Positive approximations of the inverse of fractional powers of SPD M-matrices

This study is motivated by the recent development in the fractional calculus and its applications. During last few years, several different techniques are proposed to localize the nonlocal fractional diffusion operator. They are based on transformation of the original problem to a local elliptic or pseudoparabolic problem, or to an integral representation of the solution, thus increasing the dimension of the computational domain. More recently, an alternative approach aimed at reducing the computational complexity was developed. The linear algebraic system $\cal A^\alpha \bf u=\bf f$, $0< \alpha <1$ is considered, where $\cal A$ is a properly normalized (scalded) symmetric and positive definite matrix obtained from finite element or finite difference approximation of second order elliptic problems in $\Omega\subset\mathbb{R}^d$, $d=1,2,3$. The method is based on best uniform rational approximations (BURA) of the function $t^{\beta-\alpha}$ for $0 < t \le 1$ and natural $\beta$. The maximum principles are among the major qualitative properties of linear elliptic operators/PDEs. In many studies and applications, it is important that such properties are preserved by the selected numerical solution method. In this paper we present and analyze the properties of positive approximations of $\cal A^{-\alpha}$ obtained by the BURA technique. Sufficient conditions for positiveness are proven, complemented by sharp error estimates. The theoretical results are supported by representative numerical tests

The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein

The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, and the resulting potential energy surface is visualized by constructing disconnectivity graphs. Owing to topological constraints, the low-lying portion of the landscape consists of three distinct regions, corresponding to the native knotted state and to configurations where either the N- or C-terminus is not yet folded into the knot. The fastest folding pathways from denatured states exhibit early formation of the N-terminus portion of the knot and a rate-determining step where the C-terminus is incorporated. The low-lying minima with the N-terminus knotted and the C-terminus free therefore constitute an off-pathway intermediate for this model. The insertion of both the N- and C-termini into the knot occur late in the folding process, creating large energy barriers that are the rate limiting steps in the folding process. When compared to other protein folding proteins of a similar length, this system folds over six orders of magnitude more slowly.Comment: 19 page

Laminar-turbulent transition in Raman fiber lasers:a first passage statistics based analysis

Loss of coherence with increasing excitation amplitudes and spatial size modulation is a fundamental problem in designing Raman fiber lasers. While it is known that ramping up laser pump power increases the amplitude of stochastic excitations, such higher energy inputs can also lead to a transition from a linearly stable coherent laminar regime to a non-desirable disordered turbulent state. This report presents a new statistical methodology, based on first passage statistics, that classifies lasing regimes in Raman fiber lasers, thereby leading to a fast and highly accurate identification of a strong instability leading to a laminar-turbulent phase transition through a self-consistently defined order parameter. The results have been consistent across a wide range of pump power values, heralding a breakthrough in the non-invasive analysis of fiber laser dynamics

Insulin utilizes the PI 3-kinase pathway to inhibit SP-A gene expression in lung epithelial cells

BACKGROUND: It has been proposed that high insulin levels may cause delayed lung development in the fetuses of diabetic mothers. A key event in lung development is the production of adequate amounts of pulmonary surfactant. Insulin inhibits the expression of surfactant protein A (SP-A), the major surfactant-associated protein, in lung epithelial cells. In the present study, we investigated the signal transduction pathways involved in insulin inhibition of SP-A gene expression. METHODS: H441 cells, a human lung adenocarcinoma cell line, or human fetal lung explants were incubated with or without insulin. Transcription run-on assays were used to determine SP-A gene transcription rates. Northern blot analysis was used to examine the effect of various signal transduction inhibitors on SP-A gene expression. Immunoblot analysis was used to evaluate the levels and phosphorylation states of signal transduction protein kinases. RESULTS: Insulin decreased SP-A gene transcription in human lung epithelial cells within 1 hour. Insulin did not affect p44/42 mitogen-activated protein kinase (MAPK) phosphorylation and the insulin inhibition of SP-A mRNA levels was not affected by PD98059, an inhibitor of the p44/42 MAPK pathway. In contrast, insulin increased p70 S6 kinase Thr389 phosphorylation within 15 minutes. Wortmannin or LY294002, both inhibitors of phosphatidylinositol 3-kinase (PI 3-kinase), or rapamycin, an inhibitor of the activation of p70 S6 kinase, a downstream effector in the PI 3-kinase pathway, abolished or attenuated the insulin-induced inhibition of SP-A mRNA levels. CONCLUSION: Insulin inhibition of SP-A gene expression in lung epithelial cells probably occurs via the rapamycin-sensitive PI 3-kinase signaling pathway

First-passage times in complex scale-invariant media

How long does it take a random walker to reach a given target point? This quantity, known as a first passage time (FPT), has led to a growing number of theoretical investigations over the last decade1. The importance of FPTs originates from the crucial role played by first encounter properties in various real situations, including transport in disordered media, neuron firing dynamics, spreading of diseases or target search processes. Most methods to determine the FPT properties in confining domains have been limited to effective 1D geometries, or for space dimensions larger than one only to homogeneous media1. Here we propose a general theory which allows one to accurately evaluate the mean FPT (MFPT) in complex media. Remarkably, this analytical approach provides a universal scaling dependence of the MFPT on both the volume of the confining domain and the source-target distance. This analysis is applicable to a broad range of stochastic processes characterized by length scale invariant properties. Our theoretical predictions are confirmed by numerical simulations for several emblematic models of disordered media, fractals, anomalous diffusion and scale free networks.Comment: Submitted version. Supplementary Informations available on Nature websit

(Reinforcing) factors influencing a physical education teachers use of the direct instruction model teaching games

he purpose of this study was to explore how a physical education (PE) teacher employed the direct instruction model (DIM) teaching games in a United Kingdom secondary school. The research sought to identify how the teacher utilised the DIM and those factors that influenced his use of the model. Occupational socialization was used to identify the factors that encouraged his use of the DIM. Data were collected from interviews and lesson observations. Inductive data analysis showed that while the teacher presented a ‘full version’ of the DIM, his limited content knowledge impacted on the use of the model in teaching cricket. Factors influencing his use of the model were a sporting perspective, a Post Graduate Certificate in Education mentor and the ability and behaviour of the students. These factors reinforced his undergraduate learning and subsequent use of the DIM. It is suggested that the comparable backgrounds of many PE student teachers may make the DIM an apt model to learn in undergraduate and postgraduate PE courses. However, effective use of the model requires students to be taught and to possess in-depth content knowledge of the game(s)/activities being taught and learned

Ocular disease in patients with ANCA-positive vasculitis

Anti-neutrophil cytoplasmic antibody (ANCA)-positive vasculitis—the term recently applied to Wegener's granulomatosis—is a rare multi-system inflammation characterized by necrotizing granulomas and vasculitis. We investigated the ocular manifestations of this disease in a group of patients drawn from five inflammatory eye disease clinics across the United States. Of 8,562 persons with ocular inflammation, 59 individuals were diagnosed with ANCA-positive vasculitis; 35 males and 21 females, aged 16 to 96 years, were included in this study. Ocular diagnoses were scleritis (75.0%), uveitis (17.9%), and other ocular inflammatory conditions (33.9%) including peripheral ulcerative keratitis and orbital pseudotumor. Mean duration of ocular disease was 4.6 years. Oral corticosteroids and other systemic immunosuppressive agents were used by 85.7% and 78.5% of patients, respectively. Over time, patients with ANCA-positive vasculitis experienced 2.75-fold higher mortality than other patients with inflammatory eye disease

Clarifying mammalian RISC assembly in vitro

<p>Abstract</p> <p>Background</p> <p>Argonaute, the core component of the RNA induced silencing complex (RISC), binds to mature miRNAs and regulates gene expression at transcriptional or post-transcriptional level. We recently reported that Argonaute 2 (Ago2) also assembles into complexes with miRNA precursors (pre-miRNAs). These Ago2:pre-miRNA complexes are catalytically active <it>in vitro </it>and constitute non-canonical RISCs.</p> <p>Results</p> <p>The use of pre-miRNAs as guides by Ago2 bypasses Dicer activity and complicates <it>in vitro </it>RISC reconstitution. In this work, we characterized Ago2:pre-miRNA complexes and identified RNAs that are targeted by miRNAs but not their corresponding pre-miRNAs. Using these target RNAs we were able to recapitulate <it>in vitro </it>pre-miRNA processing and canonical RISC loading, and define the minimal factors required for these processes.</p> <p>Conclusions</p> <p>Our results indicate that Ago2 and Dicer are sufficient for processing and loading of miRNAs into RISC. Furthermore, our studies suggest that Ago2 binds primarily to the 5'- and alternatively, to the 3'-end of select pre-miRNAs.</p