Monotonicity of Degrees of Generalized Alexander Polynomials of Groups and 3-Manifolds

We investigate the behavior of the higher-order degrees, db_n, of a finitely presented group G. These db_n are functions from H^1(G;Z) to Z whose values are the degrees certain higher-order Alexander polynomials. We show that if def(G) is at least 1 or G is the fundamental group of a compact, orientable 3-manifold then db_n is a monotonically increasing function of n for n at least 1. This is false for general groups. As a consequence, we show that if a 4 manifold of the form X times S^1 admits a symplectic structure then X ``looks algebraically like'' a 3-manifold that fibers over S^1, supporting a positive answer to a question of Taubes. This generalizes a theorem of S. Vidussi and is an improvement on the previous results of the author. We also find new conditions on a 3-manifold X which will guarantee that the Thurston norm of f*(psi), for psi in H^1(X;\Z) and f:Y -> X a surjective map on pi_1, will be at least as large the Thurston norm of psi. When X and Y are knot complements, this gives a partial answer to a question of J. Simon. More generally, we define Gamma-degrees, db_Gamma, corresponding to a surjective map G -> Gamma for which Gamma is poly-torsion-free-abelian. Under certain conditions, we show they satisfy a monotonicity condition if one varies the group. As a result, we show that these generalized degrees give obstructions to the deficiency of a group being positive and obstructions to a finitely presented group being the fundamental group of a compact, orientable 3-manifold.Comment: 19 page

Grading Grain Under the U.S. Grain Standards

Crop Production/Industries,

The Korteweg-de Vries equation and water waves. Part 2. Comparison with experiments

The Korteweg-de Vries (KdV) equation is tested experimentally as a model for moderate amplitude waves propagating in one direction in relatively shallow water of uniform depth. For a wide range of initial data, comparisons are made between the asymptotic wave forms observed and those predicted by the theory in terms of the number of solitons that evolve, the amplitude of the leading soliton, the asymptotic shape of the wave and other qualitative features. The KdV equation is found to predict accurately the number of evolving solitons and their shapes for initial data whose asymptotic characteristics develop in the test section of the wave tank. The accuracy of the leading-soliton amplitudes computed by the KdV equation could not be conclusively tested owing to the viscous decay of the measured wave amplitudes; however, a procedure is presented for estimating the decay in amplitude of the leading wave. Computations suggest that the KdV equation predicts the amplitude of the leading soliton to within the expected error due to viscosity (12%) when the non-decayed amplitudes are less than about a quarter of the water depth. Indeed, agreement to within about 20% is observed over the entire range of experiments examined, including those with initial data for which the non-decayed amplitudes of the leading soliton exceed half the fluid depth

Relative Abundance, Seasonal Distribution and Taxonomy of Sphingidae of Northeast Arkansas

A total of 38 species of sphingids, with keys and descriptions, are reported from Northeast Arkansas. Graphs and tables are presented to show relative abundance and seasonal distribution. Drawings of genitalia, fore tibiae, and forewings, as well as photographs of species in the key are included

Developing best practice for infilling daily river flow data

Complete river flow time series are indispensable to the sustainable management of water resources and even very short gaps can severely compromise data utility. Suitably-flagged flow estimates, derived via judicious infilling, are thus highly beneficial. The UK National River Flow Archive provides stewardship of and access to daily river flow records from over 1500 gauging stations and, whilst the majority are sensibly complete, historical validation reveals a significant quantity of gaps. A full assessment of the suitability of existing techniques for infilling such gaps is lacking. This paper therefore presents an appraisal of various simple infilling techniques, including regression, scaling and equipercentile analysis, according to their ability to generate daily flow estimates for 25 representative UK gauging stations. All of the techniques rely upon data transfer from donor stations and results reveal that the equipercentile and multiple regression approaches perform best. Case studies offer further insight and an example of infilling is presented, along with areas of future study. The results demonstrate the potential for developing generic infilling methodologies to ensure a consistent and auditable approach towards infilling, which could find wider application both within the UK and internationally

On the Cut Number of a 3-manifold

The question was raised as to whether the cut number of a 3-manifold X is bounded from below by 1/3 beta_1(X). We show that the answer to this question is `no.' For each m>0, we construct explicit examples of closed 3-manifolds X with beta_1(X)=m and cut number 1. That is, pi_1(X) cannot map onto any non-abelian free group. Moreover, we show that these examples can be assumed to be hyperbolic.Comment: Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper15.abs.htm

The narrative coherence of witness transcripts in children on the autism spectrum

Background and Aims. Autistic children often recall fewer details about witnessed events than typically developing children (of comparable age and ability), although the information they recall is generally no less accurate. Previous research has not examined the narrative coherence of such accounts, despite higher quality narratives potentially being perceived more favourably by criminal justice professionals and juries. This study compared the narrative coherence of witness transcripts produced by autistic and typically developing (TD) children (ages 6-11 years, IQs 70+). Methods and Procedures. Secondary analysis was carried out on interview transcripts from a subset of 104 participants (autism=52, TD=52) who had taken part in a larger study of eyewitness skills in autistic and TD children. Groups were matched on chronological age, IQ and receptive language ability. Coding frameworks were adopted from existing narrative research, featuring elements of ‘story grammar’. Outcomes and Results. Whilst fewer event details were reported by autistic children, there were no group differences in narrative coherence (number and diversity of ‘story grammar’ elements used), narrative length or semantic diversity. Conclusions and Implications. These findings suggest that the narrative coherence of autistic children’s witness accounts is equivalent to TD peers of comparable age and ability

Suramin inhibits the early effects of PLA(2) neurotoxins at mouse neuromuscular junctions: a twitch tension study

Several phospholipase A(2) (PLA(2)) neurotoxins from snake venoms can affect acetylcholine release at the neuromuscular junction. In isolated nerve-muscle preparations three distinct phases have been described for this phenomenon: An initial transient decrease in twitch tension; a second facilitatory phase during which twitch height is greater than control twitch height; and the last phase which causes a reduction in twitch height that finally results in paralysis. Suramin has been reported to inhibit the toxic effects of β-bungarotoxin and another PLA(2) neurotoxin, crotoxin in vitro and in vivo. We have further examined the effects of suramin on the three phases of the effects of the presynaptic PLA(2) neurotoxins β-bungarotoxin, taipoxin and ammodytoxin on mouse phrenic nerve-hemidiaphragm preparations. When preparations were pre-treated with suramin (0.3mM), the early biphasic effects (depression followed by facilitation) were abolished, and the time taken for final blockade induced by β-bungarotoxin, taipoxin and ammodytoxin A was significantly prolonged. In contrast, suramin did not significantly affect the facilitation induced by the potassium channel blocking toxin dendrotoxin I when applied under the same conditions. In addition, application of 0.3mM suramin did not prevent the facilitatory actions of 3,4-diaminopyridine (3,4-DAP) and tetraethylammonium chloride (TEA). Overall, the mechanism whereby suramin reduces the effects of PLA(2) neurotoxins remains elusive. Since suramin reduces both enzyme-dependent and enzyme-independent effects of the toxins, suramin is not acting as a simple enzyme inhibitor. Furthermore, the observation that suramin does not affect actions of standard K(+) channel blockers suggests that suramin does not stabilise nerve terminals

Halogen occultation experiment (HALOE) optical witness-plate program

An optical witness plate program was implemented to monitor buildup of molecular contamination in the clean room during the assembly and testing of the Halogen Occulation Experiment (HALOE) instrument. Travel plates to monitor molecular contamination when the instrument is not in the clean room are also measured. The instrument technique is high-resolution transmission spectroscopy in the 3 micron spectral region using a Fourier transform spectrometer. Witness specimens of low index of refraction, infrared transmitting material are used for contaminant monitoring and for spectral signature analysis. Spectral signatures of possible molecular contamination are presented. No condensible volatile material contamination of HALOE optical witness specimens have yet been found