Monomer relative affinity in a copolymer

This paper analyzes data from experiments on simple polymer chains. It measures the extent to which a particular monomer prefers to link with another of the same type. To analyze the data, it derives the likelihood function for a two‐state Markov model in which only the number in each state, but not the order, is observed. This technology is applied to a data set on which experimenters mixed lactic‐glycolic monomers with a known proportion of a contaminant consisting of an extra lactic acid. The resulting copolymers were subjected to matrix‐assisted laser desorption ionization mass spectrometry. This records the number of copolymers at each atomic weight, which can be associated with a given length of copolymer and number of contaminant monomers. Analysis of the data shows that the proportion of contaminant monomers exceeded the proportion of experimentally induced contaminant. Maximum likelihood estimates using the data show that lactic‐glycolic monomers show a positive affinity for the contaminant. Copyright © 2015 John Wiley & Sons, Ltd.     

An Approach to NMR Assignment of Intrinsically Disordered Proteins

An efficient approach to NMR assignments in intrinsically disordered proteins is presented, making use of the good dispersion of cross peaks observed in [¹⁵N,¹³C′]‐ and [¹³C′,¹H^N]‐correlation spectra. The method involves the simultaneous collection of {3D (H)NCO(CAN)H and 3D (HACA)CON(CA)HA} spectra for backbone assignments via sequential H^N and H^α correlations and {3D (H)NCO(CACS)HS and 3D (HS)CS(CA)CO(N)H} spectra for side‐chain ¹H and ¹³C assignments, employing sequential ¹H data acquisitions with direct detection of both the amide and aliphatic protons. The efficacy of the approach for obtaining resonance assignments with complete backbone and side‐chain chemical shifts is demonstrated experimentally for the 61‐residue [¹³C,¹⁵N]‐labelled peptide of a voltage‐gated potassium channel protein of the Kv1.4 channel subunit. The general applicability of the approach for the characterisation of moderately sized globular proteins is also demonstrated.     

Random forests for functional covariates

We propose a form of random forests that is especially suited for functional covariates. The method is based on partitioning the functions' domain in intervals and using the functions' mean values across those intervals as predictors in regression or classification trees. This approach appears to be more intuitive to applied researchers than usual methods for functional data, while also performing very well in terms of prediction accuracy. The intervals are obtained from randomly drawn, exponentially distributed waiting times. We apply our method to data from Raman spectra on boar meat as well as near‐infrared absorption spectra. The predictive performance of the proposed functional random forests is compared with commonly used parametric and nonparametric functional methods and with a nonfunctional random forest using the single measurements of the curve as covariates. Further, we present a functional variable importance measure, yielding information about the relevance of the different parts of the predictor curves. Our variable importance curve is much smoother and hence easier to interpret than the one obtained from nonfunctional random forests.     

Compressing strongly connected subgroups in social networks: An entropy-based approach

To detect and study cohesive subgroups of actors is a main objective in social network analysis. What are the respective relations inside such groups and what separates them from the outside. Entropy-based analysis of network structures is an up-and-coming approach. It turns out to be a powerful instrument to detect certain forms of cohesive subgroups and to compress them to superactors without loss of information about their embeddedness in the net: Compressing strongly connected subgroups leaves the whole net’s and the (super-)actors’ information theoretical indices unchanged; i.e., such compression is information-invariant. The actual article relates on the reduction of networks with hundreds of actors. All entropy-based calculations are realized in an expert system shell.     

On Cartan's theorem for linear operators

In this paper, we describe a second main theorem of holomorphic curves in , of hyper‐order strictly less than 1, that involves a general linear operator . As an application, we derive a truncated second main theorem of degenerate holomorphic curves of hyper‐order strictly less than 1 using Nochka weights.     

Necessary and Sufficient Conditions for Weak Quasi Efficiency in Nonsmooth Multiobjective Problems

In this article, a multiobjective problem with a feasible set defined by inequality, equality and set constraints is considered, where the objective and constraint functions are locally Lipschitz. Several constraint qualifications are given and the relations between them are analyzed. We establish Kuhn-Tucker and strong Kuhn-Tucker necessary optimality conditions for (weak) quasi e?ciency in terms of the Clarke subdifferential. By using two new classes of generalized convex functions, su?cient conditions for local (weak) quasi e?cient are also provided. Furthermore, we study the Mond-Weir type dual problem and establish weak, strong and converse duality results.     

Nonlinear anisotropic elliptic equations in with variable exponents and locally integrable data

In this paper, we prove existence and regularity results for weak solutions in the framework of anisotropic Sobolev spaces for a class of nonlinear anisotropic elliptic equations in the whole with variable exponents and locally integrable data. Our approach is based on the anisotropic Sobolev inequality, a smoothness, and compactness results. The functional setting involves Lebesgue–Sobolev spaces with variable exponents. Copyright © 2016 John Wiley & Sons, Ltd.     

Pseudo‐spherical normal Darboux images of curves on a lightlike surface

We introduce the notions of the pseudospherical normal Darboux images for the curve on a lightlike surface in Minkowski 3‐space and study these Darboux images by using technics of the singularity theory. Furthermore, we give a relation between these Darboux images and Darboux frame from the viewpoint of Legendrian dualities.