Modeling of complex dynamic systems, which are very complicated to establish mathematical models, requires new and modern methodologies that will exploit the existing expert knowledge, human experience and historical data. Fuzzy cognitive maps are very suitable, simple, and powerful tools for simulation and analysis of these kinds of dynamic systems. However, human experts are subjective and ca...

One of the most crucial functions in the operation and control of power system is reactive power dispatch (RPD).A hybrid Big Bang–Big Crunch (HBB–BC) optimization algorithm which consists of A Big Bang– Big Crunch algorithm combined with particle swarm optimization (PSO) is proposed in this paper in order to solve optimal reactive power dispatch (ORPD) problem. The L-index of load buses is base...

In a recent series of papers, we have shown that theories with scalar fields coupled to gravity (e.g., the standard model) can be lifted to a Weyl-invariant equivalent theory in which it is possible to unambiguously trace the classical cosmological evolution through the transition from big crunch to big bang. The key was identifying a sufficient number of finite, Weyl-invariant conserved quanti...

A graph stream, which refers to the graph with edges being updated sequentially in a form of a stream, has important applications in cyber security and social networks. Due to the sheer volume and highly dynamic nature of graph streams, the practical way of handling them is by summarization. Given a graph stream G, directed or undirected, the problem of graph stream summarization is to summariz...

We consider the inverse mean curvature flow in RobertsonWalker spacetimes that satisfy the Einstein equations and have a big crunch singularity and prove that under natural conditions the rescaled inverse mean curvature flow provides a smooth transition from big crunch to big bang. We also construct an example showing that in general the transition flow is only of class C.

Starting from the Janus solution and its gauge theory dual, we obtain the dual gauge theory description of the cosmological solution by the procedure of doubleWick rotation. The coupling is driven either to zero or to infinity at the big-bang and big-crunch singularities, which are shown to be related by the S-duality symmetry. In the dual Yang-Mills theory description, these are non singular a...

Based on concepts drawn from the ekpyrotic scenario and M-theory, we elaborate our recent proposal of a cyclic model of the Universe. In this model, the Universe undergoes an endless sequence of cosmic epochs which begin with the Universe expanding from a ‘big bang’ and end with the Universe contracting to a ‘big crunch.’ Matching from ‘big crunch’ to ‘big bang’ is performed according to the pr...

Big bang/crunch curvature singularities in exact CFT string backgrounds can be removed by turning on gauge fields. This is described within a family of SL(2)×SU(2)×U(1)x U(1)×U(1) quotient CFTs. Uncharged incoming wavefunctions from the “whiskers” of the extended universe can be fully reflected if and only if a big bang/crunch curvature singularity, from which they are scattered, exists. Extend...