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Stochastic homogenization of plasticity equations
Get PDFIn the context of infinitesimal strain plasticity with hardening, we derive a stochastic homogenization result. We assume that the coefficients of the equation are random functions: elasticity tensor, hardening parameter and
flow-rule function are given through a dynamical system on a probability space.
A parameter \epsilon > 0 denotes the typical length scale of oscillations. We derive effective equations that describe the behavior of solutions in the limit \epsion -> 0. The homogenization procedure is based on the fact that stochastic coefficients “allow averaging”: For one representative volume element, a strain evolution [0; T] \ni t \mapsto\xi(t) \in Rd^dxd _s induces a stress evolution [0; T] \ni t \mapsto\Sigma(\xi)(t) \in Rd^dxd _s . Once the hysteretic evolution law \Sigma is justified for averages, we obtain that
the macroscopic limit equation is given by -\triangledown\cdot\Sigma(\triangledown^s u) = f
Convergence to Equilibrium in Energy-Reaction–Diffusion Systems Using Vector-Valued Functional Inequalities
No full textWe discuss how the recently developed energy dissipation methods for
reaction diffusion systems can be generalized to the non-isothermal case. For this, we use concave entropies in terms of the densities of the species and the internal energy, where the importance is that the equilibrium densities may depend on the internal energy. Using the log-Sobolev estimate and variants for lower-order entropies as well as estimates for the entropy production of the nonlinear reactions, we give two methods to estimate the relative entropy by the total entropy production, namely a somewhat restrictive convexity method, which provides explicit decay rates, and a very general, but weaker compactness method
Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics
No full textInspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that our time-lagged autoencoder reliably finds low-dimensional embeddings for high-dimensional feature spaces which capture the slow dynamics of the underlying stochastic processes—beyond the capabilities of linear dimension reduction techniques
Can we distinguish respiratory viral infections based on clinical features? A prospective pediatric cohort compared to systematic literature review
No full textStudies have shown that the predictive value of “clinical diagnoses” of influenza and other respiratory viral infections is low, especially in children. In routine care, pediatricians often resort to clinical diagnoses, even in the absence of robust evidence‐based criteria.
We used a dual approach to identify clinical characteristics that may help to differentiate infections with common pathogens including influenza, respiratory syncytial virus, adenovirus, metapneumovirus, rhinovirus, bocavirus‐1, coronaviruses, or parainfluenza virus: (a) systematic review and meta‐analysis of 47 clinical studies published in Medline (June 1996 to March 2017, PROSPERO registration number: CRD42017059557) comprising 49 858 individuals and (b) data‐driven analysis of an inception cohort of 6073 children with ILI (aged 0‐18 years, 56% male, December 2009 to March 2015) examined at the point of care in addition to blinded PCR testing. We determined pooled odds ratios for the literature analysis and compared these to odds ratios based on the clinical cohort dataset.
This combined analysis suggested significant associations between influenza and fever or headache, as well as between respiratory syncytial virus infection and cough, dyspnea, and wheezing. Similarly, literature and cohort data agreed on significant associations between HMPV infection and cough, as well as adenovirus infection and fever. Importantly, none of the abovementioned features were unique to any particular pathogen but were also observed in association with other respiratory viruses.
In summary, our “real‐world” dataset confirmed published literature trends, but no individual feature allows any particular type of viral infection to be ruled in or ruled out. For the time being, laboratory confirmation remains essential. More research is needed to develop scientifically validated decision models to inform best practice guidelines and targeted diagnostic algorithms
Generic accelerated sequence alignment in SeqAn using vectorization and multi-threading
No full textMotivation
Pairwise sequence alignment is undoubtedly a central tool in many bioinformatics analyses. In this paper, we present a generically accelerated module for pairwise sequence lignments applicable for a broad range of applications. In our module, we unified the standard dynamic programming kernel used for pairwise sequence alignments and extended it with a generalized inter-sequence vectorization layout, such that many alignments can be computed simultaneously by exploiting SIMD (Single Instruction Multiple Data) instructions of modern processors. We then extended the module by adding two layers of thread-level parallelization, where we a) distribute many independent alignments on multiple threads and b) inherently parallelize a single alignment computation using a work stealing approach producing a dynamic wavefront progressing along the minor diagonal.
Results
We evaluated our alignment vectorization and parallelization on different processors, including the newest Intel® Xeon® (Skylake) and Intel® Xeon Phi™ (KNL) processors, and use cases. The instruction set AVX512-BW (Byte and Word), available on Skylake processors, can genuinely improve the performance of vectorized alignments. We could run single alignments 1600 times faster on the Xeon Phi™ and 1400 times faster on the Xeon® than executing them with our previous sequential alignment module.
Availability
The module is programmed in C++ using the SeqAn (Reinert et al., 2017) library and distributed with version 2.4. under the BSD license. We support SSE4, AVX2, AVX512 instructions and included UME::SIMD, a SIMD-instruction wrapper library, to extend our module for further instruction sets. We thoroughly test all alignment components with all major C++ compilers on various platforms
Modellieren im Mathematikunterricht gendersensibel gestalten
No full textVon der schulbezogenen Geschlechterforschung wird seit Jahren neben dem Unterrichtsgeschehen die Unterrichtsgestaltung einerseits als Problemfeld im Sinne der Inszenierung und Reproduktion von Geschlechterstereotypisierungen und geschlechterbezogenen Interessens-, Wissens- und Kompetenzrevieren und andererseits als Handlungsfeld eines gendersensiblen Unterrichts in den Blick genommen. Dennoch gibt es z. B. für das Schulfach Mathematik bis heute nur sehr wenige, tatsächlich auf die konkrete schulische Praxis bezogene Unterrichtsentwürfe für eine gendersensible Gestaltung des Mathematikunterrichts oder Beispiele für entsprechende Lernumgebungen. Diese zu entwickeln oder weiterzuentwickeln und für die Vermittlung inhalts- wie prozessbezogener mathematischer Kompetenzen im schulischen Mathematikunterricht fruchtbar zu machen, ist damit nicht nur ein Desiderat, sondern auch eine Herausforderung für die Fachdidaktik der Mathematik. Sich dieser zu stellen, ist Ziel des Beitrags, in dem exemplarisch eine von den Autorinnen nach gendersensiblen Kriterien gestaltete Lernumgebung für das Modellieren im Mathematikunterricht vorgestellt wird
Optimum Search Schemes for Approximate String Matching Using Bidirectional FM-Index
No full textFinding approximate occurrences of a pattern in a text using a full-text index is a central problem in bioinformatics and has been extensively researched. Bidirectional indices have opened new possibilities in this regard allowing the search to start from anywhere within the pattern and extend in both directions. In particular, use of search schemes (partitioning the pattern and searching the pieces in certain orders with given bounds on errors) can yield significant speed-ups. However, finding optimal search schemes is a difficult combinatorial optimization problem. Here for the first time, we propose a mixed integer program (MIP) capable to solve this optimization problem for Hamming distance with given number of pieces. Our experiments show that the optimal search schemes found by our MIP significantly improve the performance of search in bidirectional FM-index upon previous ad-hoc solutions. For example, approximate matching of 101-bp Illumina reads (with two errors) becomes 35 times faster than standard backtracking. Moreover, despite being performed purely in the index, the running time of search using our optimal schemes (for up to two errors) is comparable to the best state-of-the-art aligners, which benefit from combining search in index with in-text verification using dynamic programming. As a result, we anticipate a full-fledged aligner that employs an intelligent combination of search in the bidirectional FM-index using our optimal search schemes and in-text verification using dynamic programming outperforms today's best aligners. The development of such an aligner, called FAMOUS (Fast Approximate string Matching using OptimUm search Schemes), is ongoing as our future work
Addressing Global Uncertainty and Sensitivity in First-Principles Based Microkinetic Models by an Adaptive Sparse Grid Approach
No full textIn the last decade, first-principles-based microkinetic modeling has been developed into an important tool for a mechanistic understanding of heterogeneous catalysis. A commonly known, but hitherto barely analyzed issue in this kind of modeling is the presence of sizable errors from the use of approximate Density Functional Theory (DFT). We here address the propagation of these errors to the catalytic turnover frequency (TOF) by global sensitivity and uncertainty analysis. Both analyses require the numerical quadrature of high-dimensional integrals. To achieve this efficiently, we utilize and extend an adaptive sparse grid
approach and exploit the confinement of the strongly non-linear behavior of the TOF to local regions of the parameter space. We demonstrate the methodology on a model of the oxygen evolution reaction at the Co3O4 (110)-A surface, using a maximum entropy error model that imposes nothing but reasonable bounds on the errors. For this setting, the DFT errors lead to an absolute uncertainty of several orders of magnitude in the TOF. We nevertheless find that it is still possible to draw conclusions from such uncertain models about the atomistic aspects controlling the reactivity. A comparison with derivative-based local sensitivity analysis instead reveals that this more established approach provides incomplete information. Since the adaptive sparse grids allow for the evaluation of the integrals with only a modest number of function evaluations, this approach opens the way for a global sensitivity analysis of more complex models, for instance, models based on kinetic Monte Carlo simulations
Gradient and Generic systems in the space of fluxes, applied to reacting particle systems
Get PDFIn a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager-Machlup relations. Of particular interest is the case where the microscopic system consists of random particles, and the macroscopic quantity is the empirical measure or concentration. In this work we take the particle flux as the macroscopic quantity, which is related to the concentration via a continuity equation. By a similar argument the large deviations can induce a generalised gradient or Generic system in the space of fluxes. In a general setting we study how flux gradient or generic systems are related to gradient systems of concentrations. The arguments are explained by the example of reacting particle systems, which is later expanded to include spatial diffusion as well
Collective hydrogen-bond rearrangement dynamics in liquid water
No full textWe investigate barrier-crossing processes corresponding to collective hydrogen-bond rearrangements in liquid water using Markov state modeling techniques. The analysis is based on trajectories from classical molecular dynamics simulations and accounts for the full dynamics of relative angular and separation coordinates of water clusters and requires no predefined hydrogen bond criterium. We account for the complete 12-dimensional conformational subspace of three water molecules and distinguish five well-separated slow dynamic processes with relaxation times in the picosecond range, followed by a quasi-continuum spectrum of faster modes. By analysis of the Markov eigenstates, these processes are shown to correspond to different collective interchanges of hydrogen-bond donors and acceptors. Using a projection onto hydrogen-bond states, we also analyze the switching of one hydrogen bond between two acceptor water molecules and derive the complete transition network. The most probable pathway corresponds to a direct switch without an intermediate, in agreement with previous studies. However, a considerable fraction of paths proceeds along alternative routes that involve different intermediate states with short-lived alternative hydrogen bonds or weakly bound states