Next Generation Networks (NGNs) are expected to handle heterogeneous technologies, services, verticals and devices of increasing complexity. It is essential fathom an innovative approach automatically efficiently manage NGNs deliver adequate end-to-end Quality Experience (QoE) while reducing operational expenses. An Autonomous Network (AN) using a closed loop can self-monitor, self-evaluate sel...

An open ribbon is a square with one side called the seam. A closed ribbon is a cylinder with one boundary component called the seam. We sew an open (resp. closed) ribbon onto a graph by identifying the seam with an open (resp. closed) walk in the graph. A ribbon complex is a graph with a nite number of ribbons sewn on. We investigate when a ribbon complex embeds in 3-dimensional Euclidean space...

An oriented walk double covering of a graph G is a set of oriented closed walks which, traversed successively, combined will have traced each edge of G once in each direction. A bidirectional double tracing of a graph G is an oriented walk double covering which consists of a single closed walk. A retracting in a closed walk is the immediate succession of an edge by its inverse. Every graph with...

A word is closed if it contains a proper factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We deal with the sequence of open and closed prefixes of Sturmian words and prove that this sequence characterizes every finite or infinite Sturmian word up to isomorphisms of the alphabet. We then characterize the combinatorial structure of ...

We state a conjecture that relates the derived category of smooth representations $p$ -adic split reductive group with (quasi-)coherent sheaves on stack L-parameters. investigate in case principal block ${\rm GL}_n$ by showing functor should be given tensor product family interpolating modified Langlands correspondence over L-parameters is suggested work Helm and Emerton Helm.