On a Generalization of the Frobenius Number

We consider a generalization of the Frobenius Problem where the object of interest is the greatest integer which has exactly $j$ representations by a collection of positive relatively prime integers. We prove an analogue of a theorem of Brauer and Shockley and show how it can be used for computation.Comment: 5 page

The Two Faces of Anomaly Mediation

Anomaly mediation is a ubiquitous source of supersymmetry (SUSY) breaking which appears in almost every theory of supergravity. In this paper, we show that anomaly mediation really consists of two physically distinct phenomena, which we dub "gravitino mediation" and "Kahler mediation". Gravitino mediation arises from minimally uplifting SUSY anti-de Sitter (AdS) space to Minkowski space, generating soft masses proportional to the gravitino mass. Kahler mediation arises when visible sector fields have linear couplings to SUSY breaking in the Kahler potential, generating soft masses proportional to beta function coefficients. In the literature, these two phenomena are lumped together under the name "anomaly mediation", but here we demonstrate that they can be physically disentangled by measuring associated couplings to the goldstino. In particular, we use the example of gaugino soft masses to show that gravitino mediation generates soft masses without corresponding goldstino couplings. This result naively violates the goldstino equivalence theorem but is in fact necessary for supercurrent conservation in AdS space. Since gravitino mediation persists even when the visible sector is sequestered from SUSY breaking, we can use the absence of goldstino couplings as an unambiguous definition of sequestering.Comment: 21 pages, 1 table; v2, references added, extended discussion in introduction and appendix; v3, JHEP versio

Mechanisms of viral entry: sneaking in the front door

Recent developments in methods to study virus internalisation are providing clearer insights into mechanisms used by viruses to enter host cells. The use of dominant negative constructs, specific inhibitory drugs and RNAi to selectively prevent entry through particular pathways has provided evidence for the clathrin-mediated entry of hepatitis C virus (HCV) as well as the caveolar entry of Simian Virus 40. Moreover, the ability to image and track fluorescent-labelled virus particles in real-time has begun to challenge the classical plasma membrane entry mechanisms described for poliovirus and human immunodeficiency virus. This review will cover both well-documented entry mechanisms as well as more recent discoveries in the entry pathways of enveloped and non-enveloped viruses. This will include viruses which enter the cytosol directly at the plasma membrane and those which enter via endocytosis and traversal of internal membrane barrier(s). Recent developments in imaging and inhibition of entry pathways have provided insights into the ill-defined entry mechanism of HCV, bringing it to the forefront of viral entry research. Finally, as high-affinity receptors often define viral internalisation pathways, and tropism in vivo, host membrane proteins to which viral particles specifically bind will be discussed throughout

Data from: Fish functional traits correlated with environmental variables in a temperate biodiversity hotspot

The global biodiversity crisis has invigorated the search for generalized patterns in most disciplines within the natural sciences. Studies based on organismal functional traits attempt to broaden implications of results by identifying the response of functional traits, instead of taxonomic units, to environmental variables. Determining the functional trait responses enables more direct comparisons with, or predictions for, communities of different taxonomic composition. The North American freshwater fish fauna is both diverse and increasingly imperiled through human mediated disturbances, including climate change. The Tennessee River, USA, contains one of the most diverse assemblages of freshwater fish in North America and has more imperiled species than other rivers, but there has been no trait-based study of community structure in the system. We identified 211 localities in the upper Tennessee River that were sampled by the Tennessee Valley Authority between 2009 and 2011 and compiled fish functional traits for the observed species and environmental variables for each locality. Using fourth corner analysis, we identified significant correlations between many fish functional traits and environmental variables. Functional traits associated with an opportunistic life history strategy were correlated with localities subject to greater land use disturbance and less flow regulation, while functional traits associated with a periodic life history strategy were correlated with localities subject to regular disturbance and regulated flow. These are patterns observed at the continental scale highlighting the generalizability of trait-based methods. Contrary to studies that found no community structure differences when considering riparian buffer zones, we found that fish functional traits were correlated with different environmental variables between analyses with buffer zones vs. entire catchment area land cover proportions. Using existing databases and fourth corner analysis, our results support the broad application potential for trait-based methods and indicate trait-based methods can detect environmental filtering by riparian zone land cover

Data from: Fish functional traits correlated with environmental variables in a temperate biodiversity hotspot

The global biodiversity crisis has invigorated the search for generalized patterns in most disciplines within the natural sciences. Studies based on organismal functional traits attempt to broaden implications of results by identifying the response of functional traits, instead of taxonomic units, to environmental variables. Determining the functional trait responses enables more direct comparisons with, or predictions for, communities of different taxonomic composition. The North American freshwater fish fauna is both diverse and increasingly imperiled through human mediated disturbances, including climate change. The Tennessee River, USA, contains one of the most diverse assemblages of freshwater fish in North America and has more imperiled species than other rivers, but there has been no trait-based study of community structure in the system. We identified 211 localities in the upper Tennessee River that were sampled by the Tennessee Valley Authority between 2009 and 2011 and compiled fish functional traits for the observed species and environmental variables for each locality. Using fourth corner analysis, we identified significant correlations between many fish functional traits and environmental variables. Functional traits associated with an opportunistic life history strategy were correlated with localities subject to greater land use disturbance and less flow regulation, while functional traits associated with a periodic life history strategy were correlated with localities subject to regular disturbance and regulated flow. These are patterns observed at the continental scale highlighting the generalizability of trait-based methods. Contrary to studies that found no community structure differences when considering riparian buffer zones, we found that fish functional traits were correlated with different environmental variables between analyses with buffer zones vs. entire catchment area land cover proportions. Using existing databases and fourth corner analysis, our results support the broad application potential for trait-based methods and indicate trait-based methods can detect environmental filtering by riparian zone land cover

LocalityTraits

LocalityTrait

LandUse_Full

LandUse_Ful