Time complexity analysis of the stochastic diffusion search

The Stochastic Diffusion Search algorithm -an integral part of Stochastic Search Networks is investigated. Stochastic Diffusion Search is an alternative solution for invariant pattern recognition and focus of attention. It has been shown that the algorithm can be modelled as an ergodic, finite state Markov Chain under some non-restrictive assumptions. Sub-linear time complexity for some settings of parameters has been formulated and proved. Some properties of the algorithm are then characterised and numerical examples illustrating some features of the algorithm are presented.

Direct Computation of Stochastic Flow in Reservoirs with Uncertain Parameters

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point and to the field covariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data.

On the long time behavior of free stochastic Schrödinger evolutions

We discuss the time evolution of the wave function which is the solution of a stochastic Schrödinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and uniqueness of solutions. We observe that there exist three time regimes: the collapse regime, the classical regime and the diffusive regime. Concerning the latter, we assert that the general solution converges almost surely to a diffusing Gaussian wave function having a finite spread both in position as well as in momentum. This paper corrects and completes earlier works on this issue.

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.

The importance of friction in mountain wave drag amplification by Scorer parameter resonance

A mechanism for amplification of mountain waves, and their associated drag, by parametric resonance is investigated using linear theory and numerical simulations. This mechanism, which is active when the Scorer parameter oscillates with height, was recently classified by previous authors as intrinsically nonlinear. Here it is shown that, if friction is included in the simplest possible form as a Rayleigh damping, and the solution to the Taylor-Goldstein equation is expanded in a power series of the amplitude of the Scorer parameter oscillation, linear theory can replicate the resonant amplification produced by numerical simulations with some accuracy. The drag is significantly altered by resonance in the vicinity of n/l_0 = 2, where l_0 is the unperturbed value of the Scorer parameter and n is the wave number of its oscillation. Depending on the phase of this oscillation, the drag may be substantially amplified or attenuated relative to its non-resonant value, displaying either single maxima or minima, or double extrema near n/l_0 = 2. Both non-hydrostatic effects and friction tend to reduce the magnitude of the drag extrema. However, in exactly inviscid conditions, the single drag maximum and minimum are suppressed. As in the atmosphere friction is often small but non-zero outside the boundary layer, modelling of the drag amplification mechanism addressed here should be quite sensitive to the type of turbulence closure employed in numerical models, or to computational dissipation in nominally inviscid simulations.

The multisensory attentional consequences of tool use: a functional magnetic resonance imaging study

Background: Tool use in humans requires that multisensory information is integrated across different locations, from objects seen to be distant from the hand, but felt indirectly at the hand via the tool. We tested the hypothesis that using a simple tool to perceive vibrotactile stimuli results in the enhanced processing of visual stimuli presented at the distal, functional part of the tool. Such a finding would be consistent with a shift of spatial attention to the location where the tool is used. Methodology/Principal Findings: We tested this hypothesis by scanning healthy human participants' brains using functional magnetic resonance imaging, while they used a simple tool to discriminate between target vibrations, accompanied by congruent or incongruent visual distractors, on the same or opposite side to the tool. The attentional hypothesis was supported: BOLD response in occipital cortex, particularly in the right hemisphere lingual gyrus, varied significantly as a function of tool position, increasing contralaterally, and decreasing ipsilaterally to the tool. Furthermore, these modulations occurred despite the fact that participants were repeatedly instructed to ignore the visual stimuli, to respond only to the vibrotactile stimuli, and to maintain visual fixation centrally. In addition, the magnitude of multisensory (visual-vibrotactile) interactions in participants' behavioural responses significantly predicted the BOLD response in occipital cortical areas that were also modulated as a function of both visual stimulus position and tool position. Conclusions/Significance: These results show that using a simple tool to locate and to perceive vibrotactile stimuli is accompanied by a shift of spatial attention to the location where the functional part of the tool is used, resulting in enhanced processing of visual stimuli at that location, and decreased processing at other locations. This was most clearly observed in the right hemisphere lingual gyrus. Such modulations of visual processing may reflect the functional importance of visuospatial information during human tool use

Structure, conduct and the stochastic volatility of food markets: theory and empirics

The relationship between price volatility and competition is examined. Atheoretic, vector auto regressions on farm prices of wheat and retail prices of derivatives (flour, bread, pasta, bulgur and cookies) are compared to results from a dynamic, simultaneous-equations model with theory-based farm-to-retail linkages. Analytical results yield insights about numbers of firms and their impacts on demand- and supply-side multipliers, but the applications to Turkish time series (1988:1-1996:12) yield mixed results.

Towards a model-based integration of co-registered electroencephalography/functional magnetic resonance imaging data with realistic neural population meshes

Brain activity can be measured with several non-invasive neuroimaging modalities, but each modality has inherent limitations with respect to resolution, contrast and interpretability. It is hoped that multimodal integration will address these limitations by using the complementary features of already available data. However, purely statistical integration can prove problematic owing to the disparate signal sources. As an alternative, we propose here an advanced neural population model implemented on an anatomically sound cortical mesh with freely adjustable connectivity, which features proper signal expression through a realistic head model for the electroencephalogram (EEG), as well as a haemodynamic model for functional magnetic resonance imaging based on blood oxygen level dependent contrast (fMRI BOLD). It hence allows simultaneous and realistic predictions of EEG and fMRI BOLD from the same underlying model of neural activity. As proof of principle, we investigate here the influence on simulated brain activity of strengthening visual connectivity. In the future we plan to fit multimodal data with this neural population model. This promises novel, model-based insights into the brain's activity in sleep, rest and task conditions.

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Analysis of diffusion tensor magnetic resonance imaging data using principal component analysis

An analysis method for diffusion tensor (DT) magnetic resonance imaging data is described, which, contrary to the standard method (multivariate fitting), does not require a specific functional model for diffusion-weighted (DW) signals. The method uses principal component analysis (PCA) under the assumption of a single fibre per pixel. PCA and the standard method were compared using simulations and human brain data. The two methods were equivalent in determining fibre orientation. PCA-derived fractional anisotropy and DT relative anisotropy had similar signal-to-noise ratio (SNR) and dependence on fibre shape. PCA-derived mean diffusivity had similar SNR to the respective DT scalar, and it depended on fibre anisotropy. Appropriate scaling of the PCA measures resulted in very good agreement between PCA and DT maps. In conclusion, the assumption of a specific functional model for DW signals is not necessary for characterization of anisotropic diffusion in a single fibre.

Magnetic resonance imaging of a randomized controlled trial investigating predictors of recovery following psychological treatment in adolescents with moderate to severe unipolar depression: study protocol for Magnetic Resonance - Improving Mood with Psychoanalytic and Cognitive Therapies (MR-IMPACT)

Background Major depressive disorders (MDD) are a debilitating and pervasive group of mental illnesses afflicting many millions of people resulting in the loss of 110 million working days and more than 2,500 suicides per annum. Adolescent MDD patients attending NHS clinics show high rates of recurrence into adult life. A meta-analysis of recent research shows that psychological treatments are not as efficacious as previously thought. Modest treatment outcomes of approximately 65% of cases responding suggest that aetiological and clinical heterogeneity may hamper the better use of existing therapies and discovery of more effective treatments. Information with respect to optimal treatment choice for individuals is lacking, with no validated biomarkers to aid therapeutic decision-making. Methods/Design Magnetic resonance-Improving Mood with Psychoanalytic and Cognitive Therapies, the MR-IMPACT study, plans to identify brain regions implicated in the pathophysiology of depressions and examine whether there are specific behavioural or neural markers predicting remission and/or subsequent relapse in a subsample of depressed adolescents recruited to the IMPACT randomised controlled trial (Registration # ISRCTN83033550). Discussion MR-IMPACT is an investigative biomarker component of the IMPACT pragmatic effectiveness trial. The aim of this investigation is to identify neural markers and regional indicators of the pathophysiology of and treatment response for MDD in adolescents. We anticipate that these data may enable more targeted treatment delivery by identifying those patients who may be optimal candidates for therapeutic response.

The significance of occupancy steadiness in residential consumer response to Time of Use pricing: Evidence from a stochastic adjustment model

The recent roll-out of smart metering technologies in several developed countries has intensified research on the impacts of Time-of-Use (TOU) pricing on consumption. This paper analyses a TOU dataset from the Province of Trento in Northern Italy using a stochastic adjustment model. Findings highlight the non-steadiness of the relationship between consumption and TOU price. Weather and active occupancy can partly explain future consumption in relation to price.

The stochastic component in choice and regression to the mean

In this article, we illustrate experimentally an important consequence of the stochastic component in choice behaviour which has not been acknowledged so far. Namely, its potential to produce ‘regression to the mean’ (RTM) effects. We employ a novel approach to individual choice under risk, based on repeated multiple-lottery choices (i.e. choices among many lotteries), to show how the high degree of stochastic variability present in individual decisions can distort crucially certain results through RTM effects. We demonstrate the point in the context of a social comparison experiment.