Percolation in invariant Poisson graphs with i.i.d. degrees

Let each point of a homogeneous Poisson process in R^d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme that is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components

Review of early hospitalisation after percutaneous coronary intervention

Background: Percutaneous coronary intervention (PCI) is the most common modality of revascularization in patients with coronary artery disease. Understanding the readmission rates and reasons for readmission after PCI is important because readmissions are a quality of care indicator, in addition to being a burden to patients and healthcare services. Methods: A literature review was performed. Relevant studies are described by narrative synthesis with the use of tables to summarize study results. Results: Data suggests that 30-day readmissions are not uncommon. The rate of readmission after PCI is highly influenced by the cohort and the healthcare system studied, with 30-day readmission rates reported to be between 4.7‐% and 15.6%. Studies consistently report that a majority of readmissions within 30 days are due to a cardiac-related disorders or complication-related disorders. Female sex, peripheral vascular disease, diabetes mellitus, renal failure and non-elective PCI are predictive of readmission. Studies also suggest that there is greater risk of mortality among patients who are readmitted compared to those who are not readmitted. Conclusion: Readmission after PCI is common and its rate is highly influenced by the type of cohort studied. There is clear evidence that majority of readmissions within 30 days are cardiac related. While there are many predictors of readmission following PCI, it is not known whether targeting patients with modifiable predictors could prevent or reduce the rates of readmission

Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks

We introduce the heterogeneous-$k$-core, which generalizes the $k$-core, and contrast it with bootstrap percolation. Vertices have a threshold $k_i$ which may be different at each vertex. If a vertex has less than $k_i$ neighbors it is pruned from the network. The heterogeneous-$k$-core is the sub-graph remaining after no further vertices can be pruned. If the thresholds $k_i$ are $1$ with probability $f$ or $k \geq 3$ with probability $(1-f)$, the process forms one branch of an activation-pruning process which demonstrates hysteresis. The other branch is formed by ordinary bootstrap percolation. We show that there are two types of transitions in this heterogeneous-$k$-core process: the giant heterogeneous-$k$-core may appear with a continuous transition and there may be a second, discontinuous, hybrid transition. We compare critical phenomena, critical clusters and avalanches at the heterogeneous-$k$-core and bootstrap percolation transitions. We also show that network structure has a crucial effect on these processes, with the giant heterogeneous-$k$-core appearing immediately at a finite value for any $f > 0$ when the degree distribution tends to a power law $P(q) \sim q^{-\gamma}$ with $\gamma < 3$.Comment: 10 pages, 4 figure

On Bootstrap Percolation in Living Neural Networks

Recent experimental studies of living neural networks reveal that their global activation induced by electrical stimulation can be explained using the concept of bootstrap percolation on a directed random network. The experiment consists in activating externally an initial random fraction of the neurons and observe the process of firing until its equilibrium. The final portion of neurons that are active depends in a non linear way on the initial fraction. The main result of this paper is a theorem which enables us to find the asymptotic of final proportion of the fired neurons in the case of random directed graphs with given node degrees as the model for interacting network. This gives a rigorous mathematical proof of a phenomena observed by physicists in neural networks

The effect of N-methylprotoporphyrin IX on the synthesis of photosynthetic pigments in Cyanidium caldarium. Further evidence for the role of haem in the biosynthesis of plant bilins

N-Methylprotoporphyrin IX strongly inhibits synthesis of phycocyanobilin, but not chlorophyll a, in the dark. In the light, both phycocyanin and chlorophyll a synthesis are inhibited in parallel. These results are consistent with the intermediacy of haem in algal bilin synthesis and suggest a control mechanism for chlorophyll a synthesis, previously unknown

HIV-1 Integrates Widely throughout the Genome of the Human Blood Fluke Schistosoma mansoni.

Schistosomiasis is the most important helminthic disease of humanity in terms of morbidity and mortality. Facile manipulation of schistosomes using lentiviruses would enable advances in functional genomics in these and related neglected tropical diseases pathogens including tapeworms, and including their non-dividing cells. Such approaches have hitherto been unavailable. Blood stream forms of the human blood fluke, Schistosoma mansoni, the causative agent of the hepatointestinal schistosomiasis, were infected with the human HIV-1 isolate NL4-3 pseudotyped with vesicular stomatitis virus glycoprotein. The appearance of strong stop and positive strand cDNAs indicated that virions fused to schistosome cells, the nucleocapsid internalized and the RNA genome reverse transcribed. Anchored PCR analysis, sequencing HIV-1-specific anchored Illumina libraries and Whole Genome Sequencing (WGS) of schistosomes confirmed chromosomal integration; \u3e8,000 integrations were mapped, distributed throughout the eight pairs of chromosomes including the sex chromosomes. The rate of integrations in the genome exceeded five per 1,000 kb and HIV-1 integrated into protein-encoding loci and elsewhere with integration bias dissimilar to that of human T cells. We estimated ~ 2,100 integrations per schistosomulum based on WGS, i.e. about two or three events per cell, comparable to integration rates in human cells. Accomplishment in schistosomes of post-entry processes essential for HIV-1replication, including integrase-catalyzed integration, was remarkable given the phylogenetic distance between schistosomes and primates, the natural hosts of the genus Lentivirus. These enigmatic findings revealed that HIV-1 was active within cells of S. mansoni, and provided the first demonstration that HIV-1 can integrate into the genome of an invertebrate