Reliability and efficiency of generalized rumor spreading model on complex social networks

We introduce the generalized rumor spreading model and investigate some properties of this model on different complex social networks. Despite pervious rumor models that both the spreader-spreader ($SS$) and the spreader-stifler ($SR$) interactions have the same rate $\alpha$, we define $\alpha^{(1)}$ and $\alpha^{(2)}$ for $SS$ and $SR$ interactions, respectively. The effect of variation of $\alpha^{(1)}$ and $\alpha^{(2)}$ on the final density of stiflers is investigated. Furthermore, the influence of the topological structure of the network in rumor spreading is studied by analyzing the behavior of several global parameters such as reliability and efficiency. Our results show that while networks with homogeneous connectivity patterns reach a higher reliability, scale-free topologies need a less time to reach a steady state with respect the rumor.Comment: 11 pages, 7 figures, Accepted for publication in Communications in Theoretical Physics (CTP). arXiv admin note: text overlap with arXiv:cond-mat/0312131, arXiv:0807.1458, arXiv:physics/0609124 by other author

Topology Explains Why Automobile Sunshades Fold Oddly

We use braids and linking number to explain why automobile shades fold into an odd number of loops.Comment: 8 pages, 9 figure

Linear embeddings of K9K_9 are triple linked

We use the theory of oriented matroids to show that any linear embedding of $K_9$, the complete graph on nine vertices, contains a non-split link with three components.Comment: 7 pages, 1 figure. An updated Mathematica program and five files containing evidence that the program works correctly are available as ancillary files associated with this articl

An Algorithm for Detecting Intrinsically Knotted Graphs

We describe an algorithm that recognizes some (perhaps all) intrinsically knotted (IK) graphs, and can help find knotless embeddings for graphs that are not IK. The algorithm, implemented as a Mathematica program, has already been used by Goldberg, Mattman, and Naimi [6] to greatly expand the list of known minor minimal IK graphs, and to find knotless embeddings for some graphs that had previously resisted attempts to classify them as IK or non-IK.Comment: 9 pages, 4 figure

A Distributed Deadlock Free Quorum Based Algorithm for Mutual Exclusion

Quorum based mutual exclusion algorithms enjoy many advantages such as low message complexity and high failure resiliency. The use of quorums is a well known approach to achieving mutual exclusion in distributed environments. Several distributed based quorum mutual exclusion was presented.Comment: 7 pages, 9 figure

Exact form of Maxwell's equations and Dirac's magnetic monopole in Fock's nonlinear relativity

After having obtained previously an extended first approximation of Maxwell's equations in Fock's nonlinear relativity, we propose here the corresponding exact form. In order to achieve this goal, we were inspired mainly by the special relativistic version of Feynman's proof from which we constructed a formal approach more adapted to the noncommutative algebra. This reasoning lets us establish the exact form of the generalized first group of Maxwell's equations. To deduce the second one, we have imposed the electric-magnetic duality. As in the k-Minkowski space-time, the generalized Lorentz force depends on the mass of the particle. After having restored the R-Lorentz algebra symmetry, we have used the perturbative treatment to find the exact form of the generalized Dirac's magnetic monopole in our context. As consequence, the Universe could locally contain the magnetic charge but in its totality it is still neutral.Comment: 18 pages, 0 figure

On the number of links in a linearly embedded K3,3,1K_{3,3,1}

We show there exists a linear embedding of $K_{3,3,1}$ with n nontrivial 2-component links if and only if n = 1, 2, 3, 4, or 5.Comment: 20 pages, 6 figure

Heat dissipation and its relation to molecular orbital energies in single-molecule junctions

We present a theoretical study of the heat dissipation in single-molecule junctions. In order to investigate the heat dissipation in the electrodes and the relationship between the transmission spectra and the electronic structures, we consider a toy model that in which electrodes linked by a two-level molecular bridge. By using of the Landauer approach, we show how heat dissipation in the electrodes of a molecular junction is related to its transmission characteristics. We show that in general heat is not equally dissipated in the left and right electrodes of the junction and it depends on the bias polarity and the positions of molecule's energy levels with respect to the Fermi level. Also, we exploit the C$_{60}$ molecule as a junction and the results show a good agreement with the toy model. Our results for the heat dissipation are remarkable in the sense that they can be used to detect which energy levels of a junction are dominated in the transport process.Comment: 9 pages, 6 figure

Solvable multi-species reaction-diffusion processes, with particle-dependent hopping rates

By considering the master equation of the totally asymmetric exclusion process on a one-dimensional lattice and using two types of boundary conditions (i.e. interactions), two new families of the multi-species reaction-diffusion processes, with particle-dependent hopping rates, are investigated. In these models (i.e. reaction-diffusion and drop-push systems), we have the case of distinct particles where each particle $A_\alpha$ has its own intrinsic hopping rate $v_{\alpha}$. They also contain the parameters that control the annihilation-diffusion rates (including pair-annihilation and coagulation to the right and left). We obtain two distinct new models. It is shown that these models are exactly solvable in the sense of the Bethe anstaz. The two-particle conditional probabilities and the large-time behavior of such systems are also calculated.Comment: 17 pages, without figur

List Coloring and nn-monophilic graphs

In 1990, Kostochka and Sidorenko proposed studying the smallest number of list-colorings of a graph $G$ among all assignments of lists of a given size $n$ to its vertices. We say a graph $G$ is $n$-monophilic if this number is minimized when identical $n$-color lists are assigned to all vertices of $G$. Kostochka and Sidorenko observed that all chordal graphs are $n$-monophilic for all $n$. Donner (1992) showed that every graph is $n$-monophilic for all sufficiently large $n$. We prove that all cycles are $n$-monophilic for all $n$; we give a complete characterization of 2-monophilic graphs (which turns out to be similar to the characterization of 2-choosable graphs given by Erdos, Rubin, and Taylor in 1980); and for every $n$ we construct a graph that is $n$-choosable but not $n$-monophilic