Representation Error Research Articles

Design-based mapping of errors in remote sensing-based land use/land cover maps

Abstract For the first time, spatially explicit representation of classification errors of land use/land cover (LULC) maps is approached from a design-based perspective. Since LULC maps are typically derived from non-probabilistic training samples, these maps, like the true LULC map, are fixed in a design-based scenario so that the error maps achieved by comparing the satellite-based and true maps are fixed. Based on a probabilistic sample of locations where the true or “reference” class is obtained (i.e., the “reference” class is considered the best representation of the true class), errors can be assessed at these sample locations by comparing the map classes to the reference classes. Then, the presence or absence of errors is interpolated across the entire survey area using the nearest neighbour technique. Under very common sampling schemes used to collect reference sample data, the interpolated error maps are design consistent. A simulation study confirms the design consistency of the interpolated error maps, which converge to the true error map as the reference sample size increases. The U.S. land cover map from the LCMAP program and the Italian forest/non forest map serve as case studies.

Spatial Signatures of Electron Correlation in Least-Squares Tensor Hypercontraction.

Least-squares tensor hypercontraction (LS-THC) has received some attention in recent years as an approach to reduce the significant computational costs of wave function-based methods in quantum chemistry. However, previous work has demonstrated that LS-THC factorization performs disproportionately worse in the description of wave function components (e.g., cluster amplitudes T̂2) than Hamiltonian components (e.g., electron repulsion integrals (pq|rs)). This work develops novel theoretical methods to study the source of these errors in the context of the real-space T̂2 kernel, and reports, for the first time, the existence of a "correlation feature" in the errors of the LS-THC representation of the "exchange-like" correlation energy EX and T̂2 that is remarkably consistent across ten molecular species, three correlated wave functions, and four basis sets. This correlation feature portends the existence of a "pair point kernel" missing in the usual LS-THC representation of the wave function, which critically depends upon pairs of grid points situated close to atoms and with interpair distances between one and two Bohr radii. These findings point the way for future LS-THC developments to address these shortcomings.

Symmetric Properties of λ-Szász Operators Coupled with Generalized Beta Functions and Approximation Theory

This research work focuses on λ-Szász–Mirakjan operators coupling generalized beta function. The kernel functions used in λ-Szász operators often possess even or odd symmetry. This symmetry influences the behavior of the operator in terms of approximation and convergence properties. The convergence properties, such as uniform convergence and pointwise convergence, are studied in view of the Korovkin theorem, the modulus of continuity, and Peetre’s K-functional of these sequences of positive linear operators in depth. Further, we extend our research work for the bivariate case of these sequences of operators. Their uniform rate of approximation and order of approximation are investigated in Lebesgue measurable spaces of function. The graphical representation and numerical error analysis in terms of the convergence behavior of these operators are studied.

Can general circulation models (GCMs) represent cloud liquid water path adjustments to aerosol–cloud interactions?

Abstract. General circulation models (GCMs), unlike other lines of evidence, indicate that anthropogenic aerosols cause a global-mean increase in cloud liquid water path (ℒ) and thus a negative adjustment to radiative forcing of the climate by aerosol–cloud interactions. In part 1 of this series of papers, we showed that this is true even in models that reproduce the negative correlation observed in present-day internal variability in ℒ and cloud droplet number concentration (Nd). We studied several possible confounding mechanisms that could explain the noncausal cloud–aerosol correlations in GCMs and that possibly contaminate observational estimates of radiative adjustments. Here, we perform single-column and full-atmosphere GCM experiments to investigate the causal model-physics mechanisms underlying the model radiative adjustment estimate. We find that both aerosol–cloud interaction mechanisms thought to be operating in real clouds – precipitation suppression and entrainment evaporation enhancement – are active in GCMs and behave qualitatively in agreement with physical process understanding. However, the modeled entrainment enhancement has a negligible global-mean effect. This raises the question of whether the GCM estimate is incorrect due to parametric or base-state representation errors or whether the process understanding gleaned from a limited set of canonical cloud cases is insufficiently representative of the diversity of clouds in the real climate. Regardless, even at limited resolution, the GCM physics appears able to parameterize the small-scale microphysics–turbulence interplay responsible for the entrainment enhancement mechanism. We suggest ways to resolve tension between current and future (storm-resolving) global modeling systems and other lines of evidence in synthesis climate projections.

POE-based kinematic calibration for serial robots using left-invariant error representation and decomposed iterative method

POE-based kinematic calibration for serial robots using left-invariant error representation and decomposed iterative method

Explicit A Posteriori Error Representation for Variational Problems and Application to TV-Minimization

AbstractIn this paper, we propose a general approach for explicit a posteriori error representation for convex minimization problems using basic convex duality relations. Exploiting discrete orthogonality relations in the space of element-wise constant vector fields as well as a discrete integration-by-parts formula between the Crouzeix–Raviart and the Raviart–Thomas element, all convex duality relations are transferred to a discrete level, making the explicit a posteriori error representation –initially based on continuous arguments only– practicable from a numerical point of view. In addition, we provide a generalized Marini formula that determines a discrete primal solution in terms of a given discrete dual solution. We benchmark all these concepts via the Rudin–Osher–Fatemi model. This leads to an adaptive algorithm that yields a (quasi-optimal) linear convergence rate.

An efficient infinity norm minimization algorithm for under-determined inverse problems

The problem of solving under-determined systems of linear equations with minimum peak magnitude (ℓ∞ norm) has numerous applications in signal processing. These include Peak-to-Average Power Ratio (PAPR) reduction in MIMO-OFDM systems, vector quantization, approximate nearest neighbor search, optimal control in robotics, and power grid optimization. Several methods have been proposed to address this problem, but they often face limitations in computational speed or representation accuracy. Some methods also impose constraints on the frame matrix, such as restrictions on the type of its entries or its aspect ratio. In this paper, we present the Fast Iterative Peak Shrinkage Algorithm (FIPSA), which iterates over feasible solutions to consistently reduce peak magnitude and provably converge to near-optimal solutions. Our experimental results, conducted across various frame matrix types and aspect ratios, demonstrate that FIPSA consistently achieves near-minimal ℓ∞ norm values. In addition, it operates 1.3 to 7.3 times faster than previous methods, while maintaining an average representation error of 10−15. Notably, these advancements are achieved without imposing any constraints on the frame matrix.

Representation Results and Error Estimates for Differential Games with Applications Using Neural Networks

Representation Results and Error Estimates for Differential Games with Applications Using Neural Networks

Actuation manifold from snapshot data

We propose a data-driven methodology to learn a low-dimensional manifold of controlled flows. The starting point is resolving snapshot flow data for a representative ensemble of actuations. Key enablers for the actuation manifold are isometric mapping as encoder, and a combination of a neural network and a $k$ -nearest-neighbour interpolation as decoder. This methodology is tested for the fluidic pinball, a cluster of three parallel cylinders perpendicular to the oncoming uniform flow. The centres of these cylinders are the vertices of an equilateral triangle pointing upstream. The flow is manipulated by constant rotation of the cylinders, i.e. described by three actuation parameters. The Reynolds number based on a cylinder diameter is chosen to be $30$ . The unforced flow yields statistically symmetric periodic shedding represented by a one-dimensional limit cycle. The proposed methodology yields a five-dimensional manifold describing a wide range of dynamics with small representation error. Interestingly, the manifold coordinates automatically unveil physically meaningful parameters. Two of them describe the downstream periodic vortex shedding. The other three describe the near-field actuation, i.e. the strength of boat-tailing, the Magnus effect and forward stagnation point. The manifold is shown to be a key enabler for control-oriented flow estimation.

Turkish spelling errors by Turkish-Dutch bilingual children

The current pilot study adds to the small body of work focusing on Turkish-Dutch children's Turkish literacy attainment by investigating their spelling errors. This study deviates from the previous studies by attempting to find patterns behind the surface representation of errors (i.e. omission, substitution and addition). Fifty-three 10 to 12 year-old Turkish-Dutch bilingual children were asked to write Turkish narratives. The participants misspelled about half of the words. The errors in order of frequency were diacritic errors (i.e. confusing the graphemes with and without diacritics), orthographic ambiguity errors (i.e. phonetically spelling a word though it is not orthographically transparent), punctuation errors, capitalization errors, morphological errors (e.g. using a wrong allomorph of a suffix), spacing errors (e.g. writing two words as one), code-switching (i.e. utilizing Dutch words in Turkish sentences) and Dutch-influenced errors (i.e. using Dutch orthographic rules in Turkish such as spelling /j/ as <j> or /u/ as <oe>). The rest of the errors, which lacked a discernible pattern, were categorized as “other”. These results differed from the findings on Turkish monolingual children's spelling errors in the literature in some notable ways (e.g. the very high rate of misspelled words and the prevalence of diacritic errors).

Representation error reduction in compressive sensing using generative models with pivotal tuning

Reducing the transmitted data volume is essential for implementing networks with resource limited and energy-constrained devices. In this sense, compressive sensing becomes a powerful alternative as it moves the most computationally complex task to the central server node, in contrast to the traditional compression scheme. Recently a combination of compressive sensing and generative models has appeared, giving rise to Compressive Sensing using Generative Models (CSGM). Although CSGM reduce reconstruction errors, they introduce the so-called representation error. This paper proposes CSGM-Pivotal Tuning Inversion (CSGM-PTI), a technique based on model retraining in decompression time to reduce the representation error in CSGM. The idea of CSGM-PTI is to expand the scope of the generative model to include the desired signal. The results show robustness to noise and performance gains in signal reconstruction of up to 20% compared with Deep Image Prior (DIP), standalone CSGM, and Wavelet Thresholding (WT) techniques, all traditionally used in the related literature.

PEFusion: An infrared and visible light fusion method for enhanced representation of prominent targets and exposure errors

Infrared and visible light fusion is a pivotal technique for image enhancement. Current methodologies, however, often overlook exposure errors during the fusion process, potentially compromising the quality of the outcomes. To tackle this challenge, we introduce a novel method titled “An Infrared and Visible Light Fusion Method for Enhanced Representation of Prominent Targets and Exposure Errors” (PEFusion). This approach incorporates a multi-scale exposure correction module to refine image quality in the presence of exposure discrepancies. Furthermore, we implement targeted enhancements during the fusion process. This method facilitates the creation of fused images that not only highlight prominent targets but also maintain high overall quality. Experimental results validate that PEFusion surpasses contemporary state-of-the-art methods in both quantitative and qualitative evaluations. The integration of exposure correction and target enhancement substantially enriches the texture and visual details of the merged images, rendering it exceptionally effective for sophisticated visual tasks.

Inertial Navigation Employing a Common-Frame Error Model

This paper examines an extension of previous common-frame theory in the state-error definition for inertial navigation systems (INS). In previous work, only body-frame errors were considered in relation to quantities such as biases from strapdown gyros. Reference-frame errors found in quantities such as the translational velocity have not been considered previously. The work here derives the full INS equations where an alternative vector state-error is defined using common coordinates over all vector-error realizations, thereby providing a true-to-life representation of the actual errors. The INS is analyzed through a stationary linear analysis to show that the fundamental frequencies are unchanged; however, there are now more coupling terms within the state matrix. The performance of the INS filter is then analyzed using a simulation.

Semiotic Mathematics Representation Ability Based on Symbolic in Solving SPLSV Problems in Class VII Students

Mathematical semiotic representation is the ability to analyze and express mathematical ideas or notions of a phenomenon and everyday problem situations into the form of signs, images, symbols, and symbols that represent them and provide meaning and explanation to a package of verbal sign messages. The symbolic stage is the stage where students have understood the symbols and concepts and have ideas that are strongly influenced by language and logic skills and students are able to manipulate symbols or symbols of a particular object. The purpose of this study was to determine the representation of symbolic-based mathematical semiotics in seventh grade students of MTS Al Barokah Ajung Jember on SPLSV material using qualitative descriptive method. The instrument used by researchers in the form of written test questions consisting of two questions tailored to the symbolic representation that has two indicators that use mathematical symbols to solve problems and interpret mathematical symbols. From the results of research that has been done obtained the error of representation on indicators using mathematical symbols to solve the problem of 100% and error of representation on indicators interpreting mathematical symbols of 0%. Several studies have been carried out to explain the mistakes that students make in representation skills. This paper presents the ability of mathematical symbolic semiotic representation of students who are more specific in solving SPLSV problems that can be considered by teachers in designing learning about the ability of mathematical semiotic representation and information for observers of mathematics education.

Spelling Errors in Children With Mild to Moderate Hearing Loss: Relations to Linguistic and Audiologic Factors

The purpose of this study was to evaluate the types of spelling errors made by children with mild to moderate hearing loss (CMMHL) compared with children with typical hearing (TH) and to determine if types of spelling errors were related to linguistic or audiologic factors. CMMHL and TH completed measures of spelling, spoken language, speech production, and reading. Children's spellings were coded for linguistic-based spelling errors using the Multilinguistic Coding System. The relation of types of linguistic spelling errors and children's performance on standardized language assessments, as well as audiologic factors, was evaluated. CMMHL did not make more spelling errors than TH; however, they exhibited a higher proportion of phonological awareness errors and a lower proportion of mental grapheme representation errors in their spellings. Phonological awareness errors and mental grapheme representation errors were related to relevant linguistic performance. Better-ear pure-tone average was related to total frequency of spelling errors and phonological awareness spelling errors, and better-ear Speech Intelligibility Index (SII) was related to semantic knowledge spelling errors. This study supports the use of linguistic spelling error analysis with CMMHL and provides evidence of the relation of types of linguistic spelling errors to linguistic knowledge and audiologic factors.

Performance Evaluation of a National Seven-Day Ensemble Streamflow Forecast Service for Australia

The Australian Bureau of Meteorology offers a national operational 7-day ensemble streamflow forecast service covering regions of high environmental, economic, and social significance. This semi-automated service generates streamflow forecasts every morning and is seamlessly integrated into the Bureau’s Hydrologic Forecasting System (HyFS). Ensemble rainfall forecasts, European Centre for Medium-Range Weather Forecasts (ECMWF), and Poor Man’s Ensemble (PME), available in the Numerical Weather Prediction (NWP) suite, are used to generate these streamflow forecasts. The NWP rainfall undergoes pre-processing using the Catchment Hydrologic Pre-Processer (CHyPP) before being fed into the GR4H rainfall–runoff model, which is embedded in the Short-term Water Information Forecasting Tools (SWIFT) hydrological modelling package. The simulated streamflow is then post-processed using Error Representation and Reduction In Stages (ERRIS). We evaluated the performance of the operational rainfall and streamflow forecasts for 96 catchments using four years of operational data between January 2020 and December 2023. Performance evaluation metrics included the following: CRPS, relative CRPS, CRPSS, and PIT-Alpha for ensemble forecasts; NSE, PCC, MAE, KGE, PBias, and RMSE; and three categorical metrics, CSI, FAR, and POD, for deterministic forecasts. The skill scores, CRPS, relative CRPS, CRPSS, and PIT-Alpha, gradually decreased for both rainfall and streamflow as the forecast horizon increased from Day 1 to Day 7. A similar pattern emerged for NSE, KGE, PCC, MAE, and RMSE as well as for the categorical metrics. Forecast performance also progressively decreased with higher streamflow volumes. Most catchments showed positive performance skills, meaning the ensemble forecast outperformed climatology. Both streamflow and rainfall forecast skills varied spatially across the country—they were generally better in the high-runoff-generating catchments, and poorer in the drier catchments situated in the western part of the Great Dividing Range, South Australia, and the mid-west of Western Australia. We did not find any association between the model forecast skill and the catchment area. Our findings demonstrate that the 7-day ensemble streamflow forecasting service is robust and draws great confidence from agencies that use these forecasts to support decisions around water resource management.

Balloon drift estimation and improved position estimates for radiosondes

Abstract. When comparing model output with historical radiosonde observations, it is usually assumed that a radiosonde has risen exactly above its starting point and has not been displaced by wind. This changed only relatively recently with the availability of Global Navigation Satellite System (GNSS) receivers aboard radiosondes in the late 1990s, but even then the balloon trajectory data were often not transmitted, although this information was the basis for estimating the wind in the first place. Depending on the conditions and time of year, radiosondes can sometimes drift a few hundred kilometres, particularly at the middle latitudes during the winter months. The position errors can lead to non-negligible representation errors when the corresponding observations are assimilated. This paper presents a methodology to compute changes in the balloon position during its vertical ascent, using only limited information, such as the vertical profile of wind contained in the historical observation reports. The sensitivity of the method to various parameters is investigated, such as the vertical resolution of the input data, the assumption about the vertical ascent speed of the balloon, and the departure of the surface of Earth from a sphere. The paper considers modern GNSS sonde data reports for validation, for which the full trajectory of the balloon is available, alongside the reported wind. Evaluation is also conducted by comparison with ERA5 and by conducting low-resolution data assimilation experiments. Overall, the results indicate that the trajectory of the radiosondes can be accurately reconstructed from original data of varying vertical resolutions and that the more accurate balloon position reduces representation errors and, in some cases, systematic errors.

Quantification of Representation Error in the Neutral Winds and Ion Drifts Using Data Assimilation

AbstractIn this work we quantify the representation error of the algorithm Estimating Model Parameters from Ionospheric Reverse Engineering (EMPIRE), which estimates global neutral winds and ion drifts given time‐varying plasma densities. SAMI3 (Sami3 is A Model of the Ionosphere) serves as the background climate model and pseudo‐measurements for the EMPIRE observation system. This configuration allows the data assimilation inputs to be self‐consistent between each other and with the validation data. The estimated neutral winds and ion drifts are compared to the Horizontal Wind Model (HWM14) and SAMI3 “truth.” For both the quiet period on 25 August 2018 and subs7equent storm on 26 August, the EMPIRE estimation of ion drifts is better at low‐to‐mid geomagnetic latitudes with mean error up to 20 m/s. For the high latitudes (poleward of ±60° magnetic), the mean errors exceed 50 m/s with variances up to 200 m/s, and the relative errors are higher than the “truth.” At latitudes of ±87°, the large errors are attributed to a boundary effect. However, the neutral wind mean errors peak at 20 m/s at mid‐latitudes (40°–60° magnetic), with larger uncertainties, then converge to 0 approaching higher latitudes. By conducting this study, we define a method for obtaining the representation error covariance for future use of EMPIRE with SAMI3 as background.

Catalytic hydrogenation reaction micro-kinetic model for dibenzyltoluene as liquid organic hydrogen carrier

The implementation of the liquid organic hydrogen carrier (LOHC) technology for efficient energy storage requires the development of a reliable kinetic model for both hydrogenation and dehydrogenation processes. In this research study, the catalytic hydrocarbon saturation for a dibenzyltoluene (DBT) mixture solution, containing dibenzylbenzene (DBB), dibenzylethylbenzene (DBEB) and impurities has been performed in the presence of Ru/Al2O3 particles. The influence of different reaction conditions, such as temperature, pressure, initial reactant concentration, catalyst amount and stirring speed has been examined. A measurement-based system micro-kinetics, based on the Langmuir–Hinshelwood mechanism with dissociative H2 surface adsorption, has been derived. H2 thermodynamic solubility equilibrium was defined through Henry's law. The adsorbing, desorption and reactivity of inert solvent molecules was not considered to be relevant. The mass transfer resistance over 1000 rpm stirring speed was negligible. Relative- and mean squared error of representation were 40.9% and 1.00×10−4, respectively. Expressions gave an excellent data prediction for the profile period trends with a relatively accurate estimation of H2 intermediates' rate selectivity, H2-covered area approximation and pathway rate-determining steps. Due to the lack of commercially available standard chemical compounds for quantitative analysis techniques, a novel experiment-based numerical calibration method was developed. Mean field (micro)kinetics represent an advancement in the mesoscale mechanistic understanding of physical interface phenomena. This also enables catalysis structure–activity relationships, unlocking the methodology for new LOHC reaching beyond traditional, such as ammonia, methanol and formate, which do not release H2 alone. Integrated multiscale simulations could include fluidics later on.

General spatial photonic Ising machine based on the interaction matrix eigendecomposition method

The spatial photonic Ising machine has achieved remarkable advancements in solving combinatorial optimization problems. However, it still remains a huge challenge to flexibly map an arbitrary problem to the Ising model. In this paper, we propose a general spatial photonic Ising machine based on the interaction matrix eigendecomposition method. The arbitrary interaction matrix can be configured in the two-dimensional Fourier transformation based spatial photonic Ising model by using values generated by matrix eigendecomposition. The error in the structural representation of the Hamiltonian decreases substantially with the growing number of eigenvalues utilized to form the Ising machine. In combination with the optimization algorithm, as low as ∼65% of the eigenvalues are required by intensity modulation to guarantee the best probability of optimal solution for a 20-vertex graph Max-cut problem, and this percentage decreases to below ∼20% for near-zero probability. The 4-spin experiments and error analysis demonstrate the Hamiltonian linear mapping and ergodic optimization. Our work provides a viable approach for spatial photonic Ising machines to solve arbitrary combinatorial optimization problems with the help of the multi-dimensional optical property.