Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

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.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

Small animal bone healing models : standards, tips, and pitfalls results of a consensus meeting

Small animal fracture models have gained increasing interest in fracture healing studies. To achieve standardized and defined study conditions, various variables must be carefully controlled when designing fracture healing experiments in mice or rats. The strain, age and sex of the animals may influence the process of fracture healing. Furthermore, the choice of the fracture fixation technique depends on the questions addressed, whereby intra- and extramedullary implants as well as open and closed surgical approaches may be considered. During the last few years, a variety of different, highly sophisticated implants for fracture fixation in small animals have been developed. Rigid fixation with locking plates or external fixators results in predominantly intramembranous healing in both mice and rats. Locking plates, external fixators, intramedullary screws, the locking nail and the pin-clip device allow different degrees of stability resulting in various amounts of endochondral and intramembranous healing. The use of common pins that do not provide rotational and axial stability during fracture stabilization should be discouraged in the future. Analyses should include at least biomechanical and histological evaluations, even if the focus of the study is directed towards the elucidation of molecular mechanisms of fracture healing using the largely available spectrum of antibodies and gene-targeted animals to study molecular mechanisms of fracture healing. This review discusses distinct requirements for the experimental setups as well as the advantages and pitfalls of the different fixation techniques in rats and mice.

The impact of taxes on optimal portfolio choice : an Australian study

Taxes are an important component of investing that is commonly overlooked in both the literature and in practice. For example, many understand that taxes will reduce an investment’s return, but less understood is the risk-sharing nature of taxes that also reduces the investment’s risk. This thesis examines how taxes affect the optimal asset allocation and asset location decision in an Australian environment. It advances the model of Horan & Al Zaman (2008), improving the method by which the present value of tax liabilities are calculated, by using an after-tax risk-free discount rate, and incorporating any new or reduced tax liabilities generated into its expected risk and return estimates. The asset allocation problem is examined for a range of different scenarios using Australian parameters, including different risk aversion levels, personal marginal tax rates, investment horizons, borrowing premiums, high or low inflation environments, and different starting cost bases. The findings support the Horan & Al Zaman (2008) conclusion that equities should be held in the taxable account. In fact, these findings are strengthened with most of the efficient frontier maximising equity holdings in the taxable account instead of only half. Furthermore, these findings transfer to the Australian case, where it is found that taxed Australian investors should always invest into equities first through the taxable account before investing in super. However, untaxed Australian investors should invest their equity first through superannuation. With borrowings allowed in the taxable account (no borrowing premium), Australian taxed investors should hold 100% of the superannuation account in the risk-free asset, while undertaking leverage in the taxable account to achieve the desired risk-return. Introducing a borrowing premium decreases the likelihood of holding 100% of super in the risk-free asset for taxable investors. The findings also suggest that the higher the marginal tax rate, the higher the borrowing premium in order to overcome this effect. Finally, as the investor’s marginal tax rate increases, the overall allocation to equities should increase due to the increased risk and return sharing caused by taxation, and in order to achieve the same risk/return level as the lower taxation level, the investor must take on more equity exposure. The investment horizon has a minimal impact on the optimal allocation decision in the absence of factors such as mean reversion and human capital.

Physical characteristics of small ions and their interaction with ultrafine particles in the urban environment

In recent years, the effect of ions and ultrafine particles on ambient air quality and human health has been well documented, however, knowledge about their sources, concentrations and interactions within different types of urban environments remains limited. This thesis presents the results of numerous field studies aimed at quantifying variations in ion concentration with distance from the source, as well as identifying the dynamics of the particle ionisation processes which lead to the formation of charged particles in the air. In order to select the most appropriate measurement instruments and locations for the studies, a literature review was also conducted on studies that reported ion and ultrafine particle emissions from different sources in a typical urban environment. The initial study involved laboratory experiments on the attachment of ions to aerosols, so as to gain a better understanding of the interaction between ions and particles. This study determined the efficiency of corona ions at charging and removing particles from the air, as a function of different particle number and ion concentrations. The results showed that particle number loss was directly proportional to particle charge concentration, and that higher small ion concentrations led to higher particle deposition rates in all size ranges investigated. Nanoparticles were also observed to decrease with increasing particle charge concentration, due to their higher Brownian mobility and subsequent attachment to charged particles. Given that corona discharge from high voltage powerlines is considered one of the major ion sources in urban areas, a detailed study was then conducted under three parallel overhead powerlines, with a steady wind blowing in a perpendicular direction to the lines. The results showed that large sections of the lines did not produce any corona at all, while strong positive emissions were observed from discrete components such as a particular set of spacers on one of the lines. Measurements were also conducted at eight upwind and downwind points perpendicular to the powerlines, spanning a total distance of about 160m. The maximum positive small and large ion concentrations, and DC electric field were observed at a point 20 m downwind from the lines, with median values of 4.4×103 cm-3, 1.3×103 cm-3 and 530 V m-1, respectively. It was estimated that, at this point, less than 7% of the total number of particles was charged. The electrical parameters decreased steadily with increasing downwind distance from the lines but remained significantly higher than background levels at the limit of the measurements. Moreover, vehicles are one of the most prevalent ion and particle emitting sources in urban environments, and therefore, experiments were also conducted behind a motor vehicle exhaust pipe and near busy motorways, with the aim of quantifying small ion and particle charge concentration, as well as their distribution as a function of distance from the source. The study found that approximately equal numbers of positive and negative ions were observed in the vehicle exhaust plume, as well as near motorways, of which heavy duty vehicles were believed to be the main contributor. In addition, cluster ion concentration was observed to decrease rapidly within the first 10-15 m from the road and ion-ion recombination and ion-aerosol attachment were the most likely cause of ion depletion, rather than dilution and turbulence related processes. In addition to the above-mentioned dominant ion sources, other sources also exist within urban environments where intensive human activities take place. In this part of the study, airborne concentrations of small ions, particles and net particle charge were measured at 32 different outdoor sites in and around Brisbane, Australia, which were classified into seven different groups as follows: park, woodland, city centre, residential, freeway, powerlines and power substation. Whilst the study confirmed that powerlines, power substations and freeways were the main ion sources in an urban environment, it also suggested that not all powerlines emitted ions, only those with discrete corona discharge points. In addition to the main ion sources, higher ion concentrations were also observed environments affected by vehicle traffic and human activities, such as the city centre and residential areas. A considerable number of ions were also observed in a woodland area and it is still unclear if they were emitted directly from the trees, or if they originated from some other local source. Overall, it was found that different types of environments had different types of ion sources, which could be classified as unipolar or bipolar particle sources, as well as ion sources that co-exist with particle sources. In general, fewer small ions were observed at sites with co-existing sources, however particle charge was often higher due to the effect of ion-particle attachment. In summary, this study quantified ion concentrations in typical urban environments, identified major charge sources in urban areas, and determined the spatial dispersion of ions as a function of distance from the source, as well as their controlling factors. The study also presented ion-aerosol attachment efficiencies under high ion concentration conditions, both in the laboratory and in real outdoor environments. The outcomes of these studies addressed the aims of this work and advanced understanding of the charge status of aerosols in the urban environment.

The acute adaptations of normal and pathological human Achilles tendons to eccentric and concentric exercise

Eccentric exercise is the conservative treatment of choice for mid-portion Achilles tendinopathy. While there is a growing body of evidence supporting the medium to long term efficacy of eccentric exercise in Achilles tendinopathy treatment, very few studies have investigated the short term response of the tendon to eccentric exercise. Moreover, the mechanisms through which tendinopathy symptom resolution occurs remain to be established. The primary purpose of this thesis was to investigate the acute adaptations of the Achilles tendon to, and the biomechanical characteristics of, the eccentric exercise protocol used for Achilles tendinopathy rehabilitation and a concentric equivalent. The research was conducted with an orientation towards exploring potential mechanisms through which eccentric exercise may bring about a resolution of tendinopathy symptoms. Specifically, the morphology of tendinopathic and normal Achilles tendons was monitored using high resolution sonography prior to and following eccentric and concentric exercise, to facilitate comparison between the treatment of choice and a similar alternative. To date, the only proposed mechanism through which eccentric exercise is thought to result in symptom resolution is the increased variability in motor output force observed during eccentric exercise. This thesis expanded upon prior work by investigating the variability in motor output force recorded during eccentric and concentric exercises, when performed at two different knee joint angles, by limbs with and without symptomatic tendinopathy. The methodological phase of the research focused on establishing the reliability of measures of tendon thickness, tendon echogenicity, electromyography (EMG) of the Triceps Surae and the standard deviation (SD) and power spectral density (PSD) of the vertical ground reaction force (VGRF). These analyses facilitated comparison between the error in the measurements and experimental differences identified as statistically significant, so that the importance and meaning of the experimental differences could be established. One potential limitation of monitoring the morphological response of the Achilles tendon to exercise loading is that the Achilles tendon is continually exposed to additional loading as participants complete the walking required to carry out their necessary daily tasks. The specific purpose of the last experiment in the methodological phase was to evaluate the effect of incidental walking activity on Achilles tendon morphology. The results of this study indicated that walking activity could decrease Achilles tendon thickness (negative diametral strain) and that the decrease in thickness was dependent on both the amount of walking completed and the proximity of walking activity to the sonographic examination. Thus, incidental walking activity was identified as a potentially confounding factor for future experiments which endeavoured to monitor changes in tendon thickness with exercise loading. In the experimental phase of this thesis the thickness of Achilles tendons was monitored prior to and following isolated eccentric and concentric exercise. The initial pilot study demonstrated that eccentric exercise resulted in a greater acute decrease in Achilles tendon thickness (greater diametral strain) compared to an equivalent concentric exercise, in participants with no history of Achilles tendon pain. This experiment was then expanded to incorporate participants with unilateral Achilles tendinopathy. The major finding of this experiment was that the acute decrease in Achilles tendon thickness observed following eccentric exercise was modified by the presence of tendinopathy, with a smaller decrease (less diametral strain) noted for tendinopathic compared to healthy control tendon. Based on in vitro evidence a decrease in tendon thickness is believed to reflect extrusion of fluid from the tendon with loading. This process would appear to be limited by the presence of pathology and is hypothesised to be a result of the changes in tendon structure associated with tendinopathy. Load induced fluid movement may be important to the maintenance of tendon homeostasis and structure as it has the potential to enhance molecular movement and stimulate tendon remodelling. On this basis eccentric exercise may be more beneficial to the tendon than concentric exercise. Finally, EMG and motor output force variability (SD and PSD of VGRF) were investigated while participants with and without tendinopathy performed the eccentric and concentric exercises. Although between condition differences were identified as statistically significant for a number of force variability parameters, the differences were not greater than the limits of agreement for repeated measures. Consequently the meaning and importance of these findings were questioned. Interestingly, the EMG amplitude of all three Triceps Surae muscles did not vary with knee joint angle during the performance of eccentric exercise. This raises questions pertaining to the functional importance of performing the eccentric exercise protocol at each of the two knee joint angles as it is currently prescribed. EMG amplitude was significantly greater during concentric compared to eccentric muscle actions. Differences in the muscle activation patterns may result in different stress distributions within the tendon and be related to the different diametral strain responses observed for eccentric and concentric muscle actions.

Cabergoline Decreases Alcohol Drinking and Seeking Behaviors Via Glial Cell Line-Derived Neurotrophic Factor

Background: Cabergoline is an ergotamine derivative that increases the expression of glial cell line-derived neurotrophic factor (GDNF) in vitro. We recently showed that GDNF in the ventral tegmental area (VTA) reduces the motivation to consume alcohol. We therefore set out to determine whether cabergoline administration decreases alcohol-drinking and -seeking behaviors via GDNF. Methods: Reverse transcription polymerase chain reaction (RT-PCR) and Enzyme-Linked ImmunoSorbent Assay (ELISA) were used to measure GDNF levels. Western blot analysis was used for phosphorylation experiments. Operant self-administration in rats and a two-bottle choice procedure in mice were used to assess alcohol-drinking behaviors. Instrumental performance tested during extinction was used to measure alcohol-seeking behavior. The [35S]GTPγS binding assay was used to assess the expression and function of the dopamine D2 receptor (D2R). Results: We found that treatment of the dopaminergic-like cell line SH-SY5Y with cabergoline and systemic administration of cabergoline in rats resulted in an increase in GDNF level and in the activation of the GDNF pathway. Cabergoline treatment decreased alcohol-drinking and -seeking behaviors including relapse, and its action to reduce alcohol consumption was localized to the VTA. Finally, the increase in GDNF expression and the decrease in alcohol consumption by cabergoline were abolished in GDNF heterozygous knockout mice. Conclusions: Together, these findings suggest that cabergoline-mediated upregulation of the GDNF pathway attenuates alcohol-drinking behaviors and relapse. Alcohol abuse and addiction are devastating and costly problems worldwide. This study puts forward the possibility that cabergoline might be an effective treatment for these disorders. © 2009 Society of Biological Psychiatry.

Attractive subfamilies of BLS curves for implementing high-security pairings

Barreto-Lynn-Scott (BLS) curves are a stand-out candidate for implementing high-security pairings. This paper shows that particular choices of the pairing-friendly search parameter give rise to four subfami- lies of BLS curves, all of which offer highly efficient and implementation- friendly pairing instantiations. Curves from these particular subfamilies are defined over prime fields that support very efficient towering options for the full extension field. The coefficients for a specific curve and its correct twist are automat-ically determined without any computational effort. The choice of an extremely sparse search parameter is immediately reflected by a highly efficient optimal ate Miller loop and final exponentiation. As a resource for implementors, we give a list with examples of implementation-friendly BLS curves through several high-security levels.

Topological map induction using neighbourhood information of places

In topological mapping, perceptual aliasing can cause different places to appear indistinguishable to the robot. In case of severely corrupted or non-available odometry information, topological mapping is difficult as the robot is challenged with the loop-closing problem; that is to determine whether it has visited a particular place before. In this article we propose to use neighbourhood information to disambiguate otherwise indistinguishable places. Using neighbourhood information for place disambiguation is an approach that neither depends on a specific choice of sensors nor requires geometric information such as odometry. Local neighbourhood information is extracted from a sequence of observations of visited places. In experiments using either sonar or visual observations from an indoor environment the benefits of using neighbourhood clues for the disambiguation of otherwise identical vertices are demonstrated. Over 90% of the maps we obtain are isomorphic with the ground truth. The choice of the robot’s sensors does not impact the results of the experiments much.