Recently DTW (dynamic time warping) has been recognized as the most robust distance function to measure the similarity between two time series, and this fact has spawned a flurry of research on this topic. Most indexing methods proposed for DTW are based on the R-tree structure. Because of high dimensionality and loose lower bounds for time warping distance, the pruning power of these tree stru...

In this paper we estimated the temperatures and brightnesses of the Monoceros radio loop at 1420, 820 and 408 MHz. Linear spectrum is estimated for mean temperatures versus frequency between 1420, 820 and 408 MHz. The spectral index of Monoceros loop is also obtained. The brightness temperatures and surface brightnesses of the loop are computed using data taken from radio-continuum surveys at t...

The degree distance of a graph G is     , 1 1 1 2 n n i j i i j D G d d L        j , where and i d j d are the degrees of vertices , and is the distance between them. The Wiener index is defined as   , i j v v V G  , i j L   , 1 1 1 2 n n i j i j W G L      . An elegant result (Gutman; Klein, Mihalić,, Plavšić and Trinajstić) is known regarding their correlation, that   ...

Finding shortest distance between two vertices in a graph is an important problem due to its numerous applications in diverse domains, including geo-spatial databases, social network analysis, and information retrieval. Classical algorithms (such as, Dijkstra) solve this problem in polynomial time, but these algorithms cannot provide real-time response for a large number of bursty queries on a ...

In this paper, we present the exact formulae for the multiplicative version of degree distance and the multiplicative version of Gutman index of strong product of graphs in terms of other graph invariants including the Wiener index and Zagreb index. Finally, we apply our results to the multiplicative version of degree distance and the multiplicative version of Gutman index of open and closed fe...

let g be a simple graph. the hosoya polynomial of g is ( , ) ,( , ) = { , } ( ) xd u v h g x  u v v gwhere d(u,v) denotes the distance between vertices u and v . the dendrimer nanostar is apart of a new group of macromolecules. in this paper we compute the hosoya polynomial foran infinite family of dendrimer nanostar. as a consequence we obtain the wiener index andthe hyper-wiener index of th...

The celebrated Gini(-Simpson) biodiversity index has found very useful applications in ecology, bio-environmetrics, econometry, psychometry, genetics, and lately in bioinformatics as well. In such applications, mostly, categorical data models, without possibly an ordering of the categories, crop up, which may preempt routine use of conventional measures of quantitative diversity analysis. Furth...

Given a database, answering a distance-based query means retrieving all the data objects in the database that are in close proximity to a query object. Proximity is defined by any metric distance function. Close can mean within a certain distance, a range query, k-nearest neighbor or the two in combination. Answering distance-based queries is a fundamental component of many biological applicati...

We propose a separability index that quantifies the degree of difficulty in a hard clustering problem under assumptions of a multivariate Gaussian distribution for each cluster. A preliminary index is first defined and several of its properties are explored both theoretically and numerically. Adjustments are then made to this index so that the final refinement is also interpretable in terms of ...

The Randić index R(G) of a graph G is the sum of weights (deg(u) deg(v))−0.5 over all edges uv of G, where deg(v) denotes the degree of a vertex v. We prove that for any tree T with n1 leaves R(T ) ≥ ad(T ) + max(0,n1 − 2), where ad(T ) is the average distance between vertices of T . As a consequence we resolve the conjecture R(G) ≥ ad(G) given by Fajtlowicz in 1988 for the case when G is a tree.