Search Interfaces for Mathematicians

Access to mathematical knowledge has changed dramatically in recent years, therefore changing mathematical search practices. Our aim with this study is to scrutinize professional mathematicians' search behavior. With this understanding we want to be able to reason why mathematicians use which tool for what search problem in what phase of the search process. To gain these insights we conducted 24 repertory grid interviews with mathematically inclined people (ranging from senior professional mathematicians to non-mathematicians). From the interview data we elicited patterns for the user group "mathematicians" that can be applied when understanding design issues or creating new designs for mathematical search interfaces.Comment: conference article "CICM'14: International Conference on Computer Mathematics 2014", DML-Track: Digital Math Libraries 17 page

So many genes, so little time: A practical approach to divergence-time estimation in the genomic era

Phylogenomic datasets have been successfully used to address questions involving evolutionary relationships, patterns of genome structure, signatures of selection, and gene and genome duplications. However, despite the recent explosion in genomic and transcriptomic data, the utility of these data sources for efficient divergence-time inference remains unexamined. Phylogenomic datasets pose two distinct problems for divergence-time estimation: (i) the volume of data makes inference of the entire dataset intractable, and (ii) the extent of underlying topological and rate heterogeneity across genes makes model mis-specification a real concern. “Gene shopping”, wherein a phylogenomic dataset is winnowed to a set of genes with desirable properties, represents an alternative approach that holds promise in alleviating these issues. We implemented an approach for phylogenomic datasets (available in SortaDate) that filters genes by three criteria: (i) clock-likeness, (ii) reasonable tree length (i.e., discernible information content), and (iii) least topological conflict with a focal species tree (presumed to have already been inferred). Such a winnowing procedure ensures that errors associated with model (both clock and topology) mis-specification are minimized, therefore reducing error in divergence-time estimation. We demonstrated the efficacy of this approach through simulation and applied it to published animal (Aves, Diplopoda, and Hymenoptera) and plant (carnivorous Caryophyllales, broad Caryophyllales, and Vitales) phylogenomic datasets. By quantifying rate heterogeneity across both genes and lineages we found that every empirical dataset examined included genes with clock-like, or nearly clock-like, behavior. Moreover, many datasets had genes that were clock-like, exhibited reasonable evolutionary rates, and were mostly compatible with the species tree. We identified overlap in age estimates when analyzing these filtered genes under strict clock and uncorrelated lognormal (UCLN) models. However, this overlap was often due to imprecise estimates from the UCLN model. We find that “gene shopping” can be an efficient approach to divergence-time inference for phylogenomic datasets that may otherwise be characterized by extensive gene tree heterogeneity

On the accuracy of conservation of adiabatic invariants in slow-fast systems

Let the adiabatic invariant of action variable in slow-fast Hamiltonian system with two degrees of freedom have two limiting values along the trajectories as time tends to infinity. The difference of two limits is exponentially small in analytic systems. An iso-energetic reduction and canonical transformations are applied to transform the slow-fast systems to form of systems depending on slowly varying parameters in a complexified phase space. On the basis of this method an estimate for the accuracy of conservation of adiabatic invariant is given for such systems.Comment: 27 pages, 14 figure

Blood profiles of indigenous Pedi goats fed varying levels of Vachellia karroo leaf meal in Setaria verticillata hay-based diet

Vachellia karroo (Acacia karroo) is promising fodder for goats in the critical dry season in communal rangelands. The only limitation to the use of this fodder tree is the presence of phenolic compounds, such as condensed tannins. A study was conducted to investigate the effects of tanniniferous V. karroo leaf meal feeding on blood profiles of indigenous Pedi goats fed a basal diet of Setaria verticillata grass hay. Twenty indigenous Pedi goats, weighing 18 ± 2 kg, were allocated in a completely randomized design to five dietary treatments containing V. karroo leaf meal at 20% (S80A20), 25% (S75A25), 30% (S70A30), 40% (S60A40) and 50% (S50A50) of the total diet in a 22-day trial. Twelve ml of blood were collected from the jugular vein from each goat before and after the experiment for haematological and serum biochemical assays. Daily dry matter intake (DMI) was similar across treatments, ranging from 633 g to 765 g per goat per day. There was no difference in initial and final bodyweights of goats consuming various experimental diets. However, bodyweight gains were significantly higher in goats fed a diet with 50% leaf meal as compared with other treatment groups. There were no differences in haematological indices of Pedi goats except for mean corpuscular haemoglobin (Hb) concentration. Goats fed 50% leaf meal had significantly lower mean corpuscular haemoglobin concentration (MCHC) values as compared with other treatment groups. Similarly, there were no differences in the blood serum chemistry of goats that consumed various inclusion levels of V. karroo, except for serum total protein (TP) and alanine aminotransferase (ALT). Goats fed 50% leaf meal had depressed serum TP, while serum enzyme Alanine aminotransferase (ALT) concentration decreased significantly in goats fed 25% leaf meal as compared with those on the 20% dietary treatment. Tannin concentration of 8.2 g/kg dry matter (DM) had no toxic effect on experimental animals. A 40 % inclusion of V. karroo in a Setaria verticillata hay-based diet may be fed to indigenous Pedi goats without compromising the immunity system and health of the animals.Keywords: Condensed tannin, fodder, haematology, seru

Exact two-particle eigenstates in partially reduced QED

We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. It is shown that exact few-fermion eigenstates of the resulting Hamiltonian can be obtained in the canonical equal-time formalism for the case where there are no free photons. These eigenstates lead to two- and three-body Dirac-like equations with electromagnetic interactions. Perturbative and some numerical solutions of the two-body equations are presented for positronium and muonium-like systems, for various strengths of the coupling.Comment: 33 pages, LaTex 2.09, 4 figures in EPS forma

An X-ray preionised mercury bromide discharge laser

An X-ray preionised mercury bromide discharge laser (502-504 nm) has been designed, constructed and optimised. The double pulse forming line system built to drive the laser has proven to be both versatile and reliable. It utilises multiple-paralleled thyratrons and has demonstrated the characteristics required for long life operation of high average power gas discharge lasers. The supply produces a voltage pulse of 240 nsec duration and its output impedance is variable from 300 mO to 3.6O. With twelve thyratrons in parallel current risetimes of 83 kA musec-1 into a 300 mO matched load and 2 nsec jitter have been achieved. A voltage transient on the leading edge of the discharge pulse, to aid gas breakdown, up to 1½ times the line charge voltage is possible through a 'spike line' incorporated in the system. The X-ray preioniser, based on a cold cathode field emitter, produces an exposure of 5 mR in the discharge region which is adequate for effective preionisation of the laser. A full parametric study of the laser covering gas composition and pressure. X-ray source effects energy loading and other pulsed power supply effects has been carried out. The peak output energy recorded was 710 mJ with neon buffer gas at 4 atmospheres pressure. This represents an energy extraction of 0.5 JL-1. Pulse lengths of 92 nsec (FWHM) and efficiencies greater than 1.5 % have been achieved