Application of the Cross-Entropy Method to the Buffer Allocation Problem in a Simulation-Based Environment

The buffer allocation problem (BAP) is a well-known difficult problem in the design of production lines. We present a stochastic algorithm for solving the BAP, based on the cross-entropy method, a new paradigm for stochastic optimization. The algorithm involves the following iterative steps: (a) the generation of buffer allocations according to a certain random mechanism, followed by (b) the modification of this mechanism on the basis of cross-entropy minimization. Through various numerical experiments we demonstrate the efficiency of the proposed algorithm and show that the method can quickly generate (near-)optimal buffer allocations for fairly large production lines.     

Structure in the K+-nucleon I = 0 total cross section below 1.1 GeV/c

Measurements have been carried out of total cross sections of positive kaons on hydrogen and deuterium to a statistical precision of better than ± 0.1 mb for most points in the range of laboratory momentum from 410 to 1065 MeV/c in intervals of approximately 50 MeV/c. A very broad elastic structure in the I = 0 state is inferred.     

Local and integral properties of a search algorithm of the stochastic approximation type

An optimum random-search algorithm is considered. The convergence conditions to the greatest increase (local properties) and convergence to the point of extremum (integral properties) of a function by optimizing in the presence of noise, are found. The results are used for finding a global extremum of a multiextremal function.     

Search for the decay πO → 4γ

We have searched for the decay π^O → 4γ using the decay K^± → π^±π^O as a source of kinematically defined π^O,s. No events were observed, where one event would correspond to a branching ratio (π^O → 4γ)/(π^O → 2γ) of 2.7 × 10^?5.     

Short and long distance effects in weak radiative decays

Flavour changing radiative decays for strange and charmed hadrons are studied in a model where the GIM weak interaction triggers the flavour change at the quark level and QCD corrections are taken into account. The amplitudes for photon emission are calculated for both non-factorisable (negligible) and factorisable contributions (dominant). We thereby achieve a “modern pole model” in which we include 56 and 70 intermediate states and normalise the amplitude in terms of the fundamental quark weak interaction.We generate large parity-violating amplitudes and explain qualitatively the relative size of all processes. We find a pattern of allowed (Λ→n + γ), (Ξ⁰→Σ⁰γ) and (Ξ⁰→Λγ), suppressed (Σ⁺→p + γ) and doubly suppressed decay $\text{(Ω}{}^{\mathrm{?}}\text{→Ξ + γ)}$ which show the complex pattern of symmetry and dynamical cancellations and enhancements.Following Shifman et al., we also show that short distance effects are negligible. Other approaches are discussed and in particular it is shown that the asymmetry in Σ⁺→p + γ poses no theoretical problem. Many predictions can be tested with the forthcoming new generation experiments.     

Minimal curvature-constrained networks

This paper introduces an exact algorithm for the construction of a shortest curvature-constrained network interconnecting a given set of directed points in the plane and a gradient descent method for doing so in 3D space. Such a network will be referred to as a minimum Dubins tree, since its edges are Dubins paths (or slight variants thereof). The problem of constructing a minimum Dubins tree appears in the context of underground mining optimisation, where the objective is to construct a least-cost network of tunnels navigable by trucks with a minimum turning radius. The Dubins tree problem is similar to the Steiner tree problem, except the terminals are directed and there is a curvature constraint. We propose the minimum curvature-constrained Steiner point algorithm for determining the optimal location of the Steiner point in a 3-terminal network. We show that when two terminals are fixed and the third varied in the planar version of the problem, the Steiner point traces out a limaçon.     

\mathbb Z _2-Thurston norm and complexity of 3-manifolds

A new lower bound on the complexity of a 3-manifold is given using the ${\mathbb Z }_2$ -Thurston norm. This bound is shown to be sharp, and the minimal triangulations realising it are characterised using normal surfaces consisting entirely of quadrilateral discs.     

Helicoidal Patterning of Nanorods with Polymer Ligands

Chiral packing of ligands on the surface of nanoparticles (NPs) is of fundamental and practical importance, as it determines how NPs interact with each other and with the molecular world. Herein, for gold nanorods (NRs) capped with end‐grafted nonchiral polymer ligands, we show a new mechanism of chiral surface patterning. Under poor solvency conditions, a smooth polymer layer segregates into helicoidally organized surface‐pinned micelles (patches). The helicoidal morphology is dictated by the polymer grafting density and the ratio of the polymer ligand length to nanorod radius. Outside this specific parameter space, a range of polymer surface structures was observed, including random, shish‐kebab, and hybrid patches, as well as a smooth polymer layer. We characterize polymer surface morphology by theoretical and experimental state diagrams. The helicoidally organized polymer patches on the NR surface can be used as a template for the helicoidal organization of other NPs, masked synthesis on the NR surface, as well as the exploration of new NP self‐assembly modes.     

"Supramolecular" assembly of gold nanorods end-terminated with polymer "pom-poms": effect of pom-pom structure on the association modes

We report a predefined self-organization of gold nanorods (NRs) end-terminated with multiple polymer arms ("pom-poms") in higher-order structures. The assembly of polymer-tethered NRs was controlled by changing the structure of the polymer pom-poms. We show that the variation in the molecular weight of the polymer molecules and their relative location with respect to the long side of the NRs resulted in two competing association modes of the nanorods, that is, their side-by-side and end-to-end assembly, and produced bundles, chains, rings, and bundled chains of the NRs. The superposition of the two variables controlling the organization of NRs allowed us to create a map showing the variation in the longitudinal plasmonic bands of the NRs achieved by their self-assembly.