Extended Lorenz majorization and frequencies of distances in an undirected network

Purpose:To contribute to the study of networks and graphs.Design/methodology/approach:We apply standard mathematical thinking.Findings:We show that the distance distribution in an undirected network Lorenz majorizes the one of a chain.As a consequence,the average and median distances in any such network are smaller than or equal to those of a chain.Research limitations:We restricted our investigations to undirected,unweighted networks.Practical implications:We are convinced that these results are useful in the study of small worlds and the so-called six degrees of separation property.Originality/value:To the best of our knowledge our research contains new network results,especially those related to frequencies of distances.

VECTORIAL EKELAND'S VARIATIONAL PRINCIPLE WITH A W-DISTANCE AND ITS EQUIVALENT THEOREMS

By using the properties of w-distances and Gerstewitz＇s functions, we first give a vectorial Takahashi＇s nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland＇s variational principle, where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value. From the general vectorial variational principle, we deduce a vectorial Caristfs fixed point theorem with a w-distance. Finally we show that the above three theorems are equivalent to each other. The related known results are generalized and improved. In particular, some conditions in the theorems of [Y. Araya, Ekeland＇s variational principle and its equivalent theorems in vector optimization, J. Math. Anal. Appl. 346（2008）, 9-16] are weakened or even completely relieved.

Computing All Pairs Shortest Paths on Sparse Graphs with Articulation Points

In most network analysis tools the computation of the shortest paths between all pairs of nodes is a fundamental step to the discovery of other properties. Among other properties is the computation of closeness centrality, a measure of the nodes that shows how central a vertex is on a given network. In this paper, the authors present a method to compute the All Pairs Shortest Paths on graphs that present two characteristics： abundance of nodes with degree value one, and existence of articulation points along the graph. These characteristics are present in many real life networks especially in networks that show a power law degree distribution as is the case of biological networks. The authors＇ method compacts the single nodes to their source, and then by using the network articulation points it disconnects the network and computes the shortest paths in the biconnected components. At the final step the authors proposed methods merges the results to provide the whole network shortest paths. The authors＇ method achieves remarkable speedup compared to state of the art methods to compute the shortest paths, as much as 7 fold speed up in artificial graphs and 3.25 fold speed up in real application graphs. The authors＇ performance improvement is unlike previous research as it does not involve elaborated setups since the authors algorithm can process significant instances on a popular workstation.

An Identity and Its Applications Concerning Two Mass-points Systems

In this paper, we first give and prove a geometric identity for distance between any point and mass-points of two mass-points systems in n-dimensional Euclidean space Rn.As its application, we obtain an equality for two mass-points systems and its radius of the circumscribed sphere and an inequality for distance between mass-points of two mass-points systems and its k-dimensional volume.

Common Fixed Point Theorems for Commuting Maps on a Complete Metric Space

The concept of w distance on a metric space is introduced and three common fixed points theorems for commuting maps on a complete metric space are proved. These results extended fixed point theorems of Jungck and Ciric.

The Fermat-Torricelli problem on surfaces

In this note a simple proof of the famous Fermat-Torricelli problem is given. For the vertices of a given triangle, Fermat asks for a fourth point such that the sum of its Euclidean distances to the three given points is minimized. Many authors present geometric approaches to the Fermat-Torricelli problem. We solve the problem by analytic and geometrical method and extend it to the sphere, we also characterize the median point P on the general regular surface.

Method to reconnoiter pulse amplitude train for phased array radar based on Hausdorff distance

This paper presents a method to estimate beam pointing of phased array radar by the pulse amplitude train, which is significant in radar electronic reconnaissance and electronic support measure. Firstly, the antenna patterns modeling of the phased array system is exploited to build the radar sweeping model and the signal propagation model. Secondly, the relationship between the variation of the radiated power and the antenna beam pointing angles in the given airspace is analyzed. Based on the above two points, the sample with obvious amplitude characteristics of the pulse amplitude train can be screened out after detecting the train peaks. Finally, the sample is matched to the subsequent pulse amplitude train based on the Hausdorff distance. The proposed methods have less prior knowledge and higher efficiency and are easier to process. By cross correlating the sample of the pulse amplitude train with the sample data of the antenna follow-up radiation, the probability of detection of the beam pointing direction becomes larger in case that the subsequent antenna beam returns to the specific position.

Fixed Point Results by Altering Distances in Fuzzy Metric Spaces

We establish fixed point theorems in complete fuzzy metric space by using notion of altering distance, initiated by Khan et al. [Bull. Austral. Math. Soc. 30 (1984), 1-9]. Also, we find an affirmative answer in fuzzy metric space to the problem of Sastry [TamkangJ. Math., 31(3) (2000), 243-250].

Effect of lens focusing distance on laser-induced silicon plasmas at different sample temperatures

We investigated the dependence of laser-induced breakdown spectral intensity on the focusing position of a lens at different sample temperatures(room temperature to 300 ℃) in atmosphere.A Q-switched Nd:YAG nanosecond pulsed laser with 1064 nm wavelength and 10 ns pulse width was used to ablate silicon to produce plasma. It was confirmed that the increase in the sample's initial temperature could improve spectral line intensity. In addition, when the distance from the target surface to the focal point increased, the intensity firstly rose, and then dropped.The trend of change with distance was more obvious at higher sample temperatures. By observing the distribution of the normalized ratio of Si atomic spectral line intensity and Si ionic spectral line intensity as functions of distance and temperature, the maximum value of normalized ratio appeared at the longer distance as the initial temperature was higher, while the maximum ratio appeared at the shorter distance as the sample temperature was lower.

Design Criterion for Fixture Layout Based on the State Space Model in M ultistation Assembly Processes

The fixture layout is crucial to assure the product quality in a multistation assembly process （MAP）. A well-designed fixture layout will make the final product＇s variability be insensitive to the fixture variation inputs. As the basis of the fixture layout design, the design criterion plays an important role in the effectiveness of a solution and the optimization efficiency. In this paper, an effective and efficient design criterion is proposed for the fixture layout with a fixed reference point （FRP） in an MAP. First of all, a state space model for the individual port＇s variation propagation and accumulation is developed, which is the mathematical foundation of the proposed criterion. Then, based on this model, a novel design criterion used to evaluate the performance of the fixture layout is proposed for the fixture layout with an FRP. Finally, a method extracted from the proposed design criterion is developed for quick fixture layout design. A four-station assembly process is used to validate the effectiveness and efficiency of the proposed models and methods.

Common Fixed Point Results for Quasi-contractions Involving Altering Distance Functions in Ordered Cone Metric Spaces

Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.

Mathematical modeling for selecting center locations for medical and health supplies reserve in Hainan Province

Objective:To explore how to choose the center locations to build the medical and health supplies reserve among many island towns.Methods:The center locations were selected from 18 towns Hainan Province,it's maximum service range(distance)was required to reach the minimum,or to minimize.Results:Three scenarios were considered,the center locations included only one town,two towns,three towns.By the use of graph theory and MATLAB programming,a mathematical model was established to obtain the shortest distance and the shortest path between arbitrary two towns.Conclusions:We find out the center sites under certain conditions,and determine the specific service ranges of the center sites.

Research on Distance Judgement Method from Point to Line to Generate a Line

Regarding the problem that the traditional straight-line generating has a low accuracy, we study straightline generating with the distance of point to line. We explore generating a line to approximate the ideal line and the issue is to pick out the pixel point of approximating the ideal line. The paper plays a significant scientific role in elucidating linear optimization norm and it lays a foundation for showing a straight line. The algorithm is valuable for computer graphics.

Certain Fixed Point Theorems and Application to the Fractal Space

In this paper, we present some important generalizations of the Banach contraction principle, in which the Lipschitz constant k is replaced by some real- valued control function. For the applications to the fractal space, we obtain the fixed point theorem of the some generalized contraction in the space of fractals.

Population assessment and habitat associations of the Visayan Hornbill(Penelopides panini)in Northwest Panay,Philippines

Background:Seven out of ten hornbill species in the Philippines are threatened with extinction.Among these is the endangered Visayan Hornbill(Penelopides panini),found on the islands of Panay and Negros.Threatened by habitat loss and hunting,its population size is thought to have declined from 1800 individuals 20 years ago to less than 1000.However,a recent study on Negros estimated 3564 individuals across three core forest blocks.This study aims to quantify the Visayan Hornbill population size in and around the Northwest Panay Peninsula Natural Park(NWPPNP)on Panay,the largest contiguous low-elevation forest landscape remaining across its range,and its broad habitat associations across a gradient of environmental degradation.Methods:Hornbills were surveyed using 10-min distance sampling point counts(n=367)along transects(average length 1.1 km).Environmental variables were recorded along transects,while habitat was classified into primary forest,secondary forest,plantation,or open habitat.Distance software was used to estimate population densities stratified by habitat,with the overall population estimate taken as a mean of habitat density estimates weighted by habitat area.Using generalized linear mixed models,hornbill occurrence was modelled using combinations of nine environmental variables as main and two-way fixed effects.Results:Surveys covered 204.4 km^(2) of the 374.8 km^(2) Northwest Panay Peninsula.Hornbills were not recorded in plantations or open habitats.Hornbill density was significantly higher in primary forest(17.8 individuals/km~2±26.9%CV)than in secondary forest(3.7 individuals/km^(2)±33.2%CV;z=15.212,P<0.001).The overall population estimate for the NWPPNP and environs is 2109 individuals,and 2673 individuals for the entire Northwest Panay Peninsula.Hornbill presence was best explained by a model including distance from the Park boundary alongside five interaction effects and transect as a random effect.Distance,and the interaction between distance and medium-sized trees were significant predictors of hornbill presence.Conclusions:Our study evidences the habitat preference of the Visayan Hornbill,highlights the importance of the NWPPNP for the species'conservation,and provides strong evidence for re-assessing the global population size.

Distribution of Deviation Distance to Alternative Fuel Stations

This paper derives the distribution of the deviation distance to visit an alternative fuel station. Distance is measured as the Euclidean distance on a continuous plane. The distribution explicitly considers the vehicle range and whether the round trip between origin and destination can be made. Three cases are examined: fuel is available at both origin and destination, fuel is available at either origin or destination, and fuel is available at neither origin nor destination. The analytical expressions for the distribution demonstrate how the vehicle range, the shortest distance, and the refueling availability at origin and destination affect the deviation distance. The distribution will thus be useful to estimate the number of vehicles refueled at a station.

A plotless density estimator with a Norton-Rice distribution for ordered distances

A Norton-Rice distribution(NRD)is a versatile,flexible distribution for k ordered distances from a random location to the k nearest objects.In a context of plotless density estimation(PDE)with n randomly chosen sample locations,and distances measured to the k=6 nearest objects,the NRD provided a good fit to distance data from seven populations with a census of forest tree stem locations.More importantly,the three parameters of a NRD followed a simple trend with the order(1,…,6)of observed distances.The trend is quantified and exploited in a proposed new PDE through a joint maximum likelihood estimation of the NRD parameters expressed as a functions of distance order.In simulated probability sampling from the seven populations,the proposed PDE had the lowest overall bias with a good performance potential when compared to three alternative PDEs.However,absolute bias increased by 0.8 percentage points when sample size decreased from 20 to 10.In terms of root mean squared error(RMSE),the new proposed estimator was at par with an estimator published in Ecology when this study was wrapping up,but otherwise superior to the remaining two investigated PDEs.Coverage of nominal 95%confidence intervals averaged 0.94 for the new proposed estimators and 0.90,0.96,and 0.90 for the comparison PDEs.Despite tangible improvements in PDEs over the last decades,a globally least biased PDE remains elusive.

Finding Starting Points for Tracing Surface Intersections

To find starting points for all the intersection curves, one of the surfaces is subdivided into some small surface patches. Based on a correlative algorithm of computing the minimum distance of two surfaces, the intersections of every patch with another surface are detected, and starting points are calculated by dichotomy. This algorithm shows superior efficiency in the computational complexity and number of iterations needed. It can be used to determine exact starting points on all possible solution curves between any kinds of parametric sculptured surfaces.

远距离和遮挡下三维目标检测算法研究

针对现有三维目标检测算法对存在遮挡及距离较远目标检测效果差的问题,以基于点云的三维目标检测算法(3D object proposal generation and detection from point cloud,PointRCNN)为基础,对网络进行改进,提高三维目标检测精度。对区域生成网络(region proposal network,RPN)获取的提议区域(region of interest,ROI)体素化处理,同时构建不同尺度的区域金字塔来捕获更加广泛的兴趣点;加入点云Transformer模块来增强对网格中心点局部特征的学习;在网络中加入球查询半径预测模块,使得模型可以根据点云密度自适应调整球查询的范围。最后,对所提算法的有效性进行了试验验证,在KITTI数据集下对模型的性能进行评估测试,同时设计相应的消融试验验证模型中各模块的有效性。

基于邻域点聚合和全连接残差特征的分片隐式曲面学习网络

针对形状全局表面隐式场学习的点云曲面重建中通常缺乏形状表面局部细节的问题,采用基于面片的分片表示并训练三维形状的局部符号距离场,提出一种基于邻域点聚合和全连接残差特征的分片隐式曲面学习网络.以离散点云数据为输入,首先采用最远点采样策略得到表征形状球形面片的初始中心位置和半径;然后分别计算每个面片内各采样点相对面片中心的偏移值,并将其作为采样点的相对位置,其中,处于重叠区域内的面片采样点具有多个相对位置;在神经网络编码器中,利用邻域点聚合模块将各相对坐标编码为256维隐向量,以提取相邻采样点的特征信息,并对每个形状面片中的采样点隐向量进行最大化操作,以表征该面片的隐特征;在神经网络解码器中,利用多层全连接残差特征解码模块进行解码,得到各采样点相对位置的形状符号距离值,而对位于不同面片重叠区域内采样点的符号距离值进行加权求和,得到其相应的符号距离值;最后利用Marching Cube算法提取采样点符号距离值的零等值面,得到三维形状网格模型.在ShapeNet,ABC和Famous这3个数据集上的实验结果表明,所提网络在有效地重建形状整体结构的同时,能很好地保持其形状表面细节;在ShapeNet数据集上,IoU指标为83.9,CD指标为0.032,取得了比DeepSDF、占用网络和卷积占用网络更好的重建结果.