The transmission problem for quasi-linear elliptic second order equations in a conical domain

We investigate the behavior of weak solutions to the transmission problem for quasi-linear elliptic divergence second order equations in a neighborhood of the boundary conical point

Good covers are algorithmically unrecognizable

A good cover in R^d is a collection of open contractible sets in R^d such that the intersection of any subcollection is either contractible or empty. Motivated by an analogy with convex sets, intersection patterns of good covers were studied intensively. Our main result is that intersection patterns of good covers are algorithmically unrecognizable. More precisely, the intersection pattern of a good cover can be stored in a simplicial complex called nerve which records which subfamilies of the good cover intersect. A simplicial complex is topologically d-representable if it is isomorphic to the nerve of a good cover in R^d. We prove that it is algorithmically undecidable whether a given simplicial complex is topologically d-representable for any fixed d \geq 5. The result remains also valid if we replace good covers with acyclic covers or with covers by open d-balls. As an auxiliary result we prove that if a simplicial complex is PL embeddable into R^d, then it is topologically d-representable. We also supply this result with showing that if a "sufficiently fine" subdivision of a k-dimensional complex is d-representable and k \leq (2d-3)/3, then the complex is PL embeddable into R^d.Comment: 22 pages, 5 figures; result extended also to acyclic covers in version

Benthic and Pelagic Pathways of Methylmercury Bioaccumulation in Estuarine Food Webs of the Northeast United States

Methylmercury (MeHg) is a contaminant of global concern that bioaccumulates and bioamagnifies in marine food webs. Lower trophic level fauna are important conduits of MeHg from sediment and water to estuarine and coastal fish harvested for human consumption. However, the sources and pathways of MeHg to these coastal fisheries are poorly known particularly the potential for transfer of MeHg from the sediment to biotic compartments. Across a broad gradient of human land impacts, we analyzed MeHg concentrations in food webs at ten estuarine sites in the Northeast US (from the Hackensack Meadowlands, NJ to the Gulf of Maine). MeHg concentrations in water column particulate material, but not in sediments, were predictive of MeHg concentrations in fish (killifish and Atlantic silversides). Moreover, MeHg concentrations were higher in pelagic fauna than in benthic-feeding fauna suggesting that MeHg delivery to the water column from methylation sites from within or outside of the estuary may be an important driver of MeHg bioaccumulation in estuarine pelagic food webs. In contrast, bulk sediment MeHg concentrations were only predictive of concentrations of MeHg in the infaunal worms. Our results across a broad gradient of sites demonstrate that the pathways of MeHg to lower trophic level estuarine organisms are distinctly different between benthic deposit feeders and forage fish. Thus, even in systems with contaminated sediments, transfer of MeHg into estuarine food webs maybe driven more by the efficiency of processes that determine MeHg input and bioavailability in the water column

Combinatorial Stokes formulas via minimal resolutions

We describe an explicit chain map from the standard resolution to the minimal resolution for the finite cyclic group Z_k of order k. We then demonstrate how such a chain map induces a "Z_k-combinatorial Stokes theorem", which in turn implies "Dold's theorem" that there is no equivariant map from an n-connected to an n-dimensional free Z_k-complex. Thus we build a combinatorial access road to problems in combinatorics and discrete geometry that have previously been treated with methods from equivariant topology. The special case k=2 for this is classical; it involves Tucker's (1949) combinatorial lemma which implies the Borsuk-Ulam theorem, its proof via chain complexes by Lefschetz (1949), the combinatorial Stokes formula of Fan (1967), and Meunier's work (2006).Comment: 18 page

A coupled terrestrial and aquatic biogeophysical model of the Upper Merrimack River watershed, New Hampshire, to inform ecosystem services evaluation and management under climate and land-cover change

Accurate quantification of ecosystem services (ES) at regional scales is increasingly important for making informed decisions in the face of environmental change. We linked terrestrial and aquatic ecosystem process models to simulate the spatial and temporal distribution of hydrological and water quality characteristics related to ecosystem services. The linked model integrates two existing models (a forest ecosystem model and a river network model) to establish consistent responses to changing drivers across climate, terrestrial, and aquatic domains. The linked model is spatially distributed, accounts for terrestrial–aquatic and upstream–downstream linkages, and operates on a daily time-step, all characteristics needed to understand regional responses. The model was applied to the diverse landscapes of the Upper Merrimack River watershed, New Hampshire, USA. Potential changes in future environmental functions were evaluated using statistically downscaled global climate model simulations (both a high and low emission scenario) coupled with scenarios of changing land cover (centralized vs. dispersed land development) for the time period of 1980–2099. Projections of climate, land cover, and water quality were translated into a suite of environmental indicators that represent conditions relevant to important ecosystem services and were designed to be readily understood by the public. Model projections show that climate will have a greater influence on future aquatic ecosystem services (flooding, drinking water, fish habitat, and nitrogen export) than plausible changes in land cover. Minimal changes in aquatic environmental indicators are predicted through 2050, after which the high emissions scenarios show intensifying impacts. The spatially distributed modeling approach indicates that heavily populated portions of the watershed will show the strongest responses. Management of land cover could attenuate some of the changes associated with climate change and should be considered in future planning for the region

Nuclear Repulsion Enables Division Autonomy in a Single Cytoplasm

SummaryBackgroundCurrent models of cell-cycle control, based on classic studies of fused cells, predict that nuclei in a shared cytoplasm respond to the same CDK activities to undergo synchronous cycling. However, synchrony is rarely observed in naturally occurring syncytia, such as the multinucleate fungus Ashbya gossypii. In this system, nuclei divide asynchronously, raising the question of how nuclear timing differences are maintained despite sharing a common milieu.ResultsWe observe that neighboring nuclei are highly variable in division-cycle duration and that neighbors repel one another to space apart and demarcate their own cytoplasmic territories. The size of these territories increases as a nucleus approaches mitosis and can influence cycling rates. This nonrandom nuclear spacing is regulated by microtubules and is required for nuclear asynchrony, as nuclei that transiently come in very close proximity will partially synchronize. Sister nuclei born of the same mitosis are generally not persistent neighbors over their lifetimes yet remarkably retain similar division cycle times. This indicates that nuclei carry a memory of their birth state that influences their division timing and supports that nuclei subdivide a common cytosol into functionally distinct yet mobile compartments.ConclusionsThese findings support that nuclei use cytoplasmic microtubules to establish “cells within cells.” Individual compartments appear to push against one another to compete for cytoplasmic territory and insulate the division cycle. This provides a mechanism by which syncytial nuclei can spatially organize cell-cycle signaling and suggests size control can act in a system without physical boundaries

Effectively Transparent Front Contacts for Optoelectronic Devices

Effectively transparent front contacts for optoelectronic devices achieve a measured transparency of up to 99.9% and a measured sheet resistance of 4.8 Ω sq^(−1). The 3D microscale triangular cross-section grid fingers redirect incoming photons efficiently to the active semiconductor area and can replace standard grid fingers as well as transparent conductive oxide layers in optoelectronic devices