Eigenvalue confinement and spectral gap for random simplicial complexes

We consider the adjacency operator of the Linial‐Meshulam model for random simplicial complexes on n vertices, where each d‐cell is added independently with probability p to the complete ‐skeleton. Under the assumption , we prove that the spectral gap between the smallest eigenvalues and the remaining eigenvalues is with high probability. This estimate follows from a more general result on eigenvalue confinement. In addition, we prove that the global distribution of the eigenvalues is asymptotically given by the semicircle law. The main ingredient of the proof is a Füredi‐Komlós‐type argument for random simplicial complexes, which may be regarded as sparse random matrix models with dependent entries. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 506–537, 2017     

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.     

Detection challenges in quantitative polymer analysis by liquid chromatography

Accurate quantification of polymer distributions is one of the main challenges in polymer analysis by liquid chromatography. The response of contemporary detectors is typically influenced by compositional features such as molecular weight, chain composition, end groups, and branching. This renders the accurate quantification of complex polymers of which there are no standards available, extremely challenging. Moreover, any (programmed) change in mobile‐phase composition may further limit the applicability of detection techniques. Current methods often rely on refractive index detection, which is not accurate when dealing with complex samples as the refractive‐index increment is often unknown. We review current and emerging detection methods in liquid chromatography with the aim of identifying detectors, which can be applied to the quantitative analysis of complex polymers.     

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.