical models for metric spaces and completeness
Categories enriched in the opposite poset of non-negative reals can be viewed as generalizations of metric spaces, known as Lawvere metric spaces. In this article, we develop model structures on the categories $\mathbb{R}\text-\mathbf{Cat}$ and $\mathbb{R}\text-\mathbf{Cat}^\mathrm{sym}$ of Lawvere metric spaces and symmetric Lawvere metric spaces, each of which capture different features pertinent to the study of metric spaces. More precisely, in the three model structures we construct, the fi…

Near Field Communications for DMA-NOMA Networks
Zheng Zhang, Yuanwei Liu, Zhaolin Wang, Jian Chen, Dong In Kim
https://arxiv.org/abs/2403.04925 https://

Near Field Communications for DMA-NOMA Networks
A novel near-field transmission framework is proposed for dynamic metasurface antenna (DMA)-enabled non-orthogonal multiple access (NOMA) networks. The base station (BS) exploits the hybrid beamforming to communicate with multiple near users (NUs) and far users (FUs) using the NOMA principle. Based on this framework, two novel beamforming schemes are proposed. 1) For the case of the grouped users distributed in the same direction, a beam-steering scheme is developed. The metric of beam pattern …

This https://arxiv.org/abs/2401.01283 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

Quality and Quantity of Machine Translation References for Automatic Metrics
Automatic machine translation metrics typically rely on human translations to determine the quality of system translations. Common wisdom in the field dictates that the human references should be of very high quality. However, there are no cost-benefit analyses that could be used to guide practitioners who plan to collect references for machine translation evaluation. We find that higher-quality references lead to better metric correlations with humans at the segment-level. Having up to 7 refer…

[2024-04-11 Thu (UTC), 1 new article found for math.MG Metric Geometry]

Security Assessment of the LG Cryptosystem
\'Etienne Burle, Herv\'e Tal\'e Kalachi, Freddy Lende Metouke, Ayoub Otmani
https://arxiv.org/abs/2404.06815

Security Assessment of the LG Cryptosystem
The LG cryptosystem is a public-key encryption scheme in the rank metric using the recent family of $\lambdav-$Gabidulin codes and introduced in 2019 by Lau and Tan. In this paper, we present a cryptanalysis showing that the security of several parameters of the scheme have been overestimated. We also show the existence of some weak keys allowing an attacker to find in polynomial time an alternative private key.

Improved Lower Bound for Differentially Private Facility Location
Pasin Manurangsi
https://arxiv.org/abs/2403.04874 https://arxiv.org…

Improved Lower Bound for Differentially Private Facility Location
We consider the differentially private (DP) facility location problem in the so called super-set output setting proposed by Gupta et al. [SODA 2010]. The current best known expected approximation ratio for an $ε$-DP algorithm is $O\left(\frac{\log n}{\sqrtε}\right)$ due to Cohen-Addad et al. [AISTATS 2022] where $n$ denote the size of the metric space, meanwhile the best known lower bound is $Ω(1/\sqrtε)$ [NeurIPS 2019]. In this short note, we give a lower bound of $\tildeΩ\left(\min\lef…

A fixed point results of Kannan-type for multi-valued mapping on fuzzy metric spaces
Shunya Hashimoto, Aqib Saghir
https://arxiv.org/abs/2405.04179 https:/…

A fixed point results of Kannan-type for multi-valued mapping on fuzzy metric spaces
We prove a Kannan-type fixed point theorem for multi-valued mappings on G-complete fuzzy metric spaces. The proof uses the Hausdorff fuzzy metric space which was introduced by Rodriguez-Lopez and Romaguera [19].

K-stable valuations and Calabi-Yau metrics on affine spherical varieties
Tran-Trung Nghiem
https://arxiv.org/abs/2405.05833 https://a…

K-stable valuations and Calabi-Yau metrics on affine spherical varieties
After providing an explicit K-stability condition for a $\mathbb{Q}$-Gorenstein log spherical cone, we prove the existence and uniqueness of an equivariant K-stable degeneration of the cone, and deduce uniqueness of the asymptotic cone of a given complete $K$-invariant Calabi-Yau metric in the trivial class of an affine $G$-spherical manifold, $K$ being the maximal compact subgroup of $G$. Next, we prove that the valuation induced by $K$-invariant Calabi-Yau metrics on affine $G$-spherical ma…

This https://arxiv.org/abs/2301.05289 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The covariance metric in the Blaschke locus
We prove that the Blaschke locus has the structure of a finite dimensional smooth manifold away from the Teichm{ü}ller space and study its Riemannian manifold structure with respect to the covariance metric introduced by Guillarmou, Knieper and Lefeuvre in \cite{GeodesicStretch}. We also identify some families of geodesics in the Blaschke locus arising from Hitchin representations for orbifolds and show that they have infinite length with respect to the covariance metric.

This https://arxiv.org/abs/2311.15272 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Cosmological Time Crystals from Gauss-Bonnet Gravity in Four Dimensions
We investigate various cosmological aspects of a 4-Dimensional Gauss-Bonnet Lagrangian, which is integrated into the Einstein Lagrangian with an arbitrary sign, using the Friedman-Lemaître-Robertson-Walker (FLRW) metric. We consider a general potential term, $V(a)$, that depends on the scale factor $a$, and we analyze several scenarios by investigating the critical points of the dynamical equations and stability conditions to understand how the universe's behavior is affected by the Gauss-Bonn…

ROUGE-K: Do Your Summaries Have Keywords?
Sotaro Takeshita, Simone Paolo Ponzetto, Kai Eckert
https://arxiv.org/abs/2403.05186 https://

ROUGE-K: Do Your Summaries Have Keywords?
Keywords, that is, content-relevant words in summaries play an important role in efficient information conveyance, making it critical to assess if system-generated summaries contain such informative words during evaluation. However, existing evaluation metrics for extreme summarization models do not pay explicit attention to keywords in summaries, leaving developers ignorant of their presence. To address this issue, we present a keyword-oriented evaluation metric, dubbed ROUGE-K, which provides…

This https://arxiv.org/abs/2308.13776 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A VMiPG method for composite optimization with nonsmooth term having no closed-form proximal mapping
This paper concerns the minimization of the sum of a twice continuously differentiable function $f$ and a nonsmooth convex function $g$ without closed-form proximal mapping. For this class of nonconvex and nonsmooth problems, we propose a line-search based variable metric inexact proximal gradient (VMiPG) method with uniformly bounded positive definite variable metric linear operators. This method computes in each step an inexact minimizer of a strongly convex model such that the difference bet…

[2024-05-10 Fri (UTC), 2 new articles found for math.MG Metric Geometry]

A fixed point results of Kannan-type for multi-valued mapping on fuzzy metric spaces
Shunya Hashimoto, Aqib Saghir
https://arxiv.org/abs/2405.04179 https:/…

A fixed point results of Kannan-type for multi-valued mapping on fuzzy metric spaces
We prove a Kannan-type fixed point theorem for multi-valued mappings on G-complete fuzzy metric spaces. The proof uses the Hausdorff fuzzy metric space which was introduced by Rodriguez-Lopez and Romaguera [19].

This https://arxiv.org/abs/2311.03619 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Construction and Fast Decoding of Binary Linear Sum-Rank-Metric Codes
Sum-rank-metric codes have wide applications in the multishot network coding and the distributed storage. Linearized Reed-Solomon codes, sum-rank BCH codes and their Welch-Berlekamp type decoding algorithms were proposed and studied. They are sum-rank versions of Reed-Solomon codes and BCH codes in the Hamming metric. In this paper, we construct binary linear sum-rank-metric codes of the matrix size $2 \times 2$, from BCH, Goppa and additive quaternary Hamming metric codes. Larger sum-rank-metr…

This https://arxiv.org/abs/2309.11491 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Vacuum Spacetime With Multipole Moments: The Minimal Size Conjecture, Black Hole Shadow, and Gravitational Wave Observables
In this work, we explicitly construct the vacuum solution of Einstein's equations with prescribed multipole moments. By observing the behavior of the multipole spacetime metric at small distances, we conjecture that for a sufficiently large multipole moment, there is a minimal size below which no object in nature can support such a moment. The examples we have investigated suggest that such minimal size scales as $(M_n)^{1/(n+1)}$ (instead of $(M_n/M)^{1/n}$), where $M$ is the mass and $M_n$ is…

ROUGE-K: Do Your Summaries Have Keywords?
Sotaro Takeshita, Simone Paolo Ponzetto, Kai Eckert
https://arxiv.org/abs/2403.05186 https://

ROUGE-K: Do Your Summaries Have Keywords?
Keywords, that is, content-relevant words in summaries play an important role in efficient information conveyance, making it critical to assess if system-generated summaries contain such informative words during evaluation. However, existing evaluation metrics for extreme summarization models do not pay explicit attention to keywords in summaries, leaving developers ignorant of their presence. To address this issue, we present a keyword-oriented evaluation metric, dubbed ROUGE-K, which provides…

This https://arxiv.org/abs/2304.06088 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Gravitational Edge Mode in Asymptotically AdS$_2$: JT Gravity Revisited
We study the gravitational edge mode of the Jackiw-Teitelboim (JT) gravity and its $sl(2,\mathbb{R})$ BF theory description with the asymptotic AdS$_2$ boundary condition. We revisit the derivation of the Schwarzian theory from the wiggling boundary as an action for the gravitational edge mode. We present an alternative description for the gravitational edge mode from the metric fluctuation with the fixed boundary, which is often referred as "would-be gauge mode". We clarify the relation betwee…

This https://arxiv.org/abs/2303.00536 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the prevalence of the periodicity of maximizing measures
For a continuous map $T: X\rightarrow X$ on a compact metric space $(X,d)$, we say that a function $f: X \rightarrow \mathbb{R}$ has the property $\mathscr{P}_T$ if its time averages along forward orbits of $T$ are maximized at a periodic orbit. In this paper, we prove that for the one-side full shift of two symbols, the property $\mathscr{P}_T$ is prevalent (in the sense of Hunt--Sauer--Yorke) in spaces of Lipschitz functions with respect to metrics with mildly fast decaying rate on the diamet…

[2024-05-10 Fri (UTC), 2 new articles found for math.MG Metric Geometry]

This https://arxiv.org/abs/2404.03095 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Analyzing Warp Drive Spacetimes with Warp Factory
The field of warp research has been dominated by analytical methods to investigate potential solutions. However, these approaches often favor simple metric forms that facilitate analysis but ultimately limit the range of exploration of novel solutions. So far the proposed solutions have been unphysical, requiring energy condition violations and large energy requirements. To overcome the analytical limitations in warp research, we introduce Warp Factory: a numerical toolkit designed for modeling…

This https://arxiv.org/abs/2405.05003 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Nilpotent structures of oriented neutral vector bundles
In this paper, we study nilpotent structures of an oriented vector bundle $E$ of rank $4n$ with a neutral metric $h$ and an $h$-connection $\nabla$. We define $H$-nilpotent structures of $(E, h, \nabla )$ for a Lie subgroup $H$ of $SO(2n, 2n)$ related to neutral hyperKähler structures. We observe that there exist a complex structure $I$ and paracomplex structures $J_1$, $J_2$ of $E$ such that $h$, $\nabla$, $I$, $J_1$, $J_2$ form a neutral hyperKähler structure of $E$ if and only if there exi…

On three-point generalizations of Banach and Edelstein fixed point theorems
Christian Bey, Evgeniy Petrov, Ruslan Salimov
https://arxiv.org/abs/2404.05740 …

On three-point generalizations of Banach and Edelstein fixed point theorems
Let $X$ be a metric space. Recently in~[1] it was considered a new type of mappings $T\colon X\to X$ which can be characterized as mappings contracting perimeters of triangles. These mappings are defined by the condition based on the mapping of three points of the space instead of two, as it is adopted in many fixed-point theorems. In the present paper we consider so-called $(F,G)$-contracting mappings, which form a more general class of mappings than mappings contracting perimeters of triangle…

This https://arxiv.org/abs/2311.01863 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Gravitational Waves Generated by Null Cosmic Strings
Null cosmic strings are shown to disturb gravitational fields of massive bodies and create outgoing gravitational waves (GW). Perturbations of the metric caused by a straight null string and a point-like massive source are found as solutions to linearized Einstein equations on a flat space-time. An analytic approximation for their asymptotic at future null infinity is derived. A space-time created by the source and the string is shown to have asymptotically polyhomogeneous form. We calculate GW…

[2024-03-11 Mon (UTC), no new articles found for math.MG Metric Geometry]

Multiple mixing in ergodic theory
Valery V. Ryzhikov
https://arxiv.org/abs/2404.06476 https://arxiv.org/pdf/2404.06476

Multiple mixing in ergodic theory
In 1949 V.A. Rokhlin introduced into ergodic theory the k-fold mixing and puzzled the mathematical community with the problem of the mismatch of these invariants. Here's what Rokhlin wrote: "The proposed work arose from the author's attempts to solve the well-known spectral problem of the theory of dynamical systems: are there any metrically different dynamical systems with the same continuous (in particular, Lebesgue) spectrum? Using new metric invariants introduced for this purpose, the aut…

Survey on the Canonical Metrics on the Teichm\"{u}ller Spaces and the Moduli Spaces of Riemann Surfaces
Kin Wai Chan
https://arxiv.org/abs/2405.00761 …

Survey on the Canonical Metrics on the Teichmüller Spaces and the Moduli Spaces of Riemann Surfaces
This thesis results from an intensive study on the canonical metrics on the Teichmüller spaces and the moduli spaces of Riemann surfaces. There are several renowned classical metrics on $T_g$ and $\mathcal{M}_g$, including the Weil-Petersson metric, the Teichmüller metric, the Kobayashi metric, the Bergman metric, the Carathéodory metric and the Kähler-Einstein metric. The Teichmüller metric, the Kobayashi metric and the Carathéodory metric are only (complete) Finsler metrics, but they ar…

This https://arxiv.org/abs/2404.17798 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Torsion and Chern-Simons gravity in 4D space-times from a Geometrodynamical four-form
In Hermann Minkowski's pioneering formulation of special relativity, the space-time geometry in any inertial frame is described by the line-element $ds^2= η_{μν} dx^μdx^ν$. It is interesting to note that not only the Minkowski metric $η_{μν} $ is invariant under proper Lorentz transformations, the totally antisymmetric Levi-Civita tensor $e_{μναβ} $ too is. In general relativity (GR), $η_{μν} $ of the flat space-time gets generalized to a dynamical, space-time dependent metric te…

[2024-04-10 Wed (UTC), no new articles found for math.MG Metric Geometry]

This https://arxiv.org/abs/2309.12544 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Stability and Statistical Inversion of Travel time Tomography
In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward and inverse stability estimates for simple conformal metrics under some a priori conditions. We then apply the stability estimates to show the consistency of a Bayesian statistical inversion technique for travel time tomography with discrete, noisy measureme…

This https://arxiv.org/abs/2404.17798 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Torsion and Chern-Simons gravity in 4D space-times from a Geometrodynamical four-form
In Hermann Minkowski's pioneering formulation of special relativity, the space-time geometry in any inertial frame is described by the line-element $ds^2= η_{μν} dx^μdx^ν$. It is interesting to note that not only the Minkowski metric $η_{μν} $ is invariant under proper Lorentz transformations, the totally antisymmetric Levi-Civita tensor $e_{μναβ} $ too is. In general relativity (GR), $η_{μν} $ of the flat space-time gets generalized to a dynamical, space-time dependent metric te…

Encoder-Decoder Framework for Interactive Free Verses with Generation with Controllable High-Quality Rhyming
Tommaso Pasini, Alejo L\'opez-\'Avila, Husam Quteineh, Gerasimos Lampouras, Jinhua Du, Yubing Wang, Ze Li, Yusen Sun
https://arxiv.org/abs/2405.05176

Encoder-Decoder Framework for Interactive Free Verses with Generation with Controllable High-Quality Rhyming
Composing poetry or lyrics involves several creative factors, but a challenging aspect of generation is the adherence to a more or less strict metric and rhyming pattern. To address this challenge specifically, previous work on the task has mainly focused on reverse language modeling, which brings the critical selection of each rhyming word to the forefront of each verse. On the other hand, reversing the word order requires that models be trained from scratch with this task-specific goal and ca…

[2024-04-10 Wed (UTC), no new articles found for math.MG Metric Geometry]

A note on the volume entropy on a harmonic manifold of hypergeometric type
Hiroyasu Satoh
https://arxiv.org/abs/2405.05896 https://ar…

A note on the volume entropy on a harmonic manifold of hypergeometric type
Harmonic manifolds of hypergeometric type form a class of non-compact harmonic manifolds that includes rank one symmetric spaces of non-compact type and Damek-Ricci spaces. When normalizing the metric of a harmonic manifold of hypergeometric type to satisfy the Ricci curvature $\mathrm{Ric} = -(n-1)$, we show that the volume entropy of this manifold satisfies a certain inequality. Additionally, we show that manifolds yielding the upper bound of volume entropy are only real hyperbolic spaces wit…

This https://arxiv.org/abs/2306.04298 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Regular black hole from regular initial data
Recently there has been an interest in exploring black holes that are regular in the sense that the central curvature singularity is avoided. Here, we depict a method to obtain a regular black hole (RBH) spacetime $(\mathcal{M}, \Tilde{g})$ from the unhindered gravitational collapse from regular initial data of a spherically symmetric perfect fluid $(\mathcal{M}, g)$. In other words, we obtain the equilibrium metric $\Tilde g$ as a limiting case of the time-evolving metric $g$. In the spirit of…

This https://arxiv.org/abs/2405.03895 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Quasi-positive curvature and vanishing theorems
In this paper, we consider mixed curvature $\mathcal{C}_{a,b}$, which is a convex combination of Ricci curvature and holomorphic sectional curvature introduced by Chu-Lee-Tam. We prove that if a compact complex manifold M admits a Kähler metric with quasi-positive mixed curvature and $3a+2b\geq0$, then it is projective. If $a,b\geq0$, then M is rationally connected. As a corollary, the same result holds for k-Ricci curvature. We also show that any compact Kähler manifold with quasi-positive 2…

This https://arxiv.org/abs/2306.04298 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Regular black hole from regular initial data
Recently there has been an interest in exploring black holes that are regular in the sense that the central curvature singularity is avoided. Here, we depict a method to obtain a regular black hole (RBH) spacetime $(\mathcal{M}, \Tilde{g})$ from the unhindered gravitational collapse from regular initial data of a spherically symmetric perfect fluid $(\mathcal{M}, g)$. In other words, we obtain the equilibrium metric $\Tilde g$ as a limiting case of the time-evolving metric $g$. In the spirit of…

Gromov-Hausdorff distances from simply connected geodesic spaces to the circle
Sa\'ul Rodr\'iguez Mart\'in
https://arxiv.org/abs/2404.05153 htt…

Gromov-Hausdorff distances from simply connected geodesic spaces to the circle
We prove that the Gromov-Hausdorff distance from the circle with its geodesic metric to any simply connected geodesic space is never smaller than $\fracπ{4}$. We also prove that this bound is tight through the construction of a simply connected geodesic space $\mathrm{E}$ which attains the lower bound $\fracπ{4}$. We deduce the first statement from a general result that we also establish which gives conditions on how small the Gromov-Hausdorff distance between two geodesic metric spaces $(X, …

Emergent Modified Gravity
Martin Bojowald, Erick I. Duque
https://arxiv.org/abs/2404.06375 https://arxiv.org/pdf/2404.06375

Emergent Modified Gravity
A complete canonical formulation of general covariance makes it possible to construct new modified theories of gravity that are not of higher-curvature form, as shown here in a spherically symmetric setting. The usual uniqueness theorems are evaded by using a crucial and novel ingredient, allowing for fundamental fields of gravity distinct from an emergent space-time metric that provides a geometrical structure to all solutions. As specific examples, there are new expansion-shear couplings in c…

This https://arxiv.org/abs/2312.17497 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Completeness and geodesic distance properties for fractional Sobolev metrics on spaces of immersed curves
We investigate the geometry of the space of immersed closed curves equipped with reparametrization-invariant Riemannian metrics; the metrics we consider are Sobolev metrics of possible fractional order $q\in [0,\infty)$. We establish the critical Sobolev index on the metric for several key geometric properties. Our first main result shows that the Riemannian metric induces a metric space structure if and only if $q>1/2$. Our second main result shows that the metric is geodesically-complete (i.e…

This https://arxiv.org/abs/2211.07762 has been replaced.
link: https://scholar.google.com/scholar?q=a

Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures
Recent advances in the theory of metric measures spaces on the one hand, and of sub-Riemannian ones on the other hand, suggest the possibility of a "great unification" of Riemannian and sub-Riemannian geometries in a comprehensive framework of synthetic Ricci curvature lower bounds. With the aim of achieving such a unification program, in this paper we initiate the study of gauge metric measure spaces.

This https://arxiv.org/abs/2105.03805 has been replaced.
link: https://scholar.google.com/scholar?q=a

A new proof for the existence of rotationally symmetric gradient Ricci solitons
We give a new proof for the existence of rotationally symmetric steady and expanding gradient Ricci solitons in dimension $n+1$, $2\le n\le 4$, with metric $g=\frac{da^2}{h(a^2)}+a^2d\,σ$ for some function $h$ where $dσ$ is the standard metric on the unit sphere $S^n$ in $\mathbb{R}^n$. More precisely for any $λ\ge 0$, $2\le n\le 4$ and $μ_1\in\mathbb{R}$, we prove the existence of unique solution $h\in C^2((0,\infty))\cap C^1([0,\infty))$ for the equation $2r^2h(r)h_{rr}(r)=(n-1)h(r)(h(r)-…

Geometric inverse problems on gas giants
Maarten V. de Hoop, Joonas Ilmavirta, Antti Kykk\"anen, Rafe Mazzeo
https://arxiv.org/abs/2403.05475 https://…

Geometric inverse problems on gas giants
On gas giant planets the speed of sound is isotropic and goes to zero at the surface. Geometrically, this corresponds to a Riemannian manifold whose metric tensor has a conformal blow-up near the boundary. The blow-up is tamer than in asymptotically hyperbolic geometry: the boundary is at a finite distance. We study the differential geometry of such manifolds, especially the asymptotic behavior of geodesics near the boundary. We relate the geometry to the propagation of singularities of a hyd…