Forwarding and optical indices of 4-regular circulant networks

An all-to-all routing in a graph $G$ is a set of oriented paths of $G$, with exactly one path for each ordered pair of vertices. The load of an edge under an all-to-all routing $R$ is the number of times it is used (in either direction) by paths of $R$, and the maximum load of an edge is denoted by $\pi(G,R)$. The edge-forwarding index $\pi(G)$ is the minimum of $\pi(G,R)$ over all possible all-to-all routings $R$, and the arc-forwarding index $\overrightarrow{\pi}(G)$ is defined similarly by taking direction into consideration, where an arc is an ordered pair of adjacent vertices. Denote by $w(G,R)$ the minimum number of colours required to colour the paths of $R$ such that any two paths having an edge in common receive distinct colours. The optical index $w(G)$ is defined to be the minimum of $w(G,R)$ over all possible $R$, and the directed optical index $\overrightarrow{w}(G)$ is defined similarly by requiring that any two paths having an arc in common receive distinct colours. In this paper we obtain lower and upper bounds on these four invariants for $4$-regular circulant graphs with connection set $\{\pm 1,\pm s\}$, $1<s<n/2$. We give approximation algorithms with performance ratio a small constant for the corresponding forwarding index and routing and wavelength assignment problems for some families of $4$-regular circulant graphs.Comment: 19 pages, no figure in Journal of Discrete Algorithms 201

Pair production of neutralinos via photon-photon collisions

We investigated the production of neutralino pairs via photon-photon collisions in the minimal supersymmetric model(MSSM) at future linear colliders. The numerical analysis of their production rates is carried out in the mSUGRA scenario. The results show that this cross section can reach about 18 femto barn for $\tilde{\chi}^{0}_{1} \tilde{\chi}^{0}_{2}$ pair production and 9 femto barn for $\tilde{\chi}^{0}_{2}\tilde{\chi}^{0}_{2}$ pair production with our chosen input parameters.Comment: LaTex File, 3 EPS Files, 17 page

A maximum likelihood estimate of natural mortality for brown tiger prawn (Penaeus esculentus) in Moreton Bay (Australia)

The delay difference model was implemented to fit 21 years of brown tiger prawn (Penaeus esculentus) catch in Moreton Bay by maximum likelihood to assess the status of this stock. Monte Carlo simulations testing of the stock assessment software coded in C++ showed that the model could estimate simultaneously natural mortality in addition to catchability, recruitment and initial biomasses. Applied to logbooks data collected from 1990 to 2010, this implementation of the delay difference provided for the first time an estimate of natural mortality for brown tiger prawn in Moreton Bay, equal to $0.031 \pm 0.002$ week$^{-1}$. This estimate is approximately 30\% lower than the value of natural mortality (0.045 week$^{-1}$) used in previous stock assessments of this species

Electron acceleration by cascading reconnection in the solar corona I Magnetic gradient and curvature effects

Aims: We investigate the electron acceleration in convective electric fields of cascading magnetic reconnection in a flaring solar corona and show the resulting hard X-ray (HXR) radiation spectra caused by Bremsstrahlung for the coronal source. Methods: We perform test particle calculation of electron motions in the framework of a guiding center approximation. The electromagnetic fields and their derivatives along electron trajectories are obtained by linearly interpolating the results of high-resolution adaptive mesh refinement (AMR) MHD simulations of cascading magnetic reconnection. Hard X-ray (HXR) spectra are calculated using an optically thin Bremsstrahlung model. Results: Magnetic gradients and curvatures in cascading reconnection current sheet accelerate electrons: trapped in magnetic islands, precipitating to the chromosphere and ejected into the interplanetary space. The final location of an electron is determined by its initial position, pitch angle and velocity. These initial conditions also influence electron acceleration efficiency. Most of electrons have enhanced perpendicular energy. Trapped electrons are considered to cause the observed bright spots along coronal mass ejection CME-trailing current sheets as well as the flare loop-top HXR emissions.Comment: submitted to A&