Approximation Algorithms for Multi-Criteria Traveling Salesman Problems

In multi-criteria optimization problems, several objective functions have to be optimized. Since the different objective functions are usually in conflict with each other, one cannot consider only one particular solution as the optimal solution. Instead, the aim is to compute a so-called Pareto curve of solutions. Since Pareto curves cannot be computed efficiently in general, we have to be content with approximations to them. We design a deterministic polynomial-time algorithm for multi-criteria g-metric STSP that computes (min{1 +g, 2g^2/(2g^2 -2g +1)} + eps)-approximate Pareto curves for all 1/2<=g<=1. In particular, we obtain a (2+eps)-approximation for multi-criteria metric STSP. We also present two randomized approximation algorithms for multi-criteria g-metric STSP that achieve approximation ratios of (2g^3 +2g^2)/(3g^2 -2g +1) + eps and (1 +g)/(1 +3g -4g^2) + eps, respectively. Moreover, we present randomized approximation algorithms for multi-criteria g-metric ATSP (ratio 1/2 + g^3/(1 -3g^2) + eps) for g < 1/sqrt(3)), STSP with weights 1 and 2 (ratio 4/3) and ATSP with weights 1 and 2 (ratio 3/2). To do this, we design randomized approximation schemes for multi-criteria cycle cover and graph factor problems.Comment: To appear in Algorithmica. A preliminary version has been presented at the 4th Workshop on Approximation and Online Algorithms (WAOA 2006

A Statistical Semi-Empirical Model: Satellite galaxies in Groups and Clusters

We present STEEL a STatistical sEmi-Empirical modeL designed to probe the distribution of satellite galaxies in groups and clusters. Our fast statistical methodology relies on tracing the abundances of central and satellite haloes via their mass functions at all cosmic epochs with virtually no limitation on cosmic volume and mass resolution. From mean halo accretion histories and subhalo mass functions the satellite mass function is progressively built in time via abundance matching techniques constrained by number densities of centrals in the local Universe. By enforcing dynamical merging timescales as predicted by high-resolution N-body simulations, we obtain satellite distributions as a function of stellar mass and halo mass consistent with current data. We show that stellar stripping, star formation, and quenching play all a secondary role in setting the number densities of massive satellites above $M_*\gtrsim 3\times 10^{10}\, M_{\odot}$. We further show that observed star formation rates used in our empirical model over predict low-mass satellites below $M_*\lesssim 3\times 10^{10}\, M_{\odot}$, whereas, star formation rates derived from a continuity equation approach yield the correct abundances similar to previous results for centrals.Comment: 21 pages, 17 Figures. MNRAS, in pres

Thermodynamics and kinetics of reactions in protective coating systems

A study of the aluminization of Ni from packs containing various percentages of unalloyed Al confirmed that the surface aluminum content of specimens aluminized tends to decrease with time and consequently a simple parabolic law for the weight-gain vs. time relationship is not obeyed. The diffusivity-composition relationship in NiAl was examined, and a set of curves is presented. A numerical method for the calculation of coating dissolution rates was developed and applied to NiAl-Ni3Al type of coatings

A Study of Different Modeling Choices For Simulating Platelets Within the Immersed Boundary Method

The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid-structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmitting information (forces and velocities) between these two representations. Most IB simulations represent their structures with piecewise-linear approximations and utilize Hookean spring models to approximate structural forces. Our specific motivation is the modeling of platelets in hemodynamic flows. In this paper, we study two alternative representations - radial basis functions (RBFs) and Fourier-based (trigonometric polynomials and spherical harmonics) representations - for the modeling of platelets in two and three dimensions within the IB framework, and compare our results with the traditional piecewise-linear approximation methodology. For different representative shapes, we examine the geometric modeling errors (position and normal vectors), force computation errors, and computational cost and provide an engineering trade-off strategy for when and why one might select to employ these different representations.Comment: 33 pages, 17 figures, Accepted (in press) by APNU

Passive wireless antenna sensor for strain, temperature, crack and fatigue measurement

An apparatus and method is provided for monitoring a condition of a structure using a passive wireless antenna sensor having a known resonant frequency when mounted on the structure. A series of radio frequency signals are transmitted with sweeping frequencies around the known resonant frequency to the passive wireless antenna sensor. The passive wireless antenna sensor includes a dielectric substrate disposed between an antenna pattern and a ground plane such that a change in the condition of the structure will cause a change in one or more characteristics of the passive wireless sensor. A signal is received from the passive wireless antenna sensor and a resonant frequency of the passive wireless antenna sensor is determined based on the received signal. The determined resonant frequency is then compared to the known resonant frequency, whereby a change in the resonant frequency indicates a change in the condition of the structure.Board of Regents, University of Texas Syste

Practical Network Coding in Sensor Networks: Quo Vadis?

Abstract. Network coding is a novel concept for improving network ca-pacity. This additional capacity may be used to increase throughput or reliability. Also in wireless networks, network coding has been proposed as a method for improving communication. We present our experience from two studies of applying network coding in realistic wireless sen-sor networks scenarios. As we show, network coding is not as useful in practical deployments as earlier theoretical work suggested. We discuss limitations and future opportunities for network coding in sensor net-works. 1 Network Coding in Wireless Sensor Networks Network Coding was introduced by Ahlswede et al. [1], proving that it can in-crease multicast capacity. Since then, it has been investigated in several different networked scenarios which demand different traffic characteristics. Most previous research has focused on theoretical aspects of applying network coding to sensor networks. There are, however, also more practical examples of applying networ

Non destructive inspection of plates using frequency measurements

This paper examines the use of natural frequency measurements and energy formulation of vibration theory to detect damage present in a structure. The extent of change in natural frequencies of the structure due to damage, which is highly dependent on the location and size of damage, is used to detect and characterise damage. An analytical solution to detect and characterise damage in plates from just change in natural frequencies is presented here for the first time. Damage is modelled as a spring with finite stiffness which is less than that of the undamaged structure. Using the strain energies stored in the plate and that of spring, calculated from discrete values of deflection mode shapes, the location and size of the damage is determined. The applicability of this approach is demonstrated through a numerical study, where the location and size of through thickness centre cracks in simply supported plates is deduced with greater than 95 percent accuracy