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.

Mixed convection laminar flow along a horizontal plate subject to streamwise sinusoidal surface temperature

Mixed convection of a two-dimensional laminar incompressible flow along a horizontal flat plate with streamwise sinusoidal surface temperature has been numerically investigated for different values of Rayleigh number and Reynolds number for constant values of Prandtl number, amplitude and frequency of periodic temperature. The numerical scheme is based on the finite element method adapted to rectangular non-uniform mesh elements by a non-linear parametric solution algorithm. The fluid considered in this study is air. The results are obtained for the Rayleigh number and Reynolds number ranging from 102 to 104 and 1 to 100, respectively, with constant physical properties for the fluid medium considered. Velocity and temperature profiles, streamlines, isotherms, and average Nusselt numbers are presented to observe the effect of the investigating parameters on fluid flow and heat transfer characteristics. The present results show that the convective phenomena are greatly influenced by the variation of Rayleigh numbers and Reynolds number.

State of Origin : Queensland Crown Leasehold - lessons from New South Wales

Throughout Australia freehold land interests are protected by statutory schemes which grant indefeasibility of title to registered interests. Queensland freehold land interests are protected by Torrens system established by the Land Title Act 1994. However, no such protection exists for Crown land interests. The extent of Queensland occupied under some form of Crown tenure, in excess of 70%, means that Queensland Crown land users are disadvantaged when compared to freehold land users. This article examines the role indefeasibility of title has in protecting interests in Crown land. A comparative analysis is undertaken between Queensland and New South Wales land management frameworks to determine whether interests in crown land are adequately protected in Queensland.

MHD natural convection flow from an isothermal horizontal circular cylinder under consideration of temperature dependent viscosity

Magnetohydrodynamic (MHD) natural convection laminar flow from an iso-thermal horizontal circular cylinder immersed in a fluid with viscosity proportional to a linear function of temperature will be discussed with numerical simulations. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equa-tions are reduced to convenient form, which are solved numerically by two very efficient methods, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) Direct numerical scheme. Numerical results are presented by velocity and temperature distributions of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin-friction coefficient and the local Nusselt number for a wide range of magnetohydrodynamic parameter, viscosity-variation parameter and viscous dissipation parameter. MHD flow in this geometry with temperature dependent viscosity is absent in the literature. The results obtained from the numerical simulations have been veri-fied by two methodologies.

Adverse possession and Crown Leasehold in Queensland

The decision of Eckford v Stanbroke Pastoral Co Pty Ltd [2012] QSC 48 ,although a decision refusing summary judgement raises a very important question of the ability to claim adverse possession of a pastoral lease issued in 1956 under the Land Act 1962 (Queensland).Division 5 of Part 6 of the Land Title Act 1994 (Qld) which guarantees registered freehold title expressly deals with the right of adverse possession however, there is no such provision in the present Land Act 1994 unlike s 170 of the Crown Lands Act 1989(NSW) which expressly precludes claims for adverse possession of specified non freehold land. There is no mention of adverse possession in any version of the Queensland Land Acts and only s 6(4) of the Limitation of Actions Act 1974 makes it clear that “the right, title or interest of the Crown” in or to any land is not affected by any adverse possessor.It is against the background that the Court considered the right of an adverse possessor to a Crown lease.

Mixed convection over a horizontal plate with streamwise non-uniform surface temperature distribution

Numerical investigation on mixed convection of a two-dimensional incompressible laminar flow over a horizontal flat plate with streamwise sinusoidal distribution of surface temperature has been performed for different values of Rayleigh number, Reynolds number and frequency of periodic temperature for constant Prandtl number and amplitude of periodic temperature. Finite element method adapted to rectangular non-uniform mesh elements by a non-linear parametric solution algorithm basis numerical scheme has been employed. The investigating parameters are the Rayleigh number, the Reynolds number and frequency of periodic temperature. The effect of variation of individual investigating parameters on mixed convection flow characteristics has been studied to observe the hydrodynamic and thermal behavior for while keeping the other parameters constant. The fluid considered in this study is air with Prandtl number 0.72. The results are obtained for the Rayleigh number range of 102 to 104, Reynolds number ranging from 1 to 100 and the frequency of periodic temperature from 1 to 5. Isotherms, streamlines, average and local Nusselt numbers are presented to show the effect of the different values of aforementioned investigating parameters on fluid flow and heat transfer.

Applicability of the polysulphone horizontal calibration to differently inclined dosimeters

Polysulphone (PS) dosimetry has been a widely used technique for more than 30 years to quantify the erythemally effective UV dose received by anatomic sites (personal exposure). The calibration of PS dosimeters is an important issue as their spectral response is different from the erythemal action spectrum. It is performed exposing a set of PS dosimeters on a horizontal plane and measuring the UV doses received by dosimeters using calibrated spectroradiometers or radiometers. In this study, data collected during PS field campaigns (from 2004 to 2006), using horizontal and differently inclined dosimeters, were analyzed to provide some considerations on the transfer of the horizontal calibration to differently inclined dosimeters, as anatomic sites usually are. The role of sky conditions, of the angle of incidence between the sun and the normal to the slope, and of the type of surrounding surface on the calibration were investigated. It was concluded that PS horizontal calibrations apply to differently inclined dosimeters for incidence angles up to approximately 70 degrees and for surfaces excluding ones with high albedo. Caution should be used in the application of horizontal calibrations for cases of high-incidence angle and/or high albedo surfaces.

Non-Newtonian natural convection flow along an isothermal horizontal circular cylinder using modified power-law model

Laminar two-dimensional natural convection boundary-layer flow of non-Newtonian fluids along an isothermal horizontal circular cylinder has been studied using a modified power-law viscosity model. In this model, there are no unrealistic limits of zero or infinite viscosity. Therefore, the boundary-layer equations can be solved numerically by using marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning as well as shear thickening fluids in terms of the fluid velocity and temperature distributions, shear stresses and rate of heat transfer in terms of the local skin-friction and local Nusselt number respectively.

A pre-treatment verification tool for IMRT based on EPID measurements and a GEANT4 back projection application

The aim of this work is to develop software that is capable of back projecting primary fluence images obtained from EPID measurements through phantom and patient geometries in order to calculate 3D dose distributions. In the first instance, we aim to develop a tool for pretreatment verification in IMRT. In our approach, a Geant4 application is used to back project primary fluence values from each EPID pixel towards the source. Each beam is considered to be polyenergetic, with a spectrum obtained from Monte Carlo calculations for the LINAC in question. At each step of the ray tracing process, the energy differential fluence is corrected for attenuation and beam divergence. Subsequently, the TERMA is calculated and accumulated to an energy differential 3D TERMA distribution. This distribution is then convolved with monoenergetic point spread kernels, thus generating energy differential 3D dose distributions. The resulting dose distributions are accumulated to yield the total dose distribution, which can then be used for pre-treatment verification of IMRT plans. Preliminary results were obtained for a test EPID image comprised of 100 9 100 pixels of unity fluence. Back projection of this field into a 30 cm9 30 cm 9 30 cm water phantom was performed, with TERMA distributions obtained in approximately 10 min (running on a single core of a 3 GHz processor). Point spread kernels for monoenergetic photons in water were calculated using a separate Geant4 application. Following convolution and summation, the resulting 3D dose distribution produced familiar build-up and penumbral features. In order to validate the dose model we will use EPID images recorded without any attenuating material in the beam for a number of MLC defined square fields. The dose distributions in water will be calculated and compared to TPS predictions.

Towards a model of spray-canopy interactions : interception, shatter, bounce and retention of droplets on horizontal leaves

Pesticides used in agricultural systems must be applied in economically viable and environmentally sensitive ways, and this often requires expensive field trials on spray deposition and retention by plant foliage. Computational models to describe whether a spray droplet sticks (adheres), bounces or shatters on impact, and if any rebounding parent or shatter daughter droplets are recaptured, would provide an estimate of spray retention and thereby act as a useful guide prior to any field trials. Parameter-driven interactive software has been implemented to enable the end-user to study and visualise droplet interception and impaction on a single, horizontal leaf. Living chenopodium, wheat and cotton leaves have been scanned to capture the surface topography and realistic virtual leaf surface models have been generated. Individual leaf models have then been subjected to virtual spray droplets and predictions made of droplet interception with the virtual plant leaf. Thereafter, the impaction behaviour of the droplets and the subsequent behaviour of any daughter droplets, up until re-capture, are simulated to give the predicted total spray retention by the leaf. A series of critical thresholds for the stick, bounce, and shatter elements in the impaction process have been developed for different combinations of formulation, droplet size and velocity, and leaf surface characteristics to provide this output. The results show that droplet properties, spray formulations and leaf surface characteristics all influence the predicted amount of spray retained on a horizontal leaf surface. Overall the predicted spray retention increases as formulation surface tension, static contact angle, droplet size and velocity decreases. Predicted retention on cotton is much higher than on chenopodium. The average predicted retention on a single horizontal leaf across all droplet size, velocity and formulations scenarios tested, is 18, 30 and 85% for chenopodium, wheat and cotton, respectively.

Predator Crown-of-Thorns Starfish (Acanthaster planci) Outbreak, Mass Mortality of Corals, and Cascading Effects on Reef Fish and Benthic Communities

Outbreaks of the coral-killing seastar Acanthaster planci are intense disturbances that can decimate coral reefs. These events consist of the emergence of large swarms of the predatory seastar that feed on reef-building corals, often leading to widespread devastation of coral populations. While cyclic occurrences of such outbreaks are reported from many tropical reefs throughout the Indo-Pacific, their causes are hotly debated, and the spatio-temporal dynamics of the outbreaks and impacts to reef communities remain unclear. Based on observations of a recent event around the island of Moorea, French Polynesia, we show that Acanthaster outbreaks are methodic, slow-paced, and diffusive biological disturbances. Acanthaster outbreaks on insular reef systems like Moorea's appear to originate from restricted areas confined to the ocean-exposed base of reefs. Elevated Acanthaster densities then progressively spread to adjacent and shallower locations by migrations of seastars in aggregative waves that eventually affect the entire reef system. The directional migration across reefs appears to be a search for prey as reef portions affected by dense seastar aggregations are rapidly depleted of living corals and subsequently left behind. Coral decline on impacted reefs occurs by the sequential consumption of species in the order of Acanthaster feeding preferences. Acanthaster outbreaks thus result in predictable alteration of the coral community structure. The outbreak we report here is among the most intense and devastating ever reported. Using a hierarchical, multi-scale approach, we also show how sessile benthic communities and resident coral-feeding fish assemblages were subsequently affected by the decline of corals. By elucidating the processes involved in an Acanthaster outbreak, our study contributes to comprehending this widespread disturbance and should thus benefit targeted management actions for coral reef ecosystems.

Pupil shape as viewed along the horizontal visual field

Purpose: Changes in pupil size and shape are relevant for peripheral imagery by affecting aberrations and how much light enters and/or exits the eye. The purpose of this study is to model the pattern of pupil shape across the complete horizontal visual field and to show how the pattern is influenced by refractive error. Methods: Right eyes of thirty participants were dilated with 1% cyclopentolate and images were captured using a modified COAS-HD aberrometer alignment camera along the horizontal visual field to ±90°. A two lens relay system enabled fixation at targets mounted on the wall 3m from the eye. Participants placed their heads on a rotatable chin rest and eye rotations were kept to less than 30°. Best-fit elliptical dimensions of pupils were determined. Ratios of minimum to maximum axis diameters were plotted against visual field angle. Results: Participants’ data were well fitted by cosine functions, with maxima at (–)1° to (–)9° in the temporal visual field and widths 9% to 15% greater than predicted by the cosine of the field angle . Mean functions were 0.99cos[( + 5.3)/1.121], R2 0.99 for the whole group and 0.99cos[( + 6.2)/1.126], R2 0.99 for the 13 emmetropes. The function peak became less temporal, and the width became smaller, with increase in myopia. Conclusion: Off-axis pupil shape changes are well described by a cosine function which is both decentered by a few degrees and flatter by about 12% than the cosine of the viewing angle, with minor influences of refraction.

Advantages of exploiting projection structure for segmenting dense 3D point clouds

Timely and comprehensive scene segmentation is often a critical step for many high level mobile robotic tasks. This paper examines a projected area based neighbourhood lookup approach with the motivation towards faster unsupervised segmentation of dense 3D point clouds. The proposed algorithm exploits the projection geometry of a depth camera to find nearest neighbours which is time independent of the input data size. Points near depth discontinuations are also detected to reinforce object boundaries in the clustering process. The search method presented is evaluated using both indoor and outdoor dense depth images and demonstrates significant improvements in speed and precision compared to the commonly used Fast library for approximate nearest neighbour (FLANN) [Muja and Lowe, 2009].