Molecular Hydrogen Kinematics in Cepheus A

We present the radial velocity structure of the molecular hydrogen outflows associated to the star forming region Cepheus A. This structure is derived from doppler shift of the H_2 v=1-0 S(1) emission line obtained by Fabry-Perot spectroscopy. The East and West regions of emission, called Cep A(E) and Cep A(W), show radial velocities in the range -20 to 0 km/s with respect to the molecular cloud. Cep A(W) shows an increasing velocity with position offset from the core indicating the existence of a possible accelarating machanism. Cep A(E) has an almost constant mean radial velocity of -18 km/s along the region although with a large dispersion in velocity, indicating the possibility of a turbulent outflow. A detailed analysis of the Cep A(E) region shows evidence for the presence of a Mach disk on that outflow. Also, we argue that the presence of a velocity gradient in Cep A(W) is indicative of a C-shock in this region. Following Riera et al. (2003), we analyzed the data using wavelet analysis to study the line width and the central radial velocity distributions. We found that both outflows have complex spatial and velocity structures characteristic of a turbulent flow.Comment: 24 pages, 15 figure

On representations of the feasible set in convex optimization

We consider the convex optimization problem $\min \{f(x) : g_j(x)\leq 0, j=1,...,m\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex. We show that for any representation of K that satisfies a mild nondegeneracy assumption, every minimizer is a Karush-Kuhn-Tucker (KKT) point and conversely every KKT point is a minimizer. That is, the KKT optimality conditions are necessary and sufficient as in convex programming where one assumes that the $g_j$ are convex. So in convex optimization, and as far as one is concerned with KKT points, what really matters is the geometry of K and not so much its representation.Comment: to appear in Optimization Letter

A new nascent spreading centre at the Wagner Basin in the northern Gulf of California: a possible geothermal resource?

The probable geothermal reserves of Mexico sum up to only 1400 MW; however, they have been estimated on the basis of the high temperature systems and do not include the unconventional geothermal sources. Submarine hydrothermal systems may become in the near future a feasible energy source, especially those that occur at shallow depths. Recently discovered hydrothermal activity in the Wagner Basin may be harnessed to produce electricity using an environmentally friendly system

Mirror-Descent Methods in Mixed-Integer Convex Optimization

In this paper, we address the problem of minimizing a convex function f over a convex set, with the extra constraint that some variables must be integer. This problem, even when f is a piecewise linear function, is NP-hard. We study an algorithmic approach to this problem, postponing its hardness to the realization of an oracle. If this oracle can be realized in polynomial time, then the problem can be solved in polynomial time as well. For problems with two integer variables, we show that the oracle can be implemented efficiently, that is, in O(ln(B)) approximate minimizations of f over the continuous variables, where B is a known bound on the absolute value of the integer variables.Our algorithm can be adapted to find the second best point of a purely integer convex optimization problem in two dimensions, and more generally its k-th best point. This observation allows us to formulate a finite-time algorithm for mixed-integer convex optimization

Statistically optimal analysis of state-discretized trajectory data from multiple thermodynamic states

We propose a discrete transition-based reweighting analysis method (dTRAM) for analyzing configuration-space-discretized simulation trajectories produced at different thermodynamic states (temperatures, Hamiltonians, etc.) dTRAM provides maximum-likelihood estimates of stationary quantities (probabilities, free energies, expectation values) at any thermodynamic state. In contrast to the weighted histogram analysis method (WHAM), dTRAM does not require data to be sampled from global equilibrium, and can thus produce superior estimates for enhanced sampling data such as parallel/simulated tempering, replica exchange, umbrella sampling, or metadynamics. In addition, dTRAM provides optimal estimates of Markov state models (MSMs) from the discretized state-space trajectories at all thermodynamic states. Under suitable conditions, these MSMs can be used to calculate kinetic quantities (e.g. rates, timescales). In the limit of a single thermodynamic state, dTRAM estimates a maximum likelihood reversible MSM, while in the limit of uncorrelated sampling data, dTRAM is identical to WHAM. dTRAM is thus a generalization to both estimators

A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

International audienceEngineering sciences and applications of mathematics show unambiguously that positive semidefiniteness of matrices is the most important generalization of non-negative real num- bers. This notion of non-negativity for matrices has been well-studied in the literature; it has been the subject of review papers and entire chapters of books. This paper reviews some of the nice, useful properties of positive (semi)definite matrices, and insists in particular on (i) characterizations of positive (semi)definiteness and (ii) the geometrical properties of the set of positive semidefinite matrices. Some properties that turn out to be less well-known have here a special treatment. The use of these properties in optimization, as well as various references to applications, are spread all the way through. The "raison d'être" of this paper is essentially pedagogical; it adopts the viewpoint of variational analysis, shedding new light on the topic. Important, fruitful, and subtle, the positive semidefinite world is a good place to start with this domain of applied mathematics

The SuperMACHO Microlensing Survey

We present the first results from our next-generation microlensing survey, the SuperMACHO project. We are using the CTIO 4m Blanco telescope and the MOSAIC imager to carry out a search for microlensing toward the Large Magellanic Cloud (LMC). We plan to ascertain the nature of the population responsible for the excess microlensing rate seen by the MACHO project. Our observing strategy is optimized to measure the differential microlensing rate across the face of the LMC. We find this derivative to be relatively insensitive to the details of the LMC's internal structure but a strong discriminant between Galactic halo and LMC self lensing. In December 2003 we completed our third year of survey operations. 2003 also marked the first year of real-time microlensing alerts and photometric and spectroscopic followup. We have extracted several dozen microlensing candidates, and we present some preliminary light curves and related information. Similar to the MACHO project, we find SNe behind the LMC to be a significant contaminant - this background has not been completely removed from our current single-color candidate sample. Our follow-up strategy is optimized to discriminate between SNe and true microlensing.Comment: To appear in Proceedings of IAU Symposium 225: Impact of Gravitational Lensing on Cosmology, 6 page

Microbiological Implications of Periurban Agriculture and Water Reuse in Mexico City

BACKGROUND: Recycled treated or untreated wastewater represents an important health challenge in developing countries due to potential water related microbiological exposure. Our aim was to assess water quality and health implications in a Mexico City periurban agricultural area. METHODOLOGY/PRINCIPAL FINDINGS: A longitudinal study in the Xochimilco wetland area was conducted, and 42 sites were randomly selected from 211, including irrigation water canals and effluents of treatment plants. Sample collection took place during rainy and dry seasons (2000-2001). Microbiological parameters (total coliforms, fecal coliforms, streptococci/enterococci, and bacteria other than Vibrio grown on TCBS), Helicobacter pylori, and physicochemical parameters including trihalomethanes (THM) were determined. Fecal coliforms and fecal streptococci are appropriate indicators of human or animal fecal contamination. Fecal coliform counts surpass Mexican and World Health Organization irrigation water guidelines. Identified microorganisms associated with various pathologies in humans and domestic animals comprise Escherichia coli, Klebsiella spp., Salmonella spp., Enterobacter spp., Enterococcus spp., and Pseudomonas spp; H. pylori was also present in the water. An environmental characteristic of the canal system showed high Total Organic Carbon content and relatively low dissolved oxygen concentration; residual chlorine as a disinfection control is not efficient, but THMs do not represent a problem. During the rainy season, temperature and conductivity were higher; in contrast, pH, dissolved oxygen, ammonia, and residual chlorine were lower. This is related with the continuous load of feces from human and animal sources, and to the aquatic systems, which vary seasonally and exhibit evidence of lower water quality in effluents from treatment plants. CONCLUSIONS/SIGNIFICANCE: There is a need for improvement of wastewater treatment systems, as well as more efficient monitoring, regulation, and enforcement procedures for wastewater disposal into bodies of water

A study of the photometric variability of the peculiar magnetic white dwarf WD1953-011

We present and interpret simultaneous new photometric and spectroscopic observations of the peculiar magnetic white dwarf WD1953-011. The flux in the V-band filter and intensity of the Balmer spectral lines demonstrate variability with the rotation period of about 1.45 days. According to previous studies, this variability can be explained by the presence of a dark spot having a magnetic nature, analogous to a sunspot. Motivated by this idea, we examine possible physical relationships between the suggested dark spot and the strong-field magnetic structure (magnetic "spot", or "tube") recently identified on the surface of this star. Comparing the rotationally-modulated flux with the variable spectral observables related to the magnetic "spot" we establish their correlation, and therefore their physical relationship. Modeling the variable photometric flux assuming that it is associated with temperature variations in the stellar photosphere, we argue that the strong-field area and dark, low-temperature spot are comparable in size and located at the same latitudes, essentially overlapping each other with a possible slight longitudinal shift. In this paper we also present a new, improved value of the star's rotational period and constrain the characteristics of the thermal inhomogeneity over the degenerate's surface.Comment: accepted to the Ap

Social welfare and profit maximization from revealed preferences

Consider the seller's problem of finding optimal prices for her $n$ (divisible) goods when faced with a set of $m$ consumers, given that she can only observe their purchased bundles at posted prices, i.e., revealed preferences. We study both social welfare and profit maximization with revealed preferences. Although social welfare maximization is a seemingly non-convex optimization problem in prices, we show that (i) it can be reduced to a dual convex optimization problem in prices, and (ii) the revealed preferences can be interpreted as supergradients of the concave conjugate of valuation, with which subgradients of the dual function can be computed. We thereby obtain a simple subgradient-based algorithm for strongly concave valuations and convex cost, with query complexity $O(m^2/\epsilon^2)$, where $\epsilon$ is the additive difference between the social welfare induced by our algorithm and the optimum social welfare. We also study social welfare maximization under the online setting, specifically the random permutation model, where consumers arrive one-by-one in a random order. For the case where consumer valuations can be arbitrary continuous functions, we propose a price posting mechanism that achieves an expected social welfare up to an additive factor of $O(\sqrt{mn})$ from the maximum social welfare. Finally, for profit maximization (which may be non-convex in simple cases), we give nearly matching upper and lower bounds on the query complexity for separable valuations and cost (i.e., each good can be treated independently)