pde2path - A Matlab package for continuation and bifurcation in 2D elliptic systems

pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components, on general two dimensional domains, and with rather general boundary conditions. The package is based on the FEM of the Matlab pdetoolbox, and is explained by a number of examples, including Bratu's problem, the Schnakenberg model, Rayleigh-Benard convection, and von Karman plate equations. These serve as templates to study new problems, for which the user has to provide, via Matlab function files, a description of the geometry, the boundary conditions, the coefficients of the PDE, and a rough initial guess of a solution. The basic algorithm is a one parameter arclength continuation with optional bifurcation detection and branch-switching. Stability calculations, error control and mesh-handling, and some elementary time-integration for the associated parabolic problem are also supported. The continuation, branch-switching, plotting etc are performed via Matlab command-line function calls guided by the AUTO style. The software can be downloaded from www.staff.uni-oldenburg.de/hannes.uecker/pde2path, where also an online documentation of the software is provided such that in this paper we focus more on the mathematics and the example systems

pde2path - version 2.0: faster FEM, multi-parameter continuation, nonlinear boundary conditions, and periodic domains - a short manual

pdepath 2.0 is an upgrade of the continuation/bifurcation package pde2path for elliptic systems of PDEs over bounded 2D domains, based on the Matlab pdetoolbox. The new features include a more efficient use of FEM, easier switching between different single parameter continuations, genuine multi-parameter continuation (e.g., fold continuation), more efficient implementation of nonlinear boundary conditions, cylinder and torus geometries (i.e., periodic boundary conditions), and a general interface for adding auxiliary equations like mass conservation or phase equations for continuation of traveling waves. The package (library, demos, manuals) can be downloaded at www.staff.uni-oldenburg.de/hannes.uecker/pde2pat

Fast T2 Mapping with Improved Accuracy Using Undersampled Spin-echo MRI and Model-based Reconstructions with a Generating Function

A model-based reconstruction technique for accelerated T2 mapping with improved accuracy is proposed using undersampled Cartesian spin-echo MRI data. The technique employs an advanced signal model for T2 relaxation that accounts for contributions from indirect echoes in a train of multiple spin echoes. An iterative solution of the nonlinear inverse reconstruction problem directly estimates spin-density and T2 maps from undersampled raw data. The algorithm is validated for simulated data as well as phantom and human brain MRI at 3 T. The performance of the advanced model is compared to conventional pixel-based fitting of echo-time images from fully sampled data. The proposed method yields more accurate T2 values than the mono-exponential model and allows for undersampling factors of at least 6. Although limitations are observed for very long T2 relaxation times, respective reconstruction problems may be overcome by a gradient dampening approach. The analytical gradient of the utilized cost function is included as Appendix.Comment: 10 pages, 7 figure

Joint T1 and T2 Mapping with Tiny Dictionaries and Subspace-Constrained Reconstruction

Purpose: To develop a method that adaptively generates tiny dictionaries for joint T1-T2 mapping. Theory: This work breaks the bond between dictionary size and representation accuracy (i) by approximating the Bloch-response manifold by piece-wise linear functions and (ii) by adaptively refining the sampling grid depending on the locally-linear approximation error. Methods: Data acquisition was accomplished with use of an 2D radially sampled Inversion-Recovery Hybrid-State Free Precession sequence. Adaptive dictionaries are generated with different error tolerances and compared to a heuristically designed dictionary. Based on simulation results, tiny dictionaries were used for T1-T2 mapping in phantom and in vivo studies. Reconstruction and parameter mapping were performed entirely in subspace. Results: All experiments demonstrated excellent agreement between the proposed mapping technique and template matching using heuristic dictionaries. Conclusion: Adaptive dictionaries in combination with manifold projection allow to reduce the necessary dictionary sizes by one to two orders of magnitude

Messungen der atmosphärischen Radikale OH, HO 2 , RO 2 sowie des Ultraspurengases Schwefelsäure : Weiterentwicklung, Kalibration und Einsatz einer hochempfindlichen massenspektrometrischen Analysemethode

OH-, HO2- und RO2-Radikale spielen beim oxidativen Abbau von Schadstoffen in der Atmosphäre eine fundamentale Rolle. Bei diesen Oxidationsprozessen wird unter anderem auch gasförmige Schwefelsäure gebildet, die zur Partikelbildung einen wichtigen Beitrag leistet. Zur selektiven Messung dieser Substanzen wurde in der hier vorgelegten Arbeit eine hochempfindliche massenspektrometrische Analysemethode aufgebaut und verwendet, die auf der chemischen Konversion obiger Radikale in Schwefelsäure sowie deren Nachweis via Ionenmolekülreaktionsmassenspektrometrie basiert. Ein Schwerpunkt dieser Arbeit lag bei der Weiterentwicklung, Automatisierung und Adaptierung dieses Instruments an die auf Feldmesskampagnen gegebenen Bedingungen. Im Rahmen mehrerer Feldmesskampagnen erfolgten atmosphärische Messungen obiger Substanzen auf 2 europäischen Bergmessstationen in vorwiegend unbelasteten und photochemisch gealterten Luftmassen. Tagsüber wurden Maximalkonzentrationen von HO2 und RO2 von jeweils etwa 5*10(8) cm-3 gemessen. Das Verhältnis RO2 zu HO2 nahm dabei Werte zwischen 0.4 und 2 an. Nachts lag die Konzentration von HO2 meist unter 2*10(7) cm-3, während die RO2-Konzentration Werte im Bereich von etwa 4-12*10(7) cm-3 erreichte. Die vorläufigen Abschätzungen des photochemischen Gleichgewichts weisen vorwiegend gute Übereinstimmungen mit den Messungen auf. Ebenfalls recht gute Übereinstimmungen bzgl. der Konzentrationen von HO2+RO2 zeigte der informelle Vergleich mit einer anderen Methode. In einer weiteren Kampagne konnten OH und Schwefelsäure gemessen werden, die Maximalkonzentrationen von etwa 7-8*10(6) bzw. 1.5-2.5*10(7) cm-3 erreichten. Anhand von Zusatzdaten konnten die Produktions- und Verlustraten der gasförmigen Schwefelsäure berechnet und mit den gemessenen verglichen werden. Mit ihrem ersten Einsatz auf einer Feldmesskampagne konnte die Leistungsfähigkeit und die Eignung des Instruments für kontinuierlichen Langzeit-Messungen eindrucksvoll gezeigt werden

Suppression of MRI Truncation Artifacts Using Total Variation Constrained Data Extrapolation

The finite sampling of k-space in MRI causes spurious image artifacts, known as Gibbs ringing, which result from signal truncation at the border of k-space. The effect is especially visible for acquisitions at low resolution and commonly reduced by filtering at the expense of image blurring. The present work demonstrates that the simple assumption of a piecewise-constant object can be exploited to extrapolate the data in k-space beyond the measured part. The method allows for a significant reduction of truncation artifacts without compromising resolution. The assumption translates into a total variation minimization problem, which can be solved with a nonlinear optimization algorithm. In the presence of substantial noise, a modified approach offers edge-preserving denoising by allowing for slight deviations from the measured data in addition to supplementing data. The effectiveness of these methods is demonstrated with simulations as well as experimental data for a phantom and human brain in vivo

Simultaneous Multi-Slice MRI using Cartesian and Radial FLASH and Regularized Nonlinear Inversion: SMS-NLINV

Purpose: The development of a calibrationless parallel imaging method for accelerated simultaneous multi-slice (SMS) MRI based on Regularized Nonlinear Inversion (NLINV), evaluated using Cartesian and radial FLASH. Theory and Methods: NLINV is a parallel imaging method that jointly estimates image content and coil sensitivities using a Newton-type method with regularization. Here, NLINV is extended to SMS-NLINV for reconstruction and separation of all simultaneously acquired slices. The performance of the extended method is evaluated for different sampling schemes using phantom and in-vivo experiments based on Cartesian and radial SMS-FLASH sequences. Results: The basic algorithm was validated in Cartesian experiments by comparison with ESPIRiT. For Cartesian and radial sampling, improved results are demonstrated compared to single-slice experiments, and it is further shown that sampling schemes using complementary samples outperform schemes with the same samples in each partition. Conclusion: The extension of the NLINV algorithm for SMS data was implemented and successfully demonstrated in combination with a Cartesian and radial SMS-FLASH sequence.Comment: Part of this work has been presented at the ISMRM Annual Conference 2016 (Singapore) and 2017 (Honolulu). 25 pages, 8+4 figure

Disambiguate the storage class of some compound literals: change request for C23

We noticed that there is a need for clarification about the storage class of compound literals that are evaluated in the type expressions of function parameters. It turned out that clang has them as static storage duration while gcc has them as automatic. We asked WG14 to clarify this situation and consensus (13-0-8) has been reached that it should be specified asautomatic. This paper implements that change

Properly define blocks as part of the grammar: proposal for C23

Blocks are a fundamental concept in C for the definition of visibility scopes of identifiers and for the lifetime of objects. Currently, there is no closed definition what a block is and the different definitions that compose the term have to be collected in different places that spread over several clauses. In particular, the fact that dependent statements of iteration or selection statements form blocks of their own is easily overlooked and leads to misunderstandings for example concerning the lifetime of compound literals. We propose to change that situation by introducing terms primary block and secondary block in the syntax and by referring to the other definitions of blocks, namely functions definitions and lambda expressions (if added to C23), in a summary definition