Priority threat management of non-native plants to maintain ecosystem integrity across heterogeneous landscapes

Invasive non-native plants have negatively impacted on biodiversity and ecosystem functions world-wide. Because of the large number of species, their wide distributions and varying degrees of impact, we need a more effective method for prioritizing control strategies for cost-effective investment across heterogeneous landscapes. Here, we develop a prioritization framework that synthesizes scientific data, elicits knowledge from experts and stakeholders to identify control strategies, and appraises the cost-effectiveness of strategies. Our objective was to identify the most cost-effective strategies for reducing the total area dominated by high-impact non-native plants in the Lake Eyre Basin (LEB). We use a case study of the ˜120 million ha Lake Eyre Basin that comprises some of the most distinctive Australian landscapes, including Uluru-Kata Tjuta National Park. More than 240 non-native plant species are recorded in the Lake Eyre Basin, with many predicted to spread, but there are insufficient resources to control all species. Lake Eyre Basin experts identified 12 strategies to control, contain or eradicate non-native species over the next 50 years. The total cost of the proposed Lake Eyre Basin strategies was estimated at AU$1·7 billion, an average of AU$34 million annually. Implementation of these strategies is estimated to reduce non-native plant dominance by 17 million ha – there would be a 32% reduction in the likely area dominated by non-native plants within 50 years if these strategies were implemented. The three most cost-effective strategies were controlling Parkinsonia aculeata, Ziziphus mauritiana and Prosopis spp. These three strategies combined were estimated to cost only 0·01% of total cost of all the strategies, but would provide 20% of the total benefits. Over 50 years, cost-effective spending of AU$2·3 million could eradicate all non-native plant species from the only threatened ecological community within the Lake Eyre Basin, the Great Artesian Basin discharge springs. Synthesis and applications. Our framework, based on a case study of the ˜120 million ha Lake Eyre Basin in Australia, provides a rationale for financially efficient investment in non-native plant management and reveals combinations of strategies that are optimal for different budgets. It also highlights knowledge gaps and incidental findings that could improve effective management of non-native plants, for example addressing the reliability of species distribution data and prevalence of information sharing across states and regions.

Stochastic linear multistep methods for the simulation of chemical kinetics

In this paper, we introduce the Stochastic Adams-Bashforth (SAB) and Stochastic Adams-Moulton (SAM) methods as an extension of the tau-leaping framework to past information. Using the theta-trapezoidal tau-leap method of weak order two as a starting procedure, we show that the k-step SAB method with k >= 3 is order three in the mean and correlation, while a predictor-corrector implementation of the SAM method is weak order three in the mean but only order one in the correlation. These convergence results have been derived analytically for linear problems and successfully tested numerically for both linear and non-linear systems. A series of additional examples have been implemented in order to demonstrate the efficacy of this approach.

Online hidden Markov model parameter estimation and minimax robust quickest change detection in uncertain stochastic processes

Stochastic (or random) processes are inherent to numerous fields of human endeavour including engineering, science, and business and finance. This thesis presents multiple novel methods for quickly detecting and estimating uncertainties in several important classes of stochastic processes. The significance of these novel methods is demonstrated by employing them to detect aircraft manoeuvres in video signals in the important application of autonomous mid-air collision avoidance.

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.

Stochastic dynamics of interacting haematopoietic stem cell niche lineages

Since we still know very little about stem cells in their natural environment, it is useful to explore their dynamics through modelling and simulation, as well as experimentally. Most models of stem cell systems are based on deterministic differential equations that ignore the natural heterogeneity of stem cell populations. This is not appropriate at the level of individual cells and niches, when randomness is more likely to affect dynamics. In this paper, we introduce a fast stochastic method for simulating a metapopulation of stem cell niche lineages, that is, many sub-populations that together form a heterogeneous metapopulation, over time. By selecting the common limiting timestep, our method ensures that the entire metapopulation is simulated synchronously. This is important, as it allows us to introduce interactions between separate niche lineages, which would otherwise be impossible. We expand our method to enable the coupling of many lineages into niche groups, where differentiated cells are pooled within each niche group. Using this method, we explore the dynamics of the haematopoietic system from a demand control system perspective. We find that coupling together niche lineages allows the organism to regulate blood cell numbers as closely as possible to the homeostatic optimum. Furthermore, coupled lineages respond better than uncoupled ones to random perturbations, here the loss of some myeloid cells. This could imply that it is advantageous for an organism to connect together its niche lineages into groups. Our results suggest that a potential fruitful empirical direction will be to understand how stem cell descendants communicate with the niche and how cancer may arise as a result of a failure of such communication.

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

Programming: Reading, writing and reversing

In this paper, we look at the concept of reversibility, that is, negating opposites, counterbalances, and actions that can be reversed. Piaget identified reversibility as an indicator of the ability to reason at a concrete operational level. We investigate to what degree novice programmers manifest the ability to work with this concept of reversibility by providing them with a small piece of code and then asking them to write code that undoes the effect of that code. On testing entire cohorts of students in their first year of learning to program, we found an overwhelming majority of them could not cope with such a concept. We then conducted think aloud studies of novices where we observed them working on this task and analyzed their contrasting abilities to deal with it. The results of this study demonstrate the need for better understanding our students' reasoning abilities, and a teaching model aimed at that level of reality.

One practical algorithm for both stochastic and adversarial bandits

We present an algorithm for multiarmed bandits that achieves almost optimal performance in both stochastic and adversarial regimes without prior knowledge about the nature of the environment. Our algorithm is based on augmentation of the EXP3 algorithm with a new control lever in the form of exploration parameters that are tailored individually for each arm. The algorithm simultaneously applies the “old” control lever, the learning rate, to control the regret in the adversarial regime and the new control lever to detect and exploit gaps between the arm losses. This secures problem-dependent “logarithmic” regret when gaps are present without compromising on the worst-case performance guarantee in the adversarial regime. We show that the algorithm can exploit both the usual expected gaps between the arm losses in the stochastic regime and deterministic gaps between the arm losses in the adversarial regime. The algorithm retains “logarithmic” regret guarantee in the stochastic regime even when some observations are contaminated by an adversary, as long as on average the contamination does not reduce the gap by more than a half. Our results for the stochastic regime are supported by experimental validation.

Estimating the parameters of stochastic volatility models using option price data

This article describes a maximum likelihood method for estimating the parameters of the standard square-root stochastic volatility model and a variant of the model that includes jumps in equity prices. The model is fitted to data on the S&P 500 Index and the prices of vanilla options written on the index, for the period 1990 to 2011. The method is able to estimate both the parameters of the physical measure (associated with the index) and the parameters of the risk-neutral measure (associated with the options), including the volatility and jump risk premia. The estimation is implemented using a particle filter whose efficacy is demonstrated under simulation. The computational load of this estimation method, which previously has been prohibitive, is managed by the effective use of parallel computing using graphics processing units (GPUs). The empirical results indicate that the parameters of the models are reliably estimated and consistent with values reported in previous work. In particular, both the volatility risk premium and the jump risk premium are found to be significant.

Stochastic differential games with multiple modes

We have studied two person stochastic differential games with multiple modes. For the zero-sum game we have established the existence of optimal strategies for both players. For the nonzero-sum case we have proved the existence of a Nash equilibrium.

Fluctuations in protein synthesis from a single RNA template: Stochastic kinetics of ribosomes

Proteins are polymerized by cyclic machines called ribosomes, which use their messenger RNA (mRNA) track also as the corresponding template, and the process is called translation. We explore, in depth and detail, the stochastic nature of the translation. We compute various distributions associated with the translation process; one of them-namely, the dwell time distribution-has been measured in recent single-ribosome experiments. The form of the distribution, which fits best with our simulation data, is consistent with that extracted from the experimental data. For our computations, we use a model that captures both the mechanochemistry of each individual ribosome and their steric interactions. We also demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise in translation. Finally, inspired by recent advances in the experimental techniques of manipulating single ribosomes, we make theoretical predictions on the force-velocity relation for individual ribosomes. In principle, all our predictions can be tested by carrying out in vitro experiments.

Intermittent Dynamics, Stochastic Resonance and Dynamical Heterogeneity in Supercooled Liquid Water

Here we find through computer simulations and theoretical analysis that the low temperature thermodynamic anomalies of liquid water arises from the intermittent fluctuation between its high density and low density forms, consisting largely of 5-coordinated and 4-coordinated water molecules, respectively. The fluctuations exhibit strong dynamic heterogeneity (defined by the four point time correlation function), accompanied by a divergence like growth of the dynamic correlation length, of the type encountered in fragile supercooled liquids. The intermittency has been explained by invoking a two state model often employed to understand stochastic resonance, with the relevant periodic perturbation provided here by the fluctuation of the total volume of the system.

Model Predictive Static Programming: A Computationally Efficient Technique For Suboptimal Control Design

Combining the philosophies of nonlinear model predictive control and approximate dynamic programming, a new suboptimal control design technique is presented in this paper, named as model predictive static programming (MPSP), which is applicable for finite-horizon nonlinear problems with terminal constraints. This technique is computationally efficient, and hence, can possibly be implemented online. The effectiveness of the proposed method is demonstrated by designing an ascent phase guidance scheme for a ballistic missile propelled by solid motors. A comparison study with a conventional gradient method shows that the MPSP solution is quite close to the optimal solution.

Response And Stability Of A Stochastic Beam-Column Using Stochastic Fem

A beam-column resting on continuous Winkler foundation and discrete elastic supports is considered. The beam-column is of variable cross-section and the variation of sectional properties along the axis of the beam-column is deterministic. Young's modulus, mass per unit length and distributed axial loadings of the beam-column have a stochastic distribution. The foundation stiffness coefficient of the Winkler model, the stiffnesses of discrete elastic supports, stiffnesses of end springs and the end thrust, are all considered as random parameters. The material property fluctuations and distributed axial loadings are considered to constitute independent, one-dimension uni-variate homogeneous real stochastic fields in space. The foundation stiffness coefficient, stiffnesses of the discrete elastic supports, stiffnesses of end springs and the end thrust are considered to constitute independent random variables. Static response, free vibration and stability behaviour of the beam-column are studied. Hamilton's principle is used to formulate the problem using stochastic FEM. Sensitivity vectors of the response and stability parameters are evaluated. Using these statistics of free vibration frequencies, mode shapes, buckling parameters, etc., are evaluated. A numerical example is given.

Programming an FPGA to Emulate the Dynamics of DC Machines

This paper presents the programming an FPGA (Field Programmable Gate Array) to emulate the dynamics of DC machines. FPGA allows high speed real time simulation with high precision. The described design includes block diagram representation of DC machine, which contain all arithmetic and logical operations. The real time simulation of the machine in FPGA is controlled by user interfaces they are Keypad interface, LCD display on-line and digital to analog converter. This approach provides emulation of electrical machine by changing the parameters. Separately Exited DC machine implemented and experimental results are presented.