Smolyak's algorithm: A powerful black box for the acceleration of scientific computations

We provide a general discussion of Smolyak's algorithm for the acceleration of scientific computations. The algorithm first appeared in Smolyak's work on multidimensional integration and interpolation. Since then, it has been generalized in multiple directions and has been associated with the keywords: sparse grids, hyperbolic cross approximation, combination technique, and multilevel methods. Variants of Smolyak's algorithm have been employed in the computation of high-dimensional integrals in finance, chemistry, and physics, in the numerical solution of partial and stochastic differential equations, and in uncertainty quantification. Motivated by this broad and ever-increasing range of applications, we describe a general framework that summarizes fundamental results and assumptions in a concise application-independent manner

Heterobimetallic conducting polymers based on salophen complexes via electrosynthesis

In this work, we report the first electrochemical synthesis of two copolymeric bimetallic conducting polymers by a simple anodic electropolymerization method. The adopted precursors are electroactive transition metal (M = Ni, Cu and Fe) salophen complexes, which can be easily obtained by direct chemical synthesis. The resulting films, labeled poly-NiCu and poly-CuFe, were characterized by cyclic voltammetry in both organic and aqueous media, attenuated total reflectance Fourier transform infrared spectroscopy, UV-vis spectroscopy, scanning electron microscopy, and coupled energy dispersive X-ray spectroscopy. The films are conductive and exhibit great electrochemical stability in both organic and aqueous media (resistant over 100 cycles without significant loss in current response or changes in electrochemical behavior), which makes them good candidates for an array of potential applications. Electrochemical detection of ascorbic acid was performed using both materials

Effect of Stress on Viral–Bacterial Synergy in Bovine Respiratory Disease: Novel Mechanisms to Regulate Inflammation

The severity of bovine respiratory infections has been linked to a variety offactors, including environmental and nutritional changes, transportation, and socialreorganization of weaned calves. Fatal respiratory infections, however, usually occurwhen a primary viral infection compromises host defences and enhances the severityof a secondary bacterial infection. This viral–bacterial synergy can occur by a numberof different mechanisms and disease challenge models have been developed to analysehost responses during these respiratory infections. A primary bovine herpesvirus-1(BHV-1) respiratory infection followed by a secondary challenge with Mannheimia haemolyticaresults in fatal bovine respiratory disease (BRD) and host responses to these two pathogens have been studied extensively. We used this disease model todemonstrate that stress significantly altered the viral–bacterial synergy resulting infatal BRD. Functional genomic analysis revealed that BHV-1 infection enhanced toll-likereceptors (TLR) expression and increased pro-inflammatory responses whichcontribute to the severity of a Mannheimia haemolytica infection. TLRs play a criticalrole in detecting bacterial infections and inducing pro-inflammatory responses. It isdifficult to understand, however, how stress-induced corticosteroids could enhancethis form of viral–bacterial synergy. Nuclear translocation of the glucocorticoidreceptor activates cell signalling pathways which inhibit both TLR signallingand pro-inflammatory responses. The apparent conundrum between stress-inducedcorticosteroids and enhanced BRD susceptibility is discussed in terms of present data and previous investigations of stress and respiratory disease

Regularized Linear Inversion with Randomized Singular Value Decomposition

In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value decomposition, Tikhonov regularization, and general Tikhonov regularization with a smoothness penalty. One distinct feature of the proposed approach is that it explicitly preserves the structure of the regularized solution in the sense that it always lies in the range of a certain adjoint operator. We provide error estimates between the approximation and the exact solution under canonical source condition, and interpret the approach in the lens of convex duality. Extensive numerical experiments are provided to illustrate the efficiency and accuracy of the approach.Comment: 20 pages, 4 figure

Tips for implementing multigrid methods on domains containing holes

As part of our development of a computer code to perform 3D `constrained evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the efficient solution of elliptic equations on domains containing holes (i.e., excised regions), via the multigrid method. We consider as a test case the Poisson equation with a nonlinear term added, as a means of illustrating the principles involved, and move to a "real world" 3-dimensional problem which is the solution of the conformally flat Hamiltonian constraint with Dirichlet and Robin boundary conditions. Using our vertex-centered multigrid code, we demonstrate globally second-order-accurate solutions of elliptic equations over domains containing holes, in two and three spatial dimensions. Keys to the success of this method are the choice of the restriction operator near the holes and definition of the location of the inner boundary. In some cases (e.g. two holes in two dimensions), more and more smoothing may be required as the mesh spacing decreases to zero; however for the resolutions currently of interest to many numerical relativists, it is feasible to maintain second order convergence by concentrating smoothing (spatially) where it is needed most. This paper, and our publicly available source code, are intended to serve as semi-pedagogical guides for those who may wish to implement similar schemes.Comment: 18 pages, 11 figures, LaTeX. Added clarifications and references re. scope of paper, mathematical foundations, relevance of work. Accepted for publication in Classical & Quantum Gravit

Towards a unified theory of Sobolev inequalities

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1

Remarkable resilience of forest structure and biodiversity following fire in the peri-urban bushland of Sydney, Australia

In rapidly urbanizing areas, natural vegetation becomes fragmented, making conservation planning challenging, particularly as climate change accelerates fire risk. We studied urban forest fragments in two threatened eucalypt‐dominated (scribbly gum woodland, SGW, and ironbark forest, IF) communities across ~2000 ha near Sydney, Australia, to evaluate effects of fire frequency (0– 4 in last 25 years) and time since fire (0.5 to >25 years) on canopy structure, habitat quality and biodiversity (e.g., species richness). Airborne lidar was used to assess canopy height and density, and ground‐based surveys of 148 (400 m2) plots measured leaf area index (LAI), plant species com‐ position and habitat metrics such as litter cover and hollow‐bearing trees. LAI, canopy density, litter, and microbiotic soil crust increased with time since fire in both communities, while tree and mistletoe cover increased in IF. Unexpectedly, plant species richness increased with fire frequency, owing to increased shrub richness which offset decreased tree richness in both communities. These findings indicate biodiversity and canopy structure are generally resilient to a range of times since fire and fire frequencies across this study area. Nevertheless, reduced arboreal habitat quality and subtle shifts in community composition of resprouters and obligate seeders signal early concern for a scenario of increasing fire frequency under climate change. Ongoing assessment of fire responses is needed to ensure that biodiversity, canopy structure and ecosystem function are maintained in the remaining fragments of urban forests under future climate change which will likely drive hotter and more frequent fires

Anxiolytic activity of pyridoindole derivatives SMe1EC2 and SMe1M2: behavioral analysis using rat model

Anxiety and mood disorders have become very significant affections in the last decades. According to WHO at least one mental disease occurred per year in 27% of EU inhabitants (more than 82 mil. people). It is estimated that by 2020, depression will be the main cause of morbidity in the developed countries. These circumstances call for research for new prospective drugs with anxiolytic and antidepressive properties exhibiting no toxicity and withdrawal effect and possessing beneficial properties, like antioxidant and/or neuroprotective effects. The aim of this study was to obtain information about psychopharmacological properties of pyridoindole derivatives SMe1EC2 and SMe1M2, using non-invasive behavioral methods in rats