Minimal kernels of Dirac operators along maps

Let M be a closed spin manifold and let N be a closed manifold. For maps and Riemannian metrics g on M and h on N, we consider the Dirac operator of the twisted Dirac bundle . To this Dirac operator one can associate an index in . If M is 2‐dimensional, one gets a lower bound for the dimension of the kernel of out of this index. We investigate the question whether this lower bound is obtained for generic tupels .     

Generalized sensitivity analysis of nonlinear programs using a sequence of quadratic programs

ABSTRACT

Local sensitivity information is obtained for KKT points of parametric NLPs that may exhibit active set changes under parametric perturbations; under appropriate regularity conditions, computationally relevant generalized derivatives of primal and dual variable solutions of parametric NLPs are calculated. Ralph and Dempe obtained directional derivatives of solutions of parametric NLPs exhibiting active set changes from the unique solution of an auxiliary quadratic program. This article uses lexicographic directional derivatives, a newly developed tool in nonsmooth analysis, to generalize the classical NLP sensitivity analysis theory of Ralph and Dempe. By viewing said auxiliary quadratic program as a parametric NLP, the results of Ralph and Dempe are applied to furnish a sequence of coupled QPs, whose unique solutions yield generalized derivative information for the NLP. A practically implementable algorithm is provided. The theory developed here is motivated by widespread applications of nonlinear programming sensitivity analysis, such as in dynamic control and optimization problems.     

Top-down synthesis of polyoxometalate-like sub-nanometer molybdenum-oxo clusters as high-performance electrocatalysts

The top-down fabrication of catalytically active molecular metal oxide anions, or polyoxometalates, is virtually unexplored, although these materials offer unique possibilities, for catalysis, energy conversion and storage. Here, we report a novel top-down route, which enables the scalable synthesis and deposition of sub-nanometer molybdenum-oxo clusters on electrically conductive mesoporous carbon. The new approach uses a unique redox-cycling process to convert crystalline Mo^IVO₂ particles into sub-nanometer molecular molybdenum-oxo clusters with a nuclearity of ∼1–20. The resulting molybdenum-oxo cluster/carbon composite shows outstanding, stable electrocatalytic performance for the oxygen reduction reaction with catalyst characteristics comparable to those of commercial Pt/C. This new material design could give access to a new class of highly reactive polyoxometalate-like metal oxo clusters as high-performance, earth abundant (electro-)catalysts.

The top-down synthesis and deposition of polyoxometalate-like clusters on porous carbon is reported together with the high electrocatalytic oxygen reduction reactivity of the composite.     

Traveling Salesman Problem with Clustering

In the original traveling salesman problem, the traveling salesman has the task to find the shortest closed tour through a proposed set of nodes, touching each node exactly once and returning to the initial node at the end. For the sake of the tour length to be minimized, nodes close to each other might not be visited one after the other but separated in the tour. However, for some practical applications, it is useful to group nodes to clusters, such that all nodes of a cluster are visited contiguously. Here we present an approach which leads to an automatic clustering with a clustering parameter governing the sizes of the clusters.     

Covariances Simultaneous Component Analysis: a new method within a framework for modeling covariances

In modern omics research, it is more rule than exception that multiple data sets are collected in a study pertaining to the same biological organism. In such cases, it is worthwhile to analyze all data tables simultaneously to arrive at global information of the biological system. This is the area of data fusion or multi‐set analysis, which is a lively research topic in chemometrics, bioinformatics, and biostatistics. Most methods of analyzing such complex data focus on group means, treatment effects, or time courses. There is also information present in the covariances among variables within a group, because this relates directly to individual differences, heterogeneity of responses, and changes of regulation in the biological system. We present a framework for analyzing covariance matrices and a new method that fits nicely in this framework. This new method is based on combining covariance prototypes using simultaneous components and is, therefore, coined Covariances Simultaneous Component Analysis (COVSCA). We present the framework and our new method in mathematical terms, thereby explaining the (dis)similarities of the methods. Systems biology models based on differential equations illustrate the type of variation generated in real‐life biological systems and how this type of variation can be modeled within the framework and with COVSCA. The method is subsequently applied to two real‐life data sets from human and plant metabolomics studies showing biologically meaningful results. Copyright © 2015 John Wiley & Sons, Ltd.     

Experimental-based material parameter identification of oocytes

In comparison to other eukaryotic cells, mammalian oocytes are characterised by a relative high diameter allowing in turn a straightforward micromechanical testing to study their mechanical properties. The structure of mammalian oocytes is characterised by the so-called zona pellucida (ZP), a thick glycoprotein layer, surrounding the cells interior, the ooplasm. In contrast to other cells, where the load is mainly carried by inner cell structures, in case of oocytes a huge amount of external loads is carried by the ZP. Aim of this work is the determination of the mechanical properties of oocytes. Therefore, a micromechanical setup has been developed and installed on a microscope. Beside the determination of the force-strain relation during loading, the deformation of the oocytes has been recorded optically, too. Both, the force-strain curves and the optical recordings build the basis for a proper parameter identification technique based on the inverse finite element method. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Characterisation and quantification of liposome-type nanoparticles in a beverage matrix using hydrodynamic chromatography and MALDI–TOF mass spectrometry

This paper describes the characterisation of liposome-type nanoparticles (NPs) dispersed in a beverage matrix. Characterisation is based on a two-step procedure: first, liposomes are separated on the basis of size in the nanometre range by use of hydrodynamic chromatography (HDC); second, chemical characterisation is performed by use of MALDI–TOF mass spectrometry (MS). Characterisation of three types of Coatsome liposome, a commercially available type of empty liposome, was investigated. All three liposome types, Coatsome A?=?anionic, N?=?neutral, and C?=?cationic, gave single peaks in HDC, reflecting diameters of 153, 187, and 205 nm, respectively. Subsequent MALDI–TOF MS in positive mode furnished major signals at m/z?=?734.5 ([M?+?H]⁺ adduct) and m/z?=?756.6 ([M?+?Na]⁺ adduct) of l-(α)-dipalmitoylphosphatidylcholine (DPPC) monomer and dimeric adducts at m/z?=?1468.1 and m/z?=?1490.1, respectively. MALDI–TOF MS in negative mode gave a signal at m/z?=?721.3 ([M???H]^? adduct) of l-(α)-dipalmitoylphosphatidylglycerol (DPPG), except for Coatsome C which lacks this phospholipid. After HDC separation of Coatsome A NPs the major DPPC and DPPG signals can be detected in the expected fractions by use of MALDI–TOF MS in positive and negative modes, respectively. Validation of the analytical strategy revealed linearity (R ²?>?0.99), repeatability (relative standard deviation <10 %), and reproducibility (relative standard deviation between days <10 %) were good, recovery was 61?±?5 %, and the limit of quantification was 1 mg?mL^?1 in this matrix. With 4 mg Coatsome A mL^?1 20 out of 20 samples furnished the 734.5 and 756.6 signals typical of DPPC in MALDI–TOF MS characterisation.     

A Facile Ester Homologation of Carbonyl Compounds Via Ketene-O,S-Acetals

A usefull extension of the available methods for the conversion of carbonyl compounds into ketene-O,S-acetals^1,2,3 has been found in the Peterson olefination with methoxyphenylthiotrimethylsilyl-methyllithium 1 of aldehydes and ketones. The starting material for this reagent 1 was prepared by reaction of methoxyphenylthio-methyllithium^4,5 with chlorotrimethylsilane at -80°C in THF. Deprotonation of the obtained methoxyphenylthiotrimethylsilyl-methane with n-butyllithium at -80°C in THF gave 1 and subsequent addition of the carbonyl compound at -80°C gave mixtures of Z and E ketene-O,S-acetals 2.