25 papers · ranked by Valyu relevance
Qi, Daniel C., Oguri, Kenshiro
A common approach for controller design in nonlinear systems is to linearize the dynamics about a reference trajectory and apply linear control techniques within the vicinity of the reference [[2]]. Naturally, the omitted nonlinear terms from the linearization process will result in some inconsistencies between the…
Brock D. Sherlock, Marko A. A. Boon, Maria Vlasiou, Adelle C. F. Coster
Measurement error is an unavoidable feature of experimental data collection. It is common in mathematical biology to consider measurement error in the dependent variable. However, less attention has been given to errors in the independent variable. This work is focussed on the effects of independent variable…
Maël Godard, Luc Jaulin, Damien Massé
In engineering, models are often used to represent the behavior of a system. Estimators are then needed to approximate the values of the model's parameters based on observations. This approximation implies a difference between the values predicted by the model and the observations that have been made. It creates an…
Thomas G. Mayerhöfer, Isao Noda, Susanne Pahlow, Rainer Heintzmann + 2 more
'Jürgen Popp' 'Rajesh Kumar'] Recently a new family of loss functions called smart error sums has been suggested. These loss functions account for correlations within experimental data and force modeled data to obey these correlations. As a result, multiplicative systematic errors of experimental data can be revealed…
Timothy E. O’Brien, Jack W. Silcox
Use of nonlinear statistical methods and models are ubiquitous in scientific research. However, these methods may not be fully understood, and as demonstrated here, commonly-reported parameter p-values and confidence intervals may be inaccurate. The gentle introduction to nonlinear regression modelling and…
Wenguang Feng, Shibin Liu
Nonlinearity is a prominent limitation to the calibration performance for two-axis fluxgate sensors. In this paper, a novel nonlinear calibration algorithm taking into account the nonlinearity of errors is proposed. In order to establish the nonlinear calibration model, the combined effort of all time-invariant errors…
Daniele de Brito Trindade, Patrícia Leone Espinheira, Klaus Leite Pinto Vasconcellos, Jalmar Manuel Farfán Carrasco + 2 more
'Klaus Leite Pinto Vasconcellos' 'Jalmar Manuel Farfán Carrasco' 'Maria do Carmo Soares de Lima' 'Fabio Rapallo'] We propose in this paper a general class of nonlinear beta regression models with measurement errors. The motivation for proposing this model arose from a real problem we shall discuss here. The application…
Erdem Pulcu
We are living in a dynamic world in which stochastic relationships between cues and outcome events create different sources of uncertainty^1^ (e.g. the fact that not all grey clouds bring rain). Living in an uncertain world continuously probes learning systems in the brain, guiding agents to make better decisions. This…
Lintao Lan, Fangwu Hua, Fang Fang, Wei Jiang + 1 more
For two-axis electro-optical measurement equipment, there are many error sources in parts manufacturing, assembly, sensors, calibration, and so on, which cause some random errors in the final measurement results of the target. In order to eliminate the random measurement error as much as possible and improve the…
Junqing Ma, Aiguo Song, Jing Xiao
Coupling errors are major threats to the accuracy of 3-axis force sensors. Design of decoupling algorithms is a challenging topic due to the uncertainty of coupling errors. The conventional nonlinear decoupling algorithms by a standard Neural Network (NN) are sometimes unstable due to overfitting. In order to avoid…
Danny Smyl, Tyler N. Tallman, J.A. Black, Andreas Hauptmann + 1 more
'Dong Liu'] All discretized numerical models contain modelling errors – this reality is amplified when reduced-order models are used. The ability to accurately approximate modelling errors informs statistics on model confidence and improves quantitative results from frameworks using numerical models in prediction…
Authors not listed
Moving bed reactors (MBRs) are widely used in various industrial processes, making the development of mathematical models crucial for their design, optimization, and control. This study presents a semi-analytical solution (SAS) for a lumped parameter kinetic and heat transfer model of a tubular MBR, where a first-order…
Yinkun Wang, Xiangling Chen, Ying Li, Jianshu Luo
A fast non-polynomial interpolation is proposed in this paper for functions with logarithmic singularities. It can be executed fast with the discrete cosine transform. Based on this interpolation, a new quadrature is proposed for a kind of logarithmically singular integrals. The interpolation and integration errors are…
Erfan Nozari, Jennifer Stiso, Lorenzo Caciagli, Eli J. Cornblath + 5 more
A central challenge in the computational modeling of neural dynamics is the trade-off between accuracy and simplicity. At the level of individual neurons, nonlinear dynamics are both experimentally established and essential for neuronal functioning. One may therefore expect the collective dynamics of massive networks…
Authors not listed
The rapid growth of worldwide computing power has transformed in silico chemistry into a discipline that is integrated into the daily work of many chemists. Nowadays, researchers find it increasingly straightforward to predict a wide range of molecular properties and chemi- cal processes at reasonable computational…
Ying Wang, Min Li, Ronaldo García Reyes, Deirel Paz-Linares + 4 more
Parameterizing electroencephalography (EEG) signals in the spectral domain reveals physiologically relevant components of neural stochastic processes, yet the linearity or nonlinearity of these components remains debated and could not solved by the current Spectral Parameter Analysis (SPA). We address this using BiSCA…
David A. Kopriva, Andrew R. Winters, Jan Nordström
due to Inaccurate Boundary Geometry Authors: ['David A. Kopriva' 'Andrew R. Winters' 'Jan Nordström'] aDepartment of Mathematics, The Florida State University, Tallahassee, FL 32306, USA bComputational Science Research Center, San Diego State University, San Diego, CA, USA cDepartment of Mathematics, Applied…
Matthew O. Williams, T. Lovett
- Abstract. In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even implementation. We propose a pair of methods for detecting and localizing these convergence rate issues in applications that can…
Authors not listed
Inverse problems, where we seek the values of inputs to a model that lead to a desired set of outputs, are a challenges subset of problems in science and engineering. In this work we demonstrate the use of two generative AI methods to solve inverse problems. We compare this approach to two more conventional approaches…
Authors not listed
Nonlinear monotonically increasing bounded functions help to visualize and analyze data on various scales. However, many monotonic functions such as logarithm or power laws have either function values or derivatives that become unbounded at some regions of the $x-$ axis. On the other hand, sigmoid or hyperbolic…
Ikechukwu I. Udema
A burning concern among researchers studying enzyme kinetics has been ways of improving the accuracy of initial rates (v) with much greater precision. The goal of this study was to establish a formal (mathematical) way of achieving more accurate v values in enzyme assay. By adopting Bernfeld method of assay, the v…
Maria H. Rasmussen, Chenru Duan, Heather J. Kulik, Jan Halborg Jensen
With the increasingly more important role of machine learning (ML) models in chemical research, the need for putting a level of confidence to the model predictions naturally arises. Several methods for obtaining uncertainty estimates have been proposed in recent years but consensus on the evaluation of these have yet…
C. H. Fleming, J. Drescher-Lehman, M. J. Noonan, T. S. B. Akre + 34 more
Animal tracking data are being collected more frequently, in greater detail, and on smaller taxa than ever before. These data hold the promise to increase the relevance of animal movement for understanding ecological processes, but this potential will only be fully realized if their accompanying location error is…
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open- source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
Authors not listed
Two-dimensional electronic spectroscopy (2DES) is a powerful experimental technique, as it directly probes the nonlinear (third-order) response function of the system, providing key insights into ultrafast energy transfer and relaxation processes. However, 2DES experiments are generally difficult to interpret, often…