Characters of the W3 algebra

Traces of powers of the zero mode in the W3 Algebra have recently been found to be of interest, for example in relation to Black Hole thermodynamics, and arise as the terms in an expansion of the full characters of the algebra. We calculate the first few such powers in two cases. Firstly, we find the traces in the 3-state Potts model by using null vectors to derive modular differential equations for the traces. Secondly, we calculate the exact results for Verma module representations. We compare our two methods with each other and the result of brute-force diagonalisation for low levels and find complete agreement.Comment: v2: Numerous small changes, version to appear in JHEP, 22 pages. v3: Typos corrected, matches published version, 22 page

On compactness of admissible parameter sets: Convergence and stability in inverse problems for distributed parameter systems

A series of numerical examples is reported and several algorithms compared for estimation of coefficients in differential equation models. Unconstrained, constrained and Tikhonov regularization methods are tested for their behavior with regard to both convergence (of approximation methods for the states and parameters) and stability (continuity of the estimates with respect to perturbations in the data or observed states)

Production of placental alkaline phosphatase (PLAP) and PLAP-like material by epithelial germ cell and non-germ cell tumours in vitro

Placental and placental-like alkaline phosphatase (PLAP) levels in the culture media of 87 cell lines of neoplastic and 'normal' origin were measured by a conventional immunosorbent enzymatic assay (IAEA) and by a new immunoradiometric assay (IRMA). The IRMA detected immunoreactive PLAP in 37 of 80 (46%) human epithelial and germ cell cultures, while the IAEA detected PLAP in only 25 (33%). Of the 52 non-germ cell tumour cultures, the IRMA detected expression in 24 (46%) and the IAEA in only 16 (31%). In 17 cases (21%) the IRMA recorded levels double that of the IAEA, while in five cultures (6%) the reverse was true. The IRMA was much more robust than the IAEA and had considerably lower inter- and intra-assay coefficients of variation (3.75-8.5% vs 5.2-46%). Detection of PLAP(-like) expression by IAEA is dependent on neoplastic expression of enzymatically functional molecules and quantification assumes constant enzyme kinetics. PLAP-like material has a higher catalytic rate constant than PLAP and thus will give higher values on a stoichiometric basis in an IAEA. The higher detection rate and levels of PLAP-like material in neoplastic cultures when measured by the IRMA clearly demonstrate ectopic expression of non-enzymatic PLAP and PLAP-like genes. The incidence of PLAP(-like) expression by non-germ cell and possible germ cell tumours has been underestimated and its utility as a tumour marker should be re-examined using assays which measure antigen mass rather than phosphatase activity

Effects of Variable and Changing Environments on Demography: Inferences from a Lesser Snow Goose Colony

Anthropogenic pressures have caused changes in both the mean and variance of environmental conditions, with associated effects on the demography of natural populations. The demographic effects of environmental change can manifest through direct (i.e., physiological) or indirect pathways (i.e., through shifts in species interactions). For many populations, environmental change will affect multiple life cycle stages simultaneously, thereby altering vital rate correlation structures with potentially important impacts on evolutionary fitness. The effects of environmental change will also often be habitat-specific, particularly when species interactions modify demographic sensitivity to climate. As a result, the effects of climate change are likely to vary across a species range, with important implications for range expansion and population viability. In chapter 2, I examine the effects of joint vital rate responses to environmental drivers on the evolution of life histories in variable environments. I show that vital rate covariation, generated when multiple vital rates respond to a shared environmental driver, can fundamentally alter evolutionary selection pressures. Negative vital rate covariation promotes the evolution of demographic lability (stronger demographic responsiveness), while positive covariation promotes buffering (weaker demographic responsiveness), altering the range of life histories over which the evolution of buffered and labile vital rates are a predicted evolutionary outcome. By identifying the life histories for which selection pressures are most sensitive to environmentally-driven vital rate covariation, this study provides a richer understanding of both life history evolution and the capacity of species to cope with ongoing changes to contemporary environments. In chapter 3, I use a long-term study of lesser snow geese to test the hypothesis that demographic and developmental responses to climate will be weakest in habitats where resource diversity is greatest. I find support for this hypothesis, and my results indicate that gosling demography is much more responsive to climate in recently colonized, freshwater habitats where landscape diversity and gosling diet diversity is low. These results underscore the potential importance of accounting for biotic interactions when predicting spatio-temporal responses to climate. In chapter 4, I quantify the consequences of observed climate change for lesser snow goose population dynamics across habitats. I find that climate change increases population growth in all habitats, but that such increases are disproportionately large in novel inland freshwater habitats. These results suggest that in a warmer and more variable climate, the breeding range and population growth of lesser snow geese is likely to increase, counteracting current management efforts to reduce overabundant populations

Determination of the glycoforms of human chorionic gonadotropin b-core fragment by matrix-assisted laser desoption/ionisation time of flight mass spectrometry

Background: Metabolism of human chorionic gonadotropin (hCG) in the serum and kidney yields the terminal urinary product hCG ß-core fragment (hCGßcf), comprising two disulfide-linked peptides (ß6-ß40 and ß55-ß92) of which one (ß6-ß40) retains truncated N-linked sugars. Hyperglycosylated hCGßcf may indicate choriocarcinoma or Down syndrome, but the glycosylation profile of hCGßcf has not been thoroughly evaluated. Methods: hCGßcf, purified from pregnancy urine, was reduced by "on-target" dithiothreitol (DTT) reduction and analyzed by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). The mass ([M+H]+) of the primary sequence of the glycosylated peptide ß6-ß40 was subtracted from the m/z values of the discrete peaks observed to give the masses of the carbohydrate moieties. Carbohydrate structure was predicted by sequentially subtracting the masses of the monosaccharide residues corresponding to N-linked carbohydrates of the hCG ß-subunit reported in the literature. Results: Mass spectra of hCGßcf revealed a broad triple peak at m/z 8700–11300. After reduction, the triple peak was replaced by a discrete set of peaks between m/z 4156 and 6354. A peak at m/z 4156.8 corresponded to the nonglycosylated peptide (ß55-ß92). The remaining nine peaks indicated that urinary hCGßcf comprises a set of glycoforms smaller and larger than the trimannosyl core. Conclusions: hCGßcf comprises a wider set of glycoforms than reported previously. Peaks of highest mass indicate evidence of hyperglycosylated carbohydrate moieties. The data support previous reports that hCGßcf oligosaccharides lack sialic acid and galactose residues. No indication was found of a ß6-ß40 peptide that was entirely devoid of carbohydrate

The effects of beta-human chorionic gonadotrophin on the in vitro growth of bladder cancer cell lines

The effects of human chorionic gonadotrophin (hCG) and its subunits on in vitro bladder cancer cell growth have been assessed using the a tetrazolium salt reduction assay (MTT). Intact hCG, alpha-hCG and beta-core hCG all had no effect on cell growth, while beta-hCG increased MTT reduction in all four bladder cancer lines tested. The magnitude of beta-hCG stimulation was maximal in the T24 line, which does not itself produce beta-hCG and appeared to be correspondingly lower in beta-hCG-secreting lines. The addition of antibodies to beta-hCG inhibited MTT reduction among high secretors but failed to inhibit MTT reduction in non-beta-hCG producers. These results are consistent with the poor prognosis associated with beta-hCG expression by bladder tumours in vivo and suggest an autocrine/paracrine stimulation of tumour growth by endogenously produced beta-hCG

The temporary anatomical structures prominent in the first trimester may be fulfilling exchange functions assigned to the placenta in the second and third trimester

The extra-embryonic coelom (EEC) and secondary yolk sac are prominent structures in the gestational sac during the first trimester of human pregnancy, at a time before the definitive placental circulation becomes established. We propose that the EEC and yolk sac play a critical role in the nutrition of early pregnancy, fulfilling exchange functions which are assumed by the placenta at a later stage

Modular properties of characters of the W3 algebra

In a previous work, exact formulae and differential equations were found for traces of powers of the zero mode in the W3 algebra. In this paper we investigate their modular properties, in particular we find the exact result for the modular transformations of traces of $W_0^n$ for n = 1, 2, 3, solving exactly the problem studied approximately by Gaberdiel, Hartman and Jin. We also find modular differential equations satisfied by traces with a single $W_0$ inserted, and relate them to differential equations studied by Mathur et al. We find that, remarkably, these all seem to be related to weight 0 modular forms with expansions with non-negative integer coefficients.Comment: 20 pages. v2: 23 pages. v3: 23 pages, published in JHE

Direct evidence for the magnetic ordering of Nd ions in NdFeAsO by high resolution inelastic neutron scattering

We investigated the low energy excitations in the parent compound NdFeAsO of the Fe-pnictide superconductor in the $\mu$eV range by a back scattering neutron spectrometer. The energy scans on a powder NdFeAsO sample revealed inelastic peaks at E = 1.600 $\pm 0.003 \mu$eV at T = 0.055 K on both energy gain and energy loss sides. The inelastic peaks move gradually towards lower energy with increasing temperature and finally merge with the elastic peak at about 6 K. We interpret the inelastic peaks to be due to the transition between hyperfine-split nuclear level of the $^{143}$Nd and $^{145}$Nd isotopes with spin $I = 7/2$. The hyperfine field is produced by the ordering of the electronic magnetic moment of Nd at low temperature and thus the present investigation gives direct evidence of the ordering of the Nd magnetic sublattice of NdFeAsO at low temperature

Measurement of urinary beta core fragment of human chorionic gonadotrophin in women with vulvovaginal malignancy and its prognostic significance

Tumours of the vulva and vagina are rare and there are relatively few studies of circulating markers in these conditions. The urinary measurement of the core fragment of the beta-subunit of hCG has been proposed as a useful tumour marker in non-trophoblastic gynaecological malignancies. This study describe the measurement of urinary beta-core in 50 patients with vulvovaginal malignancy. In contrast to other studies corrections were made for both the effect of urine concentration and the age of the patient. Each patient was followed up for at least 24 months, and at this time their status was correlated with their initial level of urinary beta-core. The sensitivity of beta-core was only 38%, but of those patients with elevated levels 90% had died within 24 months, while only 32% of those with normal levels had died. For both patients at initial presentation and those with recurrent disease, there was a highly significant difference in the survival curve between those with elevated beta-core levels and those with normal levels. This is similar to findings in cervical carcinoma, and suggests that for lower genital tract cancer the measurement of urinary beta-core may be valuable as a prognostic indicator, allowing a more informed approach to treatment and follow-up