Intersection Of Neighborhoods Research Articles

The RBF-PU Method for Solving 2D Nonlocal Diffusion and Peridynamic Equations

The radial basis function partition of unity (RBF-PU) method  was applied to obtain the numerical solution of 2D nonlocal diffusion and peridynamic problems. The main idea is to partition the original domain into several patches, use the RBF approximation on each local domain, and then give weighting to obtain the global approximation of the unknown function. The radial basis function method based on the strong form of the equation has many advantages, such as avoiding an additional layer of integral calculation, no need to deal with intersections of neighborhoods with the mesh, and easiness of implementation. The numerical results show that, this method can solve nonlocal diffusion equations and peridynamic equations accurately and efficiently.

Rough set models in a more general manner with applications

<abstract><p>Several tools have been put forth to handle the problem of uncertain knowledge. Pawlak (1982) initiated the concept of rough set theory, which is a completely new tool for solving imprecision and vagueness (uncertainty). The main notions in this theory are the upper and lower approximations. One of the most important aims of this theory is to reduce the vagueness of a concept to uncertainty areas at their borders by decreasing the upper approximations and increasing the lower approximations. So, the object of this study is to propose four types of approximation spaces in rough set theory utilizing ideals and a new type of neighborhoods called "the intersection of maximal right and left neighborhoods". We investigate the master properties of the proposed approximation spaces and demonstrate that these spaces reduce boundary regions and improve accuracy measures. A comparative study of the present methods and the previous ones is given and shown that the current study is more general and accurate. The importance of the current paper is not only that it is introducing new kinds of approximation spaces relying mainly on ideals and a new type of neighborhoods which increases the accuracy measure and reduces the boundary region of subsets, but also that these approximation spaces are monotonic, which means that it can be successfully used to evaluate the uncertainty in the data. In the end of this paper, we provide a medical example of the heart attacks problem to show the efficiency of the current techniques in terms of approximation operators, accuracy measures, and monotonic property.</p></abstract>

Locally H-closed Spaces, Subspaces and Their Extensions

The primary goal is to characterize Locally H-closed spaces (LHC), by conditions on the remainders of their extensions. These spaces are also characterized using subspaces and their extensions as well. Characterizing these classes of spaces using the remainders of the subspaces in their extensions provide characterizations of them in terms of their boundaries. Recently, the authors have proved that these results give necessary and sufficient conditions for the space to be compact A number of equivalences are proved for Hausdorff (Urysohn) [regular] spaces. These results lead to similar characterizations of Locally Urysohn-closed (LUC) as well as Locally regular-closed (LRC) spaces. Some of these equivalent properties generalize a number of existing results on these topics. In the present article it is shown that if X is a Hausdorff LHC space then each closed set is an intersection of regularly open sets as well as each closed set is an intersection of semi-closed neighborhoods. In 1969 Porter and Thomas had shown that in a Hausdorff space a locally H-closed subspace is the intersection of an open set and a closed set. In this article, it is shown that a space X is LHC if and only if every nonempty proper regularly closed subset of X is LHC.

Sociodemographic and Built Environment Associates of Travel to School by Car among New Zealand Adolescents: Meta-Analysis

Travelling to school by car diminishes opportunities for physical activity and contributes to traffic congestion and associated noise and air pollution. This meta-analysis examined sociodemographic characteristics and built environment associates of travelling to school by car compared to using active transport among New Zealand (NZ) adolescents. Four NZ studies (2163 adolescents) provided data on participants’ mode of travel to school, individual and school sociodemographic characteristics, distance to school and home-neighbourhood built-environment features. A one-step meta-analysis using individual participant data was performed in SAS. A final multivariable model was developed using stepwise logistic regression. Overall, 60.6% of participants travelled to school by car. When compared with active transport, travelling to school by car was positively associated with distance to school. Participants residing in neighbourhoods with high intersection density and attending medium deprivation schools were less likely to travel to school by car compared with their counterparts. Distance to school, school level deprivation and low home neighbourhood intersection density are associated with higher likelihood of car travel to school compared with active transport among NZ adolescents. Comprehensive interventions focusing on both social and built environment factors are needed to reduce car travel to school.

Active Transport to School and School Neighbourhood Built Environment across Urbanisation Settings in Otago, New Zealand.

The school neighbourhood built environment (BE) can facilitate active transport to school (ATS) in adolescents. Most previous studies examining ATS were conducted in large urban centres and focused on BE of home neighbourhoods. This study examined correlations between school-level ATS rates among adolescents, objectively measured school neighbourhood BE features, and adolescents’ perceptions of the school route across different urbanisation settings. Adolescents (n = 1260; 15.2 ± 1.4 years; 43.6% male) were recruited from 23 high schools located in large, medium, and small urban areas, and rural settings in Otago, New Zealand. Adolescents completed an online survey. School neighbourhood BE features were analysed using Geographic Information Systems. School neighbourhood intersection density, residential density and walkability index were higher in large urban areas compared to other urbanisation settings. School-level ATS rates (mean 38.1%; range: 27.8%–43.9%) were negatively correlated with school neighbourhood intersection density (r = −0.58), residential density (r = −0.60), and walkability index (r = −0.64; all p < 0.01). School-level ATS rates were also negatively associated with adolescents’ perceived safety concerns for walking (r = −0.76) and cycling (r = −0.78) to school, high traffic volume (r = −0.82), and presence of dangerous intersections (r = −0.75; all p < 0.01). Future initiatives to encourage ATS should focus on school neighbourhood BE features and minimise adolescents’ traffic safety related concerns.

Road network intersection density and childhood obesity risk in the US: a national longitudinal study

ObjectivesRoad intersection density is an important indicator of walkability. The objectives of this study were to examine the trends in intersection density in the US from 2007 to 2011 and assess the associations between intersection density and childhood obesity risk at the state level. Study designLongitudinal analyses were conducted to assess the spatial-temporal changes of population-weighted intersection density in relation to the risk of childhood obesity in the US. MethodsRoad network data from the Topologically Integrated Geographic Encoding and Referencing (TIGER) (2007–2011), the prevalence of overweight and obesity data from the National Survey of Children's Health (NSCH) (2007–2011), and the American Community Survey (ACS) (2011) were used. Geographic information system (GIS) visualization and spatial and regression analyses were conducted. Mixed-effect models were fit to assess the longitudinal relationship between intersection density and childhood obesity. ResultsBetween 2007 and 2011, population-weighted intersection density remained relatively stable in most states. Low-intersection-density states were clustered in the Southeastern region in both 2007 and 2011. The high-intersection-density states were clustered in the Middle Atlantic Division. California and Nevada also were identified as high-intersection-density clusters in 2011. States with lower road intersection density corresponded with states with higher childhood obesity prevalence. Our mixed-effect model estimates suggested that increased intersection density was associated with decreased obesity prevalence. ConclusionsThis study provided empirical evidence for longitudinal associations between neighborhood intersection density and childhood obesity prevalence based on national data and offered a new perspective of the role that road network plays in childhood obesity prevention.

Attribute reducts of multi-granulation information system

In recent years, more and more methods and theories of multi-granulation information systems have been explored. However, there is very limited investigation on the attribute reducts of multi-granulation rough sets. Therefore, the main objective of this paper is to draw attention to the attribute reducts of multi-granulation information system. For any subset of information system, we usually characterize it by its upper and lower approximations. In order to calculate the upper and lower approximations faster, we must reduce the redundant information of the information system. According to the preceding analysis, we first introduce three types of attribute reduct, which are called arbitrary union reduct, neighborhood union reduct and neighborhood intersection reduct, respectively. Then many basic and important results of these reducts are deeply explored. In order to apply the theories of attribute reducts to deal with practical issues, we develop three algorithms so as to compute multi-granulation upper and lower approximations. Next, we further study the interrelationships among these attribute reducts. Finally, we present a multi-granulation information system with respect to thirty students’ exam scores and calculate the corresponding attribute reducts by using the algorithms listed in the paper.

Classes of structures and their generic limits

We consider an influence of potential structures for diagrams in generic constructions to their topological limits. The structures for intersections of neighborhoods and cardinalities of these intersections are defined.

Neighborhood walkability and particulate air pollution in a nationwide cohort of women

BackgroundFeatures of neighborhoods associated with walkability (i.e., connectivity, accessibility, and density) may also be correlated with levels of ambient air pollution, which would attenuate the health benefits of walkability. ObjectivesWe examined the relationship between neighborhood walkability and ambient air pollution in a cross-sectional analysis of a cohort study spanning the entire United States using residence-level exposure assessment for ambient air pollution and the built environment. MethodsUsing data from the Nurses’ Health Study, we used linear regression to estimate the association between a neighborhood walkability index, combining neighborhood intersection count, business count, and population density (defined from Census data, infoUSA business data, and StreetMap USA data), and air pollution, defined from a GIS-based spatiotemporal PM2.5 model. ResultsAfter adjustment for Census tract median income, median home value, and percent with no high school education, the highest tertile of walkability index, intersection count, business count, and population density was associated with a with 1.58 (95% CI 1.54, 1.62), 1.20 (95% CI 1.16, 1.24), 1.31 (95% CI 1.27, 1.35), and 1.84 (95% CI 1.80, 1.88)µg/m3 higher level of PM2.5 respectively, compared to the lowest tertile. Results varied somewhat by neighborhood socioeconomic status and greatly by region. ConclusionsThis nationwide analysis showed a positive relationship between neighborhood walkability and modeled air pollution levels, which were consistent after adjustment for neighborhood-level socioeconomic status. Regional differences in the air pollution-walkability relationship demonstrate that there are factors that vary from region to region that allow for walkable neighborhoods with low levels of air pollution.

A sufficient condition involving implicit degree and neighborhood intersection for long cycles

Let id(v) denote the implicit degree of a vertex v in a graph G. In this paper, we prove that: Let G be a 2-connected graph. If max⁡{id(u),id(v)}≥c/2 for each pair of nonadjacent vertices u and v in an induced claw, and |N(x)∩N(y)|≥2 for each pair of nonadjacent vertices x and y in an induced modified claw, then G contains either a hamiltonian cycle or a cycle of length at least c.

Degree and neighborhood intersection conditions restricted to induced subgraphs ensuring Hamiltonicity of graphs

Let claw be the graph K1,3. A graph G on n ≥ 3 vertices is called o-heavy if each induced claw of G has a pair of end-vertices with degree sum at least n, and called 1-heavy if at least one end-vertex of each induced claw of G has degree at least n/2. In this note, we show that every 2-connected o-heavy or 3-connected 1-heavy graph is Hamiltonian if we restrict Fan-type degree condition or neighborhood intersection condition to certain pairs of vertices in some small induced subgraphs of the graph. Our results improve or extend previous results of Broersma et al., Chen et al., Fan, Goodman and Hedetniemi, Gould and Jacobson, and Shi on the existence of Hamilton cycles in graphs.

A Unified Definition of Consistent Functions

In recent years, homomorphisms have been exploited to compare the structures and properties of two generalized information systems. Some of these homomorphisms are based on consistent functions, which are a class of special mappings between universal sets. The purpose of this paper is to unify and extend the consistent functions in the literature into the framework of neighborhood systems. After introducing the notion of consistent functions with respect to neighborhood systems, we explore some important properties of the extended consistent functions such as preserving the inverse images and the intersections of neighborhoods. Our results provide a sound basis for further investigating neighborhood systems via homomorphisms.

Determining Leaders and Communities on Networks Using Neighborhood Similarity

Networks are used to represent interactions in a wide variety of fields, like biology, sociology, chemistry, and more. They have a great deal of salient information contained in their structures, which have a variety of applications. One of the important topics of network analysis is finding influential nodes. These nodes are of two kinds —leader nodes and bridge nodes. In this study, we propose an algorithm to find strong leaders in a network based on a revision of neighborhood similarity. This leadership detection is combined with a neighborhood intersection clustering algorithm to produce high quality communities for various networks. We also delve into the structure of a new network, the Houghton College Twitter network, and examine the discovered leaders and their respective followers in more depth than which is frequently attempted for a network of its size. The results of the observations on this and other networks demonstrate that the community partitions found by this algorithm are very similar to those of ground truth communities.

On graphs in which the intersection of neighborhoods of vertices from every 3-coclique is a clique

On graphs in which the intersection of neighborhoods of vertices from every 3-coclique is a clique

A comparison of two kinds of definitions of rough approximations based on a similarity relation

In the present paper, we investigate the three types of Yao’s lower and upper approximations of any set with respect to any similarity relation. These types based on a right neighborhood. Also, we define and investigate other three types of approximations for any similarity relations. These new types based on the intersection of the right neighborhoods. Moreover, we give a comparison between these types. Lastly, the relationship between these definitions is introduced.

Independence Number, Neighborhood Intersection and Hamiltonian Properties

Let G be a 2-connected simple graph of order n with the independence number\alpha. We show here that \forall u; v \in V (G)\backslash\{u,v\} and any z \in \{u,v\}; w \in V (G)\backslash \{u,v\}; with d(w; z) = 2, if |N(u) \ cap N(w)| \geq \alpha - 1 or |N(v) \cap N(w)| \geq \alpha - 1, then G is Hamiltonian, unless G belongs to a kind of special graphs.

Digital Khalimsky Manifolds

We consider different possibilities to define digital manifolds that are locally homeomorphic to Khalimsky n-space. We prove existence and non-existence of certain types of Khalimsky manifolds. An embedding theorem is proved. We introduce the join operator and use it to analyze the structure of adjacency neighborhoods and of intersections of neighborhoods in ℤ n .

Comparison between different kinds of approximations by using a family of binary relations

In this paper, we discuss three types of lower and upper approximations of any set with respect to any relation based on right neighborhood. We generalize these three types of approximations into two ways by using a finite number of any binary relations. The first way based on the intersection of the right neighborhoods for a family of binary relations, the second based on the union and intersection of lower and upper approximations of a set according to a family of binary relations { R i : i = 1 , 2 , … , n } . Also, we make a comparison between these types in tables.

Terwilliger graphs with μ ≤ 3

A Terwilliger graph is a noncomplete graph in which the intersection of the neighborhoods of any two vertices at distance 2 from each other is a μ-clique. We classify connected Terwilliger graphs with μ = 3 and describe the structure of Terwilliger graphs of diameter 2 with μ = 2.

Neighborhood intersections and Hamiltonicity in almost claw-free graphs

Let G be a graph. The partially square graph G ∗ of G is a graph obtained from G by adding edges uv satisfying the conditions uv∉ E( G), and there is some w∈ N( u)∩ N( v), such that N( w)⊆ N( u)∪ N( v)∪{ u, v}. Let t>1 be an integer and Y⊆ V( G), denote n(Y)=|{v∈V(G) | min y∈Y{ dist G(v,y)}⩽2}|, I t(G)={Z | Z is an independent set of G,| Z|= t}. In this paper, we show that a k-connected almost claw-free graph with k⩾2 is hamiltonian if ∑ z∈ Z d( z)⩾ n( Z)− k in G for each Z∈I k+1(G ∗) , thereby solving a conjecture proposed by Broersma, Ryjác̆ek and Schiermeyer. Zhang's result is also generalized by the new result.