Ryser's Conjecture for Tripartite 3-Graphs

We prove that in a tripartite 3-graph . Received March 17, 1999     

Testing Monotonicity

at arguments of its choice, the test always accepts a monotone f, and rejects f with high probability if it is ε-far from being monotone (i.e., every monotone function differs from f on more than an ε fraction of the domain). The complexity of the test is O(n/ε). The analysis of our algorithm relates two natural combinatorial quantities that can be measured with respect to a Boolean function; one being global to the function and the other being local to it. A key ingredient is the use of a switching (or sorting) operator on functions. Received March 29, 1999     

Geometry of Thin Films

Journal of Nonlinear Science - We study ray optics in the context of double-mirror systems, in the limit as the two mirrors approach one another (thin films). This leads to a novel set of...     

Arrangements on Parametric Surfaces I: General Framework and Infrastructure

We introduce a framework for the construction, maintenance, and manipulation of arrangements of curves embedded on certain two-dimensional orientable parametric surfaces in three-dimensional space. The framework applies to planes, cylinders, spheres, tori, and surfaces homeomorphic to them. We reduce the effort needed to generalize existing algorithms, such as the sweep line and zone traversal algorithms, originally designed for arrangements of bounded curves in the plane, by extensive reuse of code. We have realized our approach as the Cgal package Arrangement_on_surface_2. We define a compact and modular interface for our framework; for a given application a required small subset of the interface can be identified. Then, only this subset must be implemented. A companion paper describes concretizations for several types of surfaces and curves embedded on them, and applications. This is the first implementation of a generic algorithm that can handle arrangements on a large class of parametric surfaces.     

A phase I, randomized study of combined IL-2 and therapeutic immunisation with antiretroviral therapy

Background  

Fully functional HIV-1-specific CD8 and CD4 effector T-cell responses are vital to the containment of viral activity and disease progression. These responses are lacking in HIV-1-infected patients with progressive disease. We attempted to augment fully functional HIV-1-specific CD8 and CD4 effector T-cell responses in patients with advanced chronic HIV-1 infection.     

Quantum mechanics versus realism

Quantum theory accepts the point-like indivisible (classical) character of a particle as a mere product of a measuring process, or what has become known as a collapse. Following the notion of empty waves, which accepts the particle as a real existent entity without regard to the measurement process, we propose an experiment that may shed some light on the reality of the particle and the consequences of that reality.     

Tuning of switching properties and excited-state dynamics of fulgides by structural modifications

The ultrafast photo-induced dynamics of the E-isomers of four selected photochromic fulgides with distinct structural motifs have been elucidated by femtosecond broadband transient absorption spectroscopy in n-hexane as solvent. E→C and E→Z isomerisations, respectively, with time constants of ～0.12 ± 0.02 ps and ～0.34 ± 0.03 ps taking place in parallel were found for derivatives with a methyl substituent at the central hexatriene (HT) unit. In contrast, fulgides with increased steric constraints by an iso-propyl substituent or by intramolecular bridging displayed virtually zero E→Z isomerisation, but instead a desired accelerated and more efficient ring closure in a reaction time of only ～50 ± 10 fs. Both photoisomerisations appear to follow excited-state pathways with distinctive conical intersections. For the ring closure, direct barrierless pathways with steep downhill gradients are likely. Furthermore, the results indicate conformer-specific reactions, with ring closure exclusively by the E(α) conformer and E→Z isomerisation predominantly by the E(β) conformer, because the E(α)→Z channel is unfavoured by the faster and kinetically more competitive E(α)→C reaction. DFT calculations of the equilibrium structures showed that the sterically demanding groups at the HT unit shift the conformer equilibria towards the E(α) conformers. At the same time, they appear to cause a favourable pre-orientation of the furyl unit that accelerates the conrotatory ring closure in the E(α)→C reaction. Benzo-annulation of the furyl unit has little effect on the observed dynamics. Overall, the results demonstrate how the excited-state dynamics and thereby the photoswitching properties of fulgides can be successfully tuned and improved by structural modifications at the chromophores.     

Conclaves of planes in PG (4,2) and certain planes external to the Grassmannian ${\cal G}_{1,4,2} \subset$ PG(9,2)

We show that in $\operatorname{PG}(4,2)$ there exist octets $\mathcal{P} _{8}=\{\pi_{1},\,\ldots\,,\pi_{8}\}$ of planes such that the 28 intersections $\pi_{i}\cap\pi_{j}$ are distinct points. Such conclaves (see [6]) $\mathcal{P}_{8}$ of planes in $\operatorname{PG}(4,2)$ are shown to be in bijective correspondence with those planes $P$ in $\operatorname{PG}(9,2)$ which are external to the Grassmannian $\mathcal{G}_{1,4,2}$ and which belong to the orbit $\operatorname{orb}(2\gamma)$ (see [4]). The fact that, under the action of $\operatorname{GL}(5,2),$ the stabilizer groups $\mathcal{G}_{\mathcal{P}_{8}}$ and $\mathcal{G}_{P}$ both have the structure $2^{3}:(7:3)$ is thus illuminated. Starting out from a regulus-free partial spread $\mathcal{S}_{8}$ in $\operatorname{PG}(4,2)$ we also give a construction of a conclave of planes $P\in\operatorname{orb}(2\gamma)\subset\operatorname{PG}(9,2).$     

Enantioselective Sulfoxidations Catalyzedby Horseradish Peroxidase, ManganesePeroxidase, and Myeloperoxidase

Summary.  Horseradish peroxidase (HRP), myeloperoxidase (MPO), and manganese peroxidase (MnP) have been shown to catalyze the asymmetric sulfoxidation of thioanisole. When H₂O₂ was added stepwise to MPO, a maximal yield of 78% was obtained at pH 5 (ee 23%), whereas an optimum in the enantiomeric excess (32%, (R)-sulfoxide) was found at pH 6 (60% yield). For MnP a yield of 18% and a high enantiomeric excess of 91% of the (S)-sulfoxide were obtained at pH 5 and a yield of 36% and an ee of 87% at pH 7.0. Optimization of the conversion catalyzed by horseradish peroxidase at pH 7.0 by controlled continuous addition of hydrogen peroxide during turnover and monitoring the presence of native enzyme as well as of intermediates I, II, and III led to the formation of the sulfoxide in high yield (100%) and moderate enantioselectivity (60%, (S)-sulfoxide). Received November 18, 1999. Accepted January 21, 2000