Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE.

Optimistic linear programming gives logarithmic regret for irreducible MDPs

We present an algorithm called Optimistic Linear Programming (OLP) for learning to optimize average reward in an irreducible but otherwise unknown Markov decision process (MDP). OLP uses its experience so far to estimate the MDP. It chooses actions by optimistically maximizing estimated future rewards over a set of next-state transition probabilities that are close to the estimates, a computation that corresponds to solving linear programs. We show that the total expected reward obtained by OLP up to time T is within C(P) log T of the reward obtained by the optimal policy, where C(P) is an explicit, MDP-dependent constant. OLP is closely related to an algorithm proposed by Burnetas and Katehakis with four key differences: OLP is simpler, it does not require knowledge of the supports of transition probabilities, the proof of the regret bound is simpler, but our regret bound is a constant factor larger than the regret of their algorithm. OLP is also similar in flavor to an algorithm recently proposed by Auer and Ortner. But OLP is simpler and its regret bound has a better dependence on the size of the MDP.

Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

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.

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.

A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems

Biochemical reactions underlying genetic regulation are often modelled as a continuous-time, discrete-state, Markov process, and the evolution of the associated probability density is described by the so-called chemical master equation (CME). However the CME is typically difficult to solve, since the state-space involved can be very large or even countably infinite. Recently a finite state projection method (FSP) that truncates the state-space was suggested and shown to be effective in an example of a model of the Pap-pili epigenetic switch. However in this example, both the model and the final time at which the solution was computed, were relatively small. Presented here is a Krylov FSP algorithm based on a combination of state-space truncation and inexact matrix-vector product routines. This allows larger-scale models to be studied and solutions for larger final times to be computed in a realistic execution time. Additionally the new method computes the solution at intermediate times at virtually no extra cost, since it is derived from Krylov-type methods for computing matrix exponentials. For the purpose of comparison the new algorithm is applied to the model of the Pap-pili epigenetic switch, where the original FSP was first demonstrated. Also the method is applied to a more sophisticated model of regulated transcription. Numerical results indicate that the new approach is significantly faster and extendable to larger biological models.

Peer state assessment of TxDOT maintenance program and practices : workshop and road rally findings

In an effort to evaluate and improve their practices to ensure the future excellence of the Texas highway system, the Texas Department of Transportation (TxDOT) sought a forum in which experts from other state departments of transportation could share their expertise. Thus, the Peer State Review of TxDOT Maintenance Practices project was organized and conducted for TxDOT by the Center for Transportation Research (CTR) at The University of Texas at Austin. The goal of the project was to conduct a workshop at CTR and in the Austin District that would educate the visiting peers on TxDOT’s maintenance practices and invite their feedback. CTR and TxDOT arranged the participation of the following directors of maintenance: Steve Takigawa, CA; Roy Rissky, KS; Eric Pitts, GA; Jim Carney, MO; Jennifer Brandenburg, NC; and David Bierschbach, WA. One of the means used to capture the peer reviewers’ opinions was a carefully designed booklet of 15 questions. The peers provided TxDOT with written responses to these questions, and the oral comments made during the workshop were also captured. This information was then compiled and summarized in the following report. An examination of the peers’ comments suggests that TxDOT should use a more holistic, statewide approach to funding and planning rather than funding and planning for each district separately. Additionally, the peers stressed the importance of allocating funds based on the actual conditions of the roadways instead of on inventory. The visiting directors of maintenance also recommended continuing and proliferating programs that enhance communication, such as peer review workshops.

Instantaneous phase of the autocorrelation and robustness to signal-dependent noise

The phase of an analytic signal constructed from the autocorrelation function of a signal contains significant information about the shape of the signal. Using Bedrosian's (1963) theorem for the Hilbert transform it is proved that this phase is robust to multiplicative noise if the signal is baseband and the spectra of the signal and the noise do not overlap. Higher-order spectral features are interpreted in this context and shown to extract nonlinear phase information while retaining robustness. The significance of the result is that prior knowledge of the spectra is not required.

Competition and innovation : independent production in the Chinese TV industry

Independent television production is recognised for its capacity to generate new kinds of program content, as well as deliver innovation in formats. Globally, the television industry is entering into the post-broadcasting era where audiences are fragmented and content is distributed across multiple platforms. The effects of this convergence are now being felt in China, as it both challenges old statist models and presents new opportunities for content innovation. This thesis discusses the status of independent production in China, making relevant comparisons with independent production in other countries. Independent television production has become an important element in the reform of broadcasting in China in the past decade. The first independent TV production company was registered officially in 1994. While there are now over 4000 independent companies, the term „independent. does not necessarily constitute autonomy. The question the thesis addresses is: what is the status and nature of independence in China? Is it an appropriate term to use to describe the changing environment, or is it a misnomer? The thesis argues that Chinese independents operate alongside the mainstream state-owned system; they are „dependent. on the mainstream. Therefore independent television in China is a relative term. By looking at several companies in Beijing, mainly in entertainment, TV drama and animation, the thesis shows how the sector is injecting fresh ideas into the marketplace and how it plays an important role in improving innovation in many aspects of the television industry. The thesis shows how independent television companies in China are looking to protect their property rights. It demonstrates that far from being at the cutting edge, independents are reliant on a system that has many inbuilt structural problems. The thesis outlines many of the challenges facing 'independents'.

Preventing injuries on a state-wide basis : researchers and parliamentary committees are partners in turning injury prevention and safety research into practice and policy

Context: Parliamentary committees established in Westminster parliaments, such as Queensland, provide a cross-party structure that enables them to recommend policy and legislative changes that may otherwise be difficult for one party to recommend. The overall parliamentary committee process tends to be more cooperative and less adversarial than the main chamber of parliament and, as a result, this process permits parliamentary committees to make recommendations more on the available research evidence and less on political or party considerations. Objectives: This paper considers the contributions that parliamentary committees in Queensland have made in the past in the areas of road safety, drug use as well as organ and tissue donation. The paper also discusses the importance of researchers actively engaging with parliamentary committees to ensure the best evidence based policy outcomes. Key messages: In the past, parliamentary committees have successfully facilitated important safety changes with many committee recommendations based on research results. In order to maximise the benefits of the parliamentary committee process it is essential that researchers inform committees about their work and become key stakeholders in the inquiry process. Researchers can keep committees informed by making submissions to their inquiries, responding to requests for information and appearing as witnesses at public hearings. Researchers should emphasise the key findings and implications of their research as well as considering the jurisdictional implications and political consequences. It is important that researchers understand the differences between lobbying and providing informed recommendations when interacting with committees. Discussion and conclusions: Parliamentary committees in Queensland have successfully assisted in the introduction of evidence based policy and legislation. In order to present best practice recommendations, committees rely on the evidence presented to them including the results of researchers. Actively engaging with parliamentary committees will help researchers to turn their results into practice with a corresponding decrease in injuries and fatalities. Developing an understanding of parliamentary committees, and the typical inquiry process used by these committees, will help researchers to present their research results in a manner that will encourage the adoption of their ideas by parliamentary committees, the presentation of these results as recommendations within the report and the subsequent enactment of the committee’s recommendations by the government.

State of the art and future challenges for information literacy research

This short paper focuses on strategic issues and important research questions.