Multiadaptive Galerkin Methods for ODEs III: A Priori Error Estimates

The multiadaptive continuous/discontinuous Galerkin methods mcG(q) and mdG(q) for the numerical solution of initial value problems for ordinary differential equations are based on piecewise polynomial approximation of degree q on partitions in time with time steps which may vary for different components of the computed solution. In this paper, we prove general order a priori error estimates for the mcG(q) and mdG(q) methods. To prove the error estimates, we represent the error in terms of a discrete dual solution and the residual of an interpolant of the exact solution. The estimates then follow from interpolation estimates, together with stability estimates for the discrete dual solution

Computational Modeling of Dynamical Systems

In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be very costly. By resolving the fast time scales in a short time simulation, a model for the effect of the small time scale variation on large time scales can be determined, making solution possible on a long time interval. This process of computational modeling can be completely automated. Two examples are presented, including a simple model problem oscillating at a time scale of 1e-9 computed over the time interval [0,100], and a lattice consisting of large and small point masses

Pressure-induced and Composition-induced Structural Quantum Phase Transition in the Cubic Superconductor (Sr/Ca)_3Ir_4Sn_{13}

We show that the quasi-skutterudite superconductor Sr_3Ir_4Sn_{13} undergoes a structural transition from a simple cubic parent structure, the I-phase, to a superlattice variant, the I'-phase, which has a lattice parameter twice that of the high temperature phase. We argue that the superlattice distortion is associated with a charge density wave transition of the conduction electron system and demonstrate that the superlattice transition temperature T* can be suppressed to zero by combining chemical and physical pressure. This enables the first comprehensive investigation of a superlattice quantum phase transition and its interplay with superconductivity in a cubic charge density wave system.Comment: 4 figures, 5 pages (excluding supplementary material). To be published in Phys. Rev. Let

Protein kinase A controls yeast growth in visible light

Background: A wide variety of photosynthetic and non-photosynthetic species sense and respond to light, having developed protective mechanisms to adapt to damaging effects on DNA and proteins. While the biology of UV light-induced damage has been well studied, cellular responses to stress from visible light (400–700 nm) remain poorly understood despite being a regular part of the life cycle of many organisms. Here, we developed a high-throughput method for measuring growth under visible light stress and used it to screen for light sensitivity in the yeast gene deletion collection. Results: We found genes involved in HOG pathway signaling, RNA polymerase II transcription, translation, diphthamide modifications of the translational elongation factor eEF2, and the oxidative stress response to be required for light resistance. Reduced nuclear localization of the transcription factor Msn2 and lower glycogen accumulation indicated higher protein kinase A (cAMP-dependent protein kinase, PKA) activity in many light-sensitive gene deletion strains. We therefore used an ectopic fluorescent PKA reporter and mutants with constitutively altered PKA activity to show that repression of PKA is essential for resistance to visible light. Conclusion: We conclude that yeast photobiology is multifaceted and that protein kinase A plays a key role in the ability of cells to grow upon visible light exposure. We propose that visible light impacts on the biology and evolution of many non-photosynthetic organisms and have practical implications for how organisms are studied in the laboratory, with or without illumination

Dynamics of skyrmionic states in confined helimagnetic nanostructures

In confined helimagnetic nanostructures, skyrmionic states in the form of incomplete and isolated skyrmion states can emerge as the ground state in absence of both external magnetic field and magnetocrystalline anisotropy. In this work, we study the dynamic properties (resonance frequencies and corresponding eigenmodes) of skyrmionic states in thin film FeGe disk samples. We employ two different methods in finite-element based micromagnetic simulation: eigenvalue and ringdown method. The eigenvalue method allows us to identify all resonance frequencies and corresponding eigenmodes that can exist in the simulated system. However, using a particular experimentally feasible excitation can excite only a limited set of eigenmodes. Because of that, we perform ringdown simulations that resemble the experimental setup using both in-plane and out-of-plane excitations. In addition, we report the nonlinear dependence of resonance frequencies on the external magnetic bias field and disk sample diameter and discuss the possible reversal mode of skyrmionic states. We compare the power spectral densities of incomplete skyrmion and isolated skyrmion states and observe several key differences that can contribute to the experimental identification of the state present in the sample. We measure the FeGe Gilbert damping, and using its value we determine what eigenmodes can be expected to be observed in experiments. Finally, we show that neglecting the demagnetization energy contribution or ignoring the magnetization variation in the out-of-film direction—although not changing the eigenmode's magnetization dynamics significantly—changes their resonance frequencies substantially. Apart from contributing to the understanding of skyrmionic states physics, this systematic work can be used as a guide for the experimental identification of skyrmionic states in confined helimagnetic nanostructures

3D Reconstruction for Partial Data Electrical Impedance Tomography Using a Sparsity Prior

In electrical impedance tomography the electrical conductivity inside a physical body is computed from electro-static boundary measurements. The focus of this paper is to extend recent result for the 2D problem to 3D. Prior information about the sparsity and spatial distribution of the conductivity is used to improve reconstructions for the partial data problem with Cauchy data measured only on a subset of the boundary. A sparsity prior is enforced using the $\ell_1$ norm in the penalty term of a Tikhonov functional, and spatial prior information is incorporated by applying a spatially distributed regularization parameter. The optimization problem is solved numerically using a generalized conditional gradient method with soft thresholding. Numerical examples show the effectiveness of the suggested method even for the partial data problem with measurements affected by noise.Comment: 10 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1405.655

An incremental approach to automated protein localisation

Tscherepanow M, Jensen N, Kummert F. An incremental approach to automated protein localisation. BMC Bioinformatics. 2008;9(1): 445.Background: The subcellular localisation of proteins in intact living cells is an important means for gaining information about protein functions. Even dynamic processes can be captured, which can barely be predicted based on amino acid sequences. Besides increasing our knowledge about intracellular processes, this information facilitates the development of innovative therapies and new diagnostic methods. In order to perform such a localisation, the proteins under analysis are usually fused with a fluorescent protein. So, they can be observed by means of a fluorescence microscope and analysed. In recent years, several automated methods have been proposed for performing such analyses. Here, two different types of approaches can be distinguished: techniques which enable the recognition of a fixed set of protein locations and methods that identify new ones. To our knowledge, a combination of both approaches – i.e. a technique, which enables supervised learning using a known set of protein locations and is able to identify and incorporate new protein locations afterwards – has not been presented yet. Furthermore, associated problems, e.g. the recognition of cells to be analysed, have usually been neglected. Results: We introduce a novel approach to automated protein localisation in living cells. In contrast to well-known techniques, the protein localisation technique presented in this article aims at combining the two types of approaches described above: After an automatic identification of unknown protein locations, a potential user is enabled to incorporate them into the pre-trained system. An incremental neural network allows the classification of a fixed set of protein location as well as the detection, clustering and incorporation of additional patterns that occur during an experiment. Here, the proposed technique achieves promising results with respect to both tasks. In addition, the protein localisation procedure has been adapted to an existing cell recognition approach. Therefore, it is especially well-suited for high-throughput investigations where user interactions have to be avoided. Conclusion: We have shown that several aspects required for developing an automatic protein localisation technique – namely the recognition of cells, the classification of protein distribution patterns into a set of learnt protein locations, and the detection and learning of new locations – can be combined successfully. So, the proposed method constitutes a crucial step to render image-based protein localisation techniques amenable to large-scale experiments