Algorithmic and Hardness Results for the Colorful Components Problems

In this paper we investigate the colorful components framework, motivated by applications emerging from comparative genomics. The general goal is to remove a collection of edges from an undirected vertex-colored graph $G$ such that in the resulting graph $G'$ all the connected components are colorful (i.e., any two vertices of the same color belong to different connected components). We want $G'$ to optimize an objective function, the selection of this function being specific to each problem in the framework. We analyze three objective functions, and thus, three different problems, which are believed to be relevant for the biological applications: minimizing the number of singleton vertices, maximizing the number of edges in the transitive closure, and minimizing the number of connected components. Our main result is a polynomial time algorithm for the first problem. This result disproves the conjecture of Zheng et al. that the problem is $NP$-hard (assuming $P \neq NP$). Then, we show that the second problem is $APX$-hard, thus proving and strengthening the conjecture of Zheng et al. that the problem is $NP$-hard. Finally, we show that the third problem does not admit polynomial time approximation within a factor of $|V|^{1/14 - \epsilon}$ for any $\epsilon > 0$, assuming $P \neq NP$ (or within a factor of $|V|^{1/2 - \epsilon}$, assuming $ZPP \neq NP$).Comment: 18 pages, 3 figure

Effectiveness evaluation of STOL transport operations

A short-takeoff and landing (STOL) systems simulation model has been developed and implemented in a computer code (known as STOL OPS) which permits evaluation of the operation of a STOL aircraft and its avionics in a commercial airline operating environment. STOL OPS concentrated on the avionics functions of navigation, guidance, control, communication, hazard aviodance, and systems management. External world factors influencing the operation of the STOL aircraft include each airport and its geometry, air traffic at each airport, air traffic control equipment and procedures, weather (including winds and visibility), and the flight path between each airport served by the route. The development of the STOL OPS program provides NASA a set of computer programs which can be used for detailed analysis of a STOL aircraft and its avionics and permit establishment of system requirements as a function of airline mission performance goals

Review of the Laguerre-Gauss mode technology research program at Birmingham

Gravitational wave detectors from the advanced generation onwards are expected to be limited in sensitivity by thermal noise of the optics, making the reduction of this noise a key factor in the success of such detectors. A proposed method for reducing the impact of this noise is to use higher-order Laguerre-Gauss (LG) modes for the readout beam, as opposed to the currently used fundamental mode. We present here a synopsis of the research program undertaken by the University of Birmingham into the suitability of LG mode technology for future gravitational wave detectors. This will cover our previous and current work on this topic, from initial simulations and table-top LG mode experiments up to implementation in a prototype scale suspended cavity and high-power laser bench

Experimental demonstration of a suspended diffractively coupled optical cavity

All-reflective optical systems are under consideration for future gravitational wave detector topologies. One approach in proposed designs is to use diffraction gratings as input couplers for Fabry–Perot cavities. We present an experimental demonstration of a fully suspended diffractively coupled cavity and investigate the use of conventional Pound–Drever–Hall length sensing and control techniques to maintain the required operating condition

Antiprotons Annihilation in the Galaxy As A Source of Diffuse Gamma Background

The existence of antimatter domains in baryon asymmetrical Universe can appear as the cosmological consequence of particle theory in inflationary models with non-homogeneous baryosynthesis. Such a domain can survive in the early Universe and form globular cluster of antimatter stars in our Galaxy. The model of antimatter pollution of Galaxy and annihilation with matter gas is developed. The proton-antiproton annihilation gamma flux is shown to reproduce the observed galactic gamma background measured by EGRET. From comparison with observational data the estimation on the maximally allowed amount of antimatter stars, possibly present in our Galaxy, is found.Comment: LaTeX2e, 18 pages, 3 PostScript figures. Submitted to Yad.Fi

Unsteady 1-D thrust modeling with EOS effects for ram accelerator experiments at different bores

Advances made to the unsteady, one-dimensional (1-D) modeling of the thermally choked ram accelerator thrust-Mach number characteristics include the use of real-gas equations of state to account for the compressibility effects of the combustion products. Equations of state based on generalized empirical and theoretical considerations are incorporated into a 1-D computer code to predict the combustion end state equilibrium conditions when the propellant starts out a relatively high fill pressure (>2.5 MPa) and the projectile acceleration exceeds 100 km/s2. The objective of this work is to improve the unsteady 1-D model as a useful tool to predict the thrust of the thermally choked ram accelerator propulsive mode by utilizing key results from the more computationally intensive 2-D or 3-D simulations. New thrust-Mach number calculations compared with experimental data from 25-mm, 30-mm, 38-mm, 90-mm, and 120-mm-bore experiments are generally in good agreement until the point where enhanced accelerations are observed, presumably due to projectile material combustion. The results of this investigation indicate the need for more research on ram accelerator flow fields and the role projectile material may play in the combustion process

Pulse solutions for an extended Klausmeier model with spatially varying coefficients

Analysis and Stochastic