Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with Gaussian process models

Several methods based on Kriging have recently been proposed for calculating a probability of failure involving costly-to-evaluate functions. A closely related problem is to estimate the set of inputs leading to a response exceeding a given threshold. Now, estimating such a level set—and not solely its volume—and quantifying uncertainties on it are not straightforward. Here we use notions from random set theory to obtain an estimate of the level set, together with a quantification of estimation uncertainty. We give explicit formulae in the Gaussian process set-up and provide a consistency result. We then illustrate how space-filling versus adaptive design strategies may sequentially reduce level set estimation uncertainty.

Achieving a more realistic assessment of rockfall hazards by coupling three-dimensional process models and field-based tree-ring data

Sound knowledge of the spatial and temporal patterns of rockfalls is fundamental for the management of this very common hazard in mountain environments. Process-based, three-dimensional simulation models are nowadays capable of reproducing the spatial distribution of rockfall occurrences with reasonable accuracy through the simulation of numerous individual trajectories on highly-resolved digital terrain models. At the same time, however, simulation models typically fail to quantify the ‘real’ frequency of rockfalls (in terms of return intervals). The analysis of impact scars on trees, in contrast, yields real rockfall frequencies, but trees may not be present at the location of interest and rare trajectories may not necessarily be captured due to the limited age of forest stands. In this article, we demonstrate that the coupling of modeling with tree-ring techniques may overcome the limitations inherent to both approaches. Based on the analysis of 64 cells (40 m × 40 m) of a rockfall slope located above a 1631-m long road section in the Swiss Alps, we illustrate results from 488 rockfalls detected in 1260 trees. We illustrate that tree impact data cannot only be used (i) to reconstruct the real frequency of rockfalls for individual cells, but that they also serve (ii) the calibration of the rockfall model Rockyfor3D, as well as (iii) the transformation of simulated trajectories into real frequencies. Calibrated simulation results are in good agreement with real rockfall frequencies and exhibit significant differences in rockfall activity between the cells (zones) along the road section. Real frequencies, expressed as rock passages per meter road section, also enable quantification and direct comparison of the hazard potential between the zones. The contribution provides an approach for hazard zoning procedures that complements traditional methods with a quantification of rockfall frequencies in terms of return intervals through a systematic inclusion of impact records in trees.

Global Optimization with Sparse and Local Gaussian Process Models

We present a novel surrogate model-based global optimization framework allowing a large number of function evaluations. The method, called SpLEGO, is based on a multi-scale expected improvement (EI) framework relying on both sparse and local Gaussian process (GP) models. First, a bi-objective approach relying on a global sparse GP model is used to determine potential next sampling regions. Local GP models are then constructed within each selected region. The method subsequently employs the standard expected improvement criterion to deal with the exploration-exploitation trade-off within selected local models, leading to a decision on where to perform the next function evaluation(s). The potential of our approach is demonstrated using the so-called Sparse Pseudo-input GP as a global model. The algorithm is tested on four benchmark problems, whose number of starting points ranges from 102 to 104. Our results show that SpLEGO is effective and capable of solving problems with large number of starting points, and it even provides significant advantages when compared with state-of-the-art EI algorithms.

Perennial Snow and Ice Variations (2000-2008) in the Arctic Circumpolar Land Area from Satellite Observations

Perennial snow and ice (PSI) extent is an important parameter of mountain environments with regard to its involvement in the hydrological cycle and the surface energy budget. We investigated interannual variations of PSI in nine mountain regions of interest (ROI) between 2000 and 2008. For that purpose, a novel MODIS data set processed at the Canada Centre for Remote Sensing at 250 m spatial resolution was utilized. The extent of PSI exhibited significant interannual variations, with coefficients of variation ranging from 5% to 81% depending on the ROI. A strong negative relationship was found between PSI and positive degree-days (threshold 0°C) during the summer months in most ROIs, with linear correlation coefficients (r) being as low as r = −0.90. In the European Alps and Scandinavia, PSI extent was significantly correlated with annual net glacier mass balances, with r = 0.91 and r = 0.85, respectively, suggesting that MODIS-derived PSI extent may be used as an indicator of net glacier mass balances. Validation of PSI extent in two land surface classifications for the years 2000 and 2005, GLC-2000 and Globcover, revealed significant discrepancies of up to 129% for both classifications. With regard to the importance of such classifications for land surface parameterizations in climate and land surface process models, this is a potential source of error to be investigated in future studies. The results presented here provide an interesting insight into variations of PSI in several ROIs and are instrumental for our understanding of sensitive mountain regions in the context of global climate change assessment.

Change mechanisms of schema-centered group psychotherapy with personality disorder patients

Background This study addressed the temporal properties of personality disorders and their treatment by schema-centered group psychotherapy. It investigated the change mechanisms of psychotherapy using a novel method by which psychotherapy can be modeled explicitly in the temporal domain. Methodology and Findings 69 patients were assigned to a specific schema-centered behavioral group psychotherapy, 26 to social skills training as a control condition. The largest diagnostic subgroups were narcissistic and borderline personality disorder. Both treatments offered 30 group sessions of 100 min duration each, at a frequency of two sessions per week. Therapy process was described by components resulting from principal component analysis of patients' session-reports that were obtained after each session. These patient-assessed components were Clarification, Bond, Rejection, and Emotional Activation. The statistical approach focused on time-lagged associations of components using time-series panel analysis. This method provided a detailed quantitative representation of therapy process. It was found that Clarification played a core role in schema-centered psychotherapy, reducing rejection and regulating the emotion of patients. This was also a change mechanism linked to therapy outcome. Conclusions/Significance The introduced process-oriented methodology allowed to highlight the mechanisms by which psychotherapeutic treatment became effective. Additionally, process models depicted the actual patterns that differentiated specific diagnostic subgroups. Time-series analysis explores Granger causality, a non-experimental approximation of causality based on temporal sequences. This methodology, resting upon naturalistic data, can explicate mechanisms of action in psychotherapy research and illustrate the temporal patterns underlying personality disorders.

Relations between the attentional blink and aspects of psychometric intelligence: A fixed-links modeling approach

The attentional blink phenomenon (AB) represents impaired identification of the second of two targets presented in rapid succession within a stream of stimuli. Despite the well-known association between attentional processes and psychometric intelligence (PI), evidence for a relationship between AB and PI is highly inconsistent. Theory and empirical findings suggest AB to be multifaceted. Hence, relations between AB and PI may be blurred when AB is measured as a single process. Furthermore, different aspects of PI might be differentially related to AB. The present study explored the relationship between processes underlying AB and general PI as well as specific aspects of PI (Reasoning, Speed, Memory, and Creativity) in 201 female students. Fixed-links modeling revealed three processes underlying AB: (1) a U-shaped process positively related to Speed and negatively related to Memory but unrelated to Reasoning, Creativity, and general PI, (2) an increasing process positively related to Reasoning, Speed, Memory, and general PI but not to Creativity, and (3) a decreasing process positively related to general PI and Memory but not to other aspects of PI. Our findings demonstrate that dissociating processes underlying AB and considering specific aspects of PI is required to understand the relationship between AB and PI.

The association between implicit alcohol attitudes and drinking behavior is moderated by baseline activation in the lateral prefrontal cortex

OBJECTIVE Intense alcohol consumption is a risk factor for a number of health problems. Dual-process models assume that self-regulatory behavior such as drinking alcohol is guided by both reflective and impulsive processes. Evidence suggests that (a) impulsive processes such as implicit attitudes are more strongly associated with behavior when executive functioning abilities are low, and (b) higher neural baseline activation in the lateral prefrontal cortex (PFC) is associated with better inhibitory control. The present study integrates these 2 strands of research to investigate how individual differences in neural baseline activation in the lateral PFC moderate the association between implicit alcohol attitudes and drinking behavior. METHOD Baseline cortical activation was measured with resting electroencephalography (EEG) in 89 moderate drinkers. In a subsequent behavioral testing session they completed measures of implicit alcohol attitudes and self-reported drinking behavior. RESULTS Implicit alcohol attitudes were related to self-reported alcohol consumption. Most centrally, implicit alcohol attitudes were more strongly associated with drinking behavior in individuals with low as compared with high baseline activation in the right lateral PFC. CONCLUSIONS These findings are in line with predictions made on the basis of dual-process models. They provide further evidence that individual differences in neural baseline activation in the right lateral PFC may contribute to executive functioning abilities such as inhibitory control. Moreover, individuals with strongly positive implicit alcohol attitudes coupled with a low baseline activation in the right lateral PFC may be at greater risk of developing unhealthy drinking patterns than others.

Single fluoroscopic image based 2D/3D reconstruction of a scaled, patient-specific vertebral model

Purpose Accurate three-dimensional (3D) models of lumbar vertebrae can enable image-based 3D kinematic analysis. The common approach to derive 3D models is by direct segmentation of CT or MRI datasets. However, these have the disadvantages that they are expensive, timeconsuming and/or induce high-radiation doses to the patient. In this study, we present a technique to automatically reconstruct a scaled 3D lumbar vertebral model from a single two-dimensional (2D) lateral fluoroscopic image. Methods Our technique is based on a hybrid 2D/3D deformable registration strategy combining a landmark-to-ray registration with a statistical shape model-based 2D/3D reconstruction scheme. Fig. 1 shows different stages of the reconstruction process. Four cadaveric lumbar spine segments (total twelve lumbar vertebrae) were used to validate the technique. To evaluate the reconstruction accuracy, the surface models reconstructed from the lateral fluoroscopic images were compared to the associated ground truth data derived from a 3D CT-scan reconstruction technique. For each case, a surface-based matching was first used to recover the scale and the rigid transformation between the reconstructed surface model Results Our technique could successfully reconstruct 3D surface models of all twelve vertebrae. After recovering the scale and the rigid transformation between the reconstructed surface models and the ground truth models, the average error of the 2D/3D surface model reconstruction over the twelve lumbar vertebrae was found to be 1.0 mm. The errors of reconstructing surface models of all twelve vertebrae are shown in Fig. 2. It was found that the mean errors of the reconstructed surface models in comparison to their associated ground truths after iterative scaled rigid registrations ranged from 0.7 mm to 1.3 mm and the rootmean squared (RMS) errors ranged from 1.0 mm to 1.7 mm. The average mean reconstruction error was found to be 1.0 mm. Conclusion An accurate, scaled 3D reconstruction of the lumbar vertebra can be obtained from a single lateral fluoroscopic image using a statistical shape model based 2D/3D reconstruction technique. Future work will focus on applying the reconstructed model for 3D kinematic analysis of lumbar vertebrae, an extension of our previously-reported imagebased kinematic analysis. The developed method also has potential applications in surgical planning and navigation.

Simulating Cortical Development as a Self Constructing Process: A Novel Multi-Scale Approach Combining Molecular and Physical Aspects

Current models of embryological development focus on intracellular processes such as gene expression and protein networks, rather than on the complex relationship between subcellular processes and the collective cellular organization these processes support. We have explored this collective behavior in the context of neocortical development, by modeling the expansion of a small number of progenitor cells into a laminated cortex with layer and cell type specific projections. The developmental process is steered by a formal language analogous to genomic instructions, and takes place in a physically realistic three-dimensional environment. A common genome inserted into individual cells control their individual behaviors, and thereby gives rise to collective developmental sequences in a biologically plausible manner. The simulation begins with a single progenitor cell containing the artificial genome. This progenitor then gives rise through a lineage of offspring to distinct populations of neuronal precursors that migrate to form the cortical laminae. The precursors differentiate by extending dendrites and axons, which reproduce the experimentally determined branching patterns of a number of different neuronal cell types observed in the cat visual cortex. This result is the first comprehensive demonstration of the principles of self-construction whereby the cortical architecture develops. In addition, our model makes several testable predictions concerning cell migration and branching mechanisms.

Reconstruction of 3D Vertebral Models from a Single 2D Lateral Fluoroscopic Image

Accurate three-dimensional (3D) models of lumbar vertebrae are required for image-based 3D kinematics analysis. MRI or CT datasets are frequently used to derive 3D models but have the disadvantages that they are expensive, time-consuming or involving ionizing radiation (e.g., CT acquisition). In this chapter, we present an alternative technique that can reconstruct a scaled 3D lumbar vertebral model from a single two-dimensional (2D) lateral fluoroscopic image and a statistical shape model. Cadaveric studies are conducted to verify the reconstruction accuracy by comparing the surface models reconstructed from a single lateral fluoroscopic image to the ground truth data from 3D CT segmentation. A mean reconstruction error between 0.7 and 1.4 mm was found.