Chromatic Numbers of Simplicial Manifolds

Higher chromatic numbers $\chi_s$ of simplicial complexes naturally generalize the chromatic number $\chi_1$ of a graph. In any fixed dimension $d$, the $s$-chromatic number $\chi_s$ of $d$-complexes can become arbitrarily large for $s\leq\lceil d/2\rceil$ [6,18]. In contrast, $\chi_{d+1}=1$, and only little is known on $\chi_s$ for $\lceil d/2\rceil<s\leq d$. A particular class of $d$-complexes are triangulations of $d$-manifolds. As a consequence of the Map Color Theorem for surfaces [29], the 2-chromatic number of any fixed surface is finite. However, by combining results from the literature, we will see that $\chi_2$ for surfaces becomes arbitrarily large with growing genus. The proof for this is via Steiner triple systems and is non-constructive. In particular, up to now, no explicit triangulations of surfaces with high $\chi_2$ were known. We show that orientable surfaces of genus at least 20 and non-orientable surfaces of genus at least 26 have a 2-chromatic number of at least 4. Via a projective Steiner triple systems, we construct an explicit triangulation of a non-orientable surface of genus 2542 and with face vector $f=(127,8001,5334)$ that has 2-chromatic number 5 or 6. We also give orientable examples with 2-chromatic numbers 5 and 6. For 3-dimensional manifolds, an iterated moment curve construction [18] along with embedding results [6] can be used to produce triangulations with arbitrarily large 2-chromatic number, but of tremendous size. Via a topological version of the geometric construction of [18], we obtain a rather small triangulation of the 3-dimensional sphere $S^3$ with face vector $f=(167,1579,2824,1412)$ and 2-chromatic number 5.Comment: 22 pages, 11 figures, revised presentatio

A person-time analysis of hospital activity among cancer survivors in England.

BACKGROUND: There are around 2 million cancer survivors in the UK. This study describes the inpatient and day case hospital activity among the population of cancer survivors in England. This is one measure of the burden of cancer on the individual and the health service. METHODS: The national cancer registry data set for England (1990-2006) is linked to the NHS Hospital Episode Statistics (HES) database. Cohorts of survivors were defined as those people recorded in the cancer registry data with a diagnosis of breast, colorectal, lung or prostate cancer before 2007. The person-time of prevalence in 2006 for each cohort of survivors was calculated according to the cancer type, sex, age and time since diagnosis. The corresponding HES episodes of care in 2006 were used to calculate the person-time of admitted hospital care for each cohort of survivors. The average proportion of time spent in hospital by survivors in each cohort was calculated as the summed person-time of hospital activity divided by the summed person-time of prevalence. The analysis was conducted separately for cancer-related episodes and non-cancer-related episodes. RESULTS: Lung cancer survivors had the highest intensity of cancer-related hospital activity. For all cancers, cancer-related hospital activity was highest in the first year following diagnosis. Breast and prostate cancer survivors had peaks of cancer-related hospital activity in the relatively young and relatively old age groups. The proportion of time spent in hospital for non-cancer-related care was much lower than that for cancer-related care and increased gradually with age but was generally constant regardless of time since diagnosis. CONCLUSION: The person-time approach used in this study is more revealing than a simple enumeration of cancer survivors and hospital admissions. Hospital activity among cancer survivors is highest soon after diagnosis. The effect of age on the amount of hospital activity is different for each type of cancer

Spectral characterisation of red pigment in Italian-type dry-cured ham. Increasing lipophilicity druing processing and maturation

Spectroscopic studies of Parma ham during processing revealed a gradual transformation of muscle myoglobin, initiated by salting and continuing during ageing. Electron spin resonance spectra did, however, conclusively show that the pigment in dry-cured Parma ham at no stage is a nitrosyl complex of ferrous myoglobin as found in brine-cured ham and Spanish Serrano hams. Both near-infra red reflectance spectra of sliced ham and UV/visible absorption spectra of extract of hams, obtained with aqueous buffer or acetone, showed the presence of different red pigments at varying processing stages for both solvents. Especially, the pigment extracted with aqueous buffer exhibited unique spectral features different from those of well-known myoglobin derivatives. At the end of processing, the pigment(s) becomes less water extractable, while the fraction of red pigment(s) extractable with acetone/water (75%/25%) increases throughout the processing time up to full maturation at 18 months. The chemical identity of the 6th ligand of myoglobin could not be conclusively established, but possible candidates are discussed. The partition of the pigment(s) between pentane and acetone/water showed a strong preference for pentane, suggesting that only the heme moiety is present in the acetone/water extract, and that Parma ham pigment is gradually transformed from a myoglobin derivative into a non-protein heme complex, which was found to be thermally stable in acetone/water solutio

EDITORIAL

Editorial to the second issue of CLa

Asymptotic statistics of the n-sided planar Voronoi cell: II. Heuristics

We develop a set of heuristic arguments to explain several results on planar Poisson-Voronoi tessellations that were derived earlier at the cost of considerable mathematical effort. The results concern Voronoi cells having a large number n of sides. The arguments start from an entropy balance applied to the arrangement of n neighbors around a central cell. It is followed by a simplified evaluation of the phase space integral for the probability p_n that an arbitrary cell be n-sided. The limitations of the arguments are indicated. As a new application we calculate the expected number of Gabriel (or full) neighbors of an n-sided cell in the large-n limit.Comment: 22 pages, 10 figure

Thermal and photochemical degradation of myoglobin pigments in relation to colour stability of sliced dry-cured Parma ham and sliced dry-cured ham produced with nitrite salt

Lipophilic and hydrophilic extracts of the red pigments from Parma ham and nitrosylated pigment of dry-cured ham produced with nitrite salt were prepared with acetone/water (75/25 v/v %) solution and aqueous phosphate buffer, respectively. The spectral characteristics differed for both the lipophilic and the hydrophilic Parma ham pigment compared with the dry-cured ham produced with nitrite salt. The red lipophilic pigment(s) extractable from Parma ham was(were) found to be very stable towards thermal degradation in acetone/water (75/25 v/v %) solution for temperatures up to 70 °C in contrast to the lipophilic pigment(s) extractable from dry-cured ham produced with nitrite salt, which was(were) found to have an energy of activation of 99 kJ/mol for thermal degradation. In contrast, quantum yields for photodegradation of the lipophilic ham pigments exposed to 366 nm (420 nm) monochromatic light were larger for Parma ham than for nitrite-cured ham [1.6×10–5 (6.9×10–6) versus 1.6×10–6 (2×10–6) mol einstein–1] as determined for acetone/water (75/25 v/v %) solution. In agreement with these findings for the extracted lipophilic pigments, sliced Parma ham showed better colour stability than sliced dry-cured ham produced with nitrite salt, when stored in the dark at low oxygen concentration, in contrast to a faster initial discolouration for Parma ham when exposed to light, as shown for chilled storage for 35 days under retail conditions for the two products each packed at two oxygen levels (0.4 and 21%)

Usability Testing of User Manuals

Many guidelines and several standards exist for the development of good user manuals. But even though technical writers comply with all guidelines, problems will typically arise when users apply the manual in practice. Therefore, it is useful to have real users test the manual before it is published. This article discusses user tests in the form of think-aloud tests, with examples from the research project ”User Manuals for older adults”

Studies on the antioxidative activity of red pigments in Italian-type dry-cured ham

Aqueous phosphate buffer extracts and acetone/water extracts of pigments from Parma ham were assessed as antioxidants by (1) electron spin resonance spectroscopy using a spin probing technique to evaluate their efficiencies as scavengers of free radicals, and (2) by electrochemical measurement of oxygen depletion rate in an aqueous methyl linoleate emulsion to evaluate their efficiencies as chain-breaking antioxidant, and using both methods, compared with the effect of apomyoglobin and nitrosylmyoglobin. Aqueous phosphate extracts and acetone/water extracts of Parma ham pigment both scavenged a semi-stable nitroxide radical (Fremy's salt), and both extracts reduced the rate of oxygen consumption for lipid peroxidation (initiated by metmyoglobin) very efficiently. For apomyoglobin no antioxidative capacity was observed, and the heme moiety of the pigment(s) of Parma ham were concluded to have antioxidative properties. The more lipophilic pigment, as extracted by acetone/water, had the most significant effect, and its ability to inhibit lipid oxidation was further tested in a model food system based on cooked pork. The lipid oxidation was increasingly inhibited by increasing additions from 0.12 ppm to 0.24 ppm Parma ham pigment, and the pigment protected a-tocopherol against degradation in a concentration dependent manner

The future burden of cancer in London compared with England.

BACKGROUND: The future burden of cancer in England is predicted to increase by 33% by 2020. Those planning health services are often interested in predictions at a local level. This study aimed to estimate the future burden of cancer in London and compare this with estimates for England. METHODS: Predictions for London were based on cancer registration data (1985-2003) and population projections up until 2024. The number of future cases and age-standardized incidence rates (ASRs) were projected using an age-period-cohort model developed for the analysis of cancer trends and projections in the Nordic countries. Estimates for England were taken from an earlier publication. RESULTS: In London, ASRs for all cancers (excluding non-melanoma skin cancer) decreased for both sexes, whereas in England, ASRs decreased in males and increased slightly in females. In London, the number of cases for both sexes is predicted to increase from approximately 27,000 in 2002 to approximately 28,500 in 2022, an increase of 5%. In England, a greater increase is predicted, from approximately 224,000 in 2001 to approximately 299,000 in 2020, an increase of 33%. CONCLUSIONS: Projections of the future burden of cancer are particularly sensitive to demographic population trends. They are likely to be different for cities compared with rural areas or entire countries