Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes

Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social and collaboration networks. Here we characterize the structure of simplicial complexes using their generalized degrees that capture fundamental properties of one, two, three or more linked nodes. Moreover we introduce the configuration model and the canonical ensemble of simplicial complexes, enforcing respectively the sequence of generalized degrees of the nodes and the sequence of the expected generalized degrees of the nodes. We evaluate the entropy of these ensembles, finding the asymptotic expression for the number of simplicial complexes in the configuration model. We provide the algorithms for the construction of simplicial complexes belonging to the configuration model and the canonical ensemble of simplicial complexes. We give an expression for the structural cutoff of simplicial complexes that for simplicial complexes of dimension $d=1$ reduces to the structural cutoff of simple networks. Finally we provide a numerical analysis of the natural correlations emerging in the configuration model of simplicial complexes without structural cutoff.Comment: (16 pages, 6 figures

Farmer's Knowledge of Horticultural Traits and Participatory Selection of African Eggplant Varieties (Solanum aethiopicum) in Tanzania

Participatory selection was conducted in 2008 through 2009 to identify farmers' preference for species and horticultural traits that may constitute future breeding objectives. Vegetable farmers were selected from Moshi and Arusha regions, test population comprised twenty-six accessions from four Solanum species (eggplant and relatives). Purposive sampling was used to select the farming communities with high African eggplant production activities; a multistage random sampling procedure was adopted to select farmers from three regions for participatory meeting. The focus group discussion sessions identified fruit shape, taste, earliness, medicinal properties, marketability and resistance to diseases as farmers' preferred traits in S. aethiopicum; taste and marketability for S. melongena, taste and medicinal properties among S. macrocarpon and S. anguivi. Fruits characterized by cream colour at commercial harvest are most preferred compared to green, to a lesser extent is purple. Interestingly high fruits per plant, fruits per cluster and fruit cluster per plant best described S. anguivi. Fruit yield was superior in Db3 (S. aethiopicum Gilo group), top five accessions for organoleptic properties are Db3, Ab2, MM 1619, S00052 and MM 1086. Characters indicated above may constitute breeding objectives and population identified may serve as pollen parents for development of new varieties in african eggplant. Intraspecific hybridization within S. aethiopicum Gilo cultigroup, hybridization among Gilo and Shum cultigroups and interspecific hybridization between S. aethiopicum and S. anguivi may evolve new population aimed at improving fruit yield

El món funerari medieval a la Plana de Vic: El cas de Sant Andreu del Castell de Tona

Aquest article és fruit d’un treball de recerca de 2n de batxillerat que ha dut a terme l’estudiant Ot Ordeig, que el 2010 va participar en les excavacions al Camp de les Lloses. Es tracta d’un estudi de les restes òssies localitzades a les necròpolis de l’Esquerda (Roda de Ter) i l’església de Sant Andreu del Castell. Aquí es presenten els resultats pel que fa a Tona, a partir de l’anàlisi del material que havia estat localitzat en diverses campanyes dins l’església i al solar de la Rectoria Vella o cal Campaner, al costat del temple

Influenza A(H1N1)pdm09 in England, 2009 to 2011: a greater burden of severe illness in the year after the pandemic than in the pandemic year.

Influenza pandemics are often perceived as single-year events, but the burden of previous influenza pandemics has in reality been spread over a number of years. The aim of this paper is to compare the burden of influenza in the pandemic year 2009/10 with that in the year immediately after (2010/11) in England. We compared four measures of disease. There was a greater burden of severe illness in 2010/11 compared with 2009/10: more deaths (474 vs 361), more critical care admissions (2,200 vs 1,700), and more hospital admissions (8,797 vs 7,879). In contrast, there were fewer general practice consultations in 2010/11 compared with 2009/10 (370,000 vs 580,000). There was also much less public interest in influenza, as assessed by number of Google searches. This is a worrying finding, as by the time of the second influenza season, much had been learnt about the potential impact of the influenza A(H1N1)pdm09 virus and an effective vaccine developed. We suggest that a widespread assumption of 'mildness' led to insufficient ongoing action to prevent influenza and hence to avoidable influenza-related deaths. This offers a lesson to all countries, both for future influenza seasons and for pandemic preparedness planning

Combined models for pre- and post-treatment longitudinal biomarker data: an application to CD4 counts in HIV-patients.

BACKGROUND: There has been some debate in the literature as to whether baseline values of a measurement of interest at treatment initiation should be treated as an outcome variable as part of a model for longitudinal change or instead used as a predictive variable with respect to the response to treatment. We develop a new approach that involves a combined statistical model for all pre- and post-treatment observations of the biomarker of interest, in which the characteristics of response to treatment are treated as a function of the 'true' value of the biomarker at treatment initiation. METHODS: The modelling strategy developed is applied to a dataset of CD4 counts from patients in the UK Register of HIV Seroconverters (UKR) cohort who initiated highly active antiretroviral therapy (HAART). The post-HAART recovery in CD4 counts for each individual is modelled as following an asymptotic curve in which the speed of response to treatment and long-term maximum are functions of the 'true' underlying CD4 count at initiation of HAART and the time elapsed since seroconversion. Following previous research in this field, the models developed incorporate non-stationary stochastic process components, and the possibility of between-patient differences in variability over time was also considered. RESULTS: A variety of novel models were successfully fitted to the UKR dataset. These provide reinforcing evidence for findings that have previously been reported in the literature, in particular that there is a strong positive relationship between CD4 count at initiation of HAART and the long-term maximum in each patient, but also reveal potentially important features of the data that would not have been easily identified by other methods of analysis. CONCLUSION: Our proposed methodology provides a unified framework for the analysis of pre- and post-treatment longitudinal biomarker data that will be useful for epidemiological investigations and simulations in this context. The approach developed allows use of all relevant data from observational cohorts in which many patients are missing pre-treatment measurements and in which the timing and number of observations vary widely between patients

Influenza A(H1N1)pdm09 in England, 2009 to 2011: a greater burden of severe illness in the year after the pandemic than in the pandemic year.

Influenza pandemics are often perceived as single-year events, but the burden of previous influenza pandemics has in reality been spread over a number of years. The aim of this paper is to compare the burden of influenza in the pandemic year 2009/10 with that in the year immediately after (2010/11) in England. We compared four measures of disease. There was a greater burden of severe illness in 2010/11 compared with 2009/10: more deaths (474 vs 361), more critical care admissions (2,200 vs 1,700), and more hospital admissions (8,797 vs 7,879). In contrast, there were fewer general practice consultations in 2010/11 compared with 2009/10 (370,000 vs 580,000). There was also much less public interest in influenza, as assessed by number of Google searches. This is a worrying finding, as by the time of the second influenza season, much had been learnt about the potential impact of the influenza A(H1N1)pdm09 virus and an effective vaccine developed. We suggest that a widespread assumption of 'mildness' led to insufficient ongoing action to prevent influenza and hence to avoidable influenza-related deaths. This offers a lesson to all countries, both for future influenza seasons and for pandemic preparedness planning