Random tree growth by vertex splitting

We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model generalises the preferential attachment model and Ford's $\alpha$-model for phylogenetic trees. We develop a mean field theory for the vertex degree distribution, prove that the mean field theory is exact in some special cases and check that it agrees with numerical simulations in general. We calculate various correlation functions and show that the intrinsic Hausdorff dimension can vary from one to infinity, depending on the parameters of the model.Comment: 47 page

Appearance of vertices of infinite order in a model of random trees

We study an equilibrium statistical mechanical model of tree graphs which are made up of a linear subgraph (the spine) to which leaves are attached. We prove that the model has two phases, a generic phase where the spine becomes infinitely long in the thermodynamic limit and all vertices have finite order and a condensed phase where the spine is finite with probability one and a single vertex of infinite order appears in the thermodynamic limit. We calculate the spectral dimension of the graphs in both phases and prove the existence of a Gibbs measure. We discuss generalizations of this model and the relationship with models of nongeneric random trees.Comment: 22 pages, 5 figure

A new family of Markov branching trees: the alpha-gamma model

We introduce a simple tree growth process that gives rise to a new two-parameter family of discrete fragmentation trees that extends Ford's alpha model to multifurcating trees and includes the trees obtained by uniform sampling from Duquesne and Le Gall's stable continuum random tree. We call these new trees the alpha-gamma trees. In this paper, we obtain their splitting rules, dislocation measures both in ranked order and in sized-biased order, and we study their limiting behaviour

Sedentary lifestyle as a risk factor for low back pain : a systematic review

Objectives To review systematically studies examining the association between sedentary lifestyle and low back pain (LBP) using a comprehensive definition of sedentary behaviour including prolonged sitting both at work and during leisure time.Methods Journal articles published between 1998 and 2006 were obtained by searching computerized bibliographical databases. Quality assessment of studies employing a cohort or case&ndash;control design was performed to assess the strength of the evidence.Results Using pre-determined keywords, we identified 1,778 titles of which 1,391 were considered irrelevant. Then, 20 of the remaining 387 publications were scrutinized for full review after an examination of all the 387 abstracts. Finally, 15 studies (10 prospective cohorts and 5 case&ndash;controls) were included in the methodological quality assessment, of which 8 (6 cohorts and 2 case&ndash;controls; 53%) were classified as high-quality studies. One high-quality cohort study reported a positive association, between LBP and sitting at work only; all other studies reported no significant associations. Hence, there was limited evidence to demonstrate that sedentary behaviour is a risk factor for developing LBP.Conclusions The present review confirms that sedentary lifestyle by itself is not associated with LBP.<br /

Is transcriptomic regulation of berry development more important at night than during the day?

Diurnal changes in gene expression occur in all living organisms and have been studied on model plants such as Arabidopsis thaliana. To our knowledge the impact of the nycthemeral cycle on the genetic program of fleshly fruit development has been hitherto overlooked. In order to circumvent environmental changes throughout fruit development, young and ripening berries were sampled simultaneously on continuously flowering microvines acclimated to controlled circadian light and temperature changes. Gene expression profiles along fruit development were monitored during both day and night with whole genome microarrays (Nimblegen® vitis 12x), yielding a total number of 9273 developmentally modulated probesets. All day-detected transcripts were modulated at night, whereas 1843 genes were night-specific. Very similar developmental patterns of gene expression were observed using independent hierarchical clustering of day and night data, whereas functional categories of allocated transcripts varied according to time of day. Many transcripts within pathways, known to be up-regulated during ripening, in particular those linked to secondary metabolism exhibited a clearer developmental regulation at night than during the day. Functional enrichment analysis also indicated that diurnally modulated genes considerably varied during fruit development, with a shift from cellular organization and photosynthesis in green berries to secondary metabolism and stress-related genes in ripening berries. These results reveal critical changes in gene expression during night development that differ from daytime development, which have not been observed in other transcriptomic studies on fruit development thus far