Measuring the slopes of mass profiles for dwarf spheroidals in triaxial CDM potentials

We generate stellar distribution functions (DFs) in triaxial haloes in order to examine the reliability of slopes $\Gamma\equiv \Delta {\rm log} M / \Delta {\rm log} r$ inferred by applying mass estimators of the form $M\propto R_e\sigma^2$ (i.e. assuming spherical symmetry, where $R_e$ and $\sigma$ are luminous effective radius and global velocity dispersion, respectively) to two stellar sub-populations independently tracing the same gravitational potential. The DFs take the form $f(E)$, are dynamically stable, and are generated within triaxial potentials corresponding directly to subhaloes formed in cosmological dark-matter-only simulations of Milky Way and galaxy cluster haloes. Additionally, we consider the effect of different tracer number density profiles (cuspy and cored) on the inferred slopes of mass profiles. For the isotropic DFs considered here, we find that halo triaxiality tends to introduce an anti-correlation between $R_e$ and $\sigma$ when estimated for a variety of viewing angles. The net effect is a negligible contribution to the systematic error associated with the slope of the mass profile, which continues to be dominated by a bias toward greater overestimation of masses for more-concentrated tracer populations. We demonstrate that simple mass estimates for two distinct tracer populations can give reliable (and cosmologically meaningful) lower limits for $\Gamma$, irrespective of the degree of triaxiality or shape of the tracer number density profile.Comment: 5 pages, 4 figures, submitted to MNRA

Approximation Algorithms for Generalized MST and TSP in Grid Clusters

We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell is $1 \times 1$. In the MST version of the problem, the goal is to find a minimum tree that contains exactly one point from each non-empty grid cell (cluster). Similarly, in the TSP version of the problem, the goal is to find a minimum weight cycle containing one point from each non-empty grid cell. We give a $(1+4\sqrt{2}+\epsilon)$ and $(1.5+8\sqrt{2}+\epsilon)$-approximation algorithm for these two problems in the described setting, respectively. Our motivation is based on the problem posed in [7] for a constant approximation algorithm. The authors designed a PTAS for the more special case of the GMST where non-empty cells are connected end dense enough. However, their algorithm heavily relies on this connectivity restriction and is unpractical. Our results develop the topic further

Locating Depots for Capacitated Vehicle Routing

We study a location-routing problem in the context of capacitated vehicle routing. The input is a set of demand locations in a metric space and a fleet of k vehicles each of capacity Q. The objective is to locate k depots, one for each vehicle, and compute routes for the vehicles so that all demands are satisfied and the total cost is minimized. Our main result is a constant-factor approximation algorithm for this problem. To achieve this result, we reduce to the k-median-forest problem, which generalizes both k-median and minimum spanning tree, and which might be of independent interest. We give a (3+c)-approximation algorithm for k-median-forest, which leads to a (12+c)-approximation algorithm for the above location-routing problem, for any constant c>0. The algorithm for k-median-forest is just t-swap local search, and we prove that it has locality gap 3+2/t; this generalizes the corresponding result known for k-median. Finally we consider the "non-uniform" k-median-forest problem which has different cost functions for the MST and k-median parts. We show that the locality gap for this problem is unbounded even under multi-swaps, which contrasts with the uniform case. Nevertheless, we obtain a constant-factor approximation algorithm, using an LP based approach.Comment: 12 pages, 1 figur

Space disposal of nuclear wastes. Volume 1: Socio-political aspects

The history and interpretation of radioactive waste management in the U.S., criteria for choosing from various options for waste disposal, and the impact of nuclear power growth from 1975 to 2000 are discussed. Preconditions for the existence of high level wastes in a form suitable for space disposal are explored. The role of the NASA space shuttle program in the space disposal of nuclear wastes, and the impact on program management, resources and regulation are examined

ASP, The Art and Science of Practice: Academia-Industry Interfacing in Operations Research in Montreal

This paper reports on the 40-year experience of academia-industry interfacing in the operations research (OR) field in Montréal. We focus on five spin off companies that academic entrepreneurs from the CIRRELT and the GERAD created between 1976 and 2003: INRO Consultants, GIRO, AD OPT, Omega Optimisation/Planora, and ExPretio. The importance of university spin offs for knowledge transfer is well documented in fields such as biology and nanotechnology; however, few papers have studied university spin offs in OR. Yet, OR has an enormous impact on society, and university spin off firms play a key role in the diffusion of research to the world of practitioners. In this paper, we tell the story of five companies created by academics from two world-renowned OR research centers based in Montréal, and we derive lessons about academia-industry interfacing in the OR field. By so doing, we hope to improve our understanding of the creation of fruitful relationships between academics and OR practitioners

A real delivery problem dealt with Monte Carlo techniques

[EN] In this paper we use Monte Carlo Techniques to deal with a real world delivery problem of a food company in Valencia (Spain). The problem is modeled as a set of 11 instances of the well known Vehicle Routing Problem, VRP, with additional time constraints. Given that VRP is a NP-hard problem, a heuristic algorithm, based on Monte Carlo techniques, is implemented. The solution proposed by this heuristic algorithm reaches distance and money savings of about 20% and 5% respectively.This research was partially supported by MICINN, Project MTM2013-43540-P and by UPV, Project Programa de Apoyo a la Investigación y Desarrollo de la UPV PAID-06-12.S577181Fernández de Córdoba, P., L.M. García-Raffi and J.M. Sanchis Llopis (1998), A heuristic algorithm based on Monte Carlo methods for the Rural Postman Problem.Computers and Op. Research,25, No. 12, pp. 1097–1106, 1998.Fernández de Córdoba, P. and L.M. García-Raffi, E. Nieto and J.M. Sanchis Llopis (1999a), Aplicación de técnicas Monte Carlo a un problema real de Rutas de Vehículos.Anales de Ingeniería, Colombia. In press.Fernández de Córdoba, P., L.M. García-Raffi and J.M. Sanchis Llopis (1999b), A Constructive Parallel Algorithm based on Monte Carlo techniques for Routing Problems, Submitted toParallel Computers.Laporte, G. (1992), The Vehicle Routing Problem: an overview of exact and approximate algorithms,European Journal of Operations Research,59, 345.Laporte, G., M. Desrochers and Y. Nobert (1985), “Optimal Routing under Capacity and Distance Restrictions.Operations Research,33, pp. 1050–1073.Laporte G. and Y. Nobert (1987), Exact algorithms for The Vehicle Routing Problem,Surveys in Combinatorial Optimization (S. Martello, G. Laporte, M. Minoux and C. Ribeiro Eds.). North-HollandAmsterdamMayado, A. (1998), Organización de los itinerarios de la flota de camiones de reparto de una sociedad cooperativa. Optimización mediante técnicas de simulación Monte Carlo. Proyecto Fin de Carrera. E.T.S.I.I. Universidad Politécnica de Valencia

Lin-Kernighan Heuristic Adaptations for the Generalized Traveling Salesman Problem

The Lin-Kernighan heuristic is known to be one of the most successful heuristics for the Traveling Salesman Problem (TSP). It has also proven its efficiency in application to some other problems. In this paper we discuss possible adaptations of TSP heuristics for the Generalized Traveling Salesman Problem (GTSP) and focus on the case of the Lin-Kernighan algorithm. At first, we provide an easy-to-understand description of the original Lin-Kernighan heuristic. Then we propose several adaptations, both trivial and complicated. Finally, we conduct a fair competition between all the variations of the Lin-Kernighan adaptation and some other GTSP heuristics. It appears that our adaptation of the Lin-Kernighan algorithm for the GTSP reproduces the success of the original heuristic. Different variations of our adaptation outperform all other heuristics in a wide range of trade-offs between solution quality and running time, making Lin-Kernighan the state-of-the-art GTSP local search.Comment: 25 page

Weber's Mixed Boundary‐Value Problem in Electrodynamics

Electrodynamics problems with mixed boundary values promise to assume increasing practical importance in fields such as plasma physics. A new method of attacking such problems in three dimensions is presented and discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69922/2/JMAPAQ-8-3-518-1.pd

A robust enhancement to the Clarke-Wright savings algorithm

We address the Clarke and Wright (CW) savings algorithm proposed for the Capacitated Vehicle Routing Problem (CVRP). We first consider a recent enhancement which uses the put first larger items idea originally proposed for the bin packing problem and show that the conflicting idea of putting smaller items first has a comparable performance. Next, we propose a robust enhancement to the CW savings formulation. The proposed formulation is normalized to efficiently solve different problems, independent from the measurement units and parameter intervals. To test the performance of the proposed savings function, we conduct an extensive computational study on a large set of well-known instances from the literature. Our results show that the proposed savings function provides shorter distances in the majority of the instances and the average performance is significantly better than previously presented enhancements

A spectroscopic search for AGN activity in the reionization era

The ubiquity of Lyman alpha (Ly$\alpha$) emission in a sample of four bright [O III]-strong star-forming galaxies with redshifts above 7 has led to the suggestion that such luminous sources represent a distinct population compared to their fainter, more numerous, counterparts. The presence of Ly$\alpha$ emission within the reionization era could indicate that these sources created early ionized bubbles due to their unusually strong radiation, possibly due to the presence of active galactic nuclei. To test this hypothesis we have secured long integration spectra with XSHOOTER on the VLT for three $z\simeq$7 sources selected to have similar luminosities and prominent excess fluxes in the IRAC 3.6 or 4.5$\mu$m band, usually attributed to strong [O III] emission. We secured additional spectroscopy for one of these galaxies at $z$=7.15 using MOSFIRE at the Keck telescope. For this, the most well-studied source in our sample with the strongest IRAC excess, we detect prominent nebular emission from He II and NV indicative of a non-thermal source. For the other two sources at $z$=6.81 and $z$=6.85, for which no previous optical/near infrared spectroscopy was initially available, Ly$\alpha$ is seen in one and CIII] emission in the other. Although a modest sample, our results further support the hypothesis that the phenomenon of intense [O III] emission is associated preferentially with sources lying in early ionized bubbles. However, even though one of our sources at $z$=7.15 clearly indicates the presence of non-thermal radiation, such ionized bubbles may not uniquely arise in this manner. We discuss the unique advantages of extending such challenging diagnostic studies with JWST.Comment: 11 pages, 7 figures, submitted to Ap