Tootfinder

Metrics on Hitchin Components from H\"older Distortion
Alexander Nolte
https://arxiv.org/abs/2402.16584 https://arxiv.org/pdf/24…

Metrics on Hitchin Components from Hölder Distortion
We observe Thurston's asymmetric metric on Teichmüller space may be expressed in terms of the Hölder regularity of boundary maps. We then associate $2$-dimensional stratified loci in $\mathbb{RP}^{n-1}$ to $\text{PSL}_n(\mathbb{R})$ Hitchin representations with $n > 3$. We prove that measuring the relative Hölder distortion of these loci gives asymmetric metrics on the Hitchin component $\text{Hit}_n(S)$ with complete and geometrically meaningful symmetrizations. These are the first known ge…

Aiming for Relevance
Bar Eini Porat, Danny Eytan, Uri Shalit
https://arxiv.org/abs/2403.18668 https://arxiv.org/pdf/2403.18668…

Aiming for Relevance
Vital signs are crucial in intensive care units (ICUs). They are used to track the patient's state and to identify clinically significant changes. Predicting vital sign trajectories is valuable for early detection of adverse events. However, conventional machine learning metrics like RMSE often fail to capture the true clinical relevance of such predictions. We introduce novel vital sign prediction performance metrics that align with clinical contexts, focusing on deviations from clinical norms…

I did not know about ggplot_build() before. It can come in handy in situations where you want to access computed metrics of a #ggplot. https://ggplot2.tidyverse.org/reference/ggplot…

Build ggplot for rendering. — ggplot_build
ggplot_build() takes the plot object, and performs all steps necessary to produce an object that can be rendered. This function outputs two pieces: a list of data frames (one for each layer), and a panel object, which contain all information about axis limits, breaks etc.

i hate crap like this. please stop interrupting what i'm doing to show me something that is 100% not useful to me and is all about increasing whatever metrics you're trying to optimize 🤬🤬🤬
anyway, instead of doing something useful or enjoyable, i'm now trying to figure out how to disable this from ever appearing again. i don't care how cute your waving fox logo is
#firefox <…

This https://arxiv.org/abs/2111.00652 has been replaced.
link: https://scholar.google.com/scholar?q=a

Eguchi--Hanson metrics arising from Kahler--Einstein edge metrics
Calabi--Hirzebruch manifolds are higher-dimensional generalizations of both the football and Hirzebruch surfaces. We construct a family of Kahler--Einstein edge metrics singular along two disjoint divisors on the Calabi--Hirzebruch manifolds and study their Gromov--Hausdorff limits when either cone angle tends to its extreme value. As a very special case, we show that the celebrated Eguchi--Hanson metric arises in this way naturally as a Gromov--Hausdorff limit. We also completely describe all …

Characterizing Dependency Update Practice of NPM, PyPI and Cargo Packages
Imranur Rahman, Nusrat Zahan, Stephen Magill, William Enck, Laurie Williams
https://arxiv.org/abs/2403.17382

Characterizing Dependency Update Practice of NPM, PyPI and Cargo Packages
Keeping dependencies up-to-date prevents software supply chain attacks through outdated and vulnerable dependencies. Developers may use packages' dependency update practice as one of the selection criteria for choosing a package as a dependency. However, the lack of metrics characterizing packages' dependency update practice makes this assessment difficult. To measure the up-to-date characteristics of packages, we focus on the dependency management aspect and propose two update metrics: Time-Ou…

#Covid
This winter, Switzerland experienced a severe Covid wave. This is evident in prevalences and derived incidences, as well as in hospitalisations and mortality. The metrics correlate.
This year, the effects of SARS2 can unequivocally be discriminated from influenza.
Thread.

This https://arxiv.org/abs/2402.08893 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSI_…

Inconsistency of evaluation metrics in link prediction
Link prediction is a paradigmatic and challenging problem in network science, which predicts missing links, future links and temporal links based on known topology. Along with the increasing number of link prediction algorithms, a critical yet previously ignored risk is that the evaluation metrics for algorithm performance are usually chosen at will. This paper implements extensive experiments on hundreds of real networks and 25 well-known algorithms, revealing statistically significant inconsi…

Edit Distance of Finite State Transducers
C. Aiswarya, Amaldev Manuel, Saina Sunny
https://arxiv.org/abs/2404.16518 https://arxiv.org…

Edit Distance of Finite State Transducers
We lift metrics over words to metrics over word-to-word transductions, by defining the distance between two transductions as the supremum of the distances of their respective outputs over all inputs. This allows to compare transducers beyond equivalence. Two transducers are close (resp. $k$-close) with respect to a metric if their distance is finite (resp. at most $k$). Over integer-valued metrics computing the distance between transducers is equivalent to deciding the closeness and $k$-close…

This https://arxiv.org/abs/2302.01790 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCV_…

Understanding metric-related pitfalls in image analysis validation
Validation metrics are key for the reliable tracking of scientific progress and for bridging the current chasm between artificial intelligence (AI) research and its translation into practice. However, increasing evidence shows that particularly in image analysis, metrics are often chosen inadequately in relation to the underlying research problem. This could be attributed to a lack of accessibility of metric-related knowledge: While taking into account the individual strengths, weaknesses, and …

ACES: Evaluating Automated Audio Captioning Models on the Semantics of Sounds
Gijs Wijngaard, Elia Formisano, Bruno L. Giordano, Michel Dumontier
https://arxiv.org/abs/2403.18572 …

ACES: Evaluating Automated Audio Captioning Models on the Semantics of Sounds
Automated Audio Captioning is a multimodal task that aims to convert audio content into natural language. The assessment of audio captioning systems is typically based on quantitative metrics applied to text data. Previous studies have employed metrics derived from machine translation and image captioning to evaluate the quality of generated audio captions. Drawing inspiration from auditory cognitive neuroscience research, we introduce a novel metric approach -- Audio Captioning Evaluation on S…

This https://arxiv.org/abs/2209.14720 has been replaced.
link: https://scholar.google.com/scholar?q=a

Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII
The wonderful compactification $X_m$ of a symmetric homogeneous space of type AIII$(2,m)$ for each $m \geq 4$ is Fano, and its blowup $Y_m$ along the unique closed orbit is Fano if $m \geq 5$ and Calabi-Yau if $m = 4$. Using a combinatorial criterion for K-polystability of smooth Fano spherical varieties obtained by Delcroix, we prove that $X_m$ admits a Kähler-Einstein metric for each $m \geq 4$ and $Y_m$ admits a Kähler-Einstein metric if and only if $m = 4, 5$.

Wrote #NUT with

Approximation of functions of many variables from the generalization Nikol'skii-Besov type classes in the uniform and integral metrics
M. I. Gromyak, O. Ya. Radchenko, S. Ya. Yanchenko
https://arxiv.org/abs/2403.18414

Approximation of functions of many variables from the generalization Nikol'skii-Besov type classes in the uniform and integral metrics
We obtain the exact order estimates of the approximation of the functions of many variables from the generalized Nikol'skii-Besov classes $B^Ω_{p,θ}(\mathbb{R}^d)$ by sums of de la Vallee Poussin type in the metrics space $L_{\infty}(\mathbb{R}^d)$ and $L_{1}(\mathbb{R}^d)$. These classes of functions for some given $Ω$ coincide with the well-known classical Nikol'skii-Besov isotropic classes.

Design Principles of Dynamic Resource Management for High-Performance Parallel Programming Models
Dominik Huber, Martin Schreiber, Martin Schulz, Howard Pritchard, Daniel Holmes
https://arxiv.org/abs/2403.17107

Design Principles of Dynamic Resource Management for High-Performance Parallel Programming Models
With Dynamic Resource Management (DRM) the resources assigned to a job can be changed dynamically during its execution. From the system's perspective, DRM opens a new level of flexibility in resource allocation and job scheduling and therefore has the potential to improve system efficiency metrics such as the utilization rate, job throughput, energy efficiency, and responsiveness. From the application perspective, users can tailor the resources they request to their needs offering potential opt…

This https://arxiv.org/abs/2312.01980 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Cut-and-paste for impulsive gravitational waves with $Λ$: The mathematical analysis
Impulsive gravitational waves are theoretical models of short but violent bursts of gravitational radiation. They are commonly described by two distinct spacetime metrics, one of local Lipschitz regularity, the other one even distributional. These two metrics are thought to be `physically equivalent' since they can be formally related by a `discontinuous coordinate transformation'. In this paper we provide a mathematical analysis of this issue for the entire class of nonexpanding impulsive grav…

Characterization of Spatial-Temporal Channel Statistics from Indoor Measurement Data at D Band
Chathuri Weragama, Joonas Kokkoniemi, Mar Francis De Guzman, Katsuyuki Haneda, Pekka Kyosti, Markku Juntti
https://arxiv.org/abs/2403.18713

Characterization of Spatial-Temporal Channel Statistics from Indoor Measurement Data at D Band
Millimeter-wave (mmWave) and D Band (110--170~GHz) frequencies are poised to play a pivotal role in the advancement of sixth-generation (6G) systems and beyond, owing to their ability to enhance performance metrics such as capacity, ultra-low latency, and spectral efficiency. This paper concentrates on deriving statistical insights into power, delay, and the number of paths based on measurements conducted across four distinct locations at a center frequency of 143.1 GHz. The findings underscore…

This https://arxiv.org/abs/2403.03988 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

D6 branes wrapped on a spindle and $Y^{p,q}$ manifolds
We present new solutions of 8d gauged supergravity which, upon uplift to type IIA, represent D6 branes wrapped on spindles. A further circle uplift gives 11d supergravity on a Calabi-Yau three-fold which is the cone over five-dimensional $Y^{p,q}$ manifolds. This highlights a connection between co-homogeneity one Sasaki-Einstein metrics in general dimension and the recently introduced spindle solutions in gauged supergravity. We find that a similar connection also exists for the small resolutio…

This https://arxiv.org/abs/2403.15198 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

On the Weighted Top-Difference Distance: Axioms, Aggregation, and Approximation
We study a family of distance functions on rankings that allow for asymmetric treatments of alternatives and consider the distinct relevance of the top and bottom positions for ordered lists. We provide a full axiomatic characterization of our distance. In doing so, we retrieve new characterizations of existing axioms and show how to effectively weaken them for our purposes. This analysis highlights the generality of our distance as it embeds many (semi)metrics previously proposed in the litera…

ABC report: UK magazines' digital sales rose 15.4% YoY to an average of 2.6M per edition, including 1.2M from "all you can read" sales via Readly and others (Dominic Ponsford/Press Gazette)
https://pressgazette.…

ABCs: UK digital magazine sales surge boosted by Spotify-style bundled subscriptions
Digital sales of UK magazines rose 15.4% year on year to an average of 2.6 million per edition, according to the latest ABC figures.

The New Era of Dynamic Pricing: Synergizing Supervised Learning and Quadratic Programming
Gustavo Bramao, Ilia Tarygin
https://arxiv.org/abs/2402.14844 htt…

The New Era of Dynamic Pricing: Synergizing Supervised Learning and Quadratic Programming
In this paper, we explore a novel combination of supervised learning and quadratic programming to refine dynamic pricing models in the car rental industry. We utilize dynamic modeling of price elasticity, informed by ordinary least squares (OLS) metrics such as p-values, homoscedasticity, error normality. These metrics, when their underlying assumptions hold, are integral in guiding a quadratic programming agent. The program is tasked with optimizing margin for a given finite set target.

Decoy Effect In Search Interaction: Understanding User Behavior and Measuring System Vulnerability
Nuo Chen, Jiqun Liu, Hanpei Fang, Yuankai Luo, Tetsuya Sakai, Xiao-Ming Wu
https://arxiv.org/abs/2403.18462

Decoy Effect In Search Interaction: Understanding User Behavior and Measuring System Vulnerability
This study examines the decoy effect's underexplored influence on user search interactions and methods for measuring information retrieval (IR) systems' vulnerability to this effect. It explores how decoy results alter users' interactions on search engine result pages, focusing on metrics like click-through likelihood, browsing time, and perceived document usefulness. By analyzing user interaction logs from multiple datasets, the study demonstrates that decoy results significantly affect users'…

An interview with Apple Arcade's Senior Director Alex Rofman: the service hit record highs on all "critical metrics" in 2023, and will feature Vision Pro games (Keith Stuart/The Guardian)
https://www.theguardian.com/games/2024/apr

Labeling subtypes in a Parkinson's Cohort using Multifeatures in MRI - Integrating Grey and White Matter Information
Tanmayee Samantaray, Jitender Saini, Pramod Kumar Pal, Bithiah Grace Jaganathan, Vijaya V Saradhi, Gupta CN
https://arxiv.org/abs/2403.17332

Labeling subtypes in a Parkinson's Cohort using Multifeatures in MRI - Integrating Grey and White Matter Information
Thresholding of networks has long posed a challenge in brain connectivity analysis. Weighted networks are typically binarized using threshold measures to facilitate network analysis. Previous studies on MRI-based brain networks have predominantly utilized density or sparsity-based thresholding techniques, optimized within specific ranges derived from network metrics such as path length, clustering coefficient, and small-world index. Thus, determination of a single threshold value for facilitati…

Is Reference Necessary in the Evaluation of NLG Systems? When and Where?
Shuqian Sheng, Yi Xu, Luoyi Fu, Jiaxin Ding, Lei Zhou, Xinbing Wang, Chenghu Zhou
https://arxiv.org/abs/2403.14275

Is Reference Necessary in the Evaluation of NLG Systems? When and Where?
The majority of automatic metrics for evaluating NLG systems are reference-based. However, the challenge of collecting human annotation results in a lack of reliable references in numerous application scenarios. Despite recent advancements in reference-free metrics, it has not been well understood when and where they can be used as an alternative to reference-based metrics. In this study, by employing diverse analytical approaches, we comprehensively assess the performance of both metrics acros…

This https://arxiv.org/abs/2107.09343 has been replaced.
link: https://scholar.google.com/scholar?q=a

Neural-Network-based NLOS Identification in Angular Domain at 60-GHz
This paper introduces an identification method that determines whether a millimeter-wave wireless transmission using directional antennas is being established over a line-of-sight (LOS) or a non-line-of-sight (NLOS) cluster for indoor localization applications. The proposed technique utilizes the channel power angular spectrum that is readily available from a beam training process. In particular, the behavior of five different channel metrics, namely the spatial-domain, time-domain, and frequen…

Learning the Covariance of Treatment Effects Across Many Weak Experiments
Aur\'elien Bibaut, Winston Chou, Simon Ejdemyr, Nathan Kallus
https://arxiv.org/abs/2402.17637

Learning the Covariance of Treatment Effects Across Many Weak Experiments
When primary objectives are insensitive or delayed, experimenters may instead focus on proxy metrics derived from secondary outcomes. For example, technology companies often infer long-term impacts of product interventions from their effects on weighted indices of short-term user engagement signals. We consider meta-analysis of many historical experiments to learn the covariance of treatment effects on different outcomes, which can support the construction of such proxies. Even when experiments…

Countries pushing the boundaries of knowledge: the US dominance, China rise, and the EU stagnation
Alonso Rodriguez-Navarro
https://arxiv.org/abs/2402.15263

Countries pushing the boundaries of knowledge: the US dominance, China rise, and the EU stagnation
Knowing which countries contribute the most to pushing the boundaries of knowledge in science and technology has social and political importance. However, common citation metrics do not adequately measure this contribution. This measure requires more stringent metrics appropriate for the highly influential breakthrough papers that push the boundaries of knowledge, which are very highly cited but very rare. Here I used the recently described Rk index, specifically designed to address this issue.…

On geodesic orbit nilmanifolds
Yu. G. Nikonorov
https://arxiv.org/abs/2402.17548 https://arxiv.org/pdf/2402.17548

On geodesic orbit nilmanifolds
The paper is devoted to the study of geodesic orbit Riemannian metrics on nilpotent Lie groups. The main result is the construction of continuous families of pairwise non-isomorphic connected and simply connected nilpotent Lie groups, every of which admits geodesic orbit metrics. The minimum dimension of groups in the constructed families is $10$.

This https://arxiv.org/abs/2403.00616 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Gate-set evaluation metrics for closed-loop optimal control on nitrogen-vacancy center ensembles in diamond
A recurring challenge in quantum science and technology is the precise control of their underlying dynamics that lead to the desired quantum operations, often described by a set of quantum gates. These gates can be subject to application-specific errors, leading to a dependence of their controls on the chosen circuit, the quality measure and the gate-set itself. A natural solution would be to apply quantum optimal control in an application-oriented fashion. In turn, this requires the definition…

I wrote a small blog post about how I get (some) of my health metrics out of Apple Health to put it into my website's footer. And I used that as a good excuse to also update some pages in the #personalscience wiki. #quantifiedself
https://tzovar.as/exporting-data-apple-health/

Slide for a talk I'm giving soon

Exact Calculations of Coherent Information for Toric Codes under Decoherence: Identifying the Fundamental Error Threshold
Jong Yeon Lee
https://arxiv.org/abs/2402.16937

Exact Calculations of Coherent Information for Toric Codes under Decoherence: Identifying the Fundamental Error Threshold
The toric code is a canonical example of a topological error-correcting code. Two logical qubits stored within the toric code are robust against local decoherence, ensuring that these qubits can be faithfully retrieved as long as the error rate remains below a certain threshold. Recent studies have explored such a threshold behavior as an intrinsic information-theoretic transition, independent of the decoding protocol. These studies have shown that information-theoretic metrics, calculated usin…

This https://arxiv.org/abs/2401.17463 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Group Theoretic Metric for Robot State Estimation Leveraging Chebyshev Interpolation
We propose a new metric for robot state estimation based on the recently introduced $\text{SE}_2(3)$ Lie group definition. Our metric is related to prior metrics for SLAM but explicitly takes into account the linear velocity of the state estimate, improving over current pose-based trajectory analysis. This has the benefit of providing a single, quantitative metric to evaluate state estimation algorithms against, while being compatible with existing tools and libraries. Since ground truth data g…

ACES: Evaluating Automated Audio Captioning Models on the Semantics of Sounds
Gijs Wijngaard, Elia Formisano, Bruno L. Giordano, Michel Dumontier
https://arxiv.org/abs/2403.18572 …

ACES: Evaluating Automated Audio Captioning Models on the Semantics of Sounds
Automated Audio Captioning is a multimodal task that aims to convert audio content into natural language. The assessment of audio captioning systems is typically based on quantitative metrics applied to text data. Previous studies have employed metrics derived from machine translation and image captioning to evaluate the quality of generated audio captions. Drawing inspiration from auditory cognitive neuroscience research, we introduce a novel metric approach -- Audio Captioning Evaluation on S…

This https://arxiv.org/abs/2302.03788 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSE_…

Toward a Theory of Causation for Interpreting Neural Code Models
Neural Language Models of Code, or Neural Code Models (NCMs), are rapidly progressing from research prototypes to commercial developer tools. As such, understanding the capabilities and limitations of such models is becoming critical. However, the abilities of these models are typically measured using automated metrics that often only reveal a portion of their real-world performance. While, in general, the performance of NCMs appears promising, currently much is unknown about how such models ar…

This https://arxiv.org/abs/2311.18659 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDC_…

Comparison of Autoscaling Frameworks for Containerised Machine-Learning-Applications in a Local and Cloud Environment
When deploying machine learning (ML) applications, the automated allocation of computing resources-commonly referred to as autoscaling-is crucial for maintaining a consistent inference time under fluctuating workloads. The objective is to maximize the Quality of Service metrics, emphasizing performance and availability, while minimizing resource costs. In this paper, we compare scalable deployment techniques across three levels of scaling: at the application level (TorchServe, RayServe) and the…

Nice to see the continued growth of this count of Mastodon users… (subject to all the usual caveats about any metrics like this trying to count a decentralized system)
From: @…

A Class of Topological Pseudodistances for Fast Comparison of Persistence Diagrams
Rolando Kindelan Nu\~nez, Mircea Petrache, Mauricio Cerda, Nancy Hitschfeld
https://arxiv.org/abs/2402.14489

A Class of Topological Pseudodistances for Fast Comparison of Persistence Diagrams
Persistence diagrams (PD)s play a central role in topological data analysis, and are used in an ever increasing variety of applications. The comparison of PD data requires computing comparison metrics among large sets of PDs, with metrics which are accurate, theoretically sound, and fast to compute. Especially for denser multi-dimensional PDs, such comparison metrics are lacking. While on the one hand, Wasserstein-type distances have high accuracy and theoretical guarantees, they incur high com…

Uniqueness and convergence of resistance forms on unconstrained Sierpinski carpets
Shiping Cao, Hua Qiu
https://arxiv.org/abs/2403.17311 https://

Uniqueness and convergence of resistance forms on unconstrained Sierpinski carpets
We prove the uniqueness of self-similar $D_4$-symmetric resistance forms on unconstrained Sierpinski carpets ($\mathcal{USC}$'s). Moreover, on a sequence of $\mathcal{USC}$'s $K_n, n\geq 1$ converging in Hausdorff metric, we show that the associated diffusion processes converge in distribution if and only if the geodesic metrics on $K_n, n\geq 1$ are equicontinuous with respect to the Euclidean metric.

So, my Proxmox network configuration uses four interfaces and after an update my networking was hosed. Things I've learned over the last hour:
- Interface metrics are your friend. After configuring the interfaces with proper metrics, traffic routes to the right interface based on if it's online. Managment interface gets the lowest metric.
- There's a significant difference between `auto eth0` and `audo eth0` in the interface file...typos are friggin' lethal.

Decoy Effect In Search Interaction: Understanding User Behavior and Measuring System Vulnerability
Nuo Chen, Jiqun Liu, Hanpei Fang, Yuankai Luo, Tetsuya Sakai, Xiao-Ming Wu
https://arxiv.org/abs/2403.18462

Decoy Effect In Search Interaction: Understanding User Behavior and Measuring System Vulnerability
This study examines the decoy effect's underexplored influence on user search interactions and methods for measuring information retrieval (IR) systems' vulnerability to this effect. It explores how decoy results alter users' interactions on search engine result pages, focusing on metrics like click-through likelihood, browsing time, and perceived document usefulness. By analyzing user interaction logs from multiple datasets, the study demonstrates that decoy results significantly affect users'…

Weak Lipschitz structures and their connections with the topological structures
Tullio Valent
https://arxiv.org/abs/2404.14026 https://

Weak Lipschitz structures and their connections with the topological structures
Two approaches to Lipschitz structures for any set are presented, studied and compared. The first approach is similar to the one proposed in Fraser, Jr. R. B., Axiom systems for Lipschitz structures, Fundamenta Mathematicae, (1970), where Lipschitz structures are defined as families of pseudo-metrics satisfying suitable conditions. The other one, here introduced, is expressed by using weak pseudo-metrics, which (unlike the pseudo-metrics) do not necessarily vanish on the whole of the diagonal o…

Power Failure Cascade Prediction using Graph Neural Networks
Sathwik Chadaga, Xinyu Wu, Eytan Modiano
https://arxiv.org/abs/2404.16134 https://

Power Failure Cascade Prediction using Graph Neural Networks
We consider the problem of predicting power failure cascades due to branch failures. We propose a flow-free model based on graph neural networks that predicts grid states at every generation of a cascade process given an initial contingency and power injection values. We train the proposed model using a cascade sequence data pool generated from simulations. We then evaluate our model at various levels of granularity. We present several error metrics that gauge the model's ability to predict the…

Exit Ripple Effects: Understanding the Disruption of Socialization Networks Following Employee Departures
David Gamba, Yulin Yu, Yuan Yuan, Grant Schoenebeck, Daniel M. Romero
https://arxiv.org/abs/2402.15683

Exit Ripple Effects: Understanding the Disruption of Socialization Networks Following Employee Departures
Amidst growing uncertainty and frequent restructurings, the impacts of employee exits are becoming one of the central concerns for organizations. Using rich communication data from a large holding company, we examine the effects of employee departures on socialization networks among the remaining coworkers. Specifically, we investigate how network metrics change among people who historically interacted with departing employees. We find evidence of ``breakdown" in communication among the remaini…

Ludovic Hirlimann | Mozilla Quality Assurance
#souvenirs

Learning the Covariance of Treatment Effects Across Many Weak Experiments
Aur\'elien Bibaut, Winston Chou, Simon Ejdemyr, Nathan Kallus
https://arxiv.org/abs/2402.17637

Learning the Covariance of Treatment Effects Across Many Weak Experiments
When primary objectives are insensitive or delayed, experimenters may instead focus on proxy metrics derived from secondary outcomes. For example, technology companies often infer long-term impacts of product interventions from their effects on weighted indices of short-term user engagement signals. We consider meta-analysis of many historical experiments to learn the covariance of treatment effects on different outcomes, which can support the construction of such proxies. Even when experiments…

Tropical cyclones on tidally locked rocky planets: Dependence on rotation period
Valeria Garcia, Cole M. Smith, Daniel R. Chavas, Thaddeus D. Komacek
https://arxiv.org/abs/2402.16687

Tropical cyclones on tidally locked rocky planets: Dependence on rotation period
Tropical cyclones occur over the Earth's tropical oceans, with characteristic genesis regions and tracks tied to the warm ocean surface that provides energy to sustain these storms. The study of tropical cyclogenesis and evolution on Earth has led to the development of environmental favorability metrics that predict the strength of potential storms from the local background climate state. Simulations of the gamut of transiting terrestrial exoplanets orbiting late-type stars may offer a test of …

Central limit theorems for Green metrics on hyperbolic groups
Stephen Cantrell, Mark Pollicott
https://arxiv.org/abs/2404.11512 https://

Central limit theorems for Green metrics on hyperbolic groups
Recently, the first author and Tanaka obtained a large deviation principle comparing two Green metrics on a non-elementary hyperbolic group $Γ$ associated to finitely supported, admissable probability measures. The aim of this article is to prove the corresponding central limit theorem. Furthermore, our results apply to various other metrics including length functions associated to Anosov representations and to group actions on hyperbolic metric spaces. In the particular case that $Γ$ is th…

Robust performance metrics for imbalanced classification problems
Hajo Holzmann, Bernhard Klar
https://arxiv.org/abs/2404.07661 https://

Robust performance metrics for imbalanced classification problems
We show that established performance metrics in binary classification, such as the F-score, the Jaccard similarity coefficient or Matthews' correlation coefficient (MCC), are not robust to class imbalance in the sense that if the proportion of the minority class tends to $0$, the true positive rate (TPR) of the Bayes classifier under these metrics tends to $0$ as well. Thus, in imbalanced classification problems, these metrics favour classifiers which ignore the minority class. To alleviate thi…

TikTok launches a new creator monetization program called Creator Rewards, which will use four core metrics to determine payout, including "search value" (Mia Sato/The Verge)
https://www.theverge.com/2024/3/18/2410169

TikTok is paying creators to up its search game
TikTok’s new creator monetization program called Creator Rewards will use four core metrics to determine payout. One metric is the “search value” of content.

This https://arxiv.org/abs/2404.08838 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Predicting Traffic Congestion at Urban Intersections Using Data-Driven Modeling
Traffic congestion at intersections is a significant issue in urban areas, leading to increased commute times, safety hazards, and operational inefficiencies. This study aims to develop a predictive model for congestion at intersections in major U.S. cities, utilizing a dataset of trip-logging metrics from commercial vehicles across 4,800 intersections. The dataset encompasses 27 features, including intersection coordinates, street names, time of day, and traffic metrics (Kashyap et al., 2019).…

On CR maps between hyperquadrics and Winkelmann hypersurfaces
Michael Reiter, Duong Ngoc Son
https://arxiv.org/abs/2404.16543 https://

On CR maps between hyperquadrics and Winkelmann hypersurfaces
In this paper, we study CR maps between hyperquadrics and Winkelmann hypersurfaces. Based on a previous study on the CR Ahlfors derivative of Lamel-Son and a recent result of Huang-Lu-Tang-Xiao on CR maps between hyperquadrics, we prove that a transversal CR map from a hyperquadric into a hyperquadric or a Winkelmann hypersurface extends to a local holomorphic isometric embedding with respect to certain Kähler metrics if and only if the Hermitian part of its CR Ahlfors derivative vanishes on a…

Cowboys field one of the best EDGE duos in the NFL https://www.yardbarker.com/nfl/articles/cowboys_field_one_of_the_best_edge_duos_in_the_nfl/s1_17100_40151879

Cowboys field one of the best EDGE duos in the NFL
A recent post on Twitter/X by everyone's favorite source of advanced metrics has the NFL community talking. Pro Football Focus shared a graphic of four EDGE duos asking which duo will be the best in the upcoming 2024 season. The graphic features pass rushers TJ Watt and Alex Highsmith from Pittsburgh, Myles Garrett and Za'Darius Smith from Cleveland, Micah Parsons and DeMarcus Lawrence from Dallas, and Danielle Hunter and Will Anderson Jr. from Houston. These are all talented players set on get…

This https://arxiv.org/abs/2202.11048 has been replaced.
link: https://scholar.google.com/scholar?q=a

Listening to the Universe with Next Generation Ground-Based Gravitational-Wave Detectors
In this study, we use simple performance metrics to assess the science capabilities of future ground-based gravitational-wave detector networks -- composed of A+ or Voyager upgrades to the LIGO, Virgo, and KAGRA observatories and proposed next generation observatories such as Cosmic Explorer and Einstein Telescope. These metrics refer to coalescences of binary neutron stars (BNSs) and binary black holes (BBHs) and include: (i) network detection efficiency and detection rate of cosmological sour…

This https://arxiv.org/abs/2403.12074 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCY_…

Beyond Quantities: Machine Learning-based Characterization of Inequality in Infrastructure Quality Provision in Cities
The objective of this study is to characterize inequality in infrastructure quality across urban areas. While a growing of body of literature has recognized the importance of characterizing infrastructure inequality in cities and provided quantified metrics to inform urban development plans, the majority of the existing approaches focus primarily on measuring the quantity of infrastructure, assuming that more infrastructure is better. Also, the existing research focuses primarily on index-based…

Machine Learning in Viscoelastic Fluids via Energy-Based Kernel Embedding
Samuel E. Otto, Cassio M. Oishi, Fabio Amaral, Steven L. Brunton, J. Nathan Kutz
https://arxiv.org/abs/2404.14347

Machine Learning in Viscoelastic Fluids via Energy-Based Kernel Embedding
The ability to measure differences in collected data is of fundamental importance for quantitative science and machine learning, motivating the establishment of metrics grounded in physical principles. In this study, we focus on the development of such metrics for viscoelastic fluid flows governed by a large class of linear and nonlinear stress models. To do this, we introduce a kernel function corresponding to a given viscoelastic stress model that implicitly embeds flowfield snapshots into a …

This https://arxiv.org/abs/2305.07764 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIR_…

Long-Term Value of Exploration: Measurements, Findings and Algorithms
Effective exploration is believed to positively influence the long-term user experience on recommendation platforms. Determining its exact benefits, however, has been challenging. Regular A/B tests on exploration often measure neutral or even negative engagement metrics while failing to capture its long-term benefits. We here introduce new experiment designs to formally quantify the long-term value of exploration by examining its effects on content corpus, and connecting content corpus growth t…

TikTok launches a new creator monetization program called Creator Rewards, which will use four core metrics to determine payout, including "search value" (Mia Sato/The Verge)
https://www.theverge.com/2024/3/18/2410169

TikTok is paying creators to up its search game
TikTok’s new creator monetization program called Creator Rewards will use four core metrics to determine payout. One metric is the “search value” of content.

This https://arxiv.org/abs/2310.00778 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Minimal diffeomorphisms with $L^1$ Hopf differentials
We prove that for any two Riemannian metrics $σ_1, σ_2$ on the unit disk, a homeomorphism $\partial\mathbb{D}\to\partial\mathbb{D}$ extends to at most one quasiconformal minimal diffeomorphism $(\mathbb{D},σ_1)\to (\mathbb{D},σ_2)$ with $L^1$ Hopf differential. For minimal Lagrangian diffeomorphisms between hyperbolic disks, the result is known, but this is the first proof that does not use anti-de Sitter geometry. We show that the result fails without the $L^1$ assumption in variable curva…

This https://arxiv.org/abs/2310.15106 has been replaced.
link: https://scholar.google.com/scholar?q=a

Theoretical Analysis of the Radio Map Estimation Problem
Radio maps provide radio frequency metrics, such as the received signal strength, at every location of a geographic area. These maps, which are estimated using a set of measurements collected at multiple positions, find a wide range of applications in wireless communications, including the prediction of coverage holes, network planning, resource allocation, and path planning for mobile robots. Although a vast number of estimators have been proposed, the theoretical understanding of the radio ma…

Polyhedral CAT(0) metrics on locally finite complexes
Karim A. Adiprasito, Louis Funar
https://arxiv.org/abs/2404.14878 https://arxiv…

Polyhedral CAT(0) metrics on locally finite complexes
We prove the arborescence of any locally finite complex that is $CAT(0)$ with a polyhedral metric for which all vertex stars are convex. In particular locally finite $CAT(0)$ cube complexes or equilateral simplicial complexes are arborescent. Moreover, a triangulated manifold admits a $CAT(0)$ polyhedral metric if and only if it admits arborescent triangulations. We prove eventually that every locally finite complex which is $CAT(0)$ with a polyhedral metric has a barycentric subdivision which …

Information Elicitation in Agency Games
Serena Wang, Michael I. Jordan, Katrina Ligett, R. Preston McAfee
https://arxiv.org/abs/2402.14005 https://<…

Information Elicitation in Agency Games
Rapid progress in scalable, commoditized tools for data collection and data processing has made it possible for firms and policymakers to employ ever more complex metrics as guides for decision-making. These developments have highlighted a prevailing challenge -- deciding *which* metrics to compute. In particular, a firm's ability to compute a wider range of existing metrics does not address the problem of *unknown unknowns*, which reflects informational limitations on the part of the firm. To …

This https://arxiv.org/abs/2310.00074 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

SocREval: Large Language Models with the Socratic Method for Reference-Free Reasoning Evaluation
To comprehensively gauge the capacity of current models for complex reasoning, it is crucial to assess their step-by-step reasoning in a scalable manner. Established reference-based evaluation metrics rely on human-annotated reasoning chains as references to assess the model-derived chains. However, such "gold-standard" human-written reasoning chains may not be unique and their acquisition is often labor-intensive. Existing reference-free reasoning evaluation metrics, while eliminating the need…

Sparsity-Constrained Linear Quadratic Regulation Problem: Greedy Approach with Performance Guarantee
Shumpei Nishida, Kunihisa Okano
https://arxiv.org/abs/2403.16585

Sparsity-Constrained Linear Quadratic Regulation Problem: Greedy Approach with Performance Guarantee
We study a linear quadratic regulation problem with a constraint where the control input can be nonzero only at a limited number of times. Given that this constraint leads to a combinational optimization problem, we adopt a greedy method to find a suboptimal solution. To quantify the performance of the greedy algorithm, we employ two metrics that reflect the submodularity level of the objective function: The submodularity ratio and curvature. We first present an explicit form of the optimal con…

This https://arxiv.org/abs/2402.13005 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

SzCORE: A Seizure Community Open-source Research Evaluation framework for the validation of EEG-based automated seizure detection algorithms
The need for high-quality automated seizure detection algorithms based on electroencephalography (EEG) becomes ever more pressing with the increasing use of ambulatory and long-term EEG monitoring. Heterogeneity in validation methods of these algorithms influences the reported results and makes comprehensive evaluation and comparison challenging. This heterogeneity concerns in particular the choice of datasets, evaluation methodologies, and performance metrics. In this paper, we propose a unifi…

Super-High-Fidelity Image Compression via Hierarchical-ROI and Adaptive Quantization
Jixiang Luo, Yan Wang, Hongwei Qin
https://arxiv.org/abs/2403.13030 ht…

Super-High-Fidelity Image Compression via Hierarchical-ROI and Adaptive Quantization
Learned Image Compression (LIC) has achieved dramatic progress regarding objective and subjective metrics. MSE-based models aim to improve objective metrics while generative models are leveraged to improve visual quality measured by subjective metrics. However, they all suffer from blurring or deformation at low bit rates, especially at below $0.2bpp$. Besides, deformation on human faces and text is unacceptable for visual quality assessment, and the problem becomes more prominent on small face…

A Hilbert metric for bounded symmetric domains
Elisha Falbel, Antonin Guilloux, Pierre Will
https://arxiv.org/abs/2403.18634 https://…

A Hilbert metric for bounded symmetric domains
Bounded symmetric domains carry several natural invariant metrics, for example the Carathéodory, Kobayashi or the Bergman metric. We define another natural metric, from generalized Hilbert metric defined in [FGW20], by considering the Borel embedding of the domain as an open subset of its dual compact Hermitian symmetric space and then its Harish-Chandra realization in projective spaces. We describe this construction on the four classical families of bounded symmetric domains and compute both …

Towards Precise Observations of Neural Model Robustness in Classification
Wenchuan Mu, Kwan Hui Lim
https://arxiv.org/abs/2404.16457 https://

Towards Precise Observations of Neural Model Robustness in Classification
In deep learning applications, robustness measures the ability of neural models that handle slight changes in input data, which could lead to potential safety hazards, especially in safety-critical applications. Pre-deployment assessment of model robustness is essential, but existing methods often suffer from either high costs or imprecise results. To enhance safety in real-world scenarios, metrics that effectively capture the model's robustness are needed. To address this issue, we compare the…

Andes: Defining and Enhancing Quality-of-Experience in LLM-Based Text Streaming Services
Jiachen Liu, Zhiyu Wu, Jae-Won Chung, Fan Lai, Myungjin Lee, Mosharaf Chowdhury
https://arxiv.org/abs/2404.16283

Andes: Defining and Enhancing Quality-of-Experience in LLM-Based Text Streaming Services
The advent of large language models (LLMs) has transformed text-based services, enabling capabilities ranging from real-time translation to AI-driven chatbots. However, existing serving systems primarily focus on optimizing server-side aggregate metrics like token generation throughput, ignoring individual user experience with streamed text. As a result, under high and/or bursty load, a significant number of users can receive unfavorable service quality or poor Quality-of-Experience (QoE). In t…

Non-local gravitational corrections in black hole shadow images
Stanislav Alexeyev, Artem Baiderin, Alexandra Nemtinova, Oleg Zenin
https://arxiv.org/abs/2404.16079

Non-local gravitational corrections in black hole shadow images
With the help of Newman-Janis method new spinning black hole (BH) solution for a non-local gravity model was obtained. We show how to account the quantum gravitational correction part in BH shadows modelling using spinning BH metrics with a model independent approach. It is confirmed that in the future to follow the increasing of the experimental accuracy and therefore to reproduce new results theoretically one could take into account different field correction terms instead of introducing of n…

This https://arxiv.org/abs/2401.09777 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Injectivity radius lower bound of convex sum of tame Riemannian metrics and applications to symplectic topology
Motivated by the aspect of large-scale symplectic topology, we prove that for any pair $g_0, \, g_1$ of complete Riemannian metrics of bounded curvature and \emph{of injectivity radius bounded away from zero}, the convex sum $g_s: = (1-s ) g_0 + s g_1$ also has bounded curvature depending only on the curvature bounds $\|R_{g_i}\|_{C^0}$ of $g_0$ or $g_1$, and that the injectivity radii of $g_s$ have uniform lower bound depending only on the derivative bounds $\|R_{g_i}\|_{C^…

This https://arxiv.org/abs/2402.13787 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSI_…

Fairness Rising from the Ranks: HITS and PageRank on Homophilic Networks
In this paper, we investigate the conditions under which link analysis algorithms prevent minority groups from reaching high ranking slots. We find that the most common link-based algorithms using centrality metrics, such as PageRank and HITS, can reproduce and even amplify bias against minority groups in networks. Yet, their behavior differs: one one hand, we empirically show that PageRank mirrors the degree distribution for most of the ranking positions and it can equalize representation of m…

This https://arxiv.org/abs/2312.13938 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDC_…

How Does Stake Distribution Influence Consensus? Analyzing Blockchain Decentralization
In the PoS blockchain landscape, the challenge of achieving full decentralization is often hindered by a disproportionate concentration of staked tokens among a few validators. This study analyses this challenge by first formalizing decentralization metrics for weighted consensus mechanisms. An empirical analysis across ten permissionless blockchains uncovers significant weight concentration among validators, underscoring the need for an equitable approach. To counter this, we introduce the Squ…

This https://arxiv.org/abs/2309.06868 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Volume growth on manifolds with more than one end
For an open manifold $M$ and a function $v$ with bounded growth of derivative, there exists a Riemannian metric of bounded geometry on $M$ such that the volume growth function lies in the same growth class as $v$. This was proved by R. Grimaldi and P. Pansu with the proof focusing on the case of manifolds with a single end. We prove this in the case of manifolds with multiple ends and call the constructed metrics Grimaldi-Pansu metrics. We give uniform bounds for the volume growth function of t…

Perturbations of bimetric gravity on most general spherically symmetric spacetimes
David Brizuela, Marco de Cesare, Araceli Soler Oficial
https://arxiv.org/abs/2402.15327

Perturbations of bimetric gravity on most general spherically symmetric spacetimes
We present a formalism to study linear perturbations of bimetric gravity on any spherically symmetric background, including dynamical spacetimes. The setup is based on the Gerlach-Sengupta formalism for general relativity. Each of the two background metrics is written as a warped product between a two-dimensional Lorentzian metric and the round metric of the two-sphere. The different perturbations are then decomposed in terms of tensor spherical harmonics, which makes the two polarity (axial an…

Deep neural networks for choice analysis: Enhancing behavioral regularity with gradient regularization
Siqi Feng, Rui Yao, Stephane Hess, Ricardo A. Daziano, Timothy Brathwaite, Joan Walker, Shenhao Wang
https://arxiv.org/abs/2404.14701

Deep neural networks for choice analysis: Enhancing behavioral regularity with gradient regularization
Deep neural networks (DNNs) frequently present behaviorally irregular patterns, significantly limiting their practical potentials and theoretical validity in travel behavior modeling. This study proposes strong and weak behavioral regularities as novel metrics to evaluate the monotonicity of individual demand functions (a.k.a. law of demand), and further designs a constrained optimization framework with six gradient regularizers to enhance DNNs' behavioral regularity. The proposed framework is …

Remarks on a theorem of Eells and Sampson
Giulio Colombo, Marco Mariani, Marco Rigoli
https://arxiv.org/abs/2403.18596 https://arxiv.…

Remarks on a theorem of Eells and Sampson
We prove an extension of Eells and Sampson's rigidity theorem for harmonic maps from a closed manifold of non-negative Ricci curvature to a manifold of non-positive sectional curvature. We give an application of our result in the setting of harmonic-Einstein (or Ricci-harmonic) metrics and as a consequence we recover a classical rigidity result of Hamilton for the problem of prescribed positive definite Ricci curvature.

This https://arxiv.org/abs/2312.11234 has been replaced.
link: https://scholar.google.com/scholar?q=a

Perceptual Musical Features for Interpretable Audio Tagging
In the age of music streaming platforms, the task of automatically tagging music audio has garnered significant attention, driving researchers to devise methods aimed at enhancing performance metrics on standard datasets. Most recent approaches rely on deep neural networks, which, despite their impressive performance, possess opacity, making it challenging to elucidate their output for a given input. While the issue of interpretability has been emphasized in other fields like medicine, it has n…

On the Weighted Top-Difference Distance: Axioms, Aggregation, and Approximation
Andrea Aveni, Ludovico Crippa, Giulio Principi
https://arxiv.org/abs/2403.15198

On the Weighted Top-Difference Distance: Axioms, Aggregation, and Approximation
We study a family of distance functions on rankings that allow for asymmetric treatments of alternatives and consider the distinct relevance of the top and bottom positions for ordered lists. We provide a full axiomatic characterization of our distance. In doing so, we retrieve new characterizations of existing axioms and show how to effectively weaken them for our purposes. This analysis highlights the generality of our distance as it embeds many (semi)metrics previously proposed in the litera…

Rethinking Perceptual Metrics for Medical Image Translation
Nicholas Konz, Yuwen Chen, Hanxue Gu, Haoyu Dong, Maciej A. Mazurowski
https://arxiv.org/abs/2404.07318

Rethinking Perceptual Metrics for Medical Image Translation
Modern medical image translation methods use generative models for tasks such as the conversion of CT images to MRI. Evaluating these methods typically relies on some chosen downstream task in the target domain, such as segmentation. On the other hand, task-agnostic metrics are attractive, such as the network feature-based perceptual metrics (e.g., FID) that are common to image translation in general computer vision. In this paper, we investigate evaluation metrics for medical image translation…

The Quantum Model of Spinning Black Holes
V. P. Neznamov, S. Yu. Sedov, V. E. Shemarulin
https://arxiv.org/abs/2402.14893 https://arx…

The Quantum Model of Spinning Black Holes
We propose a quantum model of spinning black holes with the integrable ring singularities. For the charged Kerr-Newman quantum metric, the complete regularization takes place at fixing of the maximal (cut-off) energy of gravitons, $k_{UV}^{reg} = \hbar c/R_{S}^{reg}$.The domains of existence of one, two and several event horizons $r_{q}$ are shown depending on the parameters of modified Kerr and Kerr-Newman metrics.

The Strominger System and Flows by the Ricci Tensor
S\'ebastien Picard
https://arxiv.org/abs/2402.17770 https://arxiv.org/pdf/240…

The Strominger System and Flows by the Ricci Tensor
This is a survey on the Strominger system and a geometric flow known as the anomaly flow. We will discuss various aspects of non-Kähler geometry on Calabi-Yau threefolds. Along the way, we discuss balanced metrics and balanced classes, the Aeppli cohomology class associated to a solution to the Strominger system, the equations of motion of heterotic supergravity, and a version of Ricci flow in this special geometry.

Using ARIMA to Predict the Expansion of Subscriber Data Consumption
Mike Wa Nkongolo
https://arxiv.org/abs/2404.15095 https://arxiv.o…

Using ARIMA to Predict the Expansion of Subscriber Data Consumption
This study discusses how insights retrieved from subscriber data can impact decision-making in telecommunications, focusing on predictive modeling using machine learning techniques such as the ARIMA model. The study explores time series forecasting to predict subscriber usage trends, evaluating the ARIMA model's performance using various metrics. It also compares ARIMA with Convolutional Neural Network (CNN) models, highlighting ARIMA's superiority in accuracy and execution speed. The study sug…

This https://arxiv.org/abs/2403.10169 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Analytical perturbations of relativistic images in Kerr space-time
Light rays passing very close to black holes may wind several times before escaping. For any given electromagnetic source around the black hole, a distant observer would thus observe two infinite sequences of images on either side of the black hole. These images are generated by light rays performing an increasing numbers of loops. The strong deflection limit provides a simple analytic formalism to describe such higher order images for spherically symmetric metrics, while for axially symmetric …

Metric-guided Image Reconstruction Bounds via Conformal Prediction
Matt Y Cheung, Tucker J Netherton, Laurence E Court, Ashok Veeraraghavan, Guha Balakrishnan
https://arxiv.org/abs/2404.15274

Metric-guided Image Reconstruction Bounds via Conformal Prediction
Recent advancements in machine learning have led to novel imaging systems and algorithms that address ill-posed problems. Assessing their trustworthiness and understanding how to deploy them safely at test time remains an important and open problem. We propose a method that leverages conformal prediction to retrieve upper/lower bounds and statistical inliers/outliers of reconstructions based on the prediction intervals of downstream metrics. We apply our method to sparse-view CT for downstream …

Constraining spherically symmetric metrics by the gap between photon rings
Fabio Aratore, Oleg Yu. Tsupko, Volker Perlick
https://arxiv.org/abs/2402.14733 …

Constraining spherically symmetric metrics by the gap between photon rings
Gravitational lensing of luminous matter that surrounds a black hole or some other sufficiently compact object produces an infinite sequence of images. Besides the direct (or primary) image, it comprises demagnified and deformed replicas of the original known as photon rings which are progressively nearing the boundary of the socalled shadow. In the present paper, we present analytical approximation formulas for higher-order photon rings for an asymptotically flat, static, spherically symmetric…

Einstein metrics on homogeneous spaces $H\times H/\Delta K$
Jorge Lauret, Cynthia Will
https://arxiv.org/abs/2402.13407 https://arxiv…

Einstein metrics on homogeneous spaces $H\times H/ΔK$
Given any compact homogeneous space $H/K$ with $H$ simple, we consider the new space $M=H\times H/ΔK$, where $ΔK$ denotes diagonal embedding, and study the existence, classification and stability of $H\times H$-invariant Einstein metrics on $M$, as a first step into the largely unexplored case of homogeneous spaces of compact non-simple Lie groups. We find unstable Einstein metrics on $M$ for most spaces $H/K$ such that their standard metric is Einstein (e.g., isotropy irreducible) and the Ki…

Holomorphic Witten instanton complexes on stratified pseudomanifolds with K\"ahler wedge metrics
Gayana Jayasinghe
https://arxiv.org/abs/2404.13481 ht…

Holomorphic Witten instanton complexes on stratified pseudomanifolds with Kähler wedge metrics
We construct Witten instanton complexes for Kähler Hamiltonian Morse functions on stratified pseudomanifolds with wedge Kähler metrics satisfying a local conformally totally geodesic condition. We use this to extend Witten's holomorphic Morse inequalities for the $L^2$ cohomology of Dolbeault complexes, deriving versions for Poincaré Hodge polynomials, the spin Dirac and signature complexes for which we prove rigidity results, in particular establishing the rigidity of $L^2$ de Rham cohomolo…

On properties of the sets of positively curved Riemannian metrics on generalized Wallach spaces
Nurlan Abiev
https://arxiv.org/abs/2402.11692 https://

On properties of the sets of positively curved Riemannian metrics on generalized Wallach spaces
Sets related to positively curved invariant Riemannian metrics on generalized Wallach spaces are considered. The problem arises in studying of the evolution of such metrics under the normalized Ricci flow equation. For Riemannian metrics of the Wallach spaces $\operatorname{SU}(3)/T_{\max}$, $\operatorname{Sp(3)}/ \left(\operatorname{Sp(1)}\right)^3$ and $F_4/\operatorname{Spin(8)}$ which admit positive sectional curvature and belong to a given invariant surface $Σ$ of the normalized Ricci flo…

On pseudo-Riemannian Ricci-parallel Lie groups which are not Einstein
Huihui An, Zaili Yan
https://arxiv.org/abs/2404.13797 https://a…

On pseudo-Riemannian Ricci-parallel Lie groups which are not Einstein
In this paper, we mainly study left invariant pseudo-Riemannian Ricci-parallel metrics on connected Lie groups which are not Einstein. Following a result of Boubel and Bérard Bergery, there are two typical types of such metrics, which are characterized by the minimal polynomial of the Ricci operator. Namely, its form is either $(X-α)(X-\barα)$ (type I), where $α\in \mathbb{C}\setminus \mathbb{R}$, or $X^{2}$ (type II). Firstly, we obtain a complete description of Ricci-parallel metrics of t…

This https://arxiv.org/abs/2402.05927 has been replaced.
link: https://scholar.google.com/scholar?q=a

Yamabe metrics on conical manifolds
We prove existence of Yamabe metrics on singular manifolds with conical points and conical links of Einstein type that include orbifold structures. We deal with metrics of generic type and derive a counterpart of Aubin's classical result. Interestingly, the singular nature of the metric determines a different condition on the dimension, compared to the regular case. We derive asymptotic expansions on the Yamabe quotient by adding a proper and implicit lower-order correction to standard bubbles,…

Continuity of HYM connections with respect to metric variations
R\'emi Delloque
https://arxiv.org/abs/2403.16814 https://arxiv.or…

Continuity of HYM connections with respect to metric variations
We investigate the set of (real Dolbeault classes of) balanced metrics $Θ$ on a balanced manifold $X$ with respect to which a torsion-free coherent sheaf $\mathcal{E}$ on $X$ is slope stable. We prove that the set of all such $[Θ] \in H^{n - 1,n - 1}(X,\mathbb{R})$ is a convex cone defined by a finite number of linear inequalities. For this, we prove that the set of all $c_1(\mathcal{S})$ for $\mathcal{S} \subset \mathcal{E}$ saturated and coherent is finite. When $\mathcal{E}$ is a Hermiti…

This https://arxiv.org/abs/2303.12007 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Marked length spectrum rigidity for Anosov surfaces
Let $Σ$ be a smooth closed oriented surface of genus $\geq 2$. We prove that two metrics on $Σ$ with the same marked length spectrum and Anosov geodesic flow are isometric via an isometry isotopic to the identity. The proof combines microlocal tools with the geometry of complex curves.

Heavenly metrics, hyper-Lagrangians and Joyce structures
Maciej Dunajski, Timothy Moy
https://arxiv.org/abs/2402.14352 https://arxiv.…

Heavenly metrics, hyper-Lagrangians and Joyce structures
In \cite{B3}, Bridgeland defined a geometric structure, named a Joyce structure, conjectured to exist on the space $M$ of stability conditions of a $CY_3$ triangulated category. A feature of this structure is a complex hyper-Kähler metric with homothetic symmetry on the total space $X = TM$ of the holomorphic tangent bundle. \par Generalising the isomonodromy calculation which leads to the $A_2$ Joyce structure in \cite{BM}, we obtain an explicit expression for a hyper-Kähler metric with homo…

This https://arxiv.org/abs/2109.05915 has been replaced.
link: https://scholar.google.com/scholar?q=a

Two-step homogeneous geodesics in some homogeneous Finsler manifolds
A natural extension of a homogeneous geodesic in homogeneous Riemannian spaces $G/H$, known as a two-step homogeneous geodesic, can be expressed of the form $γ(t)=π(\exp(tx)\exp(ty))$, where $x$ and $y$ are elements of the Lie algebra of $G$. This paper aims to expand this concept to homogeneous Finsler spaces. We provide certain sufficient conditions for $(α,β)$ spaces and decomposable cubic spaces to possess a one-parameter family of invariant Finsler metrics that can be classified as two…

Constant $Q$-curvature metrics on a product Riemannian manifold
Salom\'on Alarc\'on, Sim\'on Masn\'u, Pedro Montero, Carolina Rey
https://arxiv.org/abs/2402.14675 …

Constant $Q$-curvature metrics on a product Riemannian manifold
Let $(M,g)$ be an analytic Riemannian manifold of dimension $n \geq 5$. In this paper, we consider the so-called constant $Q$-curvature equation \[ \varepsilon^4Δ_{g}^2 u -\varepsilon^2 b Δ_{g} u +a u = u^{p} , \qquad \text{in } M, \quad u>0, \quad u\in H^2_g(M) \] where $a,b$ are positive constants such that $b^2-4 a>0$, $p$ is a sub-critical exponent $1

Positive sectional curvature is not preserved under the Ricci flow in dimensions seven and thirteen
David Gonz\'alez-\'Alvaro, Masoumeh Zarei
https://arxiv.org/abs/2403.13764

Positive sectional curvature is not preserved under the Ricci flow in dimensions seven and thirteen
We prove that there exist $\mathsf{SU}_{3}$-invariant metrics on Aloff-Wallach spaces $W^7_{k_1, k_2}$, as well as $\mathsf{SU}_{5}$-invariant metrics on the Berger space $B^{13}$, which have positive sectional curvature and evolve under the Ricci flow to metrics with non-positively curved planes.