Numerical Study of a Field Theory for Directed Percolation

A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened sensitivity to fluctuationsattending multiplicative noise in the vicinity of an absorbing state, a useful method requires discretization of the field variable as well as of space and time. When applied to the field theory for directed percolation in 1+1 dimensions, the method yields critical exponents which compare well against accepted values.Comment: 18 pages, LaTeX, 6 figures available upon request LC-CM-94-00

The time to extinction for an SIS-household-epidemic model

We analyse a stochastic SIS epidemic amongst a finite population partitioned into households. Since the population is finite, the epidemic will eventually go extinct, i.e., have no more infectives in the population. We study the effects of population size and within household transmission upon the time to extinction. This is done through two approximations. The first approximation is suitable for all levels of within household transmission and is based upon an Ornstein-Uhlenbeck process approximation for the diseases fluctuations about an endemic level relying on a large population. The second approximation is suitable for high levels of within household transmission and approximates the number of infectious households by a simple homogeneously mixing SIS model with the households replaced by individuals. The analysis, supported by a simulation study, shows that the mean time to extinction is minimized by moderate levels of within household transmission

Self-avoiding walks and connective constants

The connective constant $\mu(G)$ of a quasi-transitive graph $G$ is the asymptotic growth rate of the number of self-avoiding walks (SAWs) on $G$ from a given starting vertex. We survey several aspects of the relationship between the connective constant and the underlying graph $G$. $\bullet$ We present upper and lower bounds for $\mu$ in terms of the vertex-degree and girth of a transitive graph. $\bullet$ We discuss the question of whether $\mu\ge\phi$ for transitive cubic graphs (where $\phi$ denotes the golden mean), and we introduce the Fisher transformation for SAWs (that is, the replacement of vertices by triangles). $\bullet$ We present strict inequalities for the connective constants $\mu(G)$ of transitive graphs $G$, as $G$ varies. $\bullet$ As a consequence of the last, the connective constant of a Cayley graph of a finitely generated group decreases strictly when a new relator is added, and increases strictly when a non-trivial group element is declared to be a further generator. $\bullet$ We describe so-called graph height functions within an account of "bridges" for quasi-transitive graphs, and indicate that the bridge constant equals the connective constant when the graph has a unimodular graph height function. $\bullet$ A partial answer is given to the question of the locality of connective constants, based around the existence of unimodular graph height functions. $\bullet$ Examples are presented of Cayley graphs of finitely presented groups that possess graph height functions (that are, in addition, harmonic and unimodular), and that do not. $\bullet$ The review closes with a brief account of the "speed" of SAW.Comment: Accepted version. arXiv admin note: substantial text overlap with arXiv:1304.721

Phase Transitions on Nonamenable Graphs

We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees

Landscape history, time lags and drivers of change : urban natural grassland remnants in Potchefstroom, South Africa

The history of the landscape directly affects biotic assemblages, resulting in time lags in species response to disturbances. In highly fragmented environments, this phenomenon often causes extinction debts. However, few studies have been carried out in urban settings. To determine if there are time lags in the response of temperate natural grasslands to urbanization. Does it differ for indigenous species and for species indicative of disturbance and between woody and open grasslands? Do these time lags change over time? What are the potential landscape factors driving these changes? What are the corresponding vegetation changes? In 1995 and 2012 vegetation sampling was carried out in 43 urban grassland sites. We calculated six urbanization and landscape measures in a 500 m buffer area surrounding each site for 1938, 1961, 1970, 1994, 1999, 2006, and 2010. We used generalized linear models and model selection to determine which time period best predicted the contemporary species richness patterns. Woody grasslands showed time lags of 20-40 years. Contemporary open grassland communities were, generally, associated with more contemporary landscapes. Altitude and road network density of natural areas were the most frequent predictors of species richness. The importance of the predictors changed between the different models. Species richness, specifically, indigenous herbaceous species, declined from 1995 to 2012. The history of urbanization affects contemporary urban vegetation assemblages. This indicates potential extinction debts, which have important consequences for biodiversity conservation planning and sustainable future scenarios.Peer reviewe

A multidisciplinary study of a small, temporarily open/closed South African estuary, with particular emphasis on the influence of mouth state on the ecology of the system

In 2005/2006 a multidisciplinary research programme that included studies on the hydrodynamics, sediment dynamics, macronutrients, microalgae, macrophytes, zoobenthos, hyperbenthos, zooplankton, ichthyoplankton, fish and birds of the temporarily open/closed East Kleinemonde Estuary was conducted. Particular attention was given to the responses of the different ecosystem components to the opening and closing of the estuary mouth and how this is driven by both riverine and marine events. Using a complementary dataset of daily estuary mouth conditions spanning a 14-year period, five distinct phases of the estuary were identified, including closed (average = 90% of the days), outflow (<1%), tidal (9%) and semi-closed (<1%). The open-mouth phase is critical for the movements of a number of estuary-associated fish (e.g. Rhabdosargus holubi) and invertebrates (e.g. Scylla serrata) between the estuary and sea. The timing of this open phase has a direct influence on the ability of certain estuaryassociated fish (e.g. Lithognathus lithognathus) and invertebrates (e.g. Palaemon peringueyi) to successfully recruit into the system, with a spring opening (October/November) being regarded as optimal for most species. The type of mouth-breaching event and outflow phase is also important in terms of the subsequent salinity regime once the berm barrier forms. A deep mouth breaching following a large river flood tends to result in major tidal inputs of marine water prior to mouth closure and therefore higher salinities (15–25). Conversely, a shallow mouth breaching with reduced tidal exchange during the open phase often leads to a much lower salinity regime at the time of mouth closure (5–15). The biota, especially the submerged macrophytes, respond very differently to the above two scenarios, with Ruppia cirrhosa benefiting from the former and Potamogeton pectinatus from the latter. River flooding and the associated outflow of large volumes of water through the estuary can result in major declines in zooplankton, zoobenthos, hyperbenthos and fish populations during this phase. However, this resetting of the estuary is necessary because certain marine invertebrate and fish species are dependent on the opening of the estuary mouth in order to facilitate recruitment of larvae and post-larvae into the system from the sea. Slight increases in the numbers of certain piscivorous and resident wading bird species were recorded when the estuary mouth opened, possibly linked to increased feeding opportunities during that phase

The TRAPUM L-band survey for pulsars in Fermi-LAT gamma-ray sources

More than 100 millisecond pulsars (MSPs) have been discovered in radio observations of gamma-ray sources detected by the Fermi Large Area Telescope (LAT), but hundreds of pulsar-like sources remain unidentified. Here we present the first results from the targeted survey of Fermi-LAT sources being performed by the Transients and Pulsars with MeerKAT (TRAPUM) Large Survey Project. We observed 79 sources identified as possible gamma-ray pulsar candidates by a Random Forest classification of unassociated sources from the 4FGL catalogue. Each source was observed for 10 minutes on two separate epochs using MeerKAT's L-band receiver (856-1712 MHz), with typical pulsed flux density sensitivities of $\sim$100$\,\mu$Jy. Nine new MSPs were discovered, eight of which are in binary systems, including two eclipsing redbacks and one system, PSR J1526$-$2744, that appears to have a white dwarf companion in an unusually compact 5 hr orbit. We obtained phase-connected timing solutions for two of these MSPs, enabling the detection of gamma-ray pulsations in the Fermi-LAT data. A follow-up search for continuous gravitational waves from PSR J1526$-$2744 in Advanced LIGO data using the resulting Fermi-LAT timing ephemeris yielded no detection, but sets an upper limit on the neutron star ellipticity of $2.45\times10^{-8}$. We also detected X-ray emission from the redback PSR J1803$-$6707 in data from the first eROSITA all-sky survey, likely due to emission from an intra-binary shock.Comment: 17 pages, 8 figures, accepted for publication in MNRA

The TRAPUM L-band survey for pulsars in Fermi-LAT gamma-ray sources

More than 100 millisecond pulsars (MSPs) have been discovered in radioobservations of gamma-ray sources detected by the Fermi Large Area Telescope(LAT), but hundreds of pulsar-like sources remain unidentified. Here we presentthe first results from the targeted survey of Fermi-LAT sources being performedby the Transients and Pulsars with MeerKAT (TRAPUM) Large Survey Project. Weobserved 79 sources identified as possible gamma-ray pulsar candidates by aRandom Forest classification of unassociated sources from the 4FGL catalogue.Each source was observed for 10 minutes on two separate epochs using MeerKAT'sL-band receiver (856-1712 MHz), with typical pulsed flux density sensitivitiesof $\sim$100$\,\mu$Jy. Nine new MSPs were discovered, eight of which are inbinary systems, including two eclipsing redbacks and one system, PSRJ1526$-$2744, that appears to have a white dwarf companion in an unusuallycompact 5 hr orbit. We obtained phase-connected timing solutions for two ofthese MSPs, enabling the detection of gamma-ray pulsations in the Fermi-LATdata. A follow-up search for continuous gravitational waves from PSRJ1526$-$2744 in Advanced LIGO data using the resulting Fermi-LAT timingephemeris yielded no detection, but sets an upper limit on the neutron starellipticity of $2.45\times10^{-8}$. We also detected X-ray emission from theredback PSR J1803$-$6707 in data from the first eROSITA all-sky survey, likelydue to emission from an intra-binary shock.<br

Teaching and Learning of Calculus

This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions