Sum Of Distances Research Articles

Local critical analysis of inequalities related to the sum of distances between n points on the unit hemisphere for $$n=4,5$$

Local critical analysis of inequalities related to the sum of distances between n points on the unit hemisphere for $$n=4,5$$

Easy pair selection method for Kinship Verification using fixed age group images

Kinship Verification (KV) by using facial images is a relevant and challenging research problem in the field of computer vision. Facial features are extracted from the input pair of images and subsequently analyzed to find out existence of kin relation between them. Weights of the training model are suitably learned and adapted for the same. In most of the existing schemes, non kin pairs are randomly generated from the existing kin pair database for the learning process of the model. Since non-kin pairs are formed randomly from the true kin pair database itself, hence there is a significant probability that some non kin pairs have more similarity in feature space which is ideally undesirable and leads to improper learning of the model and results into errors. To reduce such errors, we have proposed a new scheme called easy-pair selection method for KV. Kin and non kin pairs are categorized into easy and hard pairs based on sum of square distance with respect to the feature space of the pairs. Suitable kin-margin (KM) value is chosen to classify the pair as easy or hard. Further, selected easy pairs are used to compute the optimized training weights (W) from the training dataset. The obtained weights will ensure to minimize the distance of kin pairs and maximize the distance of non-kin pairs in feature space. A fixed age group image database (FAG) have also been proposed through this article which contains the corresponding facial images of the parents and their children from the same age group to minimize the issue of age in-variance as well. Extensive experiments have been performed to validate the accuracy of the proposed scheme and is found to outperform the existing relevant schemes for KV.

Multiview Latent Structure Learning: Local structure-guided cross-view discriminant analysis

Multiview subspace learning (MvSL) has attracted extensive research interest in many real-world applications, e.g., pattern recognition and computer vision. Existing MvSL approaches seek a discriminant common subspace by simultaneously maximizing the arithmetic mean of the between-class covariance and minimizing the global average of the within-class covariance. However, the arithmetic mean normally assigns equal weight to all between-class distances. Then, classes with small distances overlap with each other, and the largest between-class distance dominates the common subspace. In addition, the global average of within-class covariance (which is computed by the sum of within-class distances for all classes) significantly differs from the within-class covariance of a single class. This will inevitably cause the internal details of each class to be ignored and lead to lower recognition accuracy. To circumvent these issues, we develop a productive strategy to take more consideration of the relationship between any two classes and propose a novel Multiview Latent Structure Learning (MvLSL) model, which incorporates the weighted harmonic mean of pairwise between-class scatter and pairwise within-class scatter. Due to the adjustable dimensions of the common subspace, MvLSL can be naturally extended for dimensionality reduction (DR), and we utilize a reconstruction term to suppress data degradation and improve the DR performance. Our models are tested on six benchmark datasets with five evaluation criteria and compared with existing state-of-the-art methods, indicating our models’ effectiveness and superiority.

Lieb—Thirring type bounds for perturbed Schrödinger operators with single-well potentials

We prove an upper bound on the sum of distances between eigenvalues of a perturbed Schrödinger operator H0 − V and the lowest eigenvalue of H0. Our results hold for operators H0 = −Δ − V0 in one dimension with single-well potentials. We rely on a variation of the well-known commutation method. In Pöschl–Teller and Coulomb cases, we are able to use explicit factorizations to establish improved bounds.

Kirchhoff Index and Degree Kirchhoff Index of Tetrahedrane-Derived Compounds

Tetrahedrane-derived compounds consist of n crossed quadrilaterals and possess complex three-dimensional structures with high symmetry and dense spatial arrangements. As a result, these compounds hold great potential for applications in materials science, catalytic chemistry, and other related fields. The Kirchhoff index of a graph G is defined as the sum of resistive distances between any two vertices in G. This article focuses on studying a type of tetrafunctional compound with a linear crossed square chain shape. The Kirchhoff index and degree Kirchhoff index of this compound are calculated, and a detailed analysis and discussion is conducted. The calculation formula for the Kirchhoff index is obtained based on the relationship between the Kirchhoff index and Laplace eigenvalue, and the number of spanning trees is derived for linear crossed quadrangular chains. The obtained formula is validated using Ohm’s law and Cayley’s theorem. Asymptotically, the ratio of Kirchhoff index to Wiener index approaches one-fourth. Additionally, the expression for the degree Kirchhoff index of the linear crossed quadrangular chain is obtained through the relationship between the degree Kirchhoff index and the regular Laplace eigenvalue and matrix decomposition theorem.

Comparing Two Strategies for Locating Hydrogen Refueling Stations under High Demand Uncertainty

This research aims to model and compare two strategies for locating new hydrogen refueling stations (HRS) in a context of high uncertainty on H<sub>2</sub> demand and on the spatial distribution of demand points. The first strategy S1 represented by an agent-based model integrating a particle swarm optimization metaheuristic consists of finding the best HRS locations by adapting to the real evolution of the demand. A second strategy S2 consists in solving a classical capacitated <em>p</em>-median problem based on H<sub>2</sub> consumption forecasts over a given deterministic horizon in order to define in advance <em>p</em> optimal future HRS locations. Assuming that the same distributor gradually implements future HRSs in a given area between 2023 and 2030, both models minimize the sum of travel distances between each demand point and its assigned SRH. The results show that during the growth phase of the fuel cell electric vehicle (FCEV) market, with two different compound annual growth rates (medium and strong), the conservative S1 strategy performs better than S2 as these rates increase. However, while S2 remains suboptimal throughout the sales growth period, it becomes more effective once demand stabilizes. Another finding is that different uniform distributions of H<sub>2</sub> demand points in the same space have only a small long-term influence on the performance of these two models. This research advises investors to study the influence of different location strategies and models on the performance of a final HRS network in a given region. Models can be easily configured and adapted to a particular spatial distribution of demand points in a specific environment, more flexible H<sub>2</sub> production capabilities, or different behaviors of FCEV drivers that could be geo-located.

Algorithms for the genome median under a restricted measure of rearrangement

Ancestral reconstruction is a classic task in comparative genomics. Here, we study thegenome median problem, a related computational problem which, given a set of three or more genomes, asks to find a new genome that minimizes the sum of pairwise distances between it and the given genomes. Thedistancestands for the amount of evolution observed at the genome level, for which we determine the minimum number of rearrangement operations necessary to transform one genome into the other. For almost all rearrangement operations the median problem is NP-hard, with the exception of thebreakpoint medianthat can be constructed efficiently for multichromosomal circular and mixed genomes. In this work, we study the median problem under a restricted rearrangement measure calledc4-distance, which is closely related to the breakpoint and the DCJ distance. We identify tight bounds and decomposers of thec4-median and develop algorithms for its construction, one exact ILP-based and three combinatorial heuristics. Subsequently, we perform experiments on simulated data sets. Our results suggest that thec4-distance is useful for the study the genome median problem, from theoretical and practical perspectives.

Lack of effectiveness of Bebtelovimab monoclonal antibody among high-risk patients with SARS-Cov-2 Omicron during BA.2, BA.2.12.1 and BA.5 subvariants dominated era.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Omicron subvariants are expected to be resistant to Bebtelovimab (BEB) monoclonal antibody (MAb) and the real-world experience regarding its effectiveness is scarce. This retrospective cohort study reports a data analysis in Banner Healthcare System (a large not-for-profit organization) between 4/5/2022 and 8/1/2022 and included 19,778 Coronavirus disease-19 (COVID-19) positive (by PCR or direct antigen testing) patients who were selected from Cerner-Electronic Health Record after the exclusions criteria were met. The study index date for cohort was determined as the date of BEB MAb administration or the date of the first positive COVID-19 testing. The cohort consist of COVID-19 infected patients who received BEB MAb (N = 1,091) compared to propensity score (PS) matched control (N = 1,091). The primary composite outcome was the incidence of 30-day all-cause hospitalization and/or mortality. All statistical analyses were conducted on the paired (matched) dataset. For the primary composite outcome, the event counts and percentages were reported. Ninety-five percent Clopper-Pearson confidence intervals for percentages were computed. The study cohorts were 1:1 propensity matched without replacement across 26 covariates using an optimal matching algorithm that minimizes the sum of absolute pairwise distance across the matched sample after fitting and using logistic regression as the distance function. The pairs were matched exactly on patient vaccination status, BMI group, age group and diabetes status. Compared to the PS matched control group (2.6%; 95% confidence interval [CI]: 1.7%, 3.7%), BEB MAb use (2.2%; 95% CI: 1.4%, 3.3%) did not significantly reduce the incidence of the primary outcome (p = 0.67). In the subgroup analysis, we observed similar no-difference trends regarding the primary outcomes for the propensity rematched BEB MAb treated and untreated groups, stratified by patient vaccination status, age (<65 years or ≥65), and immunocompromised status (patients with HIV/AIDS or solid organ transplants or malignancy including lymphoproliferative disorder). The number needed to treat (1/0.026-0.022) with BEB MAb was 250 to avoid one hospitalization and/or death over 30 days. The BEB MAb use lacked efficacy in patients with SARS-CoV-2 Omicron subvariants (mainly BA.2, BA.2.12.1, and BA.5) in the Banner Healthcare System in the Southwestern United States.

Sums of distances on graphs and embeddings into Euclidean space

AbstractLet be a finite, connected graph. We consider a greedy selection of vertices: given a list of vertices , take to be any vertex maximizing the sum of distances to the vertices already chosen and iterate, keep adding the “most remote” vertex. The frequency with which the vertices of the graph appear in this sequence converges to a set of probability measures with nice properties. The support of these measures is, generically, given by a rather small number of vertices . We prove that this suggests that the graph G is, in a suitable sense, “m‐dimensional” by exhibiting an explicit 1‐Lipschitz embedding with good properties.

Self-supervised zero-shot dehazing network based on dark channel prior

Most learning-based methods previously used in image dehazing employ a supervised learning strategy, which is time-consuming and requires a large-scale dataset. However, large-scale datasets are difficult to obtain. Here, we propose a self-supervised zero-shot dehazing network (SZDNet) based on dark channel prior, which uses a hazy image generated from the output dehazed image as a pseudo-label to supervise the optimization process of the network. Additionally, we use a novel multichannel quad-tree algorithm to estimate atmospheric light values, which is more accurate than previous methods. Furthermore, the sum of the cosine distance and the mean squared error between the pseudo-label and the input image is applied as a loss function to enhance the quality of the dehazed image. The most significant advantage of the SZDNet is that it does not require a large dataset for training before performing the dehazing task. Extensive testing shows promising performances of the proposed method in both qualitative and quantitative evaluations when compared with state-of-the-art methods.Graphical

An Adaptive Hybrid Sampling Method for Free-Form Surfaces Based on Geodesic Distance

High precision geometric measurement of free-form surfaces has become the key to high-performance manufacturing in the manufacturing industry. By designing a reasonable sampling plan, the economic measurement of free-form surfaces can be realized. This paper proposes an adaptive hybrid sampling method for free-form surfaces based on geodesic distance. The free-form surfaces are divided into segments, and the sum of the geodesic distance of each surface segment is taken as the global fluctuation index of free-form surfaces. The number and location of the sampling points for each free-form surface segment are reasonably distributed. Compared with the common methods, this method can significantly reduce the reconstruction error under the same sampling points. This method overcomes the shortcomings of the current commonly used method of taking curvature as the local fluctuation index of free-form surfaces, and provides a new perspective for the adaptive sampling of free-form surfaces.

Quantum k -medoids algorithm using parallel amplitude estimation

Quantum computing is a promising paradigm that can provide viable solutions to high-complexity problems. The $k$-medoids algorithm is a powerful clustering method ubiquitously used in data mining, image processing, pattern recognition, etc. The core of $k$-medoids algorithm is to perform cluster assignment and center update, which are time-consuming for large data sets. A\"{\i}meur et al. proposed a quantum $k$-medoids algorithm [A\"{\i}meur, Brassard, and Gambs, Mach. Learn. 90, 261 (2013)] by quantizing the center update. Nevertheless, it has a query complexity $O({N}^{3/2})$ for one iteration, which is computationally expensive for a large $N$ where $N$ is the number of points. In this paper, we propose a complete quantum algorithm for $k$-medoids algorithm. Specifically, in cluster assignment, we devise a quantum subroutine to calculate the Manhattan distance between any two points and then assign all points to the closest center in parallel, which is faster than what is achievable classically. In center update, for a cluster, we use parallel amplitude estimation to calculate the average distance of each point to all the others. It makes our algorithm polynomially faster than the algorithm of A\"{\i}meur et al., whose sum of distances of each point to all the others is computed by adding the distances one by one. Our quantum $k$-medoids algorithm, with time complexity $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{O}({N}^{1/2})$, achieves a polynomial speedup in $N$ compared to the existing one.

Bounds for the sum of distances of spherical sets of small size

We derive upper and lower bounds on the sum of distances of a spherical code of size N in n dimensions when N=Θ(nα),0<α⩽2. The bounds are derived by specializing recent general, universal bounds on energy of spherical sets. We discuss asymptotic behavior of our bounds along with several examples of codes whose sum of distances closely follows the upper bound.

Resistance distance of generalized wheel and dumbbell graph using symmetric {1}-inverse of Laplacian matrix

A new class of graphs called dumbbell graphs, denoted by DB(Wm,n) is the graph obtained from two copies of generalized wheel graph Wm,n, m ≥ 2, n ≥ 3. It is a graph on 2 (m + n) vertices obtained by connecting m-vertices in one copy with the corresponding vertices in the other copy. The resistance distance between two vertices vi and vj, denoted by rij , is defined as the effective electrical resistance between them if each edge of G is replaced by 1 ohm resistor. The Kirchhoff index is the sum of the resistance distances between all pairs of vertices in the graph. In this paper, we formulate the resistance distance of Wm,n and DB(Wm,n) using Symmetric {1}-inverse of Laplacian matrices. We provide examples to illustrate the proposed method and also obtain the Kirchhoff indices for these examples.

Kirchhoff index of a class of polygon networks

The Kirchhoff index is a novel distance-based topological index corresponding to networks, which is the sum of resistance distances between all pairs of nodes. It plays an important role in describing the flow of a network. In this paper, we propose a polygon network model and derive the eigenvalue evolving rule between two generations of the network, and thus obtain the exact Kirchhoff index using the spectral graph theory.

Research on the Siting of Rural Public Cultural Space Based on the Path-Clustering Algorithm: A Case Study of Yumin Township, Yushu City, Jilin Province, China

Cultural revitalization is the foundation of rural revitalization. Rural public cultural spaces are important places for rural residents to participate in cultural activities and important carriers for the occurrence, inheritance and development of rural culture. In this study, we propose a siting analysis method for public cultural spaces based on a path-clustering algorithm. Then, Yumin Township in Jilin Province is used as a case study to test the method. Within the township area, public cultural spaces are divided into three types based on the difference in service scope: “single-village decentralized”, “single-village concentration” and “multi-village concentration”. This paper focuses on the analysis of the siting of the “multi-village concentration” type of public cultural spaces using a path-clustering algorithm. First, the path-clustering algorithm is written, and then its parameters, initial clustering centers and number of clusters are analyzed for their effect on the clustering results. Two parameters, within-cluster sum of path distance (WCSPD) and maximum value of the path distance within-cluster (MPDWC), are proposed to evaluate the results of the algorithm. Then, taking Yumin Township of Jilin Province as an example, the villages in the township are clustered with travel distance as the main influencing factor. It is ensured that the shortest path distance from the central village in each cluster to other villages is no greater than the set travel distance. Finally, the public cultural space is constructed in the central village to serve all villages in the cluster. This siting analysis method can output a variety of results that can be used as a reference for decision making in rural public cultural space planning.

Wiener index and graphs, almost half of whose vertices satisfy Šoltés property

The Wiener index W ( G ) of a connected graph G is a sum of distances between all pairs of vertices of G . In 1991, Šoltés formulated the problem of finding all graphs G such that for every vertex v the equality W ( G ) = W ( G − v ) holds. The cycle C 11 is the only known graph with this property. In this paper we consider the following relaxation of the original problem: find a graph with a large proportion of vertices such that removing any one of them does not change the Wiener index of a graph. As the main result, we build an infinite series of graphs with the proportion of such vertices tending to 1 2 .

Pattern Based Image Retrieval System by Using Clustering Techniques

Nowadays, the image database is growing in enormous size with heterogeneous categories. Similarly, there is rising demands from users in various ways. The most demanding domains in society are health care, Agriculture, commerce, and security. Healthcare domain is concerned with diagnosing the disease. Security domain is involved in investigation of the Criminals. Commerce domain needs analysis to recognize the right product. Agriculture domain requires processing of disease affected fruit images. The PBIR system that combines evidence from multiple digital image domains can reduce those problems of existing image retrieval systems. The PBIR system is used to find uncertain parts of the image during augmentation steps. The result is identified with various parameters (e.g., accuracy, precision, distance, sum of distance), showing that the performance of the k-medoids pam algorithm better than the existing iterative clustering algorithms

Extremal results on stepwise transmission irregular graphs

The transmission TrG(v) of a vertex v of a connected graph G is the sum of distances between v and all other vertices in G. G is a stepwise transmission irregular (STI) graph if |TrG(u) ? TrG(v)| = 1 holds for each edge uv ? E(G). In this paper, extremal results on STI graphs with respect to the size and different metric properties are proved. Two extremal families appear in all the cases, balanced complete bipartite graphs of odd order and the so called odd hatted cycles.

EXACT FORMULA OF DISTANCE SUMS ON SIERPIŃSKI SKELETON NETWORKS

The aim of this paper is to illustrate a strategy for how to get the exact formula of the distance sums of fractal networks (for example, the Sierpiń ski skeleton networks) with the technique of finite pattern [S. Wang, Z. Yu and L. Xi, Average geodesic distance of Sierpinski gasket and Sierpinski networks, Fractals 25(5) (2017) 1750044].