Efficient simulation of stochastic chemical kinetics with the Stochastic Bulirsch-Stoer extrapolation method

Background Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities. Results In this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler τ-leap, as well as two more recent τ-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie’s stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments. Conclusions The Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations.

FlexAnalytics: A flexible data analytics framework for big data applications with I/O performance improvement

Increasingly larger scale applications are generating an unprecedented amount of data. However, the increasing gap between computation and I/O capacity on High End Computing machines makes a severe bottleneck for data analysis. Instead of moving data from its source to the output storage, in-situ analytics processes output data while simulations are running. However, in-situ data analysis incurs much more computing resource contentions with simulations. Such contentions severely damage the performance of simulation on HPE. Since different data processing strategies have different impact on performance and cost, there is a consequent need for flexibility in the location of data analytics. In this paper, we explore and analyze several potential data-analytics placement strategies along the I/O path. To find out the best strategy to reduce data movement in given situation, we propose a flexible data analytics (FlexAnalytics) framework in this paper. Based on this framework, a FlexAnalytics prototype system is developed for analytics placement. FlexAnalytics system enhances the scalability and flexibility of current I/O stack on HEC platforms and is useful for data pre-processing, runtime data analysis and visualization, as well as for large-scale data transfer. Two use cases – scientific data compression and remote visualization – have been applied in the study to verify the performance of FlexAnalytics. Experimental results demonstrate that FlexAnalytics framework increases data transition bandwidth and improves the application end-to-end transfer performance.

Microscopic cooperative traffic flow: Calibration and simulation based on a next generation simulation dataset

The deployment of new emerging technologies, such as cooperative systems, allows the traffic community to foresee relevant improvements in terms of traffic safety and efficiency. Autonomous vehicles are able to share information about the local traffic state in real time, which could result in a better reaction to the mechanism of traffic jam formation. An upstream single-hop radio broadcast network can improve the perception of each cooperative driver within a specific radio range and hence the traffic stability. The impact of vehicle to vehicle cooperation on the onset of traffic congestion is investigated analytically and through simulation. A next generation simulation field dataset is used to calibrate the full velocity difference car-following model, and the MOBIL lane-changing model is implemented. The robustness of the calibration as well as the heterogeneity of the drivers is discussed. Assuming that congestion can be triggered either by the heterogeneity of drivers' behaviours or abnormal lane-changing behaviours, the calibrated car-following model is used to assess the impact of a microscopic cooperative law on egoistic lane-changing behaviours. The cooperative law can help reduce and delay traffic congestion and can have a positive effect on safety indicators.

A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems

In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multidimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel mode

Predicting tours and probabilistic simulation for BKZ lattice reduction algorithm

We investigate the terminating concept of BKZ reduction first introduced by Hanrot et al. [Crypto'11] and make extensive experiments to predict the number of tours necessary to obtain the best possible trade off between reduction time and quality. Then, we improve Buchmann and Lindner's result [Indocrypt'09] to find sub-lattice collision in SWIFFT. We illustrate that further improvement in time is possible through special setting of SWIFFT parameters and also through the combination of different reduction parameters adaptively. Our contribution also include a probabilistic simulation approach top-up deterministic simulation described by Chen and Nguyen [Asiacrypt'11] that can able to predict the Gram-Schmidt norms more accurately for large block sizes.

Simulation of pesticide behavior in a paddy block by a pesticide fate and transport model

A simulation model (PCPF-B) was developed based on the PCPF-1 model to predict the runoff of pesticides from paddy plots to a drainage canal in a paddy block. The block-scale model now comprises three modules: (1) a module for pesticide application, (2) a module for pesticide behavior in paddy fields, and (3) a module for pesticide concentration in the drainage canal. The PCPF-B model was first evaluated by published data in a single plot and then was applied to predict the concentration of bensulfuron-methyl in one paddy block in the Sakura river basin, Ibaraki, Japan, where a detailed field survey was conducted. The PCPF-B model simulated well the behavior of bensulfuron-methyl in individual paddy plots. It also reflected the runoff pattern of bensulfuron-methyl at the block outlet, although overestimation of bensulfuronmethyl concentrations occurred due to uncertainty in water balance estimation. Application of water management practice such as water-holding period and seepage control also affected the performance of the model. A probabilistic approach may be necessary for a comprehensive risk assessment in large-scale paddy areas.

Prediction of the fate of oxytetracycline and oxolinic acid in a fish pond using simulation model: A preliminary study

The fate of two popular antibiotics, oxytetracycline and oxolinic acid, in a fish pond were simulated using a computational model. The VDC model, which is designed based on a model for predicting pesticide fate and transport in paddy fields, was modified to take into account the differences between the pond and the paddies as well as those between the fish and the rice plant behaviors. The pond conditions were set following the typical practice in South East Asia aquaculture. The two antibiotics were administered to the animal in the pond through medicated feed during a period of 5 days as in actual practice. Concentrations of oxytetracycline in pond water were higher than those of oxolinic acid at the beginning of the simulation. Dissipation rate of oxytetracycline is also higher as it is more readily available for degradation in the water. For the long term, oxolinic acid was present at higher concentration than oxytetracycline in pond water as well as pond sediment. The simulated results were expected to be conservative and can be useful for the lower tier assessment of exposure risk of veterinary medicine in aquaculture industry but more data are needed for the complete validation of the model.

Fate and transport of bensulfuron-methyl and imazosulfuron in paddy fields: Experiments and model simulation

Experiments were conducted to determine the fate of bensulfuron-methyl (BSM) and imazosulfuron (IMS) under paddy conditions. Initially, laboratory experiments were conducted and the photolysis half-lives of the two herbicides were found to be much shorter than their hydrolysis half-lives in aqueous solutions. In the aerobic water–soil system, dissipation followed first-order kinetics with water half-lives of 9.1 and 11.0 days and soil half-lives of 12.4 and 18.5 days (first phase) and 35.0 and 44.1 days (second phase) for bensulfuron-methyl and imazosulfuron, respectively. However, the anaerobic soil half-lives were only 12.7 and 9.8 days for BSM and IMS, respectively. The values of K d were determined to be 16.0 and 13.8 for BSM and IMS, respectively. Subsequent field measurements for the two herbicides revealed that dissipation of both herbicides in paddy water involved biphasic first-order kinetics, with the dissipation rates in the first phase being much faster than those in the second phase. The dissipation of bensulfuron-methyl and imazosulfuron in the paddy surface soil were also followed biphasic first-order kinetics. These results were then used as input parameters for the PCPF-1 model to simulate the fate and transport of BSM and IMS in the paddy environment (water and 1-cm surface soil layer). The measured and simulated values agreed well and the mass balance error during the simulation period was −1.2 and 2.8% of applied pesticide, respectively, for BSM and IMS.

Exposure risk assessment and evaluation of the best management practice for controlling pesticide runoff from paddy fields. Part 2: Model simulation for the herbicide pretilachlor

BACKGROUND: Monitoring studies revealed high concentrations of pesticides in the drainage canal of paddy fields. It is important to have a way to predict these concentrations in different management scenarios as an assessment tool. A simulation model for predicting the pesticide concentration in a paddy block (PCPF-B) was evaluated and then used to assess the effect of water management practices for controlling pesticide runoff from paddy fields. RESULTS: The PCPF-B model achieved an acceptable performance. The model was applied to a constrained probabilistic approach using the Monte Carlo technique to evaluate the best management practices for reducing runoff of pretilachlor into the canal. The probabilistic model predictions using actual data of pesticide use and hydrological data in the canal showed that the water holding period (WHP) and the excess water storage depth (EWSD) effectively reduced the loss and concentration of pretilachlor from paddy fields to the drainage canal. The WHP also reduced the timespan of pesticide exposure in the drainage canal. CONCLUSIONS: It is recommended that: (1) the WHP be applied for as long as possible, but for at least 7 days, depending on the pesticide and field conditions; (2) an EWSD greater than 2 cm be maintained to store substantial rainfall in order to prevent paddy runoff, especially during the WHP.

Studies of water and electrolyte movement from oral rehydration solutions (rice- and glucose-based) across a normal and secreting gut using a dual isotope tracer technique in a rat perfusion model

Aims: To establish a model to measure bidirectional flow of water from a glucose oral rehydration solution (G-ORS) and a newly developed rice-based oral rehydration solution (R-ORS) using a dual isotope tracer technique in a rat perfusion model. To measure net water, sodium and potassium absorption from the ORS. Methods: In viva steady-state perfusion studies were carried out in normal and secreting (induced by cholera toxin) rat small intestine (n = 11 in each group). To determine bidirectional flow of water from the ORS the animals were initially labelled with tritium, and deuterium was added to the perfusion solution. Sequential perfusate and blood samples were collected after attainment of steady-state conditions and analysed for water and electrolyte content. Results: There was a significant increase in net water absorption from the R-ORS compared to the G-ORS in both the normal (P < 0.02) and secreting intestine (P < 0.05). Water efflux was significantly reduced in the R-ORS group compared to the G-ORS group in both the normal (P < 0.01) and the secreting intestine (P < 0.01). There was an increase in sodium absorption in the R-ORS group compared to the G-ORS. The G-ORS produced a significantly greater blood glucose level at 75 min compared to the R-ORS (P < 0.03) in the secreting intestine. Conclusions: This study demonstrates the improved water absorption from a rice-based ORS in both the normal and secreting intestine. Evidence that the absorption of water may be influenced by the osmolality of the ORS was also demonstrated.

Oxygen transport in a three-dimensional microvascular network incorporated with early tumour growth and preexisting vessel cooption: Numerical simulation study

We propose a dynamic mathematical model of tissue oxygen transport by a preexisting three-dimensional microvascular network which provides nutrients for an in situ cancer at the very early stage of primary microtumour growth. The expanding tumour consumes oxygen during its invasion to the surrounding tissues and cooption of host vessels. The preexisting vessel cooption, remodelling and collapse are modelled by the changes of haemodynamic conditions due to the growing tumour. A detailed computational model of oxygen transport in tumour tissue is developed by considering (a) the time-varying oxygen advection diffusion equation within the microvessel segments, (b) the oxygen flux across the vessel walls, and (c) the oxygen diffusion and consumption with in the tumour and surrounding healthy tissue. The results show the oxygen concentration distribution at different time points of early tumour growth. In addition, the influence of preexisting vessel density on the oxygen transport has been discussed. The proposed model not only provides a quantitative approach for investigating the interactions between tumour growth and oxygen delivery, but also is extendable to model other molecules or chemotherapeutic drug transport in the future study.

Footwear intervene of forefoot loading during landing movement

This study investigated the forefoot loading character under flexible sole condition while performing landing maneuver. Twenty healthy male volunteers have participated in the test. The insole and outsole loading were measured at the same time. The results of this study shown that the forefoot impact loading could be effectively relieved through the footwear during landing movement. The peak pressure value in the outsole was much higher than the barefoot, where the highest value in the first metatarsal of outsole was 63.6% higher than barefoot condition. Peak pressure of the third metatarsal of insole reduced the most, this has decreased about 51.2% of the barefoot experienced.

3D numerical simulation of avascular tumour growth: effect of hypoxic micro-environment in host tissue

A three-dimensional (3D) mathematical model of tumour growth at the avascular phase and vessel remodelling in host tissues is proposed with emphasis on the study of the interactions of tumour growth and hypoxic micro-environment in host tissues. The hybrid based model includes the continuum part, such as the distributions of oxygen and vascular endothelial growth factors (VEGFs), and the discrete part of tumour cells (TCs) and blood vessel networks. The simulation shows the dynamic process of avascular tumour growth from a few initial cells to an equilibrium state with varied vessel networks. After a phase of rapidly increasing numbers of the TCs, more and more host vessels collapse due to the stress caused by the growing tumour. In addition, the consumption of oxygen expands with the enlarged tumour region. The study also discusses the effects of certain factors on tumour growth, including the density and configuration of preexisting vessel networks and the blood oxygen content. The model enables us to examine the relationship between early tumour growth and hypoxic micro-environment in host tissues, which can be useful for further applications, such as tumour metastasis and the initialization of tumour angiogenesis.

Impact of coronary tortuosity on coronary pressure: Numerical simulation study

Background: Coronary tortuosity (CT) is a common coronary angiographic finding. Whether CT leads to an apparent reduction in coronary pressure distal to the tortuous segment of the coronary artery is still unknown. The purpose of this study is to determine the impact of CT on coronary pressure distribution by numerical simulation. Methods: 21 idealized models were created to investigate the influence of coronary tortuosity angle (CTA) and coronary tortuosity number (CTN) on coronary pressure distribution. A 2D incompressible Newtonian flow was assumed and the computational simulation was performed using finite volume method. CTA of 30°, 60°, 90°, 120° and CTN of 0, 1, 2, 3, 4, 5 were discussed under both steady and pulsatile conditions, and the changes of outlet pressure and inlet velocity during the cardiac cycle were considered. Results: Coronary pressure distribution was affected both by CTA and CTN. We found that the pressure drop between the start and the end of the CT segment decreased with CTA, and the length of the CT segment also declined with CTA. An increase in CTN resulted in an increase in the pressure drop. Conclusions: Compared to no-CT, CT can results in more decrease of coronary blood pressure in dependence on the severity of tortuosity and severe CT may cause myocardial ischemia.