A reduced model clarifies the role of feedback loops and time delays in the Drosophila circadian oscillator.

Although several detailed models of molecular processes essential for circadian oscillations have been developed, their complexity makes intuitive understanding of the oscillation mechanism difficult. The goal of the present study was to reduce a previously developed, detailed model to a minimal representation of the transcriptional regulation essential for circadian rhythmicity in Drosophila. The reduced model contains only two differential equations, each with time delays. A negative feedback loop is included, in which PER protein represses per transcription by binding the dCLOCK transcription factor. A positive feedback loop is also included, in which dCLOCK indirectly enhances its own formation. The model simulated circadian oscillations, light entrainment, and a phase-response curve with qualitative similarities to experiment. Time delays were found to be essential for simulation of circadian oscillations with this model. To examine the robustness of the simplified model to fluctuations in molecule numbers, a stochastic variant was constructed. Robust circadian oscillations and entrainment to light pulses were simulated with fewer than 80 molecules of each gene product present on average. Circadian oscillations persisted when the positive feedback loop was removed. Moreover, elimination of positive feedback did not decrease the robustness of oscillations to stochastic fluctuations or to variations in parameter values. Such reduced models can aid understanding of the oscillation mechanisms in Drosophila and in other organisms in which feedback regulation of transcription may play an important role.

Spectral bounds and basis results for non-self-adjoint pencils, with an application to Hagen-Poiseuille flow

We obtain eigenvalue enclosures and basisness results for eigen- and associated functions of a non-self-adjoint unbounded linear operator pencil A−λBA−λB in which BB is uniformly positive and the essential spectrum of the pencil is empty. Both Riesz basisness and Bari basisness results are obtained. The results are applied to a system of singular differential equations arising in the study of Hagen–Poiseuille flow with non-axisymmetric disturbances.

MODELLING β2AR REGULATION

The β2 adrenergic receptor (β2AR) regulates smooth muscle relaxation in the vasculature and airways. Long- and Short-acting β-agonists (LABAs/SABAs) are widely used in treatment of chronic obstructive pulmonary disorder (COPD) and asthma. Despite their widespread clinical use we do not understand well the dominant β2AR regulatory pathways that are stimulated during therapy and bring about tachyphylaxis, which is the loss of drug effects. Thus, an understanding of how the β2AR responds to various β-agonists is crucial to their rational use. Towards that end we have developed deterministic models that explore the mechanism of drug- induced β2AR regulation. These mathematical models can be classified into three classes; (i) Six quantitative models of SABA-induced G protein coupled receptor kinase (GRK)-mediated β2AR regulation; (ii) Three phenomenological models of salmeterol (a LABA)-induced GRK-mediated β2AR regulation; and (iii) One semi-quantitative, unified model of SABA-induced GRK-, protein kinase A (PKA)-, and phosphodiesterase (PDE)-mediated regulation of β2AR signalling. The various models were constrained with all or some of the following experimental data; (i) GRK-mediated β2AR phosphorylation in response to various LABAs/SABAs; (ii) dephosphorylation of the GRK site on the β2AR; (iii) β2AR internalisation; (iv) β2AR recycling; (v) β2AR desensitisation; (vi) β2AR resensitisation; (vii) PKA-mediated β2AR phosphorylation in response to a SABA; and (viii) LABA/SABA induced cAMP profile ± PDE inhibitors. The models of GRK-mediated β2AR regulation show that plasma membrane dephosphorylation and recycling of the phosphorylated β2AR are required to reconcile with the measured dephosphorylation kinetics. We further used a consensus model to predict the consequences of rapid pulsatile agonist stimulation and found that although resensitisation was rapid, the β2AR system retained the memory of prior stimuli and desensitised much more rapidly and strongly in response to subsequent stimuli. This could explain tachyphylaxis of SABAs over repeated use in rescue therapy of asthma patients. The LABA models show that the long action of salmeterol can be explained due to decreased stability of the arrestin/β2AR/salmeterol complex. This could explain long action of β-agonists used in maintenance therapy of asthma patients. Our consensus model of PKA/PDE/GRK-mediated β2AR regulation is being used to identify the dominant β2AR desensitisation pathways under different therapeutic regimens in human airway cells. In summary our models represent a significant advance towards understanding agonist-specific β2AR regulation that will aid in a more rational use of the β2AR agonists in the treatment of asthma.

Terahertz macrospin dynamics in insulating ferrimagnets

We investigate numerically the excitation of nonlinear magnetic interactions in a ferrite material by an energetic pump pulse of terahertz (THz) radiation. The calculations are performed by solving the coupled Maxwell and Landau-Lifshitz-Gilbert differential equations. In a time-resolved THz pump/THz probe scheme, it is demonstrated that Faraday rotation of a delayed THz probe pulse can be used to map these interactions. Our study is motivated by the ability of soft x-ray free electron lasers to perform time-resolved imaging of the magnetization process at the submicrometer and subpicosecond length and time scales.

Growth Codes: Intermediate Performance Analysis and Application to Video

Growth codes are a subclass of Rateless codes that have found interesting applications in data dissemination problems. Compared to other Rateless and conventional channel codes, Growth codes show improved intermediate performance which is particularly useful in applications where partial data presents some utility. In this paper, we investigate the asymptotic performance of Growth codes using the Wormald method, which was proposed for studying the Peeling Decoder of LDPC and LDGM codes. Compared to previous works, the Wormald differential equations are set on nodes' perspective which enables a numerical solution to the computation of the expected asymptotic decoding performance of Growth codes. Our framework is appropriate for any class of Rateless codes that does not include a precoding step. We further study the performance of Growth codes with moderate and large size codeblocks through simulations and we use the generalized logistic function to model the decoding probability. We then exploit the decoding probability model in an illustrative application of Growth codes to error resilient video transmission. The video transmission problem is cast as a joint source and channel rate allocation problem that is shown to be convex with respect to the channel rate. This illustrative application permits to highlight the main advantage of Growth codes, namely improved performance in the intermediate loss region.

Demographic model of the Swiss cattle population for the years 2009-2011 stratified by gender, age and production type

Demographic composition and dynamics of animal and human populations are important determinants for the transmission dynamics of infectious disease and for the effect of infectious disease or environmental disasters on productivity. In many circumstances, demographic data are not available or of poor quality. Since 1999 Switzerland has been recording cattle movements, births, deaths and slaughter in an animal movement database (AMD). The data present in the AMD offers the opportunity for analysing and understanding the dynamic of the Swiss cattle population. A dynamic population model can serve as a building block for future disease transmission models and help policy makers in developing strategies regarding animal health, animal welfare, livestock management and productivity. The Swiss cattle population was therefore modelled using a system of ordinary differential equations. The model was stratified by production type (dairy or beef), age and gender (male and female calves: 0-1 year, heifers and young bulls: 1-2 years, cows and bulls: older than 2 years). The simulation of the Swiss cattle population reflects the observed pattern accurately. Parameters were optimized on the basis of the goodness-of-fit (using the Powell algorithm). The fitted rates were compared with calculated rates from the AMD and differed only marginally. This gives confidence in the fitted rates of parameters that are not directly deductible from the AMD (e.g. the proportion of calves that are moved from the dairy system to fattening plants).

An adaptive Newton-method based on a dynamical systems approach

The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations.

Thermal dependence of luminescence lifetimes and radioluminescence in quartz

During time-resolved optical stimulation experiments (TR-OSL), one uses short light pulses to separate the stimulation and emission of luminescence in time. Experimental TR-OSL results show that the luminescence lifetime in quartz of sedimentary origin is independent of annealing temperature below 500 °C, but decreases monotonically thereafter. These results have been interpreted previously empirically on the basis of the existence of two separate luminescence centers LH and LL in quartz, each with its own distinct luminescence lifetime. Additional experimental evidence also supports the presence of a non-luminescent hole reservoir R, which plays a critical role in the predose effect in this material. This paper extends a recently published analytical model for thermal quenching in quartz, to include the two luminescence centers LH and LL, as well as the hole reservoir R. The new extended model involves localized electronic transitions between energy states within the two luminescence centers, and is described by a system of differential equations based on the Mott–Seitz mechanism of thermal quenching. It is shown that by using simplifying physical assumptions, one can obtain analytical solutions for the intensity of the light during a TR-OSL experiment carried out with previously annealed samples. These analytical expressions are found to be in good agreement with the numerical solutions of the equations. The results from the model are shown to be in quantitative agreement with published experimental data for commercially available quartz samples. Specifically the model describes the variation of the luminescence lifetimes with (a) annealing temperatures between room temperature and 900 °C, and (b) with stimulation temperatures between 20 and 200 °C. This paper also reports new radioluminescence (RL) measurements carried out using the same commercially available quartz samples. Gaussian deconvolution of the RL emission spectra was carried out using a total of seven emission bands between 1.5 and 4.5 eV, and the behavior of these bands was examined as a function of the annealing temperature. An emission band at ∼3.44 eV (360 nm) was found to be strongly enhanced when the annealing temperature was increased to 500 °C, and this band underwent a significant reduction in intensity with further increase in temperature. Furthermore, a new emission band at ∼3.73 eV (330 nm) became apparent for annealing temperatures in the range 600–700 °C. These new experimental results are discussed within the context of the model presented in this paper.