Stochastic perturbations to dynamical systems: a response theory approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.

Inhibitory control in memory: evidence for negative priming in free recall

Cognitive control mechanisms—such as inhibition—decrease the likelihood that goal-directed activity is ceded to irrelevant events. Here, we use the action of auditory distraction to show how retrieval from episodic long-term memory is affected by competitor inhibition. Typically, a sequence of to-be-ignored spoken distracters drawn from the same semantic category as a list of visually-presented to-be-recalled items impairs free recall performance. In line with competitor inhibition theory (Anderson, 2003), free recall was worse for items on a probe trial if they were a repeat of distracter items presented during the previous, prime, trial (Experiment 1). This effect was only produced when the distracters were dominant members of the same category as the to-be-recalled items on the prime. For prime trials in which distracters were low-dominant members of the to-be-remembered item category or were unrelated to that category—and hence not strong competitors for retrieval—positive priming was found (Experiments 2 & 3). These results are discussed in terms of inhibitory approaches to negative priming and memory retrieval.

Long-distance dispersal and its influence on adaptation to host resistance in a heterogeneous landscape

Small propagules like pollen or fungal spores may be dispersed by the wind over distances of hundreds or thousands of kilometres,even though the median dispersal may be only a few metres. Such long-distance dispersal is a stochastic event which may be exceptionally important in shaping a population. It has been found repeatedly in field studies that subpopulations of wind-dispersed fungal pathogens virulent on cultivars with newly introduced, effective resistance genes are dominated by one or very few genotypes. The role of propagule dispersal distributions with distinct behaviour at long distances in generating this characteristic population structure was studied by computer simulation of dispersal of clonal organisms in a heterogeneous environment with fields of unselective and selective hosts. Power-law distributions generated founder events in which new, virulent genotypes rapidly colonized fields of resistant crop varieties and subsequently dominated the pathogen population on both selective and unselective varieties, in agreement with data on rust and powdery mildew fungi. An exponential dispersal function, with extremely rare dispersal over long distances, resulted in slower colonization of resistant varieties by virulent pathogens or even no colonization if the distance between susceptible source and resistant target fields was sufficiently large. The founder events resulting from long-distance dispersal were highly stochastic and exact quantitative prediction of genotype frequencies will therefore always be difficult.

On a stochastic Trotter formula with application to spontaneous localization models

We consider the relation between so called continuous localization models—i.e. non-linear stochastic Schrödinger evolutions—and the discrete GRW-model of wave function collapse. The former can be understood as scaling limit of the GRW process. The proof relies on a stochastic Trotter formula, which is of interest in its own right. Our Trotter formula also allows to complement results on existence theory of stochastic Schrödinger evolutions by Holevo and Mora/Rebolledo.

Epoch-specific functional networks involved in working memory

Working memory (WM) is not a unitary construct. There are distinct processes involved in encoding information, maintaining it on-line, and using it to guide responses. The anatomical configurations of these processes are more accurately analyzed as functionally connected networks than collections of individual regions. In the current study we analyzed event-related functional magnetic resonance imaging (fMRI) data from a Sternberg Item Recognition Paradigm WM task using a multivariate analysis method that allowed the linking of functional networks to temporally-separated WM epochs. The length of the delay epochs was varied to optimize isolation of the hemodynamic response (HDR) for each task epoch. All extracted functional networks displayed statistically significant sensitivity to delay length. Novel information extracted from these networks that was not apparent in the univariate analysis of these data included involvement of the hippocampus in encoding/probe, and decreases in BOLD signal in the superior temporal gyrus (STG), along with default-mode regions, during encoding/delay. The bilateral hippocampal activity during encoding/delay fits with theoretical models of WM in which memoranda held across the short term are activated long-term memory representations. The BOLD signal decreases in the STG were unexpected, and may reflect repetition suppression effects invoked by internal repetition of letter stimuli. Thus, analysis methods focusing on how network dynamics relate to experimental conditions allowed extraction of novel information not apparent in univariate analyses, and are particularly recommended for WM experiments for which task epochs cannot be randomized.

(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

The short- and long-term fitness consequences of natal dispersal in a wild bird population

Dispersal is a key process in population and evolutionary ecology. Individual decisions are affected by fitness consequences of dispersal, but these are difficult to measure in wild populations. A long-term dataset on a geographically closed bird population, the Mauritius kestrel, offers a rare opportunity to explore fitness consequences. Females dispersed further when the availability of local breeding sites was limited, whereas male dispersal correlated with phenotypic traits. Female but not male fitness was lower when they dispersed longer distances compared to settling close to home. These results suggest a cost of dispersal in females. We found evidence of both short- and long-term fitness consequences of natal dispersal in females, including reduced fecundity in early life and more rapid aging in later life. Taken together, our results indicate that dispersal in early life might shape life history strategies in wild populations.

Memory as discrimination: what distraction reveals

Recalling information involves the process of discriminating between relevant and irrelevant information stored in memory. Not infrequently, the relevant information needs to be selected from amongst a series of related possibilities. This is likely to be particularly problematic when the irrelevant possibilities are not only temporally or contextually appropriate but also overlap semantically with the target or targets. Here, we investigate the extent to which purely perceptual features which discriminate between irrelevant and target material can be used to overcome the negative impact of contextual and semantic relatedness. Adopting a distraction paradigm, it is demonstrated that when distracters are interleaved with targets presented either visually (Experiment 1) or auditorily (Experiment 2), a within-modality semantic distraction effect occurs; semantically-related distracters impact upon recall more than unrelated distracters. In the semantically-related condition, the number of intrusions in recall is reduced whilst the number of correctly recalled targets is simultaneously increased by the presence of perceptual cues to relevance (color features in Experiment 1 or speaker’s gender in Experiment 2). However, as demonstrated in Experiment 3, even presenting semantically-related distracters in a language and a sensory modality (spoken Welsh) distinct from that of the targets (visual English) is insufficient to eliminate false recalls completely, or to restore correct recall to levels seen with unrelated distracters . Together, the study shows how semantic and non-semantic discriminability shape patterns of both erroneous and correct recall.

When long-range zero-lag synchronization is feasible in cortical networks

Many studies have reported long-range synchronization of neuronal activity between brain areas, in particular in the beta and gamma bands with frequencies in the range of 14–30 and 40–80 Hz, respectively. Several studies have reported synchrony with zero phase lag, which is remarkable considering the synaptic and conduction delays inherent in the connections between distant brain areas. This result has led to many speculations about the possible functional role of zero-lag synchrony, such as for neuronal communication, attention, memory, and feature binding. However, recent studies using recordings of single-unit activity and local field potentials report that neuronal synchronization may occur with non-zero phase lags. This raises the questions whether zero-lag synchrony can occur in the brain and, if so, under which conditions. We used analytical methods and computer simulations to investigate which connectivity between neuronal populations allows or prohibits zero-lag synchrony. We did so for a model where two oscillators interact via a relay oscillator. Analytical results and computer simulations were obtained for both type I Mirollo–Strogatz neurons and type II Hodgkin–Huxley neurons. We have investigated the dynamics of the model for various types of synaptic coupling and importantly considered the potential impact of Spike-Timing Dependent Plasticity (STDP) and its learning window. We confirm previous results that zero-lag synchrony can be achieved in this configuration. This is much easier to achieve with Hodgkin–Huxley neurons, which have a biphasic phase response curve, than for type I neurons. STDP facilitates zero-lag synchrony as it adjusts the synaptic strengths such that zero-lag synchrony is feasible for a much larger range of parameters than without STDP.

Quantification of chemical and physical processes influencing ozone during long-range transport using a trajectory ensemble

During long-range transport, many distinct processes – including photochemistry, deposition, emissions and mixing – contribute to the transformation of air mass composition. Partitioning the effects of different processes can be useful when considering the sensitivity of chemical transformation to, for example, a changing environment or anthropogenic influence. However, transformation is not observed directly, since mixing ratios are measured, and models must be used to relate changes to processes. Here, four cases from the ITCT-Lagrangian 2004 experiment are studied. In each case, aircraft intercepted a distinct air mass several times during transport over the North Atlantic, providing a unique dataset and quantifying the net changes in composition from all processes. A new framework is presented to deconstruct the change in O3 mixing ratio (Δ O3) into its component processes, which were not measured directly, taking into account the uncertainty in measurements, initial air mass variability and its time evolution. The results show that the net chemical processing (Δ O3chem) over the whole simulation is greater than net physical processing (Δ O3phys) in all cases. This is in part explained by cancellation effects associated with mixing. In contrast, each case is in a regime of either net photochemical destruction (lower tropospheric transport) or production (an upper tropospheric biomass burning case). However, physical processes influence O3 indirectly through addition or removal of precursor gases, so that changes to physical parameters in a model can have a larger effect on Δ O3chem than Δ O3phys. Despite its smaller magnitude, the physical processing distinguishes the lower tropospheric export cases, since the net photochemical O3 change is −5 ppbv per day in all three cases. Processing is quantified using a Lagrangian photochemical model with a novel method for simulating mixing through an ensemble of trajectories and a background profile that evolves with them. The model is able to simulate the magnitude and variability of the observations (of O3, CO, NOy and some hydrocarbons) and is consistent with the time-average OH following air-masses inferred from hydrocarbon measurements alone (by Arnold et al., 2007). Therefore, it is a useful new method to simulate air mass evolution and variability, and its sensitivity to process parameters.

Metacognitive control over memory processes under auditory distraction

Decades of research attest that memory processes suffer under conditions of auditory distraction. What is however less well understood is whether people are able to modify how their memory processes are deployed in order to compensate for disruptive effects of distraction. The metacognitive approach to memory describes a variety of ways people can exert control over their cognitive processes to optimize performance. Here we describe our recent investigations into how these control processes change under conditions of auditory distraction. We specifically looked at control of encoding in the form of decisions about how long to study a word when it is presented and control of memory reporting in the form of decisions whether to volunteer or withhold retrieved details. Regarding control of encoding, we expected that people would compensate for disruptive effects of distraction by extending study time under noise. Our results revealed, however, that when exposed to irrelevant speech, people curtail rather than extend study. Regarding control of memory reporting, we expected that people would compensate for the loss of access to memory records by volunteering responses held with lower confidence. Our results revealed, however, that people’s reporting strategies do not differ when memory task is performed in silence or under auditory distraction, although distraction seriously undermines people’s confidence in their own responses. Together, our studies reveal novel avenues for investigating the psychological effects of auditory distraction within a metacognitive framework.

Distinction between semantic and episodic memory: The underlying mechanisms for autonoetic consciousness

In 1972, episodic and semantic memories were considered to reflect different types of knowledge (Tulving, 1972). However, these early definitions encountered many difficulties. Now, Episodic and semantic memories are discussed in terms of awareness associated with retrieval (Wheeler, Stuss, & Tulving, 1997): Autonoetic consciousness (i.e., feeling of remembering) is considered associated with retrieval from the episodic memory system, while noetic consciousness (i.e., feeling of knowing) is considered characterized by retrieval from the semantic memory system. The present article investigated determinants of autonoetic consciousness in order to clarify characteristics of perceptual knowledge that is being recalled, the more strongly the individual feels autonoetic consciousness during retrieval, and that autonoetic consciousness is based on rich sensory-perceptual knowledge. Furthermore, we suggested that the parietal and frontal lobes mediate the process of generating autonoetic consciousness. This suggested that sensory-perceptual knowledge, the parietal lobe and the frontal lobe are important factors for discriminating episodic memory afrom semantic memory.

Using an individual-based model to select among alternative foraging strategies of woodpigeons: data support a memory-based model with a flocking mechanism

Population modelling is increasingly recognised as a useful tool for pesticide risk assessment. For vertebrates that may ingest pesticides with their food, such as woodpigeon (Columba palumbus), population models that simulate foraging behaviour explicitly can help predicting both exposure and population-level impact. Optimal foraging theory is often assumed to explain the individual-level decisions driving distributions of individuals in the field, but it may not adequately predict spatial and temporal characteristics of woodpigeon foraging because of the woodpigeons’ excellent memory, ability to fly long distances, and distinctive flocking behaviour. Here we present an individual-based model (IBM) of the woodpigeon. We used the model to predict distributions of foraging woodpigeons that use one of six alternative foraging strategies: optimal foraging, memory-based foraging and random foraging, each with or without flocking mechanisms. We used pattern-oriented modelling to determine which of the foraging strategies is best able to reproduce observed data patterns. Data used for model evaluation were gathered during a long-term woodpigeon study conducted between 1961 and 2004 and a radiotracking study conducted in 2003 and 2004, both in the UK, and are summarised here as three complex patterns: the distributions of foraging birds between vegetation types during the year, the number of fields visited daily by individuals, and the proportion of fields revisited by them on subsequent days. The model with a memory-based foraging strategy and a flocking mechanism was the only one to reproduce these three data patterns, and the optimal foraging model produced poor matches to all of them. The random foraging strategy reproduced two of the three patterns but was not able to guarantee population persistence. We conclude that with the memory-based foraging strategy including a flocking mechanism our model is realistic enough to estimate the potential exposure of woodpigeons to pesticides. We discuss how exposure can be linked to our model, and how the model could be used for risk assessment of pesticides, for example predicting exposure and effects in heterogeneous landscapes planted seasonally with a variety of crops, while accounting for differences in land use between landscapes.

Cognitive and environmental factors influencing the process of spatial knowledge acquisition within virtual reality environments

As the fidelity of virtual environments (VE) continues to increase, the possibility of using them as training platforms is becoming increasingly realistic for a variety of application domains, including military and emergency personnel training. In the past, there was much debate on whether the acquisition and subsequent transfer of spatial knowledge from VEs to the real world is possible, or whether the differences in medium during training would essentially be an obstacle to truly learning geometric space. In this paper, the authors present various cognitive and environmental factors that not only contribute to this process, but also interact with each other to a certain degree, leading to a variable exposure time requirement in order for the process of spatial knowledge acquisition (SKA) to occur. The cognitive factors that the authors discuss include a variety of individual user differences such as: knowledge and experience; cognitive gender differences; aptitude and spatial orientation skill; and finally, cognitive styles. Environmental factors discussed include: Size, Spatial layout complexity and landmark distribution. It may seem obvious that since every individual's brain is unique - not only through experience, but also through genetic predisposition that a one size fits all approach to training would be illogical. Furthermore, considering that various cognitive differences may further emerge when a certain stimulus is present (e.g. complex environmental space), it would make even more sense to understand how these factors can impact spatial memory, and to try to adapt the training session by providing visual/auditory cues as well as by changing the exposure time requirements for each individual. The impact of this research domain is important to VE training in general, however within service and military domains, guaranteeing appropriate spatial training is critical in order to ensure that disorientation does not occur in a life or death scenario.