Let K be a connected Lie group of compact type and let W(K ) denote the set of continuous paths in K, starting at the identity and with time-interval [0, 1]. Then W(K ) forms an infinite-dimensional group under the operation of pointwise multiplication. Let \ denote the Wiener measure on W(K ). We construct an analog of the Segal Bargmann transform for W(K ). Let KC be the complexification of K...

Quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies use statistical models to compute physical, chemical, or biological properties of a chemical substance from its molecular structure, encoded in a numerical form with the aid of various descriptors. Structural indices derived from molecular graph matrices represent an important gro...

Let (B be the cr-field of Borel sets of C. Let (0, Ct, P ) be some probability space and W be the Wiener measure on (C, <£) with the corresponding Wiener process { W t ( o ) ) : 0 S t ^ l } , coGO; that is Wt has values in C and is specified by E(Wt)=0 and E(W.Wt)=s ifs^t. Let W° be the Gaussian measure on (C, (B) constructed by setting WÏ = Wt—tWi. Then W°tEC, E ( W ? ) = 0 and E(W^TF?) 5 ( 1 ...

Complex networks abound in physical, biological and social sciences. Quantifying a network's topological structure facilitates network exploration and analysis, and network comparison, clustering and classification. A number of Wiener type indices have recently been incorporated as distance-based descriptors of complex networks, such as the R package QuACN. Wiener type indices are known to depe...