COMPLETE KAHLER METRICS WITH POSITIVE HOLOMORPHIC SECTIONAL CURVATURES ON CERTAIN LINE BUNDLES(RELATED TO A COHOMOGENEITY ONE POINT OF VIEW ON A YAU CONJECTURE)

In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.

ISO25000-Related Metrics for Evaluating the Quality of Complex Information Systems

Evaluating complex information systems necessitates deep contextual knowledge of technology, user needs, and quality. The quality evaluation challenges increase with the system’s complexity, especially when multiple services supported by varied technological modules, are offered. Existing standards for software quality, such as the ISO25000 series, provide a broad framework for evaluation. Broadness offers initial implementation ease albeit, it often lacks specificity to cater to individual system modules. This paper maps 48 data metrics and 175 software metrics on specific system modules while aligning them with ISO standard quality traits. Using the ISO25000 series as a foundation, especially ISO25010 and 25012, this research seeks to augment the applicability of these standards to multi-faceted systems, exemplified by five distinct software modules prevalent in modern information ecosystems.

Rock Mass Quality Rating Based on the Multi-Criteria Grey Metric Space

Assessment of rock mass quality significantly impacts the design and construction of underground and open-pit mines from the point of stability and economy.This study develops the novel Gromov-Hausdorff distance for rock quality(GHDQR)methodology for rock mass quality rating based on multi-criteria grey metric space.It usually presents the quality of surrounding rock by classes(metric spaces)with specified properties and adequate interval-grey numbers.Measuring the distance between surrounding rock sample characteristics and existing classes represents the core of this study.The Gromov-Hausdorff distance is an especially useful discriminant function,i.e.,a classifier to calculate these distances,and assess the quality of the surrounding rock.The efficiency of the developed methodology is analyzed using the Mean Absolute Percentage Error(MAPE)technique.Seven existing methods,such as the Gaussian cloud method,Discriminant method,Mutation series method,Artificial neural network(ANN),Support vector machine(SVM),Grey wolf optimizer and Support vector classification method(GWO-SVC)and Rock mass rating method(RMR)are used for comparison with the proposed GHDQR method.The share of the highly accurate category of 85.71%clearly indicates compliance with actual values obtained by the compared methods.The results of comparisons showed that the model enables objective,efficient,and reliable assessment of rock mass quality.

Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model

We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons,and we obtain the phase diagram of the model marked by the first Chern number.Furthermore,we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone.However,some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric,which leads to ill-defined non-integer topological Euler numbers.Nevertheless,the non-integer"Euler number"provides valuable insights and an upper bound for the absolute values of the Chern numbers.

Navigation Finsler metrics on a gradient Ricci soliton

In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.

Failure to Rescue as a Quality Metric in Congenital Heart Surgeries in a High-Complexity Service Provider Institution Located in a Middle-Income Country

Background:Failure to rescue has been an effective quality metric in congenital heart surgery.Conversely,mor-bidity and mortality depend greatly on non-modifiable individual factors and have a weak correlation with better-quality performance.We aim to measure the complications,mortality,and risk factors in pediatric patients undergoing congenital heart surgery in a high-complexity institution located in a middle-income country and compare it with other institutions that have conducted a similar study.Methods:A retrospective observational study was conducted in a high-complexity service provider institution,in Cali,Colombia.All pediatric patients undergoing any congenital heart surgery between 2019 and 2022 were included.The main outcomes evaluated in the study were complication,mortality,and failure to rescue rate.Univariate and multivariate logistic regression analysis was performed with mortality as the outcome variable.Results:We evaluated 308 congenital heart sur-geries.Regarding the outcomes,201(65%)complications occurred,23(7.5%)patients died,and the FTR of the entire cohort was 11.4%.The presence of a postoperative complication(OR 14.88,CI 3.06–268.37,p=0.009),age(OR 0.79,CI 0.57–0.96,p=0.068),and urgent/emergent surgery(OR 8.14,CI 2.97–28.66,p<0.001)were the most significant variables in predicting mortality.Conclusions:Failure to rescue is an effective and comparable quality measure in healthcare institutions and is the major contributor to postoperative mortality in congenital heart surgeries.Despite our higher mortality and complication rate,we obtained a comparable failure to rescue rate to high-income countries’health institutions.

Using Cross Entropy as a Performance Metric for Quantifying Uncertainty in DNN Image Classifiers: An Application to Classification of Lung Cancer on CT Images

Cross entropy is a measure in machine learning and deep learning that assesses the difference between predicted and actual probability distributions. In this study, we propose cross entropy as a performance evaluation metric for image classifier models and apply it to the CT image classification of lung cancer. A convolutional neural network is employed as the deep neural network (DNN) image classifier, with the residual network (ResNet) 50 chosen as the DNN archi-tecture. The image data used comprise a lung CT image set. Two classification models are built from datasets with varying amounts of data, and lung cancer is categorized into four classes using 10-fold cross-validation. Furthermore, we employ t-distributed stochastic neighbor embedding to visually explain the data distribution after classification. Experimental results demonstrate that cross en-tropy is a highly useful metric for evaluating the reliability of image classifier models. It is noted that for a more comprehensive evaluation of model perfor-mance, combining with other evaluation metrics is considered essential. .

Principal Equatorial Null Geodesic Congruences in the Kerr Metric, and Their Quantum Propagators

Using the Raychaudhuri equation, we associate quantum probability amplitudes (propagators) to equatorial principal ingoing and outgoing null geodesic congruences in the Kerr metric. The expansion scalars diverge at the ring singularity;however, the propagators remain finite, which is an indication that at the quantum level singularities might disappear or, at least, become softened.

Security Vulnerability Analyses of Large Language Models (LLMs) through Extension of the Common Vulnerability Scoring System (CVSS) Framework

Large Language Models (LLMs) have revolutionized Generative Artificial Intelligence (GenAI) tasks, becoming an integral part of various applications in society, including text generation, translation, summarization, and more. However, their widespread usage emphasizes the critical need to enhance their security posture to ensure the integrity and reliability of their outputs and minimize harmful effects. Prompt injections and training data poisoning attacks are two of the most prominent vulnerabilities in LLMs, which could potentially lead to unpredictable and undesirable behaviors, such as biased outputs, misinformation propagation, and even malicious content generation. The Common Vulnerability Scoring System (CVSS) framework provides a standardized approach to capturing the principal characteristics of vulnerabilities, facilitating a deeper understanding of their severity within the security and AI communities. By extending the current CVSS framework, we generate scores for these vulnerabilities such that organizations can prioritize mitigation efforts, allocate resources effectively, and implement targeted security measures to defend against potential risks.

Configuration Synthesis and Performance Evaluation Metrics of Lunar Rover Locomotion Systems

A method of topology synthesis based on graph theory and mechanism combination theory was applied to the configuration design of locomotion systems of lunar exploration rovers(LER).Through topology combination of wheel structural unit,suspension unit,and connecting device unit between suspension and load platform,some new locomotion system configurations were proposed and the metrics and indexes to evaluate the performance of the new locomotion system were analyzed.Performance evaluation and comparison between two LER with locomotion systems of different configurations were analyzed.The analysis results indicate that the new locomotion system configuration has good trafficability performance.

MAXWELL-EINSTEIN METRICS ON COMPLETIONS OF CERTAIN C* BUNDLES

In this paper,we prove that for some completions of certain fiber bundles there is a Maxwell-Einstein metric conformally related to any given Kahler class.

MEM-TET: Improved Triplet Network for Intrusion Detection System

With the advancement of network communication technology,network traffic shows explosive growth.Consequently,network attacks occur frequently.Network intrusion detection systems are still the primary means of detecting attacks.However,two challenges continue to stymie the development of a viable network intrusion detection system:imbalanced training data and new undiscovered attacks.Therefore,this study proposes a unique deep learning-based intrusion detection method.We use two independent in-memory autoencoders trained on regular network traffic and attacks to capture the dynamic relationship between traffic features in the presence of unbalanced training data.Then the original data is fed into the triplet network by forming a triplet with the data reconstructed from the two encoders to train.Finally,the distance relationship between the triples determines whether the traffic is an attack.In addition,to improve the accuracy of detecting unknown attacks,this research proposes an improved triplet loss function that is used to pull the distances of the same class closer while pushing the distances belonging to different classes farther in the learned feature space.The proposed approach’s effectiveness,stability,and significance are evaluated against advanced models on the Android Adware and General Malware Dataset(AAGM17),Knowledge Discovery and Data Mining Cup 1999(KDDCUP99),Canadian Institute for Cybersecurity Group’s Intrusion Detection Evaluation Dataset(CICIDS2017),UNSW-NB15,Network Security Lab-Knowledge Discovery and Data Mining(NSL-KDD)datasets.The achieved results confirmed the superiority of the proposed method for the task of network intrusion detection.

Development of an occupant restraint system model and parametric study on equivalent crash pulse in vehicle frontal offset crash

Studies were conducted to evaluate driver injury metrics with varying crash pulse in offset crash. First, a vehicle finite element （ FE ） model and an occupant restraint system （ORS） model were developed and validated against tests; then, the crash pulse collected from the test vehicle was equivalent to a dual-trapezoid shape pulse which will be quantitatively described by six parameters and was put into the ORS model; finally, parametric studies were conducted to analyze the sensitivi- ties of parameters of equivalent crash pulse on head resultant acceleration, head injury criteria （HIC）, neck axial force and chest deformation. Results showed that the second peak value of the crash pulse was statistically significant on all these injury criteria （P = 0. 001, 0. 000, 0. 000, 0. 000 re- spectively）, the first peak level had a negative significantly effect on all the criteria aforementioned except the chest deformation （P = 0. 011, 0. 038, and 0. 033 respectively）, and the interaction of the time-points of first and second peak values had a significant influence on head resultant acceleration （P = 0. 03 ）. A higher first peak value and a lower second peak value of the crash pulse could bring deeply lower injury metrics.

Timed automata for metric interval temporal logic formulae in prototype verification system

Based on analysis of the syntax structure and semantics model of the metric interval temporal logic （MITL） formulas, it is shown how to transform a formula written in the real-time temporal logic MITL formula into a fair timed automaton （TA） that recognizes its satisfying models with prototype verification system （PVS） in this paper. Both the tabular construction＇s principles and the PVS implementation details are given for the different type of MITL formula according to the corresponding semantics interpretations. After this transformation procedure, specifications expressed with MITL formula can be verified formally in the timed automata framework developed previously.

Air Traffic Operation Complexity Analysis Based on Metrics System

In order to quantitatively analyze air traffic operation complexity,multidimensional metrics were selected based on the operational characteristics of traffic flow.The kernel principal component analysis method was utilized to reduce the dimensionality of metrics,therefore to extract crucial information in the metrics.The hierarchical clustering method was used to analyze the complexity of different airspace.Fourteen sectors of Guangzhou Area Control Center were taken as samples.The operation complexity of traffic situation in each sector was calculated based on real flight radar data.Clustering analysis verified the feasibility and rationality of the method,and provided a reference for airspace operation and management.

Research on the Design and Implementation of Detection System of Nutz Framework Meteorological Metrical Device

In people’s daily life, the role of weatherforecast is self-evident. However, the accuracy offorecasting is based on the accuracy and reliability ofmeteorological data which depends on the sensitivityof meteorological device. Therefore, an importantduty of the detection institution of meteorologicalmetrical device is to have the effective detectionof meteorological device, so as to ensure a highsensitivity of the device. However, the meteorologicaldevice used by some meteorological bureaus is nottechnologically advanced and the device detectionmode is too old, which cannot meet the new regulationsissued by the China Meteorological Administration.So it is necessary for the meteorological bureau todevelop a set of devices that can easily meet the newmeteorological measurement requirements, which is ofgreat significance to ensure the accurate measurementof meteorological data.

Mining Metrics for Enhancing E-Commerce Systems User Experience

The diversity of e-commerce Business to Consumer systems and the significant increase in their use during the COVID-19 pandemic as a one of the primary channels of retail commerce, has made all the most important the need to measuring their quality using practical methods. This paper presents a quality evaluation framework for web metrics that are B2C specific. The framework uses three dimensions based on end-user interaction categories, metrics internal specs and quality sub-characteristics as defined by ISO25010. Beginning from the existing large corpus of general-purpose web metrics, e-commerce specific metrics are chosen and categorized. Analysis results are subjected to a data mining analysis to provide association rules between the various dimensions of the framework. Finally, an ontology that corresponds to the framework is developed to answer to complicated questions related to metrics use and to facilitate the production of new, user defined meta-metrics.

Metric Identification of Vertices in Polygonal Cacti

The distance between two vertices u and v in a connected graph G is the number of edges lying in a shortest path(geodesic)between them.A vertex x of G performs the metric identification for a pair(u,v)of vertices in G if and only if the equality between the distances of u and v with x implies that u=v(That is,the distance between u and x is different from the distance between v and x).The minimum number of vertices performing the metric identification for every pair of vertices in G defines themetric dimension of G.In this paper,we performthemetric identification of vertices in two types of polygonal cacti:chain polygonal cactus and star polygonal cactus.

Geometry Flow-Based Deep Riemannian Metric Learning

Deep metric learning(DML)has achieved great results on visual understanding tasks by seamlessly integrating conventional metric learning with deep neural networks.Existing deep metric learning methods focus on designing pair-based distance loss to decrease intra-class distance while increasing interclass distance.However,these methods fail to preserve the geometric structure of data in the embedding space,which leads to the spatial structure shift across mini-batches and may slow down the convergence of embedding learning.To alleviate these issues,by assuming that the input data is embedded in a lower-dimensional sub-manifold,we propose a novel deep Riemannian metric learning(DRML)framework that exploits the non-Euclidean geometric structural information.Considering that the curvature information of data measures how much the Riemannian(nonEuclidean)metric deviates from the Euclidean metric,we leverage geometry flow,which is called a geometric evolution equation,to characterize the relation between the Riemannian metric and its curvature.Our DRML not only regularizes the local neighborhoods connection of the embeddings at the hidden layer but also adapts the embeddings to preserve the geometric structure of the data.On several benchmark datasets,the proposed DRML outperforms all existing methods and these results demonstrate its effectiveness.

Metric Basis of Four-Dimensional Klein Bottle

The Metric of a graph plays an essential role in the arrangement of different dimensional structures and finding their basis in various terms.The metric dimension of a graph is the selection of the minimum possible number of vertices so that each vertex of the graph is distinctively defined by its vector of distances to the set of selected vertices.This set of selected vertices is known as the metric basis of a graph.In applied mathematics or computer science,the topic of metric basis is considered as locating number or locating set,and it has applications in robot navigation and finding a beacon set of a computer network.Due to the vast applications of this concept in computer science,optimization problems,and also in chemistry enormous research has been conducted.To extend this research to a four-dimensional structure,we studied the metric basis of the Klein bottle and proved that the Klein bottle has a constant metric dimension for the variation of all its parameters.Although the metric basis is variying in 3 and 4 values when the values of its parameter change,it remains constant and unchanged concerning its order or number of vertices.The methodology of determining the metric basis or locating set is based on the distances of a graph.Therefore,we proved the main theorems in distance forms.