Approximation Algorithms for the Joint Replenishment Problem with Deadlines

The Joint Replenishment Problem (JRP) is a fundamental optimization problem in supply-chain management, concerned with optimizing the flow of goods from a supplier to retailers. Over time, in response to demands at the retailers, the supplier ships orders, via a warehouse, to the retailers. The objective is to schedule these orders to minimize the sum of ordering costs and retailers' waiting costs. We study the approximability of JRP-D, the version of JRP with deadlines, where instead of waiting costs the retailers impose strict deadlines. We study the integrality gap of the standard linear-program (LP) relaxation, giving a lower bound of 1.207, a stronger, computer-assisted lower bound of 1.245, as well as an upper bound and approximation ratio of 1.574. The best previous upper bound and approximation ratio was 1.667; no lower bound was previously published. For the special case when all demand periods are of equal length we give an upper bound of 1.5, a lower bound of 1.2, and show APX-hardness

Preparing Your Business for Valuation

There is a tremendous need for the valuation of small businesses. Oftentimes, small businessowners do not have the wherewithal to gather the data and keep it up to date for use in situations that require valuation. Formal valuations are necessary because they provide objective evidence of value, in contrast to value set by markets on which public companies are traded. This article focuses on some factors that impact the valuation of the business and will help small businessowners feel more comfortable talking with financial professionals about how the business might be valued

Future Antarctic bed topography and its implications for ice sheet dynamics

The Antarctic bedrock is evolving as the solid Earth responds to the past and ongoing evolution of the ice sheet. A recently improved ice loading history suggests that the Antarctic Ice Sheet (AIS) has generally been losing its mass since the Last Glacial Maximum. In a sustained warming climate, the AIS is predicted to retreat at a greater pace, primarily via melting beneath the ice shelves. We employ the glacial isostatic adjustment (GIA) capability of the Ice Sheet System Model (ISSM) to combine these past and future ice loadings and provide the new solid Earth computations for the AIS. We find that past loading is relatively less important than future loading for the evolution of the future bed topography. Our computations predict that the West Antarctic Ice Sheet (WAIS) may uplift by a few meters and a few tens of meters at years AD 2100 and 2500, respectively, and that the East Antarctic Ice Sheet is likely to remain unchanged or subside minimally except around the Amery Ice Shelf. The Amundsen Sea Sector in particular is predicted to rise at the greatest rate; one hundred years of ice evolution in this region, for example, predicts that the coastline of Pine Island Bay will approach roughly 45 mm yr−1 in viscoelastic vertical motion. Of particular importance, we systematically demonstrate that the effect of a pervasive and large GIA uplift in the WAIS is generally associated with the flattening of reverse bed slope, reduction of local sea depth, and thus the extension of grounding line (GL) towards the continental shelf. Using the 3-D higher-order ice flow capability of ISSM, such a migration of GL is shown to inhibit the ice flow. This negative feedback between the ice sheet and the solid Earth may promote stability in marine portions of the ice sheet in the future

Simulated Greenland Surface Mass Balance in the GISS ModelE2 GCM: Role of the Ice Sheet Surface

The rate of growth or retreat of the Greenland and Antarctic ice sheets remains a highly uncertain component of future sea level change. Here we examine the simulation of Greenland ice sheet surface mass balance (GrIS SMB) in the NASA Goddard Institute for Space Studies (GISS) ModelE2 General Circulation Model (GCM). GCMs are often limited in their ability to represent SMB compared with polarregion Regional Climate Models (RCMs). We compare ModelE2 simulated GrIS SMB for presentday (19962005) simulations with fixed ocean conditions, at a spatial resolution of 2 latitude by 2.5 longitude (~200 km), with SMB simulated by the Modle Atmosphrique Rgionale (MAR) RCM (19962005 at a 25 km resolution). ModelE2 SMB agrees well with MAR SMB on the whole, but there are distinct spatial patterns of differences and large differences in some SMB components. The impact of changes to the ModelE2 surface are tested, including a subgridscale representation of SMB with surface elevation classes. This has a minimal effect on ice sheetwide SMB, but corrects local biases. Replacing fixed surface albedo with satellitederived values and an agedependent scheme has a larger impact, increasing simulated melt by 60100%. We also find that lower surface albedo can enhance the effects of elevation classes. Reducing ModelE2 surface roughness length to values closer to MAR reduces sublimation by ~50%. Further work is required to account for meltwater refreezing in ModelE2, and to understand how differences in atmospheric processes and model resolution influence simulated SMB

Paper Session I-C - Comparison of Surface Resistivity and Triboelectric Charge Generation Characteristics of Materials

Electrostatic discharge can be a significant threat to electronic components, equipment and personnel, especially when working around flammable materials. The development of ways to predict the susceptibility of materials to generate significant charge is important for the safety of these personnel and equipment. The classification of materials as conductors or insulators is based on the surface resistivity of the materials. Though surface resistivity is an important piece of information when choosing electrostatically safe materials, this classification system does not provide any information as to the probability of the materials to generate charge when placed in contact with other materials (triboelectric charging). Without that information, the probability for hazardous electrostatic discharge to occur is not known. In this paper we show that there is no significant correlation between surface resistivity and triboelectric charge generation and emphasize the need for a test method to predict the susceptibility of materials for triboelectric charge generation in order to better evaluate a material’s propensity to cause an electrostatic discharge

Pattern Formation of Glioma Cells: Effects of Adhesion

We investigate clustering of malignant glioma cells. \emph{In vitro} experiments in collagen gels identified a cell line that formed clusters in a region of low cell density, whereas a very similar cell line (which lacks an important mutation) did not cluster significantly. We hypothesize that the mutation affects the strength of cell-cell adhesion. We investigate this effect in a new experiment, which follows the clustering dynamics of glioma cells on a surface. We interpret our results in terms of a stochastic model and identify two mechanisms of clustering. First, there is a critical value of the strength of adhesion; above the threshold, large clusters grow from a homogeneous suspension of cells; below it, the system remains homogeneous, similarly to the ordinary phase separation. Second, when cells form a cluster, we have evidence that they increase their proliferation rate. We have successfully reproduced the experimental findings and found that both mechanisms are crucial for cluster formation and growth.Comment: 6 pages, 6 figure

Gastric plexiform fibromyxoma tumor in a child – Case report and review of the literature

AbstractPlexiform fibromyxoma tumor (PFT) is an exceedingly rare tumor, particularly in children where only four cases have been reported to date. The patient reported herein presented with abdominal pain and vomiting related to gastric outlet obstruction caused by a large, polypoid PFT. We describe the clinical features, diagnostic evaluation, and surgical treatment of this rare tumor in our patient. Further, we review the literature of FPT to bring attention to this rare gastric tumor to the Pediatric Surgeon

Development of parasitic Maculinea teleius (Lepidoptera, Lycaenidae) larvae in laboratory nests of four Myrmica ant host species

Maculinea butterflies are social parasites of Myrmica ants. Methods to study the strength of host ant specificity in the Maculinea–Myrmica association include research on chemical and acoustic mimicry as well as experiments on ant adoption and rearing behaviour of Maculinea larvae. Here we present results of laboratory experiments on adoption, survival, development and integration of M. teleius larvae within the nests of different Myrmica host species, with the objective of quantifying the degree of specialization of this Maculinea species. In the laboratory, a total of 94 nests of four Myrmica species: M. scabrinodis, M. rubra, M.ruginodis and M. rugulosa were used. Nests of M. rubra and M. rugulosa adopted M. teleius larvae more readily and quickly than M. ruginodis colonies. No significant differences were found in the survival rates of M. teleius larvae reared by different ant species. Early larval growth of M. teleius larvae differed slightly among nests of four Myrmica host species. Larvae reared by colonies of M. rugulosa which were the heaviest at the beginning of larval development had the lowest mean larval body mass after 18 weeks compared to those reared by other Myrmica species. None of the M.teleius larvae was carried by M. scabrinodis or M. rubra workers after ant nests were destroyed, which suggests a lack of integration with host colonies. Results indicate that Myrmica species coming from the same site differ in their ability to adopt and rear M. teleius larvae but there was no obvious adaptation of this butterfly species to one of the host ant species. This may explain why, under natural conditions, all four ants can be used as hosts of this butterfly species. Slight advantages of particular Myrmica species as hosts at certain points in butterfly larval development can be explained by the ant species biology and colony structure rather than by specialization of M. teleius