Spectral estimates for saddle point matrices arising in weak constraint four-dimensional variational data assimilation

We consider the large-sparse symmetric linear systems of equations that arise in the solution of weak constraint four-dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a $3 \times 3$ block structure but block eliminations can be performed to reduce them to saddle point systems with a $2 \times 2$ block structure, or further to symmetric positive definite systems. In this paper, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds

GPU implementation of Krylov solvers for block-tridiagonal eigenvalue problems

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-32149-3_18In an eigenvalue problem defined by one or two matrices with block-tridiagonal structure, if only a few eigenpairs are required it is interesting to consider iterative methods based on Krylov subspaces, even if matrix blocks are dense. In this context, using the GPU for the associated dense linear algebra may provide high performance. We analyze this in an implementation done in the context of SLEPc, the Scalable Library for Eigenvalue Problem Computations. In the case of a generalized eigenproblem or when interior eigenvalues are computed with shift-and-invert, the main computational kernel is the solution of linear systems with a block-tridiagonal matrix. We explore possible implementations of this operation on the GPU, including a block cyclic reduction algorithm.This work was partially supported by the Spanish Ministry of Economy and Competitiveness under grant TIN2013-41049-P. Alejandro Lamas was supported by the Spanish Ministry of Education, Culture and Sport through grant FPU13-06655.Lamas Daviña, A.; Román Moltó, JE. (2016). GPU implementation of Krylov solvers for block-tridiagonal eigenvalue problems. En Parallel Processing and Applied Mathematics. Springer. 182-191. https://doi.org/10.1007%2F978-3-319-32149-3_18S182191Baghapour, B., Esfahanian, V., Torabzadeh, M., Darian, H.M.: A discontinuous Galerkin method with block cyclic reduction solver for simulating compressible flows on GPUs. Int. J. Comput. Math. 92(1), 110–131 (2014)Bientinesi, P., Igual, F.D., Kressner, D., Petschow, M., Quintana-Ortí, E.S.: Condensed forms for the symmetric eigenvalue problem on multi-threaded architectures. Concur. Comput. Pract. Exp. 23, 694–707 (2011)Haidar, A., Ltaief, H., Dongarra, J.: Toward a high performance tile divide and conquer algorithm for the dense symmetric eigenvalue problem. SIAM J. Sci. Comput. 34(6), C249–C274 (2012)Heller, D.: Some aspects of the cyclic reduction algorithm for block tridiagonal linear systems. SIAM J. Numer. Anal. 13(4), 484–496 (1976)Hernandez, V., Roman, J.E., Vidal, V.: SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31(3), 351–362 (2005)Hirshman, S.P., Perumalla, K.S., Lynch, V.E., Sanchez, R.: BCYCLIC: a parallel block tridiagonal matrix cyclic solver. J. Comput. Phys. 229(18), 6392–6404 (2010)Minden, V., Smith, B., Knepley, M.G.: Preliminary implementation of PETSc using GPUs. In: Yuen, D.A., Wang, L., Chi, X., Johnsson, L., Ge, W., Shi, Y. (eds.) GPU Solutions to Multi-scale Problems in Science and Engineering. Lecture Notes in Earth System Sciences, pp. 131–140. Springer, Heidelberg (2013)NVIDIA: CUBLAS Library V7.0. Technical report, DU-06702-001 $$\_$$ v7.0, NVIDIA Corporation (2015)Park, A.J., Perumalla, K.S.: Efficient heterogeneous execution on large multicore and accelerator platforms: case study using a block tridiagonal solver. J. Parallel and Distrib. Comput. 73(12), 1578–1591 (2013)Reguly, I., Giles, M.: Efficient sparse matrix-vector multiplication on cache-based GPUs. In: Innovative Parallel Computing (InPar), pp. 1–12 (2012)Roman, J.E., Vasconcelos, P.B.: Harnessing GPU power from high-level libraries: eigenvalues of integral operators with SLEPc. In: International Conference on Computational Science. Procedia Computer Science, vol. 18, pp. 2591–2594. Elsevier (2013)Seal, S.K., Perumalla, K.S., Hirshman, S.P.: Revisiting parallel cyclic reduction and parallel prefix-based algorithms for block tridiagonal systems of equations. J. Parallel Distrib. Comput. 73(2), 273–280 (2013)Stewart, G.W.: A Krylov-Schur algorithm for large eigenproblems. SIAM J. Matrix Anal. Appl. 23(3), 601–614 (2001)Tomov, S., Nath, R., Dongarra, J.: Accelerating the reduction to upper Hessenberg, tridiagonal, and bidiagonal forms through hybrid GPU-based computing. Parallel Comput. 36(12), 645–654 (2010)Vomel, C., Tomov, S., Dongarra, J.: Divide and conquer on hybrid GPU-accelerated multicore systems. SIAM J. Sci. Comput. 34(2), C70–C82 (2012)Zhang, Y., Cohen, J., Owens, J.D.: Fast tridiagonal solvers on the GPU. In: Proceedings of the 15th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming. PPopp 2010, pp. 127–136 (2010

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

Learning health ‘safety’ within non-technical skills interprofessional simulation education: a qualitative study

Background: Healthcare increasingly recognises and focusses on the phenomena of ‘safe practice’ and ‘patient safety.’ Success with non-technical skills (NTS) training in other industries has led to widespread transposition to healthcare education, with communication and teamwork skills central to NTS frameworks. Objective: This study set out to identify how the context of interprofessional simulation learning influences NTS acquisition and development of ‘safety’ amongst learners. Methods: Participants receiving a non-technical skills (NTS) safety focussed training package were invited to take part in a focus group interview which set out to explore communication, teamwork, and the phenomenon of safety in the context of the learning experiences they had within the training programme. The analysis was aligned with a constructivist paradigm and took an interactive methodological approach. The analysis proceeded through three stages, consisting of open, axial, and selective coding, with constant comparisons taking place throughout each phase. Each stage provided categories that could be used to explore the themes of the data. Additionally, to ensure thematic saturation, transcripts of observed simulated learning encounters were then analysed. Results: Six themes were established at the axial coding level, i.e., analytical skills, personal behaviours, communication, teamwork, context, and pedagogy. Underlying these themes, two principal concepts emerged, namely: intergroup contact anxiety – as both a result of and determinant of communication – and teamwork, both of which must be considered in relation to context. These concepts have subsequently been used to propose a framework for NTS learning. Conclusions: This study highlights the role of intergroup contact anxiety and teamwork as factors in NTS behaviour and its dissipation through interprofessional simulation learning. Therefore, this should be a key consideration in NTS education. Future research is needed to consider the role of the affective non-technical attributes of intergroup contact anxiety and teamwork as focuses for education and determinants of safe behaviour

A Jacobi-Davidson type method with a correction equation tailored for integral operators

The final publication is available at Springer via http://dx.doi.org/10.1007/s11075-012-9656-9We propose two iterative numerical methods for eigenvalue computations of large dimensional problems arising from finite approximations of integral operators, and describe their parallel implementation. A matrix representation of the problem on a space of moderate dimension, defined from an infinite dimensional one, is computed along with its eigenpairs. These are taken as initial approximations and iteratively refined, by means of a correction equation based on the reduced resolvent operator and performed on the moderate size space, to enhance their quality. Each refinement step requires the prolongation of the correction equation solution back to a higher dimensional space, defined from the infinite dimensional one. This approach is particularly adapted for the computation of eigenpair approximations of integral operators, where prolongation and restriction matrices can be easily built making a bridge between coarser and finer discretizations. We propose two methods that apply a Jacobi–Davidson like correction: Multipower Defect-Correction (MPDC), which uses a single-vector scheme, if the eigenvalues to refine are simple, and Rayleigh–Ritz Defect-Correction (RRDC), which is based on a projection onto an expanding subspace. Their main advantage lies in the fact that the correction equation is performed on a smaller space while for general solvers it is done on the higher dimensional one. We discuss implementation and parallelization details, using the PETSc and SLEPc packages. Also, numerical results on an astrophysics application, whose mathematical model involves a weakly singular integral operator, are presented.This work was partially supported by European Regional Development Fund through COMPETE, FCT-Fundacao para a Ciencia e a Tecnologia through CMUP-Centro de Matematica da Universidade do Porto and Spanish Ministerio de Ciencia e Innovacion under projects TIN2009-07519 and AIC10-D-000600.Vasconcelos, PB.; D'almeida, FD.; Román Moltó, JE. (2013). A Jacobi-Davidson type method with a correction equation tailored for integral operators. Numerical Algorithms. 64(1):85-103. doi:10.1007/s11075-012-9656-9S85103641Absil, P.A., Mahony, R., Sepulchre, R., Dooren, P.V.: A Grassmann–Rayleigh quotient iteration for computing invariant subspaces. SIAM Rev. 44(1), 57–73 (2002)Ahues, M., Largillier, A., Limaye, B.V.: Spectral Computations with Bounded Operators. Chapman and Hall, Boca Raton (2001)Ahues, M., d’Almeida, F.D., Largillier, A., Titaud, O., Vasconcelos, P.: An L 1 refined projection approximate solution of the radiation transfer equation in stellar atmospheres. J. Comput. Appl. Math. 140(1–2), 13–26 (2002)Ahues, M., d’Almeida, F.D., Largillier, A., Vasconcelos, P.B.: Defect correction for spectral computations for a singular integral operator. Commun. Pure Appl. Anal. 5(2), 241–250 (2006)Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., van der Vorst, H. (eds.): Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. Society for Industrial and Applied Mathematics, Philadelphia (2000)Balay, S., Buschelman, K., Eijkhout, V., Gropp, W.D., Kaushik, D., Knepley, M., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc Users Manual. Tech. Rep. ANL-95/11 - Revision 3.1, Argonne National Laboratory (2010)Chatelin, F.: Spectral Approximation of Linear Operators. SIAM, Philadelphia (2011)d’Almeida, F.D., Vasconcelos, P.B.: Convergence of multipower defect correction for spectral computations of integral operators. Appl. Math. Comput. 219(4), 1601–1606 (2012)Falgout, R.D., Yang, U.M.: Hypre: A library of high performance preconditioners. In: Sloot, P.M.A., Tan, C.J.K., Dongarra, J., Hoekstra, A.G. (eds.) Computational Science - ICCS 2002, International Conference, Amsterdam, The Netherlands, April 21–24, 2002. Proceedings, Part III, Lecture Notes in Computer Science, vol. 2331, pp. 632–641. Springer (2002)Henson, V.E., Yang, U.M.: BoomerAMG: A parallel algebraic multigrid solver and preconditioner. Appl. Numer. Math. 41(1), 155–177 (2002)Hernandez, V., Roman, J.E., Vidal, V.: SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31(3), 351–362 (2005)Hernandez, V., Roman, J.E., Tomas, A., Vidal, V.: SLEPc Users Manual. Tech. Rep. DSIC-II/24/02 - Revision 3.1, D. Sistemas Informáticos y Computación, Universidad Politécnica de Valencia (2010)Saad, Y.: Iterative methods for sparse linear systems, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia (2003)Simoncini, V., Eldén, L.: Inexact Rayleigh quotient-type methods for eigenvalue computations. BIT 42(1), 159–182 (2002)Sleijpen, G.L.G., van der Vorst, H.A.: A Jacobi–Davidson iteration method for linear eigenvalue problems. SIAM Rev. 42(2), 267–293 (2000)Sorensen, D.C.: Implicit application of polynomial filters in a k-step Arnoldi method. SIAM J. Matrix Anal. Appl. 13, 357–385 (1992)Stewart, G.W.: A Krylov–Schur algorithm for large eigenproblems. SIAM J. Matrix Anal. Appl. 23(3), 601–614 (2001

Prior Mating Experience Modulates the Dispersal of Drosophila in Males More Than in Females

Cues from both an animal’s internal physiological state and its local environment may influence its decision to disperse. However, identifying and quantifying the causative factors underlying the initiation of dispersal is difficult in uncontrolled natural settings. In this study, we automatically monitored the movement of fruit flies and examined the influence of food availability, sex, and reproductive status on their dispersal between laboratory environments. In general, flies with mating experience behave as if they are hungrier than virgin flies, leaving at a greater rate when food is unavailable and staying longer when it is available. Males dispersed at a higher rate and were more active than females when food was unavailable, but tended to stay longer in environments containing food than did females. We found no significant relationship between weight and activity, suggesting the behavioral differences between males and females are caused by an intrinsic factor relating to the sex of a fly and not simply its body size. Finally, we observed a significant difference between the dispersal of the natural isolate used throughout this study and the widely-used laboratory strain, Canton-S, and show that the difference cannot be explained by allelic differences in the foraging gene

Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/050809

Advances in prevention and therapy of neonatal dairy calf diarrhoea : a systematical review with emphasis on colostrum management and fluid therapy

Neonatal calf diarrhoea remains the most common cause of morbidity and mortality in preweaned dairy calves worldwide. This complex disease can be triggered by both infectious and non-infectious causes. The four most important enteropathogens leading to neonatal dairy calf diarrhoea are Escherichia coli, rota-and coronavirus, and Cryptosporidium parvum. Besides treating diarrhoeic neonatal dairy calves, the veterinarian is the most obvious person to advise the dairy farmer on prevention and treatment of this disease. This review deals with prevention and treatment of neonatal dairy calf diarrhoea focusing on the importance of a good colostrum management and a correct fluid therapy

The impact of illness in patients with moderate to severe gastro-esophageal reflux disease

BACKGROUND: Gastro-esophageal reflux disease (GERD) is a common disease. It impairs health related quality of life (HRQL). However, the impact on utility scores and work productivity in patients with moderate to severe GERD is not well known. METHODS: We analyzed data from 217 patients with moderate to severe GERD (mean age 50, SD 13.7) across 17 Canadian centers. Patients completed three utility instruments – the standard gamble (SG), the feeling thermometer (FT), and the Health Utilities Index 3 (HUI 3) – and several HRQL instruments, including Quality of Life in Reflux and Dyspepsia (QOLRAD) and the Medical Outcomes Short Form-36 (SF-36). All patients received a proton pump inhibitor, esomeprazole 40 mg daily, for four to six weeks. RESULTS: The mean scores on a scale from 0 (dead) to 1 (full health) obtained for the FT, SG, and HUI 3 were 0.67 (95% CI, 0.64 to 0.70), 0.76 (95% CI, 0.75 to 0.80), and 0.80 (95% CI, 0.77 to 0.82) respectively. The mean scores on the SF-36 were lower than the previously reported Canadian and US general population mean scores and work productivity was impaired. CONCLUSION: GERD has significant impact on utility scores, HRQL, and work productivity in patients with moderate to severe disease. Furthermore, the FT and HUI 3 provide more valid measurements of HRQL in GERD than the SG. After treatment with esomeprazole, patients showed improved HRQL