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.

The Future of Wastewater Monitoring for the Public Health

This Article thus expands the extant literature by considering the legal and ethical dimensions of wastewater surveillance more thoroughly and more broadly. It arrives at an auspicious time, as the United States moves into a vaccine-mediated phase in which COVID-19 is less likely to give rise to broad stay-at-home orders and more likely to trigger narrower, more targeted interventions. It seeks to offer guidance for the legal and ethical use of wastewater surveillance along two dimensions. The first dimension considers the circumstances under which wastewater monitoring should be deployed for detecting and responding to COVID-19 specifically. The second dimension zooms out, to consider whether and how this surveillance infrastructure, largely created in response to the COVID-19 pandemic, might be deployed for other uses, and examines the legal and ethical difficulties that may attend these broader uses

Spitzer Constraints on the z=6.56 Galaxy Lensed by Abell 370

We report on Spitzer IRAC observations of the spectroscopically confirmed z=6.56 lensed Ly-alpha emitting source HCM 6A which was found behind the cluster Abell 370. Detection of the source at 3.6 and 4.5 microns, corresponding to rest-frame optical emission, allows us to study the stellar population of this primeval galaxy. The broadband flux density at 4.5 microns is enhanced compared to the continuum at other wavelengths, likely due to the presence of strong H-alpha in emission. The derived H-alpha line flux corresponds to a star-formation rate of around 140 M_{sun}/yr, more than an order of magnitude larger than estimates from the ultraviolet continuum and Ly-alpha emission line. The dust extinction required to explain the discrepancy is A_V of about 1 mag. The inference of dust at such high redshifts is surprising and implies that the first epoch of star-formation in this galaxy occurred at z~20.Comment: 11 pages, 3 figures, ApJ Letters in pres

DSS Value and Time-Constrained Decision Making

This paper examines an important source of the value of decision support systems (DSS), namely, decision flexibility. It proposes a framework for systematically analyzing, understanding, and possibly quantifying flexibility resulting from the use of DSS in decision situations with time constraints, based on real options theory. The proposed framework is compared with anecdotal evidence of DSS value from the MIS literature. This framework has interesting implications for DSS developmen