An augmented Lagrangian method for optimization problems with structured geometric constraints

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints are nonconvex and possibly complicated, but allow for a fast computation of projections onto this nonconvex set. Typical problem classes which satisfy this requirement are optimization problems with disjunctive constraints (like complementarity or cardinality constraints) as well as optimization problems over sets of matrices which have to satisfy additional rank constraints. The key idea behind our method is to keep these complicated constraints explicitly in the constraints and to penalize only the remaining constraints by an augmented Lagrangian function. The resulting subproblems are then solved with the aid of a problem-tailored nonmonotone projected gradient method. The corresponding convergence theory allows for an inexact solution of these subproblems. Nevertheless, the overall algorithm computes so-called Mordukhovich-stationary points of the original problem under a mild asymptotic regularity condition, which is generally weaker than most of the respective available problem-tailored constraint qualifications. Extensive numerical experiments addressing complementarity- and cardinality-constrained optimization problems as well as a semidefinite reformulation of MAXCUT problems visualize the power of our approach.

     

Selective Aptamer‐Based Control of Intraneuronal Signaling

Cellular behavior is orchestrated by the complex interactions of a myriad of intracellular signal transduction pathways. To understand and investigate the role of individual components in such signaling networks, the availability of specific inhibitors is of paramount importance. We report the generation and validation of a novel variant of an RNA aptamer that selectively inhibits the mitogen‐activated kinase pathway in neurons. We demonstrate that the aptamer retains function under intracellular conditions and that application of the aptamer through the patch‐clamp pipette efficiently inhibits mitogen‐activated kinase‐dependent synaptic plasticity. This approach introduces synthetic aptamers as generic tools, readily applicable to inhibit different components of intraneuronal signaling networks with utmost specificity.     

Lithium intercalation into disordered carbon/SiCN composite. Part 2: Raman spectroscopy and <Superscript>7</Superscript>Li MAS NMR investigation of lithium storage sites

Within this work, we analyze the lithium storage sites within carbon/silicon carbonitride (SiCN) composites. Commercial carbons, HD3 (hard carbon) and LD1N and LD2N (soft carbons), of varying porosity are impregnated with polysilazane (HTT 1800) and pyrolysed at 1100 °C. It is found in the first part of this study (Graczyk-Zajac et al. J Solid State Electrochem 19:2763–2769, 2015) that the initial porosity of the carbon phase plays an important role in determining the lithium insertion capacity and rate capability of the composite material. By applying Raman spectroscopy and solid-state ⁷Li MAS NMR on pristine, lithiated, and delithiated samples, we investigate the lithium storage sites within the composite materials. By means of Raman spectroscopy, it has been found that lithium storage in hard carbon-derived composites occurs in a significant extent via adsorption-like process within unorganized carbon, whereas for the soft carbon composites, storage in turbostratic carbon is identified. ⁷Li solid-state NMR confirms these findings revealing that more than 33 % of lithium stored in HD3/SiCN is adsorbed in ionic form at the surface and in pores of the composite, while around 38 % is stored between carbon layers. LD1N and LD2N composites store more than 50 % of lithium in the intercalation-type sites.     

Bayesian inference using a noninformative prior for linear Gaussian random coefficient regression with inhomogeneous within-class variances

A Bayesian inference for a linear Gaussian random coefficient regression model with inhomogeneous within-class variances is presented. The model is motivated by an application in metrology, but it may well find interest in other fields. We consider the selection of a noninformative prior for the Bayesian inference to address applications where the available prior knowledge is either vague or shall be ignored. The noninformative prior is derived by applying the Berger and Bernardo reference prior principle with the means of the random coefficients forming the parameters of interest. We show that the resulting posterior is proper and specify conditions for the existence of first and second moments of the marginal posterior. Simulation results are presented which suggest good frequentist properties of the proposed inference. The calibration of sonic nozzle data is considered as an application from metrology. The proposed inference is applied to these data and the results are compared to those obtained by alternative approaches.     

Experimental and theoretical characterization of the aromatization, epimerization, and fragmentation reactions of bi-2H-azirin-2-yls prepared from 1,4-diazidobuta-1,3-dienes

1,4‐Diazidobuta‐1,3‐dienes (Z,Z)‐ 10 , 17 , and 21 were photolyzed and thermolyzed to yield the pyridazines 13 , 20 , and 23 , respectively. To explain these aromatic final products, the generation of highly strained bi‐2H‐azirin‐2‐yls 12 , 19 , and 22 and their valence isomerization were postulated. In the case of meso‐ and rac‐ 22 , nearly quantitative formation from diazide 21 , isolation as stable solids, and complete characterization were possible. On the thermolysis of 22 , aromatization to 23 was only a side reaction, whereas equilibration of meso‐ and rac‐ 22 and fragmentation, which led to alkyne 24 and acetonitrile, dominated. Prolonged irradiation of 22 gave mainly the pyrimidine 25 . The change of the configuration at C‐2 of the 2H‐azirine unit was observed not only in the case of bi‐2H‐azirin‐2‐yls 22 but also for simple spirocyclic 2H‐azirines 29 at a relatively low temperature (75 °C). The fragmentation of rac‐ 22 to give alkyne 24 and two molecules of acetonitrile was also studied by high‐level quantum chemical calculations. For a related model system 30 (methyl instead of phenyl groups), two transition states TS‐ 30 – 31 of comparable energy with multiconfigurational electronic states could be localized on the energy hypersurface for this one‐step conversion. The symmetrical transition state complies with the definition of a coarctate mechanism.     

Divergent synthetic approach to 6'-modified α-GalCer analogues

A synthetic approach is presented for the synthesis of galacturonic acid and D-fucosyl modified KRN7000. The approach allows for late-stage functionalisation of both the sugar 6'-OH and the sphingosine amino groups, which enables convenient synthesis of promising 6'-modified KRN7000 analogues.     

The aqueous phase behavior of polyion-surfactant ion complex salts mixed with nonionic surfactants

The aim of this work was to study intermolecular interactions in systems containing charged polyion (polyacrylate, PA(-)), charged surfactant (C(16)TA(+)) and nonionic surfactant (C(12)E(5) or C(12)E(8)). To achieve this we have created four different phase diagrams using two different so-called complex salts, C(16)TAPA(25) and C(16)TAPA(6000), both consisting of positively charged surfactant (C(16)TA(+)) with polyacrylate (PA(-)) as counterions (no simple salt). The difference between the salts is the length of the polyion (25 or 6000 monomers). Both are insoluble in water. The results revealed that decreasing polyion length and increasing the PEO chain length of the nonionic surfactant were important factors for increasing the solubility of the complex salt. We also found that the curvature effects are quite small at low water content when gradually exchanging C(12)E(8) for either one of the complex salts while there is a gradual change in curvature for the systems containing C(12)E(5). Another interesting observation was the possibility for relatively large amounts of complex salt to be incorporated into a V(1) (Ia3d, bicontinuous) phase in the C(12)E(8)-containing systems. This gives rise to several questions regarding arrangements and dynamics of the polyion in this phase. In the dilute regime several different liquid crystalline phases can coexist with a dilute liquid phase containing the nonionic surfactant.     

[Rb2(H2O)2][Re3(μ-Cl)3Br7(H2O)2]2 · H2O,ein gemischtes Halogenid-Hydrat mit anionischen Dimeren {[Re3(μ-Cl)3Br7(H2O)2]2 · H2O}2−

[Rb₂(H₂O)₂][Re₃(μ-Cl)₃Br₇(H₂O)₂]₂ · H₂O, a Mixed Halide-Hydrate with the Anionic Dimer {[Re₃(μ-Cl)₃Br₇(H₂O)₂]₂ · H₂O}^2? [Rb₂(H₂O)₂][Re₃(μ-Cl)₃Br₇(H₂O)₂]₂ · H₂O crystallizes as dark redbrown single crystals from an hydrobromic-acid solution of ReCl₃ and RbBr at 0°C. An important feature of the crystal structure (monoclinic, C2/c; a = 1494.61(8); b = 835.71(4); c = 3079.96(19) pm; β = 97.801(4)°; V_m = 573.9(4) cm³mol^?1; R = 0.060; R_w = 0.038) is the connection of two anions [Re₃(μ-Cl)₃Br₇(H₂O)₂]^? via a water molecule to dimers, {[Re₃(μ-Cl)₃Br₇(H₂O)₂]₂ · H₂O}^2?. These dimeric units are contained in slabs that are stacked in the [001] direction and held together by Rb⁺ cations and crystal water.