The Network Design Problem with Relays

Cataloged from PDF version of article.The network design problem with relays (NDPR) is defined on an undirected graph G = (V,E,K), where V = {1,...,n} is a vertex set, E = {(i,j):i,j 2 V,i < j} is an edge set. The set K = {(o(k),d(k))} is a set of communication pairs (or commodities): o(k) 2 V and d(k) 2 V denote the origin and the destination of the kth commodity, respectively. With each edge (i,j) are associated a cost cij and a length dij. With vertex i is associated a fixed cost fi of locating a relay at i. The NDPR consists of selecting a subset E of edges of E and of locating relays at a subset V of vertices of V in such a way that: (1) the sum Q of edge costs and relay costs is minimized; (2) there exists a path linking the origin and the destination of each commodity in which the length between the origin and the first relay, the last relay and the destination, or any two consecutive relays does not exceed a preset upper bound k. This article develops a lower bound procedure and four heuristics for the NPDR. These are compared on several randomly generated instances with |V| 6 1002 and |E| 6 1930. 2006 Elsevier B.V. All rights reserved

The first Frontier Fields cluster: 4.5{\mu}m excess in a z~8 galaxy candidate in Abell 2744

We present in this letter the first analysis of a z~8 galaxy candidate found in the Hubble and Spitzer imaging data of Abell 2744, as part of the Hubble Frontier Fields legacy program. We applied the most commonly-used methods to select exceptionally high-z galaxies by combining non-detection and color-criteria using seven HST bands. We used GALFIT on IRAC images for fitting and subtracting contamination of bright nearby sources. The physical properties have been inferred from SED-fitting using templates with and without nebular emission. This letter is focussed on the brightest candidate we found (m$_{F160W}$=26.2) over the 4.9 arcmin$^2$ field of view covered by the WFC3. It shows a non-detection in the ACS bands and at 3.6{\mu}m whereas it is clearly detected at 4.5{\mu}m with rather similar depths. This break in the IRAC data could be explained by strong [OIII]+H{\beta} lines at z~8 which contribute to the 4.5{\mu}m photometry. The best photo-z is found at z~8.0$^{+0.2}_{-0.5}$, although solutions at low-redshift (z~1.9) cannot be completely excluded, but they are strongly disfavoured by the SED-fitting work. The amplification factor is relatively small at {\mu}=1.49$\pm$0.02. The Star Formation Rate in this object is ranging from 8 to 60 Mo/yr, the stellar mass is in the order of M$_{\star}$=(2.5-10) x 10$^{9}$Mo and the size is r~0.35$\pm$0.15 kpc. This object is one of the first z~8 LBG candidates showing a clear break between 3.6{\mu}m and 4.5{\mu}m which is consistent with the IRAC properties of the first spectroscopically confirmed galaxy at a similar redshift. Due to its brightness, the redshift of this object could potentially be confirmed by near infrared spectroscopy with current 8-10m telescopes. The nature of this candidate will be revealed in the coming months with the arrival of new ACS and Spitzer data, increasing the depth at optical and near-IR wavelengths.Comment: 4 pages, 2 figures, Accepted for publication in Astronomy and Astrophysics Letter

Resolving Ambiguities in the Inferred Star Formation Histories of Intense [O III] Emitters in the Reionisation Era

Early JWST spectroscopic campaigns have confirmed the presence of strong [O III] line-emitting galaxies in the redshift interval $7<z<9$. Although deduced earlier from Spitzer photometry as indicative of young stellar populations, some studies suggested the relevant photometric excesses attributed to [O III] emission could, in part, be due to Balmer breaks arising from older stars. We demonstrate that this is likely the case by exploiting medium-band near-infrared JWST photometry in the Hubble Ultra Deep Field. We locate a sample of 6 galaxies with redshifts 8.2$<z<$8.6 for which the relevant medium-band filters enables us to separate the contributions of [O III] emission and a Balmer break, thereby breaking earlier degeneracies of interpretation. The technique is particularly valuable since it provides photometric redshifts whose precision, $\Delta\,z\simeq\,\pm0.08$, approaches that of spectroscopic campaigns now underway with JWST. Although some sources are young, a third of our sample have prominent Balmer breaks consistent with stellar ages of $\geq$150 Myr. Our results indicate that even intense [O III] emitters experienced episodes of earlier star formation to $z\sim$10 and beyond, as is now being independently deduced from direct detection of the progenitors of similar systems.Comment: 8 pages, submitted to MNRA

The ALMA Frontier Fields Survey - IV. Lensing-corrected 1.1 mm number counts in Abell 2744, MACSJ0416.1-2403 and MACSJ1149.5+2223

[abridged] Characterizing the number counts of faint, dusty star-forming galaxies is currently a challenge even for deep, high-resolution observations in the FIR-to-mm regime. They are predicted to account for approximately half of the total extragalactic background light at those wavelengths. Searching for dusty star-forming galaxies behind massive galaxy clusters benefits from strong lensing, enhancing their measured emission while increasing spatial resolution. Derived number counts depend, however, on mass reconstruction models that properly constrain these clusters. We estimate the 1.1 mm number counts along the line of sight of three galaxy clusters, i.e. Abell 2744, MACSJ0416.1-2403 and MACSJ1149.5+2223, which are part of the ALMA Frontier Fields Survey. We perform detailed simulations to correct these counts for lensing effects. We use several publicly available lensing models for the galaxy clusters to derive the intrinsic flux densities of our sources. We perform Monte Carlo simulations of the number counts for a detailed treatment of the uncertainties in the magnifications and adopted source redshifts. We find an overall agreement among the number counts derived for the different lens models, despite their systematic variations regarding source magnifications and effective areas. Our number counts span ~2.5 dex in demagnified flux density, from several mJy down to tens of uJy. Our number counts are consistent with recent estimates from deep ALMA observations at a 3$\sigma$ level. Below $\approx$ 0.1 mJy, however, our cumulative counts are lower by $\approx$ 1 dex, suggesting a flattening in the number counts. In our deepest ALMA mosaic, we estimate number counts for intrinsic flux densities $\approx$ 4 times fainter than the rms level. This highlights the potential of probing the sub-10 uJy population in larger samples of galaxy cluster fields with deeper ALMA observations.Comment: 19 pages, 14 figures, 3 tables. Accepted for publication in A&

Opening the doors of memory: Is declarative memory a natural kind?

Klein's target article argues that autonoetic consciousness is a necessary condition for memory; this unusually narrow view of the scope of memory implies that only episodic memory is, strictly speaking, memory. The narrow view is opposed to the standard broad view, on which causal connection with past experience is sufficient for memory; on the broad view, both declarative (i.e., episodic and semantic) and procedural memory count as genuine forms of memory. Klein mounts a convincing attack on the broad view, arguing that it opens the "doors of memory" too far, but this commentary contends that the narrow view does not open them far enough. It may be preferable to adopt an intermediate view of the scope of memory, on which causal connection is sufficient for memory only when it involves encoding, storage, and retrieval of content. More demanding than the simple causal condition but less demanding than the autonoesis condition, the encoding-storage-retrieval condition implies that both episodic and semantic memory count as genuine forms of memory but that procedural memory does not

A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope

A derivation of the Ces\`aro-Fedorov relation from the Selberg trace formula on an orbifolded 2-sphere is elaborated and extended to higher dimensions using the known heat-kernel coefficients for manifolds with piecewise-linear boundaries. Several results are obtained that relate the coefficients, $b_i$, in the Shephard-Todd polynomial to the geometry of the fundamental domain. For the 3-sphere we show that $b_4$ is given by the ratio of the volume of the fundamental tetrahedron to its Schl\"afli reciprocal.Comment: Plain TeX, 26 pages (eqn. (86) corrected

Dynamic Collection Scheduling Using Remote Asset Monitoring: Case Study in the UK Charity Sector

Remote sensing technology is now coming onto the market in the waste collection sector. This technology allows waste and recycling receptacles to report their fill levels at regular intervals. This reporting enables collection schedules to be optimized dynamically to meet true servicing needs in a better way and so reduce transport costs and ensure that visits to clients are made in a timely fashion. This paper describes a real-life logistics problem faced by a leading UK charity that services its textile and book donation banks and its high street stores by using a common fleet of vehicles with various carrying capacities. Use of a common fleet gives rise to a vehicle routing problem in which visits to stores are on fixed days of the week with time window constraints and visits to banks (fitted with remote fill-monitoring technology) are made in a timely fashion so that the banks do not become full before collection. A tabu search algorithm was developed to provide vehicle routes for the next day of operation on the basis of the maximization of profit. A longer look-ahead period was not considered because donation rates to banks are highly variable. The algorithm included parameters that specified the minimum fill level (e.g., 50%) required to allow a visit to a bank and a penalty function used to encourage visits to banks that are becoming full. The results showed that the algorithm significantly reduced visits to banks and increased profit by up to 2.4%, with the best performance obtained when the donation rates were more variable

Young Galaxy Candidates in the Hubble Frontier Fields - III. MACSJ0717.5+3745

In this paper we present the results of our search for and study of $z \gtrsim 6$ galaxy candidates behind the third Frontier Fields (FF) cluster, MACSJ0717.5+3745, and its parallel field, combining data from Hubble and Spitzer. We select 39 candidates using the Lyman Break technique, for which the clear non-detection in optical make the extreme mid-$z$ interlopers hypothesis unlikely. We also take benefit from $z \gtrsim 6$ samples selected using previous Frontier Fields datasets of Abell 2744 and MACS0416 to improve the constraints on the properties of very high-redshift objects. We compute the redshift and the physical properties, such emission lines properties, star formation rate, reddening, and stellar mass for all Frontier Fields objects from their spectral energy distribution using templates including nebular emission lines. We study the relationship between several physical properties and confirm the trend already observed in previous surveys for evolution of star formation rate with galaxy mass, and between the size and the UV luminosity of our candidates. The analysis of the evolution of the UV Luminosity Function with redshift seems more compatible with an evolution of density. Moreover, no robust $z\ge$8.5 object is selected behind the cluster field, and few $z$$\sim$9 candidates have been selected in the two previous datasets from this legacy survey, suggesting a strong evolution in the number density of galaxies between $z$$\sim$8 and 9. Thanks to the use of the lensing cluster, we study the evolution of the star formation rate density produced by galaxies with L$>$0.03L$^{\star}$, and confirm the strong decrease observed between $z$$\sim$8 and 9.Comment: 21 pages - Accepted for publication in ApJ - v2: small correction