# The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one interval case Returns $I(p_2$ in $N_{CS}(p_1,t,c))$ for points $p_1$ and $p_2$, that is, returns 1 if $p_2$ is in $N_{CS}(p_1,t,c)$, returns 0 otherwise, where $N_{CS}(x,t,c)$ is the CS proximity region for point $x$ with expansion parameter $t>0$ and centrality parameter $c \in (0,1)$. CS proximity region is constructed with respect to the interval $(a,b)$. This function works whether $p_1$ and $p_2$ are inside or outside the interval `int`. Vertex regions for middle intervals are based on the center associated with the centrality parameter $c \in (0,1)$. If $p_1$ and $p_2$ are identical, then it returns 1 regardless of their locations (i.e., loops are allowed in the digraph). See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:revstat-2016;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r IarcCSint(p1, p2, int, t, c = 0.5) ``` ## Arguments - `p1`: A 1D point for which the proximity region is constructed. - `p2`: A 1D point for which it is checked whether it resides in the proximity region of $p_1$ or not. - `int`: A `vector` of two real numbers representing an interval. - `t`: A positive real number which serves as the expansion parameter in CS proximity region. - `c`: A positive real number in $(0,1)$ parameterizing the center inside `int`$=(a,b)$ with the default `c=.5`. For the interval, `int`$=(a,b)$, the parameterized center is $M_c=a+c(b-a)$. ## Returns $I(p_2$ in $N_{CS}(p_1,t,c))$ for p2, that is, returns 1 if $p_2$ in $N_{CS}(p_1,t,c)$, returns 0 otherwise ## Examples ```r c<-.4 t<-2 a<-0; b<-10; int<-c(a,b) IarcCSint(7,5,int,t,c) IarcCSint(17,17,int,t,c) IarcCSint(15,17,int,t,c) IarcCSint(1,3,int,t,c) IarcCSint(-17,17,int,t,c) IarcCSint(3,5,int,t,c) IarcCSint(3,3,int,t,c) IarcCSint(4,5,int,t,c) IarcCSint(a,5,int,t,c) c<-.4 r<-2 a<-0; b<-10; int<-c(a,b) IarcCSint(7,5,int,t,c) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `IarcCSmid.int`, `IarcCSend.int` and `IarcPEint` ## Author(s) Elvan Ceyhan

IarcCSint function