It has often been argued (e.g., Frank, 1992) that distance is sufficient to describe proximity concepts denoted by linguistic expressions such as near, close, far. However, how can we explain that an ant which is 20 m away from a high rise building is considered to be far away from ...
Out convention for drawing the diagrams will be to assume the edges round each vertex labelled so that 1 is denoted by either “straight through” or “turn right”. 1 2 d d d d a d d d 2 d1 d 2 2 s d s d © a d 1 d1 ...
The cutoff distance dc that is denoted by dround(m×tcutoff) is determined, where round represents a function that rounds the value m×tcutoff to the nearest integer, and tcutoff is a cutoff index that is set to 1.5% here; (d) The local density ρi(i=1,2,…,n) with the formula...
It is often denoted using units such as meters, kilometers, feet, miles, or yards, depending on the system of measurement that is being used. Distance is an essential concept in physics, mathematics, engineering, geography, and many other fields, as it helps to describe the location or ...
For a fixed B-spline fitting curve P (t), the Euclidean distance from data point X k to P (t) is denoted by dk = P (tk) − X k , where P (tk) is the foot point of X k on P (t). Then, for evaluating the approximation error, we defi...
where the infimum is among all bivariate probability measures \(\pi \in {\mathcal {P}}(\Xi \times {{\tilde{\Xi }}})\). The optimal value of (2.1), the nested distance of order r, is denoted by \({\varvec{d}}^r({\mathbb {P}},\tilde{{\mathbb {P}}})\). For discrete...
fromGby assigning a direction to each edge. We often denote an orientation ofGbyG→. We say that an orientation isstrongif there is a path from every vertex to every other vertex inG→. Theoriented diameterofGis the smallest diameter among all strong orientations ofGand is denoted bydiam→...
Thetotalvariationdistance,denotedby∆(P,Q)(andsometimesby P−Q TV ),ishalf theabovequantity.Itisaneasyexercisetocheckthat ∆(P,Q)=max S⊆[n] |P(S)−Q(S)|.(12.1.1) Becauseoftheaboveequality,thisisalsoreferredtoasthestatisticaldistance. Takingthe 1 normofthedifferencemadesensebec...
The weighted Minkowski metric is a variation of the metric that allows us to assign weights to each element of the vector. We do this by creating a vector of weights in Rn, denoted by (w1,w2,…,wn). The weighted Minkowski metric is then in Eq. (2.8): (2.8)dp(x,y)=∑i=1nwi...
The minimum cardinality of a distance two-dominating set in G is called a distance two-domination number and is denoted by γ 2 ( G ). In this note we obtain various upper bounds for γ 2 ( G ) and characterize the classes of graphs attaining these bounds....