Regularization of Ill-Posed Problems by Envelope Guided Conjugate Gradients

Abstract

We propose a new way to iteratively solve large scale ill-posed problems by exploiting the relation between Tikhonov regularization and multiobjective optimization to obtain, iteratively, approximations to the Tikhonov L-curve and its corner. Monitoring the change of the approximate L-curves allows us to adjust the regularization parameter adaptively during a preconditioned conjugate gradient iteration, so that the desired solution can be reconstructed with a low number of iterations. We apply the technique to an idealized image reconstruction problem in positron emission tomography.     

Mechanism of the rhodium(III)-catalyzed arylation of imines via C-H bond functionalization: inhibition by substrate

Rh(III)-catalyzed arylation of imines provides a new method for C-C bond formation while simultaneously introducing an α-branched amine as a functional group. This detailed mechanistic study provides insights for the rational future development of this new reaction. Relevant intermediate Rh(III) complexes have been isolated and characterized, and their reactivities in stoichiometric reactions with relevant substrates have been monitored. The reaction was found to be first order in the catalyst resting state and inverse first order in the C-H activation substrate.     

Design and development of a field-deployable single-molecule detector (SMD) for the analysis of molecular markers

Single-molecule detection (SMD) has demonstrated some attractive benefits for many types of biomolecular analyses including enhanced processing speed by eliminating processing steps, elimination of ensemble averaging and single-molecule sensitivity. However, it's wide spread use has been hampered by the complex instrumentation required for its implementation when using fluorescence as the readout modality. We report herein a simple and compact fluorescence single-molecule instrument that is straightforward to operate and consisted of fiber optics directly coupled to a microfluidic device. The integrated fiber optics served as waveguides to deliver the laser excitation light to the sample and collecting the resulting emission, simplifying the optical requirements associated with traditional SMD instruments by eliminating the need for optical alignment and simplification of the optical train. Additionally, the use of a vertical cavity surface emitting laser and a single photon avalanche diode serving as the excitation source and photon transducer, respectively, as well as a field programmable gate array (FPGA) integrated into the processing electronics assisted in reducing the instrument footprint. This small footprint SMD platform was tested using fluorescent microspheres and single AlexaFluor 660 molecules to determine the optimal operating parameters and system performance. As a demonstration of the utility of this instrument for biomolecular analyses, molecular beacons (MBs) were designed to probe bacterial cells for the gene encoding Gram-positive species. The ability to monitor biomarkers using this simple and portable instrument will have a number of important applications, such as strain-specific detection of pathogenic bacteria or the molecular diagnosis of diseases requiring rapid turn-around-times directly at the point-of-use.     

Rigorous filtering using linear relaxations

This paper presents rigorous filtering methods for continuous constraint satisfaction problems based on linear relaxations, designed to efficiently handle the linear inequalities coming from a linear relaxation of quadratic constraints. Filtering or pruning stands for reducing the search space of constraint satisfaction problems. Discussed are old and new approaches for rigorously enclosing the solution set of linear systems of inequalities, as well as different methods for computing linear relaxations. This allows custom combinations of relaxation and filtering. Care is taken to ensure that all methods correctly account for rounding errors in the computations. The methods are implemented in the GloptLab environment for solving quadratic constraint satisfaction problems. Demonstrative examples and tests comparing the different linear relaxation methods are also presented.     

Synthesis, Reactivity, and Resolution of a C(2)-Symmetric, P-Stereogenic Benzodiphosphetane, a Building Block for Chiral Bis(phosphines)

Although the pyramidal inversion barriers in diphosphines (R(2)P-PR(2)) are similar to those in phosphines (PR(3)), P-stereogenic chiral diphosphines have rarely been exploited as building blocks in asymmetric synthesis. The synthesis, reactivity, and resolution of the benzodiphosphetane trans-1,2-(P(t-Bu))(2)C(6)H(4) are reported. Alkylation with MeOTf followed by addition of a nucleophile gave the useful C(2)-symmetric P-stereogenic ligand BenzP* and novel analogues.     

Spin-state transition of iron in ( perovskite

The redox behavior of iron during heating of a high-performance perovskite for ceramic oxygen separation membranes was studied by combined electron energy-loss (EELS, esp. ELNES) and Mössbauer spectroscopical in situ methods. At room temperature, the iron in (Ba_0.5Sr_0.5)(Fe_0.8Zn_0.2)O_3-δ (BSFZ) is in a mixed valence state of 75% Fe⁴⁺ in the high-spin state and 25% Fe³⁺ predominantly in the low-spin state. When heated to , a slight reduction of iron is observed that increases the quantity of Fe³⁺ species. However, the dominant occurrence is a gradual transition in the spin-state of trivalent iron from a mixed low-spin/high-spin to a pure high-spin configuration. In addition, a remarkable amount of hybridization is found in the Fe–O bonds that are highly polar rather than purely ionic. The coupled valence/spin-state transition correlates with anomalies in thermogravimetry and thermal expansion behavior observed by X-ray diffraction and dilatometry, respectively. Since the effective cationic radii depend not only on the valence but also on the spin-state, both have to be considered when estimating under which conditions a cubic perovskite will tolerate specific cations. It is concluded that an excellent phase stability of perovskite-based membrane materials demands a tailoring, which enables pure high-spin states under operational conditions, even if mixed valence states are present. The low spin-state transition temperature of BSFZ provides that all iron species are in a pure high-spin configuration already above ca. making this ceramic highly attractive for intermediate temperature applications ().     

Fuzzy controller of the air system of a diesel engine: Real-time simulation

In this paper a fuzzy controller is proposed to regulate the intake manifold pressure and the fresh mass airflow of diesel engines simultaneously. The instrumentation set usually embedded in a mass-produced passenger car has been considered. Unlike many multi-variable controllers, the proposed structure requires neither an internal model nor identification algorithms. In comparison to controllers embedded at present in standard engine control units (ECUs), it improves the trajectory tracking of desired outputs during simulation of EURO cycles. Because of its performance, the fuzzy controller has been implemented in an electronics control unit. Some real-time results are presented.     

Synthesis,structures and full characterization of p-tert-butylcalix[5]arene mono-, di-, tri- and pentaanionic ligand precursors

The synthesis, complete characterization, and solid state conformation of a new series of p-tert-butylcalix[5]arene (Bu^tC5) mono-, di-, tri- and pentaanions are reported. X-ray structures of the alkali metal salts illustrate the strong influence of the alkali metal ion on the structure of the calixanion. The strength of the alkali metal base and its reaction stoichiometry play an important role in the conformation and level of deprotonation of the resulting anion. Reaction of Bu^tC5 in a 2:1 molar ratio with alkali metal bases M₂CO₃ (M = Rb, Cs), or in a 1:1 ratio with M₂CO₃ (M = Na, K), MOH (M = Na, K, Rb, Cs) or MH (M = Li, Na) produces Bu^tC5 monoanions, but Bu^tC5 reacts in a 1:1 molar ratio with M₂CO₃ (M = Rb, Cs) or a 1:2 molar ratio with MOC(CH₃)₃ (M = Na, K) to afford Bu^tC5 dianions. Due to the steric bulkiness of the Bu^t group no polymeric structures are observed. Alkali metal salts of trianionic Bu^tC5 were obtained in high yields from reactions of Bu^tC5 with MOC(CH₃)₃ (M = Li, Na, K), BuⁿLi, LiH and LiOH in a 1:3 molar ratio. Pentaanionic Bu^tC5 salts were obtained by the reaction with MOC(CH₃)₃ (M = Li, Na, K) or BuⁿLi in a 5:1 ratio. X-ray crystal structures of Bu^tC5 · Na and Bu^tC5 · Cs indicate that the size of the alkali metal influences the level of cation-π arene interactions and therefore the conformation of the Bu^tC5 unit; for example, Bu^tC5 · Na has a cone conformation while Bu^tC5 · Cs shows a flattened cone conformation. Cation-π arene interactions are observed in most of the calixarene salts.