Competing contact processes in the Watts-Strogatz network

We investigate two competing contact processes on a set of Watts--Strogatz networks with the clustering coefficient tuned by rewiring. The base for network construction is one-dimensional chain of $N$ sites, where each site $i$ is directly linked to nodes labelled as $i\pm 1$ and $i\pm 2$. So initially, each node has the same degree $k_i=4$. The periodic boundary conditions are assumed as well. For each node $i$ the links to sites $i+1$ and $i+2$ are rewired to two randomly selected nodes so far not-connected to node $i$. An increase of the rewiring probability $q$ influences the nodes degree distribution and the network clusterization coefficient $\mathcal{C}$. For given values of rewiring probability $q$ the set $\mathcal{N}(q)=\{\mathcal{N}_1, \mathcal{N}_2, \cdots, \mathcal{N}_M \}$ of $M$ networks is generated. The network's nodes are decorated with spin-like variables $s_i\in\{S,D\}$. During simulation each $S$ node having a $D$-site in its neighbourhood converts this neighbour from $D$ to $S$ state. Conversely, a node in $D$ state having at least one neighbour also in state $D$-state converts all nearest-neighbours of this pair into $D$-state. The latter is realized with probability $p$. We plot the dependence of the nodes $S$ final density $n_S^T$ on initial nodes $S$ fraction $n_S^0$. Then, we construct the surface of the unstable fixed points in $(\mathcal{C}, p, n_S^0)$ space. The system evolves more often toward $n_S^T=1$ for $(\mathcal{C}, p, n_S^0)$ points situated above this surface while starting simulation with $(\mathcal{C}, p, n_S^0)$ parameters situated below this surface leads system to $n_S^T=0$. The points on this surface correspond to such value of initial fraction $n_S^*$ of $S$ nodes (for fixed values $\mathcal{C}$ and $p$) for which their final density is $n_S^T=\frac{1}{2}$.Comment: 5 pages, 5 figure

The human, primate and rabbit ultraviolet action spectra

A 5000 watt xenon-mercury high pressure lamp was used to produce a continuous ultraviolet spectrum. Human and animal exposures were made to establish the photokeratitis threshold and abiotic action spectrum. The lower limit of the abiotic action spectrum was 220 nm while the upper limit was 310 nm. The radiant exposure threshold at 270 nm was 0.005 watts/sq cm for the rabbit, 0.004 watts/sq cm for the primate, and 0.004 watts/ sq cm for the human. The rabbit curve was bi-peaked with minimums at 220 nm, 240 nm and 270 nm. The primate curve was tri-peaked with minimums at 220 nm, 240 nm and 270 nm. The human data showed a rather shallow curve with a minimum at 270 nm. Formulas and calculations are given to predict minimum exposure times for ocular damage to man in outer space, to establish valid safety criteria, and to establish protective design criteria

byron C. Watts v. Ardith D. Watts : Respondent\u27s Brief

Appeal from the Judgment of the Third District Court in and for Salt Lake County, Utah the Honorable D. Frank Wilkins, Judg

D-branes, Orientifolds and K-theory

The complete D-brane spectrum in ZZ[squared] orientifolds is computed. Stable non-BPS D-branes with both integral and torsion charges are found. The relation to K-theory is discussed and a new K-theory relevant to orientifolds is suggested

byron C. Watts v. Ardith D. Watts : Appellant\u27s Brief

Appeal from the Judgment of the Third District Court in and for Salt Lake County, Utah the Honorable D. Frank Wilkins, Judg

Order-disorder phase transition in a cliquey social network

We investigate the network model of community by Watts, Dodds and Newman (D. J. Watts et al., Science 296 (2002) 1302) as a hierarchy of groups, each of 5 individuals. A homophily parameter $\alpha$ controls the probability proportional to $\exp(-\alpha x)$ of selection of neighbours against distance $x$. The network nodes are endowed with spin-like variables $s_i = \pm 1$, with Ising interaction $J>0$. The Glauber dynamics is used to investigate the order-disorder transition. The transition temperature $T_c$ is close to 3.8 for $\alpha < 0.0$ and it falls down to zero above this value. The result provides a mathematical illustration of the social ability to a collective action {\it via} weak ties, as discussed by Granovetter in 1973.Comment: 10 pages, 7 figure

Hermetic-coaxial package design for microwave transistors

Semiconductor package has been developed for high power semiconductor devices that operate in the GHz-frequency range at several watts. Package includes stud, insulating ring, electrically conductive washer, insulating washer, braze ring, and cap. It is mechanically strong and can be used with variety of circuits