Terms Of Error Research Articles

Absence of differential protection from extinction in human causal learning.

Elemental models of associative learning typically employ a common prediction-error term. Following a conditioning trial, they predict that the change in the strength of an association between a cue and an outcome is dependent upon how well the outcome was predicted. When multiple cues are present, they each contribute to that prediction. The same rule applies both to increases in associative strength during excitatory conditioning and the loss of associative strength during extinction. In five experiments using an allergy prediction task, we tested the involvement of a common error term in the extinction of causal learning. Two target cues were each paired with an outcome prior to undergoing extinction in compound either with a second excitatory cue or with a cue that had previously undergone extinction in isolation. At test, there was no difference in the causal ratings of the two target cues. Manipulations designed to bias participants toward elemental processing of cue compounds, to promote the acquisition of inhibitory associations, or to reduce generalization decrement between training and test were each without effect. These results are not consistent with common error term models of associative learning. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Integrating endogeneity in survey sampling using instrumental-variable calibration estimator

The endogeneity problem arises when the auxiliary variables correlate to the error terms. In such cases, appropriate instrumental variables ensure efficient estimation. Calibration has recognized itself as an important methodological tool at a large scale to estimate the population total in survey sampling. Which does not offer efficient estimation in the presence of endogeneity. When endogeneity is present in the auxiliary variables, the calibration using endogenous auxiliary variables may produce biasedness and increase variance due to inappropriate model assumptions. In this article, we propose instrumental-variable calibrated estimators by using the classical instrumental-variables approach for the case of exact identification that are more efficient than conventional calibration estimators when some auxiliary variables are endogenous. The necessary properties of the proposed estimators are presented. Our study is backed by both the simulation study and a real data example to check the performance of the proposed estimators.

SPD Manifold Deep Metric Learning for Image Set Classification.

By characterizing each image set as a nonsingular covariance matrix on the symmetric positive definite (SPD) manifold, the approaches of visual content classification with image sets have made impressive progress. However, the key challenge of unhelpfully large intraclass variability and interclass similarity of representations remains open to date. Although, several recent studies have mitigated the two problems by jointly learning the embedding mapping and the similarity metric on the original SPD manifold, their inherent shallow and linear feature transformation mechanism are not powerful enough to capture useful geometric features, especially in complex scenarios. To this end, this article explores a novel approach, termed SPD manifold deep metric learning (SMDML), for image set classification. Specifically, SMDML first selects a prevailing SPD manifold neural network (SPDNet) as the backbone (encoder) to derive an SPD matrix nonlinear representation. To counteract the degradation of structural information during multistage feature embedding, we construct a Riemannian decoder at the end of the encoder, trained by a reconstruction error term (RT), to induce the generated low-dimensional feature manifold of the hidden layer to capture the pivotal information about the visual data describing the imaged scene. We demonstrate through theory and experiments that it is feasible to replace the Riemannian metric with Euclidean distance in RT. Then, the ReCov layer is introduced into the established Riemannian network to regularize the local statistical information within each input feature matrix, which enhances the effectiveness of the learning process. The theoretical analysis of the activation function used in the ReCov layer in terms of continuity and conditions for generating positive definite matrices is beneficial for network design. Inspired by the fact that the single cross-entropy loss used for training is unable to effectively parse the geometric distribution of the deep representations, we finally endow the suggested model with a novel metric learning regularization term. By explicitly incorporating the encoding and processing of the data variations into the network learning process, this term can not only derive a powerful Riemannian representation but also train an effective classifier. The experimental results show the superiority of the proposed approach on three typical visual classification tasks.

Rejection of parametric model errors in a recursive Kalman filter for virtual sensing applications

The performance of the Kalman filter is often hindered by the discrepancies between a model used to realize the filter and the true model of the data-generating system. While some methods to account for those errors exists, the majority is restricted to Luenberger's observers. The objective of this work is to develop a Kalman filter where the effect of parametric model errors is rejected from the state and observation equations before the development of the state estimate, and without the explicit knowledge of the error terms. For this purpose, errors in a physical parameter of a parametrized mechanical system are modelled as additive terms in the state and observation equations by means of first-order perturbation analysis. The rejection step is achieved with an injection of a shaped output nullifying the effect of the added terms. A state observer is then derived under the assumption that the injected shaped outputs and the system states are uncorrelated. The performance of the proposed approach is illustrated on an experimental data of a plate system.

Strolling through common meadows

This paper establishes a connection between rings, lattices and common meadows. Meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. Common meadows are meadows that introduce, as the inverse of zero, an error term a which is absorbent for addition. We show that common meadows are unions of rings which are ordered by a partial order that defines a lattice. These results allow us to extend some classical algebraic constructions to the setting of common meadows. We also briefly consider common meadows from a categorical perspective.

Using a spatial autoregressive model with spatial autoregressive disturbances to investigate origin-destination trip flows.

Spatial interaction models with spatial origin-destination (OD) filters are powerful tools to characterize trip flows in space, which is a classic and important problem in regional science. To the authors' knowledge, existing studies adopting OD filters mostly specify the spatial dependence as an autoregressive process, which may not be the full picture of spatial effects. To examine the problem, this paper proposes the hypotheses that 1) spatial OD dependences can take place in both the spatial autoregressive term and the spatial error term in a spatial interaction model. 2) Estimating a spatial autoregressive model with spatial autoregressive disturbances (SARAR) model with OD filters would disentangle where the spatial dependence exists and by how much. 3) The marginal effects obtained from SARAR models would be preferred to analysts when SARAR models outperform spatial autoregressive (SAR) models and spatial error models (SEM) from the statistical point of view. To assess these hypotheses, this paper specifies, estimates, and applies SARAR models with OD filters to investigate trip distributions. By comparing against alternative models, this paper investigates the estimation results in SAR, SEM and SARAR models using an empirical data collected from Hangzhou, China. The contribution of this paper is to be the first in developing an SARAR model with OD filters for trip distribution analyses and examining its performance.

A resolution theorem for extriangulated categories with applications to the index

Quillen's Resolution Theorem in algebraic K-theory provides a powerful computational tool for calculating K-groups of exact categories. At the level of K0, this result goes back to Grothendieck. In this article, we first establish an extriangulated version of Grothendieck's Resolution Theorem.Second, we use this Extriangulated Resolution Theorem to gain new insight into the index theory of triangulated categories. Indeed, we propose an index with respect to an extension-closed subcategory N of a triangulated category C and we prove an additivity formula with error term. Our index recovers the index with respect to a contravariantly finite, rigid subcategory X defined by Jørgensen and the second author, as well as an isomorphism between K0sp(X) and the Grothendieck group of a relative extriangulated structure CRX on C when X is n-cluster tilting. In addition, we generalize and enhance some results of Fedele. Our perspective allows us to remove certain restrictions and simplify some arguments.Third, as another application of our ExtriangulatedResolution Theorem, we show that if X is n-cluster tilting in an abelian category, then the index introduced by Reid gives an isomorphism K0(CRX)≅K0sp(X).

Testing a theory of strategic multi-product choice

This paper tests a theory of strategic multi-product choice (SMPC) using empirical evidence from a large-scale choice experiment, two smaller longitudinal choice experiments, and multi-market panel data. Multi-product choice involves two stages. In the first stage, the consumer chooses a set of substitutable products, where “set” refers to both the variety of alternatives and the quantities of each. In the second stage, the set is consumed. Assuming consumers are strategic, their consumption decisions will consider both the utility of whichever product is selected for consumption and the expected utility (i.e., value) of the set that remains. SMPC therefore requires a dynamic model. We test two such dynamic models in this paper. These models are derived from a basic random utility framework with a stochastic error term for the utility of each product alternative at the moment of consumption. Despite maintaining state variables for the quantity of every alternative, these SMPC dynamic models offer both a value function and optimal consumption policy in closed form. These structures allow us to test for strategic consumption in the second stage and for optimality of the choice sets selected in the first stage. Data from the large-scale choice experiment and the smaller longitudinal choice experiments support strategic consumer decision-making, consistent with SMPC theory. SMPC theory further predicts that the amount of variety consumers select will be higher for lower consumption rates and lower for higher consumption rates. Evidence from panel data of yogurt purchases supports this prediction. While we find that consumption choices are consistent with SMPC theory, they are not consistent with alternative explanations such as variety seeking or diversification bias. Viewed in its entirety, the empirical evidence presented in this paper confirms that both the choice set selected and the way it is consumed are consistent with dynamic models of future preference uncertainty.

Forecasting and Comparison of Nonlinear Statistical Growth Models for Fish Seed Production in Eastern Coastal States of India

The study was carried out to compare the goodness of fit of three non–linear growth models viz., Monomolecular, Logistic and Gompertz growth models and analysing the instability index among the collected fish seed Production data from the eastern costal states of Indian for the period from 1994–1995 to 2019–2020. The parameters of each model were estimated using Levenberg–Marquardt (LM) iterative method. The ‘independence’ and ‘normality’ of error terms were examined by using ‘Run–test’ and ‘Shapiro–Wilk test’. Among the three models tested, monomolecular model was found as best model to describe variation in fish seed production in all Eastern Costal States of India. The values of CDI for fish seed production were 146.94 %, 79.30 % and 63.41% respectively which revealed that fish seed production had high instability in Odisha, Tamil Nadu and Andhra Pradesh while low instability (14.93 % and 13.13%) in West Bengal and India.

On the Fourier Coefficients for General Product 𝐿-Functions

Let 𝑓 be a normalized primitive cusp form of even integral weight for the full modular group Γ = 𝑆𝐿(2, ℤ). In this paper, we investigate upper bounds for the error terms related to the average behavior of Fourier coefficients 𝜆𝑓 ⊗𝑓 ⊗⋯⊗𝑙𝑓 (𝑛) of 𝑙-fold product 𝐿-functions, where 𝑓 ⊗ 𝑓 ⊗ ⋯ ⊗𝑙 𝑓 denotes the 𝑙-fold product of 𝑓. These results improves and generalizes the recent developments of Venkatasubbareddy and Sankaranarayanan [41]. We also provide some other similar results related to the error terms of general product 𝐿-functions.

An improved error term for counting D4$D_4$‐quartic fields

AbstractWe prove that the number of quartic fields with discriminant whose Galois closure is equals , improving the error term in a well‐known result of Cohen, Diaz y Diaz, and Olivier. We prove an analogous result for counting quartic dihedral extensions over an arbitrary base field.

The impact of aquaculture economics expansion on marine water quality in the EU Region

Water scarcity is a growing condition caused by climate change and human activity, and it influences and interacts with other stressors in freshwater and marine ecosystems, such as chemical pollution. Aquaculture production has a significant impact on the EU27 region's water stress and water contamination discharge levels. Therefore, the primary goal of this research is to examine how the aquaculture industry affects water contamination discharge in European Union developed countries (EU14) and European Union developing countries (EU13) from 1990 to 2023. Since the dependent variable's error terms are correlated with the independent variables, the endogeneity problem was solved with the use of robust least squares (RLS), two-stage least squares (2SLS), and ordinary least squares (OLS) estimators, which produced the major findings. According to the precise effect sizes, the aquaculture industry and gross domestic product are more important in determining water contamination discharge in developed EU14 countries than in developing EU13 countries. The precise magnitudes of the effect demonstrate that, compared to EU14 developed countries, water contamination discharge in EU13 developing countries is mostly determined by the use of hydrocarbons. However, as the precise magnitudes of the three estimators demonstrate, governance is more important in EU14 developed countries than in EU13 developing countries when it comes to controlling water contamination discharge. The authors advise policymakers to give policies targeted at improving the aquaculture industry's efficiency and green development top priority, especially in EU13 developing countries with unplanned aquaculture expansion and inefficient aquaculture industry outgrowth. The authors advise policymakers in the EU14 developed countries to take actions targeted at improving governance efficiency top priority.

Asymptotic freeness through unitaries generated by polynomials of Wigner matrices

We study products of functions evaluated at self-adjoint polynomials in deterministic matrices and independent Wigner matrices; we compute the deterministic approximations of such products and control the fluctuations. We focus on minimizing the assumption of smoothness on those functions while optimizing the error term with respect to N, the size of the matrices. As an application, we build on the idea that the long-time Heisenberg evolution associated to Wigner matrices generates asymptotic freeness as first shown in [9]. More precisely given P a self-adjoint non-commutative polynomial and YN a d-tuple of independent Wigner matrices, we prove that the quantum evolution associated to the operator P(YN) yields asymptotic freeness for large times.

Kinematics characterizing with dual quaternion and parametric modeling of geometric error terms based on measuring path planning of CNC machine tools

Kinematics characterizing with dual quaternion and parametric modeling of geometric error terms based on measuring path planning of CNC machine tools

Research on the Validity of Bootstrap LM-Error Test in Spatial Random Effect Models

Under the condition of non-classical distributed errors, the test for spatial dependence in spatial panel data models is still a problem waiting to be solved. In this paper, we apply the FDB (Fast Double Bootstrap) method to spatial panel data models to test spatial dependence. In order to research the validity of the Bootstrap LM-Error test in spatial random effect models under the condition that the error term obeys a normal distribution, heteroscedasticity, or time-series correlation, we construct Bootstrap LM-Error statistics and make use of Monte Carlo simulation from size distortion and power aspects to carry out our research. The Monte Carlo simulation results show that the asymptotic LM-Error test in the spatial random effects model has a large size of distortion when the error term disobeys classical distribution. However, the FDB LM-Error test can effectively correct the size distortion of the asymptotic test with the precondition that there is nearly no loss of power in the FDB test. Obviously, compared to the asymptotic LM-Error test, the FDB LM-Error test is a more valid method to test spatial dependence in a spatial random effects model.

Prime and Möbius correlations for very short intervals in $\fq[x

abstract: We investigate function field analogs of the distribution of primes, and prime $k$-tuples, in ``very short intervals'' of the form $I(f):=\{f(x) + a : a \in\fp\}$ for $f(x)\in\fp[x]$ and $p$ prime, as well as cancellation in sums of function field analogs of the M\"{o}bius $\mu$ function and its correlations (similar to sums appearing in Chowla's conjecture). For generic $f$, i.e., for $f$ a Morse polynomial, the error terms are roughly of size $O(\sqrt{p})$ (with typical main terms of order $p$). For non-generic $f$ we prove that independence still holds for ``generic'' set of shifts. We can also exhibit examples for which there is no cancellation at all in M\"{o}bius/Chowla type sums (in fact, it turns out that (square root) cancellation in M\"{o}bius sums is {\em equivalent} to (square root) cancellation in Chowla type sums), as well as intervals where the heuristic ``primes are independent'' fails badly. The results are deduced from a general theorem on correlations of arithmetic class functions; these include characteristic functions on primes, the M\"{o}bius $\mu$ function, and divisor functions (e.g., function field analogs of the Titchmarsh divisor problem can be treated). We also prove analogous, but slightly weaker, results in the more delicate fixed characteristic setting, i.e., for $f(x)\in\fq[x]$ and intervals of the form $f(x)+a$ for $a\in\fq$, where $p$ is fixed and $q=p^{l}$ grows.

Rough solutions of the relativistic Euler equations

We prove that the time of classical existence of smooth solutions to the relativistic Euler equations can be bounded from below in terms of norms that measure the “(sound) wave-part” of the data in Sobolev space and “transport-part” in higher regularity Sobolev space and Hölder spaces. The solutions are allowed to have nontrivial vorticity and entropy. We use the geometric framework from [M. M. Disconzi and J. Speck, The relativistic Euler equations: Remarkable null structures and regularity properties, Ann. Henri Poincaré 20(7) (2019) 2173–2270], where the relativistic Euler flow is decomposed into a “wave-part”, that is, geometric wave equations for the velocity components, density and enthalpy, and a “transport-part”, that is, transport-div-curl systems for the vorticity and entropy gradient. Our main result is that the Sobolev norm [Formula: see text] of the variables in the “wave-part” and the Hölder norm [Formula: see text] of the variables in the “transport-part” can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption [Formula: see text] is the optimal result for the variables in the “wave-part”. Compared to low-regularity results for quasilinear wave equations and the three-dimensional (3D) non-relativistic compressible Euler equations, the main new challenge of the paper is that when controlling the acoustic geometry and bounding the wave equation energies, we must deal with the difficulty that the vorticity and entropy gradient are four-dimensional space-time vectors satisfying a space-time div-curl-transport system, where the space-time div-curl part is not elliptic. Due to lack of ellipticity, one cannot immediately rely on the approach taken in [M. M. Disconzi and J. Speck, The relativistic Euler equations: Remarkable null structures and regularity properties, Ann. Henri Poincaré 20(7) (2019) 2173–2270] to control these terms. To overcome this difficulty, we show that the space-time div-curl systems imply elliptic div-curl-transport systems on constant-time hypersurfaces plus error terms that involve favorable differentiations and contractions with respect to the four-velocity. By using these structures, we are able to adequately control the vorticity and entropy gradient with the help of energy estimates for transport equations, elliptic estimates, Schauder estimates and Littlewood–Paley theory.

Asymptotic Completeness for a Scalar Quasilinear Wave Equation Satisfying the Weak Null Condition

In this paper, we prove the first asymptotic completeness result for a scalar quasilinear wave equation satisfying the weak null condition. The main tool we use in the study of this equation is the geometric reduced system introduced in Yu (Modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition, 2021). Starting from a global solution u u to the quasilinear wave equation, we rigorously show that well chosen asymptotic variables solve the same reduced system with small error terms. This allows us to recover the scattering data for our system, as well as to construct a matching exact solution to the reduced system.

Novel hybrid data-driven modeling integrating variational modal decomposition and dual-stage self-attention model: Applied to industrial petrochemical process

Data-driven modeling methods are extensively employed in the vast landscape of petrochemical industries. Due to their accuracy and rapidity, these models play a guiding role in the simulation and control of industrial petrochemical processes, such as the fluid catalytic cracking (FCC) process. However, in industrial process, there is a high degree of nonlinearity between influencing variables and predictive variables, making it challenging for models to accurately capture the relationship. Additionally, there are temporal and spatial characteristics, which conventional models struggle to learn. To tackle this challenge, a novel hybrid data-driven modeling is proposed, which combines variational mode decomposition (VMD) and dual-stage attention long short-term memory (DA-LSTM), incorporating error compensation (EC). VMD decomposes the predictive variables into multiple components to alleviate the nonlinear between the influencing and predictive variables. Each component is predicted by the DA-LSTM model, a dual-stage self-attention model that incorporates feature and time attention mechanisms. The EC method predicts the error term, primarily originating from residuals in the VMD decomposition and inaccuracies in the predictions made by DA-LSTM. The superiority of the proposed model is verified by the prediction of industrial data in FCC, Tennessee Eastman and debutanizer column processes.

Exploiting residual errors in nonlinear online prediction

We introduce a novel online (or sequential) nonlinear prediction approach that incorporates the residuals, i.e., prediction errors in the past observations, as additional features for the current data. Including the past error terms in an online prediction algorithm naturally improves prediction performance significantly since this information is essential for an algorithm to adjust itself based on its past errors. These terms are well exploited in many linear statistical models such as ARMA, SES, and Holts-Winters models. However, the past error terms are rarely or in a certain sense not optimally exploited in nonlinear prediction models since training them requires complex nonlinear state-space modeling. To this end, for the first time in the literature, we introduce a nonlinear prediction framework that utilizes not only the current features but also the past error terms as additional features, thereby exploiting the residual state information in the error terms, i.e., the model’s performance on the past samples. Since the new feature vectors contain error terms that change with every update, our algorithm jointly optimizes the model parameters and the feature vectors simultaneously. We achieve this by introducing new update equations that handle the effects resulting from the changes in the feature vectors in an online manner. We use soft decision trees and neural networks as the nonlinear prediction algorithms since these are the most widely used methods in highly publicized competitions. However, as we show, our methods are generic and any algorithm supporting gradient calculations can be straightforwardly used. We show through our experiments on the well-known real-life competition datasets that our method significantly outperforms the state-of-the-art. We also provide the implementation of our approach including the source code to facilitate reproducibility (https://github.com/ahmetberkerkoc/SDT-ARMA).