Stochastic structure and individual-tree growth models

The majority of past and current individual-tree growth modelling methodologies have failed to characterise and incorporate structured stochastic components. Rather, they have relied on deterministic predictions or have added an unstructured random component to predictions. In particular, spatial stochastic structure has been neglected, despite being present in most applications of individual-tree growth models. Spatial stochastic structure (also called spatial dependence or spatial autocorrelation) eventuates when spatial influences such as competition and micro-site effects are not fully captured in models. Temporal stochastic structure (also called temporal dependence or temporal autocorrelation) eventuates when a sequence of measurements is taken on an individual-tree over time, and variables explaining temporal variation in these measurements are not included in the model. Nested stochastic structure eventuates when measurements are combined across sampling units and differences among the sampling units are not fully captured in the model. This review examines spatial, temporal, and nested stochastic structure and instances where each has been characterised in the forest biometry and statistical literature. Methodologies for incorporating stochastic structure in growth model estimation and prediction are described. Benefits from incorporation of stochastic structure include valid statistical inference, improved estimation efficiency, and more realistic and theoretically sound predictions. It is proposed in this review that individual-tree modelling methodologies need to characterise and include structured stochasticity. Possibilities for future research are discussed. (C) 2001 Elsevier Science B.V. All rights reserved.

The influence of memory for prior instances on performance in a conflict detection task

In 3 experiments, the authors examined the role of memory for prior instances for making relative judgments in conflict detection. Participants saw pairs of aircraft either repeatedly conflict with each other or pass safely before being tested on new aircraft pairs, which varied in similarity to the training pairs. Performance was influenced by the similarity between aircraft pairs. Detection time was faster when a conflict pair resembled a pair that had repeatedly conflicted. Detection time was slower, and participants missed conflicts, when a conflict pair resembled a pair that had repeatedly passed safely. The findings identify aircraft features that are used as inputs into the memory decision process and provide an indication of the processes involved in the use of memory for prior instances to make relative judgments.

Optimal strategies in political elections

In the Majoritarian Parliamentary System, the government has a constitutional right to call an early election. This right provides the government a control to achieve its objective to remain in power for as long as possible. We model the early election problem mathematically using opinion polls data as a stochastic process to proxy the government's probability of re-election. These data measure the difference in popularity between the government and the opposition. We fit a mean reverting Stochastic Differential Equation to describe the behaviour of the process and consider the possibility for the government to use other control tools, which are termed 'boosts' to induce shocks to the opinion polls by making timely policy announcements or economic actions. These actions improve the government's popularity and have some impact upon the early-election exercise boundary. © Austral. Mathematical Soc. 2005.

A framework for valuing derivative securities

This paper develops a general framework for valuing a wide range of derivative securities. Rather than focusing on the stochastic process of the underlying security and developing an instantaneously-riskless hedge portfolio, we focus on the terminal distribution of the underlying security. This enables the derivative security to be valued as the weighted sum of a number of component pieces. The component pieces are simply the different payoffs that the security generates in different states of the world, and they are weighted by the probability of the particular state of the world occurring. A full set of derivations is provided. To illustrate its use, the valuation framework is applied to plain-vanilla call and put options, as well as a range of derivatives including caps, floors, collars, supershares, and digital options.

Testing the relationship between morphological and molecular rates of change along phylogenies

Molecular evolution has been considered to be essentially a stochastic process, little influenced by the pace of phenotypic change. This assumption was challenged by a study that demonstrated an association between rates of morphological and molecular change estimated for total-evidence phylogenies, a finding that led some researchers to challenge molecular date estimates of major evolutionary radiations. Here we show that Omland's (1997) result is probably due to methodological bias, particularly phylogenetic nonindependence, rather than being indicative of an underlying evolutionary phenomenon. We apply three new methods specifically designed to overcome phylogenetic bias to 13 published phylogenetic datasets for vertebrate taxa, each of which includes both morphological characters and DNA sequence data. We find no evidence of an association between rates of molecular and morphological rates of change.

Evolving noisy oscillatory dynamics in genetic regulatory networks

We introduce a genetic programming (GP) approach for evolving genetic networks that demonstrate desired dynamics when simulated as a discrete stochastic process. Our representation of genetic networks is based on a biochemical reaction model including key elements such as transcription, translation and post-translational modifications. The stochastic, reaction-based GP system is similar but not identical with algorithmic chemistries. We evolved genetic networks with noisy oscillatory dynamics. The results show the practicality of evolving particular dynamics in gene regulatory networks when modelled with intrinsic noise.

The number of long-lasting functional memory CD8(+) T cells generated depends on the nature of the initial nonspecific stimulation

The mechanism of generation of memory cytotoxic T cells (CTL) following immunization remains controversial. Using tumor protection and IFN-gamma ELISPOT assays in mice to detect functional CTL, we show that the initial effector CTL burst size after immunization is not directly related to the amount of functional memory CTL formed, suggesting that memory CTL are unlikely to arise stochastically from effector CTL. Induction of MHC class II-restricted T helper cells at the time of immunization by inclusion of a T helper peptide or protein in the immunogen, is necessary to generate memory CTL, although no T helper cell induction is required to generate effector CTL to a strong MHC class I-binding peptide. Host protective T cell memory correlates with the number of CTL epitope responsive IFN-gamma-secreting memory T cells as measured in an ELISPOT assay at the time of tumor challenge. We conclude that a different antigen presenting environment is required to induce long-lasting functional memory CTL, and non-cognate stimulation of the immune system is essential to allow generation of a long-lasting host protective memory CTL response.

What do students remember? Episodic memory and the development of schematization

Research examining changes in memory and memory awareness during learning suggests that early in the process, students primarily have representations that are episodic in nature and experience, 'remember' awareness during recall. However, as learning continues and schematization occurs, students' knowledge is more likely to be dominated by semantic memory representations and 'just know' awareness is experienced during recall. The greater the amount of remembering experienced early in learning, the more likely it is that the shift to knowing will occur in students. In this study, university students studied either material rich in distinctive features that may serve as cues to episodic memory, or material lacking in these features. Students' knowledge was tested after a 2-day and a 5-wk interval. In contrast to students who studied the material lacking distinctive features, students who studied the distinctively rich material showed a predominance of remember awareness on the first test, and on the follow-up test showed a predominance of know awareness and were able to recall more details of the learning material. Copyright (C) 2004 John Wiley Sons, Ltd.

Stochastic modelling of the invasion process of nematodes in fly larvae

Stochastic models based on Markov birth processes are constructed to describe the process of invasion of a fly larva by entomopathogenic nematodes. Various forms for the birth (invasion) rates are proposed. These models are then fitted to data sets describing the observed numbers of nematodes that have invaded a fly larval after a fixed period of time. Non-linear birthrates are required to achieve good fits to these data, with their precise form leading to different patterns of invasion being identified for three populations of nematodes considered. One of these (Nemasys) showed the greatest propensity for invasion. This form of modelling may be useful more generally for analysing data that show variation which is different from that expected from a binomial distribution.

Quantum noise in optical fibers. I. Stochastic equations

We analyze the quantum dynamics of radiation propagating in a single-mode optical fiber with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known nonlinear effects and quantum-noise sources, including linear gain and loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are treated. This treatment allows quantum Langevin equations, which have a classical form except for additional quantum-noise terms, to be calculated. In practical calculations, it is more useful to transform to Wigner or 1P quasi-probability operator representations. These transformations result in stochastic equations that can be analyzed by use of perturbation theory or exact numerical techniques. The results have applications to fiber-optics communications, networking, and sensor technology.

Optical study of a light diaphragm rupture process in an expansion tube

Rupture of a light cellophane diaphragm in an expansion tube has been studied by an optical method. The influence of the light diaphragm on test flow generation has long been recognised, however the diaphragm rupture mechanism is less well known. It has been previously postulated that the diaphragm ruptures around its periphery due to the dynamic pressure loading of the shock wave, with the diaphragm material at some stage being removed from the flow to allow the shock to accelerate to the measured speeds downstream. The images obtained in this series of experiments are the first to show the mechanism of diaphragm rupture and mass removal in an expansion tube. A light diaphragm was impulsively loaded via a shock wave and a series of images was recorded holographically throughout the rupture process, showing gradual destruction of the diaphragm. Features such as the diaphragm material, the interface between gases, and a reflected shock were clearly visualised. Both qualitative and quantitative aspects of the rupture dynamics were derived from the images and compared with existing one-dimensional theory.

The collision branching process

We consider a branching model, which we call the collision branching process (CBP), that accounts for the effect of collisions, or interactions, between particles or individuals. We establish that there is a unique CBP, and derive necessary and sufficient conditions for it to be nonexplosive. We review results on extinction probabilities, and obtain explicit expressions for the probability of explosion and the expected hitting times. The upwardly skip-free case is studied in some detail.

Effects of memory load and distraction on performance and event-related slow potentials in a visuospatial working memory task

Brain electrical activity related to working memory was recorded at 15 scalp electrodes during a visuospatial delayed response task. Participants (N = 18) touched the remembered position of a target on a computer screen after either a 1 or 8 sec delay. These memory trials were compared to sensory trials in which the target remained present throughout the delay and response periods. Distracter stimuli identical to the target were briefly presented during the delay on 30% of trials. Responses were less accurate in memory than sensory trials, especially after the long delay. During the delay slow potentials developed that were significantly more negative in memory than sensory trials. The difference between memory and sensory trials was greater at anterior than posterior electrodes. On trials with distracters, the slow potentials generated by memory trials showed further enhancement of negativity whereas there were minimal effects on accuracy of performance. The results provide evidence that engagement of visuospatial working memory generates slow wave negativity with a timing and distribution consistent with frontal activation. Enhanced brain activity associated with working memory is required to maintain performance in the presence of distraction. © 1997 by the Massachusetts Institute of Technology