Combined location-routing problems—a neural network approach

While in location planning it is often assumed that deliveries are made on a direct-trip basis, in fact deliveries, e.g., to the different supermarkets belonging to a specific chain or to retail outlets of any kind, usually are performed as round-trips. Therefore, it is often necessary to combine the two issues of locating a depot and of planning tours in one problem formulation.In this paper, a neural network approach based on a self-organizing map is proposed for solving such single-depot location-routing problems in the plane. The results derived by this approach are compared with those which can be found by different well-known heuristics, and it is shown that the self-organising map approach competes well with these concepts. Moreover, some modifications which rely on ideas from Tabu Search can be shown to be especially useful for increasing the number of feasible solutions found by the self-organising map approach. Finally, the implementation of the Weiszfeld procedure for a final improvement of the optimal depot location proves to be a useful device.     

Eulerian series as modular forms

In 1988, Hickerson proved the celebrated ``mock theta conjectures' in a collection of ten identities from Ramanujan's ``lost notebook' which express certain modular forms as linear combinations of mock theta functions. In the context of Maass forms, these identities arise from the peculiar phenomenon that two different harmonic Maass forms may have the same non-holomorphic parts. Using this perspective, we construct several infinite families of modular forms which are differences of mock theta functions.

     

Almost-invariant sets and invariant manifolds — Connecting probabilistic and geometric descriptions of coherent structures in flows

We study the transport and mixing properties of flows in a variety of settings, connecting the classical geometrical approach via invariant manifolds with a probabilistic approach via transfer operators. For non-divergent fluid-like flows, we demonstrate that eigenvectors of numerical transfer operators efficiently decompose the domain into invariant regions. For dissipative chaotic flows such a decomposition into invariant regions does not exist; instead, the transfer operator approach detects almost-invariant sets. We demonstrate numerically that the boundaries of these almost-invariant regions are predominantly comprised of segments of co-dimension 1 invariant manifolds. For a mixing periodically driven fluid-like flow we show that while sets bounded by stable and unstable manifolds are almost-invariant, the transfer operator approach can identify almost-invariant sets with smaller mass leakage. Thus the transport mechanism of lobe dynamics need not correspond to minimal transport.The transfer operator approach is purely probabilistic; it directly determines those regions that minimally mix with their surroundings. The almost-invariant regions are identified via eigenvectors of a transfer operator and are ranked by the corresponding eigenvalues in the order of the sets’ invariance or “leakiness”. While we demonstrate that the almost-invariant sets are often bounded by segments of invariant manifolds, without such a ranking it is not at all clear which intersections of invariant manifolds form the major barriers to mixing. Furthermore, in some cases invariant manifolds do not bound sets of minimal leakage.Our transfer operator constructions are very simple and fast to implement; they require a sample of short trajectories, followed by eigenvector calculations of a sparse matrix.     

Photo‐induced and Rapid Labeling of Tetrazine‐Bearing Proteins via Cyclopropenone‐Caged Bicyclononynes

Inverse electron‐demand Diels–Alder cycloadditions (iEDDAC) between tetrazines and strained alkenes/alkynes have emerged as essential tools for studying and manipulating biomolecules. A light‐triggered version of iEDDAC (photo‐iEDDAC) is presented that confers spatio‐temporal control to bioorthogonal labeling in vitro and in cellulo. A cyclopropenone‐caged dibenzoannulated bicyclo[6.1.0]nonyne probe (photo‐DMBO) was designed that is unreactive towards tetrazines before light‐activation, but engages in iEDDAC after irradiation at 365 nm. Aminoacyl tRNA synthetase/tRNA pairs were discovered for efficient site‐specific incorporation of tetrazine‐containing amino acids into proteins in living cells. In situ light activation of photo‐DMBO conjugates allows labeling of tetrazine‐modified proteins in living E. coli. This allows proteins in living cells to be modified in a spatio‐temporally controlled manner and may be extended to photo‐induced and site‐specific protein labeling in animals.     

A Jacobi–Davidson like method for nonlinear eigenvalue problems based on singularity theory

We present a Jacobi–Davidson like correction formula for left and right eigenvector approximations for non-Hermitian nonlinear eigenvalue problems. It exploits techniques from singularity theory for characterizing singular points of nonlinear equations. Unlike standard nonlinear Jacobi-Davidson, the correction formula does not contain derivative information and works with orthogonal projectors only. Moreover, the basic method is modified in that the new eigenvalue approximation is taken as a nonlinear Rayleigh functional obtained as root of a certain scalar nonlinear equation the existence of which – as well as a first order perturbation expansion – is shown. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient ribosomal peptidyl transfer critically relies on the presence of the ribose 2'-OH at A2451 of 23S rRNA

The ribosomal peptidyl transferase center is a ribozyme catalyzing peptide bond synthesis in all organisms. We applied a novel modified nucleoside interference approach to identify functional groups at 9 universally conserved active site residues. Owing to their immediate proximity to the chemical center, the 23S rRNA nucleosides A2451, U2506 and U2585 were of particular interest. Our study ruled out U2506 and U2585 as contributors of vital chemical groups for transpeptidation. In contrast the ribose 2'-OH of A2451 was identified as the prime ribosomal group with potential functional importance. This 2'-OH renders almost full catalytic power to the ribosome even when embedded into an active site of six neighboring 2'-deoxyribose nucleosides. These data highlight the unique functional role of the A2451 2'-OH for peptide bond synthesis among all other functional groups at the ribosomal peptidyl transferase active site.     

Novel macrocyclic templates by ring enlargement of ansa-steroids

Ring enlargement of ansa-steroids leads to a variety of novel templates which are suitable for the preparation of diverse libraries of natural product derivatives. Key steps for the synthesis of these highly functionalized templates were either an ozonolysis-derivatization-ring closing metathesis-sequence or a macrolactonization.     

Über das Verhalten von markiertem Coniferin in der verholzenden Pflanze

Zusammenfassung Coniferin-(3-¹⁴C) wurde in verholzendes Fichtengewebe implantiert. Nach Extraktion geringer löslicher Anteile wurde das Holzpulver einer Äthanolyse unterworfen, wobei aktives Vanilloylacetyl-(3-¹⁴C) isoliert werden konnte. Die Lokalisierung der Aktivität in der Seitenkette des Vanilloylacetyls wird beschrieben.Die Aktivität aller Äthanolyseprodukte wurde gemessen, einzelne oxydativ zu Vanillin, Vanillinsäure und Oxalsäure abgebaut. Durch Vergleich der molaren spezifischen Aktivität der isolierten Reinsubstanzen mit der Aktivität des eingesetzten Coniferins konnten Verdünnungsgrade errechnet werden, die das Ausmaß der Umwandlung des Coniferins in die einzelnen Fraktionen wiedergeben.Herrn Prof.F. Wessely zum 60. Geburtstag in Verehrung gewidmet.     

Zur Sauerstoffoxidation von Kreosolderivaten in alkalisch-wäßriger Lösung

Creosol (1), bicreosol (4) and other monomeric and dimeric creosols are oxidized in 0.25M-NaOH (5 equivalents base per phenolic hydroxyl group) by molecular oxygen at 70°C. Creosol is fragmented under these conditions to low molecular weight products without previous dimerization. The importance of fragmentation processes without cleavage of the C?C-bond between the oxygen substituted ring atoms in the case of bicreosol, and its considerable stability against oxidation compared with other compounds investigated can be explained by the ability of the monoanion of4 to exist in a conformation allowing hydrogen bonding between the phenolic oxygens of the two rings.     

Transport of Mars-crossing asteroids from the quasi-Hilda region

We employ set oriented methods in combination with graph partitioning algorithms to identify key dynamical regions in the Sun-Jupiter-particle three-body system. Transport rates from a region near the 3:2 Hilda resonance into the realm of orbits crossing Mars' orbit are computed. In contrast to common numerical approaches, our technique does not depend on single long term simulations of the underlying model. Thus, our statistical results are particularly reliable since they are not affected by a dynamical behavior which is almost nonergodic (i.e., dominated by strongly almost invariant sets).