Extrapolation Methodology Research Articles

Th e compositional device «shpilbreacher»: Russian musical classics and modernity

The article is devoted to the formal “shpilbreacher” technique, which is regularly found in the works of outstanding Russian composers — M. Glinka, P. Tchaikovsky, D. Shostakovich. In the context of classical composers, the technique is considered on the example of the work of the famous St. Petersburg composer Vadim Bibergan. The compositional solution of the “shpilbrecher” technique is aimed at marking the climax due to the qualitative transformation of the sounding material and changing the logic of its development. Methodology of extrapolation and comparative studies, appeals to the legacy of M. Glinka, P. Tchaikovsky, D. Shostakovich made it possible to further study this technique in the works of modern composers. The appeal to reception in the works of M. Glinka, P. Tchaikovsky, D. Shostakovich emphasizes the independence of its functioning from style, genre and musical epoch. The result of the work was the identification, definition and description of the reception based on the material selected for analysis and the conclusion that the reception can be important both for performers and for a wide range of interested persons.

Panamax cargo-vessel excessive-roll dynamics based on novel deconvolution method

This study presents a state-of-the-art extreme-value-prediction methodology based on deconvolution that can be utilized in marine, offshore, and naval-engineering applications. First, a measured gust-windspeed dataset is utilized to illustrate the accuracy of the deconvolution method. Second, a real-time roll dynamics raw dataset measured onboard an operating loaded TEU2800 container vessel is analyzed, and the vessel motion data are measured during numerous trans-Atlantic crossings. The risk of container loss owing to excessive rolling motion is a key issue in cargo vessel transportation. The complex nonlinear and nonstationary characteristics of incoming waves and the associated cargo vessel movements render it challenging to accurately forecast excessive vessel roll angles. When a loaded cargo vessel sails through a harsh stormy environment, higher-order dynamic motion effects become evident and the effect of nonlinearities may increase significantly. Meanwhile, laboratory testing are affected by the wave parameters and similarity ratios used. Consequently, raw/unfiltered motion data obtained from cargo vessels traversing in adverse weather conditions provide valuable insights into cargo vessel reliability. Parametric extrapolations based on certain functional classes are typically employed to extrapolate and fit probability distributions estimated from the underlying dataset. This investigation aims to present an alternative nonparametric extrapolation methodology based on the intrinsic properties of the raw underlying dataset without introducing any assumptions regarding the extrapolation functional class.This novel extrapolation deconvolution method is suitable for contemporary marine-engineering and design applications, as well as serves as an alternative to existing reliability methods. The prediction accuracy of the deconvolution methodology is demonstrated by comparing it with a modified four-parameter Weibull-type extrapolation technique. Compared with its counterpart sub-asymptotic statistical methods, such as the modified Weibull-type fit, peaks over the threshold, and generalized Pareto, the advocated deconvolution method is superior in term of its extrapolation numerical stability.

Scale Effects in Wind Tunnel Testing: Extrapolation of the Drag Coefficient

Subscale wind tunnel data extrapolation is both a necessary and challenging undertaking. Most readily available wind tunnel facilities can achieve Reynolds numbers that are typically an order of magnitude lower than those of the full-scale flight article. Consequently, the wind tunnel data need to be scaled, with the Reynolds number disparity impacting force and moment measurements. Although computational fluid dynamics is ascending as a valuable tool for enabling scaling, the most common extrapolation methodologies are analytic and semi-empirical in nature. Consequently, a new approach is presented to scale both the minimum drag coefficient and the sectional pressure drag coefficient that uses the subscale data to define extrapolation exponents. Implementation requires a minimum of two subscale tests to enable specification of the exponents determined through coalescence of the extrapolated subscale tests. The approach is simple to implement and can be applied to both airfoils and wings. Numerous cases are presented for method validation.

МЕТОДИКА ІНТЕРПОЛЯЦІЇ ТА ЕКСТРАПОЛЯЦІЇ ДАНИХ ПРИ НЕРАВНОМІРНОМУ КРОКУ ЗМІНИ ПАРАМЕТРІВ ЕКСПЕРИМЕНТУ

The problem with using experimental data is the limited range and uneven measurement step for individual variables. This reduces the accuracy of determining the value of the desired function. The method of further research is to increase the number of values of the sought function based on limited experimental data. The research method involves developing a methodology for interpolation and extrapolation of experimental data using the functions of the Matlab package. The result of the investigation is that the technique allows you to create a uniform grid of reference values, fill it with the required step of changing variables, extrapolate data to the boundaries of the data space, where the influence of a given argument on the function is zero, isolate the contribution of individual arguments to the value of the function, synthesize the value of the function in new nodes reference grid of values The application of a standardized method was introduced to form a space of values of the relative rate of aging of cellulose insulation of power transformer windings as a function of temperature, humidity and oxygen access, which made it possible to increase the amount of data at least 4 times compared to the experiment.

A simulation study of extrapolation uncertainty in exposure assessment – Use of pilot study results for site investigation

Accurate characterization of soil contaminant concentrations is often crucial for assessing risks to human and ecological health. However, fine-scale assessments of large tracts of land can be cost prohibitive due to the number of samples needed. One solution to this problem is to extrapolate sampling results from one area to another unsampled area. In the absence of a validated extrapolation methodology, regulatory agencies have employed policy-based techniques for large sites, but the likelihood of decision errors resulting from these extrapolations is largely unexplored. This study describes the results of a simulation study aimed at guiding environmental sampling for sites where extrapolation concepts are of interest. The objective of this study is to provide practical recommendations to regulatory agencies for extrapolating sampling results on large tracts of land while minimizing errors that are detrimental to human health. A variety of site investigation scenarios representative of environmental conditions and sampling schemes were tested using adaptive sampling when collecting discrete samples or applying incremental sampling methodology (ISM). These simulations address extrapolation uncertainty in cases where a Pilot Study might result in either false noncompliance or false compliance conclusions. A wide range of plausible scenarios were used that reflect the variety of heterogeneity seen at large sites. This simulation study demonstrates that ISM can be reliably applied in a Pilot Study for purposes of extrapolating the outcome to a large area site because it decreases the likelihood of false non-compliance errors while also providing reliable estimates of true compliance across unsampled areas. The results demonstrate how errors depend on the magnitude of the 95% upper confidence limit for the mean concentration (95UCL) relative to the applicable action level, and that error rates are highest when the 95UCL is within 10%–40% of the action level. The false compliance rate can be reduced to less than 5% when 30% or more of the site is characterized with ISM. False compliance error rates using ISM are insensitive to the fraction of the decision units (DUs) that are characterized with three replicates (with a minimum of 10 percent), so long as 95UCLs are calculated for the DUs with one replicate using the average coefficient of variation from the three replicate DUs.

Effect and Determination of Oxide Trapped Charge and Interface Trapped Charge Density of Threshold Voltage Shift in Irradiated MOSFET by Subthreshold Methodology

This paper presents the effects and determination of oxide and interface trapped charge density of threshold voltage shift in irradiated MOSFET by subthreshold methodology. The designed dimension, channel width per channel length (W/L) is 20 µm/20 µm. The threshold voltage is extracted by a linear extrapolation methodology. The over all threshold voltage shifts are caused by oxide trapped charge and interface trapped charge. The subthreshold methodology determines the interface trapped charge. The 60Co gamma-ray source was used for irradiation to a total dose of 10 kGy. The results showed that the threshold voltage shift is approximately -24 mV/kGy for NMOS and -27 mV/kGy for PMOS. The subthreshold swing shift is approximately 1.2 mV/dec.kGy for NMOS and 0.9 mV/dec.kGy for PMOS. The oxide trapped charge density NOT and interface trapped charge density NIT are found to be increased in NMOS and PMOS respectively. The ratio of ΔNOT/ΔNIT was approximately 2.2 times for NMOS and 2.8 times. Due to the structure, the channel of NMOS is a surface channel whereas the channel of PMOS is a buried channel. Finally, the effect of gamma irradiation on the PMOS was greater than the effect on NMOS observed from the change in threshold voltage and the ratio of ΔNOT/ΔNIT.

EE688 Case for Clear Communication and Justification of Survival Extrapolation Methodology: A Review of NICE Submissions in Oncology

EE688 Case for Clear Communication and Justification of Survival Extrapolation Methodology: A Review of NICE Submissions in Oncology

A Novel Flight Dynamics Modeling Using Robust Support Vector Regression against Adversarial Attacks

<div>An accurate Unmanned Aerial System (UAS) Flight Dynamics Model (FDM) allows us to design its efficient controller in early development phases and to increase safety while reducing costs. Flight tests are normally conducted for a pre-established number of flight conditions, and then mathematical methods are used to obtain the FDM for the entire flight envelope. For our UAS-S4 Ehecatl, 216 local FDMs corresponding to different flight conditions were utilized to create its Local Linear Scheduled Flight Dynamics Model (LLS-FDM). The initial flight envelope data containing 216 local FDMs was further augmented using interpolation and extrapolation methodologies, thus increasing the number of trimmed local FDMs of up to 3,642. Relying on this augmented dataset, the Support Vector Machine (SVM) methodology was used as a benchmarking regression algorithm due to its excellent performance when training samples could not be separated linearly. The trained Support Vector Regression (SVR) predicted the FDM for the entire flight envelope. Although the SVR-FDM showed excellent performance, it remained vulnerable to adversarial attacks. Hence, we modified it using an adversarial retraining defense algorithm by transforming it into a Robust SVR-FDM. For validation studies, the quality of predicted UAS-S4 FDM was evaluated based on the Root Locus diagram. The closeness of predicted eigenvalues to the original eigenvalues confirmed the high accuracy of the UAS-S4 SVR-FDM. The SVR prediction accuracy was evaluated at 216 flight conditions, for different numbers of neighbors, and a variety of kernel functions were also considered. In addition, the regression performance was analyzed based on the step response of state variables in the closed-loop control architecture. The SVR-FDM provided the shortest rise time and settling time, but it failed when adversarial attacks were imposed on the SVR. The Robust-SVR-FDM step response properties showed that it could provide more accurate results than the LLS-FDM approach while protecting the controller from adversarial attacks.</div>

Modified 5-point fractional formula with Richardson extrapolation

<abstract><p>In this paper, we establish a novel fractional numerical modification of the 5-point classical central formula; called the modified 5-point fractional formula for approximating the first fractional-order derivative in the sense of the Caputo operator. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability.</p></abstract>

Extreme springing response statistics of a tethered platform by deconvolution

The research examines the motion response and hydrodynamic wave loads of a deep-water Tension Leg Platform (TLP), emphasising the impacts of the wave sum frequency on the restrained modes of heave, roll, and pitch. The stochastic TLP structural reaction in a random sea state was precisely computed using a Volterra series representation of the TLP corner vertical displacement, which was selected as a response process. The wave loading was evaluated using the second-order diffraction code WAMIT and applied to a linear damped mass-spring model representing the dynamic system. Then, platform displacement response at the design low probability level has been determined using a novel deconvolution approach. Since the Volterra series represented the analytical solution, the exact Volterra and the approximated predictions have been compared in this study. The latter provided an accurate way to validate the effectiveness and precision of the proposed novel deconvolution method. Compared to existing engineering techniques, the most attractive advantage of the proposed deconvolution method is that it does not rely on any pre-assumed asymptotic probability distribution class. The latter may be an attractive point for practical engineering design. Thus the primary objective of this work was to validate a novel deconvolution approach using exact quasi-analytical solutions. This work also highlights the limitations of mean up-crossing rate-based extrapolation methodologies for the situation of narrowband effects, including clustering, which are often included in the springing type of response.

A refined Weissman estimator for extreme quantiles

Weissman extrapolation methodology for estimating extreme quantiles from heavy-tailed distributions is based on two estimators: an order statistic to estimate an intermediate quantile and an estimator of the tail-index. The common practice is to select the same intermediate sequence for both estimators. In this work, we show how an adapted choice of two different intermediate sequences leads to a reduction of the asymptotic bias associated with the resulting refined Weissman estimator. The asymptotic normality of the latter estimator is established and a data-driven method is introduced for the practical selection of the intermediate sequences. Our approach is compared to the Weissman estimator and to six bias reduced estimators of extreme quantiles on a large scale simulation study. It appears that the refined Weissman estimator outperforms its competitors in a wide variety of situations, especially in the challenging high bias cases. Finally, an illustration on an actuarial real data set is provided.

Modified Three-Point Fractional Formulas with Richardson Extrapolation

In this paper, we introduce new three-point fractional formulas which represent three generalizations for the well-known classical three-point formulas; central, forward and backward formulas. This has enabled us to study the function’s behavior according to different fractional-order values of α numerically. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability.

Characterisation of intravenous pharmacokinetics in Göttingen minipig and clearance prediction using established in vitro to in vivo extrapolation methodologies

The use of the Göttingen minipig as an animal model for drug safety testing and prediction of human pharmacokinetics (PK) continues to gain momentum in pharmaceutical research and development. The aim of this study was to evaluate in vitro to in vivo extrapolation (IVIVE) methodologies for prediction of hepatic, metabolic clearance (CLhep,met) in Göttingen minipig, using a comprehensive set of compounds. In vivo clearance was determined in Göttingen minipig by intravenous cassette dosing and hepatocyte intrinsic clearance, plasma protein binding and non-specific incubation binding were determined in vitro. Prediction of CLhep,met was performed by IVIVE using conventional and adapted formats of the well-stirred liver model. The best prediction of in vivo CLhep,met from scaled in vitro kinetic data was achieved using an empirical correction factor based on a ‘regression offset’ of the IVIV relationship. In summary, these results expand the in vitro and in vivo PK knowledge in Göttingen minipig. We show regression corrected IVIVE provides superior prediction of in vivo CLhep,met in minipig offering a practical, unified scaling approach to address systematic under-predictions. Finally, we propose a reference set for researchers to establish their own ‘lab-specific’ regression correction for IVIVE in minipig.

Quantification of influence of monitoring duration on measured traffic action effects on fatigue of RC deck slabs of road bridges

The safety of existing bridges may be assessed using data from monitoring. The fatigue damage induced during observation period is extrapolated to the total service duration of a structure, and the reserve capacity is estimated. However, due to the randomness of road traffic, there exists a risk of underestimation of damage using a short-term monitoring campaign. This paper analyses the influence of monitoring duration on the obtained results using datasets collected during two long-term (>3 years) dynamic monitoring campaigns. Two road bridges with different nature of traffic are considered: (a) a heavily loaded two-lane highway viaduct and (b) a road viaduct with a bi-directional traffic. The deck slabs of both bridges are monitored using strain gauges installed on reinforcement bars. The daily, seasonal, year-to-year and COVID-19 lockdown-induced variations of measured action effects and calculated equivalent fatigue damage are discussed. The resampling method is used for simulation of possible short-term monitoring campaigns during the period considered, with different order of heavy vehicles arriving. The Extreme Value Theory serves to answer what is the required monitoring duration for reliable results. Possible ways of considering the monitoring duration in the fatigue damage calculation are discussed, and the methodology for damage extrapolation proposed.

Use of Physiologically Based Kinetic Modeling-Facilitated Reverse Dosimetry to Predict In Vivo Acute Toxicity of Tetrodotoxin in Rodents.

In this study, the ability of a new in vitro/in silico quantitative in vitro–in vivo extrapolation (QIVIVE) methodology was assessed to predict the in vivo neurotoxicity of tetrodotoxin (TTX) in rodents. In vitro concentration–response data of TTX obtained in a multielectrode array assay with primary rat neonatal cortical cells and in an effect study with mouse neuro-2a cells were quantitatively extrapolated into in vivo dose–response data, using newly developed physiologically based kinetic (PBK) models for TTX in rats and mice. Incorporating a kidney compartment accounting for active renal excretion in the PBK models proved to be essential for its performance. To evaluate the predictions, QIVIVE-derived dose–response data were compared with in vivo data on neurotoxicity in rats and mice upon oral and parenteral dosing. The results revealed that for both rats and mice the predicted dose–response data matched the data from available in vivo studies well. It is concluded that PBK modeling-based reserve dosimetry of in vitro TTX effect data can adequately predict the in vivo neurotoxicity of TTX in rodents, providing a novel proof-of-principle for this methodology.

A vertical-mode extrapolation scheme applied to the Brazil Current domain: quasi-synoptic scenarios

The Brazil Current (BC) is a western boundary current, with an average vertical extension of 500 m, which occupies the southwestern margin of Atlantic Ocean. Recently, the South Brazil Bight - SBB (23º S - 28º S) has been intensively explored by the oil and gas industries, which brought a high demand in operational oceanography and ocean state monitoring. In this study we present a new technique based on the vertical dynamic modes of oscillation, to extrapolate velocity profiles in the SBB, with potential applications to data acquired by Vessel Mounted Acoustic Doppler Current Profilers (VMADCP). Using four quasi-synoptic crosssectional velocity data, acquired by Lowered Acoustic Doppler Current Profilers (LADCP), we observed that the mean circulation of this region can be characterized as a 2-dynamical mode system. This mean circulation is mainly dominated at surface by the BC and at intermediate levels by the Intermediate Western Boundary Current (IWBC), which flows northward. Furthermore, observed mesoscale vortical features in the SBB, such as eddies and meanders, are shown to be primarily barotropic-mode dominated. In our extrapolation methodology, the use of an independent set of velocity time series obtained by four moorings has shown to be a valid way for obtaining the relative contribution of each dynamical mode in the velocity field in the SBB. Normalized mean squared errors below 10% and radar diagrams show that the presented methodology was able to reproduce the main dynamic features observed by LADCP transects. Also, with this technique, we extrapolated three VMADCP sections and the results agreed with previous observations.

Estimation of radiation absorbed dose in man from 166Ho-EDTMP based on biodistribution data in Wistar rats

Bone marrow malignancies including multiple myeloma are treated by the myeloablative radiotherapy and subsequent stem cell transplantation. Radiopharmaceuticals are used for the selective delivery of radiation absorbed dose to bone marrow. In this work, the radiation absorbed dose of various organs of the adult man from 166Ho-EDTMP radiopharmaceutical was estimated based on biodistribution data in Wistar rats. The MIRD dose calculation method and the Sparks and Aydogan methodology for extrapolation of %IA of organs from animal to human were applied. The results shows that, more than 61% of injected activity is cumulated on the surface of the trabecular and cortical bones. Red marrow and osteogenic cells radiation absorbed doses were estimated to about 1.4 and 3.1 mGy/MBq, respectively. Compared to other aminophosphonate radiopharmaceuticals, 166Ho-EDTMP requires a minimum activity to deliver a therapeutic dose of 25 Gy to the red bone marrow. The result were compared with available data from literature.

Exponent determination in a poorly gauged basin system in Nigeria based on flow characteristics investigation and regionalization method

In this study, a method for estimating the exponent “n” values of the catchment-area equations of four sub-basins within the poorly gauged Benin-Owena River Basin Development Authority (BORBDA) in Nigeria is presented to enable the estimation of flows at ungauged sites within the basin and the determination of small hydropower (SHP) potential at different locations in each sub-basin and the entire basin. Optimal prediction of streamflow characteristics in poorly gauged basin requires developing a methodology for extrapolation of data from gauged to ungauged sites within the basin. Four sub-catchments of BORBDA, a poorly gauged basin in Nigeria, were investigated using Remote Sensing (RS), Geographic Information System (GIS), statistical techniques, and Natural Resources Conservation Service-Curve Number (NRCS-CN) hydrological model. Discharge values at gauged sites (Qg) were obtained from recorded discharge values collected for 12 months at an established gauging station in each sub-basin. RS and GIS techniques were used to develop classification maps and obtain crucial data like curve number (CN), elevation, Hydrologic Soil Group (HSG), rainfall intensity, slope, area of gauged and ungauged required for evaluating spatial discharge (ungauged) utilizing NRCS-CN model. From the established model for each sub-basin, exponent “n” in the relationship between discharge and catchment area was obtained to be 0.23, 0.41, 0.71, and 0.74. Using the lumped modeling approach, which considers a watershed as a single unit for computation, where watershed parameters and variables were to be averaged produced “n” = 0.52 for BORBDA area, which is within the range of 0.5–0.85 suggested by previous researchers. Obtained BORBDA exponent “n” was validated for use in the entire basin through soil homogeneity test by generating BORBDA soil map which confirms the four sub-basins investigated share similar HSG A, B, and D with BORBDA. The exponent “n” value is useful for predicting flows in ungauged parts of the basin. The exponent “n” value obtained for the basin is helpful in the assessment of discharge and determination of SHP potential at different locations within the poorly gauged BORBDA basin, and the dissemination of the research findings will find practical use and guide to practicing hydrologists in Nigeria and locations around the world with similar challenges of poorly gauged basins particularly Africa and other developing countries.

Posological review of dose extrapolation methodologies in animal studies, early-phase clinical trials and special populations

Identifying the right dose is arguably an essential step in the design of experiments related to drug discovery and development. Often, dose extrapolation is done to scale the doses of a drug from one species to another. However, literature is replete with cases that warrant against the careless and inadequate application of dose-extrapolation methodologies. Increasing costs of research and the development and ethical considerations of experimentation in animals and humans do not condone injudicious design of experiments. This call to caution forms the essential premise of the current review, which focuses on the methodology of the dose extrapolation and its place in early-phase clinical trials and animal studies. Furthermore, the review also provides an update on within-species dose extrapolation to address the issues of adapting adult human doses to pediatric and geriatric settings.

Flat-histogram extrapolation as a useful tool in the age of big data

ABSTRACT Here we review recent work by the authors to revisit the concept of extrapolating thermodynamic properties of classical systems using statistical mechanical principles. Specifically, we discuss how the combination of these principles with biased sampling techniques enables the prediction of free energy landscapes and other detailed information, such as structural properties, of the system in question. Remarkably accurate estimates of physical properties across a broad range of conditions have been achieved using this approach, greatly reducing the number of simulations needed to explore a given system's behaviour. While approximate, these extrapolations significantly amplify the amount of reasonably accurate information that can be extracted from simulations enabling a small set of them to feed data-intensive regression algorithms such as neural networks. Thus, this extrapolation methodology represents a useful tool for performing tasks such as high-throughput screening of physical properties, optimising force field parameters, exploring equilibrium phase behaviour, and enabling theory-guided data science for these systems.