Shift techniques for Quasi-Birth and Death processes: canonical factorizations and matrix equations

We revisit the shift technique applied to Quasi-Birth and Death (QBD) processes (He, Meini, Rhee, SIAM J. Matrix Anal. Appl., 2001) by bringing the attention to the existence and properties of canonical factorizations. To this regard, we prove new results concerning the solutions of the quadratic matrix equations associated with the QBD. These results find applications to the solution of the Poisson equation for QBDs

General solution of the Poisson equation for Quasi-Birth-and-Death processes

We consider the Poisson equation $(I-P)\boldsymbol{u}=\boldsymbol{g}$, where $P$ is the transition matrix of a Quasi-Birth-and-Death (QBD) process with infinitely many levels, $\bm g$ is a given infinite dimensional vector and $\bm u$ is the unknown. Our main result is to provide the general solution of this equation. To this purpose we use the block tridiagonal and block Toeplitz structure of the matrix $P$ to obtain a set of matrix difference equations, which are solved by constructing suitable resolvent triples

Computing the Exponential of Large Block-Triangular Block-Toeplitz Matrices Encountered in Fluid Queues

The Erlangian approximation of Markovian fluid queues leads to the problem of computing the matrix exponential of a subgenerator having a block-triangular, block-Toeplitz structure. To this end, we propose some algorithms which exploit the Toeplitz structure and the properties of generators. Such algorithms allow to compute the exponential of very large matrices, which would otherwise be untreatable with standard methods. We also prove interesting decay properties of the exponential of a generator having a block-triangular, block-Toeplitz structure

c-Jun reprograms Schwann cells of injured nerves to generate a repair cell essential for regeneration.

The radical response of peripheral nerves to injury (Wallerian degeneration) is the cornerstone of nerve repair. We show that activation of the transcription factor c-Jun in Schwann cells is a global regulator of Wallerian degeneration. c-Jun governs major aspects of the injury response, determines the expression of trophic factors, adhesion molecules, the formation of regeneration tracks and myelin clearance and controls the distinctive regenerative potential of peripheral nerves. A key function of c-Jun is the activation of a repair program in Schwann cells and the creation of a cell specialized to support regeneration. We show that absence of c-Jun results in the formation of a dysfunctional repair cell, striking failure of functional recovery, and neuronal death. We conclude that a single glial transcription factor is essential for restoration of damaged nerves, acting to control the transdifferentiation of myelin and Remak Schwann cells to dedicated repair cells in damaged tissue

MicroRNA-194 modulates glucose metabolism and its skeletal muscle expression is reduced in diabetes

BACKGROUND: The regulation of microRNAs (miRNAs) at different stages of the progression of type 2 diabetes mellitus (T2DM) and their role in glucose homeostasis was investigated. METHODS: Microarrays were used to assess miRNA expression in skeletal muscle biopsies taken from healthy individuals and patients with pre-diabetes or T2DM, and insulin resistant offspring of rat dams fed a high fat diet during pregnancy. RESULTS: Twenty-three miRNAs were differentially expressed in patients with T2DM, and 7 in the insulin resistant rat offspring compared to their controls. Among these, only one miRNA was similarly regulated: miR-194 expression was significantly reduced by 25 to 50% in both the rat model and in human with pre-diabetes and established diabetes. Knockdown of miR-194 in L6 skeletal muscle cells induced an increase in basal and insulin-stimulated glucose uptake and glycogen synthesis. This occurred in conjunction with an increased glycolysis, indicated by elevated lactate production. Moreover, oxidative capacity was also increased as we found an enhanced glucose oxidation in presence of the mitochondrial uncoupler FCCP. When miR-194 was down-regulated in vitro, western blot analysis showed an increased phosphorylation of AKT and GSK3β in response to insulin, and an increase in expression of proteins controlling mitochondrial oxidative phosphorylation. CONCLUSIONS: Type 2 diabetes mellitus is associated with regulation of several miRNAs in skeletal muscle. Interestingly, miR-194 was a unique miRNA that appeared regulated across different stages of the disease progression, from the early stages of insulin resistance to the development of T2DM. We have shown miR-194 is involved in multiple aspects of skeletal muscle glucose metabolism from uptake, through to glycolysis, glycogenesis and glucose oxidation, potentially via mechanisms involving AKT, GSK3 and oxidative phosphorylation. MiR-194 could be down-regulated in patients with early features of diabetes as an adaptive response to facilitate tissue glucose uptake and metabolism in the face of insulin resistance

Switching of excited states in cyclometalated platinum complexes incorporating pyridyl-acetylide ligands (Pt-C[triple bond, length as m-dash]C-py): a combined experimental and theoretical study

International audienceThis article presents the design of cyclometalated platinum(II) complexes incorporating pyridyl-appended acetylide ligands of the form Pt-C[triple bond, length as m-dash]C-py, acting either as sites for protonation or methylation reactions or as a host receptor for binding metal cations. The complexes studied are Pt(t-Bu2phbpy)(-C[triple bond, length as m-dash]C-py), 2, which can undergo protonation at the pyridyl N; its cationic N-methylated derivative [Pt(t-Bu2phbpy)(-C[triple bond, length as m-dash]C-pyMe)]+, 4, which serves as a model of the N-protonated species; and a derivative in which the pyridyl ring is incorporated into a macrocyclic diamide-crown ether ligand (3). The co-ligand t-Bu2phbpy is a cyclometalated, N[caret]N[caret]C-coordinated phenylbipyridine ligand carrying tert-butyl groups at the 4-positions of the pyridyl rings. The photophysical properties of the neutral compounds 2 and 3 have been compared to those of the pyridinium, methyl-pyridinium or metal-complexed species (namely 2-H+, 4 and 3-Pb2+). Detailed TD-DFT calculations provide a theoretical basis to account for the experimentally-observed changes upon protonation/methylation/complexation. The joint TD-DFT and experimental studies provide evidence for an unprecedented molecular switch in the nature of the excited state (from mixed L′LCT/MLCT to ML′CT) in which the acceptor ligand in the CT process switches from being the N[caret]N[caret]C ligand to the pyridyl acetylide

A Spectral Algorithm with Additive Clustering for the Recovery of Overlapping Communities in Networks

This paper presents a novel spectral algorithm with additive clustering designed to identify overlapping communities in networks. The algorithm is based on geometric properties of the spectrum of the expected adjacency matrix in a random graph model that we call stochastic blockmodel with overlap (SBMO). An adaptive version of the algorithm, that does not require the knowledge of the number of hidden communities, is proved to be consistent under the SBMO when the degrees in the graph are (slightly more than) logarithmic. The algorithm is shown to perform well on simulated data and on real-world graphs with known overlapping communities.Comment: Journal of Theoretical Computer Science (TCS), Elsevier, A Para\^itr

Analysis and design of randomised clinical trials involving competing risks endpoints

<p>Abstract</p> <p>Background</p> <p>In randomised clinical trials involving time-to-event outcomes, the failures concerned may be events of an entirely different nature and as such define a classical competing risks framework. In designing and analysing clinical trials involving such endpoints, it is important to account for the competing events, and evaluate how each contributes to the overall failure. An appropriate choice of statistical model is important for adequate determination of sample size.</p> <p>Methods</p> <p>We describe how competing events may be summarised in such trials using cumulative incidence functions and Gray's test. The statistical modelling of competing events using proportional cause-specific and subdistribution hazard functions, and the corresponding procedures for sample size estimation are outlined. These are illustrated using data from a randomised clinical trial (SQNP01) of patients with advanced (non-metastatic) nasopharyngeal cancer.</p> <p>Results</p> <p>In this trial, treatment has no effect on the competing event of loco-regional recurrence. Thus the effects of treatment on the hazard of distant metastasis were similar via both the cause-specific (unadjusted <it>csHR </it>= 0.43, 95% CI 0.25 - 0.72) and subdistribution (unadjusted <it>subHR </it>0.43; 95% CI 0.25 - 0.76) hazard analyses, in favour of concurrent chemo-radiotherapy followed by adjuvant chemotherapy. Adjusting for nodal status and tumour size did not alter the results. The results of the logrank test (<it>p </it>= 0.002) comparing the cause-specific hazards and the Gray's test (<it>p </it>= 0.003) comparing the cumulative incidences also led to the same conclusion. However, the subdistribution hazard analysis requires many more subjects than the cause-specific hazard analysis to detect the same magnitude of effect.</p> <p>Conclusions</p> <p>The cause-specific hazard analysis is appropriate for analysing competing risks outcomes when treatment has no effect on the cause-specific hazard of the competing event. It requires fewer subjects than the subdistribution hazard analysis for a similar effect size. However, if the main and competing events are influenced in opposing directions by an intervention, a subdistribution hazard analysis may be warranted.</p

MAGMA : inference and prediction using multi-task Gaussian processes with common mean

A novel multi-task Gaussian process (GP) framework is proposed, by using a common mean process for sharing information across tasks. In particular, we investigate the problem of time series forecasting, with the objective to improve multiple-step-ahead predictions. The common mean process is defined as a GP for which the hyper-posterior distribution is tractable. Therefore an EM algorithm is derived for handling both hyper-parameters optimisation and hyper-posterior computation. Unlike previous approaches in the literature, the model fully accounts for uncertainty and can handle irregular grids of observations while maintaining explicit formulations, by modelling the mean process in a unified GP framework. Predictive analytical equations are provided, integrating information shared across tasks through a relevant prior mean. This approach greatly improves the predictive performances, even far from observations, and may reduce significantly the computational complexity compared to traditional multi-task GP models. Our overall algorithm is called MAGMA (standing for Multi tAsk GPs with common MeAn). The quality of the mean process estimation, predictive performances, and comparisons to alternatives are assessed in various simulated scenarios and on real datasets