Beurling zeta functions, generalised primes, and fractal membranes

We study generalised prime systems P (1 < p(1) <= p(2) <= ..., with p(j) is an element of R tending to infinity) and the associated Beurling zeta function zeta p(s) = Pi(infinity)(j=1)(1 - p(j)(-s))(-1). Under appropriate assumptions, we establish various analytic properties of zeta p(s), including its analytic continuation, and we characterise the existence of a suitable generalised functional equation. In particular, we examine the relationship between a counterpart of the Prime Number Theorem (with error term) and the properties of the analytic continuation of zeta p(s). Further we study 'well-behaved' g-prime systems, namely, systems for which both the prime and integer counting function are asymptotically well-behaved. Finally, we show that there exists a natural correspondence between generalised prime systems and suitable orders on N-2. Some of the above results are relevant to the second author's theory of 'fractal membranes', whose spectral partition functions are given by Beurling-type zeta functions, as well as to joint work of that author and R. Nest on zeta functions attached to quasicrystals.

Mixture models for capture-recapture count data

The contribution investigates the problem of estimating the size of a population, also known as the missing cases problem. Suppose a registration system is targeting to identify all cases having a certain characteristic such as a specific disease (cancer, heart disease, ...), disease related condition (HIV, heroin use, ...) or a specific behavior (driving a car without license). Every case in such a registration system has a certain notification history in that it might have been identified several times (at least once) which can be understood as a particular capture-recapture situation. Typically, cases are left out which have never been listed at any occasion, and it is this frequency one wants to estimate. In this paper modelling is concentrating on the counting distribution, e.g. the distribution of the variable that counts how often a given case has been identified by the registration system. Besides very simple models like the binomial or Poisson distribution, finite (nonparametric) mixtures of these are considered providing rather flexible modelling tools. Estimation is done using maximum likelihood by means of the EM algorithm. A case study on heroin users in Bangkok in the year 2001 is completing the contribution.

Elephants and ivory

Counting elephants ought to be easy. It is not. Counting elephants lost to poaching is even harder. But, without knowledge of both, how can we know whether banning the sale of ivory is helping to save elephants?Bob Burn explains the problems.

The use of image analysis to estimate population growth rate in Daphnia magna

1. Population growth rate (PGR) is central to the theory of population ecology and is crucial for projecting population trends in conservation biology, pest management and wildlife harvesting. Furthermore, PGR is increasingly used to assess the effects of stressors. Image analysis that can automatically count and measure photographed individuals offers a potential methodology for estimating PGR. 2. This study evaluated two ways in which the PGR of Daphnia magna, exposed to different stressors, can be estimated using an image analysis system. The first method estimated PGR as the ratio of counts of individuals obtained at two different times, while the second method estimated PGR as the ratio of population sizes at two different times, where size is measured by the sum of the individuals' surface areas, i.e. total population surface area. This method is attractive if surface area is correlated with reproductive value (RV), as it is for D. magna, because of the theoretical result that PGR is the rate at which the population RV increases. 3. The image analysis system proved reliable and reproducible in counting populations of up to 440 individuals in 5 L of water. Image counts correlated well with manual counts but with a systematic underestimate of about 30%. This does not affect accuracy when estimating PGR as the ratio of two counts. Area estimates of PGR correlated well with count estimates, but were systematically higher, possibly reflecting their greater accuracy in the study situation. 4. Analysis of relevant scenarios suggested the correlation between RV and body size will generally be good for organisms in which fecundity correlates with body size. In these circumstances, area estimation of PGR is theoretically better than count estimation. 5. Synthesis and applications. There are both theoretical and practical advantages to area estimation of population growth rate when individuals' reproductive values are consistently well correlated with their surface areas. Because stressors may affect both the number and quality of individuals, area estimation of population growth rate should improve the accuracy of predicting stress impacts at the population level.

The use of bioluminescence for monitoring in planta growth dynamics of a Pseudomonas syringae plant pathogen

The use of bioluminescence was evaluated as a tool to study Pseudomonas syringae population dynamics in susceptible and resistant plant environments. Plasmid pGLITE, containing the luxCDABE genes from Photorhabdus luminescens, was introduced into Pseudomonas syringae pv. phaseolicola race 7 strain 1449B, a Gram-negative pathogen of bean (Phaseolus vulgaris). Bacteria recovered from plant tissue over a five-day period were enumerated by counting numbers of colony forming units and by measurement of bioluminescence. Direct measurement of bioluminescence from leaf disc homogenates consistently reflected bacterial growth as determined by viable counting, but also detected subtle effects of the plant resistance response on bacterial viability. This bioluminescence procedure enables real time measurement of bacterial metabolism and population dynamics in planta, obviates the need to carry out labour intensive and time consuming traditional enumeration techniques and provides a sensitive assay for studying plant effects on bacterial cells.

Studies on the parallel synthesis and evaluation of new heterocyclic extractants for the partitioning of minor actinides

Multiple parallel synthesis and evaluation have been combined in order to identify new nitrogen heterocycles for the partitioning of minor actinides(III) such as americium(III) from lanthanides such as europium(Ill). An array of triazine-containing molecules was made using multiple parallel syntheses from diketones and amide hydrazides. An excess of each of the resulting purified reagents was dissolved in 1,1,2,2-tetrachloroethane containing 2-bromodecanoic acid, and equilibrated with an aqueous solution containing the radiotracers Eu-152 and Am-241 in nitric acid ([Eu] + [Am] < 400 nanomol dm(-3)). Gamma counting of the organic and aqueous phases led to the identification of several new reagents for the selective extraction of americium(III). In particular, 6-(2-pyridyl)-2-(5,6-dialkyl-1,2,4-triazaphenyl)pyridines were found to be effective reagents for the separation of americium(III) from europium(III), (SFAm/Eu was ca. 30 in [HNO3] = 0.013 mol/L).

Stubs versus swabs? A comparison of gunshot residue collection techniques

The collection efficiency of two widely used gunshot residue (GSR) collection techniques—carbon-coated adhesive stubs and alcohol swabs—has been compared by counting the number of characteristic GSR particles collected from the firing hand of a shooter after firing one round. Samples were analyzed with both scanning electron microscopy and energy dispersive X-rays by an experienced GSR analyst, and the number of particles on each sample containing Pb, Ba, and Sb counted. The adhesive stubs showed a greater collection efficiency as all 24 samples gave positive results for GSR particles whereas the swabs gave only positive results for half of the 24 samples. Results showed a statistically significant collection efficiency for the stub collection method and likely reasons for this are considered.

Retrievals of thick cloud optical depth from the Geoscience Laser Altimeter System (GLAS) by calibration of solar background signal

Laser beams emitted from the Geoscience Laser Altimeter System (GLAS), as well as other spaceborne laser instruments, can only penetrate clouds to a limit of a few optical depths. As a result, only optical depths of thinner clouds (< about 3 for GLAS) are retrieved from the reflected lidar signal. This paper presents a comprehensive study of possible retrievals of optical depth of thick clouds using solar background light and treating GLAS as a solar radiometer. To do so one must first calibrate the reflected solar radiation received by the photon-counting detectors of the GLAS 532-nm channel, the primary channel for atmospheric products. Solar background radiation is regarded as a noise to be subtracted in the retrieval process of the lidar products. However, once calibrated, it becomes a signal that can be used in studying the properties of optically thick clouds. In this paper, three calibration methods are presented: (i) calibration with coincident airborne and GLAS observations, (ii) calibration with coincident Geostationary Opera- tional Environmental Satellite (GOES) and GLAS observations of deep convective clouds, and (iii) cali- bration from first principles using optical depth of thin water clouds over ocean retrieved by GLAS active remote sensing. Results from the three methods agree well with each other. Cloud optical depth (COD) is retrieved from the calibrated solar background signal using a one-channel retrieval. Comparison with COD retrieved from GOES during GLAS overpasses shows that the average difference between the two retriev- als is 24%. As an example, the COD values retrieved from GLAS solar background are illustrated for a marine stratocumulus cloud field that is too thick to be penetrated by the GLAS laser. Based on this study, optical depths for thick clouds will be provided as a supplementary product to the existing operational GLAS cloud products in future GLAS data releases.

Oxygen isotope composition of bivalve seasonal growth increments and ambient water in the rivers Rhine and Meuse

The application of oxygen isotope ratios ({delta}18O) from freshwater bivalves as a proxy for river discharge conditions in the Rhine and Meuse rivers is investigated. We compared a dataset of water temperature and water {delta}18O values with a selection of recent shell {delta}18O records for two species of the genus Unio in order to establish: (1) whether differences between the rivers in water {delta}18O values, reflecting river discharge conditions, are recorded in unionid shells; and (2) to what extent ecological parameters influence the accuracy of bivalve shell {delta}18O values as proxies of seasonal, water oxygen isotope conditions in these rivers. The results show that shells from the two rivers differ significantly in {delta}18O values, reflecting different source waters for these two rivers. The seasonal shell {delta}18O records show truncated sinusoidal patterns with narrow peaks and wide troughs, caused by temperature fractionation and winter growth cessation. Interannual growth rate reconstructions show an ontogenetic growth rate decrease. Growth lines in the shell often, but not always, coincide with winter growth cessations in the {delta}18O record, suggesting that growth cessations in the shell {delta}18O records are a better age estimator than counting internal growth lines. Seasonal predicted and measured {delta}18O values correspond well, supporting the hypothesis that these unionids precipitate their shells in oxygen isotopic equilibrium. This means that (sub-) fossil unionids can be used to reconstruct spring-summer river discharge conditions, such as Meuse low-discharge events caused by droughts and Rhine meltwater-influx events caused by melting of snow in the Alps.

Ω-results for Beurling's zeta function and lower bounds for the generalised Dirichlet divisor problem

In this paper we study generalised prime systems for which the integer counting function NP(x) is asymptotically well behaved, in the sense that NP(x)=ρx+O(xβ), where ρ is a positive constant and . For such systems, the associated zeta function ζP(s) is holomorphic for . We prove that for , for any ε>0, and also for ε=0 for all such σ except possibly one value. The Dirichlet divisor problem for generalised integers concerns the size of the error term in NkP(x)−Ress=1(ζPk(s)xs/s), which is O(xθ) for some θ<1. Letting αk denote the infimum of such θ, we show that .

The impact of an insecticide on insect flower visitation and pollination in an agricultural landscape

1 Pesticides are considered a threat to pollinators but little is known about the potential impacts of their widespread use on pollinators. Less still is known about the impacts on pollination, comprising the ecosystem service that pollinators provide to wildflowers and crops. 2 The present study measured flower visitation and pollination in an agricultural landscape, by placing potted flowering plants (Petunia sp.) in vine fields sprayed with a highly toxic insecticide (fenitrothion). During two sampling rounds, insect visitors to the petunias were observed and measures of pollination were recorded by counting and weighing seeds. 3 In the earlier sampling round, a lower species richness of insect visitors was observed in fields that had received an early application of insecticide. No negative impacts were found from later applications. The results obtained suggest a greater potential harm to insect pollinators and flower visitation as a result of insecticide application early in the season. 4 No reduction in pollination was found in fields that received an early insecticide application. Pollination was greater with two insecticide applications between sampling rounds rather than one application. 5 In the present study system, insecticide application had a negative effect on pollinators but a possible positive effect on pollination services. In some cases, it may be that actions for conserving biodiversity will not benefit pollination services to all plants.

The effect of farming system and fertilisers on pests and natural enemies: A synthesis of current research

Organic agriculture is becoming widespread due to increased consumer demand and regulatory and political support. Organic agriculture can increase arthropod diversity but the response of pests and their natural enemies is variable. Fertiliser is an important component of agricultural systems and its effects on pests and natural enemies will influence agroecosystems. In this study, meta-analysis and vote-counting techniques were used to compare farming system (organic and conventional) and fertiliser effects on arthropod pests and their natural enemies. The meta-analyses indicated that pests generally benefitted from organic techniques, this is particularly evident when experiments were carried out on a smaller scale. Pest responses to organic and conventional fertiliser types were divergent, plant composts benefitted pest arthropods while the opposite was true for manures, this has implications for pest management. Most natural enemy groups responded positively to organic farming although this was not true for Coleopterans. Experimental scale had a prominent impact on natural enemy responses with farm scale studies showing particularly positive effects of organic agriculture on natural enemies. This suggests that it is large scale features of organic agriculture such as landscape heterogeneity that are beneficial to natural enemies. Natural enemy responses to organic fertilisers were positive indicating that field scale management practices including fertiliser can also be important in pest management.

A novel bogie design made of glass fibre reinforced plastic

This paper presents a completely new design of a bogie-frame made of glass fibre reinforced composites and its performance under various loading conditions predicted by finite element analysis. The bogie consists of two frames, with one placed on top of the other, and two axle ties connecting the axles. Each frame consists of two side arms and a transom between. The top frame is thinner and more compliant and has a higher curvature compared with the bottom frame. Variable vertical stiffness can be achieved before and after the contact between the two frames at the central section of the bogie to cope with different load levels. Finite element analysis played a very important role in the design of this structure. Stiffness and stress levels of the full scale bogie presented in this paper under various loading conditions have been predicted by using Marc provided by MSC Software. In order to verify the finite element analysis (FEA) models, a fifth scale prototype of the bogie has been made and tested under quasi-static loading conditions. Results of testing on the fifth scale bogie have been used to fine tune details like contact and friction in the fifth scale FEA models. These conditions were then applied to the full scale models. Finite element analysis results show that the stress levels in all directions are low compared with material strengths.

Activated mast cells in proximity to colonic nerves correlate with abdominal pain in irritable bowel syndrome

BACKGROUND & AIMS: The mechanisms underlying abdominal pain perception in irritable bowel syndrome (IBS) are poorly understood. Intestinal mast cell infiltration may perturb nerve function leading to symptom perception. We assessed colonic mast cell infiltration, mediator release, and spatial interactions with mucosal innervation and their correlation with abdominal pain in IBS patients. METHODS: IBS patients were diagnosed according to Rome II criteria and abdominal pain quantified according to a validated questionnaire. Colonic mucosal mast cells were identified immunohistochemically and quantified with a computer-assisted counting method. Mast cell tryptase and histamine release were analyzed immunoenzymatically. Intestinal nerve to mast cell distance was assessed with electron microscopy. RESULTS: Thirty-four out of 44 IBS patients (77%) showed an increased area of mucosa occupied by mast cells as compared with controls (9.2% +/- 2.5% vs. 3.3 +/- 0.8%, respectively; P < 0.001). There was a 150% increase in the number of degranulating mast cells (4.76 +/- 3.18/field vs. 2.42 +/- 2.26/field, respectively; P = 0.026). Mucosal content of tryptase was increased in IBS and mast cells spontaneously released more tryptase (3.22 +/- 3.48 pmol/min/mg vs. 0.87 +/- 0.65 pmol/min/mg, respectively; P = 0.015) and histamine (339.7 +/- 59.0 ng/g vs. 169.3 +/- 130.6 ng/g, respectively; P = 0.015). Mast cells located within 5 microm of nerve fibers were 7.14 +/- 3.87/field vs. 2.27 +/- 1.63/field in IBS vs. controls (P < 0.001). Only mast cells in close proximity to nerves were significantly correlated with severity and frequency of abdominal pain/discomfort (P < 0.001 and P = 0.003, respectively). CONCLUSIONS: Colonic mast cell infiltration and mediator release in proximity to mucosal innervation may contribute to abdominal pain perception in IBS patients.