Modelling error propagation in vector-based overlay analysis

The error propagation among estimated parameters reflects the correlation among the parameters. We study the capability of machine learning of “learning” the correlation of estimated parameters. We show that machine learning can recover the relation between the uncertainties of different parameters, especially, as predicted by the error propagation formula. Gravitational lensing can be used to probe both astrophysics and cosmology. As a practical application, we show that the machine learning is able to intelligently find the error propagation among the gravitational lens parameters (effective lens mass M L and Einstein radius θ E ) in accordance with the theoretical formula for the singular isothermal ellipse (SIE) lens model. The relation of errors of lens mass and Einstein radius, (e.g., the ratio of standard deviations =σMLˆ/σθEˆ ) predicted by the deep convolution neural network are consistent with the error propagation formula of the SIE lens model. As a proof-of-principle test, a toy model of linear relation with Gaussian noise is presented. We found that the predictions obtained by machine learning indeed indicate the information about the law of error propagation and the distribution of noise. Error propagation plays a crucial role in identifying the physical relation among parameters, rather than a coincidence relation, therefore we anticipate our case study on the error propagation of machine learning predictions could extend to other physical systems on searching the correlation among parameters.

The Earth’s synthetic gravitational and density models can be used to validate numerical procedures applied for global (or large-scale regional) gravimetric forward and inverse modeling. Since the Earth’s lithospheric structure is better constrained by tomographic surveys than a deep mantle, most existing 3D density models describe only a lithospheric density structure, while 1D density models are typically used to describe a deep mantle density structure below the lithosphere-asthenosphere boundary. The accuracy of currently available lithospheric density models is examined in this study. The error analysis is established to assess the accuracy of modeling the sub-lithospheric mantle geoid while focusing on the largest errors (according to our estimates) that are attributed to lithospheric thickness and lithospheric mantle density uncertainties. Since a forward modeling of the sub-lithospheric mantle geoid also comprises numerical procedures of adding and subtracting gravitational contributions of similar density structures, the error propagation is derived for actual rather than random errors (that are described by the Gauss’ error propagation law). Possible systematic errors then either lessen or sum up after applying particular corrections to a geoidal geometry that are attributed to individual lithospheric density structures (such as sediments) or density interfaces (such as a Moho density contrast). The analysis indicates that errors in modeling of the sub-lithospheric mantle geoid attributed to lithospheric thickness and lithospheric mantle density uncertainties could reach several hundreds of meters, particularly at locations with the largest lithospheric thickness under cratonic formations. This numerical finding is important for the calibration and further development of synthetic density models of which mass equals the Earth’s total mass (excluding the atmosphere). Consequently, the (long-to-medium wavelength) gravitational field generated by a synthetic density model should closely agree with the Earth’s gravitational field.

The paper deals with analysis of turbine governor positioning system of hydroelectric power plant regarding nonlinear jump. The term resonance is used in the case of a sudden jump of amplitude and/or frequency and/or phase of a periodic output signal of a nonlinear system. Resonance jump cannot occur if excitation is such that the response of the system is transient and cannot be defined by solving nonlinear differential equations. Resonance jumps can cause severe damage and the mechanical, hydraulic and electrical systems with the saturation should be analyzed with the respect to the possibility of occurrence of jump. In the paper the analysis of the water turbine governor positioning system with the respect to the occurrence of jump is described. Two methods of analyzing system with the respect to jumps are described: the simulation method and the analytical method. When using the simulation method, the analysis of the variations of important parameters, including dead zone is performed and the simulation procedures are detailed. Then, the confirmation of the results of simulation is given by the analytical analysis method based on the describing function approach. At the end, the fuzzy regulator for avoidance of nonlinear jump in turbine governor positioning system is involved.

Software cost estimation techniques predict the amount of effort required to develop a software system. Cost estimates are needed throughout the software lifecycle to determine feasibility of software projects and to provide for appropriate allocation or reallocation of available resources. To assess the effect of imprecise evaluations, a comprehensive sensitivity analysis was performed on a major cost estimation model, COCOMO II. Results of this analysis are described and explicated in this paper. To reduce risk of drawing biased conclusions, three different methods for sensitivity analysis were employed: the mathematical analysis of the estimating equation, Monte Carlo simulation, and error propagation. The results of the first two methods are very consistent and confirm expected highest sensitivity of the model to the imprecision of the size estimate. Error propagation allows determination of the combined impact of imprecision in multiple inputs and it is therefore most valuable from the practical point of view. The results obtained by this technique also indicate very strong sensitivity to the imprecision in size estimates. A possible way to cope with imprecise information in software cost estimation is also indicated.

This study proposed a recursion‐based analytical approach to assess measurement precision of ability estimation and classification accuracy in multistage adaptive tests (MSTs). A simulation study was conducted to compare the proposed recursion‐based analytical method with an analytical method proposed by Park, Kim, Chung, and Dodd and with the more commonly used Monte Carlo (MC) simulation approaches. The results from the simulation study indicate that the recursion‐based analytical method produced more stable measurement properties in MST than the MC‐based simulation method. It also produced more credible measurement performance than the analytical approach of Park, Kim, Chung, and Dodd. We expect that the recursion‐based analytical method would be especially efficient in instances when multiple MST designs need to be compared to determine which one has better measurement performance.

This paper presents a modular method for the mechanical error analysis of complex planar linkages. The topology of the linkage under investigation is decomposed into several class II Assur group kinematic chains (AGKCs) combined in a given sequence. Therefore, the mechanical error of the whole linkage can be analyzed by investigating the error propagations of adopted AGKCs in successive order. Because class II AGKCs are first served as modules, the mechanical error equations of these AGKCs in terms of each error in link lengths and joint variables can be pre-formulated and embedded in form of subroutines in any programmable language. Once the AGKCs constituting the linkage topology are identified, the corresponding subroutines are introduced to compute the error propagations in the linkage. Therefore, the presented modular approach can facilitate the analysis by concentrating on the topology decomposition instead of the algebraic derivation. Numerical examples are provided to illustrate the advantage and flexibility of the modular approach.

This work focuses on devising an efficient hierarchy of higher-order methods for linear transient analysis, equipped with an effective dissipative action on the spurious high modes of the response. The proposed strategy stems from the Norsett idea and is based on a multi-stage algorithm, designed to hierarchically improve accuracy while retaining the desired dissipative behaviour. Computational efficiency is pursued by requiring that each stage should involve just one set of implicit equations of the size of the problem to be solved (as standard time integration methods) and, in addition, all the stages should share the same coefficient matrix. This target is achieved by rationally formulating the methods based on the discontinuous collocation approach. The resultant procedure is shown to be well suited for adaptive solution strategies. In particular, it embeds two natural tools to effectively control the error propagation. One estimates the local error through the next-stage solution, which is one-order more accurate, the other through the solution discontinuity at the beginning of the current time step, which is permitted by the present formulation. The performance of the procedure and the quality of the two error estimators are experimentally verified on different classes of problems. Some typical numerical tests in transient heat conduction and elasto-dynamics are presented. Copyright © 2006 John Wiley & Sons, Ltd.

Describes the setting up of a moiré topographic system to measure three‐dimensional convex and concave surfaces of moulded brassière cups. The essential features of the system consisted of a photographic instrument which precisely controlled the position of the light source, the camera, the grid and the cup sample. As the uniformity of the grid was most crucial to produce a high contrast moiré picture, a photochemical‐machined grid plate was developed, and a pneumatic grid translation device was incorporated into the system to produce a clear image. The tolerance of the instrumental error was derived by the law of error propagation and the confidence with the moiré set‐up was assured.

Hydrodynamically limited precision of gradient techniques in flow injection analysis

Widespread white matter tract aberrations in youth with familial risk for bipolar disorder

From the first applications of AT-cut quartz crystals as sensors in solutions more than 20 years ago, the so-called quartz crystal microbalance (QCM) sensor is becoming into a good alternative analytical method in a great deal of applications such as biosensors, analysis of biomolecular interactions, study of bacterial adhesion at specific interfaces, pathogen and microorganism detection, study of polymer film-biomolecule or cell-substrate interactions, immunosensors and an extensive use in fluids and polymer characterization and electrochemical applications among others. The appropriate evaluation of this analytical method requires recognizing the different steps involved and to be conscious of their importance and limitations. The first step involved in a QCM system is the accurate and appropriate characterization of the sensor in relation to the specific application. The use of the piezoelectric sensor in contact with solutions strongly affects its behavior and appropriate electronic interfaces must be used for an adequate sensor characterization. Systems based on different principles and techniques have been implemented during the last 25 years. The interface selection for the specific application is important and its limitations must be known to be conscious of its suitability, and for avoiding the possible error propagation in the interpretation of results. This article presents a comprehensive overview of the different techniques used for AT-cut quartz crystal microbalance in in-solution applications, which are based on the following principles: network or impedance analyzers, decay methods, oscillators and lock-in techniques. The electronic interfaces based on oscillators and phase-locked techniques are treated in detail, with the description of different configurations, since these techniques are the most used in applications for detection of analytes in solutions, and in those where a fast sensor response is necessary.

To research the dynamic characteristics of a planar piezoelectric six-axis force/torque(F/T) sensor in an actual measurement, a mathematical model method, a simulation method, and a calibration method are presented. The structure model of the sensor, its working principle, and research method are explained. A mass-spring equivalent model with multi-degrees of vibration based on the sensor is established, and differential equations based on the vibration system are derived from this model. According to the experimental prototype parameters of the sensor, its numerical model is established, the numerical simulation method and dynamic characteristic are investigated, and the amplitude–frequency and phase–frequency characteristics are analysed using the harmonic response method. The natural frequency of this sensor is calibrated using the impact response method. The experimental results indicate that the natural frequency in the six directions of the planar piezoelectric six-axis F/T sensor is higher than 3.95 kHz, and that the results of the analytical mathematical method and numerical simulation method are consistent with the calibration results. The proposed analytical mathematical method, simulation method, and calibration method can be used in the design, prediction, and calibration of the dynamic characteristics of these six-axis F/T sensors.

Ghost imaging (GI) has found application across diverse fields owing to its distinctive benefits. When employing the rotating ground-glass scheme and utilizing second-order correlation for image reconstruction, the efficiency of imaging is hindered by the multiple sampling of reference patterns. To address this, the orthonormalization method has been employed to enhance image quality and reduce the required number of measurements. Despite its effectiveness, the original orthonormalization method is prone to accumulating imaging noise and errors as the number of measurements increases, leading to a significant degradation in image quality. To overcome this limitation, this paper introduces the grouped orthonormalization method (GO-GI) as an extension of the orthonormalization technique. By adjusting the ‘group size’, this method enables control over the accumulation of errors, resulting in an improvement in image quality. The evaluation of image quality in terms of Contrast-to-Noise demonstrates the significant advantages of the GO-GI method in both simulation and experimental results. This study establishes the GO-GI method as a simple yet practical approach in the realm of GI.

Development of energy-saving technologies offers good opportunities for selecting building energy supply methods through the use of alternative energy sources and power network types. Research in the field of energy saving is mainly focused on finding methods of energy saving by power consumers and individual power industry facilities. At the same time, collaboration of different energy networks as a unified power supply system of the city and a feasibility study of the energy load redistribution between different energy networks in the process of territorial development remains a poorly studied problem. The aim of the study is to develop a method that allows comparing the use of different power supply sources and types of individual buildings based on a single criterion of changing the total cost of transmission, conversion and consumption of energy in the city. The study employed methods of development and analysis of energy balances of a territory, methods for calculating gas, heat and electricity consumption of residential buildings, methods of power network losses calculation and methods of network and overlay analysis in GIS, materials of power providers’ and public utilities’ databases. A method has been proposed and implemented in the software package form for automating the calculation of the city’s housing sector energy balance for various placement options, power equipment deployment and connection of new or reconstructed buildings to the energy networks. The method is based on the use of an urban area energy balance spatial model in a GIS environment. The article presents an example of calculating the influence of different power supply options of one of the buildings in the city of Ivanovo on the energy balance of the city. The obtained results demonstrate the possibility of a comparative analysis of the options of connecting buildings to various energy network types based on a single criterion of minimizing municipal energy costs. The developed method and its implementation can be used to create decision-making information systems for regional and city governments.

Bicistronic reporter assay systems have become a mainstay of molecular biology. While the assays themselves encompass a broad range of diverse and unrelated experimental protocols, the numerical data garnered from these experiments often have similar statistical properties. In general, a primary dataset measures the paired expression of two internally controlled reporter genes. The expression ratio of these two genes is then normalized to an external control reporter. The end result is a ‘ratio of ratios’ that is inherently sensitive to propagation of the error contributed by each of the respective numerical components. The statistical analysis of this data therefore requires careful handling in order to control for the propagation of error and its potentially misleading effects. A careful survey of the literature found no consistent method for the statistical analysis of data generated from these important and informative assay systems. In this report, we present a detailed statistical framework for the systematic analysis of data obtained from bicistronic reporter assay systems. Specifically, a dual luciferase reporter assay was employed to measure the efficiency of four programmed −1 frameshift signals. These frameshift signals originate from the L-A virus, the SARS-associated Coronavirus and computationally identified frameshift signals from two Saccharomyces cerevisiae genes. Furthermore, these statistical methods were applied to prove that the effects of anisomycin on programmed −1 frameshifting are statistically significant. A set of Microsoft Excel spreadsheets, which can be used as templates for data generated by dual reporter assay systems, and an online tutorial are available at our website (http://dinmanlab.umd.edu/statistics). These spreadsheets could be easily adapted to any bicistronic reporter assay system.