A weighted configuration model and inhomogeneous epidemics

A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight according to a distribution that is allowed to depend on the degree of its vertex. Half-edges with the same weight are then paired randomly to create edges. An expression for the threshold for the appearance of a giant component in the resulting graph is derived using results on multi-type branching processes. The same technique also gives an expression for the basic reproduction number for an epidemic on the graph where the probability that a certain edge is used for transmission is a function of the edge weight. It is demonstrated that, if vertices with large degree tend to have large (small) weights on their edges and if the transmission probability increases with the edge weight, then it is easier (harder) for the epidemic to take off compared to a randomized epidemic with the same degree and weight distribution. A recipe for calculating the probability of a large outbreak in the epidemic and the size of such an outbreak is also given. Finally, the model is fitted to three empirical weighted networks of importance for the spread of contagious diseases and it is shown that $R_0$ can be substantially over- or underestimated if the correlation between degree and weight is not taken into account

Loss of genetic integrity and biological invasions result from stocking and introductions of Barbus barbus: Insights from rivers in England

Anthropogenic activities, including the intentional releases of fish for enhancing populations (stocking), are recognized as adversely impacting the adaptive potential of wild populations. Here, the genetic characteristics of European barbel Barbus barbus were investigated using 18 populations in England, where it is indigenous to eastern-flowing rivers and where stocking has been used to enhance these populations. Invasive populations are also present in western-flowing rivers following introductions of translocated fish. Two genetic clusters were evident in the indigenous range, centered on catchments in northeast and southeast England. However, stocking activities, including the release of hatchery-reared fish, have significantly reduced the genetic differentiation across the majority of this range. In addition, in smaller indigenous rivers, populations appeared to mainly comprise fish of hatchery origin. In the nonindigenous range, genetic data largely aligned to historical stocking records, corroborating information that one particular river (Kennet) in southeast England was the original source of most invasive B. barbus in England. It is recommended that these genetic outputs inform management measures to either restore or maintain the original genetic diversity of the indigenous rivers, as this should help ensure populations can maintain their ability to adapt to changing environmental conditions. Where stocking is considered necessary, it is recommended that only broodstock from within the catchment is used

Radio Astronomical Polarimetry and the Lorentz Group

In radio astronomy the polarimetric properties of radiation are often modified during propagation and reception. Effects such as Faraday rotation, receiver cross-talk, and differential amplification act to change the state of polarized radiation. A general description of such transformations is useful for the investigation of these effects and for the interpretation and calibration of polarimetric observations. Such a description is provided by the Lorentz group, which is intimately related to the transformation properties of polarized radiation. In this paper the transformations that commonly arise in radio astronomy are analyzed in the context of this group. This analysis is then used to construct a model for the propagation and reception of radio waves. The implications of this model for radio astronomical polarimetry are discussed.Comment: 10 pages, accepted for publication in Astrophysical Journa

Spatial synchronization and extinction of species under external forcing

We study the interplay between synchronization and extinction of a species. Using a general model we show that under a common external forcing, the species with a quadratic saturation term in the population dynamics first undergoes spatial synchronization and then extinction, thereby avoiding the rescue effect. This is because the saturation term reduces the synchronization time scale but not the extinction time scale. The effect can be observed even when the external forcing acts only on some locations provided there is a synchronizing term in the dynamics. Absence of the quadratic saturation term can help the species to avoid extinction.Comment: 4 pages, 2 figure

Variability for Traits Used to Estimate Silage Quality in Forage Sorghum Hybrids

The variation among 49 F1 forage sorghum [Sorghum bicolor (L.) Moench.] hybrids from a 7 X 7 cross-classified design was explored in 1979 and 1980 for the following silage traits: dry matter (DM), crude protein, in vitro dry matter disappearance (IVDMD), neutral detergent fiber, acid detergent fiber, acid detergent lignin, ammonia, lactate, and Brix of the juice from fresh stalks. Wider ranges generally were found for male than for female parental means. Means for most traits were significantly different among entries. Significant differences among hybrid means over males and over females were found for only DM, IVDMD, and Brix. Interactions with years existed for most traits. Genetic ratios calculated from the mean squares indicated that general combining ability was important for DM, IVDMD, and Brix. Simple correlation coefficients between traits measured on silage and on fresh-dried samples from the same hybrids were all significant. In view of the effort required to make and evaluate silage samples, initial selection for traits used to estimate quality in fresh-dried samples appears to be the best approach for improving the quality of forage sorghum silage

Variability for Traits Used to Estimate Silage Quality in Forage Sorghum Hybrids

The variation among 49 F1 forage sorghum [Sorghum bicolor (L.) Moench.] hybrids from a 7 X 7 cross-classified design was explored in 1979 and 1980 for the following silage traits: dry matter (DM), crude protein, in vitro dry matter disappearance (IVDMD), neutral detergent fiber, acid detergent fiber, acid detergent lignin, ammonia, lactate, and Brix of the juice from fresh stalks. Wider ranges generally were found for male than for female parental means. Means for most traits were significantly different among entries. Significant differences among hybrid means over males and over females were found for only DM, IVDMD, and Brix. Interactions with years existed for most traits. Genetic ratios calculated from the mean squares indicated that general combining ability was important for DM, IVDMD, and Brix. Simple correlation coefficients between traits measured on silage and on fresh-dried samples from the same hybrids were all significant. In view of the effort required to make and evaluate silage samples, initial selection for traits used to estimate quality in fresh-dried samples appears to be the best approach for improving the quality of forage sorghum silage

Scalable ion traps for quantum information processing

We report on the design, fabrication, and preliminary testing of a 150 zone array built in a `surface-electrode' geometry microfabricated on a single substrate. We demonstrate transport of atomic ions between legs of a `Y'-type junction and measure the in-situ heating rates for the ions. The trap design demonstrates use of a basic component design library that can be quickly assembled to form structures optimized for a particular experiment