Statistical dynamics of dislocation systems: The influence of dislocation-dislocation correlations.

During plastic deformation of crystalline materials, the collective dynamics of interacting dislocations gives rise to various patterning phenomena. A crucial and still open question is whether the long range dislocation-dislocation interactions which do not have an intrinsic range can lead to spatial patterns which may exhibit well-defined characteristic scales. It is demonstrated for a general model of two-dimensional dislocation systems that spontaneously emerging dislocation pair correlations introduce a length scale which is proportional to the mean dislocation spacing. General properties of the pair correlation functions are derived, and explicit calculations are performed for a simple special case, viz pair correlations in single-glide dislocation dynamics. It is shown that in this case the dislocation system exhibits a patterning instability leading to the formation of walls normal to the glide plane. The results are discussed in terms of their general implications for dislocation patterning.

A new modelling framework for statistical cumulus dynamics

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying assumptions are made, a diagnostic dependence of convection on the large-scale environment and the limit of many plumes often being imposed from the outset. Some recent studies have sought to remove one or the other of those assumptions. The proposed framework removes both, and is explicitly time-dependent and stochastic in its basic character. The statistical dynamics of the plume collection are defined through simple probabilistic rules applied at the level of individual plumes, and van Kampen's system size expansion is then used to construct the macroscopic limit of the microscopic model. Through suitable choices of the microscopic rules, the model is shown to encompass previous studies in the appropriate limits, and to allow their natural extensions beyond those limits.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

Conceptual and statistical modelling of environmental effects in population dynamics

Population dynamics are generally viewed as the result of intrinsic (purely density dependent) and extrinsic (environmental) processes. Both components, and potential interactions between those two, have to be modelled in order to understand and predict dynamics of natural populations; a topic that is of great importance in population management and conservation. This thesis focuses on modelling environmental effects in population dynamics and how effects of potentially relevant environmental variables can be statistically identified and quantified from time series data. Chapter I presents some useful models of multiplicative environmental effects for unstructured density dependent populations. The presented models can be written as standard multiple regression models that are easy to fit to data. Chapters II IV constitute empirical studies that statistically model environmental effects on population dynamics of several migratory bird species with different life history characteristics and migration strategies. In Chapter II, spruce cone crops are found to have a strong positive effect on the population growth of the great spotted woodpecker (Dendrocopos major), while cone crops of pine another important food resource for the species do not effectively explain population growth. The study compares rate- and ratio-dependent effects of cone availability, using state-space models that distinguish between process and observation error in the time series data. Chapter III shows how drought, in combination with settling behaviour during migration, produces asymmetric spatially synchronous patterns of population dynamics in North American ducks (genus Anas). Chapter IV investigates the dynamics of a Finnish population of skylark (Alauda arvensis), and point out effects of rainfall and habitat quality on population growth. Because the skylark time series and some of the environmental variables included show strong positive autocorrelation, the statistical significances are calculated using a Monte Carlo method, where random autocorrelated time series are generated. Chapter V is a simulation-based study, showing that ignoring observation error in analyses of population time series data can bias the estimated effects and measures of uncertainty, if the environmental variables are autocorrelated. It is concluded that the use of state-space models is an effective way to reach more accurate results. In summary, there are several biological assumptions and methodological issues that can affect the inferential outcome when estimating environmental effects from time series data, and that therefore need special attention. The functional form of the environmental effects and potential interactions between environment and population density are important to deal with. Other issues that should be considered are assumptions about density dependent regulation, modelling potential observation error, and when needed, accounting for spatial and/or temporal autocorrelation.

Kinetics and Statistical Distributions of Single-Molecule Conformational Dynamics

We developed a coarse-grained yet microscopic detailed model to study the statistical fluctuations of single-molecule protein conformational dynamics of adenylate kinase. We explored the underlying conformational energy landscape and found that the system has two basins of attractions, open and closed conformations connected by two separate pathways. The kinetics is found to be nonexponential, consistent with single-molecule conformational dynamics experiments. Furthermore, we found that the statistical distribution of the kinetic times for the conformational transition has a long power law tail, reflecting the exponential density of state of the underlying landscape. We also studied the joint distribution of the two pathways and found memory effects.

Single molecule dynamics and statistical fluctuations of gene regulatory networks: A repressilator

The authors developed a time dependent method to study the single molecule dynamics of a simple gene regulatory network: a repressilator with three genes mutually repressing each other. They quantitatively characterize the time evolution dynamics of the repressilator. Furthermore, they study purely dynamical issues such as statistical fluctuations and noise evolution. They illustrated some important features of the biological network such as monostability, spirals, and limit cycle oscillation. Explicit time dependent Fano factors which describe noise evolution and show statistical fluctuations out of equilibrium can be significant and far from the Poisson distribution. They explore the phase space and the interrelationships among fluctuations, order, amplitude, and period of oscillations of the repressilators. The authors found that repressilators follow ordered limit cycle orbits and are more likely to appear in the lower fluctuating regions. The amplitude of the repressilators increases as the suppressing of the genes decreases and production of proteins increases. The oscillation period of the repressilators decreases as the suppressing of the genes decreases and production of proteins increases.

Dynamics and intrinsic statistical fluctuations of a gene switch

We studied a simple gene regulatory network, the toggle switch. Specifically, we examined the means and statistical fluctuations in numbers of proteins. We found that when omega, the ratio of rates of protein-gene unbinding to protein degradation, was between similar to 10(-3) and similar to 10, the fluctuations were much larger than those we would have expected from Poisson statistics. In addition, we examined characteristic time values for system relaxation and found both that they increased with omega and that they have significant phase transition effects, with a secondary time scale appearing near the boundary between bistable and other phases. Last, we discuss the bistability of the toggle switch.

Statistical-mechanical description of classical test-particle dynamics in the presence of an external force field: modelling noise and damping from first principles

Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly coupled to a large heat-bath in thermal equilibrium. Both subsystems are subject to an external force field. From the (time-non-local) generalized master equation a Fokker-Planck-type equation follows as a "quasi-Markovian" approximation. The kinetic operator thus defined is shown to be ill-defined; in specific, it does not preserve the positivity of the test-particle distribution function f(x, v; t). Adopting an alternative approach, previously introduced for quantum open systems, is proposed to lead to a correct kinetic operator, which yields all the expected properties. A set of explicit expressions for the diffusion and drift coefficients are obtained, allowing for modelling macroscopic diffusion and dynamical friction phenomena, in terms of an external field and intrinsic physical parameters.

Modelling the dynamics of genetic algorithms using statistical mechanics

A formalism for modelling the dynamics of Genetic Algorithms (GAs) using methods from statistical mechanics, originally due to Prugel-Bennett and Shapiro, is reviewed, generalized and improved upon. This formalism can be used to predict the averaged trajectory of macroscopic statistics describing the GA's population. These macroscopics are chosen to average well between runs, so that fluctuations from mean behaviour can often be neglected. Where necessary, non-trivial terms are determined by assuming maximum entropy with constraints on known macroscopics. Problems of realistic size are described in compact form and finite population effects are included, often proving to be of fundamental importance. The macroscopics used here are cumulants of an appropriate quantity within the population and the mean correlation (Hamming distance) within the population. Including the correlation as an explicit macroscopic provides a significant improvement over the original formulation. The formalism is applied to a number of simple optimization problems in order to determine its predictive power and to gain insight into GA dynamics. Problems which are most amenable to analysis come from the class where alleles within the genotype contribute additively to the phenotype. This class can be treated with some generality, including problems with inhomogeneous contributions from each site, non-linear or noisy fitness measures, simple diploid representations and temporally varying fitness. The results can also be applied to a simple learning problem, generalization in a binary perceptron, and a limit is identified for which the optimal training batch size can be determined for this problem. The theory is compared to averaged results from a real GA in each case, showing excellent agreement if the maximum entropy principle holds. Some situations where this approximation brakes down are identified. In order to fully test the formalism, an attempt is made on the strong sc np-hard problem of storing random patterns in a binary perceptron. Here, the relationship between the genotype and phenotype (training error) is strongly non-linear. Mutation is modelled under the assumption that perceptron configurations are typical of perceptrons with a given training error. Unfortunately, this assumption does not provide a good approximation in general. It is conjectured that perceptron configurations would have to be constrained by other statistics in order to accurately model mutation for this problem. Issues arising from this study are discussed in conclusion and some possible areas of further research are outlined.

Complexity of classical dynamics of molecular systems. II. Finite statistical complexity of a water-Na+ system

The computational mechanics approach has been applied to the orientational behavior of water molecules in a molecular dynamics simulated water–Na + system. The distinctively different statistical complexity of water molecules in the bulk and in the first solvation shell of the ion is demonstrated. It is shown that the molecules undergo more complex orientational motion when surrounded by other water molecules compared to those constrained by the electric field of the ion. However the spatial coordinates of the oxygen atom shows the opposite complexity behavior in that complexity is higher for the solvation shell molecules. New information about the dynamics of water molecules in the solvation shell is provided that is additional to that given by traditional methods of analysis.

Intensity dynamics and statistical properties of random distributed feedback fiber laser

We present first experimental investigation of fast-intensity dynamics of random distributed feedback (DFB) fiber lasers. We found that the laser dynamics are stochastic on a short time scale and exhibit pronounced fluctuations including generation of extreme events. We also experimentally characterize statistical properties of radiation of random DFB fiber lasers. We found that statistical properties deviate from Gaussian and depend on the pump power.

The importance of gestation process dynamics

Principal Topic In this paper we seek to highlight the important intermediate role that the gestation process plays in entrepreneurship by examining its key antecedents and its consequences for new venture emergence. In doing so we take a behavioural perspective and argue that it is not only what a nascent venture is, but what it does (Katz & Gartner, 1988; Shane & Delmar, 2004; Reynolds, 2007) and when it does it during start-up (Reynolds & Miller, 1992; Lichtenstein, Carter, Dooley & Gartner, 2007) that is important. To extend an analogy from biological development, what we suggest is that the way a new venture is nurtured is just as fundamental as its nature. Much prior research has focused on the nature of new ventures and attempted to attribute variations in outcomes directly to the impact resource endowments and investments have. While there is little doubt that venture resource attributes such as human capital, and specifically prior entrepreneurial experience (Alsos & Kolvereid, 1998), access to social (Davidsson & Honig, 2003) and financial capital have an influence. Resource attributes themselves are distal from successful start-up endeavours and remain inanimate if not for the actions of the nascent venture. The key contribution we make is to shift focus from whether or not actions are taken, but when these actions happen and how that is situated in the overall gestation process. Thus, we suggest that it is gestation process dynamics, or when gestation actions occur, that is more proximal to venture outcomes and we focus on this. Recently scholars have highlighted the complexity that exists in the start-up or gestation process, be it temporal or contextual (Liao, Welsch & Tan, 2005; Lichtenstein et al. 2007). There is great variation in how long a start-up process might take (Reynolds & Miller, 1992), some processes require less action than others (Carter, Gartner & Reynolds, 1996), and the overall intensity of the start-up effort is also deemed important (Reynolds, 2007). And, despite some evidence that particular activities are more influential than others (Delmar & Shane, 2003), the order in which events may happen is, until now, largely indeterminate as regard its influence on success (Liao & Welsch, 2008). We suggest that it is this complexity of the intervening gestation process that attenuates the effect of resource endowment and has resulted in mixed findings in previous research. Thus, in order to reduce complexity we shall take a holistic view of the gestation process and argue that it is its’ dynamic properties that determine nascent venture attempt outcomes. Importantly, we acknowledge that particular gestation processes of themselves would not guarantee successful start-up, but it is more correctly the fit between the process dynamics and the ventures attributes (Davidsson, 2005) that is influential. So we aim to examine process dynamics by comparing sub-groups of venture types by resource attributes. Thus, as an initial step toward unpacking the complexity of the gestation process, this paper aims to establish the importance of its role as an intermediary between attributes of the nascent venture and the emergence of that venture. Here, we make a contribution by empirically examining gestation process dynamics and their fit with venture attributes. We do this by firstly, examining that nature of the influence that venture attributes such as human and social capital have on the dynamics of the gestation process, and secondly by investigating the effect that gestation process dynamics have on venture creation outcomes. Methodology and Propositions In order to explore the importance that gestation processes dynamics have in nascent entrepreneurship we conduct an empirical study of ventures start-ups. Data is drawn from a screened random sample of 625 Australian nascent business ventures prior to them achieving consistent outcomes in the market. This data was collected during 2007/8 and 2008/9 as part of the Comprehensive Australian Study of Entrepreneurial Emergence (CAUSEE) project (Davidsson et al., 2008). CAUSEE is a longitudinal panel study conducted over four years, sourcing information from annually administered telephone surveys. Importantly for our study, this methodology allows for the capture and tracking of active nascent venture creation as it happens, thus reducing hindsight and selection biases. In addition, improved tests of causality may be made given that outcome measures are temporally removed from preceding events. The data analysed in this paper represents the first two of these four years, and for the first time has access to follow-up outcome measures for these venture attempts: where 260 were successful, 126 were abandoned, and 191 are still in progress. With regards to venture attributes as gestation process antecedents, we examine specific human capital measured as successful prior experience in entrepreneurship, and direct social capital of the venture as ‘team start-ups’. In assessing gestation process dynamics we follow Lichtenstein et al. (2007) to suggest that the rate, concentration and timing of gestation activities may be used to summarise the complexity dynamics of that process. In addition, we extend this set of measures to include the interaction of discovery and exploitation by way of changes made to the venture idea. Those ventures with successful prior experience or those who conduct symbiotic parallel start-up attempts may be able to, or be forced to, leave their gestation action until later and still derive a successful outcome. In addition access to direct social capital may provide the support upon which the venture may draw in order to persevere in the face of adversity, turning a seemingly futile start-up attempt into a success. On the other hand prior experience may engender the foresight to terminate a venture attempt early should it be seen to be going nowhere. The temporal nature of these conjectures highlight the importance that process dynamics play and will be examined in this research Statistical models are developed to examine gestation process dynamics. We use multivariate general linear modelling to analyse how human and social capital factors influence gestation process dynamics. In turn, we use event history models and stratified Cox regression to assess the influence that gestation process dynamics have on venture outcomes. Results and Implications What entrepreneurs do is of interest to both scholars and practitioners’ alike. Thus the results of this research are important since they focus on nascent behaviour and its outcomes. While venture attributes themselves may be influential this is of little actionable assistance to practitioners. For example it is unhelpful to say to the prospective first time entrepreneur “you’ll be more successful if you have lots of prior experience in firm start-ups”. This research attempts to close this relevance gap by addressing what gestation behaviours might be appropriate, when actions best be focused, and most importantly in what circumstances. Further, we make a contribution to the entrepreneurship literature, examining the role that gestation process dynamics play in outcomes, by specifically attributing these to the nature of the venture itself. This extension is to the best of our knowledge new to the research field.