Stochastic simulation for spatial modelling of dynamic process in a living cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

Parallel implementation of stochastic simulation for large scale cellular processes

Experimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. In recent years stochastic models have been used successfully for studying noise in biological pathways, and stochastic modelling of biological systems has become a very important research field in computational biology. One of the challenge problems in this field is the reduction of the huge computing time in stochastic simulations. Based on the system of the mitogen-activated protein kinase cascade that is activated by epidermal growth factor, this work give a parallel implementation by using OpenMP and parallelism across the simulation. Special attention is paid to the independence of the generated random numbers in parallel computing, that is a key criterion for the success of stochastic simulations. Numerical results indicate that parallel computers can be used as an efficient tool for simulating the dynamics of large-scale genetic regulatory networks and cellular processes

Heat-producing crust regulation of subsurface temperatures : a stochastic model re-evaluation of the geothermal potential in western Queensland, Australia

A large subsurface, elevated temperature anomaly is well documented in Central Australia. High Heat Producing Granites (HHPGs) intersected by drilling at Innamincka are often assumed to be the dominant cause of the elevated subsurface temperatures, although their presence in other parts of the temperature anomaly has not been confirmed. Geological controls on the temperature anomaly remain poorly understood. Additionally, methods previously used to predict temperature at 5 km depth in this area are simplistic and possibly do not give an accurate representation of the true distribution and magnitude of the temperature anomaly. Here we re-evaluate the geological controls on geothermal potential in the Queensland part of the temperature anomaly using a stochastic thermal model. The results illustrate that the temperature distribution is most sensitive to the thermal conductivity structure of the top 5 km. Furthermore, the results indicate the presence of silicic crust enriched in heat producing elements between and 40 km.

Coherent design methodology using modelling, simulation and optimisation

There is an increasing demand for optimising complete systems and the devices within that system, including capturing the interactions between the various multi-disciplinary (MD) components involved. Furthermore confidence in robust solutions is esential. As a consequence the computational cost rapidly increases and in many cases becomes infeasible to perform such conceptual designs. A coherent design methodology is proposed, where the aim is to improve the design process by effectively exploiting the potential of computational synthesis, search and optimisation and conventional simulation, with a reduction of the computational cost. This optimization framework consists of a hybrid optimization algorithm to handles multi-fidelity simulations. Simultaneously and in order to handles uncertainty without recasting the model and at affordable computational cost, a stochastic modelling method known as non-intrusive polynomial chaos is introduced. The effectiveness of the design methodology is demonstrated with the optimisation of a submarine propulsion system.

Recovery or decline of the Northwestern Black Sea: A societal choice revealed by socio-ecological modelling

During recent decades anthropogenic activities have dramatically impacted the Black Sea ecosystem. High levels of riverine nutrient input during the 1970s and 1980s caused eutrophic conditions including intense algal blooms resulting in hypoxia and the subsequent collapse of benthic habitats on the northwestern shelf. Intense fishing pressure also depleted stocks of many apex predators, contributing to an increase in planktivorous fish that are now the focus of fishing efforts. Additionally, the Black Sea's ecosystem changed even further with the introduction of exotic species. Economic collapse of the surrounding socialist republics in the early 1990s resulted in decreased nutrient loading which has allowed the Black Sea ecosystem to start to recover, but under rapidly changing economic and political conditions, future recovery is uncertain. In this study we use a multidisciplinary approach to integrate information from socio-economic and ecological systems to model the effects of future development scenarios on the marine environment of the northwestern Black Sea shelf. The Driver–Pressure–State-Impact-Response framework was used to construct conceptual models, explicitly mapping impacts of socio-economic Drivers on the marine ecosystem. Bayesian belief networks (BBNs), a stochastic modelling technique, were used to quantify these causal relationships, operationalise models and assess the effects of alternative development paths on the Black Sea ecosystem. BBNs use probabilistic dependencies as a common metric, allowing the integration of quantitative and qualitative information. Under the Baseline Scenario, recovery of the Black Sea appears tenuous as the exploitation of environmental resources (agriculture, fishing and shipping) increases with continued economic development of post-Soviet countries. This results in the loss of wetlands through drainage and reclamation. Water transparency decreases as phytoplankton bloom and this deterioration in water quality leads to the degradation of coastal plant communities (Cystoseira, seagrass) and also Phyllophora habitat on the shelf. Decomposition of benthic plants results in hypoxia killing flora and fauna associated with these habitats. Ecological pressure from these factors along with constant levels of fishing activity results in target stocks remaining depleted. Of the four Alternative Scenarios, two show improvements on the Baseline ecosystem condition, with improved waste water treatment and reduced fishing pressure, while the other two show a worsening, due to increased natural resource exploitation leading to rapid reversal of any recent ecosystem recovery. From this we conclude that variations in economic policy have significant consequences for the health of the Black Sea, and ecosystem recovery is directly linked to social–economic choices.

Stochastic analysis of seepage under water-retaining structures

This paper investigated the problem of confined flow under dams and water retaining structuresusing stochastic modelling. The approach advocated in the study combined a finite elementsmethod based on the equation governing the dynamics of incompressible fluid flow through aporous medium with a random field generator that generates random hydraulic conductivity basedon lognormal probability distribution. The resulting model was then used to analyse confined flowunder a hydraulic structure. Cases for a structure provided with cutoff wall and when the wall didnot exist were both tested. Various statistical parameters that reflected different degrees ofheterogeneity were examined and the changes in the mean seepage flow, the mean uplift forceand the mean exit gradient observed under the structure were analysed. Results reveal that underheterogeneous conditions, the reduction made by the sheetpile in the uplift force and exit hydraulicgradient may be underestimated when deterministic solutions are used.

Stochastic Inventory with/without Service Time, Reneging and Retrial of Customers

This thesis Entitled Stochastic modelling and analysis.This thesis is divided into six chapters including this introductory chapter. In second chapter, we consider an (s,S) inventory model with service, reneging of customers and finite shortage of items.In the third chapter, we consider an (s,S) inventoiy system with retrial of customers. Arrival of customers forms a Poisson process with rate. When the inventory level depletes to s due to demands, an order for replenishment is placed.In Chapter 4, we analyze and compare three (s,S) inventory systems with positive service time and retrial of customers. In all these systems, arrivals of customers form a Poisson process and service times are exponentially distributed. In chapter 5, we analyze and compare three production inventory systems with positive service time and retrial of customers. In all these systems, arrivals of customers form a Poisson process and service times are exponentially distributed.In chapter 6, we consider a PH /PH /l inventory model with reneging of customers and finite shortage of items.

Symmetry in biology: from genetic code to stochastic gene regulation

Mathematical models, as instruments for understanding the workings of nature, are a traditional tool of physics, but they also play an ever increasing role in biology - in the description of fundamental processes as well as that of complex systems. In this review, the authors discuss two examples of the application of group theoretical methods, which constitute the mathematical discipline for a quantitative description of the idea of symmetry, to genetics. The first one appears, in the form of a pseudo-orthogonal (Lorentz like) symmetry, in the stochastic modelling of what may be regarded as the simplest possible example of a genetic network and, hopefully, a building block for more complicated ones: a single self-interacting or externally regulated gene with only two possible states: ` on` and ` off`. The second is the algebraic approach to the evolution of the genetic code, according to which the current code results from a dynamical symmetry breaking process, starting out from an initial state of complete symmetry and ending in the presently observed final state of low symmetry. In both cases, symmetry plays a decisive role: in the first, it is a characteristic feature of the dynamics of the gene switch and its decay to equilibrium, whereas in the second, it provides the guidelines for the evolution of the coding rules.

Parallel implementation of stochastic simulation for large scale cellular processes

Experimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. In recent years stochastic models have been used successfully for studying noise in biological pathways, and stochastic modelling of biological systems has become a very important research field in computational biology. One of the challenge problems in this field is the reduction of the huge computing time in stochastic simulations. Based on the system of the mitogen-activated protein kinase cascade that is activated by epidermal growth factor, this work give a parallel implementation by using OpenMP and parallelism across the simulation. Special attention is paid to the independence of the generated random numbers in parallel computing, that is a key criterion for the success of stochastic simulations. Numerical results indicate that parallel computers can be used as an efficient tool for simulating the dynamics of large-scale genetic regulatory networks and cellular processes

Analyzing interrelated stochastic trend and seasonality on the example of energy trading data

The correct modelling of long- and short-term seasonality is a very interesting issue. The choice between the deterministic and stochastic modelling of trend and seasonality and their implications are as relevant as the case of deterministic and stochastic trends itself. The study considers the special case when the stochastic trend and seasonality do not evolve independently and the usual differencing filters do not apply. The results are applied to the day-ahead (spot) trading data of some main European energy exchanges (power and natural gas).

Analyzing interrelated stochastic trend and seasonality on the example of energy trading data

The correct modelling of long- and short-term seasonality is a very interesting issue. The choice between the deterministic and stochastic modelling of trend and seasonality and their implications are as relevant as the case of deterministic and stochastic trends itself. The study considers the special case when the stochastic trend and seasonality do not evolve independently and the usual differencing filters do not apply. The results are applied to the day-ahead (spot) trading data of some main European energy exchanges (power and natural gas).

Real-time assessment of GNSS observation noise with single receivers

Stochastic modelling is critical in GNSS data processing. Currently, GNSS data processing commonly relies on the empirical stochastic model which may not reflect the actual data quality or noise characteristics. This paper examines the real-time GNSS observation noise estimation methods enabling to determine the observation variance from single receiver data stream. The methods involve three steps: forming linear combination, handling the ionosphere and ambiguity bias and variance estimation. Two distinguished ways are applied to overcome the ionosphere and ambiguity biases, known as the time differenced method and polynomial prediction method respectively. The real time variance estimation methods are compared with the zero-baseline and short-baseline methods. The proposed method only requires single receiver observation, thus applicable to both differenced and un-differenced data processing modes. However, the methods may be subject to the normal ionosphere conditions and low autocorrelation GNSS receivers. Experimental results also indicate the proposed method can result on more realistic parameter precision.

Estimate of Lagrangian integral scales in shallow tidal water using high resolution GPS-tracked drifters

In estuaries and natural water channels, the estimate of velocity and dispersion coefficients is critical to the knowledge of scalar transport and mixing. This estimate is rarely available experimentally at sub-tidal time scale in shallow water channels where high frequency is required to capture its spatio-temporal variation. This study estimates Lagrangian integral scales and autocorrelation curves, which are key parameters for obtaining velocity fluctuations and dispersion coefficients, and their spatio-temporal variability from deployments of Lagrangian drifters sampled at 10 Hz for a 4-hour period. The power spectral densities of the velocities between 0.0001 and 0.8 Hz were well fitted with a slope of 5/3 predicted by Kolmogorov’s similarity hypothesis within the inertial subrange, and were similar to the Eulerian power spectral previously observed within the estuary. The result showed that large velocity fluctuations determine the magnitude of the integral time scale, TL. Overlapping of short segments improved the stability of the estimate of TL by taking advantage of the redundant data included in the autocorrelation function. The integral time scales were about 20 s and varied by up to a factor of 8. These results are essential inputs for spatial binning of velocities, Lagrangian stochastic modelling and single particle analysis of the tidal estuary.

Heat-producing element enrichment in granitic rocks, the role of crustal composition and evolution

This study greatly enhanced our knowledge of the potential for geothermal energy development in Queensland as a viable clean energy source in the coming decades. Key outcomes of the project were understanding the first-order controls on the concentration of the heat-producing elements: uranium, thorium and potassium in granitic rocks, and constraining where rocks with the greatest heat-producing potential lie at depth in Queensland. Importantly, new temperature and heat flow maps for southwest Queensland were developed that will greatly assist future exploration efforts.