Identifying influential nodes in dynamical processes is crucial in understanding network structure and function. Degree, H-index and coreness are widely used metrics, but previously treated as unrelated. Here we show their relation by constructing an operator , in terms of which degree, H-index and coreness are the initial, intermediate and steady states of the sequences, respectively. We obtai...

I derive the set of recurrence relations between the amplitudes of multiparticle production at threshold in the standard large-N limit of the O(N)-symmetric φ 4 theory which sums all relevant diagrams with arbitrary number of loops. I find an exact solution to the recurrence relations using the Gelfand–Diki˘ ı representation of the diagonal resolvent of the Schrödinger operator. The result coin...

We introduce complex cones and associated projective gauges, generalizing a real Birkhoff cone and its Hilbert metric to complex vector spaces. We deduce a variety of spectral gap theorems in complex Banach spaces. We prove a dominated complex cone-contraction Theorem and use it to extend the classical Perron-Frobenius Theorem to complex matrices, Jentzsch’s Theorem to complex integral operator...

Dynamic security analysis is performed to ensure that a power system will survive any recognized contingency and will transfer to a new but acceptable steady-state condition. This article deals with one of the very important dynamic security indices – the critical clearing time. Some of the popular methods of calculating the critical clearing time (CCT) have been reviewed. A more recent method ...

In the present work we investigate the multiscale nature of the correlations for high frequency data (1 min) in different futures markets over a period of two years, starting on the 1st of January 2003 and ending on the 31st of December 2004. In particular, by using the concept of local Hurst exponent, we point out how the behaviour of this parameter, usually considered as a benchmark for persi...

The systematics of indices of physico-chemical properties of codons and amino acids across the genetic code are examined. Using a simple numerical labelling scheme for nucleic acid bases, A=(-1,0), C=(0,-1), G=(0,1), U=(1,0), data can be fitted as low order polynomials of the six coordinates in the 64-dimensional codon weight space. The work confirms and extends the recent studies by Siemion et...

As a data structure, a tree is an optimal presentation of hierarchical objects. Many irregular and dynamical phenomena studied for example in biology, medical sciences, meteorology, and geomorphology can be modelled as a tree. In addition, objects initially modelled as a graph can sometimes be transformed to a tree, say to a minimum spanning tree. This paper presents new techniques for indexing...

The twin concepts of Scaling and Universality have played an important role in the description of statistical systems. Hydrodynamics contains many applications of scaling including descriptions of the behavior of boundary layers (Prandtl, Blasius) and of the fluctuating velocity in turbulent flow (Kolmogorov, Heisenberg, Onsager). Phenomenological theories of behavior near critical points of ph...

Fundamental principles and recent methods for investigating the nonlinear dynamics of legged robot motions with respect to control, stability and design are discussed. One of them is the still challenging problem of producing dynamically stable gaits. The generation of fast walking or running motions require methods and algorithms adept at handling the nonlinear dynamical effects and stability ...

A MATLAB toolbox has been developed to handle the basic problems of discrete event dynamical systems that are modeled by Petri nets. In the Petri Net Toolbox five types of Petri nets (untimed, transition-timed, place-timed, stochastic and generalized stochastic), with finite or infinite capacity, can be used. A user-friendly graphical interface allows activating three simulation modes (accompan...