Tutte polynomial of pseudofractal scale-free web

The Tutte polynomial of a graph is a 2-variable polynomial which is quite important in both combinatorics and statistical physics. It contains various numerical invariants and polynomial invariants, such as the number of spanning trees, the number of spanning forests, the number of acyclic orientations, the reliability polynomial, chromatic polynomial and flow polynomial. In this paper, we study and gain recursive formulas for the Tutte polynomial of pseudofractal scale-free web (PSW) which implies logarithmic complexity algorithm is obtained to calculate the Tutte polynomial of PSW although it is NP-hard for general graph. We also obtain the rigorous solution for the the number of spanning trees of PSW by solving the recurrence relations derived from Tutte polynomial, which give an alternative approach for explicitly determining the number of spanning trees of PSW. Further more, we analysis the all-terminal reliability of PSW and compare the results with that of Sierpinski gasket which has the same number of nodes and edges with PSW. In contrast with the well-known conclusion that scale-free networks are more robust against removal of nodes than homogeneous networks (e.g., exponential networks and regular networks). Our results show that Sierpinski gasket (which is a regular network) are more robust against random edge failures than PSW (which is a scale-free network). Whether it is true for any regular networks and scale-free networks, is still a unresolved problem.Comment: 19pages,7figures. arXiv admin note: text overlap with arXiv:1006.533

The 'At-risk mental state' for psychosis in adolescents : clinical presentation, transition and remission.

Despite increased efforts over the last decade to prospectively identify individuals at ultra-high risk of developing a psychotic illness, limited attention has been specifically directed towards adolescent populations (<18 years). In order to evaluate how those under 18 fulfilling the operationalised criteria for an At-Risk Mental State (ARMS) present and fare over time, we conducted an observational study. Participants (N = 30) generally reported a high degree of functional disability and frequent and distressing perceptual disturbance, mainly in the form of auditory hallucinations. Seventy percent (21/30) were found to fulfil the criteria for a co-morbid ICD-10 listed mental health disorder, with mood (affective; 13/30) disorders being most prevalent. Overall transition rates to psychosis were low at 24 months follow-up (2/28; 7.1 %) whilst many participants demonstrated a significant reduction in psychotic-like symptoms. The generalisation of these findings may be limited due to the small sample size and require replication in a larger sample

Fourientations and the Tutte polynomial

A fourientation of a graph is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. Fixing a total order on the edges and a reference orientation of the graph, we investigate properties of cuts and cycles in fourientations which give trivariate generating functions that are generalized Tutte polynomial evaluations of the form (k + m)[superscript n−1](k + l)[superscript gT](αk + βl + m/k + m , γ k + l + δm/ k + l) for α, γ ∈ {0, 1, 2} and β, δ ∈ {0, 1}. We introduce an intersection lattice of 64 cut–cycle fourientation classes enumerated by generalized Tutte polynomial evaluations of this form. We prove these enumerations using a single deletion–contraction argument and classify axiomatically the set of fourientation classes to which our deletion–contraction argument applies. This work unifies and extends earlier results for fourientations due to Gessel and Sagan (Electron J Combin 3(2):Research Paper 9, 1996), results for partial orientations due to Backman (Adv Appl Math, forthcoming, 2014. arXiv:1408.3962), and Hopkins and Perkinson (Trans Am Math Soc 368(1):709–725, 2016), as well as results for total orientations due to Stanley (Discrete Math 5:171–178, 1973; Higher combinatorics (Proceedings of NATO Advanced Study Institute, Berlin, 1976). NATO Advanced Study Institute series, series C: mathematical and physical sciences, vol 31, Reidel, Dordrecht, pp 51–62, 1977), Las Vergnas (Progress in graph theory (Proceedings, Waterloo silver jubilee conference 1982), Academic Press, New York, pp 367–380, 1984), Greene and Zaslavsky (Trans Am Math Soc 280(1):97–126, 1983), and Gioan (Eur J Combin 28(4):1351–1366, 2007), which were previously unified by Gioan (2007), Bernardi (Electron J Combin 15(1):Research Paper 109, 2008), and Las Vergnas (Tutte polynomial of a morphism of matroids 6. A multi-faceted counting formula for hyperplane regions and acyclic orientations, 2012. arXiv:1205.5424). We conclude by describing how these classes of fourientations relate to geometric, combinatorial, and algebraic objects including bigraphical arrangements, cycle–cocycle reversal systems, graphic Lawrence ideals, Riemann–Roch theory for graphs, zonotopal algebra, and the reliability polynomial. Keywords: Partial graph orientations, Tutte polynomial, Deletion–contraction, Hyperplane arrangements, Cycle–cocycle reversal system, Chip-firing, G-parking functions, Abelian sandpile model, Riemann–Roch theory for graphs, Lawrence ideals, Zonotopal algebra, Reliability polynomialNational Science Foundation (U.S.) (Grant 1122374

Metabolic syndrome and risk factors for cardiovascular disease: are nonagenarians protected?

This study assessed cardiovascular disease risk factors in three groups of human subjects aged 20–34 [young, 20 male (M)/33 female (F)], 60–74 (aged, 29M/29F), and > 90 years (nonagenarian, 47M/50F). Components of the metabolic syndrome, cardiovascular disease, and markers of inflammation and oxidative stress were assessed. Nonagenarians weighed less than the two other groups (P < 0.001); however, there was no difference in percent fat among the three groups. Aged individuals had the highest prevalence of the metabolic syndrome (P < 0.001) according to the Adult Treatment Panel III classification. Both fibrinogen and homocysteine concentrations were significantly higher in the nonagenarians compared to younger groups. However, there were no significant differences between groups in fasting insulin, high sensitive C-reactive protein, and plasminogen activator inhibitor 1 concentrations. There were also no relationships between inflammation/ oxidative stress and the metabolic syndrome or cardiovascular disease although nonagenarians appear to be protected from oxidative damage to DNA

The Na(+)–H(+ )exchanger-1 induces cytoskeletal changes involving reciprocal RhoA and Rac1 signaling, resulting in motility and invasion in MDA-MB-435 cells

INTRODUCTION: An increasing body of evidence shows that the tumour microenvironment is essential in driving neoplastic progression. The low serum component of this microenvironment stimulates motility/invasion in human breast cancer cells via activation of the Na(+)–H(+ )exchanger (NHE) isoform 1, but the signal transduction systems that underlie this process are still poorly understood. We undertook the present study to elucidate the role and pattern of regulation by the Rho GTPases of this serum deprivation-dependent activation of both NHE1 and subsequent invasive characteristics, such as pseudopodia and invadiopodia protrusion, directed cell motility and penetration of normal tissues. METHODS: The present study was performed in a well characterized human mammary epithelial cell line representing late stage metastatic progression, MDA-MB-435. The activity of RhoA and Rac1 was modified using their dominant negative and constitutively active mutants and the activity of NHE1, cell motility/invasion, F-actin content and cell shape were measured. RESULTS: We show for the first time that serum deprivation induces NHE1-dependent morphological and cytoskeletal changes in metastatic cells via a reciprocal interaction of RhoA and Rac1, resulting in increased chemotaxis and invasion. Deprivation changed cell shape by reducing the amount of F-actin and inducing the formation of leading edge pseudopodia. Serum deprivation inhibited RhoA activity and stimulated Rac1 activity. Rac1 and RhoA were antagonistic regulators of both basal and stimulated tumour cell NHE1 activity. The regulation of NHE1 activity by RhoA and Rac1 in both conditions was mediated by an alteration in intracellular proton affinity of the exchanger. Interestingly, the role of each of these G-proteins was reversed during serum deprivation; basal NHE1 activity was regulated positively by RhoA and negatively by Rac1, whereas RhoA negatively and Rac1 positively directed the stimulation of NHE1 during serum deprivation. Importantly, the same pattern of RhoA and Rac1 regulation found for NHE1 activity was observed in both basal and serum deprivation dependent increases in motility, invasion and actin cytoskeletal organization. CONCLUSION: Our findings suggest that the reported antagonistic roles of RhoA and Rac1 in cell motility/invasion and cytoskeletal organization may be due, in part, to their concerted action on NHE1 activity as a convergence point

Improved accuracy of co-morbidity coding over time after the introduction of ICD-10 administrative data

BACKGROUND: Co-morbidity information derived from administrative data needs to be validated to allow its regular use. We assessed evolution in the accuracy of coding for Charlson and Elixhauser co-morbidities at three time points over a 5-year period, following the introduction of the International Classification of Diseases, 10th Revision (ICD-10), coding of hospital discharges.METHODS: Cross-sectional time trend evaluation study of coding accuracy using hospital chart data of 3'499 randomly selected patients who were discharged in 1999, 2001 and 2003, from two teaching and one non-teaching hospital in Switzerland. We measured sensitivity, positive predictive and Kappa values for agreement between administrative data coded with ICD-10 and chart data as the 'reference standard' for recording 36 co-morbidities.RESULTS: For the 17 the Charlson co-morbidities, the sensitivity - median (min-max) - was 36.5% (17.4-64.1) in 1999, 42.5% (22.2-64.6) in 2001 and 42.8% (8.4-75.6) in 2003. For the 29 Elixhauser co-morbidities, the sensitivity was 34.2% (1.9-64.1) in 1999, 38.6% (10.5-66.5) in 2001 and 41.6% (5.1-76.5) in 2003. Between 1999 and 2003, sensitivity estimates increased for 30 co-morbidities and decreased for 6 co-morbidities. The increase in sensitivities was statistically significant for six conditions and the decrease significant for one. Kappa values were increased for 29 co-morbidities and decreased for seven.CONCLUSIONS: Accuracy of administrative data in recording clinical conditions improved slightly between 1999 and 2003. These findings are of relevance to all jurisdictions introducing new coding systems, because they demonstrate a phenomenon of improved administrative data accuracy that may relate to a coding 'learning curve' with the new coding system

Reduced expression of a gene proliferation signature is associated with enhanced malignancy in colon cancer

The association between cell proliferation and the malignant potential of colon cancer is not well understood. Here, we evaluated this association using a colon-specific gene proliferation signature (GPS). The GPS was derived by combining gene expression data obtained from the analysis of a cancer cell line model and a published colon crypt profile. The GPS was overexpressed in both actively cycling cells in vitro and the proliferate compartment of colon crypts. K-means clustering was used to independantly stratify two cohorts of colon tumours into two groups with high and low GPS expression. Notably, we observed a significant association between reduced GPS expression and an increased likelihood of recurrence (P<0.05), leading to shorter disease-free survival in both cohorts. This finding was not a result of methodological bias as we verified the well-established association between breast cancer malignancy and increased proliferation, by applying our GPS to public breast cancer data. In this study, we show that reduced proliferation is a biological feature characterizing the majority of aggressive colon cancers. This contrasts with many other carcinomas such as breast cancer. Investigating the reasons underlying this unusual observation may provide important insight into the biology of colon cancer progression and putative novel therapy options

Declining Orangutan Encounter Rates from Wallace to the Present Suggest the Species Was Once More Abundant

BACKGROUND: Bornean orangutans (Pongo pygmaeus) currently occur at low densities and seeing a wild one is a rare event. Compared to present low encounter rates of orangutans, it is striking how many orangutan each day historic collectors like Alfred Russel Wallace were able to shoot continuously over weeks or even months. Does that indicate that some 150 years ago encounter rates with orangutans, or their densities, were higher than now? METHODOLOGY/PRINCIPAL FINDINGS: We test this hypothesis by quantifying encounter rates obtained from hunting accounts, museum collections, and recent field studies, and analysing whether there is a declining trend over time. Logistic regression analyses of our data support such a decline on Borneo between the mid-19th century and the present. Even when controlled for variation in the size of survey and hunting teams and the durations of expeditions, mean daily encounter rates appear to have declined about 6-fold in areas with little or no forest disturbance. CONCLUSIONS/SIGNIFICANCE: This finding has potential consequences for our understanding of orangutans, because it suggests that Bornean orangutans once occurred at higher densities. We explore potential explanations-habitat loss and degradation, hunting, and disease-and conclude that hunting fits the observed patterns best. This suggests that hunting has been underestimated as a key causal factor of orangutan density and distribution, and that species population declines have been more severe than previously estimated based on habitat loss only. Our findings may require us to rethink the biology of orangutans, with much of our ecological understanding possibly being based on field studies of animals living at lower densities than they did historically. Our approach of quantifying species encounter rates from historic data demonstrates that this method can yield valuable information about the ecology and population density of species in the past, providing new insight into species' conservation needs

Allergic rhinitis: evidence for impact on asthma

BACKGROUND: This paper reviews the current evidence indicating that comorbid allergic rhinitis may have clinically relevant effects on asthma. DISCUSSION: Allergic rhinitis is very common in patients with asthma, with a reported prevalence of up to 100% in those with allergic asthma. While the temporal relation of allergic rhinitis and asthma diagnoses can be variable, the diagnosis of allergic rhinitis often precedes that of asthma. Rhinitis is an independent risk factor for the subsequent development of asthma in both atopic and nonatopic individuals. Controlled studies have provided conflicting results regarding the benefits for asthma symptoms of treating comorbid allergic rhinitis with intranasal corticosteroids. Effects of other treatments for comorbid allergic rhinitis, including antihistamines, allergen immunotherapy, systemic anti-IgE therapy, and antileukotriene agents, have been examined in a limited number of studies; anti-IgE therapy and antileukotriene agents such as the leukotriene receptor antagonists have benefits for treating both allergic rhinitis and asthma. Results of observational studies indicate that treating comorbid allergic rhinitis results in a lowered risk of asthma-related hospitalizations and emergency visits. Results of several retrospective database studies in the United States and in Europe indicate that, for patients with asthma, the presence of comorbid allergic rhinitis is associated with higher total annual medical costs, greater prescribing frequency of asthma-related medications, as well as increased likelihood of asthma-related hospital admissions and emergency visits. There is therefore evidence suggesting that comorbid allergic rhinitis is a marker for more difficult to control asthma and worsened asthma outcomes. CONCLUSION: These findings highlight the potential for improving asthma outcomes by following a combined therapeutic approach to comorbid allergic rhinitis and asthma rather than targeting each condition separately

Cancer cell adaptation to chemotherapy

BACKGROUND: Tumor resistance to chemotherapy may be present at the beginning of treatment, develop during treatment, or become apparent on re-treatment of the patient. The mechanisms involved are usually inferred from experiments with cell lines, as studies in tumor-derived cells are difficult. Studies of human tumors show that cells adapt to chemotherapy, but it has been largely assumed that clonal selection leads to the resistance of recurrent tumors. METHODS: Cells derived from 47 tumors of breast, ovarian, esophageal, and colorectal origin and 16 paired esophageal biopsies were exposed to anticancer agents (cisplatin; 5-fluorouracil; epirubicin; doxorubicin; paclitaxel; irinotecan and topotecan) in short-term cell culture (6 days). Real-time quantitative PCR was used to measure up- or down-regulation of 16 different resistance/target genes, and when tissue was available, immunohistochemistry was used to assess the protein levels. RESULTS: In 8/16 paired esophageal biopsies, there was an increase in the expression of multi-drug resistance gene 1 (MDR1) following epirubicin + cisplatin + 5-fluorouracil (ECF) chemotherapy and this was accompanied by increased expression of the MDR-1 encoded protein, P-gp. Following exposure to doxorubicin in vitro, 13/14 breast carcinomas and 9/12 ovarian carcinomas showed >2-fold down-regulation of topoisomerase IIα (TOPOIIα). Exposure to topotecan in vitro, resulted in >4-fold down-regulation of TOPOIIα in 6/7 colorectal tumors and 8/10 ovarian tumors. CONCLUSION: This study suggests that up-regulation of resistance genes or down-regulation in target genes may occur rapidly in human solid tumors, within days of the start of treatment, and that similar changes are present in pre- and post-chemotherapy biopsy material. The molecular processes used by each tumor appear to be linked to the drug used, but there is also heterogeneity between individual tumors, even those with the same histological type, in the pattern and magnitude of response to the same drugs. Adaptation to chemotherapy may explain why prediction of resistance mechanisms is difficult on the basis of tumor type alone or individual markers, and suggests that more complex predictive methods are required to improve the response rates to chemotherapy