Upper bounds for number of removed edges in the Erased Configuration Model

Models for generating simple graphs are important in the study of real-world complex networks. A well established example of such a model is the erased configuration model, where each node receives a number of half-edges that are connected to half-edges of other nodes at random, and then self-loops are removed and multiple edges are concatenated to make the graph simple. Although asymptotic results for many properties of this model, such as the limiting degree distribution, are known, the exact speed of convergence in terms of the graph sizes remains an open question. We provide a first answer by analyzing the size dependence of the average number of removed edges in the erased configuration model. By combining known upper bounds with a Tauberian Theorem we obtain upper bounds for the number of removed edges, in terms of the size of the graph. Remarkably, when the degree distribution follows a power-law, we observe three scaling regimes, depending on the power law exponent. Our results provide a strong theoretical basis for evaluating finite-size effects in networks

Ocean impact on decadal Atlantic climate variability revealed by sea-level observations

Decadal variability is a notable feature of the Atlantic Ocean and the climate of the regions it influences. Prominently, this is manifested in the Atlantic Multidecadal Oscillation (AMO) in sea surface temperatures. Positive (negative) phases of the AMO coincide with warmer (colder) North Atlantic sea surface temperatures. The AMO is linked with decadal climate fluctuations, such as Indian and Sahel rainfall1, European summer precipitation2, Atlantic hurricanes3 and variations in global temperatures4. It is widely believed that ocean circulation drives the phase changes of the AMO by controlling ocean heat content5. However, there are no direct observations of ocean circulation of sufficient length to support this, leading to questions about whether the AMO is controlled from another source6. Here we provide observational evidence of the widely hypothesized link between ocean circulation and the AMO. We take a new approach, using sea level along the east coast of the United States to estimate ocean circulation on decadal timescales. We show that ocean circulation responds to the first mode of Atlantic atmospheric forcing, the North Atlantic Oscillation, through circulation changes between the subtropical and subpolar gyres—the intergyre region7. These circulation changes affect the decadal evolution of North Atlantic heat content and, consequently, the phases of the AMO. The Atlantic overturning circulation is declining8 and the AMO is moving to a negative phase. This may offer a brief respite from the persistent rise of global temperatures4, but in the coupled system we describe, there are compensating effects. In this case, the negative AMO is associated with a continued acceleration of sea-level rise along the northeast coast of the United States9, 10

Meat consumption and K-ras mutations in sporadic colon and rectal cancer in The Netherlands Cohort Study

Case–cohort analyses were performed on meat and fish consumption in relation to K-ras mutations in 448 colon and 160 rectal cancers that occurred during 7.3 years of follow-up, excluding the first 2.3 years, and 2948 subcohort members of The Netherlands Cohort Study on diet and cancer. Adjusted incidence rate ratios and 95% confidence intervals were computed for colon and rectal cancer and for K-ras mutation status subgroups. Total fresh meat, most types of fresh meat and fish were not associated with colon or rectal cancer, neither overall nor with K-ras mutation status. However, several weak associations were observed for tumours with a wild-type K-ras, including beef and colon tumours, and an inverse association for pork with colon and rectal tumours; for meat products, an increased association was observed with wild-type K-ras tumours in the colon and possibly with G>A transitions in rectal tumours

Associations between diet and disease activity in ulcerative colitis patients using a novel method of data analysis

BACKGROUND: The relapsing nature and varying geographical prevalence of ulcerative colitis (UC) implicates environmental factors such as diet in its aetiology. METHODS: In order to determine which foods might be related to disease activity in UC a new method of dietary analysis was developed and applied. Eighty-one UC patients were recruited at all stages of the disease process. Following completion of a 7 d diet diary, clinical assessment including a sigmoidoscopic examination (scale 0 (normal mucosa) to 6 (very active disease)) was conducted. Food weights for each person were adjusted (divided) by the person's calorific intake for the week. Each food consumed was given a food sigmoidoscopy score (FSS) calculated by summing the products of the (adjusted) weight of food consumed and sigmoidoscopy score for each patient and occurrence of food and dividing by the total (adjusted) weight of the food consumed by all 81 patients. Thus, foods eaten in large quantities by patients with very active disease have high FSSs and vice versa. Foods consumed by <10 people or weighing <1 kg for the whole group were excluded, leaving 75 foods. RESULTS: High FSS foods were characterized by high levels of the anti-thiamin additive sulfite (Mann-Whitney, p < 0.001), i.e. bitter, white wine, burgers, soft drinks from concentrates, sausages, lager and red wine. Caffeine also has anti-thiamin properties and decaffeinated coffee was associated with a better clinical state than the caffeine containing version. Beneficial foods (average intake per week) included pork (210 g), breakfast cereals (200 g), lettuce (110 g), apples and pears (390 g), milk (1250 ml), melon (350 g), bananas (350 g), bacon (120 g), beef and beef products (500 g), tomatoes (240 g), soup (700 g), citrus fruits (300 g), fish (290 g), yogurt (410 g), cheese (110 g), potatoes (710 g) and legumes (120 g). CONCLUSIONS: The dietary analysis method described provides a new tool for establishing relationships between diet and disease and indicates a potentially therapeutic diet for UC

Comparative in situ analyses of cell wall matrix polysaccharide dynamics in developing rice and wheat grain

Cell wall polysaccharides of wheat and rice endosperm are an important source of dietary fibre. Monoclonal antibodies specific to cell wall polysaccharides were used to determine polysaccharide dynamics during the development of both wheat and rice grain. Wheat and rice grain present near synchronous developmental processes and significantly different endosperm cell wall compositions, allowing the localisation of these polysaccharides to be related to developmental changes. Arabinoxylan (AX) and mixed-linkage glucan (MLG) have analogous cellular locations in both species, with deposition of AX and MLG coinciding with the start of grain filling. A glucuronoxylan (GUX) epitope was detected in rice, but not wheat endosperm cell walls. Callose has been reported to be associated with the formation of cell wall outgrowths during endosperm cellularisation and xyloglucan is here shown to be a component of these anticlinal extensions, occurring transiently in both species. Pectic homogalacturonan (HG) was abundant in cell walls of maternal tissues of wheat and rice grain, but only detected in endosperm cell walls of rice in an unesterified HG form. A rhamnogalacturonan-I (RG-I) backbone epitope was observed to be temporally regulated in both species, detected in endosperm cell walls from 12 DAA in rice and 20 DAA in wheat grain. Detection of the LM5 galactan epitope showed a clear distinction between wheat and rice, being detected at the earliest stages of development in rice endosperm cell walls, but not detected in wheat endosperm cell walls, only in maternal tissues. In contrast, the LM6 arabinan epitope was detected in both species around 8 DAA and was transient in wheat grain, but persisted in rice until maturity

Untangling the relationship between diet and visceral fat mass through blood metabolomics and gut microbiome profiling

BACKGROUND/OBJECTIVES: Higher visceral fat mass (VFM) is associated with an increased risk for developing cardio-metabolic diseases. The mechanisms by which an unhealthy diet pattern may influence VF development has yet to be examined through cutting-edge multi-omic methods. Therefore, our objective was to examine the dietary influences on VFM and identify gut microbiome and metabolite profiles that link food intakes to VFM. SUBJECTS/METHODS: In 2218 twins with VFM, food intake and metabolomics data available we identified food intakes most strongly associated with VFM in 50% of the sample, then constructed and tested the ‘VFM diet score’ in the remainder of the sample. Using linear regression (adjusted for covariates, including BMI and total fat mass) we investigated associations between the VFM diet score, the blood metabolomics profile and the faecal microbiome (n=889), and confirmed these associations with VFM. We replicated top findings in monozygotic (MZ) twins discordant (greater than or equal to1 s.d. apart) for VFM, matched for age, sex and the baseline genetic sequence. RESULTS: Four metabolites were associated with the VFM diet score and VFM: hippurate, alpha-hydroxyisovalerate, bilirubin (Z,Z) and butyrylcarnitine. We replicated associations between VFM and the diet score (Beta[s.e.]: 0.281[0.091]; P=0.002), butyrylcarnitine (0.199[0.087]; P=0.023) and hippurate (−0.297[0.095]; P=0.002) in VFM-discordant MZ twins. We identified a single species, Eubacterium dolichum to be associated with the VFM diet score (0.042[0.011], P=8.47 × 10−5), VFM (0.057[0.019], P=2.73 × 10−3) and hippurate (−0.075[0.032], P=0.021). Moreover, higher blood hippurate was associated with elevated adipose tissue expression neuroglobin, with roles in cellular oxygen homeostasis (0.016[0.004], P=9.82 × 10−6). CONCLUSION: We linked a dietary VFM score and VFM to Eubacterium dolichum and four metabolites in the blood. In particular, the relationship between hippurate, a metabolite derived from microbial metabolism of dietary polyphenols, and reduced VFM, the microbiome and increased adipose tissue expression of neuroglobin provides potential mechanistic insight into the influence of diet on VFM

Characterizing blood metabolomics profiles associated with self-reported food intakes in female twins

Using dietary biomarkers in nutritional epidemiological studies may better capture exposure and improve the level at which diet-disease associations can be established and explored. Here, we aimed to identify and evaluate reproducibility of novel biomarkers of reported habitual food intake using targeted and non-targeted metabolomic blood profiling in a large twin cohort. Reported intakes of 71 food groups, determined by FFQ, were assessed against 601 fasting blood metabolites in over 3500 adult female twins from the TwinsUK cohort. For each metabolite, linear regression analysis was undertaken in the discovery group (excluding MZ twin pairs discordant [≥1 SD apart] for food group intake) with each food group as a predictor adjusting for age, batch effects, BMI, family relatedness and multiple testing (1.17x10-6 = 0.05/[71 food groups x 601 detected metabolites]). Significant results were then replicated (non-targeted: P<0.05; targeted: same direction) in the MZ discordant twin group and results from both analyses meta-analyzed. We identified and replicated 180 significant associations with 39 food groups (P<1.17x10-6), overall consisting of 106 different metabolites (74 known and 32 unknown), including 73 novel associations. In particular we identified trans-4-hydroxyproline as a potential marker of red meat intake (0.075[0.009]; P = 1.08x10-17), ergothioneine as a marker of mushroom consumption (0.181[0.019]; P = 5.93x10-22), and three potential markers of fruit consumption (top association: apple and pears): including metabolites derived from gut bacterial transformation of phenolic compounds, 3-phenylpropionate (0.024[0.004]; P = 1.24x10-8) and indolepropionate (0.026[0.004]; P = 2.39x10-9), and threitol (0.033[0.003]; P = 1.69x10-21). With the largest nutritional metabolomics dataset to date, we have identified 73 novel candidate biomarkers of food intake for potential use in nutritional epidemiological studies. We compiled our findings into the DietMetab database (http://www.twinsuk.ac.uk/dietmetab-data/), an online tool to investigate our top associations