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

The Stellar Initial Mass Function at the Epoch of Reionization

I provide estimates of the ultraviolet and visible light luminosity density at z~6 after accounting for the contribution from faint galaxies below the detection limit of deep Hubble and Spitzer surveys. I find the rest-frame V-band luminosity density is a factor of ~2-3 below the ultraviolet luminosity density at z~6. This implies that the maximal age of the stellar population at z~6, for a Salpeter initial mass function, and a single, passively evolving burst, must be <100 Myr. If the stars in z~6 galaxies are remnants of the star-formation that was responsible for ionizing the intergalactic medium, reionization must have been a brief process that was completed at z<7. This assumes the most current estimates of the clumping factor and escape fraction and a Salpeter slope extending up to 200 M_{\sun} for the stellar initial mass function (IMF; dN/dM \propto M^{\alpha}, \alpha=-2.3). Unless the ratio of the clumping factor to escape fraction is less than 60, a Salpeter slope for the stellar IMF and reionization redshift higher than 7 is ruled out. In order to maintain an ionized intergalactic medium from redshift 9 onwards, the stellar IMF must have a slope of \alpha=-1.65 even if stars as massive as ~200 M_{\sun} are formed. Correspondingly, if the intergalactic medium was ionized from redshift 11 onwards, the IMF must have \alpha~-1.5. The range of stellar mass densities at z~6 straddled by IMFs which result in reionization at z>7 is 1.3+/-0.4\times10^{7} Msun/Mpc^3.Comment: 25 pages, 2 tables, 6 figures, ApJ, in press, v680 n

Global soil moisture bimodality in satellite observations and climate models

A new diagnostic metric based on soil moisture bimodality is developed in order to examine and compare soil moisture from satellite observations and Earth System Models. The methodology to derive this diagnostic is based on maximum likelihood estimator encoded into an iterative algorithm, which is applied to the soil moisture probability density function. This metric is applied to satellite data from the Advanced Microwave Scanning Radiometer for the Earth Observing System and global climate models data from the Coupled Model Intercomparison Project Phase 5 (CMIP5). Results show high soil moisture bimodality in transitional climate areas and high latitudes, potentially associated with land-atmosphere feedback processes. When comparing satellite versus climate models, a clear difference in their soil moisture bimodality is observed, with systematically higher values in the case of CMIP5 models. These differences appear related to areas where land-atmospheric feedback may be overestimated in current climate models

MEAT AND POULTRY PLANTS' FOOD SAFETY INVESTMENTS: SURVEY FINDINGS

Results from the first national survey of the types and amounts of food safety investments made by meat and poultry slaughter and processing plants since the late 1990s provide evidence that market forces have worked in conjunction with regulation to promote the use of more sophisticated food safety technologies. From 1996 through 2000, U.S. plants as a group spent about $380 million annually and made$570 million in long-term investments to comply with USDA's 1996 Pathogen Reduction/Hazard Analysis and Critical Control Point (PR/HACCP) regulation, according to a survey initiated by the Economic Research Service. The U.S. meat and poultry industry as a whole during the same time period spent an additional $360 million on food safety investments that were not required by the PR/HACCP rule. Implementation of the regulation began in 1997 and was mandated by early 2000 in all sizes and types of meat and poultry slaughter and processing plants. The full HACCP surveys referenced in this technical bulletin are available at: http://www.ers.usda.gov/data/haccpsurveyFood Consumption/Nutrition/Food Safety, Livestock Production/Industries,

Exploration of The Duality Between Generalized Geometry and Extraordinary Magnetoresistance

We outline the duality between the extraordinary magnetoresistance (EMR), observed in semiconductor-metal hybrids, and non-symmetric gravity coupled to a diffusive $U(1)$ gauge field. The corresponding gravity theory may be interpreted as the generalized complex geometry of the semi-direct product of the symmetric metric and the antisymmetric Kalb-Ramond field: ($g_{\mu\nu}+\beta_{\mu\nu}$). We construct the four dimensional covariant field theory and compute the resulting equations of motion. The equations encode the most general form of EMR within a well defined variational principle, for specific lower dimensional embedded geometric scenarios. Our formalism also reveals the emergence of additional diffusive pseudo currents for a completely dynamic field theory of EMR. The proposed equations of motion now include terms that induce geometrical deformations in the device geometry in order to optimize the EMR. This bottom-up dual description between EMR and generalized geometry/gravity lends itself to a deeper insight into the EMR effect with the promise of potentially new physical phenomena and properties.Comment: 13 pages and 6 figures. Revised/edited for clarity and purpose. Several references added. Updated title based on suggestions and comments received. Version accepted for publication in Phys.Rev.

Approximately Fair Cost Allocation in Metric Traveling Salesman Games

A traveling salesman game is a cooperative game ${\mathcal{G}}=(N,c_{D})$ . Here N, the set of players, is the set of cities (or the vertices of the complete graph) andc D is the characteristic function where D is the underlying cost matrix. For all S⊆N, define c D (S) to be the cost of a minimum cost Hamiltonian tour through the vertices of S∪{0} where $0\not \in N$ is called as the home city. Define Core ({\mathcal{G}})=\{x\in \Re^{|N|}:x(N)=c_{D}(N)\ \mbox{and}\ \forall S\subseteq N,x(S)\le c_{D}(S)\} as the core of a traveling salesman game ${\mathcal{G}}$ . Okamoto (Discrete Appl. Math. 138:349-369, [2004]) conjectured that for the traveling salesman game ${\mathcal{G}}=(N,c_{D})$ with D satisfying triangle inequality, the problem of testing whether Core $({\mathcal{G}})$ is empty or not is $\mathsf{NP}$ -hard. We prove that this conjecture is true. This result directly implies the $\mathsf{NP}$ -hardness for the general case when D is asymmetric. We also study approximately fair cost allocations for these games. For this, we introduce the cycle cover games and show that the core of a cycle cover game is non-empty by finding a fair cost allocation vector in polynomial time. For a traveling salesman game, let \epsilon\mbox{-Core}({\mathcal{G}})=\{x\in \Re^{|N|}:x(N)\ge c_{D}(N) and ∀ S⊆N, x(S)≤ε⋅c D (S)} be an ε-approximate core, for a given ε>1. By viewing an approximate fair cost allocation vector for this game as a sum of exact fair cost allocation vectors of several related cycle cover games, we provide a polynomial time algorithm demonstrating the non-emptiness of the log 2(|N|−1)-approximate core by exhibiting a vector in this approximate core for the asymmetric traveling salesman game. We improve it further by finding a $(\frac{4}{3}\log_{3}(|N|)+c)$ -approximate core in polynomial time for some constantc. We also show that there exists an ε 0>1 such that it is $\mathsf{NP}$ -hard to decide whether ε 0-Core $({\mathcal{G}})$ is empty or no

Fluxon Dynamics of a Long Josephson Junction with Two-gap Superconductors

We investigate the phase dynamics of a long Josephson junction (LJJ) with two-gap superconductors. In this junction, two channels for tunneling between the adjacent superconductor (S) layers as well as one interband channel within each S layer are available for a Cooper pair. Due to the interplay between the conventional and interband Josephson effects, the LJJ can exhibit unusual phase dynamics. Accounting for excitation of a stable 2$\pi$-phase texture arising from the interband Josephson effect, we find that the critical current between the S layers may become both spatially and temporally modulated. The spatial critical current modulation behaves as either a potential well or barrier, depending on the symmetry of superconducting order parameter, and modifies the Josephson vortex trajectories. We find that these changes in phase dynamics result in emission of electromagnetic waves as the Josephson vortex passes through the region of the 2$\pi$-phase texture. We discuss the effects of this radiation emission on the current-voltage characteristics of the junction.Comment: 14 pages, 6 figure

Use of replication technology in a global software development environment

In this article, we have proposed a new global software development support system. Until now, the technological challenges in global software development support have been addressed on a semi-automatic ad hoc basis by Groupware technologies such aS electronic mail, teleconferencing, electronic meetings, calendaring and scheduling, and workflow. These methods are usefid but do not address the issues of site autonomy, and transactional consistency. Our proposed software development support system is based on replication technology. In our system, each software development center has the ability to make additions and modifications. Further, the system also maintains transactional consistency so all sites have the identical copy of documents in near real-time

Spitzer Observations of the z=2.73 Lensed Lyman Break Galaxy, MS1512-cB58

We present Spitzer infrared (IR) photometry and spectroscopy of the lensed Lyman break galaxy (LBG), MS1512-cB58 at z=2.73. The large (factor ~30) magnification allows for the most detailed infrared study of an L*_UV(z=3) LBG to date. Broadband photometry with IRAC (3-10 micron), IRS (16 micron), and MIPS (24, 70 & 160 micron) was obtained as well as IRS spectroscopy spanning 5.5-35 microns. A fit of stellar population models to the optical/near-IR/IRAC photometry gives a young age (~9 Myr), forming stars at ~98 M_sun/yr, with a total stellar mass of ~10^9 M_sun formed thus far. The existence of an old stellar population with twice the stellar mass can not be ruled out. IR spectral energy distribution fits to the 24 and 70 micron photometry, as well as previously obtained submm/mm, data give an intrinsic IR luminosity L_IR = 1-2 x10^11 L_sun and a star formation rate, SFR ~20-40 M_sun/yr. The UV derived star formation rate (SFR) is ~3-5 times higher than the SFR determined using L_IR or L_Halpha because the red UV spectral slope is significantly over predicting the level of dust extinction. This suggests that the assumed Calzetti starburst obscuration law may not be valid for young LBGs. We detect strong line emission from Polycyclic Aromatic Hydrocarbons (PAHs) at 6.2, 7.7, and 8.6 microns. The line ratios are consistent with ratios observed in both local and high redshift starbursts. Both the PAH and rest-frame 8 micron luminosities predict the total L_IR based on previously measured relations in starbursts. Finally, we do not detect the 3.3 micron PAH feature. This is marginally inconsistent with some PAH emission models, but still consistent with PAH ratios measured in many local star-forming galaxies.Comment: Accepted for publication in ApJ. aastex format, 18 pages, 7 figure