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

Probing Cosmic Dawn: Modelling the Assembly History, SEDs, and Dust Content of Selected z∼9z\sim9 Galaxies

The presence of spectroscopically confirmed Balmer breaks in galaxy spectral energy distributions (SEDs) at $z>9$ provides one of the best probes of the assembly history of the first generations of stars in our Universe. Recent observations of the gravitationally lensed source, MACS 1149_JD1 (JD1), indicate that significant amounts of star formation likely occurred at redshifts as high as $z\simeq15$. The inferred stellar mass, dust mass, and assembly history of JD1, or any other galaxy at these redshifts that exhibits a strong Balmer break, can provide a strong test of our best theoretical models from high-resolution cosmological simulations. In this work, we present the results from a cosmological radiation-hydrodynamics simulation of the region surrounding a massive Lyman-break galaxy. For two of our most massive systems, we show that dust preferentially resides in the vicinity of the young stars thereby increasing the strength of the measured Balmer break such that the simulated SEDs are consistent with the photometry of JD1 and two other $z>9$ systems (GN-z10-3 and GN-z9-1) that have proposed Balmer breaks at high redshift. We find strong variations in the shape and luminosity of the SEDs of galaxies with nearly identical stellar and halo masses, indicating the importance of morphology, assembly history, and dust distribution in making inferences on the properties of individual galaxies at high redshifts. Our results stress the importance that dust may play in modulating the observable properties of galaxies, even at the extreme redshifts of $z>9$.Comment: 16 pages, 13 Figures, Accepted to MNRA

Interactions of technology and society: Impacts of improved airtransport. A study of airports at the grass roots

The feasibility of applying a particular conception of technology and social change to specific examples of technological development was investigated. The social and economic effects of improved airport capabilities on rural communities were examined. Factors which led to the successful implementation of a plan to construct sixty small airports in Ohio are explored and implications derived for forming public policies, evaluating air transportation development, and assessing technology

Fluorescent C II* 1335A emission spectroscopically resolved in a galaxy at z = 5.754

We report the discovery of the first spectroscopically resolved C II /C II* 1334, 1335A doublet in the Lyman-break galaxy J0215-0555 at z = 5.754. The separation of the resonant and fluorescent emission channels was possible thanks to the large redshift of the source and long integration time, as well as the small velocity width of the feature, 0.6 +- 0.2A. We model this emission and find that at least two components are required to reproduce the combination of morphologies of C II* emission, C II absorption and emission, and Lyman-alpha emission from the object. We suggest that the close alignment between the fluorescence and Lyman-alpha emission could indicate an ionisation escape channel within the object. While the faintness of such a C II /C II* doublet makes it prohibitively difficult to pursue for similar systems with current facilities, we suggest it can become a valuable porosity diagnostic in the era of JWST and the upcoming generations of ELTs.Comment: 5 pages, 3 figures; accepted for publication in MNRAS Letter

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

Effect of rainfall patterns on soil surface CO(2 )efflux, soil moisture, soil temperature and plant growth in a grassland ecosystem of northern Ontario, Canada: implications for climate change

BACKGROUND: The effect of rainfall patterns on soil surface CO(2 )efflux, soil moisture, soil temperature and plant growth was investigated in a grassland ecosystem of northern Ontario, Canada, where climatic change is predicted to introduce new precipitation regimes. Rain shelters were established in a fallow field consisting mainly of Trifolium hybridum L., Trifolium pratense L., and Phleum pratense L. Daytime ambient air temperatures within the shelters increased by an average of 1.9°C similar to predicted future increases in air temperatures for this region. To simulate six precipitation regimes which cover the maximum range to be expected under climate change, a portable irrigation system was designed to modify the frequency of monthly rainfall events with a constant delivery rate of water, while maintaining contemporary average precipitation volumes. Controls consisted of blocks irrigated with frequencies and total monthly precipitation consistent with the 25 year average rainfall for this location. RESULTS: Seasonal soil moisture correlated with soil surface CO(2 )efflux (R = 0.756, P < 0.001) and above ground plant biomass (R = 0.447, P = 0.029). By reducing irrigation frequency, soil surface CO(2 )efflux decreased by 80%, P < 0.001, while soil moisture content decreased by 42%, P < 0.001. CONCLUSIONS: Manipulating the number of precipitation events and inter-rainfall intervals, while maintaining monthly rainfall averages impacted CO(2 )efflux and plant growth. Even with monthly rainfall averages that are similar to contemporary monthly precipitation averages, decreasing the number of monthly rainfall events reduced soil surface CO(2 )efflux and plant growth through soil moisture deficits. Although many have speculated that climate change will increase ecosystem productivity, our results show that a reduction in the number of monthly rainfall events while maintaining monthly averages will limit carbon dynamics

Spectroscopic Constraints on UV Metal Line Emission at z~6-9: The Nature of Lyman-alpha Emitting Galaxies in the Reionization-Era

Recent studies have revealed intense UV metal emission lines in a modest sample of z>7 Lyman-alpha emitters, indicating a hard ionizing spectrum is present. If such high ionization features are shown to be common, it may indicate that extreme radiation fields play a role in regulating the visibility of Lyman-alpha in the reionization era. Here we present deep near-infrared spectra of seven galaxies with Lyman-alpha emission at 5.4<z<8.7 (including a newly-confirmed lensed galaxy at z=6.031) and three bright z>7 photometric targets. In nine sources we do not detect UV metal lines. However in the z=8.683 galaxy EGSY8p7, we detect a 4.6 sigma emission line in the narrow spectral window expected for NV 1243. The feature is unresolved (FWHM<90 km/s) and is likely nebular in origin. A deep H-band spectrum of EGSY8p7 reveals non-detections of CIV, He II, and OIII]. The presence of NV requires a substantial flux of photons above 77 eV, pointing to a hard ionizing spectrum powered by an AGN or fast radiative shocks. Regardless of its origin, the intense radiation field of EGSY8p7 may aid the transmission of Lyman-alpha through what is likely a partially neutral IGM. With this new detection, five of thirteen known Lyman-alpha emitters at z>7 have now been shown to have intense UV line emission, suggesting that extreme radiation fields are commonplace among the Lyman-alpha population. Future observations with JWST will eventually clarify the origin of these features and explain their role in the visibility of Lyman-alpha in the reionization era.Comment: 15 pages, 3 tables and 7 figures. Accepted for publication in MNRA

Disk Heating, Galactoseismology, and the Formation of Stellar Halos

Deep photometric surveys of the Milky Way have revealed diffuse structures encircling our Galaxy far beyond the "classical" limits of the stellar disk. This paper reviews results from our own and other observational programs, which together suggest that, despite their extreme positions, the stars in these structures were formed in our Galactic disk. Mounting evidence from recent observations and simulations implies kinematic connections between several of these distinct structures. This suggests the existence of collective disk oscillations that can plausibly be traced all the way to asymmetries seen in the stellar velocity distribution around the Sun. There are multiple interesting implications of these findings: they promise new perspectives on the process of disk heating, they provide direct evidence for a stellar halo formation mechanism in addition to the accretion and disruption of satellite galaxies, and, they motivate searches of current and near-future surveys to trace these oscillations across the Galaxy. Such maps could be used as dynamical diagnostics in the emerging field of "Galactoseismology", which promises to model the history of interactions between the Milky Way and its entourage of satellites, as well examine the density of our dark matter halo. As sensitivity to very low surface brightness features around external galaxies increases, many more examples of such disk oscillations will likely be identified. Statistical samples of such features not only encode detailed information about interaction rates and mergers, but also about long sought-after dark matter halo densities and shapes. Models for the Milky Way's own Galactoseismic history will therefore serve as a critical foundation for studying the weak dynamical interactions of galaxies across the universe.Comment: 20 pages, 5 figures, accepted in for publication in a special edition of the journal "Galaxies", reporting the proceedings of the conference "On the Origin (and Evolution) of Baryonic Galaxy Halos", Puerto Ayora, Ecuador, March 13-17 2017, Eds. Duncan A. Forbes and Ericson D. Lope