Multiscale analysis and reconstruction of time series of stochastic cascade processes

We propose a new method to generate synthetical time series of hierarchical stochastic processes. Based on the statistics of n–scale joint PDFs, the stochastic properties of a time series are modeled simultaneously on many scales. The application to a data set of turbulent velocities is demonstrated, showing the ability of the approach to reproduce the correct statistics of the original time series on all considered scales. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Photoredox-mediated hydroalkylation and hydroarylation of functionalized olefins for DNA-encoded library synthesis

DNA-encoded library (DEL) technology features a time- and cost-effective interrogation format for the discovery of therapeutic candidates in the pharmaceutical industry. To develop DEL platforms, the implementation of water-compatible transformations that facilitate the incorporation of multifunctional building blocks (BBs) with high C(sp³) carbon counts is integral for success. In this report, a decarboxylative-based hydroalkylation of DNA-conjugated trifluoromethyl-substituted alkenes enabled by single-electron transfer (SET) and subsequent hydrogen atom termination through electron donor–acceptor (EDA) complex activation is detailed. In a further photoredox-catalyzed hydroarylation protocol, the coupling of functionalized, electronically unbiased olefins is achieved under air and within minutes of blue light irradiation through the intermediacy of reactive (hetero)aryl radical species with full retention of the DNA tag integrity. Notably, these processes operate under mild reaction conditions, furnishing complex structural scaffolds with a high density of pendant functional groups.

DNA-encoded library (DEL) technology facilitates the rapid identification of therapeutic candidates in pharmaceutical settings. Herein, the development of photoredox-mediated hydrocarbofunctionalization protocols of olefins is described.     

Regularity of the Speed of Biased Random Walk in a One-Dimensional Percolation Model

We consider biased random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. Axelson-Fisk and Häggström established for this model a phase transition for the asymptotic linear speed \(\overline{\hbox {v}}\) of the walk. Namely, there exists some critical value \(\lambda _{\hbox {c}}>0\) such that \(\overline{\hbox {v}}>0\) if \(\lambda \in (0,\lambda _{\hbox {c}})\) and \(\overline{\hbox {v}}=0\) if \(\lambda \ge \lambda _{\hbox {c}}\). We show that the speed \(\overline{\hbox {v}}\) is continuous in \(\lambda \) on \((0,\infty )\) and differentiable on \((0,\lambda _{\hbox {c}}/2)\). Moreover, we characterize the derivative as a covariance. For the proof of the differentiability of \(\overline{\hbox {v}}\) on \((0,\lambda _{\hbox {c}}/2)\), we require and prove a central limit theorem for the biased random walk. Additionally, we prove that the central limit theorem fails to hold for \(\lambda \ge \lambda _{\hbox {c}}/2\).     

Perspectives of antiferromagnetic spintronics

Antiferromagnets are promising for future spintronic applications owing to their advantageous properties: They are magnetically ordered, but neighboring magnetic moments point in opposite directions, which results in zero net magnetization. This means antiferromagnets produce no stray fields and are insensitive to external magnetic field perturbations. Furthermore, they show intrinsic high frequency dynamics, exhibit considerable spin–orbit and magneto-transport effects. Over the past decade, it has been realized that antiferromagnets have more to offer than just being utilized as passive components in exchange bias applications. This development resulted in a paradigm shift, which opens the pathway to novel concepts using antiferromagnets for spin-based technologies and applications. This article gives a broad perspective on antiferromagnetic spintronics. In particular, the manipulation and detection of antiferromagnetic states by spintronics effects, as well as spin transport and dynamics in antiferromagnetic materials will be discussed. We will also outline current challenges and future research directions in this emerging field.     

On a Model of Associative Memory with Huge Storage Capacity

In Krotov et al. (in: Lee (eds) Advances in Neural Information Processing Systems, Curran Associates, Inc., Red Hook, 2016) Krotov and Hopfield suggest a generalized version of the well-known Hopfield model of associative memory. In their version they consider a polynomial interaction function and claim that this increases the storage capacity of the model. We prove this claim and take the ”limit” as the degree of the polynomial becomes infinite, i.e. an exponential interaction function. With this interaction we prove that model has an exponential storage capacity in the number of neurons, yet the basins of attraction are almost as large as in the standard Hopfield model.     

Gamma Convergence of a Family of Surface–Director Bending Energies with Small Tilt

We prove a Gamma-convergence result for a family of bending energies defined on smooth surfaces in \({\mathbb{R}^3}\) equipped with a director field. The energies strongly penalize the deviation of the director from the surface unit normal and control the derivatives of the director. Such types of energies arise, for example, in a model for bilayer membranes introduced by Peletier and Röger (Arch Ration Mech Anal 193(3), 475–537, 2009). Here we prove in three space dimensions in the vanishing-tilt limit a Gamma-liminf estimate with respect to a specific curvature energy. In order to obtain appropriate compactness and lower semi-continuity properties we use tools from geometric measure theory, in particular the concept of generalized Gauss graphs and curvature varifolds.     

Incorporation of 4J-HMBC and NOE Data into Computer-Assisted Structure Elucidation with WebCocon

Over the past decades, different software programs have been developed for the Computer-Assisted Structure Elucidation (CASE) with NMR data using with various approaches. WebCocon is one of them that has been continuously improved over the past 20 years. Here, we present the inclusion of 4J_CH correlations (4J-HMBC) in the HMBC interpretation of Cocon and NOE data in WebCocon. The 4J-HMBC data is used during the structure generation process, while the NOE data is used in post-processing of the results. The marine natural product oxocyclostylidol was selected to demonstrate WebCocon’s enhanced HMBC data processing capabilities. A systematic study of the 4J_CH correlations of oxocyclostylidol was performed. The application of NOEs in CASE is demonstrated using the NOE correlations of the diterpene pyrone asperginol A known from the literature. As a result, we obtained a conformation that corresponds very well to the existing X-ray structure.     

Gerichtete Evolution und rationales Design. Maßgeschneiderte Enzyme

While most enzymes are highly adapted to their natural role, few biocatalysts meet the requirements for industrial applications such as high activity, high stability and excellent selectivity. Modern methods of protein evolution allow the optimisation of enzymes by the alteration of the amino acid sequence and hence the modification of chemical and catalytic properties. This article gives an overview about the strategies rational protein design and directed evolution. The scope and limitations of both methods are outlined by the discussion of very recent examples on the optimisation of stability and selectivity and the creation of novel biocatalysts.