Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems

We consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle-point problems or, in particular, regularizations thereof. Such methods require preconditioners that preserve certain sub-blocks from the original systems but allow considerable flexibility for the remaining blocks. We construct a number of families of implicit factorizations that are capable of reproducing the required sub-blocks and (some) of the remainder. These generalize known implicit factorizations for the unregularized case. Improved eigenvalue clustering is possible if additionally some of the noncrucial blocks are reproduced. Numerical experiments confirm that these implicit-factorization preconditioners can be very effective in practice.

Diacylglycerol-induced protection against injury during ischemia and reperfusion can be achieved without activation of protein kinase C in the rat heart: Comparative studies with ischemic preconditioning

The role of protein kinase C (PKC) activation in ischemic preconditioning remains controversial. Since diacylglycerol is the endogenous activator of PKC and as such might be expected cardioprotective, we have investigated whether: (i) the diacylglycerol analog 1,2-dioctanoyl-sn-glycerol (DOG) can protect against injury during ischemia and reperfusion; (ii) any effect is mediated via PKC activation; and (iii) the outcome is influenced by the time of administration. Isolated rat hearts were perfused with buffer at 37°C and paced at 400 bpm. In Study 1, hearts (n=6/group) were subjected to one of the following: (1) 36 min aerobic perfusion (controls); (2) 20 min aerobic perfusion plus ischemic preconditioning (3 min ischemia/3 min reperfusion+5 min ischemia/5 min reperfusion); (3) aerobic perfusion with buffer containing DOG (10 μM) given as a substitute for ischemic preconditioning; (4) aerobic perfusion with DOG (10 μM) during the last 2 min of aerobic perfusion. All hearts then were subjected to 35 min of global ischemia and 40 min reperfusion. A further group (5) were perfused with DOG (10 μM) for the first 2 min of reperfusion. Ischemic preconditioning improved postischemic recovery of LVDP from 24±3% in controls to 71±2% (P<0.05). Recovery of LVDP also was enhanced by DOG when given just before ischemia (54±4%), however, DOG had no effect on the recovery of LVDP when used as a substitute for ischemic preconditioning (22±5%) or when given during reperfusion (29±6%). In Study 2, the first four groups of study were repeated (n=4–5/group) without imposing the periods of ischemia and reperfusion, instead hearts were taken for the measurement of PKC activity (pmol/min/mg protein±SEM). PKC activity after 36 min in groups (1), (2), (3) and (4) was: 332±102, 299±63, 521±144, and 340±113 and the membrane:cytosolic PKC activity ratio was: 5.6±1.5, 5.3±1.8, 6.6±2.7, and 3.9±2.1 (P=NS in each instance). In conclusion, DOG is cardioprotective but under the conditions of the present study is less cardioprotective than ischemic preconditioning, furthermore the protection does not appear to necessitate PKC activation prior to ischemia.

Phorbol ester, but not ischemic preconditioning, activates protein kinase D in the rat heart

The signal transduction pathways that mediate the cardioprotective effects of ischemic preconditioning remain unclear. Here we have determined the role of a novel kinase, protein kinase D (PKD), in mediating preconditioning in the rat heart. Isolated rat hearts (n=6/group) were subjected to either: (i) 36 min aerobic perfusion (control); (ii) 20 min aerobic perfusion plus 3 min no-flow ischemia, 3 min reperfusion, 5 min no-flow ischemia, 5 min reperfusion (ischemic preconditioning); (iii) 20 min aerobic perfusion plus 200 nmol/l phorbol 12-myristate 13-acetate (PMA) given as a substitute for ischemic preconditioning. The left ventricle then was excised, homogenized and PKD immunoprecipitated from the homogenate. Activity of the purified kinase was determined following bincubation with [γ32P]-ATP±syntide-2, a substrate for PKD. Significant PKD autophosphorylation and syntide-2 phosphorylation occurred in PMA-treated hearts, but not in control or preconditioned hearts. Additional studies confirmed that recovery of LVDP was greater and initiation of ischemic contracture and time-to-peak contracture were less, in ischemic preconditioned hearts compared with controls (P<0.05). Our results suggest that the early events that mediate ischemic preconditioning in the rat heart occur via a PKD-independent mechanism.

Conditioning and preconditioning of the variational data assimilation problem

Numerical weather prediction (NWP) centres use numerical models of the atmospheric flow to forecast future weather states from an estimate of the current state. Variational data assimilation (VAR) is used commonly to determine an optimal state estimate that miminizes the errors between observations of the dynamical system and model predictions of the flow. The rate of convergence of the VAR scheme and the sensitivity of the solution to errors in the data are dependent on the condition number of the Hessian of the variational least-squares objective function. The traditional formulation of VAR is ill-conditioned and hence leads to slow convergence and an inaccurate solution. In practice, operational NWP centres precondition the system via a control variable transform to reduce the condition number of the Hessian. In this paper we investigate the conditioning of VAR for a single, periodic, spatially-distributed state variable. We present theoretical bounds on the condition number of the original and preconditioned Hessians and hence demonstrate the improvement produced by the preconditioning. We also investigate theoretically the effect of observation position and error variance on the preconditioned system and show that the problem becomes more ill-conditioned with increasingly dense and accurate observations. Finally, we confirm the theoretical results in an operational setting by giving experimental results from the Met Office variational system.

Rapid preconditioning of data for accelerating convex hull algorithms

Given a dataset of two-dimensional points in the plane with integer coordinates, the method proposed reduces a set of n points down to a set of s points s ≤ n, such that the convex hull on the set of s points is the same as the convex hull of the original set of n points. The method is O(n). It helps any convex hull algorithm run faster. The empirical analysis of a practical case shows a percentage reduction in points of over 98%, that is reflected as a faster computation with a speedup factor of at least 4.

Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.

PKC-dependent activation of p46/p54 JNKs during ischemic preconditioning in conscious rabbits.

A conscious rabbit model was used to study the effect of ischemic preconditioning (PC) on stress-activated kinases [c-Jun NH(2)-terminal kinases (JNKs) and p38 mitogen-activated protein kinase (MAPK)] in an environment free of surgical trauma and attending external stress. Ischemic PC (6 cycles of 4-min ischemia/4-min reperfusion) induced significant activation of protein kinase C (PKC)-epsilon in the particulate fraction, which was associated with activation of p46 JNK in the nuclear fraction and p54 JNK in the cytosolic fraction; all of these changes were completely abolised by the PKC inhibitor chelerythrine. Selective enhancement of PKC-epsilon activity in adult rabbit cardiac myocytes resulted in enhanced activity of p46/p54 JNKs, providing direct in vitro evidence that PKC-epsilon is coupled to both kinases. Studies in rabbits showed that the activation of p46 JNK occurred during ischemia, whereas that of p54 JNK occurred after reperfusion. A single 4-min period of ischemia induced a robust activation of the p38 MAPK cascade, which, however, was attenuated after 5 min of reperfusion and disappeared after six cycles of 4-min ischemia/reperfusion. Overexpression of PKC-epsilon in cardiac myocytes failed to increase the p38 MAPK activity. These results demonstrate that ischemic PC activates p46 and p54 JNKs via a PKC-epsilon-dependent signaling pathway and that there are important differences between p46 and p54 JNKs with respect to the subcellular compartment (cytosolic vs. nuclear) and the mechanism (ischemia vs. reperfusion) of their activation after ischemic PC.

Preconditioning 2D integer data for fast convex hull computations

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved.

Approximate factorization constraint preconditioners for saddle-point matrices

We consider the application of the conjugate gradient method to the solution of large, symmetric indefinite linear systems. Special emphasis is put on the use of constraint preconditioners and a new factorization that can reduce the number of flops required by the preconditioning step. Results concerning the eigenvalues of the preconditioned matrix and its minimum polynomial are given. Numerical experiments validate these conclusions.

Formulation of a live bacterial vaccine for stable room temperature storage results in loss of acid, bile and bile salt resistance

Live bacterial vaccines have great promise both as vaccines against enteric pathogens and as heterologous antigen vectors against diverse diseases. Ideally, room temperature stable dry formulations of live bacterial vaccines will allow oral vaccination without cold-chain storage or injections. Attenuated Salmonella can cross the intestinal wall and deliver replicating antigen plus innate immune activation signals directly to the intestinal immune tissues, however the ingested bacteria must survive firstly gastric acid and secondly the antimicrobial defences of the small intestine. We found that the way in which cells are grown prior to formulation markedly affects sensitivity to acid and bile. Using a previously published stable storage formulation that maintained over 10% viability after 56 days storage at room temperature, we found dried samples of an attenuated S. typhimurium vaccine lost acid and bile resistance compared to the same bacteria taken from fresh culture. The stable formulation utilised osmotic preconditioning in defined medium plus elevated salt concentration to induce intracellular trehalose accumulation before drying. Dried bacteria grown in rich media without osmotic preconditioning showed more resistance to bile, but less stability during storage, suggesting a trade-off between bile resistance and stability. Further optimization is needed to produce the ultimate room-temperature stable oral live bacterial vaccine formulation.

Dynamical evolution of North Atlantic ridges and poleward Jet Stream displacements

The development of a particular wintertime atmospheric circulation regime over the North Atlantic, comprising a northward shift of the North Atlantic eddy-driven jet stream and an associated strong and persistent ridge in the subtropics, is investigated. Several different methods of analysis are combined to describe the temporal evolution of the events and relate it to shifts in the phase of the North Atlantic Oscillation and East Atlantic pattern. First, the authors identify a close relationship between northward shifts of the eddy-driven jet, the establishment and maintenance of strong and persistent ridges in the subtropics, and the occurrence of upper-tropospheric anticyclonic Rossby wave breaking over Iberia. Clear tropospheric precursors are evident prior to the development of the regime, suggesting a preconditioning of the Atlantic jet stream and an upstream influence via a large-scale Rossby wave train from the North Pacific. Transient (2–6 days) eddy forcing plays a dual role, contributing to both the initiation and then the maintenance of the circulation anomalies. During the regime there is enhanced occurrence of anticyclonic Rossby wave breaking, which may be described as low-latitude blocking-like events over the southeastern North Atlantic. A strong ridge is already established at the time of wave-breaking onset, suggesting that the role of wave-breaking events is to amplify the circulation anomalies rather than to initiate them. Wave breaking also seems to enhance the persistence, since it is unlikely that a persistent ridge event occurs without being also accompanied by wave breaking.

Vertical structure and physical processes of the Madden-Julian oscillation: exploring key model physics in climate simulations

Aimed at reducing deficiencies in representing the Madden-Julian oscillation (MJO) in general circulation models (GCMs), a global model evaluation project on vertical structure and physical processes of the MJO was coordinated. In this paper, results from the climate simulation component of this project are reported. It is shown that the MJO remains a great challenge in these latest generation GCMs. The systematic eastward propagation of the MJO is only well simulated in about one-fourth of the total participating models. The observed vertical westward tilt with altitude of the MJO is well simulated in good MJO models, but not in the poor ones. Damped Kelvin wave responses to the east of convection in the lower troposphere could be responsible for the missing MJO preconditioning process in these poor MJO models. Several process-oriented diagnostics were conducted to discriminate key processes for realistic MJO simulations. While large-scale rainfall partition and low-level mean zonal winds over the Indo-Pacific in a model are not found to be closely associated with its MJO skill, two metrics, including the low-level relative humidity difference between high and low rain events and seasonal mean gross moist stability, exhibit statistically significant correlations with the MJO performance. It is further indicated that increased cloud-radiative feedback tends to be associated with reduced amplitude of intraseasonal variability, which is incompatible with the radiative instability theory previously proposed for the MJO. Results in this study confirm that inclusion of air-sea interaction can lead to significant improvement in simulating the MJO.

Activation of mitogen-activated protein kinases (p38-MAPKs, SAPKs/JNKs and ERKs) by adenosine in the perfused rat heart.

Adenosine and mitogen-activated protein kinases (MAPKs) have been separately implicated in cardiac ischaemic preconditioning. We investigated the activation of MAPK subfamilies by adenosine in perfused rat hearts. p38-MAPK was rapidly phosphorylated and activated (10-fold activation, maximal at 5 min) by 10 mM adenosine, as was the p38-MAPK substrate, MAPKAPK2 (4.5-fold). SAPKs/JNKs were activated (5-fold) and ERKs were phosphorylated (both maximal at 5 min). The concentration dependences of activation of p38-MAPK and ERKs were biphasic with a 'high affinity' component (maximal at 10-100 microM adenosine) and a 'low affinity' component that had not saturated at 10 mM. SAPKs/JNKs were activated only by 10 mM adenosine. These results are consistent with MAPK involvement in adenosine-mediated ischaemic preconditioning.

Lightning as a space-weather hazard: UK thunderstorm activity modulated by the passage of the heliospheric current sheet

Lightning flash rates, RL, are modulated by corotating interaction regions (CIRs) and the polarity of the heliospheric magnetic field (HMF) in near-Earth space. As the HMF polarity reverses at the heliospheric current sheet (HCS), typically within a CIR, these phenomena are likely related. In this study, RL is found to be significantly enhanced at the HCS and at 27 days prior/after. The strength of the enhancement depends on the polarity of the HMF reversal at the HCS. Near-Earth solar and galactic energetic particle fluxes are also ordered by HMF polarity, though the variations qualitatively differ from RL, with the main increase occurring prior to the HCS crossing. Thus, the CIR effect on lightning is either the result of compression/amplification of the HMF (and its subsequent interaction with the terrestrial system) or that energetic particle preconditioning of the Earth system prior to the HMF polarity change is central to solar wind lightning coupling mechanism.