Stochastic simulation of rare events

Stochastic simulation is an important and practical technique for computing probabilities of rare events, like the payoff probability of a financial option, the probability that a queue exceeds a certain level or the probability of ruin of the insurer's risk process. Rare events occur so infrequently, that they cannot be reasonably recorded during a standard simulation procedure: specifc simulation algorithms which thwart the rarity of the event to simulate are required. An important algorithm in this context is based on changing the sampling distribution and it is called importance sampling. Optimal Monte Carlo algorithms for computing rare event probabilities are either logarithmic eficient or possess bounded relative error.

Monitoring of antiretroviral therapy and mortality in HIV programmes in Malawi, South Africa and Zambia: mathematical modelling study

OBJECTIVES Mortality in patients starting antiretroviral therapy (ART) is higher in Malawi and Zambia than in South Africa. We examined whether different monitoring of ART (viral load [VL] in South Africa and CD4 count in Malawi and Zambia) could explain this mortality difference. DESIGN Mathematical modelling study based on data from ART programmes. METHODS We used a stochastic simulation model to study the effect of VL monitoring on mortality over 5 years. In baseline scenario A all parameters were identical between strategies except for more timely and complete detection of treatment failure with VL monitoring. Additional scenarios introduced delays in switching to second-line ART (scenario B) or higher virologic failure rates (due to worse adherence) when monitoring was based on CD4 counts only (scenario C). Results are presented as relative risks (RR) with 95% prediction intervals and percent of observed mortality difference explained. RESULTS RRs comparing VL with CD4 cell count monitoring were 0.94 (0.74-1.03) in scenario A, 0.94 (0.77-1.02) with delayed switching (scenario B) and 0.80 (0.44-1.07) when assuming a 3-times higher rate of failure (scenario C). The observed mortality at 3 years was 10.9% in Malawi and Zambia and 8.6% in South Africa (absolute difference 2.3%). The percentage of the mortality difference explained by VL monitoring ranged from 4% (scenario A) to 32% (scenarios B and C combined, assuming a 3-times higher failure rate). Eleven percent was explained by non-HIV related mortality. CONCLUSIONS VL monitoring reduces mortality moderately when assuming improved adherence and decreased failure rates.

Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories

Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, AbelianU(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev’s toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is nonperturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.

Reconstruction of a flash flood with large wood transport and its influence on hazard patterns in an ungauged mountain basin

The reconstruction of past flash floods in ungauged basins leads to a high level of uncertainty, which increases if other processes are involved such as the transport of large wood material. An important flash flood occurred in 1997 in Venero Claro (Central Spain), causing significant economic losses. The wood material clogged bridge sections, raising the water level upstream. The aim of this study was to reconstruct this event, analysing the influence of woody debris transport on the flood hazard pattern. Because the reach in question was affected by backwater effects due to bridge clogging, using only high water mark or palaeostage indicators may overestimate discharges, and so other methods are required to estimate peak flows. Therefore, the peak discharge was estimated (123 ± 18 m3 s–1) using indirect methods, but one-dimensional hydraulic simulation was also used to validate these indirect estimates through an iterative process (127 ± 33 m3 s–1) and reconstruct the bridge obstruction to obtain the blockage ratio during the 1997 event (~48%) and the bridge clogging curves. Rainfall–Runoff modelling with stochastic simulation of different rainfall field configurations also helped to confirm that a peak discharge greater than 150 m3 s–1 is very unlikely to occur and that the estimated discharge range is consistent with the estimated rainfall amount (233 ± 27 mm). It was observed that the backwater effect due to the obstruction (water level ~7 m) made the 1997 flood (~35-year return period) equivalent to the 50-year flood. This allowed the equivalent return period to be defined as the recurrence interval of an event of specified magnitude, which, where large woody debris is present, is equivalent in water depth and extent of flooded area to a more extreme event of greater magnitude. These results highlight the need to include obstruction phenomena in flood hazard analysis.

Economic efficiency analysis of different strategies to control post-weaning multi-systemic wasting syndrome and porcine circovirus type 2 subclinical infection in 3-weekly batch system farms.

The study assessed the economic efficiency of different strategies for the control of post-weaning multi-systemic wasting syndrome (PMWS) and porcine circovirus type 2 subclinical infection (PCV2SI), which have a major economic impact on the pig farming industry worldwide. The control strategies investigated consisted on the combination of up to 5 different control measures. The control measures considered were: (1) PCV2 vaccination of piglets (vac); (2) ensuring age adjusted diet for growers (diets); (3) reduction of stocking density (stock); (4) improvement of biosecurity measures (bios); and (5) total depopulation and repopulation of the farm for the elimination of other major pathogens (DPRP). A model was developed to simulate 5 years production of a pig farm with a 3-weekly batch system and with 100 sows. A PMWS/PCV2SI disease and economic model, based on PMWS severity scores, was linked to the production model in order to assess disease losses. This PMWS severity scores depends on the combination post-weaning mortality, PMWS morbidity in younger pigs and proportion of PCV2 infected pigs observed on farms. The economic analysis investigated eleven different farm scenarios, depending on the number of risk factors present before the intervention. For each strategy, an investment appraisal assessed the extra costs and benefits of reducing a given PMWS severity score to the average score of a slightly affected farm. The net present value obtained for each strategy was then multiplied by the corresponding probability of success to obtain an expected value. A stochastic simulation was performed to account for uncertainty and variability. For moderately affected farms PCV2 vaccination alone was the most cost-efficient strategy, but for highly affected farms it was either PCV2 vaccination alone or in combination with biosecurity measures, with the marginal profitability between 'vac' and 'vac+bios' being small. Other strategies such as 'diets', 'vac+diets' and 'bios+diets' were frequently identified as the second or third best strategy. The mean expected values of the best strategy for a moderately and a highly affected farm were £14,739 and £57,648 after 5 years, respectively. This is the first study to compare economic efficiency of control strategies for PMWS and PCV2SI. The results demonstrate the economic value of PCV2 vaccination, and highlight that on highly affected farms biosecurity measures are required to achieve optimal profitability. The model developed has potential as a farm-level decision support tool for the control of this economically important syndrome.

Computational and experimental methodology for site-matched investigations of the influence of mineral mass fraction and collagen orientation on the axial indentation modulus of lamellar bone

Relationships between mineralization, collagen orientation and indentation modulus were investigated in bone structural units from the mid-shaft of human femora using a site-matched design. Mineral mass fraction, collagen fibril angle and indentation moduli were measured in registered anatomical sites using backscattered electron imaging, polarized light microscopy and nano-indentation, respectively. Theoretical indentation moduli were calculated with a homogenization model from the quantified mineral densities and mean collagen fibril orientations. The average indentation moduli predicted based on local mineralization and collagen fibers arrangement were not significantly different from the average measured experimentally with nanoindentation (p=0.9). Surprisingly, no substantial correlation of the measured indentation moduli with tissue mineralization and/or collagen fiber arrangement was found. Nano-porosity, micro-damage, collagen cross-links, non-collagenous proteins or other parameters affect the indentation measurements. Additional testing/simulation methods need to be considered to properly understand the variability of indentation moduli, beyond the mineralization and collagen arrangement in bone structural units.

Knowledge transfer in software-maintenance offshore outsourcing

Software-maintenance offshore outsourcing (SMOO) projects have been plagued by tedious knowledge transfer during the service transition to the vendor. Vendor engineers risk being over-strained by the high amounts of novel information, resulting in extra costs that may erode the business case behind offshoring. Although stakeholders may desire to avoid these extra costs by implementing appropriate knowledge transfer practices, little is known on how effective knowledge transfer can be designed and managed in light of the high cognitive loads in SMOO transitions. The dissertation at hand addresses this research gap by presenting and integrating four studies. The studies draw on cognitive load theory, attributional theory, and control theory and they apply qualitative, quantitative, and simulation methods to qualitative data from eight in-depth longitudinal cases. The results suggest that the choice of appropriate learning tasks may be more central to knowledge transfer than the amount of information shared with vendor engineers. Moreover, because vendor staff may not be able to and not dare to effectively self-manage learn-ing tasks during early transition, client-driven controls may be initially required and subsequently faded out. Collectively, the results call for people-based rather than codification-based knowledge management strategies in at least moderately specific and complex software environments.

Oberflächenveränderung verschiedener zahnmedizinischer Werk-stoffe nach in-vitro Alterung

Susceptibility of different restorative materials to toothbrush abrasion and coffee staining Objective: The aim of this study was to evaluate the susceptibility of different restorative materials to surface alterations after an aging simulation. Methods: Specimens (n=15 per material) of five different restorative materials (CER: ceramic/Vita Mark II; EMP: composite/Empress Direct; LAV: CAD/CAM composite/Lava Ultimate; COM: prefabricated composite/Componeer; VEN: prefabricated composite/Venear) were produced. Whereas CER was glazed, EMP and LAV were polished with silicon polishers, and COM and VEN were left untreated. Mean roughness (Ra and Rz) and colorimetric parameters (L*a*b*), expressed as colour change (E), were measured. The specimens underwent an artificial aging procedure. After baseline measurements (M1), the specimens were successively immersed for 24 hours in coffee (M2), abraded in a toothbrushing simulator (M3), immersed in coffee (M4), abraded (M5) and repeatedly abraded (M6). After each aging procedure (M2-M6), surface roughness and colorimetric parameters were recorded. Differences between the materials regarding Ra/Rz and E were analysed with a nonparametric ANOVA analysis. The level of significance was set at α=0.05. Results: The lowest roughness values were obtained for CER. A significant increase in Ra was detected for EMP, COM and VEN compared to CER. The Ra/Rz values were found to be highly significantly different for the materials and measuring times (M) (p<0.0001). Regarding E most alterations were found for EMP and COM, whereas CER and LAV remained mostly stable. The E values were significantly different for the materials and M (p<0.0001). Conclusion: The ceramic and the CAD/CAM composite were the most stable materials with regard to roughness and colour change and the only materials that resulted in Ra values below 0.2 μm (the clinically relevant threshold). Venears and Componeers were more inert than the direct composite material and thus might be an alternative for extensive restorations in the aesthetic zone.

Computer Assisted Diagnosis and Treatment Planning of Femoroacetabular Impingement (FAI)

Femoroacetabular impingement (FAI) is a dynamic conflict of the hip defined by a pathological, early abutment of the proximal femur onto the acetabulum or pelvis. In the past two decades, FAI has received increasing focus in both research and clinical practice as a cause of hip pain and prearthrotic deformity. Anatomical abnormalities such as an aspherical femoral head (cam-type FAI), a focal or general overgrowth of the acetabulum (pincer-type FAI), a high riding greater or lesser trochanter (extra-articular FAI), or abnormal torsion of the femur have been identified as underlying pathomorphologies. Open and arthroscopic treatment options are available to correct the deformity and to allow impingement-free range of motion. In routine practice, diagnosis and treatment planning of FAI is based on clinical examination and conventional imaging modalities such as standard radiography, magnetic resonance arthrography (MRA), and computed tomography (CT). Modern software tools allow three-dimensional analysis of the hip joint by extracting pelvic landmarks from two-dimensional antero-posterior pelvic radiographs. An object-oriented cross-platform program (Hip2Norm) has been developed and validated to standardize pelvic rotation and tilt on conventional AP pelvis radiographs. It has been shown that Hip2Norm is an accurate, consistent, reliable and reproducible tool for the correction of selected hip parameters on conventional radiographs. In contrast to conventional imaging modalities, which provide only static visualization, novel computer assisted tools have been developed to allow the dynamic analysis of FAI pathomechanics. In this context, a validated, CT-based software package (HipMotion) has been introduced. HipMotion is based on polygonal three-dimensional models of the patient’s pelvis and femur. The software includes simulation methods for range of motion, collision detection and accurate mapping of impingement areas. A preoperative treatment plan can be created by performing a virtual resection of any mapped impingement zones both on the femoral head-neck junction, as well as the acetabular rim using the same three-dimensional models. The following book chapter provides a summarized description of current computer-assisted tools for the diagnosis and treatment planning of FAI highlighting the possibility for both static and dynamic evaluation, reliability and reproducibility, and its applicability to routine clinical use.

Evidence for Emergency Vaccination Having Played a Crucial Role to Control the 1965/66 Foot-and-Mouth Disease Outbreak in Switzerland.

Foot-and-mouth disease (FMD) is a highly contagious disease that caused several large outbreaks in Europe in the last century. The last important outbreak in Switzerland took place in 1965/66 and affected more than 900 premises and more than 50,000 animals were slaughtered. Large-scale emergency vaccination of the cattle and pig population has been applied to control the epidemic. In recent years, many studies have used infectious disease models to assess the impact of different disease control measures, including models developed for diseases exotic for the specific region of interest. Often, the absence of real outbreak data makes a validation of such models impossible. This study aimed to evaluate whether a spatial, stochastic simulation model (the Davis Animal Disease Simulation model) can predict the course of a Swiss FMD epidemic based on the available historic input data on population structure, contact rates, epidemiology of the virus, and quality of the vaccine. In addition, the potential outcome of the 1965/66 FMD epidemic without application of vaccination was investigated. Comparing the model outcomes to reality, only the largest 10% of the simulated outbreaks approximated the number of animals being culled. However, the simulation model highly overestimated the number of culled premises. While the outbreak duration could not be well reproduced by the model compared to the 1965/66 epidemic, it was able to accurately estimate the size of the area infected. Without application of vaccination, the model predicted a much higher mean number of culled animals than with vaccination, demonstrating that vaccination was likely crucial in disease control for the Swiss FMD outbreak in 1965/66. The study demonstrated the feasibility to analyze historical outbreak data with modern analytical tools. However, it also confirmed that predicted epidemics from a most carefully parameterized model cannot integrate all eventualities of a real epidemic. Therefore, decision makers need to be aware that infectious disease models are useful tools to support the decision-making process but their results are not equal valuable as real observations and should always be interpreted with caution.

Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging

Phase-sensitive X-ray imaging shows a high sensitivity towards electron density variations, making it well suited for imaging of soft tissue matter. However, there are still open questions about the details of the image formation process. Here, a framework for numerical simulations of phase-sensitive X-ray imaging is presented, which takes both particle- and wave-like properties of X-rays into consideration. A split approach is presented where we combine a Monte Carlo method (MC) based sample part with a wave optics simulation based propagation part, leading to a framework that takes both particle- and wave-like properties into account. The framework can be adapted to different phase-sensitive imaging methods and has been validated through comparisons with experiments for grating interferometry and propagation-based imaging. The validation of the framework shows that the combination of wave optics and MC has been successfully implemented and yields good agreement between measurements and simulations. This demonstrates that the physical processes relevant for developing a deeper understanding of scattering in the context of phase-sensitive imaging are modelled in a sufficiently accurate manner. The framework can be used for the simulation of phase-sensitive X-ray imaging, for instance for the simulation of grating interferometry or propagation-based imaging.

The Equidistant Method - a novel hip joint simulation algorithm for detection of femoroacetabular impingement

A novel computerized algorithm for hip joint motion simulation and collision detection, called the Equidistant Method, has been developed. This was compared to three pre-existing methods having different properties regarding definition of the hip joint center and behavior after collision detection. It was proposed that the Equidistant Method would be most accurate in detecting the location and extent of femoroacetabular impingement.

Rarely selected distractors in high stakes medical multiple-choice examinations and their recognition by item authors: A simulation and survey

Background Many medical exams use 5 options for multiple choice questions (MCQs), although the literature suggests that 3 options are optimal. Previous studies on this topic have often been based on non-medical examinations, so we sought to analyse rarely selected, 'non-functional' distractors (NF-D) in high stakes medical examinations, and their detection by item authors as well as psychometric changes resulting from a reduction in the number of options. Methods Based on Swiss Federal MCQ examinations from 2005-2007, the frequency of NF-D (selected by <1% or <5% of the candidates) was calculated. Distractors that were chosen the least or second least were identified and candidates who chose them were allocated to the remaining options using two extreme assumptions about their hypothetical behaviour: In case rarely selected distractors were eliminated, candidates could randomly choose another option - or purposively choose the correct answer, from which they had originally been distracted. In a second step, 37 experts were asked to mark the least plausible options. The consequences of a reduction from 4 to 3 or 2 distractors - based on item statistics or on the experts' ratings - with respect to difficulty, discrimination and reliability were modelled. Results About 70% of the 5-option-items had at least 1 NF-D selected by <1% of the candidates (97% for NF-Ds selected by <5%). Only a reduction to 2 distractors and assuming that candidates would switch to the correct answer in the absence of a 'non-functional' distractor led to relevant differences in reliability and difficulty (and to a lesser degree discrimination). The experts' ratings resulted in slightly greater changes compared to the statistical approach. Conclusions Based on item statistics and/or an expert panel's recommendation, the choice of a varying number of 3-4 (or partly 2) plausible distractors could be performed without marked deteriorations in psychometric characteristics.