Modeling ion channel dynamics through reflected stochastic differential equations

Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks. © 2012 American Physical Society.

Modeling fault among motorcyclists involved in crashes

Singapore crash statistics from 2001 to 2006 show that the motorcyclist fatality and injury rates per registered vehicle are higher than those of other motor vehicles by 13 and 7 times respectively. The crash involvement rate of motorcyclists as victims of other road users is also about 43%. The objective of this study is to identify the factors that contribute to the fault of motorcyclists involved in crashes. This is done by using the binary logit model to differentiate between at-fault and not-at-fault cases and the analysis is further categorized by the location of the crashes, i.e., at intersections, on expressways and at non-intersections. A number of explanatory variables representing roadway characteristics, environmental factors, motorcycle descriptions, and rider demographics have been evaluated. Time trend effect shows that not-at-fault crash involvement of motorcyclists has increased with time. The likelihood of night time crashes has also increased for not-at-fault crashes at intersections and expressways. The presence of surveillance cameras is effective in reducing not-at-fault crashes at intersections. Wet road surfaces increase at-fault crash involvement at non-intersections. At intersections, not-at-fault crash involvement is more likely on single lane roads or on median lane of multi-lane roads, while on expressways at-fault crash involvement is more likely on the median lane. Roads with higher speed limit have higher at-fault crash involvement and this is also true on expressways. Motorcycles with pillion passengers or with higher engine capacity have higher likelihood of being at-fault in crashes on expressways. Motorcyclists are more likely to be at-fault in collisions involving pedestrians and this effect is higher at night. In multi-vehicle crashes, motorcyclists are more likely to be victims than at fault. Young and older riders are more likely to be at-fault in crashes than middle-aged group of riders. The findings of this study will help to develop more targeted countermeasures to improve motorcycle safety and more cost-effective safety awareness program in motorcyclist training.

Modeling random effect and excess zeros in road traffic accident prediction

Poisson distribution has often been used for count like accident data. Negative Binomial (NB) distribution has been adopted in the count data to take care of the over-dispersion problem. However, Poisson and NB distributions are incapable of taking into account some unobserved heterogeneities due to spatial and temporal effects of accident data. To overcome this problem, Random Effect models have been developed. Again another challenge with existing traffic accident prediction models is the distribution of excess zero accident observations in some accident data. Although Zero-Inflated Poisson (ZIP) model is capable of handling the dual-state system in accident data with excess zero observations, it does not accommodate the within-location correlation and between-location correlation heterogeneities which are the basic motivations for the need of the Random Effect models. This paper proposes an effective way of fitting ZIP model with location specific random effects and for model calibration and assessment the Bayesian analysis is recommended.

Hotspot Identification: A Full Bayesian Hierarchical Modeling Approach

This study proposes a full Bayes (FB) hierarchical modeling approach in traffic crash hotspot identification. The FB approach is able to account for all uncertainties associated with crash risk and various risk factors by estimating a posterior distribution of the site safety on which various ranking criteria could be based. Moreover, by use of hierarchical model specification, FB approach is able to flexibly take into account various heterogeneities of crash occurrence due to spatiotemporal effects on traffic safety. Using Singapore intersection crash data(1997-2006), an empirical evaluate was conducted to compare the proposed FB approach to the state-of-the-art approaches. Results show that the Bayesian hierarchical models with accommodation for site specific effect and serial correlation have better goodness-of-fit than non hierarchical models. Furthermore, all model-based approaches perform significantly better in safety ranking than the naive approach using raw crash count. The FB hierarchical models were found to significantly outperform the standard EB approach in correctly identifying hotspots.

Modeling collision avoidance decisions in navigation

Due to grave potential human, environmental and economical consequences of collisions at sea, collision avoidance has become an important safety concern in navigation. To reduce the risk of collisions at sea, appropriate collision avoidance actions need to be taken in accordance with the regulations, i.e., International Regulations for Preventing Collisions at Sea. However, the regulations only provide qualitative rules and guidelines, and therefore it requires navigators to decide on collision avoidance actions quantitatively by using their judgments which often leads to making errors in navigation. To better help navigators in collision avoidance, this paper develops a comprehensive collision avoidance decision making model for providing whether a collision avoidance action is required, when to take action and what action to be taken. The model is developed based on three types of collision avoidance actions, such as course change only, speed change only, and a combination of both. The model has potential to reduce the chance of making human error in navigation by assisting navigators in decision making on collision avoidance actions.

Navigational safety in port waters: Techniques for modeling collision risk

Navigational collisions are one of the major safety concerns for many seaports. Continuing growth of shipping traffic in number and sizes is likely to result in increased number of traffic movements, which consequently could result higher risk of collisions in these restricted waters. This continually increasing safety concern warrants a comprehensive technique for modeling collision risk in port waters, particularly for modeling the probability of collision events and the associated consequences (i.e., injuries and fatalities). A number of techniques have been utilized for modeling the risk qualitatively, semi-quantitatively and quantitatively. These traditional techniques mostly rely on historical collision data, often in conjunction with expert judgments. However, these techniques are hampered by several shortcomings, such as randomness and rarity of collision occurrence leading to obtaining insufficient number of collision counts for a sound statistical analysis, insufficiency in explaining collision causation, and reactive approach to safety. A promising alternative approach that overcomes these shortcomings is the navigational traffic conflict technique (NTCT), which uses traffic conflicts as an alternative to the collisions for modeling the probability of collision events quantitatively. This article explores the existing techniques for modeling collision risk in port waters. In particular, it identifies the advantages and limitations of the traditional techniques and highlights the potentials of the NTCT in overcoming the limitations. In view of the principles of the NTCT, a structured method for managing collision risk is proposed. This risk management method allows safety analysts to diagnose safety deficiencies in a proactive manner, which consequently has great potential for managing collision risk in a fast, reliable and efficient manner.

Aspect oriented business process modeling with precedence

Complexity is a major concern which is aimed to be overcome by people through modeling. One way of reducing complexity is separation of concerns, e.g. separation of business process from applications. One sort of concerns are cross-cutting concerns i.e. concerns which are scattered and tangled through one of several models. In business process management, examples of such concerns are security and privacy policies. To deal with these cross-cutting concerns, the aspect orientated approach was introduced in the software development area and recently also in the business process management area. The work presented in this paper elaborates on aspect oriented process modelling. It extends earlier work by defining a mechanism for capturing multiple concerns and specifying a precedence order according to which they should be handled in a process. A formal syntax of the notation is presented precisely capturing the extended concepts and mechanisms. Finally, the relevant of the approach is demonstrated through a case study.

Mixed-dimensional consistent coupling by multi-point constraint equations for efficient multi-scale modeling

Finding an appropriate linking method to connect different dimensional element types in a single finite element model is a key issue in the multi-scale modeling. This paper presents a mixed dimensional coupling method using multi-point constraint equations derived by equating the work done on either side of interface connecting beam elements and shell elements for constructing a finite element multiscale model. A typical steel truss frame structure is selected as case example and the reduced scale specimen of this truss section is then studied in the laboratory to measure its dynamic and static behavior in global truss and local welded details while the different analytical models are developed for numerical simulation. Comparison of dynamic and static response of the calculated results among different numerical models as well as the good agreement with those from experimental results indicates that the proposed multi-scale model is efficient and accurate.

Modeling and Analyzing the Carbon Footprint of Business Processes

Many corporations and individuals realize that environmental sustainability is an urgent problem to address. In this chapter, we contribute to the emerging academic discussion by proposing two innovative approaches for engaging in the development of environmentally sustainable business processes. Specifically, we describe an extended process modeling approach for capturing and documenting the dioxide emissions produced during the execution of a business process. For illustration, we apply this approach to the case of a governmental Shared Services provider. Second, we then introduce an analysis method for measuring the carbon dioxide emissions produced during the execution of a business process. To illustrative this approach, we apply it in the real-life case of an European airport and show how this information can be leveraged in the re-design of “green” busi-ness processes.

Modeling train delays in urban networks

The reliability of urban passenger trains is a critical performance measure for passenger satisfaction and ultimately market share. A delay to one train in a peak period can have a severe effect on the schedule adherence of other trains. This paper presents an analytically based model to quantify the expected positive delay for individual passenger trains and track links in an urban rail network. The model specifically addresses direct delay to trains, knock-on delays to other trains, and delays at scheduled connections. A solution to the resultant system of equations is found using an iterative refinement algorithm. Model validation, which is carried out using a real-life suburban train network consisting of 157 trains, shows the model estimates to be on average within 8% of those obtained from a large scale simulation. Also discussed, is the application of the model to assess the consequences of increased scheduled slack time as well as investment strategies designed to reduce delay.

Assessing of circuit breaker restrike risks using computer simulation and wavelet analysis

A breaker restrike is an abnormal arcing phenomenon, leading to a possible breaker failure. Eventually, this failure leads to interruption of the transmission and distribution of the electricity supply system until the breaker is replaced. Before 2008, there was little evidence in the literature of monitoring techniques based on restrike measurement and interpretation produced during switching of capacitor banks and shunt reactor banks in power systems. In 2008 a non-intrusive radiometric restrike measurement method and a restrike hardware detection algorithm were developed by M.S. Ramli and B. Kasztenny. However, the limitations of the radiometric measurement method are a band limited frequency response as well as limitations in amplitude determination. Current restrike detection methods and algorithms require the use of wide bandwidth current transformers and high voltage dividers. A restrike switch model using Alternative Transient Program (ATP) and Wavelet Transforms which support diagnostics are proposed. Restrike phenomena become a new diagnostic process using measurements, ATP and Wavelet Transforms for online interrupter monitoring. This research project investigates the restrike switch model Parameter „A. dielectric voltage gradient related to a normal and slowed case of the contact opening velocity and the escalation voltages, which can be used as a diagnostic tool for a vacuum circuit-breaker (CB) at service voltages between 11 kV and 63 kV. During current interruption of an inductive load at current quenching or chopping, a transient voltage is developed across the contact gap. The dielectric strength of the gap should rise to a point to withstand this transient voltage. If it does not, the gap will flash over, resulting in a restrike. A straight line is fitted through the voltage points at flashover of the contact gap. This is the point at which the gap voltage has reached a value that exceeds the dielectric strength of the gap. This research shows that a change in opening contact velocity of the vacuum CB produces a corresponding change in the slope of the gap escalation voltage envelope. To investigate the diagnostic process, an ATP restrike switch model was modified with contact opening velocity computation for restrike waveform signature analyses along with experimental investigations. This also enhanced a mathematical CB model with the empirical dielectric model for SF6 (sulphur hexa-fluoride) CBs at service voltages above 63 kV and a generalised dielectric curve model for 12 kV CBs. A CB restrike can be predicted if there is a similar type of restrike waveform signatures for measured and simulated waveforms. The restrike switch model applications are used for: computer simulations as virtual experiments, including predicting breaker restrikes; estimating the interrupter remaining life of SF6 puffer CBs; checking system stresses; assessing point-on-wave (POW) operations; and for a restrike detection algorithm development using Wavelet Transforms. A simulated high frequency nozzle current magnitude was applied to an Equation (derived from the literature) which can calculate the life extension of the interrupter of a SF6 high voltage CB. The restrike waveform signatures for a medium and high voltage CB identify its possible failure mechanism such as delayed opening, degraded dielectric strength and improper contact travel. The simulated and measured restrike waveform signatures are analysed using Matlab software for automatic detection. Experimental investigation of a 12 kV vacuum CB diagnostic was carried out for the parameter determination and a passive antenna calibration was also successfully developed with applications for field implementation. The degradation features were also evaluated with a predictive interpretation technique from the experiments, and the subsequent simulation indicates that the drop in voltage related to the slow opening velocity mechanism measurement to give a degree of contact degradation. A predictive interpretation technique is a computer modeling for assessing switching device performance, which allows one to vary a single parameter at a time; this is often difficult to do experimentally because of the variable contact opening velocity. The significance of this thesis outcome is that it is a non-intrusive method developed using measurements, ATP and Wavelet Transforms to predict and interpret a breaker restrike risk. The measurements on high voltage circuit-breakers can identify degradation that can interrupt the distribution and transmission of an electricity supply system. It is hoped that the techniques for the monitoring of restrike phenomena developed by this research will form part of a diagnostic process that will be valuable for detecting breaker stresses relating to the interrupter lifetime. Suggestions for future research, including a field implementation proposal to validate the restrike switch model for ATP system studies and the hot dielectric strength curve model for SF6 CBs, are given in Appendix A.

Langevin dynamics modeling of the water diffusion tensor in partially aligned collagen networks

In this work, a Langevin dynamics model of the diffusion of water in articular cartilage was developed. Numerical simulations of the translational dynamics of water molecules and their interaction with collagen fibers were used to study the quantitative relationship between the organization of the collagen fiber network and the diffusion tensor of water in model cartilage. Langevin dynamics was used to simulate water diffusion in both ordered and partially disordered cartilage models. In addition, an analytical approach was developed to estimate the diffusion tensor for a network comprising a given distribution of fiber orientations. The key findings are that (1) an approximately linear relationship was observed between collagen volume fraction and the fractional anisotropy of the diffusion tensor in fiber networks of a given degree of alignment, (2) for any given fiber volume fraction, fractional anisotropy follows a fiber alignment dependency similar to the square of the second Legendre polynomial of cos(θ), with the minimum anisotropy occurring at approximately the magic angle (θMA), and (3) a decrease in the principal eigenvalue and an increase in the transverse eigenvalues is observed as the fiber orientation angle θ progresses from 0◦ to 90◦. The corresponding diffusion ellipsoids are prolate for θ < θMA, spherical for θ ≈ θMA, and oblate for θ > θMA. Expansion of the model to include discrimination between the combined effects of alignment disorder and collagen fiber volume fraction on the diffusion tensor is discussed.