Successive eigenvalue relaxation: a new method for the generalized eigenvalue problem and convergence estimates

We present a new subspace iteration method for the efficient computation of several smallest eigenvalues of the generalized eigenvalue problem Au = lambda Bu for symmetric positive definite operators A and B. We call this method successive eigenvalue relaxation, or the SER method (homoechon of the classical successive over-relaxation, or SOR method for linear systems). In particular, there are two significant features of SER which render it computationally attractive: (i) it can effectively deal with preconditioned large-scale eigenvalue problems, and (ii) its practical implementation does not require any information about the preconditioner used: it can routinely accommodate sophisticated preconditioners designed to meet more exacting requirements (e.g. three-dimensional elasticity problems with small thickness parameters). We endow SER with theoretical convergence estimates allowing for multiple and clusters of eigenvalues and illustrate their usefulness in a numerical example for a discretized partial differential equation exhibiting clusters of eigenvalues

Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in hypre and PETSc

We describe our software package Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) publicly released recently. BLOPEX is available as a stand-alone serial library, as an external package to PETSc (``Portable, Extensible Toolkit for Scientific Computation'', a general purpose suite of tools for the scalable solution of partial differential equations and related problems developed by Argonne National Laboratory), and is also built into {\it hypre} (``High Performance Preconditioners'', scalable linear solvers package developed by Lawrence Livermore National Laboratory). The present BLOPEX release includes only one solver--the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method for symmetric eigenvalue problems. {\it hypre} provides users with advanced high-quality parallel preconditioners for linear systems, in particular, with domain decomposition and multigrid preconditioners. With BLOPEX, the same preconditioners can now be efficiently used for symmetric eigenvalue problems. PETSc facilitates the integration of independently developed application modules with strict attention to component interoperability, and makes BLOPEX extremely easy to compile and use with preconditioners that are available via PETSc. We present the LOBPCG algorithm in BLOPEX for {\it hypre} and PETSc. We demonstrate numerically the scalability of BLOPEX by testing it on a number of distributed and shared memory parallel systems, including a Beowulf system, SUN Fire 880, an AMD dual-core Opteron workstation, and IBM BlueGene/L supercomputer, using PETSc domain decomposition and {\it hypre} multigrid preconditioning. We test BLOPEX on a model problem, the standard 7-point finite-difference approximation of the 3-D Laplacian, with the problem size in the range $10^5-10^8$.Comment: Submitted to SIAM Journal on Scientific Computin

Genetic diversity and origin of the feral horses in Theodore Roosevelt National Park

Feral horses in Theodore Roosevelt National Park (TRNP) represent an iconic era of the North Dakota Badlands. Their uncertain history raises management questions regarding origins, genetic diversity, and long-term genetic viability. Hair samples with follicles were collected from 196 horses in the Park and used to sequence the control region of mitochondrial DNA (mtDNA) and to profile 12 autosomal short tandem repeat (STR) markers. Three mtDNA haplotypes found in the TRNP horses belonged to haplogroups L and B. The control region variation was low with haplotype diversity of 0.5271, nucleotide diversity of 0.0077 and mean pairwise difference of 2.93. We sequenced one mitochondrial genome from each haplotype determined by the control region. Two complete mtDNA sequences of haplogroup L were closely related to the mtDNA of American Paint horse. The TRNP haplotype B did not have close matches in GenBank. The phylogenetic test placed this sequence in a group consisting of two horses from China, one from Yakutia, and one from Italy raising a possibility of historical transportation of horses from Siberia and East Asia to North America. Autosomal STR loci were polymorphic and indicated that the TRNP horses were distinctly different from 48 major horse breeds. Heterozygosity, mean number of alleles, and other measures of diversity indicated that TRNP herd diversity was below that observed for most other feral herds and domestic breeds. Both mtDNA and STRs demonstrated that the existing genetic data sets of horses are insufficient to determine the exact origins of the TRNP horses. However, measures of nuclear and mitochondrial diversity have elucidated management needs. It is recommended that new genetic stock be introduced and that adaptive management principles are employed to ensure that unique mitochondrial lineages are preserved and genetic diversity is increased and maintained over time

Motion-corrected reconstruction of parametric images from dynamic PET data with the Synergistic Image Reconstruction Framework (SIRF)

Motion correction has been added to a PET-MR reconstruction tool, SIRF, by incorporating a registration package, NiftyReg. New functionality has been demonstrated in the context of estimating kinetic parameters in the left temporal lobe, comparing direct and indirect reconstructions and evaluating the impact of using motion correction.Principal component analysis was used to detect motion and to determine time frames, while STIR's parametric-OSEM was used to perform the motion-corrected direct parametric reconstruction.It was found that the variance in the left temporal lobe decreased when motion correction was performed, and the same was true of direct reconstructions compared to indirect.With SIRF, the entirety of the demonstrated functionality can be performed from a single Matlab or Python script

Versatile regularisation toolkit for iterative image reconstruction with proximal splitting algorithms

Ill-posed image recovery requires regularisation to ensure stability. The presented open-source regularisation toolkit consists of state-of-the-art variational algorithms which can be embedded in a plug-and-play fashion into the general framework of proximal splitting methods. The packaged regularisers aim to satisfy various prior expectations of the investigated objects, e.g., their structural characteristics, smooth or non-smooth surface morphology. The flexibility of the toolkit helps with the design of more advanced model-based iterative reconstruction methods for different imaging modalities while operating with simpler building blocks. The toolkit is written for CPU and GPU architectures and wrapped for Python/MATLAB. We demonstrate the functionality of the toolkit in application to Positron Emission Tomography (PET) and X-ray synchrotron computed tomography (CT)

Recent Progress in STIR 5.0

STIR is an open source software for Emission Tomography data manipulation and image reconstruction, covering both PET and SPECT. In this work recent additions to the STIR code base are highlighted, namely the ability to read General Electric (GE) Raw Data Format 9 (RDF9) files, incorporation of GPU operators for forward and back projection, as well as work towards quantitative imaging for both PET and SPECT

Motion estimation and correction for simultaneous PET/MR using SIRF and CIL

SIRF is a powerful PET/MR image reconstruction research tool for processing data and developing new algorithms. In this research, new developments to SIRF are presented, with focus on motion estimation and correction. SIRF's recent inclusion of the adjoint of the resampling operator allows gradient propagation through resampling, enabling the MCIR technique. Another enhancement enabled registering and resampling of complex images, suitable for MRI. Furthermore, SIRF's integration with the optimization library CIL enables the use of novel algorithms. Finally, SPM is now supported, in addition to NiftyReg, for registration. Results of MR and PET MCIR reconstructions are presented, using FISTA and PDHG, respectively. These demonstrate the advantages of incorporating motion correction and variational and structural priors. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 2'

Data Descriptor: A global multiproxy database for temperature reconstructions of the Common Era

Reproducible climate reconstructions of the Common Era (1 CE to present) are key to placing industrial-era warming into the context of natural climatic variability. Here we present a community-sourced database of temperature-sensitive proxy records from the PAGES2k initiative. The database gathers 692 records from 648 locations, including all continental regions and major ocean basins. The records are from trees, ice, sediment, corals, speleothems, documentary evidence, and other archives. They range in length from 50 to 2000 years, with a median of 547 years, while temporal resolution ranges from biweekly to centennial. Nearly half of the proxy time series are significantly correlated with HadCRUT4.2 surface temperature over the period 1850-2014. Global temperature composites show a remarkable degree of coherence between high-and low-resolution archives, with broadly similar patterns across archive types, terrestrial versus marine locations, and screening criteria. The database is suited to investigations of global and regional temperature variability over the Common Era, and is shared in the Linked Paleo Data (LiPD) format, including serializations in Matlab, R and Python.(TABLE)Since the pioneering work of D'Arrigo and Jacoby1-3, as well as Mann et al. 4,5, temperature reconstructions of the Common Era have become a key component of climate assessments6-9. Such reconstructions depend strongly on the composition of the underlying network of climate proxies10, and it is therefore critical for the climate community to have access to a community-vetted, quality-controlled database of temperature-sensitive records stored in a self-describing format. The Past Global Changes (PAGES) 2k consortium, a self-organized, international group of experts, recently assembled such a database, and used it to reconstruct surface temperature over continental-scale regions11 (hereafter, ` PAGES2k-2013').This data descriptor presents version 2.0.0 of the PAGES2k proxy temperature database (Data Citation 1). It augments the PAGES2k-2013 collection of terrestrial records with marine records assembled by the Ocean2k working group at centennial12 and annual13 time scales. In addition to these previously published data compilations, this version includes substantially more records, extensive new metadata, and validation. Furthermore, the selection criteria for records included in this version are applied more uniformly and transparently across regions, resulting in a more cohesive data product.This data descriptor describes the contents of the database, the criteria for inclusion, and quantifies the relation of each record with instrumental temperature. In addition, the paleotemperature time series are summarized as composites to highlight the most salient decadal-to centennial-scale behaviour of the dataset and check mutual consistency between paleoclimate archives. We provide extensive Matlab code to probe the database-processing, filtering and aggregating it in various ways to investigate temperature variability over the Common Era. The unique approach to data stewardship and code-sharing employed here is designed to enable an unprecedented scale of investigation of the temperature history of the Common Era, by the scientific community and citizen-scientists alike