3,070 research outputs found
Holonomy of a class of bundles with fibre metrics
This paper is concerned with the holonomy of a class of spaces which includes Landsberg spaces of Finsler geometry. The methods used are those of Lie groupoids and algebroids as developed by Mackenzie. We prove a version of the Ambrose-Singer Theorem for such spaces. The paper ends with a discussion of how the results may be extended to Finsler spaces and homogeneous nonlinear connections in general
PLSS: A Projected Linear Systems Solver
We propose iterative projection methods for solving square or rectangular
consistent linear systems . Projection methods use sketching matrices
(possibly randomized) to generate a sequence of small projected subproblems,
but even the smaller systems can be costly. We develop a process that appends
one column each iteration to the sketching matrix and that converges in a
finite number of iterations independent of whether the sketch is random or
deterministic. In general, our process generates orthogonal updates to the
approximate solution . By choosing the sketch to be the set of all
previous residuals, we obtain a simple recursive update and convergence in at
most rank() iterations (in exact arithmetic). By choosing a sequence of
identity columns for the sketch, we develop a generalization of the Kaczmarz
method. In experiments on large sparse systems, our method (PLSS) with residual
sketches is competitive with LSQR, and our method with residual and identity
sketches compares favorably to state-of-the-art randomized methods
solveME: fast and reliable solution of nonlinear ME models.
BackgroundGenome-scale models of metabolism and macromolecular expression (ME) significantly expand the scope and predictive capabilities of constraint-based modeling. ME models present considerable computational challenges: they are much (>30 times) larger than corresponding metabolic reconstructions (M models), are multiscale, and growth maximization is a nonlinear programming (NLP) problem, mainly due to macromolecule dilution constraints.ResultsHere, we address these computational challenges. We develop a fast and numerically reliable solution method for growth maximization in ME models using a quad-precision NLP solver (Quad MINOS). Our method was up to 45 % faster than binary search for six significant digits in growth rate. We also develop a fast, quad-precision flux variability analysis that is accelerated (up to 60Ă— speedup) via solver warm-starts. Finally, we employ the tools developed to investigate growth-coupled succinate overproduction, accounting for proteome constraints.ConclusionsJust as genome-scale metabolic reconstructions have become an invaluable tool for computational and systems biologists, we anticipate that these fast and numerically reliable ME solution methods will accelerate the wide-spread adoption of ME models for researchers in these fields
MINRES-QLP: a Krylov subspace method for indefinite or singular symmetric systems
CG, SYMMLQ, and MINRES are Krylov subspace methods for solving symmetric
systems of linear equations. When these methods are applied to an incompatible
system (that is, a singular symmetric least-squares problem), CG could break
down and SYMMLQ's solution could explode, while MINRES would give a
least-squares solution but not necessarily the minimum-length (pseudoinverse)
solution. This understanding motivates us to design a MINRES-like algorithm to
compute minimum-length solutions to singular symmetric systems.
MINRES uses QR factors of the tridiagonal matrix from the Lanczos process
(where R is upper-tridiagonal). MINRES-QLP uses a QLP decomposition (where
rotations on the right reduce R to lower-tridiagonal form). On ill-conditioned
systems (singular or not), MINRES-QLP can give more accurate solutions than
MINRES. We derive preconditioned MINRES-QLP, new stopping rules, and better
estimates of the solution and residual norms, the matrix norm, and the
condition number.Comment: 26 pages, 6 figure
Reading Instruction for Children who use AAC: Considerations in the Pursuit of Generalizable Results
Our purpose was to review evidence-based literacy instruction for children with severe speech impairment (SSI) who communicate with AAC. This review focuses on three issues important to researchers in this area: participant heterogeneity, assessment and instruction, and research design. We found 8 articles that reported attempts to teach phonological awareness and individual-word reading to a total of 26 children with SSI who used AAC. We evaluated these studies based on reporting of participant characteristics, assessment and instruction modifications, and the strength of research designs. We conclude by highlighting the need for standard assessments that can be used across studies, discussing strategies for facilitating metaanalyses, and suggesting the creation of an online database for researchers to share results on literacy instruction for this population
Best Care at Lower Cost: The Path to Continuously Learning Health Care in America
http://www.iom.edu/Reports/2012/Best-Care-at-Lower-Cost-The-Path-to-Continuously-Learning-Health-Care-in-America.asp
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