Generalized binomial Tau-leap method for biochemical kinetics incorporating both delay and intrinsic noise

The delay stochastic simulation algorithm (DSSA) by Barrio et al. [Plos Comput. Biol.2, 117–E (2006)] was developed to simulate delayed processes in cell biology in the presence of intrinsic noise, that is, when there are small-to-moderate numbers of certain key molecules present in a chemical reaction system. These delayed processes can faithfully represent complex interactions and mechanisms that imply a number of spatiotemporal processes often not explicitly modeled such as transcription and translation, basic in the modeling of cell signaling pathways. However, for systems with widely varying reaction rate constants or large numbers of molecules, the simulation time steps of both the stochastic simulation algorithm (SSA) and the DSSA can become very small causing considerable computational overheads. In order to overcome the limit of small step sizes, various τ-leap strategies have been suggested for improving computational performance of the SSA. In this paper, we present a binomial τ- DSSA method that extends the τ-leap idea to the delay setting and avoids drawing insufficient numbers of reactions, a common shortcoming of existing binomial τ-leap methods that becomes evident when dealing with complex chemical interactions. The resulting inaccuracies are most evident in the delayed case, even when considering reaction products as potential reactants within the same time step in which they are produced. Moreover, we extend the framework to account for multicellular systems with different degrees of intercellular communication. We apply these ideas to two important genetic regulatory models, namely, the hes1 gene, implicated as a molecular clock, and a Her1/Her 7 model for coupled oscillating cells.

A plasmonic 'ac Wheatstone bridge' circuit for high-sensitivity phase measurement and single-molecule detection

In this paper, a plasmonic “ac Wheatstone bridge” circuit is proposed and theoretically modeled for the first time. The bridge circuit consists of three metallic nanoparticles, shaped as rectangular prisms, with two nanoparticles acting as parallel arms of a resonant circuit and the third bridging nanoparticle acting as an optical antenna providing an output signal. Polarized light excites localized surface plasmon resonances in the two arms of the circuit, which generate an optical signal dependent on the phase-sensitive excitations of surface plasmons in the antenna. The circuit is analyzed using a plasmonic coupling theory and numerical simulations. The analyses show that the plasmonic circuit is sensitive to phase shifts between the arms of the bridge and has the potential to detect the presence of single molecules.

Analysis of efficiency and optimization of plasmon energy coupling into nanofocusing metal wedges

In this paper, we investigate theoretically and numerically the efficiency of energy coupling from a plasmon generated by a grating coupler at one of the interfaces of a metal wedge into the plasmonic eigenmode (i.e., symmetric or quasisymmetric plasmon) experiencing nanofocusing in the wedge. Thus the energy efficiency of energy coupling into metallic nanofocusing structure is analyzed. Two different nanofocusing structures with the metal wedge surrounded by a uniform dielectric (symmetric structure) and with the metal wedge enclosed between a substrate and a cladding with different dielectricpermittivities (asymmetric structure) are considered by means of the geometrical optics (adiabatic) approximation. It is demonstrated that the efficiency of the energy coupling from the plasmon generated by the grating into the symmetric or quasisymmetric plasmon experiencing nanofocusing may vary between ∼50% to ∼100%. In particular, even a very small difference (of ∼1%–2%) between the permittivities of the substrate and the cladding may result in a significant increase in the efficiency of the energy coupling (from ∼50% up to ∼100%) into the plasmon experiencing nanofocusing. Distinct beat patterns produced by the interference of the symmetric (quasisymmetric) and antisymmetric (quasiantisymmetric) plasmons are predicted and analyzed with significant oscillations of the magnetic and electric field amplitudes at both the metal wedge interfaces. Physical interpretations of the predicted effects are based upon the behavior, dispersion, and dissipation of the symmetric (quasisymmetric) and antisymmetric (quasiantisymmetric) filmplasmons in the nanofocusing metal wedge. The obtained results will be important for optimizing metallic nanofocusing structures and minimizing coupling and dissipative losses.

A compact interferometric sensor design using three waveguide coupling

The use of metal stripes for the guiding of plasmons is a well established technique for the infrared regime and has resulted in the development of a myriad of passive optical components and sensing devices. However, the plasmons suffer from large losses around sharp bends, making the compact design of nanoscale sensors and circuits problematic. A compact alternative would be to use evanescent coupling between two sufficiently close stripes, and thus we propose a compact interferometer design using evanescent coupling. The sensitivity of the design is compared with that achieved using a hand-held sensor based on the Kretschmann style surface plasmon resonance technique. Modeling of the new interferometric sensor is performed for various structural parameters using finite-difference time-domain and COMSOL Multiphysics. The physical mechanisms behind the coupling and propagation of plasmons in this structure are explained in terms of the allowed modes in each section of the device.

Coherent superposition of exciton states in quantum dots induced by surface plasmons

We present an experimental demonstration of strong optical coupling between CdSequantum dots of different sizes which is induced by a surface plasmon propagating on a planar silver thin film. Attenuated total reflection measurements demonstrate the hybridization of exciton states, characterized by the observation of two avoided crossings in the energy dispersion measured for the interacting system.

Look before you leap : a confidence-based method for selecting species criticality while avoiding negative populations in τ-leaping

The stochastic simulation algorithm was introduced by Gillespie and in a different form by Kurtz. There have been many attempts at accelerating the algorithm without deviating from the behavior of the simulated system. The crux of the explicit τ-leaping procedure is the use of Poisson random variables to approximate the number of occurrences of each type of reaction event during a carefully selected time period, τ. This method is acceptable providing the leap condition, that no propensity function changes “significantly” during any time-step, is met. Using this method there is a possibility that species numbers can, artificially, become negative. Several recent papers have demonstrated methods that avoid this situation. One such method classifies, as critical, those reactions in danger of sending species populations negative. At most, one of these critical reactions is allowed to occur in the next time-step. We argue that the criticality of a reactant species and its dependent reaction channels should be related to the probability of the species number becoming negative. This way only reactions that, if fired, produce a high probability of driving a reactant population negative are labeled critical. The number of firings of more reaction channels can be approximated using Poisson random variables thus speeding up the simulation while maintaining the accuracy. In implementing this revised method of criticality selection we make use of the probability distribution from which the random variable describing the change in species number is drawn. We give several numerical examples to demonstrate the effectiveness of our new method.

Stochastic chemical kinetics and the quasi-steady-state assumption : application to the stochastic simulation algorithm and chemical master equation

Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and slow-scale SSA. Improved numerical efficiency is obtained by respecting the vastly different time scales characterizing the system and then by advancing only the slow reactions exactly, based on a suitable approximation to the fast reactions. We considerably extend these works by applying the QSSA to numerical methods for the direct solution of the chemical master equation (CME) and, in particular, to the finite state projection algorithm [Munsky and Khammash, J. Chem. Phys. 124, 044104 (2006)], in conjunction with Krylov methods. In addition, we point out some important connections to the literature on the (deterministic) total QSSA (tQSSA) and place the stochastic analogue of the QSSA within the more general framework of aggregation of Markov processes. We demonstrate the new methods on four examples: Michaelis–Menten enzyme kinetics, double phosphorylation, the Goldbeter–Koshland switch, and the mitogen activated protein kinase cascade. Overall, we report dramatic improvements by applying the tQSSA to the CME solver.

Optical waveguide and cavity effects on whispering-gallery mode resonances in a ZnO nanonail

Spatially resolved cathodoluminescence (CL) study of a ZnO nanonail, having thin shank, tapered neck, and hexagonal head sections, is reported. Monochromatic imaging and line scan profiling indicate that the wave guiding and leaking from growth imperfections in addition to the oxygen deficiency variation determine the spatial contrast of CL emissions. Occurrence of resonance peaks at identical wavelengths regardless of CL-excitation spots is inconsistent with the whispering-gallery mode (WGM) resonances of a two-dimensional cavity in the finite difference time domain simulation. However, three dimensioanl cavity simulation produced WGM peaks that are consistent with the experimental spectra, including transverse-electric resonances that are comparable to transverse-magnetic ones.

Identification of dispersion-dependent hexagonal cavity modes of an individual ZnO nanonail

The hexagonal resonator characteristics of an individual ZnO-nanonail’s head were investigated via spatially resolved cathodoluminescence (CL) at room temperature. The positions of most of distinct CL peaks in visible range were well matched to those of whispering gallery modes (WGMs) of a hexagonal dielectric cavity when we took birefringence and dispersion of refractive indices into account. The broad and weak peaks for TE polarization in long wavelength range were consistent with refractive-index values below the threshold for total internal inflection. CL peaks that were not matched to WGMs were identified as either triangular quasi-WGM or Fabry–Pérot resonance modes.

Simulations of the effect of waveguide cross-section on quantum dot – plasmon coupling

Quantum dot - plasmon waveguide systems are of interest for the active control of plasmon propagation, and consequently, the development of active nanophotonic devices such as nano-sized optical transistors. This paper is concerned with how varying aspect ratio of the waveguide crosssection affects the quantum dot - plasmon coupling. We compare a stripe waveguide with an equivalent nanowire, illustrating that both waveguides have a similar coupling strength to a nearby quantum dot for small waveguide cross-section, thereby indicating that stripe lithographic waveguides have strong potential use in quantum dot –plasmon waveguide systems. We also demonstrate that changing the aspect ratio of both stripe and wire waveguides can increase the spontaneous emission rate of the quantum dot into the plasmon mode, by up to a factor of five. The results of this paper will contribute to the optimisation of quantum dot - plasmon waveguide systems and help pave the way for the development of active nanophotonics devices.

New design rules for the shear strength of LiteSteel Beams

Abstract: The LiteSteel Beam (LSB) is a new cold-formed hollow flange channel section produced using dual electric resistance welding and automated continuous roll-forming technologies. The innovative LSB sections have many beneficial characteristics and are commonly used as flexural members in building construction. However, limited research has been undertaken on the shear behaviour of LSBs. Therefore a detailed investigation including both numerical and experimental studies was undertaken to investigate the shear behaviour of LSBs. Finite element models of LSBs in shear were developed to simulate the nonlinear ultimate strength behaviour of LSBs including their elastic buckling characteristics, and were validated by comparing their results with experimental test results. Validated finite element models were then used in a detailed parametric study into the shear behaviour of LSBs. The parametric study results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LSBs. Significant improvements to web shear buckling occurred due to the presence of torsionally rigid rectangular hollow flanges while considerable post-buckling strength was also observed. This paper therefore proposes improved shear strength design rules for LSBs within the current cold-formed steel code guidelines. It presents the details of the parametric study and the new shear strength equations. The new equations were also developed based on the direct strength method. The proposed shear strength equations have the potential to be used with other conventional cold-formed steel sections such as lipped channel sections.

The Influence of work motivation on project success : towards a framework

The purpose of this paper is to suggest a framework to study the influence of 'Work motivation' on 'Project success' from a team members' perspective. Results from a literature review of 1345 articles on ' Project success' and 1063 articles of 'Work motivation' appearing in peer-reviewed journals between 1985 and 2005 are presented. We then propose a framework to study the impact of 'Work motivation' on 'Project success' by incorporating the key constructs pertaining to these variables derived from the literature review.

Non-compositional concepts and quantum tests

Compositionality is a frequently made assumption in linguistics, and yet many human subjects reveal highly non-compositional word associations when confronted with novel concept combinations. This article will show how a non-compositional account of concept combinations can be supplied by modelling them as interacting quantum systems.