A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.

Beverton and Holt equations: spreadsheet functions and uncertainty

This contribution illustrates how modern spreadsheets aid the calculation and visualization of yield models and how the effects of uncertainties may be incorporated using Monte Carlo simulation. It is argued that analogous approaches can be implemented for other assessment models of simple to medium complexity justifying wider use of spreadsheets in fisheries analysis and training.

Model structure and uncertainty for stochastic non-point source modelling applications

The uncertainty associated with a rainfall-runoff and non-point source loading (NPS) model can be attributed to both the parameterization and model structure. An interesting implication of the areal nature of NPS models is the direct relationship between model structure (i.e. sub-watershed size) and sample size for the parameterization of spatial data. The approach of this research is to find structural limitations in scale for the use of the conceptual NPS model, then examine the scales at which suitable stochastic depictions of key parameter sets can be generated. The overlapping regions are optimal (and possibly the only suitable regions) for conducting meaningful stochastic analysis with a given NPS model. Previous work has sought to find optimal scales for deterministic analysis (where, in fact, calibration can be adjusted to compensate for sub-optimal scale selection); however, analysis of stochastic suitability and uncertainty associated with both the conceptual model and the parameter set, as presented here, is novel; as is the strategy of delineating a watershed based on the uncertainty distribution. The results of this paper demonstrate a narrow range of acceptable model structure for stochastic analysis in the chosen NPS model. In the case examined, the uncertainties associated with parameterization and parameter sensitivity are shown to be outweighed in significance by those resulting from structural and conceptual decisions. © 2011 Copyright IAHS Press.

Modulation of pain ratings by expectation and uncertainty: Behavioral characteristics and anticipatory neural correlates.

Expectations about the magnitude of impending pain exert a substantial effect on subsequent perception. However, the neural mechanisms that underlie the predictive processes that modulate pain are poorly understood. In a combined behavioral and high-density electrophysiological study we measured anticipatory neural responses to heat stimuli to determine how predictions of pain intensity, and certainty about those predictions, modulate brain activity and subjective pain ratings. Prior to receiving randomized laser heat stimuli at different intensities (low, medium or high) subjects (n=15) viewed cues that either accurately informed them of forthcoming intensity (certain expectation) or not (uncertain expectation). Pain ratings were biased towards prior expectations of either high or low intensity. Anticipatory neural responses increased with expectations of painful vs. non-painful heat intensity, suggesting the presence of neural responses that represent predicted heat stimulus intensity. These anticipatory responses also correlated with the amplitude of the Laser-Evoked Potential (LEP) response to painful stimuli when the intensity was predictable. Source analysis (LORETA) revealed that uncertainty about expected heat intensity involves an anticipatory cortical network commonly associated with attention (left dorsolateral prefrontal, posterior cingulate and bilateral inferior parietal cortices). Relative certainty, however, involves cortical areas previously associated with semantic and prospective memory (left inferior frontal and inferior temporal cortex, and right anterior prefrontal cortex). This suggests that biasing of pain reports and LEPs by expectation involves temporally precise activity in specific cortical networks.

Integrating design attributes, knowledge and uncertainty in aerospace sector

The delivery of integrated product and service solutions is growing in the aerospace industry, driven by the potential of increasing profits. Such solutions require a life cycle view at the design phase in order to support the delivery of the equipment. The influence of uncertainty associated with design for services is increasingly a challenge due to information and knowledge constraints. There is a lack of frameworks that aim to define and quantify relationship between information and knowledge with uncertainty. Driven by this gap, the paper presents a framework to illustrate the link between uncertainty and knowledge within the design context for services in the aerospace industry. The paper combines industrial interaction and literature review to initially define the design attributes, the associated knowledge requirements and the uncertainties experienced. The framework is then applied in three cases through development of causal loop models (CLMs), which are validated by industrial and academic experts. The concepts and inter-linkages are developed with the intention of developing a software prototype. Future recommendations are also included. © 2014 CIRP.

Spatial distribution of soil heavy metal pollution estimated by different interpolation methods: Accuracy and uncertainty analysis

Mapping the spatial distribution of contaminants in soils is the basis of pollution evaluation and risk control. Interpolation methods are extensively applied in the mapping processes to estimate the heavy metal concentrations at unsampled sites. The performances of interpolation methods (inverse distance weighting, local polynomial, ordinary kriging and radial basis functions) were assessed and compared using the root mean square error for cross validation. The results indicated that all interpolation methods provided a high prediction accuracy of the mean concentration of soil heavy metals. However, the classic method based on percentages of polluted samples, gave a pollution area 23.54-41.92% larger than that estimated by interpolation methods. The difference in contaminated area estimation among the four methods reached 6.14%. According to the interpolation results, the spatial uncertainty of polluted areas was mainly located in three types of region: (a) the local maxima concentration region surrounded by low concentration (clean) sites, (b) the local minima concentration region surrounded with highly polluted samples; and (c) the boundaries of the contaminated areas. (C) 2010 Elsevier Ltd. All rights reserved.