The kth power of a graph G, denoted by Gk , is a graph with the same vertex set as G such that two vertices are adjacent in Gk if and only if their distance is at most k in G. The Wiener index is a distance-based topological index defined as the sum of distances between all pairs of vertices in a graph. In this note, we give the bounds on the Wiener index of the graph Gk . The Nordhaus–Gaddum-t...

A new method for continuous focusing on dynamic images is described. The focusing is based on a sharpness criterion. The criterion which is most robust for static images is shown to be Tenengrad criterion, which maximizes the high frequency contents in the image. In order to apply the method on real-time image sequences, stabilization of the input image and the edge width criterion which evalua...

Architectural Morphology: Investigative modeling and spatial analysis. Research workshop, KTH School of Architecture, May 14 2013. Ed. Daniel Koch, Pablo Miranda Carranza. The workshop is part of the project RIBS that has received funding from the European Union Seventh Framework Programme (FP7/20072013) under grant agreement number 242497. © Copyright by the authors, this specific layout the a...

Lech WOSINSKI1,3*, Xu SUN1,3, Lars THYLEN2,3,4 1 School of Information and Communication Technology, KTH Royal Institute of Technology, 164 40, Kista, Sweden 2 Dept. of Theoretical Chemistry and Biology, KTH Royal Institute of Technology, 106 91 Stockholm, Sweden 3 JORCEP, Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University (China). 4 Hewlett...

We study the persistent homology of random Čech complexes. Generalizing a method of Penrose for studying random geometric graphs, we first describe an appropriate theoretical framework in which we can state and address our main questions. Then we define the kth persistent Betti number of a random Čech complex and determine its asymptotic order in the subcritical regime. This extends a result of...

#Electrical, Electronic & Computer Engineering The University of Southern Queensland Toowoomba, Queensland 4350, Australia [email protected] Abstract In a real world bilevel decision-making, the lower level of a bilevel decision usually involves multiple decision units. This paper proposes the Kth-best approach for linear bilevel multifollower programming problems with shared variables among fol...

Symmetries of the auto-cumulant function (the generalization of the auto-covariance function) of a kth-order stationary time series are derived through a connection with the symmetric group of degree k. Using theory of group representations, symmetries of the auto-cumulant function are demystified and lag-window functions are symmetrized to satisfy these symmetries. A generalized Gabr-Rao optim...

Inequalities on reaction time distribution functions for parallel processing models with an unlimited capacity assumption are presented, extending previous work on first-terminating and exhaustive stopping rules to kth-terminating processes. This extension thus generates predictions for situations in which the observer’s response is determined by the kth-terminating subprocess. Moreover, method...