Evolving genetic regulatory networks performing as stochastic switches

Recent studies have shown that small genetic regulatory networks (GRNs) can be evolved in silico displaying certain dynamics in the underlying mathematical model. It is expected that evolutionary approaches can help to gain a better understanding of biological design principles and assist in the engineering of genetic networks. To take the stochastic nature of GRNs into account, our evolutionary approach models GRNs as biochemical reaction networks based on simple enzyme kinetics and simulates them by using Gillespie’s stochastic simulation algorithm (SSA). We have already demonstrated the relevance of considering intrinsic stochasticity by evolving GRNs that show oscillatory dynamics in the SSA but not in the ODE regime. Here, we present and discuss first results in the evolution of GRNs performing as stochastic switches.

Modelling passenger flow at airport terminals : individual agent decision model for stochastic passenger behaviour

Airport system is complex. Passenger dynamics within it appear to be complicate as well. Passenger behaviours outside standard processes are regarded more significant in terms of public hazard and service rate issues. In this paper, we devised an individual agent decision model to simulate stochastic passenger behaviour in airport departure terminal. Bayesian networks are implemented into the decision making model to infer the probabilities that passengers choose to use any in-airport facilities. We aim to understand dynamics of the discretionary activities of passengers.

A stochastic thermostat algorithm for coarse-grained thermomechanical modeling of large-scale soft matters : theory and application to microfilaments

As all-atom molecular dynamics method is limited by its enormous computational cost, various coarse-grained strategies have been developed to extend the length scale of soft matters in the modeling of mechanical behaviors. However, the classical thermostat algorithm in highly coarse-grained molecular dynamics method would underestimate the thermodynamic behaviors of soft matters (e.g. microfilaments in cells), which can weaken the ability of materials to overcome local energy traps in granular modeling. Based on all-atom molecular dynamics modeling of microfilament fragments (G-actin clusters), a new stochastic thermostat algorithm is developed to retain the representation of thermodynamic properties of microfilaments at extra coarse-grained level. The accuracy of this stochastic thermostat algorithm is validated by all-atom MD simulation. This new stochastic thermostat algorithm provides an efficient way to investigate the thermomechanical properties of large-scale soft matters.

Corporate credit risk prediction under stochastic volatility and jumps

This paper examines the impact of allowing for stochastic volatility and jumps (SVJ) in a structural model on corporate credit risk prediction. The results from a simulation study verify the better performance of the SVJ model compared with the commonly used Merton model, and three sources are provided to explain the superiority. The empirical analysis on two real samples further ascertains the importance of recognizing the stochastic volatility and jumps by showing that the SVJ model decreases bias in spread prediction from the Merton model, and better explains the time variation in actual CDS spreads. The improvements are found particularly apparent in small firms or when the market is turbulent such as the recent financial crisis.

A model-framed evaluation of elephant effects on tree and fire dynamics in African savannas

There is a concern that high densities of elephants in southern Africa could lead to the overall reduction of other forms of biodiversity. We present a grid-based model of elephant-savanna dynamics, which differs from previous elephant-vegetation models by accounting for woody plant demographics, tree-grass interactions, stochastic environmental variables (fire and rainfall), and spatial contagion of fire and tree recruitment. The model projects changes in height structure and spatial pattern of trees over periods of centuries. The vegetation component of the model produces long-term tree-grass coexistence, and the emergent fire frequencies match those reported for southern African savannas. Including elephants in the savanna model had the expected effect of reducing woody plant cover, mainly via increased adult tree mortality, although at an elephant density of 1.0 elephant/km2, woody plants still persisted for over a century. We tested three different scenarios in addition to our default assumptions. (1) Reducing mortality of adult trees after elephant use, mimicking a more browsing-tolerant tree species, mitigated the detrimental effect of elephants on the woody population. (2) Coupling germination success (increased seedling recruitment) to elephant browsing further increased tree persistence, and (3) a faster growing woody component allowed some woody plant persistence for at least a century at a density of 3 elephants/km2. Quantitative models of the kind presented here provide a valuable tool for exploring the consequences of management decisions involving the manipulation of elephant population densities. © 2005 by the Ecological Society of America.

Stochastic analysis of a radial-inflow turbine in the presence of parametric uncertainties

This paper presents an uncertainty quantification study of the performance analysis of the high pressure ratio single stage radial-inflow turbine used in the Sundstrand Power Systems T-100 Multi-purpose Small Power Unit. A deterministic 3D volume-averaged Computational Fluid Dynamics (CFD) solver is coupled with a non-statistical generalized Polynomial Chaos (gPC) representation based on a pseudo-spectral projection method. One of the advantages of this approach is that it does not require any modification of the CFD code for the propagation of random disturbances in the aerodynamic and geometric fields. The stochastic results highlight the importance of the blade thickness and trailing edge tip radius on the total-to-static efficiency of the turbine compared to the angular velocity and trailing edge tip length. From a theoretical point of view, the use of the gPC representation on an arbitrary grid also allows the investigation of the sensitivity of the blade thickness profiles on the turbine efficiency. The gPC approach is also applied to coupled random parameters. The results show that the most influential coupled random variables are trailing edge tip radius coupled with the angular velocity.

Modelling the movement of interacting cell populations: A moment dynamics approach

Mathematical models describing the movement of multiple interacting subpopulations are relevant to many biological and ecological processes. Standard mean-field partial differential equation descriptions of these processes suffer from the limitation that they implicitly neglect to incorporate the impact of spatial correlations and clustering. To overcome this, we derive a moment dynamics description of a discrete stochastic process which describes the spreading of distinct interacting subpopulations. In particular, we motivate our model by mimicking the geometry of two typical cell biology experiments. Comparing the performance of the moment dynamics model with a traditional mean-field model confirms that the moment dynamics approach always outperforms the traditional mean-field approach. To provide more general insight we summarise the performance of the moment dynamics model and the traditional mean-field model over a wide range of parameter regimes. These results help distinguish between those situations where spatial correlation effects are sufficiently strong, such that a moment dynamics model is required, from other situations where spatial correlation effects are sufficiently weak, such that a traditional mean-field model is adequate.

Effects of environmental variation on ecological and evolutionary dynamics

Environmental variation is a fact of life for all the species on earth: for any population of any particular species, the local environmental conditions are liable to vary in both time and space. In today's world, anthropogenic activity is causing habitat loss and fragmentation for many species, which may profoundly alter the characteristics of environmental variation in remaining habitat. Previous research indicates that, as habitat is lost, the spatial configuration of remaining habitat will increasingly affect the dynamics by which populations are governed. Through the use of mathematical models, this thesis asks how environmental variation interacts with species properties to influence population dynamics, local adaptation, and dispersal evolution. More specifically, we couple continuous-time continuous-space stochastic population dynamic models to landscape models. We manipulate environmental variation via parameters such as mean patch size, patch density, and patch longevity. Among other findings, we show that a mixture of high and low quality habitat is commonly better for a population than uniformly mediocre habitat. This conclusion is justified by purely ecological arguments, yet the positive effects of landscape heterogeneity may be enhanced further by local adaptation, and by the evolution of short-ranged dispersal. The predicted evolutionary responses to environmental variation are complex, however, since they involve numerous conflicting factors. We discuss why the species that have high levels of local adaptation within their ranges may not be the same species that benefit from local adaptation during range expansion. We show how habitat loss can lead to either increased or decreased selection for dispersal depending on the type of habitat and the manner in which it is lost. To study the models, we develop a recent analytical method, Perturbation expansion, to enable the incorporation of environmental variation. Within this context, we use two methods to address evolutionary dynamics: Adaptive dynamics, which assumes mutations occur infrequently so that the ecological and evolutionary timescales can be separated, and via Genotype distributions, which assume mutations are more frequent. The two approaches generally lead to similar predictions yet, exceptionally, we show how the evolutionary response of dispersal behaviour to habitat turnover may qualitatively depend on the mutation rate.

Ecological communities in variable environments : dynamics and diversity under coloured environmental stochasticity

While environmental variation is an ubiquitous phenomenon in the natural world which has for long been appreciated by the scientific community recent changes in global climatic conditions have begun to raise consciousness about the economical, political and sociological ramifications of global climate change. Climate warming has already resulted in documented changes in ecosystem functioning, with direct repercussions on ecosystem services. While predicting the influence of ecosystem changes on vital ecosystem services can be extremely difficult, knowledge of the organisation of ecological interactions within natural communities can help us better understand climate driven changes in ecosystems. The role of environmental variation as an agent mediating population extinctions is likely to become increasingly important in the future. In previous studies population extinction risk in stochastic environmental conditions has been tied to an interaction between population density dependence and the temporal autocorrelation of environmental fluctuations. When populations interact with each other, forming ecological communities, the response of such species assemblages to environmental stochasticity can depend, e.g., on trophic structure in the food web and the similarity in species-specific responses to environmental conditions. The results presented in this thesis indicate that variation in the correlation structure between species-specific environmental responses (environmental correlation) can have important qualitative and quantitative effects on community persistence and biomass stability in autocorrelated (coloured) environments. In addition, reddened environmental stochasticity and ecological drift processes (such as demographic stochasticity and dispersal limitation) have important implications for patterns in species relative abundances and community dynamics over time and space. Our understanding of patterns in biodiversity at local and global scale can be enhanced by considering the relevance of different drift processes for community organisation and dynamics. Although the results laid out in this thesis are based on mathematical simulation models, they can be valuable in planning effective empirical studies as well as in interpreting existing empirical results. Most of the metrics considered here are directly applicable to empirical data.

Prediction of inplane damping from deterministic and stochastic models

This paper reviews computational reliability, computer algebra, stochastic stability and rotating frame turbulence (RFT) in the context of predicting the blade inplane mode stability, a mode which is at best weakly damped. Computational reliability can be built into routine Floquet analysis involving trim analysis and eigenanalysis, and a highly portable special purpose processor restricted to rotorcraft dynamics analysis is found to be more economical than a multipurpose processor. While the RFT effects are dominant in turbulence modeling, the finding that turbulence stabilizes the inplane mode is based on the assumption that turbulence is white noise.

Learning dynamic prices in multiseller electronic retail markets with price sensitive customers, stochastic demands, and inventory replenishments

In this paper, we use reinforcement learning (RL) as a tool to study price dynamics in an electronic retail market consisting of two competing sellers, and price sensitive and lead time sensitive customers. Sellers, offering identical products, compete on price to satisfy stochastically arriving demands (customers), and follow standard inventory control and replenishment policies to manage their inventories. In such a generalized setting, RL techniques have not previously been applied. We consider two representative cases: 1) no information case, were none of the sellers has any information about customer queue levels, inventory levels, or prices at the competitors; and 2) partial information case, where every seller has information about the customer queue levels and inventory levels of the competitors. Sellers employ automated pricing agents, or pricebots, which use RL-based pricing algorithms to reset the prices at random intervals based on factors such as number of back orders, inventory levels, and replenishment lead times, with the objective of maximizing discounted cumulative profit. In the no information case, we show that a seller who uses Q-learning outperforms a seller who uses derivative following (DF). In the partial information case, we model the problem as a Markovian game and use actor-critic based RL to learn dynamic prices. We believe our approach to solving these problems is a new and promising way of setting dynamic prices in multiseller environments with stochastic demands, price sensitive customers, and inventory replenishments.

Confinement induced stochastic sensing of charged coronene and perylene aggregates in alpha-hemolysin nanochannels

Biological nanopores provide optimum dimensions and an optimal environment to study early aggregation kinetics of charged polyaromatic molecules in the nano-confined regime. It is expected that probing early stages of nucleation will enable us to design a strategy for supramolecular assembly and biocrystallization processes. Specifically, we have studied translocation dynamics of coronene and perylene based salts, through the alpha-hemolysin (alpha-HL) protein nanopore. The characteristic blocking events in the time-series signal are a function of concentration and bias voltage. We argue that different blocking events arise due to different aggregation processes as captured by all atomistic molecular dynamics (MD) simulations. These confinement induced aggregations of polyaromatic chromophores during the different stages of translocation are correlated with the spatial symmetry and charge distribution of the molecules.

Finite-temperature dynamics of vortices in Bose-Einstein condensates

We study the dynamics of a single vortex and a pair of vortices in quasi two-dimensional Bose-Einstein condensates at finite temperatures. To this end, we use the stochastic Gross-Pitaevskii equation, which is the Langevin equation for the Bose-Einstein condensate. For a pair of vortices, we study the dynamics of both the vortex-vortex and vortex-antivortex pairs, which are generated by rotating the trap and moving the Gaussian obstacle potential, respectively. Due to thermal fluctuations, the constituent vortices are not symmetrically generated with respect to each other at finite temperatures. This initial asymmetry coupled with the presence of random thermal fluctuations in the system can lead to different decay rates for the component vortices of the pair, especially in the case of two corotating vortices.

Globally coupled stochastic two-state oscillators: Fluctuations due to finite numbers

Infinite arrays of coupled two-state stochastic oscillators exhibit well-defined steady states. We study the fluctuations that occur when the number N of oscillators in the array is finite. We choose a particular form of global coupling that in the infinite array leads to a pitchfork bifurcation from a monostable to a bistable steady state, the latter with two equally probable stationary states. The control parameter for this bifurcation is the coupling strength. In finite arrays these states become metastable: The fluctuations lead to distributions around the most probable states, with one maximum in the monostable regime and two maxima in the bistable regime. In the latter regime, the fluctuations lead to transitions between the two peak regions of the distribution. Also, we find that the fluctuations break the symmetry in the bimodal regime, that is, one metastable state becomes more probable than the other, increasingly so with increasing array size. To arrive at these results, we start from microscopic dynamical evolution equations from which we derive a Langevin equation that exhibits an interesting multiplicative noise structure. We also present a master equation description of the dynamics. Both of these equations lead to the same Fokker-Planck equation, the master equation via a 1/N expansion and the Langevin equation via standard methods of Ito calculus for multiplicative noise. From the Fokker-Planck equation we obtain an effective potential that reflects the transition from the monomodal to the bimodal distribution as a function of a control parameter. We present a variety of numerical and analytic results that illustrate the strong effects of the fluctuations. We also show that the limits N -> infinity and t -> infinity(t is the time) do not commute. In fact, the two orders of implementation lead to drastically different results.

Scaling law characterizing the dynamics of the transition of HIV-1 to error catastrophe

Increasing the mutation rate, mu, of viruses above a threshold, mu(c), has been predicted to trigger a catastrophic loss of viral genetic information and is being explored as a novel intervention strategy. Here, we examine the dynamics of this transition using stochastic simulations mimicking within-host HIV-1 evolution. We find a scaling law governing the characteristic time of the transition: tau approximate to 0.6/(mu - mu(c)). The law is robust to variations in underlying evolutionary forces and presents guidelines for treatment of HIV-1 infection with mutagens. We estimate that many years of treatment would be required before HIV-1 can suffer an error catastrophe.