Numerical analysis of a new space-time variable fractional order advection-dispersion equation

Many physical processes appear to exhibit fractional order behavior that may vary with time and/or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider a new space–time variable fractional order advection–dispersion equation on a finite domain. The equation is obtained from the standard advection–dispersion equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order α(x)∈(0,1]α(x)∈(0,1], and the first-order and second-order space derivatives by the Riemann–Liouville derivatives of order γ(x,t)∈(0,1]γ(x,t)∈(0,1] and β(x,t)∈(1,2]β(x,t)∈(1,2], respectively. We propose an implicit Euler approximation for the equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Post-transcriptional regulation in the nucleus and cytoplasm: study of mean time to threshold (MTT) and narrow escape problem

Messenger RNAs (mRNAs) can be repressed and degraded by small non-coding RNA molecules. In this paper, we formulate a coarsegrained Markov-chain description of the post-transcriptional regulation of mRNAs by either small interfering RNAs (siRNAs) or microRNAs (miRNAs). We calculate the probability of an mRNA escaping from its domain before it is repressed by siRNAs/miRNAs via cal- culation of the mean time to threshold: when the number of bound siRNAs/miRNAs exceeds a certain threshold value, the mRNA is irreversibly repressed. In some cases,the analysis can be reduced to counting certain paths in a reduced Markov model. We obtain explicit expressions when the small RNA bind irreversibly to the mRNA and we also discuss the reversible binding case. We apply our models to the study of RNA interference in the nucleus, examining the probability of mRNAs escaping via small nuclear pores before being degraded by siRNAs. Using the same modelling framework, we further investigate the effect of small, decoy RNAs (decoys) on the process of post-transcriptional regulation, by studying regulation of the tumor suppressor gene, PTEN : decoys are able to block binding sites on PTEN mRNAs, thereby educing the number of sites available to siRNAs/miRNAs and helping to protect it from repression. We calculate the probability of a cytoplasmic PTEN mRNA translocating to the endoplasmic reticulum before being repressed by miRNAs. We support our results with stochastic simulations

Estimation of the time of a linear trend in monitoring survival time

Change point estimation is recognized as an essential tool of root cause analyses within quality control programs as it enables clinical experts to search for potential causes of change in hospital outcomes more effectively. In this paper, we consider estimation of the time when a linear trend disturbance has occurred in survival time following an in-control clinical intervention in the presence of variable patient mix. To model the process and change point, a linear trend in the survival time of patients who underwent cardiac surgery is formulated using hierarchical models in a Bayesian framework. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. We use Markov Chain Monte Carlo to obtain posterior distributions of the change point parameters including the location and the slope size of the trend and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time cumulative sum control chart (CUSUM) control charts for different trend scenarios. In comparison with the alternatives, step change point model and built-in CUSUM estimator, more accurate and precise estimates are obtained by the proposed Bayesian estimator over linear trends. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

Separable spatiotemporal priors for convex reconstruction of time-varying 3D point clouds

Reconstructing 3D motion data is highly under-constrained due to several common sources of data loss during measurement, such as projection, occlusion, or miscorrespondence. We present a statistical model of 3D motion data, based on the Kronecker structure of the spatiotemporal covariance of natural motion, as a prior on 3D motion. This prior is expressed as a matrix normal distribution, composed of separable and compact row and column covariances. We relate the marginals of the distribution to the shape, trajectory, and shape-trajectory models of prior art. When the marginal shape distribution is not available from training data, we show how placing a hierarchical prior over shapes results in a convex MAP solution in terms of the trace-norm. The matrix normal distribution, fit to a single sequence, outperforms state-of-the-art methods at reconstructing 3D motion data in the presence of significant data loss, while providing covariance estimates of the imputed points.

A directed continuous time random walk model with jump length depending on waiting time

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P(x,t) of finding the walker at position at time is completely determined by the Laplace transform of the probability density function φ(t) of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived.

Real-time wind speed estimation and compensation for improved flight

This paper presents the development and experimental validation of a prototype system for online estimation and compensation of wind disturbances onboard small Rotorcraft unmanned aerial systems (RUAS). The proposed approach consists of integrating a small pitot-static system onboard the vehicle and using simple but effective algorithms for estimating the wind speed in real time. The baseline flight controller has been augmented with a feed-forward term to compensate for these wind disturbances, thereby improving the flight performance of small RUAS in windy conditions. The paper also investigates the use of online airspeed measurements in a closed-loop for controlling the RUAS forward motion without the aid of a global positioning system (GPS). The results of more than 80 flights with a RUAS confirm the validity of our approach.

Factors influencing first-time mothers’ introduction of complementary foods: A qualitative exploration

Background Optimal infant nutrition comprises exclusive breastfeeding, with complementary foods introduced from six months of age. How parents make decisions regarding this is poorly studied. This study begins to address the dearth of research into the decision-making processes used by first-time mothers relating to the introduction of complementary foods. Methods This qualitative explorative study was conducted using interviews (13) and focus groups (3). A semi-structured interview guide based on the Theory of Planned Behaviour (TPB). The TPB, a well-validated decision-making model, identifies the key determinants of a behaviour through behavioural beliefs, subjective norms, and perceived behavioural control over the behaviour. It is purported that these beliefs predict behavioural intention to perform the behaviour, and performing the behaviour. A purposive, convenience, sample of 21 metropolitan parents recruited through advertising at local playgroups and childcare centres, and electronically through the University community email list self-selected to participate. Data were analysed thematically within the theoretical constructs: behavioural beliefs, subjective norms and perceived behavioural control. Data relating to sources of information about the introduction of complementary foods were also collected. Results Overall, first-time mothers found that waiting until six months was challenging despite knowledge of the WHO recommendations and an initial desire to comply with this guideline. Beliefs that complementary foods would assist the infants' weight gain, sleeping patterns and enjoyment at meal times were identified. Barriers preventing parents complying with the recommendations included subjective and group norms, peer influences, infant cues indicating early readiness and food labelling inconsistencies. The most valued information source was from peers who had recently introduced complementary foods. Conclusions First-time mothers in this study did not demonstrate a good understanding of the rationale behind the WHO recommendations, nor did they understand fully the signs of readiness of infants to commence solid foods. Factors that assisted waiting until six months were a trusting relationship with a health professional whose practice and advice was consistent with the recommendations and/or when their infant was developmentally ready for complementary foods at six months and accepted them with ease and enthusiasm. Barriers preventing parents complying with the recommendations included subjective and group norms, peer influences, infant cues indicating early readiness and food labelling inconsistencies.

Time, place and space – student group collaboration using Google Drive

Virtual working environments are intrinsic to the contemporary workplace and collaborative skills are a vital graduate capability. To develop students’ collaborative skills, first year medical laboratory science students undertake a group poster project, based on a blended learning model. Learning is scaffolded in lectures, workshops in collaborative learning spaces, practitioner mentoring sessions, and online resources. Google Drive provides an online collaborative space for students to realise tangible outcomes from this learning. A Google Drive document is created for each group and shared with members. In this space, students assign tasks and plan workflow, share research, progressively develop poster content, reflect and comment on peer contributions and use the messaging functions to ‘talk’ to group members. This provides a readily accessible, transparent record of group work, crucial in peer assessment, and a communication channel for group members and the lecturer, who can support groups if required. This knowledge creation space also augments productivity and effectiveness of face-to-face collaboration. As members are randomly allocated to groups and are often of diverse backgrounds and unknown to each other, resilience is built as students navigate the uncertainties and complexities of group dynamics, learning to focus on the goal of the team task as they constructively and professionally engage in team dialogue. Students are responsible and accountable for individual and group work. The use of Google Drive was evaluated in a survey including Likert scale and open ended qualitative questions. Statistical analysis was carried out. Results show students (79%) valued the inclusion of online space in collaborative work and highly appreciated (78%) the flexibility provided by Google Drive, while recognising the need for improved notification functionality. Teaching staff recognised the advantages in monitoring and moderating collaborative group work, and the transformational progression in student collaborative as well as technological skill acquisition, including professional dialogue.

Unsteady-Flow Of A Viscous-Fluid Between 2 Parallel Disks With A Time-Varying Gap Width And A Magnetic-Field

The unsteady incompressible viscous fluid flow between two parallel infinite disks which are located at a distance h(t*) at time t* has been studied. The upper disk moves towards the lower disk with velocity h'(t*). The lower disk is porous and rotates with angular velocity Omega(t*). A magnetic field B(t*) is applied perpendicular to the two disks. It has been found that the governing Navier-Stokes equations reduce to a set of ordinary differential equations if h(t*), a(t*) and B(t*) vary with time t* in a particular manner, i.e. h(t*) = H(1 - alpha t*)(1/2), Omega(t*) = Omega(0)(1 - alpha t*)(-1), B(t*) = B-0(1 - alpha t*)(-1/2). These ordinary differential equations have been solved numerically using a shooting method. For small Reynolds numbers, analytical solutions have been obtained using a regular perturbation technique. The effects of squeeze Reynolds numbers, Hartmann number and rotation of the disk on the flow pattern, normal force or load and torque have been studied in detail

Leveraging coherent distributed space-time codes for noncoherent communication in relay networks via training

For point to point multiple input multiple output systems, Dayal-Brehler-Varanasi have proved that training codes achieve the same diversity order as that of the underlying coherent space time block code (STBC) if a simple minimum mean squared error estimate of the channel formed using the training part is employed for coherent detection of the underlying STBC. In this letter, a similar strategy involving a combination of training, channel estimation and detection in conjunction with existing coherent distributed STBCs is proposed for noncoherent communication in Amplify-and-Forward (AF) relay networks. Simulation results show that the proposed simple strategy outperforms distributed differential space-time coding for AF relay networks. Finally, the proposed strategy is extended to asynchronous relay networks using orthogonal frequency division multiplexing.

Time-Resolved Resonance Raman Spectroscopic Studies on the Radical Anions of Menaquinone and Naphthoquinone

Quinones and their radical ion intermediates have been much studied by vibrational spectroscopy to understand their structure-function relationships in various biological processes. In this paper, we present a comprehensive analysis of vibrational spectra in the structure-sensitive region of both the naphthoquinone (NQ) and 2-methyl-1,4-naphthoquinone (MQ, menaquinone) radical anions using time-resolved resonance Raman and ab initio studies. Specific vibrational mode assignments have been made to all the vibrational frequencies recorded in the experiment. It is observed that the carbonyl and C-C stretching frequencies show considerable coupling in NQ and MQ radical anions. Further, the asymmetric substitution present in MQ with respect to NQ shows important signatures in the radical anion spectrum. It is concluded that assignments of vibrational frequencies of asymmetrically substituted quinones must take into consideration the influence of asymmetry on structure and reactivity.

Time-temperature histories of spherical food products during bulk forced-air precooling

A general mathematical model for forced air precooling of spherical food products in bulk is developed. The food products are arranged inline to form a rectangular parallelepiped. Chilled air is blown along the height of the package. The governing equations for the transient two-dimensional conduction with internal heat generation in the product, simultaneous heat and mass transfer at the product-air interface and one-dimensional transient energy and species conservation equations for the moist air are solved numerically using finite difference methods. Results are presented in the form of time-temperature histories. Experiments are conducted with model foods in a laboratory scale air precooling tunnel. The agreement between the theoretical and experimental results is found to be good. In general, a single product analysis fails to predict the precooling characteristics of bulk loads of food products. In the range of values investigated, the respiration heat is found to have a negligible effect.

In situ reaction furnace for real-time XRD studies

The new furnace at the Materials Characterization by X-ray Diffraction beamline at Elettra has been designed for powder diffraction measurements at high temperature (up to 1373 K at the present state). Around the measurement region the geometry of the radiative heating element assures a negligible temperature gradient along the capillary and can accommodate either powder samples in capillary or small flat samples. A double capillary holder allows flow-through of gas in the inner sample capillary while the outer one serves as the reaction chamber. The furnace is coupled to a translating curved imaging-plate detector, allowing the collection of diffraction patterns up to 2[theta] [asymptotically equal to] 130°.

Breastfeeding duration and authoritative feeding practices in first-time mothers

Background Longer breastfeeding duration appears to have a protective effect against childhood obesity. This effect may be partially mediated by maternal feeding practices during the first years of life. However, the few studies that have examined links between breastfeeding duration and subsequent feeding practices have yielded conflicting results. Objective Using a large sample of first-time mothers and a newly validated, comprehensive measure of maternal feeding (the Feeding Practices and Structure Questionnaire1), this study examined associations between breastfeeding duration and maternal feeding practices at child age 24 months. Methods Mothers (n = 458) enrolled in the NOURISH trial2 provided data on breastfeeding at child age 4, 14 and 24 months, and on feeding practices at 24 months. Structural Equation Modelling was used to examine associations between breastfeeding duration and five non-responsive and four structure-related ‘authoritative’ feeding practices, adjusting for a range of maternal and child characteristics. Results The model showed acceptable fit (χ2/df = 1.68; RMSEA = .04, CFI = .91 and TLI = .89) and longer breastfeeding duration was negatively associated with four out of five non-responsive feeding practices and positively associated with three out of four structure-related feeding practices. Overall, these results suggest that mothers who breastfeed longer reported using more appropriate feeding practices. Conclusion These data demonstrate an association between longer breastfeeding duration and authoritative feeding practices characterised by responsiveness and structure, which may partly account for the apparent protective effect of breastfeeding on childhood obesity.

Enhanced sensitivity in detection of Kerr rotation by double modulation and time averaging based on Allan variance

Experiments in spintronics necessarily involve the detection of spin polarization. The sensitivity of this detection becomes an important factor to consider when extending the low temperature studies on semiconductor spintronic devices to room temperature, where the spin signal is weaker. In pump-probe experiments, which optically inject and detect spins, the sensitivity is often improved by using a photoelastic modulator (PEM) for lock-in detection. However, spurious signals can arise if diode lasers are used as optical sources in such experiments, along with a PEM. In this work, we eliminated the spurious electromagnetic coupling of the PEM onto the probe diode laser, by the double modulation technique. We also developed a test for spurious modulated interference in the pump-probe signal, due to the PEM. Besides, an order of magnitude enhancement in the sensitivity of detection of spin polarization by Kerr rotation, to 3x10(-8) rad was obtained by using the concept of Allan variance to optimally average the time series data over a period of 416 s. With these improvements, we are able to experimentally demonstrate at room temperature, photoinduced steady-state spin polarization in bulk GaAs. Thus, the advances reported here facilitate the use of diode lasers with a PEM for sensitive pump-probe experiments. They also constitute a step toward detection of spin-injection in Si at room temperature.