Geometric Distance Measure Research Articles

Cepheids with giant companions: A new, abundant source of Cepheid astrophysics

AbstractWe present a progress report of our project aiming to increase the number of known Cepheids in double-lined binary (SB2) systems from six to 100 or more. This will allow us, among other goals, to accurately measure masses for a large sample of Cepheids. Currently, only six accurate Cepheid masses are available, which hinders our understanding of their physical properties and renders the Cepheid mass–luminosity relation poorly constrained. At the same time, Cepheids are widely used for essential measurements (e.g., extragalactic distances, the Hubble constant). To examine Cepheid period–luminosity relations, we selected as binary candidates Cepheids that are too bright for their periods. To date, we have confirmed 56 SB2 systems, including the detection of significant orbital motions of the components for 32. We identified systems with orbital periods up to five times shorter than the shortest reported period to date, as well as systems with mass ratios significantly different from unity (suggesting past merger events). Both features are essential to understand how multiplicity affects the formation and destruction of Cepheid progenitors and what effect this has on global Cepheid properties. We also present eight new systems composed of two Cepheids (only one such system was known before). Among confirmed SB2 Cepheids, there are also several wide-orbit systems. In the future, these may facilitate independent accurate geometric distance measurements to the Large and Small Magellanic Clouds.

Complex intuitionistic fuzzy ordered weighted distance measure

Compared with the complex fuzzy set (CFS) and the intuitionistic fuzzy set (IFS), the complex intuitionistic fuzzy set (CIFS) can handle the two-dimensional and uncertain information simultaneously, and thus strengthen the capability of capturing useful information. In this paper, we consider the situation with complex intuitionistic fuzzy environment, where the importance of certain information is also taken into consideration. To deal with these situations, we develop the complex intuitionistic fuzzy ordered weighted distance (CIFOWD) measure and investigate its main properties. We find that the CIFOWD measure provides a parameterized family of aggregation distance measures, which includes, for example, complex intuitionistic fuzzy ordered weighted geometric distance (CIFOWGD) measure, complex intuitionistic fuzzy ordered weighted Hamming distance (CIFOWHD) measure, and complex intuitionistic fuzzy ordered weighted Euclidean distance (CIFOWED) measure as special types. The CIFOWD measure is capable of alleviating the influence of excessively large or excessively small deviations on the aggregation results via weight vector. Based on these distance measures, a multiple criteria group decision-making approach is presented under the CIFSs environment. An illustrative example regarding coronavirus vaccine selection on COVID-19 is taken for demonstrating the effectiveness of the proposed approach. Finally, the proposed results are compared with the results obtained from the existing methods.

Research on service quality evaluation of sports clubs with Pythagorean fuzzy information

In this paper, considering the traditional geometric operation laws and Pythagorean fuzzy information, a varies of new distance measures of Pythagorean fuzzy set are proposed, such as generalized Pythagorean fuzzy ordered geometric distance (GPFOWGD) measures and generalized Pythagorean fuzzy hybrid weighted geometric distance (GPFHWGD) measures. Besides, some special issues including Hamming distance, Euclidean distance and Hausdorff distance of these raised geometric distance measures are investigated. To testify the valid of these new presented distance measures, a decision-making model is built and illustrated by a mathematical calculation example to evaluate the service quality of sports clubs using Pythagorean fuzzy information. The results display that the approach is uncomplicated, valid and simple to compute. The example illustrates that the method presented in the paper can be used to deal with problems of uncertainty such as dynamic multiple attribute decision making.

Research on Evaluation of Sustainable Development of New Urbanization from the Perspective of Urban Agglomeration under the Pythagorean Fuzzy Sets

In this study, considering the traditional geometric operation laws and Pythagorean fuzzy information, we propose a variety of new distance measures of Pythagorean fuzzy sets such as generalized Pythagorean fuzzy geometric distance (GPFGD) measures and generalized Pythagorean fuzzy weighted geometric distance (GPFWGD) measures. Besides, some special issues including Hamming distance, Euclidean distance, and Hausdorff distance of these raised geometric distance measures are investigated. To testify the valid of these new presented distance measures, we build a decision-making model illustrated by a mathematical calculation example to evaluate the sustainable development of new urbanization from the perspective of urban agglomeration using Pythagorean fuzzy information.

An Effective Feature Extraction Method of Quantitative Recognition of Ultrasonic Echo for Bonding Quality of Composite Sheet

In this paper, a set of effective ultrasonic echo feature extraction method is proposed for the quantitative identification of thin plate composite bonding quality, which opens up a new research idea for the research of ultrasonic echo feature extraction for quantitative identification of thin plate bonding quality, and also lays a foundation for further quantitative identification of bonding structure debonding degree of thin plate. In addition to the time and frequency domain analysis, the empirical mode time-frequency analysis method is used to highlight the time-frequency characteristics of the echo signal, improve the resolution of the signal analysis, and expand the space for the echo signal feature extraction. The feature validity evaluation theory of fault diagnosis is introduced to evaluate the feature validity of high-dimensional signal parameters, and the invalid signal parameters are eliminated to obtain an effective echo signal feature set with low dimension. Using the exhaustive search strategy of feature selection theory, geometric distance measurement and information measurement evaluation criteria, and through the classification verification of support vector machine classifier, the effective feature vector for quantitative identification of adhesive quality is obtained.

Hitch Angle Estimation of a Towing Vehicle With Arbitrary Configuration

In this paper, ultra-sonic sensors along with kinematics and dynamics equations of a towing vehicle are used to develop three approaches for hitch angle estimation. The first approach is based on direct calculation of hitch angle using certain a priori geometric information and distance measurements of four ultra-sonic sensors. An angle estimate is generated for each of the six possible sensor-pair combinations, and these six estimates are passed through a voting algorithm to produce a single estimate. As the second and third approaches, kinematic and dynamic models of the tractor-trailer system are used to develop least-squares and Kalman filtering based recursive hitch angle estimations. A more reliable hitch angle estimation scheme is then proposed as the integration of the algorithms developed following each of the three approaches via a switching data fusion logic. It is shown that the proposed integrated hitch angle estimation scheme can be used for any ball type box trailer with a flat or symmetric V-nose frontal face without any priori information on the trailer parameters. Based on the validity of the assumptions, the proposed scheme can estimate the hitch angle in both low-speed using the kinematic model, and high-speed using the dynamic model of the tractor-trailer system. Experimental results corroborate the algorithms in estimating the hitch angle estimates in various cases conducted in this study.

SMKFC-ER: Semi-supervised multiple kernel fuzzy clustering based on entropy and relative entropy

The present study aimed to present a new algorithm called Semi-supervised Multiple Kernel Fuzzy Clustering based on Entropy and Relative entropy (SMKFC-ER) by focusing on external knowledge related to the labeled data. In the proposed method, entropy coefficient and relative entropy divergence measure are applied instead of fuzzifier for unsupervised section and the geometric distance measure for semi-supervised section respectively, by emphasizing on combining unsupervised and semi-supervised sections explicitly. The use of relative entropy and entropy in the objective function results in sharing more consistent concepts for the semi-supervised section, controlling the fuzziness of the extracted clusters, and determining the kernel weights regularly for the unsupervised section. Finally, using relative entropy with entropy simultaneously derives a closed-form solution. The performance and supremacy of the proposed method on non-spherical synthetic and real-world datasets are shown by comparing unsupervised and semi-supervised fuzzy clustering methods.

The Megamaser Cosmology Project. XIII. Combined Hubble Constant Constraints

Abstract We present a measurement of the Hubble constant made using geometric distance measurements to megamaser-hosting galaxies. We have applied an improved approach for fitting maser data and obtained better distance estimates for four galaxies previously published by the Megamaser Cosmology Project: UGC 3789, NGC 6264, NGC 6323, and NGC 5765b. Combining these updated distance measurements with those for the maser galaxies CGCG 074-064 and NGC 4258, and assuming a fixed velocity uncertainty of 250 km s−1 associated with peculiar motions, we constrain the Hubble constant to be H 0 = 73.9 ± 3.0 km s−1 Mpc−1 independent of distance ladders and the cosmic microwave background. This best value relies solely on maser-based distance and velocity measurements, and it does not use any peculiar velocity corrections. Different approaches for correcting peculiar velocities do not modify H 0 by more than ±1σ, with the full range of best-fit Hubble constant values spanning 71.8–76.9 km s−1 Mpc−1. We corroborate prior indications that the local value of H 0 exceeds the early-universe value, with a confidence level varying from 95% to 99% for different treatments of the peculiar velocities.

Uncertain Data Clustering Based on Probability Distribution in Obstacle Space

In the case of current technology, most of the measurements are focused on geometric distance, and the distribution of data is not considered. In order to compensate for this shortcoming of geometric distance measurement, this paper uses the KL distance as the similarity measurement standard for uncertain data, and the DOUD_C algorithm and COUD_C algorithm are proposed respectively in the discrete domain and continuous domain. In order to solve the problem of efficient clustering of the high dimensional data, this paper considers the data structure of grid, and BROUD_C algorithm is proposed. According to the adjacency characteristic of the grid, the cluster process is extended continuously, the algorithm can find clusters of arbitrary shapes, and we can filter a large number of isolated points, it solves the uncertain data clustering problem effectively in the obstacle space. The experimental results show that compared to the OBS_UK_means with VPA and SDA pruning algorithm and FOPTICS algorithm, the clustering performance of BROUD_C algorithm is more significant and CPU has less execution time in the obstacle space.

A geometric distance measurement to the Galactic center black hole with 0.3% uncertainty

We present a 0.16% precise and 0.27% accurate determination of R0, the distance to the Galactic center. Our measurement uses the star S2 on its 16-year orbit around the massive black hole Sgr A* that we followed astrometrically and spectroscopically for 27 years. Since 2017, we added near-infrared interferometry with the VLTI beam combiner GRAVITY, yielding a direct measurement of the separation vector between S2 and Sgr A* with an accuracy as good as 20 μas in the best cases. S2 passed the pericenter of its highly eccentric orbit in May 2018, and we followed the passage with dense sampling throughout the year. Together with our spectroscopy, in the best cases with an error of 7 km s−1, this yields a geometric distance estimate of R0 = 8178 ± 13stat. ± 22sys. pc. This work updates our previous publication, in which we reported the first detection of the gravitational redshift in the S2 data. The redshift term is now detected with a significance level of 20σ with fredshift = 1.04 ± 0.05.

A Comparative Analysis on Geometric Measure in Intuitionistic Fuzzy Set and Interval-Valued Intuitionistic Fuzzy Set

Intuitionistic Fuzzy set (IFS) was proposed in early 80’s. It is a well known theory. As a developer in Fuzzy Mathematics, interval – valued Intuitionistic Fuzzy sets (IVIFS) were developed afterwards by Gargo and Atanssov. It has a wide range of applications in the field of Optimization and algebra. There are many distance measure in Fuzzy such as Hamming, Normalized Hamming, Euclidean, Normalized Euclidean, Geometric, Normalized Geometric etc… to calculate the distance between two fuzzy numbers. In this paper, the comparison between Geometric distance measure in Intuitionistic Fuzzy set and interval – valued Intuitionistic Fuzzy sets is explored. The step-wise conservation of Intuitionistic Fuzzy set and interval – valued Intuitionistic Fuzzy sets is also proposed. This type of comparative analysis shows that the distance between Intuitionistic Fuzzy set and interval – valued Intuitionistic Fuzzy sets varies slightly due to boundaries of interval – valued Intuitionistic Fuzzy sets.

INTEGRATION OF SEMANTIC 3D CITY MODELS AND 3D MESH MODELS FOR ACCURACY IMPROVEMENTS OF SOLAR POTENTIAL ANALYSES

Abstract. High-resolution 3D mesh models are an inexpensive and increasingly available data source for 3D models of cities and landscapes of high visual quality and rich geometric detail. However, because of their simple data structure, their analytic capabilites are limited. Semantic 3D city model contain rich thematic information and are well suited for analytics due to their deeply structured semantic data model. In this work an approach for the integration of semantic 3D city models with 3D mesh models is presented. The method is based on geometric distance measures between mesh triangles and semantic surfaces and a region growing approach using plane fitting. The resulting semantic segmentation of mesh triangles is stored in a CityGML data set, to enrich the semantic model with an additional detailed geometric representation of its surfaces and a broad range of unrepresented features like technical building installations, balconies, dormers, chimneys, and vegetation. The potential of the approach is demonstrated on the example of a solar potential analysis, which estimation quality is significantly improved due to the mesh integration. The impact of the method is quantified on a case study using open data from the city of Helsinki.

Modern Geometric Methods of Distance Determination

Building a 3D picture of the Universe at any distance is one of the major challenges in astronomy, from the nearby Solar System to distant Quasars and galaxies. This goal has forced astronomers to develop techniques to estimate or to measure the distance of point sources on the sky. While most distance estimates used since the beginning of the 20th century are based on our understanding of the physics of objects of the Universe: stars, galaxies, QSOs, the direct measures of distances are based on the geometric methods as developed in ancient Greece: the parallax, which has been applied to stars for the first time in the mid-19th century. In this review, different techniques of geometrical astrometry applied to various stellar and cosmological (Megamaser) objects are presented. They consist in parallax measurements from ground based equipment or from space missions, but also in the study of binary stars or, as we shall see, of binary systems in distant extragalactic sources using radio telescopes. The Gaia mission will be presented in the context of stellar physics and galactic structure, because this key space mission in astronomy will bring a breakthrough in our understanding of stars, galaxies and the Universe in their nature and evolution with time. Measuring the distance to a star is the starting point for an unbiased description of its physics and the estimate of its fundamental parameters like its age. Applying these studies to candles such as the Cepheids will impact our large distance studies and calibration of other candles. The text is constructed as follows: introducing the parallax concept and measurement, we shall present briefly the Gaia satellite which will be the future base catalogue of stellar astronomy in the near future. Cepheids will be discussed just after to demonstrate the state of the art in distance measurements in the Universe with these variable stars, with the objective of 1% of error in distances that could be applied to our closest galaxy the LMC, and better constrain the distances of large sub-structures around the Milky Way. Then exciting objects like X-Ray binaries will be presented in two parts corresponding to “low” or “high” mass stars with compact objects observed with X-ray satellites. We shall demonstrate the capability of these objects to have their distances measured with high accuracy with not only helps in the study of these objects but could also help to measure the distance of the structure they belong. For cosmological objects and large distances of megaparsecs, we shall present what has been developed for more than 20 years in the geometric distance measurements of MegaMasers, the ultimate goal being the estimation of the $H_{0}$ parameter.

Measurement of a Cosmographic Distance Ratio with Galaxy and Cosmic Microwave Background Lensing.

We measure the gravitational lensing shear signal around dark matter halos hosting constant mass galaxies using light sources at z∼1 (background galaxies) and at the surface of last scattering at z∼1100 (the cosmic microwave background). The galaxy shear measurement uses data from the CFHTLenS survey, and the microwave background shear measurement uses data from the Planck satellite. The ratio of shears from these cross-correlations provides a purely geometric distance measurement across the longest possible cosmological lever arm. This is because the matter distribution around the halos, including uncertainties in galaxy bias and systematic errors such as miscentering, cancels in the ratio for halos in thin redshift slices. We measure this distance ratio in three different redshift slices of the constant mass (CMASS) sample and combine them to obtain a 17% measurement of the distance ratio, r=0.390_{-0.062}^{+0.070}, at an effective redshift of z=0.53. This is consistent with the predicted ratio from the Planck best-fit cold dark matter model with a cosmological constant cosmology of r=0.419.

Self-adapted mixture distance measure for clustering uncertain data

Distance measure plays an important role in clustering uncertain data. However, existing distance measures for clustering uncertain data suffer from some issues. Geometric distance measure can not identify the difference between uncertain objects with different distributions heavily overlapping in locations. Probability distribution distance measure can not distinguish the difference between different pairs of completely separated uncertain objects. In this paper, we propose a self-adapted mixture distance measure for clustering uncertain data which considers the geometric distance and the probability distribution distance simultaneously, thus overcoming the issues in previous distance measures. The proposed distance measure consists of three parts: (1) The induced kernel distance: it can be used to measure the geometric distance between uncertain objects. (2) The Jensen–Shannon divergence: it can be used to measure the probability distribution distance between uncertain objects. (3) The self-adapted weight parameter: it can be used to adjust the importance degree of the induced kernel distance and the Jensen–Shannon divergence according to the location overlapping information of the dataset. The proposed distance measure is symmetric, finite and parameter adaptive. Furthermore, we integrate the self-adapted mixture distance measure into the partition-based and density-based algorithms for clustering uncertain data. Extensive experimental results on synthetic datasets, real benchmark datasets and real world uncertain datasets show that our proposed distance measure outperforms the existing distance measures for clustering uncertain data.

Data-dependent dissimilarity measure: an effective alternative to geometric distance measures

Nearest neighbor search is a core process in many data mining algorithms. Finding reliable closest matches of a test instance is still a challenging task as the effectiveness of many general-purpose distance measures such as $$\ell _p$$ -norm decreases as the number of dimensions increases. Their performances vary significantly in different data distributions. This is mainly because they compute the distance between two instances solely based on their geometric positions in the feature space, and data distribution has no influence on the distance measure. This paper presents a simple data-dependent general-purpose dissimilarity measure called ‘ $$m_p$$ -dissimilarity’. Rather than relying on geometric distance, it measures the dissimilarity between two instances as a probability mass in a region that encloses the two instances in every dimension. It deems two instances in a sparse region to be more similar than two instances of equal inter-point geometric distance in a dense region. Our empirical results in k-NN classification and content-based multimedia information retrieval tasks show that the proposed $$m_p$$ -dissimilarity measure produces better task-specific performance than existing widely used general-purpose distance measures such as $$\ell _p$$ -norm and cosine distance across a wide range of moderate- to high-dimensional data sets with continuous only, discrete only, and mixed attributes.

Point-models for the set of oriented line-elements – a survey

We study point-models for the set L→ of oriented line-elements by reviewing existing ones and by constructing them from different approaches proposed in the literature. We distinguish between point-models resulting from transformations and those implied by representations, where we also pursue the strategy to represent oriented line-elements by oriented line-segments with a constant length. For path planning in robotics (e.g. approximation, interpolation, optimization, ...) it is desirable to have a metric on L→, thus we also study geometric meaningful distance measures. Based on the resulting metric spaces we finally discuss the problem of motion design.

A Method for Group Decision Making Based on Interval-Valued Intuitionistic Fuzzy Geometric Distance Measures

In this paper, at first, we develop some new geometric distance measures for interval-valued intuitionistic fuzzy information, including the interval-valued intuitionistic fuzzy weighted geometric distance (IVIFWGD) measure, the interval-valued intuitionistic fuzzy ordered weighted geometric distance (IVIFOWGD) measure and the interval-valued intuitionistic fuzzy hybrid weighted geometric distance (IVIFHWGD) measure. Also, several desirable properties of these new distance measures are studied and a numerical example is given to show application of the distance measure to pattern recognition problems. And then, based on the developed distance measures a consensus reaching process with interval-valued intuitionistic fuzzy preference information for group decision making is proposed. Finally, an illustrative example with interval-valued intuitionistic fuzzy information is given.

SPECTROSCOPIC SURVEY OF G AND K DWARFS IN THE HIPPARCOS CATALOG. I. COMPARISON BETWEEN THE HIPPARCOS AND PHOTOMETRIC PARALLAXES

ABSTRACT The tension between the Hipparcos parallax of the Pleiades and other independent distance estimates continues even after the new reduction of the Hipparcos astrometric data and the development of a new geometric distance measurement for the cluster. A short Pleiades distance from the Hipparcos parallax predicts a number of stars in the solar neighborhood that are sub-luminous at a given photospheric abundance. We test this hypothesis using the spectroscopic abundances for a subset of stars in the Hipparcos catalog, which occupy the same region as the Pleiades in the color–magnitude diagram. We derive stellar parameters for 170 nearby G- and K-type field dwarfs in the Hipparcos catalog based on high-resolution spectra obtained using KPNO 4 m echelle spectrograph. Our analysis shows that, when the Hipparcos parallaxes are adopted, most of our sample stars follow empirical color–magnitude relations. A small fraction of stars are too faint compared to main-sequence fitting relations by Δ M V ≳ 0.3 ?> mag, but the differences are marginal at a 2 &sgr; ?> level, partly due to relatively large parallax errors. On the other hand, we find that the photometric distances of stars showing signatures of youth as determined from lithium absorption line strengths and R HK ′ ?> chromospheric activity indices are consistent with the Hipparcos parallaxes. Our result is contradictory to a suggestion that the Pleiades distance from main-sequence fitting is significantly altered by stellar activity and/or the young age of its stars, and provides an additional supporting evidence for the long-distance scale of the Pleiades.

THE MEGAMASER COSMOLOGY PROJECT. VIII. A GEOMETRIC DISTANCE TO NGC 5765b

ABSTRACT As part of the Megamaser Cosmology Project, here we present a new geometric distance measurement to the megamaser galaxy NGC 5765b. Through a series of very long baseline interferometry observations, we have confirmed the water masers trace a thin, sub-parsec Keplerian disk around the nucleus, implying an enclosed mass of 4.55 ± 0.40 × 107 M ⊙. Meanwhile, from single-dish monitoring of the maser spectra over two years, we measured the secular drifts of maser features near the systemic velocity of the galaxy with rates between 0.5 and 1.2 km s−1 yr−1. Fitting a warped, thin-disk model to these measurements, we determine a Hubble Constant H 0 of 66.0 ± 6.0 km s−1 Mpc−1 with an angular-diameter distance to NGC 5765b of 126.3 ± 11.6 Mpc. Apart from the distance measurement, we also investigate some physical properties related to the maser disk in NGC 5765b. The high-velocity features are spatially distributed into several clumps, which may indicate the existence of a spiral density wave associated with the accretion disk. For the redshifted features, the envelope defined by the peak maser intensities increases with radius. The profile of the systemic masers in NGC 5765b is smooth and shows almost no structural changes over the two years of monitoring time, which differs from the more variable case of NGC 4258.