Strong Feller Property of Sticky Reflected Distorted Brownian Motion

Using Girsanov transformations we construct from sticky reflected Brownian motion on \([0,\infty )\) a conservative diffusion on \(E:=[0,\infty )^n\), \(n \in \mathbb {N}\), and prove that its transition semigroup possesses the strong Feller property for a specified general class of drift functions. By identifying the Dirichlet form of the constructed process we characterize it as sticky reflected distorted Brownian motion. In particular, the relations of the underlying analytic Dirichlet form methods to the probabilistic methods of random time changes and Girsanov transformations are presented. Our studies of the mathematical model are motivated by its applications to the dynamical wetting model with \(\delta \)-pinning and repulsion.     

Convergence of the SMC Implementation of the PHD Filte

The probability hypothesis density (PHD) filter is a first moment approximation to the evolution of a dynamic point process which can be used to approximate the optimal filtering equations of the multiple-object tracking problem. We show that, under reasonable assumptions, a sequential Monte Carlo (SMC) approximation of the PHD filter converges in mean of order , and hence almost surely, to the true PHD filter. We also present a central limit theorem for the SMC approximation, show that the variance is finite under similar assumptions and establish a recursion for the asymptotic variance. This provides a theoretical justification for this implementation of a tractable multiple-object filtering methodology and generalises some results from sequential Monte Carlo theory.      

Stability radii of positive higher order difference systems under fractional perturbations

In this paper we study stability radii of positive higher order difference systems under fractional perturbations and affine perturbations of the coefficient matrices. It is shown that real and complex stability radii coincide and can be computed by a simple formula. Finally, a simple example is given to illustrate the obtained results.     

Promoter Activation in Δhfq Mutants as an Efficient Tool for Specialized Metabolite Production Enabling Direct Bioactivity Testing

Natural products (NPs) from microorganisms have been important sources for discovering new therapeutic and chemical entities. While their corresponding biosynthetic gene clusters (BGCs) can be easily identified by gene‐sequence‐similarity‐based bioinformatics strategies, the actual access to these NPs for structure elucidation and bioactivity testing remains difficult. Deletion of the gene encoding the RNA chaperone, Hfq, results in strains losing the production of most NPs. By exchanging the native promoter of a desired BGC against an inducible promoter in Δhfq mutants, almost exclusive production of the corresponding NP from the targeted BGC in Photorhabdus, Xenorhabdus and Pseudomonas was observed including the production of several new NPs derived from previously uncharacterized non‐ribosomal peptide synthetases (NRPS). This easyPACId approach (easy Promoter Activated Compound Identification) facilitates NP identification due to low interference from other NPs. Moreover, it allows direct bioactivity testing of supernatants containing secreted NPs, without laborious purification.     

A Hopfield neural network with multiple attractors and its FPGA design

Neural network is important for a wide range of applications. Especially, a small neural network can display various complex behaviors. In this work, the investigations of a Hopfield neural network and its field programmable gate array (FPGA) implementation have been reported. The considered Hopfield neural network is simple because it includes only three neurons. It is interesting that we observed chaos and numerous coexisting attractors in such a network. In addition, the network has been implemented via an FPGA platform to verify its feasibility.     

The photoluminescence excitation spectra of multicomponent media

With no restrictions on the value of optical density, we derive an equation that describes the photoluminescence excitation spectra of separate components with overlapping absorption bands in a multicomponent medium. Based on the equation obtained, we propose methods for measuring the ratios of absorption optical densities of the components and quantum yields of their luminescence. The applicability of the proposed methods is demonstrated by measuring the characteristics of coumarin and porphyrin dissolved in different proportions in ethanol. We have also measured the quantum yield and luminescence decay time of the radiationinduced color centers F ₃ ⁺ in the lithium fluoride crystal and calculated probabilities of radiative and nonradiative transitions from the first excited singlet state of these centers.     

Microstructural analysis of liquid and amorphous SiO2 nanoparticles

Microstructural properties of liquid and amorphous SiO₂ nanoparticles have been investigated via molecular dynamics (MD) simulations with the interatomic potentials that have weak Coulomb interaction and Morse-type short-range interaction under non-periodic boundary conditions. Structural properties of spherical nanoparticles with different sizes of 2, 4 and 6 nm obtained at 3500 K have been studied through partial radial distribution functions (PRDFs), coordination number and bond-angle distributions, and compared with those observed in the bulk. The core and surface structures of liquid SiO₂ nanoparticles have been studied in detail. We found significant size effects on structure of nanoparticles. Calculations also show that if the size is larger than 4 nm, liquid SiO₂ nanoparticles at the temperature of 3500 K have a lightly distorted tetrahedral network structure with the mean coordination number Z_Si-O≈4.0 and Z_O-Si≈2.0 like those observed in the bulk. Moreover, temperature dependence of structural defects and SiO_x stoichiometry in nanoparticles on cooling from the melt has been found and presented.     

Cooling rate effects on structure and thermodynamics of amorphous nanoparticles

Cooling rate effects on structure and thermodynamics of amorphous nanoparticles were studied in a spherical model using Molecular Dynamics (MD) method. The good equilibrium melts are cooling down by three different cooling rates in order to observe the cooling rate effects. We find that cooling rate effects on thermodynamic quantities such as potential energy and surface energy are more pronounced than those for static quantities. Microstructure of amorphous nanoparticles is analyzed via radial distribution function (RDF) and coordination number distributions. Relatively weak cooling rate effects on such quantities are found. Microstructure of surface and core of amorphous nanoparticles are analyzed.     

Observation of slow down of polystyrene nanogels diffusivities in contact with swollen polystyrene brushes

The diffusion of dilute colloids in contact with swollen polymer brushes has been studied by evanescent wave dynamic light scattering. Two polystyrene nanogels with 16 nm and 42 nm radius were put into contact with three polystyrene brushes with varying grafting densities. Partial penetration of the nanogels within the brushes was revealed by the evanescent wave penetration depth-dependent scattering intensities. The experimental short-time diffusion coefficients of the penetrating particles were measured and found to strongly slow down as the nanoparticles get deeper into the brushes. The slow down is much more marked for the smaller (16 nm) nanogels, suggesting a size exclusion type of mechanism and the existence of a characteristic length scale present in the outer part of the brush.