Добірка наукової літератури з теми "Confidence intervals for local weights"

AbstractWe develop an efficient, adaptive locally weighted projection regression (ALWPR) framework for uncertainty quantification (UQ) of systems governed by ordinary and partial differential equations. The algorithm adaptively selects the new input points with the largest predictive variance and decides when and where to add new local models. It effectively learns the local features and accurately quantifies the uncertainty in the prediction of the statistics. The developed methodology provides predictions and confidence intervals at any query input and can deal with multi-output cases. Numerical examples are presented to show the accuracy and efficiency of the ALWPR framework including problems with non-smooth local features such as discontinuities in the stochastic space.

In an effort to recognize adults from juveniles in late summer and early fall, carcasses of Northern Pocket Gophers (Thomomys talpoides) captured from April to October 1994 in a pure alfalfa (Medicago spp.) field in Camrose and a mixed alfalfa-orchard grass (Dactylis glomerata)-dandelion (Taraxacum spp.) field in Lacombe, in central Alberta were analyzed. Mean weights of adult males and females were significantly (P < 0.05) larger than those of juveniles with near-adult body sizes in late summer and early fall. On the basis of the limits of 95% confidence intervals for individual values in Camrose and Lacombe, live-captured males weighing < 130 g could be classified as juveniles; those that are > 180 g would be adults. Males weighing between 130 and 180 g could be either juveniles or adults. Live-captured females weighing < 110 g would likely be juveniles. With larger animals, the pubic symphysis should be used to distinguish young females from adults. Given the variability of body weight in Northern Pocket Gophers, it is suggested that criteria for aging based on weight be derived for local populations in specific habitat types. On average, Northern Pocket Gopher males and females from Camrose were significantly (P < 0.05) heavier than those of Lacombe. Animals from both fields were, on average, heavier than those previously studied in natural-vegetation communities. Differences in the food nutritional quality may explain the observed variation in body weights among populations.

The market in the telecom industry is often segmented into three categories namely long distance, local and wireless services. In their survey, Green and Teece (1998) used this approach to study the telecom market segmentations of the United Kingdom, Australia, United States and New Zealand. In line with its policy of openness, transparency, fairness and participatory regulation, the commission informed stakeholders in September 2012 of its intent to conduct a study on the level of competition in the relevant markets of Nigeria’s Telecommunications Industry. It held meetings with a cross section of industry operators. This study shows that as the availability of mobile phone technology increases, the volume of import increases and more technology is transferred. Thus, the findings by Freund and Weinhold (2002, 2004) and Arrow (1969) are reconfirmed by the study’s empirical result. Therefore, technology helps to reduce distributional inequality of economic benefits. In fact, this does not necessarily imply reduction in inequality among rich and poor classes of these societies in the respective rich and poor states. The finding suggests that the availability of mobile phone technology increases state economic growth by different marginal weights. However, these marginal weights statistical significance across the states in both 90% and 95% confidence intervals could not be ascertained because the covariance has to be estimated using bootstrap. It is therefore left for future research.

AbstractObjectiveTo verify an association, if it exists, between obesity and blood pressure raised beyond the 90th percentile in children and adolescents, and to determine the measure of adiposity that best correlates with blood pressure in these subjects.DesignCross-sectional study.SettingA school-based study in Belo Horizonte, Brazil.ParticipantsWe selected randomly 1,403 students, aged from 6 to 18 years, from 545,046 students attending 521 public and private schools. Those selected completed the study.Main measures of outcomeWe recorded the weight, height, skin fold in the triceps, subscapular, and suprailiac areas, waist and hip circumference, body-mass index, and resting systolic and diastolic blood pressures using a mercury sphygmomanometer.ResultsIn univariate analyses, body mass index greater or lesser than 85th percentile, measurements of skin thickness in the subscapular and suprailiac areas, and the sum of all measurements of skinfold thickness, were associated with both systolic and diastolic measurements of blood pressure. After multivariate analyses that adjusted for all measurements of adiposity except itself, and age, race, and socioeconomic state, we found that the increased body mass index was associated with a 3.6-fold increased frequency of elevated systolic measurements of blood pressure, with 95% confidence intervals from 2.2 to 5.8, and a 2.7-fold increased frequency of elevated measurements of diastolic blood pressure, with 95% confidence intervals from 1.9 to 4.0.ConclusionsBody-mass index serves as a better predictor of elevated blood pressure among children than do local measurements of adiposity.

Background: Local health departments (LHDs) are increasingly involved in Community Health Improvement Plans (CHIPs), a collaborative planning process that represents an opportunity for prioritizing physical activity. We determined the proportion of LHDs reporting active transportation strategies in CHIPs and associations between LHD characteristics and such strategies. Methods: A national probability survey of US LHDs (<500,000 residents; 30.2% response rate) was conducted in 2017 (n = 162). LHDs reported the inclusion of 8 active transportation strategies in a CHIP. We calculated the proportion of LHDs reporting each strategy. Multivariate logistic regression models determined the associations between LHD characteristics and inclusion of strategies in a CHIP. Inverse probability weights were applied for each stratum. Results: 45.6% of US LHDs reported participating in a CHIP with ≥1 active transportation strategy. Proportions for specific strategies ranged from 22.3% (Safe Routes to School) to 4.1% (Transit-Oriented Development). Achieving national accreditation (odds ratio [OR] = 3.67; 95% confidence interval [CI], 1.11–12.05), pursuing accreditation (OR = 3.40; 95% CI, 1.25–9.22), using credible resources (OR = 5.25; 95% CI, 1.77–15.56), and collaborating on a Community Health Assessment (OR = 4.48; 95% CI, 1.23–16.29) were associated with including a strategy in a CHIP after adjusting for covariates. Conclusions: CHIPs are untapped tools, but national accreditation, using credible resources, and Community Health Assessment collaboration may support strategic planning efforts to improve physical activity.

Abstract Context: Rapid postnatal weight gain has been associated with subsequent increased childhood adiposity. However, the contribution of rapid weight gain during specific infancy periods is not clear. Objective: We aimed to determine which periods of infancy weight gain are related to childhood adiposity and also to age at menarche in UK girls. Design, Setting, and Participants: A total of 2715 girls from a prospective UK birth cohort study participated in the study. Main Outcome Measures: Routinely measured weights and lengths at ages 2, 9, and 19 months were extracted from the local child health computer database. Body composition was assessed by dual-energy x-ray absorptiometry at age 10 yr, and age at menarche was assessed by questionnaire (categorized into three groups: &lt;12.0, 12.0–13.0, and &gt;13.0 yr). Results: Faster early infancy weight gain between 0 and 2 months and also 2 to 9 months were associated with increased body fat mass relative to lean mass at age 10 yr and also with earlier age at menarche. Each +1 unit gain in weight sd score between 0 and 9 months was associated with an odds ratio (95% confidence interval) = 1.48 (1.27–1.60) for overweight (body mass index &gt; 85th centile) at 10 yr, and 1.34 (1.21–1.49) for menarche at less than 12 yr. In contrast, subsequent weight gain between 9 and 19 months was not associated with later adiposity or age at menarche. Conclusions: In developed settings, rapid weight gain during the first 9 months of life is a risk factor for both increased childhood adiposity and early menarche in girls.

Context Knee injuries account for a substantial percentage of all athletic injuries. The relative rates of knee injury for a variety of sports by sex and age need to be understood so we can better allocate resources, such as athletic trainers, to properly assess and treat injuries and reduce injury risk. Objective To describe the epidemiology of patients with sport-related knee strain and sprain presenting to US emergency departments from 2002 to 2011. Design Cross-sectional study. Setting Using the Consumer Products Safety Commission's National Electronic Injury Surveillance System and the US Census Bureau, we extracted raw data to estimate national rates of patients with knee strain and sprain presenting to emergency departments. Patients or Other Participants Participants were individuals sustaining a knee strain or sprain at sports or recreation venues and presenting to local emergency departments for treatment. We included 12 popular sports for males and 11 for females. Ages were categorized in six 5-year increments for ages 5 to 34 years and one 10-year increment for ages 35 to 44 years. Main Outcome Measure(s) Incidence rates were calculated using weights provided by the National Electronic Injury Surveillance System and reported with their 95% confidence intervals for sport, sex, and age. Results Strain and sprain injury rates varied greatly by sport, sex, and age group. The highest injury rates occurred in football and basketball for males and in soccer and basketball for females. The most at-risk population was 15 to 19 years for both sexes. Conclusions Athletes experience different rates of knee strain and sprain according to sport, sex, and age. Increased employment of athletic trainers to care for the highest-risk populations, aged 10 to 19 years, is recommended to reduce emergency department use and implement injury-prevention practices.

Background: Although preterm delivery and low birth weight (LBW) have been studied in India, findings may not be generalisable to rural areas such as the Marathwada region of Maharashtra state. There is limited information available on maternal and child health indicators from this region. We aimed to present some local estimates of preterm delivery and LBW in the Osmanabad district of Marathwada and assess available maternal risk factors. Methods: The study used routinely collected data on all in-hospital births in the maternity department of Halo Medical Foundation’s hospital from 1st January 2008 to 31st December 2014. Multivariable logistic regression analysis provided odds ratios (OR) with 95% confidence intervals (CI) for preterm delivery and LBW according to each maternal risk factor. Results: We analysed 655 live births, of which 6.1% were preterm deliveries. Of the full term births (N=615), 13.8% were LBW (<2.5 kilograms at birth). The odds of preterm delivery were three times higher (OR=3.23, 95% CI 1.36 to 7.65) and the odds of LBW were double (OR=2.03, 95% CI 1.14 to 3.60) among women <22 years of age compared with older women. The odds of both preterm delivery and LBW were reduced in multigravida compared with primigravida women regardless of age. Anaemia (Hb<11g/dl), which was prevalent in 91% of women tested, was not significantly related to these birth outcomes. Conclusions: The odds of preterm delivery and LBW were much higher in mothers under 22 years of age in this rural Indian population. Future studies should explore other related risk factors and the reasons for poor birth outcomes in younger mothers in this population, to inform the design of appropriate public health policies that address this issue.

Робота виконана в Інституті прикладного системного аналізу Національного технічного університету України «Київський політехнічний інститут імені Ігоря Сікорського»
У дисертаційній роботі запропоновано методологію підтримки прийняття рішень, яка з використанням розробленого системного підходу дозволяє підвищити достовірність розв’язків в складних слабко структурованих системах на основі ієрархічних та мережевих моделей і включає нові та удосконалені методи: оцінювання і підвищення узгодженості матриць парних порівнянь загального виду залежно від властивостей цих матриць, розрахунку довірчих інтервалів для локальних ваг, розрахунку нечітких локальних ваг, гібридний метод розрахунку локальних та агрегованих ваг, метод комплексного оцінювання чутливості розв'язку та спосіб оцінювання реверсу рангів при використанні різних правил комбінування функцій довіри. Розроблено нові методики, засоби та система моделювання експертного оцінювання. Практичне значення одержаних результатів полягає у створенні інструментарію у вигляді системи підтримки прийняття рішень, який застосовано при розв'язанні практичних задач на замовлення міністерств і відомств України.
In the dissertation work, an important scientific and technical problem has been solved, which deals with development of mathematical and methodological support for increasing the reliability of solutions to decision analysis problems in complex weakly structured systems based on hierarchical and network models. The scientific novelty of the work is determined by the following theoretical and practical results obtained by author. Using proposed systematic approach, a new methodology of decision support is developed, which allows to increase the reliability of solutions of decision analysis problems in complex weakly structured systems on the basis of hierarchical and network models. This methodology includes the proposed and described below methods and techniques. A new method for evaluating and improving the consistency of expert judgements, which are given in a form of pairwise comparison matrix, is developed. Features of the method include an analysis of property of weak inconsistency, the presence of cycles in a pairwise comparison matrix and a search for the most inconsistent element of this matrix. The method can be applied to pairwise comparison matrices of various types, including multiplicative, additive, fuzzy and other. A Transitiv method for searching the most inconsistent elements of the matrix is proposed. A method of flows for finding the most inconsistent element of the matrix is improved by taking into account the input flow. The simulation shows that the developed Transitiv method and the method of flows are more efficient than existing methods. Usage of the proposed method of consistency evaluating and improving allows to obtain pairwise comparison matrices of acceptable quality for all elements of the model and these matrices can be used further to find local weights of model’s elements. A new method for calculating confidence intervals of local weights is developed, which, unlike others, takes into account the uncertainty of scale, expert's personal qualities such as optimism and pessimism, and does not require comparison of groups of elements with the frame. The method is based on notions of the Dempster-Schafer theory of evidence and results of computer simulation of expert's judgments. An uncertainty index of expert judgments is proposed, assuming that this uncertainty is caused by above factors. An improved method for calculating fuzzy local weights on basis of fuzzy pairwise comparison matrix is proposed, which differs from others in estimating and increasing the consistency of the matrix and taking into account properties of weak and strong order preservation on a set of calculated fuzzy weights. This method, unlike existing ones, makes it possible to determine the weak inconsistency of fuzzy matrix, to assess the acceptability of inconsistency level of fuzzy matrix for reliable local weights calculation, and to find the most inconsistent elements of the matrix using methods developed for crisp matrices. A hybrid method for calculating aggregated weights of hierarchical model elements with interdependent decision criteria has been improved, when input data for evaluation are fuzzy expert judgments. Improvement consists in using the developed more effective methods for assessment and increasing of crisp and fuzzy expert judgements consistency. A method for complex sensitivity analysis of results has been improved by taking into account sensitivity analysis of local rankings of model’s elements. In the developed method for estimating local sensitivity, intervals and indices of stability of pairwise comparison matrix elements are calculated, which retain the best decision alternative and all ranking of alternatives. Resulting stability intervals allow to find critical elements of the problem that require more careful analysis. A new technique for estimating the rank reversal is suggested, which can appear after applying combination rules of confidence functions for model’s elements. Using this technique, the Dempster, Yager, Zhang, Dubois and Prada and other combination rules were examined. Cases and features of rank reversals appearance in these rules were revealed. New techniques and tools for modeling a process of decision alternatives evaluation by an expert of high competence, expert-optimist and expert-pessimist while performing pairwise comparisons are developed. Using these techniques and tools, efficiency of proposed methods has been proved. A decision support system has been constructed on basis of proposed methods and techniques. This system has been used to solve several practical problems. Within the work with the Ministry of Education and Science of Ukraine, critical technologies of the Ukrainian energy industry were assessed, priorities of technologies were calculated and aggregated according to hierarchical model of criteria, and on their basis the most priority technologies for implementation were identified. In the course of research work together with the Institute of Space Research, directions of the expedient use of space information for remote sensing of the Earth for geoinformation systems were evaluated and the relative demand for the space information in the national economy of Ukraine was determined. On order of the Kyiv City State Administration, social problems of the Kyiv city were estimated in terms of benefits, costs, opportunities and risks, followed by selection of priority activities for implementation and evaluation of scenarios of the transport system development. Results of the dissertation work have been introduced into the educational process of the department "Mathematical methods of system analysis" of Institute for applied system analysis of National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”.
В диссертационной работе предложена методология поддержки принятия решений, которая с использованием разработанного системного подхода позволяет повысить достоверность решений в сложных слабо структурированных системах на основе иерархических и сетевых моделей и включает новые и усовершенствованные методы: оценки и повышения согласованности матриц парных сравнений общего вида в зависимости от свойств этих матриц, расчета доверительных интервалов для локальных весов, расчета нечетких локальных весов, гибридный метод расчета локальных и агрегированных весов, метод комплексной оценки чувствительности решения, а также способ оценки реверса рангов при использовании различных правил комбинирования функций доверия. Разработаны новые методики, средства и система моделирования экспертного оценивания. Практическое значение полученных результатов заключается в создании инструментария в виде системы поддержки принятия решений, который применен при решении практических задач по заказу министерств и ведомств Украины.

Робота виконана в Інституті прикладного системного аналізу Національного технічного університету України «Київський політехнічний інститут імені Ігоря Сікорського»
У дисертаційній роботі запропоновано методологію підтримки прийняття рішень, яка з використанням розробленого системного підходу дозволяє підвищити достовірність розв’язків в складних слабко структурованих системах на основі ієрархічних та мережевих моделей і включає нові та удосконалені методи: оцінювання і підвищення узгодженості матриць парних порівнянь загального виду залежно від властивостей цих матриць, розрахунку довірчих інтервалів для локальних ваг, розрахунку нечітких локальних ваг, гібридний метод розрахунку локальних та агрегованих ваг, метод комплексного оцінювання чутливості розв'язку та спосіб оцінювання реверсу рангів при використанні різних правил комбінування функцій довіри. Розроблено нові методики, засоби та система моделювання експертного оцінювання. Практичне значення одержаних результатів полягає у створенні інструментарію у вигляді системи підтримки прийняття рішень, який застосовано при розв'язанні практичних задач на замовлення міністерств і відомств України.

La segmentation d'images est un domaine important dans le traitement d'images et un grand nombre d'approches différentes ent été développées pendant ces dernières décennies. L'approche des contours actifs est un des plus populaires. Dans ce cadre, cette thèse vise à développer des algorithmes robustes, qui peuvent segmenter des images avec des inhomogénéités d'intensité. Nous nous concentrons sur l'étude des énergies externes basées région dans le cadre des ensembles de niveaux. Précisément, nous abordons la difficulté de choisir l'échelle de la fenêtre spatiale qui définit la localité. Notre contribution principale est d'avoir proposé une échelle adaptative pour les méthodes de segmentation basées sur les statistiques locales. Nous utilisons l'approche d'Intersection des Intervalles de Confiance pour définir une échelle position-dépendante pour l'estimation des statistiques image. L'échelle est optimale dans le sens où elle donne le meilleur compromis entre le biais et la variance de l'approximation polynomiale locale de l'image observée conditionnellement à la segmentation actuelle. De plus, pour le model de segmentation basé sur une interprétation Bahésienne avec deux noyaux locaux, nous suggérons de considérer leurs valeurs séparément. Notre proposition donne une segmentation plus lisse avec moins de délocalisations que la méthode originale. Des expériences comparatives de notre proposition à d'autres méthodes de segmentation basées sur des statistiques locales sont effectuées. Les résultats quantitatifs réalisés sur des images ultrasonores de simulation, montrent que la méthode proposée est plus robuste au phénomène d'atténuation. Des expériences sur des images réelles montrent également l'utilité de notre approche.

Intra-archipelago waterways, including tidal strait networks, present a complex set of barriers to, and conduits for sediment transport between marine basins. Tidal straits may also be the least well understood tide-dominated sedimentary environment. To address these issues, currents, sediment transport pathways, and seabed sedimentology & geomorphology were studied in the central Salish Sea (Gulf and San Juan Islands region) of British Columbia, Canada and Washington State, USA. A variety of data types were integrated: 3D & 2D tidal models, multibeam bathymetry & backscatter, seabed video, grab samples, cores and seismic reflection. This dissertation included the first regional sediment transport modelling study of the central Salish Sea. Lagrangian particle dispersal simulations were driven by 2D tidal hydrodynamics (~59-days). It was found that flood-tide dominance through narrow intra-archipelago connecting straits resulted in the transfer of sediment into the inland Strait of Georgia, an apparent sediment sink. The formative/maintenance processes at a variety of seabed landforms, including a banner bank with giant dunes, were explained with modelled tides and sediment transport. Deglacial history and modern lateral sedimentological and morphological transitions were also considered. Based on this modern environment, adjustments to the tidal strait facies model were identified. In addition, erosion and deposition patterns across the banner bank (dune complex) were monitored with 8-repeat multibeam sonar surveys (~10 years). With these data, spatially variable bathymetric change detection techniques were explored: A) a cell-by-cell probabilistic depth uncertainty-based threshold (t-test); and B) coherent clusters of change pixels identified with the local Moran's Ii spatial autocorrelation statistic. Uncertainty about volumetric change is a considerable challenge in seabed change research, compared to terrestrial studies. Consideration of volumetric change confidence intervals tempers interpretations and communicates metadata. Techniques A & B may both be used to restrict volumetric change calculations in area, to exclude low relative bathymetric change signal areas.
Graduate
2018-12-07

A 2D, plane-strain, finite element model, with perfectly-matched layer elements acting as absorbing boundaries, is used to investigate the effect of soil inhomogeneity on resultant surface vibration. The stiffness and mass matrices for the perfectly-matched layer element is derived and included for reference. Stochastic variability of the soil’s shear wave velocity is introduced using a K-L expansion; the shear wave velocity is assumed to have a log-normal distribution and a modified exponential co-variance kernel. Results suggest that local soil inhomogeneity can significantly affect surface velocity predictions; 90% confidence intervals showing 7dB averages and peak values up to 11dB are computed. This is a significant source of uncertainty and should be considered when using predictions from models assuming homogeneous soil properties.

In this paper, we propose a two-step approach to addressing the question of how reliable the practice of applying laboratory data on fracture toughness to full-scale structures and components is. In the first step, we construct a two-level eight-factor 16-run-plus-a-center-point fractional factorial orthogonal design of experiments and conduct an analysis using literature fracture toughness and parameter data, where the eight factors are: (1) the Young’s modulus, E, (2) a material property constant, α, as defined in a Ramberg-Osgood stress-strain model, (3) the work hardening exponent, n, of the same model, (4) the yield stress, σy, (5) the critical local fracture stress, σf, (6) a chemical composition parameter in the form of the ratio of manganese to carbon content, Mn/C, (7) the crack depth/width ratio, a/W, and (8) the critical microstructural distance, rc, from the crack tip. Based on the 17-run data and the design of experiments analysis, we first obtain a ranking of the relative importance of those eight factors and then select two most important ones, to be named “key parameters”, to perform a multi-linear least square fit of the fracture toughness data as a function of those two key parameters. This simplification allows us to calculate, for the number of tests equal to N (= 17), the best estimate of the fracture toughness with 95% confidence prediction intervals. In the second step, we apply the statistical concept of a tolerance interval for a fixed sample size N and three coverages, 90%, 95%, and 99%, to a conversion of the results of the first step (the prediction intervals) to a set of tolerance intervals for the fracture toughness of a full-scale structure. Significance and limitations of this novel approach to answering the question of reliability from laboratory data to full scale structures are discussed at the end of this presentation.

We present work towards validating a multidimensional computer model capable of simulating two-phase, non-isothermal transport in PEMFCs under a wide variety of conditions. The specific hardware used to gather the experimental data is a state-of-the-art 10×10 segmented bipolar plate attached to a 50 cm2 single cell. The five-way serpentine flow field, bipolar plates and membrane-electrode assembly are all resolved in the model. The data has been collected at Los Alamos National Laboratories under several sets of operating conditions, including different relative humidity of 25%, 50%, 75% and 100% RH and temperatures of 80 and 60 C. Current best practices for model validation are applied, including uncertainty quantification (UQ). Variability in measured data is incorporated by included uncertainty bounds on the data (using either interval bounds or statistical confidence intervals). Sensitivity analysis of model input parameters on predictions is performed using an interface to the the DAKOTA toolkit. The model is calibrated using cell polarization data with uncertainty and then used to predict the local current distribution data.

Accurate prediction of the energy consumption is critical for energy-efficient production systems. However, the majority of existing prediction models aim at providing only point predictions and can be affected by uncertainties in the model parameters and input data. In this paper, a prediction model that generates prediction intervals (PIs) for estimating energy consumption of a milling machine is proposed. PIs are used to provide information on the confidence in the prediction by accounting for the uncertainty in both the model parameters and the noise in the input variables. An ensemble model of neural networks (NNs) is used to estimate PIs. A k-nearest-neighbors (k-nn) approach is applied to identify similar patterns between training and testing sets to increase the accuracy of the results by using local information from the closest patterns of the training sets. Finally, a case study that uses a dataset obtained by machining 18 parts through face-milling, contouring, slotting and pocketing, spiraling, and drilling operations is presented. Of these six operations, the case study focuses on face milling to demonstrate the effectiveness of the proposed energy prediction model.

An integrated performance modeling system is presented for use in general decision making problems including engineering design, manufacturing process and quality control, and other applications. The system relies on a function matrix that relates decision variables to performance variables. The system utilizes both global and local linearization of non-linear functions, after which the Extensive Simplex Method is used to derive the set of all feasible decisions based upon the specification limits for the performance variables and the control limits on the decision variables. Beyond current Six Sigma best practices, the described system explicitly considers both modeling uncertainty and uncontrolled variation. The specification limits may be automatically tightened by the confidence intervals and variation limits to ensure feasibility to a desired level of confidence and robustness. Three sets of feasible decisions are established including 1) the global feasible set that establishes the extreme limits of feasibility by allowing all the decision variables to vary simultaneously within their range of the control limits, 2) the local feasibility, which shows the immediate feasibility for each decision variable holding other decision variables at their current value, and 3) the controllable feasibility for each performance variable holding other performance variables at their current value. The system provides a perspective view of 1) the function matrix, 2) a historical view of the decision variables which may be used in a manner similar to statistical process control X-Bar charts, 3) a historical view of the performance variables which may be used in a manner similar to statistical quality control charts, 4) a set of decision windows showing the joint feasibility of all pairs of decision variables, which may be used in a manner similar to process windows, and 5) a set of performance windows showing the joint feasibility of all pairs of performance variables, which may be used in a manner similar to Pareto Optimal graphs. An example is provided for a beam design model with four decision variables and three performance variables.

Abstract The transition of satellite InSAR technology to a ground-based system provides a proven risk reduction technology if combined with a critical slope monitoring (CSM) program. Together the technology with the active engagement of a defined program can detect the onset of slope displacement, acceleration, and provide a method to determine slope collapse. Recently, using the radar software, Guardian, and its ability to document surface velocity in intervals of 24-hours or less has allowed for the development of site-specific levels of rockfall risk. The ground-based InSAR (interferometric synthetic aperture radar) systems and their near real-time capabilities allow for proactive and early warning monitoring. The technical requirements include the ability to operate 24/7 in all weather conditions, acquire data in near real-time, and visually present data in an interpretable format that requires no end user processing. Since slope failure without acceleration is unlikely, the rapid visual presentation of processed data becomes a crucial component for a CSM technology. The definition of the CSM program not only requires short intervals for data acquisition, processing, and visual presentation but also requires a monitoring professional that can interpret and communicate changes in slope movement. A specific CSM technology requirement demands, acquiring data at a continuous interval of 2-minutes or less, 24 hours per day for the duration of the monitoring project. Also, the CSM technology must be able to transmit alarm messages at the moment thresholds are met, visually present data with various time series plots, including displacement, and velocity maps while acquired radar data is continuously updated and with no end-user processing. A site-specific document called a trigger action response plan (TARP) needs to be prepared at the start of any CSM project. Currently, only the IBIS-FM and ArcSAR radars developed by IDS (Ingegneria Dei Sistemi) GeoRadar can meet the technical requirements of the defined CSM technology. During a CSM program, the short interval between each data acquisition provides two specific advantages. First, the short acquisition interval decreases interpolation, which automatically increases data confidence. Second, the short intervals also decrease the effects of atmospheric changes that are a part of all data acquisitions. Although the IBIS-FM and ArcSAR radar systems can operate in nearly all-weather conditions, sudden changes in local atmospheric conditions can still exhibit data effects. Both radar systems include active proprietary algorithms that account for ongoing atmospheric changes during acquisitions. In comparison, some remote sensing data acquired from, LIDAR, and total station technologies can be critically affected by sudden changes in local atmospheric conditions. Combining the near real-time capabilities of an interferometric synthetic aperture radar system with a dedicated professional will decrease risk to people and property by allowing slope movement trends to be identified and observed in near real-time, 24-hours per/day. The paper will discuss the highlights of several successful CSM programs. We describe deployment versatility, the ability to identify the onset of displacement accurately, and the critical identification of the onset of acceleration.

Abstract This paper presents local Nusselt numbers computed from experimental measurements of surface temperature of compressor discs in a multiple rotating cavity test rig with axial through-flow. A validated 2D steady state heat conduction analysis methodology is presented, using the actual test geometry, and 95% confidence intervals calculated using Monte Carlo simulation. Sensitivity of the solution to curve fitting types, geometric simplification and surface instrumentation are explored. The results indicate that polynomial curves fits, whilst computational simple, are unsuitable especially at higher orders. It is shown that geometric simplifications, that typically simplify the algorithmic implementation, may also omit significant variation in heat flux at critical stress relieving locations. The effect of reducing measurement points in the analysis is to both over-predict heat transfer and increase the uncertainty of the results. Finally, the methodology is applied to previously published thermal data from the University of Sussex, facilitating qualitative discussion on the influence of the governing parameters. Whilst this study does not overcome the inherent uncertainty associated with inverse solutions it is intended to present a methodology that is readily available to the wider community for the analysis of thermal test data and suggests some guidelines at the planning and post-processing stages. The range of experiment reported here covers: 1.13 × 105 &lt; Rez &lt; 5.14 × 105, 1.65 × 106 &lt; Reθ &lt; 3.16 × 106, 0.10 &lt; Ro &lt; 0.60 and 3.40 × 1011 &lt; Gr &lt; 1.25 × 1012.

1.1 Macroeconomic summary Economic recovery has consistently outperformed the technical staff’s expectations following a steep decline in activity in the second quarter of 2020. At the same time, total and core inflation rates have fallen and remain at low levels, suggesting that a significant element of the reactivation of Colombia’s economy has been related to recovery in potential GDP. This would support the technical staff’s diagnosis of weak aggregate demand and ample excess capacity. The most recently available data on 2020 growth suggests a contraction in economic activity of 6.8%, lower than estimates from January’s Monetary Policy Report (-7.2%). High-frequency indicators suggest that economic performance was significantly more dynamic than expected in January, despite mobility restrictions and quarantine measures. This has also come amid declines in total and core inflation, the latter of which was below January projections if controlling for certain relative price changes. This suggests that the unexpected strength of recent growth contains elements of demand, and that excess capacity, while significant, could be lower than previously estimated. Nevertheless, uncertainty over the measurement of excess capacity continues to be unusually high and marked both by variations in the way different economic sectors and spending components have been affected by the pandemic, and by uneven price behavior. The size of excess capacity, and in particular the evolution of the pandemic in forthcoming quarters, constitute substantial risks to the macroeconomic forecast presented in this report. Despite the unexpected strength of the recovery, the technical staff continues to project ample excess capacity that is expected to remain on the forecast horizon, alongside core inflation that will likely remain below the target. Domestic demand remains below 2019 levels amid unusually significant uncertainty over the size of excess capacity in the economy. High national unemployment (14.6% for February 2021) reflects a loose labor market, while observed total and core inflation continue to be below 2%. Inflationary pressures from the exchange rate are expected to continue to be low, with relatively little pass-through on inflation. This would be compatible with a negative output gap. Excess productive capacity and the expectation of core inflation below the 3% target on the forecast horizon provide a basis for an expansive monetary policy posture. The technical staff’s assessment of certain shocks and their expected effects on the economy, as well as the presence of several sources of uncertainty and related assumptions about their potential macroeconomic impacts, remain a feature of this report. The coronavirus pandemic, in particular, continues to affect the public health environment, and the reopening of Colombia’s economy remains incomplete. The technical staff’s assessment is that the COVID-19 shock has affected both aggregate demand and supply, but that the impact on demand has been deeper and more persistent. Given this persistence, the central forecast accounts for a gradual tightening of the output gap in the absence of new waves of contagion, and as vaccination campaigns progress. The central forecast continues to include an expected increase of total and core inflation rates in the second quarter of 2021, alongside the lapse of the temporary price relief measures put in place in 2020. Additional COVID-19 outbreaks (of uncertain duration and intensity) represent a significant risk factor that could affect these projections. Additionally, the forecast continues to include an upward trend in sovereign risk premiums, reflected by higher levels of public debt that in the wake of the pandemic are likely to persist on the forecast horizon, even in the context of a fiscal adjustment. At the same time, the projection accounts for the shortterm effects on private domestic demand from a fiscal adjustment along the lines of the one currently being proposed by the national government. This would be compatible with a gradual recovery of private domestic demand in 2022. The size and characteristics of the fiscal adjustment that is ultimately implemented, as well as the corresponding market response, represent another source of forecast uncertainty. Newly available information offers evidence of the potential for significant changes to the macroeconomic scenario, though without altering the general diagnosis described above. The most recent data on inflation, growth, fiscal policy, and international financial conditions suggests a more dynamic economy than previously expected. However, a third wave of the pandemic has delayed the re-opening of Colombia’s economy and brought with it a deceleration in economic activity. Detailed descriptions of these considerations and subsequent changes to the macroeconomic forecast are presented below. The expected annual decline in GDP (-0.3%) in the first quarter of 2021 appears to have been less pronounced than projected in January (-4.8%). Partial closures in January to address a second wave of COVID-19 appear to have had a less significant negative impact on the economy than previously estimated. This is reflected in figures related to mobility, energy demand, industry and retail sales, foreign trade, commercial transactions from selected banks, and the national statistics agency’s (DANE) economic tracking indicator (ISE). Output is now expected to have declined annually in the first quarter by 0.3%. Private consumption likely continued to recover, registering levels somewhat above those from the previous year, while public consumption likely increased significantly. While a recovery in investment in both housing and in other buildings and structures is expected, overall investment levels in this case likely continued to be low, and gross fixed capital formation is expected to continue to show significant annual declines. Imports likely recovered to again outpace exports, though both are expected to register significant annual declines. Economic activity that outpaced projections, an increase in oil prices and other export products, and an expected increase in public spending this year account for the upward revision to the 2021 growth forecast (from 4.6% with a range between 2% and 6% in January, to 6.0% with a range between 3% and 7% in April). As a result, the output gap is expected to be smaller and to tighten more rapidly than projected in the previous report, though it is still expected to remain in negative territory on the forecast horizon. Wide forecast intervals reflect the fact that the future evolution of the COVID-19 pandemic remains a significant source of uncertainty on these projections. The delay in the recovery of economic activity as a result of the resurgence of COVID-19 in the first quarter appears to have been less significant than projected in the January report. The central forecast scenario expects this improved performance to continue in 2021 alongside increased consumer and business confidence. Low real interest rates and an active credit supply would also support this dynamic, and the overall conditions would be expected to spur a recovery in consumption and investment. Increased growth in public spending and public works based on the national government’s spending plan (Plan Financiero del Gobierno) are other factors to consider. Additionally, an expected recovery in global demand and higher projected prices for oil and coffee would further contribute to improved external revenues and would favor investment, in particular in the oil sector. Given the above, the technical staff’s 2021 growth forecast has been revised upward from 4.6% in January (range from 2% to 6%) to 6.0% in April (range from 3% to 7%). These projections account for the potential for the third wave of COVID-19 to have a larger and more persistent effect on the economy than the previous wave, while also supposing that there will not be any additional significant waves of the pandemic and that mobility restrictions will be relaxed as a result. Economic growth in 2022 is expected to be 3%, with a range between 1% and 5%. This figure would be lower than projected in the January report (3.6% with a range between 2% and 6%), due to a higher base of comparison given the upward revision to expected GDP in 2021. This forecast also takes into account the likely effects on private demand of a fiscal adjustment of the size currently being proposed by the national government, and which would come into effect in 2022. Excess in productive capacity is now expected to be lower than estimated in January but continues to be significant and affected by high levels of uncertainty, as reflected in the wide forecast intervals. The possibility of new waves of the virus (of uncertain intensity and duration) represents a significant downward risk to projected GDP growth, and is signaled by the lower limits of the ranges provided in this report. Inflation (1.51%) and inflation excluding food and regulated items (0.94%) declined in March compared to December, continuing below the 3% target. The decline in inflation in this period was below projections, explained in large part by unanticipated increases in the costs of certain foods (3.92%) and regulated items (1.52%). An increase in international food and shipping prices, increased foreign demand for beef, and specific upward pressures on perishable food supplies appear to explain a lower-than-expected deceleration in the consumer price index (CPI) for foods. An unexpected increase in regulated items prices came amid unanticipated increases in international fuel prices, on some utilities rates, and for regulated education prices. The decline in annual inflation excluding food and regulated items between December and March was in line with projections from January, though this included downward pressure from a significant reduction in telecommunications rates due to the imminent entry of a new operator. When controlling for the effects of this relative price change, inflation excluding food and regulated items exceeds levels forecast in the previous report. Within this indicator of core inflation, the CPI for goods (1.05%) accelerated due to a reversion of the effects of the VAT-free day in November, which was largely accounted for in February, and possibly by the transmission of a recent depreciation of the peso on domestic prices for certain items (electric and household appliances). For their part, services prices decelerated and showed the lowest rate of annual growth (0.89%) among the large consumer baskets in the CPI. Within the services basket, the annual change in rental prices continued to decline, while those services that continue to experience the most significant restrictions on returning to normal operations (tourism, cinemas, nightlife, etc.) continued to register significant price declines. As previously mentioned, telephone rates also fell significantly due to increased competition in the market. Total inflation is expected to continue to be affected by ample excesses in productive capacity for the remainder of 2021 and 2022, though less so than projected in January. As a result, convergence to the inflation target is now expected to be somewhat faster than estimated in the previous report, assuming the absence of significant additional outbreaks of COVID-19. The technical staff’s year-end inflation projections for 2021 and 2022 have increased, suggesting figures around 3% due largely to variation in food and regulated items prices. The projection for inflation excluding food and regulated items also increased, but remains below 3%. Price relief measures on indirect taxes implemented in 2020 are expected to lapse in the second quarter of 2021, generating a one-off effect on prices and temporarily affecting inflation excluding food and regulated items. However, indexation to low levels of past inflation, weak demand, and ample excess productive capacity are expected to keep core inflation below the target, near 2.3% at the end of 2021 (previously 2.1%). The reversion in 2021 of the effects of some price relief measures on utility rates from 2020 should lead to an increase in the CPI for regulated items in the second half of this year. Annual price changes are now expected to be higher than estimated in the January report due to an increased expected path for fuel prices and unanticipated increases in regulated education prices. The projection for the CPI for foods has increased compared to the previous report, taking into account certain factors that were not anticipated in January (a less favorable agricultural cycle, increased pressure from international prices, and transport costs). Given the above, year-end annual inflation for 2021 and 2022 is now expected to be 3% and 2.8%, respectively, which would be above projections from January (2.3% and 2,7%). For its part, expected inflation based on analyst surveys suggests year-end inflation in 2021 and 2022 of 2.8% and 3.1%, respectively. There remains significant uncertainty surrounding the inflation forecasts included in this report due to several factors: 1) the evolution of the pandemic; 2) the difficulty in evaluating the size and persistence of excess productive capacity; 3) the timing and manner in which price relief measures will lapse; and 4) the future behavior of food prices. Projected 2021 growth in foreign demand (4.4% to 5.2%) and the supposed average oil price (USD 53 to USD 61 per Brent benchmark barrel) were both revised upward. An increase in long-term international interest rates has been reflected in a depreciation of the peso and could result in relatively tighter external financial conditions for emerging market economies, including Colombia. Average growth among Colombia’s trade partners was greater than expected in the fourth quarter of 2020. This, together with a sizable fiscal stimulus approved in the United States and the onset of a massive global vaccination campaign, largely explains the projected increase in foreign demand growth in 2021. The resilience of the goods market in the face of global crisis and an expected normalization in international trade are additional factors. These considerations and the expected continuation of a gradual reduction of mobility restrictions abroad suggest that Colombia’s trade partners could grow on average by 5.2% in 2021 and around 3.4% in 2022. The improved prospects for global economic growth have led to an increase in current and expected oil prices. Production interruptions due to a heavy winter, reduced inventories, and increased supply restrictions instituted by producing countries have also contributed to the increase. Meanwhile, market forecasts and recent Federal Reserve pronouncements suggest that the benchmark interest rate in the U.S. will remain stable for the next two years. Nevertheless, a significant increase in public spending in the country has fostered expectations for greater growth and inflation, as well as increased uncertainty over the moment in which a normalization of monetary policy might begin. This has been reflected in an increase in long-term interest rates. In this context, emerging market economies in the region, including Colombia, have registered increases in sovereign risk premiums and long-term domestic interest rates, and a depreciation of local currencies against the dollar. Recent outbreaks of COVID-19 in several of these economies; limits on vaccine supply and the slow pace of immunization campaigns in some countries; a significant increase in public debt; and tensions between the United States and China, among other factors, all add to a high level of uncertainty surrounding interest rate spreads, external financing conditions, and the future performance of risk premiums. The impact that this environment could have on the exchange rate and on domestic financing conditions represent risks to the macroeconomic and monetary policy forecasts. Domestic financial conditions continue to favor recovery in economic activity. The transmission of reductions to the policy interest rate on credit rates has been significant. The banking portfolio continues to recover amid circumstances that have affected both the supply and demand for loans, and in which some credit risks have materialized. Preferential and ordinary commercial interest rates have fallen to a similar degree as the benchmark interest rate. As is generally the case, this transmission has come at a slower pace for consumer credit rates, and has been further delayed in the case of mortgage rates. Commercial credit levels stabilized above pre-pandemic levels in March, following an increase resulting from significant liquidity requirements for businesses in the second quarter of 2020. The consumer credit portfolio continued to recover and has now surpassed February 2020 levels, though overall growth in the portfolio remains low. At the same time, portfolio projections and default indicators have increased, and credit establishment earnings have come down. Despite this, credit disbursements continue to recover and solvency indicators remain well above regulatory minimums. 1.2 Monetary policy decision In its meetings in March and April the BDBR left the benchmark interest rate unchanged at 1.75%.