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

Near-Field Intensity Correlations in Semicontinuous Metal-Dielectric Films

Spatial intensity correlation functions are obtained from near-field scanning optical microscope measurements of semicontinuous metal-dielectric films. The concentration of metal particles on a dielectric surface is varied over a wide range to control the scattering strength. At low and high metal coverages where scattering is weak, the intensity correlation functions exhibit oscillations in the direction of incident light due to excitation of propagating surface waves. In the intermediate regime of metal concentration, the oscillatory behavior is replaced by a monotonic decay as a result of strong scattering and anomalous absorption. Significant differences in the near-field intensity correlations between metallic and dielectric random systems are demonstrated

Development of SNP markers present in expressed genes of the plant-pathogen interaction: Theobroma cacao - Moniliophtora perniciosa

We report the detection, validation and analysis of SNPs in the plant-pathogen interaction between cacao and Moniliophthora perniciosa ESTs using resequencing. This analysis in 73 EST sequences allowed the identification of 185 SNPs, 57% of them corresponding to transversion, 29% to transition and 14% to indels. The ESTs containing SNPs were classified into 14 main functional categories. After validation, 91 SNPs were confirmed, categorized and the parameters of nucleotide diversity and haplotype were calculated. Haplotype-based gene diversity and polymorphic information content (PIC) ranged from 0.559 to 0.56 and 0.115 to 0.12; respectively. Also, it was the advantage when considering haplotypes structure for each locus in place of single SNPs. Most of the gene fragments had a major haplotype combined to a series of low frequency haplotypes. Thus, the re-sequencing approach proved to be a valuable resource to identify useful SNPs for wide genetic applications. Furthermore, the cacao genome sequence availability allow a positional selection of DNA fragments to be re-sequenced enhancing the usefulness of the discovered SNPs. These results indicate the potential use of SNPs markers to identify allelic status of cacao resistance genes through marker-assisted selection to support the development of promising genotypes with high resistance to witch's broom disease. (Résumé d'auteur

Cholinergic Interneurons Mediate Fast VGluT3-Dependent Glutamatergic Transmission in the Striatum

The neurotransmitter glutamate is released by excitatory projection neurons throughout the brain. However, non-glutamatergic cells, including cholinergic and monoaminergic neurons, express markers that suggest that they are also capable of vesicular glutamate release. Striatal cholinergic interneurons (CINs) express the Type-3 vesicular glutamate transporter (VGluT3), although whether they form functional glutamatergic synapses is unclear. To examine this possibility, we utilized mice expressing Cre-recombinase under control of the endogenous choline acetyltransferase locus and conditionally expressed light-activated Channelrhodopsin2 in CINs. Optical stimulation evoked action potentials in CINs and produced postsynaptic responses in medium spiny neurons that were blocked by glutamate receptor antagonists. CIN-mediated glutamatergic responses exhibited a large contribution of NMDA-type glutamate receptors, distinguishing them from corticostriatal inputs. CIN-mediated glutamatergic responses were insensitive to antagonists of acetylcholine receptors and were not seen in mice lacking VGluT3. Our results indicate that CINs are capable of mediating fast glutamatergic transmission, suggesting a new role for these cells in regulating striatal activity

An investigation of cognitive 'branching' processes in major depression

<p>Abstract</p> <p>Background</p> <p>Patients with depression demonstrate cognitive impairment on a wide range of cognitive tasks, particularly putative tasks of frontal lobe function. Recent models of frontal lobe function have argued that the frontal pole region is involved in cognitive branching, a process requiring holding in mind one goal while performing sub-goal processes. Evidence for this model comes from functional neuroimaging and frontal-pole lesion patients. We have utilised these new concepts to investigate the possibility that patients with depression are impaired at cognitive 'branching'.</p> <p>Methods</p> <p>11 non-medicated patients with major depression were compared to 11 matched controls in a behavioural study on a task of cognitive 'branching'. In the version employed here, we recorded participant's performance as they learnt to perform the task. This involved participants completing a control condition, followed by a working memory condition, a dual-task condition and finally the branching condition, which integrates processes in the working memory and dual-task conditions. We also measured participants on a number of other cognitive tasks as well as mood-state before and after the branching experiment.</p> <p>Results</p> <p>Patients took longer to learn the first condition, but performed comparably to controls after six runs of the task. Overall, reaction times decreased with repeated exposure on the task conditions in controls, with this effect attenuated in patients. Importantly, no differences were found between patients and controls on the branching condition. There was, however, a significant change in mood-state with patients increasing in positive affect and decreasing in negative affect after the experiment.</p> <p>Conclusion</p> <p>We found no clear evidence of a fundamental impairment in anterior prefrontal 'branching processes' in patients with depression. Rather our data argue for a contextual learning impairment underlying cognitive dysfunction in this disorder. Our data suggest that MDD patients are able to perform high-level cognitive control tasks comparably to controls provided they are well trained. Future work should replicate these preliminary findings in a larger sample of MDD patients.</p

Implementing rapid, robust, cost-effective, patient-centred, routine genetic testing in ovarian cancer patients.

Advances in DNA sequencing have made genetic testing fast and affordable, but limitations of testing processes are impeding realisation of patient benefits. Ovarian cancer exemplifies the potential value of genetic testing and the shortcomings of current pathways to access testing. Approximately 15% of ovarian cancer patients have a germline BRCA1 or BRCA2 mutation which has substantial implications for their personal management and that of their relatives. Unfortunately, in most countries, routine implementation of BRCA testing for ovarian cancer patients has been inconsistent and largely unsuccessful. We developed a rapid, robust, mainstream genetic testing pathway in which testing is undertaken by the trained cancer team with cascade testing to relatives performed by the genetics team. 207 women with ovarian cancer were offered testing through the mainstream pathway. All accepted. 33 (16%) had a BRCA mutation. The result informed management of 79% (121/154) women with active disease. Patient and clinician feedback was very positive. The pathway offers a 4-fold reduction in time and 13-fold reduction in resource requirement compared to the conventional testing pathway. The mainstream genetic testing pathway we present is effective, efficient and patient-centred. It can deliver rapid, robust, large-scale, cost-effective genetic testing of BRCA1 and BRCA2 and may serve as an exemplar for other genes and other diseases

Evaluation of the current knowledge limitations in breast cancer research: a gap analysis

BACKGROUND A gap analysis was conducted to determine which areas of breast cancer research, if targeted by researchers and funding bodies, could produce the greatest impact on patients. METHODS Fifty-six Breast Cancer Campaign grant holders and prominent UK breast cancer researchers participated in a gap analysis of current breast cancer research. Before, during and following the meeting, groups in seven key research areas participated in cycles of presentation, literature review and discussion. Summary papers were prepared by each group and collated into this position paper highlighting the research gaps, with recommendations for action. RESULTS Gaps were identified in all seven themes. General barriers to progress were lack of financial and practical resources, and poor collaboration between disciplines. Critical gaps in each theme included: (1) genetics (knowledge of genetic changes, their effects and interactions); (2) initiation of breast cancer (how developmental signalling pathways cause ductal elongation and branching at the cellular level and influence stem cell dynamics, and how their disruption initiates tumour formation); (3) progression of breast cancer (deciphering the intracellular and extracellular regulators of early progression, tumour growth, angiogenesis and metastasis); (4) therapies and targets (understanding who develops advanced disease); (5) disease markers (incorporating intelligent trial design into all studies to ensure new treatments are tested in patient groups stratified using biomarkers); (6) prevention (strategies to prevent oestrogen-receptor negative tumours and the long-term effects of chemoprevention for oestrogen-receptor positive tumours); (7) psychosocial aspects of cancer (the use of appropriate psychosocial interventions, and the personal impact of all stages of the disease among patients from a range of ethnic and demographic backgrounds). CONCLUSION Through recommendations to address these gaps with future research, the long-term benefits to patients will include: better estimation of risk in families with breast cancer and strategies to reduce risk; better prediction of drug response and patient prognosis; improved tailoring of treatments to patient subgroups and development of new therapeutic approaches; earlier initiation of treatment; more effective use of resources for screening populations; and an enhanced experience for people with or at risk of breast cancer and their families. The challenge to funding bodies and researchers in all disciplines is to focus on these gaps and to drive advances in knowledge into improvements in patient care