Formalizing Triggers: A Learning Model for Finite Spaces

In a recent seminal paper, Gibson and Wexler (1993) take important steps to formalizing the notion of language learning in a (finite) space whose grammars are characterized by a finite number of parameters. They introduce the Triggering Learning Algorithm (TLA) and show that even in finite space convergence may be a problem due to local maxima. In this paper we explicitly formalize learning in finite parameter space as a Markov structure whose states are parameter settings. We show that this captures the dynamics of TLA completely and allows us to explicitly compute the rates of convergence for TLA and other variants of TLA e.g. random walk. Also included in the paper are a corrected version of GW's central convergence proof, a list of "problem states" in addition to local maxima, and batch and PAC-style learning bounds for the model.

Determining WWW User's Next Access and Its Application to Pre-fetching

World-Wide Web (WWW) services have grown to levels where significant delays are expected to happen. Techniques like pre-fetching are likely to help users to personalize their needs, reducing their waiting times. However, pre-fetching is only effective if the right documents are identified and if user's move is correctly predicted. Otherwise, pre-fetching will only waste bandwidth. Therefore, it is productive to determine whether a revisit will occur or not, before starting pre-fetching. In this paper we develop two user models that help determining user's next move. One model uses Random Walk approximation and the other is based on Digital Signal Processing techniques. We also give hints on how to use such models with a simple pre-fetching technique that we are developing.

Discounting the distant future: How much do uncertain rates increase valuations?

We demonstrate that when the future path of the discount rate is uncertain and highly correlated, the distant future should be discounted at significantly lower rates than suggested by the current rate. We then use two centuries of US interest rate data to quantify this effect. Using both random walk and mean-reverting models, we compute the "certainty-equivalent rate" that summarizes the effect of uncertainty and measures the appropriate forward rate of discount in the future. Under the random walk model we find that the certainty-equivalent rate falls continuously from 4% to 2% after 100 years, 1% after 200 years, and 0.5% after 300 years. At horizons of 400 years, the discounted value increases by a factor of over 40,000 relative to conventional discounting. Applied to climate change mitigation, we find that incorporating discount rate uncertainty almost doubles the expected present value of mitigation benefits. © 2003 Elsevier Science (USA). All rights reserved.

Encounter success of free-ranging marine predator movements across a dynamic prey landscape

Movements of wide-ranging top predators can now be studied effectively using satellite and archival telemetry. However, the motivations underlying movements remain difficult to determine because trajectories are seldom related to key biological gradients, such as changing prey distributions. Here, we use a dynamic prey landscape of zooplankton biomass in the north-east Atlantic Ocean to examine active habitat selection in the plankton-feeding basking shark Cetorhinus maximus. The relative success of shark searches across this landscape was examined by comparing prey biomass encountered by sharks with encounters by random-walk simulations of ‘model’ sharks. Movements of transmitter-tagged sharks monitored for 964 days (16754km estimated minimum distance) were concentrated on the European continental shelf in areas characterized by high seasonal productivity and complex prey distributions. We show movements by adult and sub-adult sharks yielded consistently higher prey encounter rates than 90% of random-walk simulations. Behavioural patterns were consistent with basking sharks using search tactics structured across multiple scales to exploit the richest prey areas available in preferred habitats. Simple behavioural rules based on learned responses to previously encountered prey distributions may explain the high performances. This study highlights how dynamic prey landscapes enable active habitat selection in large predators to be investigated from a trophic perspective, an approach that may inform conservation by identifying critical habitat of vulnerable species.

Basking sharks and oceanographic fronts: quantifying associations in the north‐east Atlantic

Understanding the mechanisms linking oceanographic processes and marine vertebrate habitat use is critical to effective management of populations of conservation concern. The basking shark Cetorhinus maximus has been shown to associate with oceanographic fronts – physical interfaces at the transitions between water masses – to exploit foraging opportunities resulting from aggregation of zooplankton. However, the scale, significance and variability of these observed associations have not yet been established. Here, we quantify the influence of mesoscale (10s – 100s km) frontal activity on habitat use over timescales of weeks to months. We use animal-mounted archival tracking with composite front mapping via Earth Observation (EO) remote sensing to provide an oceanographic context to individual shark movements. We investigate levels of association with fronts occurring over two spatio-temporal scales, (i) broad-scale seasonally persistent frontal zones and (ii) contemporaneous mesoscale thermal and chl-a fronts. Using random walk simulations and logistic regression within an iterative generalised linear mixed modelling (GLMM) framework, we find that seasonal front frequency is a significant predictor of shark presence. Temporally-matched oceanographic metrics also indicate that sharks demonstrate a preference for productive regions, and associate with contemporaneous thermal and chl-a fronts more frequently than could be expected at random. Moreover, we highlight the importance of cross-frontal temperature change and persistence, which appear to interact to affect the degree of prey aggregation along thermal fronts. These insights have clear implications for understanding the preferred habitats of basking sharks in the context of anthropogenic threat management and marine spatial planning in the northeast Atlantic.

Basking sharks and oceanographic fronts: quantifying associations in the north-east Atlantic

Understanding the mechanisms linking oceanographic processes and marine vertebrate habitat use is critical to effective management of populations of conservation concern. The basking shark Cetorhinus maximus has been shown to associate with oceanographic fronts – physical interfaces at the transitions between water masses – to exploit foraging opportunities resulting from aggregation of zooplankton. However, the scale, significance and variability of these observed associations have not yet been established. Here, we quantify the influence of mesoscale (10s – 100s km) frontal activity on habitat use over timescales of weeks to months. We use animal-mounted archival tracking with composite front mapping via Earth Observation (EO) remote sensing to provide an oceanographic context to individual shark movements. We investigate levels of association with fronts occurring over two spatio-temporal scales, (i) broad-scale seasonally persistent frontal zones and (ii) contemporaneous mesoscale thermal and chl-a fronts. Using random walk simulations and logistic regression within an iterative generalised linear mixed modelling (GLMM) framework, we find that seasonal front frequency is a significant predictor of shark presence. Temporally-matched oceanographic metrics also indicate that sharks demonstrate a preference for productive regions, and associate with contemporaneous thermal and chl-a fronts more frequently than could be expected at random. Moreover, we highlight the importance of cross-frontal temperature change and persistence, which appear to interact to affect the degree of prey aggregation along thermal fronts. These insights have clear implications for understanding the preferred habitats of basking sharks in the context of anthropogenic threat management and marine spatial planning in the northeast Atlantic.

Can benthic community structure be used to predict the process of bioturbation in real ecosystems

Disentangling the roles of environmental change and natural environmental variability on biologically mediated ecosystem processes is paramount to predict future marine ecosystem functioning. Bioturbation, the biogenic mixing of sediments, has a regulating role in marine biogeochemical processes. However, our understanding of bioturbation as a community level process and of its environmental drivers is still limited by loose use of terminology, and a lack of consensus about what bioturbation is. To help resolve these challenges, this empirical study investigated the links between four different attributes of bioturbation (bioturbation depth, activity and distance, and biodiffusive transport); the ability of an index of bioturbation (BPc) to predict each of them; and their relation to seasonality, in a shallow coastal system – the Western Channel Observatory, UK. Bioturbation distance depended on changes in benthic community structure, while the other three attributes were more directly influenced by seasonality in food availability. In parallel, BPc successfully predicted bioturbation distance but not the other attributes of bioturbation. This study therefore highlights that community bioturbation results from this combination of processes responding to environmental variability at different time-scales. However, community level measurements of bioturbation across environmental variability are still scarce, and BPc is calculated using commonly available data on benthic community structure and the functional classification of invertebrates. Therefore, BPc could be used to support the growth of landscape scale bioturbation research, but future uses of the index need to consider which bioturbation attributes the index actually predicts. As BPc predicts bioturbation distance, estimated here using a random-walk model applicable to community settings, studies using either of the metrics should be directly comparable and contribute to a more integrated future for bioturbation research.

Basking sharks and oceanographic fronts: quantifying associations in the north-east Atlantic

Understanding the mechanisms linking oceanographic processes and marine vertebrate habitat use is critical to effective management of populations of conservation concern. The basking shark Cetorhinus maximus has been shown to associate with oceanographic fronts – physical interfaces at the transitions between water masses – to exploit foraging opportunities resulting from aggregation of zooplankton. However, the scale, significance and variability of these observed associations have not yet been established. Here, we quantify the influence of mesoscale (10s – 100s km) frontal activity on habitat use over timescales of weeks to months. We use animal-mounted archival tracking with composite front mapping via Earth Observation (EO) remote sensing to provide an oceanographic context to individual shark movements. We investigate levels of association with fronts occurring over two spatio-temporal scales, (i) broad-scale seasonally persistent frontal zones and (ii) contemporaneous mesoscale thermal and chl-a fronts. Using random walk simulations and logistic regression within an iterative generalised linear mixed modelling (GLMM) framework, we find that seasonal front frequency is a significant predictor of shark presence. Temporally-matched oceanographic metrics also indicate that sharks demonstrate a preference for productive regions, and associate with contemporaneous thermal and chl-a fronts more frequently than could be expected at random. Moreover, we highlight the importance of cross-frontal temperature change and persistence, which appear to interact to affect the degree of prey aggregation along thermal fronts. These insights have clear implications for understanding the preferred habitats of basking sharks in the context of anthropogenic threat management and marine spatial planning in the northeast Atlantic.

How simple grazing rules can lead to persistent boundaries in vegetation communities.

Natural landscape boundaries between vegetation communities are dynamically influenced by the selective grazing of herbivores. Here we show how this may be an emergent property of very simple animal decisions, without the need for any sophisticated choice rules etc., using a model based on biased diffusion. Animal grazing intensity is coupled with plant competition, resulting in reaction-diffusion dynamics, from which stable boundaries spontaneously emerge. In the model, animals affect their resources by both consumption and trampling. It is assumed that forage consists of two heterogeneously distributed competing resource species, one that is preferred (grass) over the other (heather) by the animals. The solutions to the resulting system of differential equations for three cases a) optimal foraging, b) random walk foraging and c) taxis-diffusion are presented. Optimal and random foraging gave unrealistic results, but taxis-diffusion accorded well with field observations. Persistent boundaries between patches of near-monoculture vegetation were predicted, with these boundaries drifting in response to overall grazing pressure (grass advancing with increased grazing and vice versa). The reaction-taxis-diffusion model provides the first mathematical explanation for such vegetation mosaic dynamics and the parameters of the model are open to experimental testing.

Marine04 marine radiocarbon age calibration, 0-26 cal kyr BP

New radiocarbon calibration curves, IntCal04 and Marine04, have been constructed and internationally ratified to replace the terrestrial and marine components of IntCal98. The new calibration data sets extend an additional 2000 yr, from 0–26 cal kyr BP (Before Present, 0 cal BP = AD 1950), and provide much higher resolution, greater precision, and more detailed structure than IntCal98. For the Marine04 curve, dendrochronologically-dated tree-ring samples, converted with a box diffusion model to marine mixed-layer ages, cover the period from 0–10.5 cal kyr BP. Beyond 10.5 cal kyr BP, high-resolution marine data become available from foraminifera in varved sediments and U/Th-dated corals. The marine records are corrected with site-specific 14C reservoir age information to provide a single global marine mixed-layer calibration from 10.5–26.0 cal kyr BP. A substantial enhancement relative to IntCal98 is the introduction of a random walk model, which takes into account the uncertainty in both the calendar age and the 14C age to calculate the underlying calibration curve (Buck and Blackwell, this issue). The marine data sets and calibration curve for marine samples from the surface mixed layer (Marine04) are discussed here. The tree-ring data sets, sources of uncertainty, and regional offsets are presented in detail in a companion paper by Reimer et al. (this issue).

Microscopic models for dielectric relaxation in disordered systems

It is shown how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to yield the empirical Havriliak-Negami (HN) equation of anomalous dielectric relaxation from a microscopic model based on a kinetic equation just as in the Debye model. This kinetic equation is obtained by means of a generalization of the noninertial Fokker-Planck equation of conventional Brownian motion (generally known as the Smoluchowski equation) to fractional kinetics governed by the HN relaxation mechanism. For the simple case of noninteracting dipoles it may be solved by Fourier transform techniques to yield the Green function and the complex dielectric susceptibility corresponding to the HN anomalous relaxation mechanism.

IntCal04 terrestrial radiocarbon age calibration, 0-26 cal kyr BP

A new calibration curve for the conversion of radiocarbon ages to calibrated (cal) ages has been constructed and internationally ratified to replace IntCal98, which extended from 0-24 cal kyr BP (Before Present, 0 cal BP = AD 1950). The new calibration data set for terrestrial samples extends from 0-26 cal kyr BP, but with much higher resolution beyond 11.4 cal kyr BP than IntCal98. Dendrochronologically-dated tree-ring samples cover the period from 0-12.4 cal kyr BP. Beyond the end of the tree rings, data from marine records (corals and foraminifera) are converted to the atmospheric equivalent with a site-specific marine reservoir correction to provide terrestrial calibration from 12.4-26.0 cal kyr BP. A substantial enhancement relative to IntCal98 is the introduction of a coherent statistical approach based on a random walk model, which takes into account the uncertainty in both the calendar age and the (super 14) C age to calculate the underlying calibration curve (Buck and Blackwell, this issue). The tree-ring data sets, sources of uncertainty, and regional offsets are discussed here. The marine data sets and calibration curve for marine samples from the surface mixed layer (Marine04) are discussed in brief, but details are presented in Hughen et al. (this issue a). We do not make a recommendation for calibration beyond 26 cal kyr BP at this time; however, potential calibration data sets are compared in another paper (van der Plicht et al., this issue).

Solving the advection-dispersion equation using the discrete puff particle method

A flexible, mass-conservative numerical technique for solving the advection-dispersion equation for miscible contaminant transport is presented. The method combines features of puff transport models from air pollution studies with features from the random walk particle method used in water resources studies, providing a deterministic time-marching algorithm which is independent of the grid Peclet number and scales from one to higher dimensions simply. The concentration field is discretised into a number of particles, each of which is treated as a point release which advects and disperses over the time interval. The dispersed puff is itself discretised into a spatial distribution of particles whose masses can be pre-calculated. Concentration within the simulation domain is then calculated from the mass distribution as an average over some small volume. Comparison with analytical solutions for a one-dimensional fixed-duration concentration pulse and for two-dimensional transport in an axisymmetric flow field indicate that the algorithm performs well. For a given level of accuracy the new method has lower computation times than the random walk particle method.

A New Theory for Perpendicular Transport of Cosmic Rays

We present an improved nonlinear theory for the perpendicular transport of charged particles. This approach is based on an improved nonlinear treatment of field-line random walk in combination with a generalized compound diffusion model. The generalized compound diffusion model employed is more systematic and reliable, in comparison with previous theories. Furthermore, the theory shows remarkably good agreement with test-particle simulations and solar wind observations.

Analytical description of stochastic field-Line wandering in magnetic turbulence

A nonperturbative nonlinear statistical approach is presented to describe turbulent magnetic systems embedded in a uniform mean magnetic field. A general formula in the form of an ordinary differential equation for magnetic field-line wandering (random walk) is derived. By considering the solution of this equation for different limits several new results are obtained. As an example, it is demonstrated that the stochastic wandering of magnetic field-lines in a two-component turbulence model leads to superdiffusive transport, contrary to an existing diffusive picture. The validity of quasilinear theory for field-line wandering is discussed, with respect to different turbulence geometry models, and previous diffusive results are shown to be deduced in appropriate limits.