Optimization of Fishing Strategies in Space and Time as a Non-convex Optimal Control Problem

The behavior of a fishing fleet and its impact onto the biomass of fish can be described by a nonlinear parabolic diffusion–reaction equation. Looking for an optimal fishing strategy leads to a non-convex optimal control problem with a bilinear control action. In this work, we present such an optimal control formulation, prove its well-posedness and derive first- and second-order optimality conditions. These results provide a basis for tailored finite element discretization as well as for Newton type optimization algorithms. First numerical test problems show typical features as so-called No-Take-Zones and maximal fishing quota (total allowable catches) as parts of an optimal fishing strategy.     

Spatially adaptive sparse grids for high-dimensional data-driven problems

Sparse grids allow one to employ grid-based discretization methods in data-driven problems. We present an extension of the classical sparse grid approach that allows us to tackle high-dimensional problems by spatially adaptive refinement, modified ansatz functions, and efficient regularization techniques. The competitiveness of this method is shown for typical benchmark problems with up to 166 dimensions for classification in data mining, pointing out properties of sparse grids in this context. To gain insight into the adaptive refinement and to examine the scope for further improvements, the approximation of non-smooth indicator functions with adaptive sparse grids has been studied as a model problem. As an example for an improved adaptive grid refinement, we present results for an edge-detection strategy.     

Direct Regioselective Dehydrogenation of α-Substituted Cyclic Ketones

We disclose a highly regioselective, catalytic one-step dehydrogenation of α-substituted cyclic ketones in the presence of 2,3-dichlorobenzo-5,6-dicyano-1,4-benzoquinone (DDQ). The high regioselectivity originates from a phosphoric acid-catalyzed enolization, selectively affording the thermodynamically preferred enol, followed by the subsequent oxidation event. Our method provides reliable access to several α-aryl and α-alkyl substituted α,β-unsaturated ketones.     

Deterministic random walks on regular trees

Jim Propp's rotor–router model is a deterministic analog of a random walk on a graph. Instead of distributing chips randomly, each vertex serves its neighbors in a fixed order. Cooper and Spencer (Comb Probab Comput 15 (2006) 815–822) show a remarkable similarity of both models. If an (almost) arbitrary population of chips is placed on the vertices of a grid ?^d and does a simultaneous walk in the Propp model, then at all times and on each vertex, the number of chips on this vertex deviates from the expected number the random walk would have gotten there by at most a constant. This constant is independent of the starting configuration and the order in which each vertex serves its neighbors. This result raises the question if all graphs do have this property. With quite some effort, we are now able to answer this question negatively. For the graph being an infinite k‐ary tree (k ≥ 3), we show that for any deviation D there is an initial configuration of chips such that after running the Propp model for a certain time there is a vertex with at least D more chips than expected in the random walk model. However, to achieve a deviation of D it is necessary that at least exp(Ω(D²)) vertices contribute by being occupied by a number of chips not divisible by k at a certain time. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Computational study of fluoroquinolone binding to and its applicability to future drug design

Fluoroquinolones are an important therapeutic class in the targeting of new and resistant bacterial infections. Fluoroquinolones bind to bacterial type II topoisomerase via a water‐Mg²⁺ bridge. However, binding to magnesium‐containing molecules outside of the target cells increases the minimum inhibitory concentration (MIC) and promotes drug resistance. As a result, fluoroquinolones are counter‐indicated with magnesium and multivalent metal cation containing drugs, such as antacids. The antibiotic efficacy of fluoroquinolones has also been shown to be pH dependent, as we show the effect of protonation state on magnesium binding. This work presents a systematic computational study of fluoroquinolones' magnesium‐binding properties. We use B3LYP density functional theory and triple‐zeta basis sets, to evaluate binding affinities. Complexation is predicted to be thermodynamically favorable at neutral and basic compared to acidic pH. The calculated complexation energies broadly capture experimental binding affinities, suggesting this is a valid approach for designing new fluoroquinolones with a target magnesium binding affinity. We also investigate the effect of chemical substitution at the carboxylic acid to help in the identification of potential new antibiotics based on the fluoroquinolone pharmacophore.     

Aggregation‐Induced Emission of Hexaphenyl‐1,3‐butadiene

A new type of AIE molecules based on hexaphenyl‐1,3‐butadienes was reported with respect to the synthesis and characterization. This material exhibited different maximum emission wavelength and enhanced emission intensity at different aggregate state (amorphous and crystalline state).     

A Model Equation for Wavepacket Solitary Waves Arising from Capillary-Gravity Flows

A model equation governing the primitive dynamics of wave packets near an extremum of the linear dispersion relation at finite wavenumber is derived. In two spatial dimensions, we include the effects of weak variation of the wave in the direction transverse to the direction of propagation. The resulting equation is contrasted with the Kadomtsev–Petviashvilli and Nonlinear Schrödinger (NLS) equations. The model is derived as an approximation to the equations for deep water gravity-capillary waves, but has wider applications. Both line solitary waves and solitary waves which decay in both the transverse and propagating directions—lump solitary waves—are computed. The stability of these waves is investigated and their dynamics are studied via numerical time evolution of the equation.     

Protein profile of osteoarthritic human articular cartilage using tandem mass spectrometry

Articular cartilage contains both chondrocyte cells and extracellular matrix (ECM) components. Currently, comprehensive information concerning the protein composition of human articular cartilage tissue is somewhat lacking. In this report we detail the use of tandem mass spectrometry (MS/MS) for a preliminary global identification of proteins from human articular knee cartilage tissue from patients diagnosed with osteoarthritis. Knee cartilage supernatant was fractionated using one-dimensional sodium dodecyl sulfate polyacrylamide gel electrophoresis (1D-SDS-PAGE), in-gel digested and peptide sequences were then determined by performing on-line nano-liquid chromatography (LC)/MS/MS experiments using an ion trap mass spectrometer. Altogether, over 100 different proteins from nearly 700 unique peptide sequences were detected by MS/MS. The majority of the proteins identified are involved in ECM organization (35%), signal transduction and cell communication (14%), immune response (11%) and metabolism and energy pathways (11%). Proteins observed included several well-known cartilage components as well as lower abundant lesser known ECM proteins. Possible degradation products in the cartilage sample, such as from cartilage link protein, could also be detected by our mass spectrometry methods. We show here that mass spectrometry can be utilized as a tool for a fast, accurate and sensitive analysis of a complex mixture of cartilage proteins. It is believed that this type of proteomic analysis will aid future work centered on investigating the pathology of this and other related joint diseases.