Recoverable DTN Routing based on a Relay of Cyclic Message-Ferries on a MSQ Network

An interrelation between a topological design of network and efficient algorithm on it is important for its applications to communication or transportation systems. In this paper, we propose a design principle for a reliable routing in a store-carry-forward manner based on autonomously moving message-ferries on a special structure of fractal-like network, which consists of a self-similar tiling of equilateral triangles. As a collective adaptive mechanism, the routing is realized by a relay of cyclic message-ferries corresponded to a concatenation of the triangle cycles and using some good properties of the network structure. It is recoverable for local accidents in the hierarchical network structure. Moreover, the design principle is theoretically supported with a calculation method for the optimal service rates of message-ferries derived from a tandem queue model for stochastic processes on a chain of edges in the network. These results obtained from a combination of complex network science and computer science will be useful for developing a resilient network system.Comment: 6 pages, 12 figures, The 3rd Workshop on the FoCAS(Fundamentals of Collective Adaptive Systems) at The 9th IEEE International Conference on SASO(Self-Adaptive and Self-Organizing systems), Boston, USA, Sept.21, 201

Forbidden Subgraphs in Connected Graphs

Given a set $\xi=\{H_1,H_2,...\}$ of connected non acyclic graphs, a $\xi$-free graph is one which does not contain any member of $$ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let {\gr{W}}_{k,\xi} be theexponential generating function (EGF for brief) of connected $\xi$-free graphs of excess equal to $k$ ($k \geq 1$). For each fixed $\xi$, a fundamental differential recurrence satisfied by the EGFs {\gr{W}}_{k,\xi} is derived. We give methods on how to solve this nonlinear recurrence for the first few values of $k$ by means of graph surgery. We also show that for any finite collection $\xi$ of non-acyclic graphs, the EGFs {\gr{W}}_{k,\xi} are always rational functions of the generating function, $T$, of Cayley's rooted (non-planar) labelled trees. From this, we prove that almost all connected graphs with $n$ nodes and $n+k$ edges are $\xi$-free, whenever $k=o(n^{1/3})$ and $|\xi| < \infty$ by means of Wright's inequalities and saddle point method. Limiting distributions are derived for sparse connected $\xi$-free components that are present when a random graph on $n$ nodes has approximately $\frac{n}{2}$ edges. In particular, the probability distribution that it consists of trees, unicyclic components, $...$, $(q+1)$-cyclic components all $\xi$-free is derived. Similar results are also obtained for multigraphs, which are graphs where self-loops and multiple-edges are allowed

Geometric Phase of Three-level Systems in Interferometry

We present the first scheme for producing and measuring an Abelian geometric phase shift in a three-level system where states are invariant under a non-Abelian group. In contrast to existing experiments and proposals for experiments, based on U(1)-invariant states, our scheme geodesically evolves U(2)-invariant states in a four-dimensional SU(3)/U(2) space and is physically realized via a three-channel optical interferometer.Comment: 4 pages, 3 figure

Effect of base–acid properties of the mixtures of water with methanol on the solution enthalpy of selected cyclic ethers in this mixture at 298.15 K

The enthalpies of solution of cyclic ethers: 1,4- dioxane, 12-crown-4 and 18-crown-6 in the mixture of water and methanol have been measured within the whole mole fraction range at T = 298.15 K. Based on the obtained data, the effect of base–acid properties of water– methanol mixtures on the solution enthalpy of cyclic ethers in these mixtures has been analyzed. The solution enthalpy of cyclic ethers depends on acid properties of water– methanol mixtures in the range of high and medium water contents in the mixture. Based on the analysis performed, it can be assumed that in the mixtures of high methanol contents, cyclic ethe