Error Propagation Research Articles

Differentiable pixel-super-resolution lensless imaging

Conventional lensless imaging systems require complex phase diversity measurements and sequential processing steps, limiting their practical application despite their compact design. We present a differentiable end-to-end pixel-super-resolution (dPSR) technique that unifies PSR hologram synthesis, autofocusing, and complex-field reconstruction within a single optimization framework. By jointly optimizing these traditionally separate processes, our method eliminates both phase diversity requirements and error accumulation from sequential processing. Our method achieves superior position estimation accuracy (mean error 0.0282 pixels versus 0.1172 pixels with conventional methods), delivering precise autofocusing with accuracy better than 0.3 µm, and enabling a twofold resolution enhancement beyond the sensor’s native pixel size. This robust performance is validated through both simulated and experimental results, including challenging phase objects and label-free cell imaging, establishing dPSR as a practical solution for high-resolution microscopy applications.

Can We Constrain Geographical Variability in the Biological Carbon Pump's Transfer Efficiency From Observations?

AbstractThe biological carbon pump (BCP) transfers large amounts of carbon from the atmosphere into the ocean's interior, contributing to carbon sequestration. Studies on latitudinal variability in organic carbon transfer to depth have yielded inconsistent results, likely due to methodological differences. To address this, we compiled particulate organic carbon (POC) flux data and BCP metrics from time‐series locations across biogeographically distinct ocean regions. We integrated multiple BCP observational techniques, including diverse collection and processing protocols, capturing diverse facets of POC flux at varying spatio‐temporal resolutions. To ensure comparability, we harmonized errors and used Monte Carlo error propagation to calculate uncertainties consistently. Our analysis reveals large local uncertainties that obscure expected latitudinal variations in BCP metrics. While such variations may exist, they remain difficult to identify with current observational data. Our findings underscore the need for sustained POC flux observations, standardization of protocols, and intercalibration of technologies to identify geographic BCP patterns.

Computational Approaches to Compressible Micropolar Fluid Flow in Moving Parallel Plate Configurations

In this paper, we consider the unsteady flow of a compressible micropolar fluid between two moving, thermally isolated parallel plates. The fluid is characterized as viscous and thermally conductive, with polytropic thermodynamic properties. Although the mathematical model is inherently three-dimensional, we assume that the variables depend on only a single spatial dimension, reducing the problem to a one-dimensional formulation. The non-homogeneous boundary conditions representing the movement of the plates lead to moving domain boundaries. The model is formulated in mass Lagrangian coordinates, which leads to a time-invariant domain. This work focuses on numerical simulations of the fluid flow for different configurations. Two computational approaches are used and compared. The first is based on the finite difference method and the second is based on the Faedo–Galerkin method. To apply the Faedo–Galerkin method, the boundary conditions must first be homogenized and the model equations reformulated. On the other hand, in the finite difference method, the non-homogeneous boundary conditions are implemented directly, which reduces the computational complexity of the numerical scheme. In the performed numerical experiments, it was observed that, for the same accuracy, the Faedo–Galerkin method was approximately 40 times more computationally expensive compared to the finite difference method. However, on a dense numerical grid, the finite difference method required a very small time step, which could lead to an accumulation of round-off errors. On the other hand, the Faedo–Galerkin method showed the convergence of the solutions as the number of expansion terms increased, despite the higher computational cost. Comparisons of the obtained results show good agreement between the two approaches, which confirms the consistency and validity of the numerical solutions.

Error evaluation of partial scattering functions obtained from contrast-variation small-angle neutron scattering

Contrast-variation small-angle neutron scattering (CV-SANS) is a powerful tool to evaluate the structure of multi-component systems by decomposing the scattering intensities I measured with different scattering contrasts into partial scattering functions S of self- and cross-correlations between components. The measured I contains a measurement error ΔI, and ΔI results in an uncertainty in the partial scattering functions ΔS. However, the error propagation from ΔI to ΔS has not been quantitatively clarified. In this work, we have established deterministic and statistical approaches to determine ΔS from ΔI. We have applied the two methods to (i) computational data for a core–shell sphere, and experimental CV-SANS data of (ii) clay/polyethylene glycol aqueous solutions and (iii) polyrotaxane solutions, and have successfully estimated the errors in S. The quantitative error estimation in S offers a strategy to optimize the combination of scattering contrasts to minimize error propagation.

State of Health Estimation of Lithium-Ion Batteries Based on Hybrid Neural Networks with Residual Connections

Accurately estimating the state of health (SOH) of lithium-ion batteries is essential for ensuring the stability and safety of the battery. Although the hybrid neural network model demonstrates strong performance in estimating the SOH, network degradation becomes a significant issue as the depth of the neural network increases, potentially undermining the accuracy of the estimation. This paper presents a hybrid neural network estimation model with residual connections to address the issue of network degradation. First, the model utilizes a combination of convolutional neural networks and an attention mechanism to automatically extract feature information highly correlated with SOH from the partial charging data of lithium-ion batteries. Subsequently, a multi-layer gated recurrent unit (GRU) is employed to capture temporal information within the extracted features. To address the issue of network degradation that arises from stacking multiple layers of neural networks, residual connections are incorporated into the multi-layer GRUs, mitigating the accumulation of errors within deep networks. Finally, three distinct datasets are employed to validate the proposed model. The experimental results demonstrate that the model exhibits an average mean absolute error and root mean square error of less than 1.8% on both of these datasets.

On the cluster of the families of hybrid polynomial kernels in kernel density estimation

This study introduces a novel cluster of hybrid polynomial kernel families, designed to achieve significantly lower asymptotic mean integrated squared error compared to traditional kernels. These hybrid kernels are developed by heuristically combining classical polynomial kernels using probability axioms. An in-depth analysis of error propagation within these kernels is conducted, utilizing both simulation experiments and real-life datasets, including the Life Span of Batteries and COVID-19 datasets. The findings consistently demonstrate that the proposed hybrid kernels outperform their classical counterparts in various density estimation tasks across different distribution types and sample sizes. This research highlights the potential of hybrid polynomial kernels to enhance accuracy in density estimation, advocating for their adoption in statistical modelling and analysis.

A tracker pose optimization method for robotic measuring system based on spatial distance constraints

In large-scale metrology (LSM), the transformation of the tracker base frame (TBF) is a predominant method to enlarge the field of view (FOV) of the tracking sensor for full-field 3D measurements. Nevertheless, such a process will introduce cumulative errors and significantly diminish the global point cloud alignment accuracy. To address this problem, we propose a novel tracker pose optimization method for TBF transformation. A pose graph optimization (PGO) model based on spatial distance constraints is implemented to improve the tracker pose accuracy. We also adopt a robust coefficient and a damping factor to simplify the experimental process and stabilize the convergence results. Simulations and experiments on high-speed train surfaces are conducted to validate our method’s accuracy and effectiveness. The results indicate that our optimization method outperforms two existing methods in spatial positioning accuracy and point cloud alignment accuracy, which showcases its practical applicability and superiority in manufacturing scenarios.

Seq2Seq model with attention for predicting nonlinear propagation of ultrafast pulses in optical fibers

The propagation of ultrashort pulses in optical fibers exhibits highly complex nonlinear dynamics, which plays a central role in the development of light sources and photonic technologies. The mainstream of the existing methods for modeling and predicting complex nonlinear propagation dynamics of ultrashort pulses in optical fibers is based on recurrent neural networks (RNNs), which use a Multi-In-Single-Out (MISO) architecture to predict the optical pulse evolution recursively. This autoregressive model is severely limited by the error accumulation problem and also requires significant computational resources. Affected by the error accumulation problem, this method often leads to severe performance degradation in long sequence prediction tasks, thus limiting the practical application of the prediction model. In this work, we propose a new non-autoregressive model using a Single-In-Multi-Out (SIMO) architecture to simulate the highly nonlinear dynamics of ultrashort pulse propagation in optical fibers. Our model is validated on the public dataset. The results show that our model can significantly reduce the prediction error in modeling and predicting the complex nonlinear propagation of ultrashort pulses in optical fibers. In addition, the required computational resources and time spent are significantly reduced. As a whole, our proposed method comprehensively outperforms the mainstream methods in terms of efficiency, accuracy and practicality. We believe our work could bring new insights into the modeling and analysis of complex ultrafast nonlinear dynamics.

Characteristics of the IBEX Ribbon and Their Implications for a Source Region Outside the Heliopause

Abstract This paper presents a comprehensive exploration of the Interstellar Boundary Explorer energetic neutral atom (ENA) ribbon, focusing on its spatial and temporal variations over 14 yr. Methodological advancements, including a refined map modeling procedure and a new ribbon separation technique with appropriate error propagation, enable a detailed investigation of the ribbon’s features. Utilizing statistically robust metrics, this study reveals details of the ribbon across energy and time. Key findings include energy- and time-dependent variations in flux, angular radius, ribbon profile width, and higher moments. By applying these metrics, we reveal new complexity to the evolution of the ribbon over time, highlighting the nuanced relationship between it and the solar wind. Furthermore, the study examines for the first time the ribbon as it passes through the starboard/heliotail region (LonEC 120°–180°), revealing properties distinct from other portions of the ribbon. The analysis uncovers an anticorrelation between ribbon width and flux, which provides quantitative support for a multisource ribbon created by a combination of solar wind neutrals that generate a spatiall narrow ribbon component and heliosheath neutrals giving rise to a broad component. Finally, differences in the temporal evolution of the ENA flux at different energies provide additional support that the location of the ribbon source region is beyond the heliopause.

Dual-wavelength synchronous control method for liquid crystal optical phased array

The liquid crystal optical phased array (LCOPA), as a key beam steering device, has gained increasing significance in the field of space laser communication. With the rapid advancement of space laser communication technology, the demand for precise synchronous control of multi-wavelength beams has significantly increased, particularly in ensuring reliable communication links through synchronized control of signal and beacon beams. The signal beam is primarily utilized for data transmission, while the beacon beam is responsible for path calibration and real-time tracking. However, due to the limitations of natural dispersion effects, conventional LCOPA control methods struggle to achieve synchronized manipulation of beams at different wavelengths, resulting in error accumulation and response delays in communication links, thereby compromising the accuracy and efficiency of information transmission. To address this challenge, this study proposes and validates a dual-wavelength synchronous control method based on LCOPA. The method establishes a phase optimization principle centered on minimizing the least-squares error of complex amplitudes and expands the phase modulation capability of LCOPA hardware, thereby overcoming the natural dispersion governed by the grating equation. Simulation and experimental results demonstrate that this method achieves exceptionally high beam pointing accuracy, meeting the demands of high-precision information transmission in multi-wavelength laser communication. This study provides an innovative technical pathway for the application of LCOPA in multi-wavelength laser communication and establishes a solid theoretical foundation for future experimental research on multi-wavelength control.

Re-scaling images using a SVD-based approach

There are many instances in computer science where computational operations must be performed on matrices of different sizes. In the field of machine learning, particularly when interpreting images, it is often necessary to resize and re-scale images to achieve higher resolutions. While there are various methods for this, they typically involve fitting a simple linear or cubic model to scale the image. The singular value decomposition (SVD) is a powerful tool for dimension reduction and projection. Our proposed state-of-the-art method leverages the capabilities of SVD to create a technique for re-scaling images. This method is primarily based on modifications of the eigenvectors derived from SVD. Previous work has shown that by editing only these Eigenvectors, it is possible to minimize error propagation through the images. When applied to several well-known image processing tasks, it is possible to scale an image with reduced error compared to the current state-of-the-art methods. Additionally, we show that our method can improve the results of machine learning approaches.

Effect of Axial Modification on the Meshing Performance of Involute Beveloid Gear Pair

In order to enhance the load-bearing capacity of the involute beveloid gear pair, this study proposes research on improving the contact stress through axial modification. Under the condition of segmented parabolic axial modification, the mathematical equation for the tooth flank of the beveloid gear is derived. A simulation meshing model for the beveloid gear pair is constructed to investigate the effects of different amounts and lengths of axial modification on the meshing performance, changes in flank and root stress, and transmission error before and after modification. The results indicate that as the modification amount increases, the maximum equivalent stress initially decreases and then exhibits a tendency towards stability. Moreover, an increase in modification length concentrates the contact zone towards the middle of the tooth flank while expanding the range of tooth root stress distribution, and it also leads to a decrease in maximum equivalent stress. The implementation of the modification has been observed to result in a reduction in cumulative transmission error and an effective reduction in edge load on the beveloid gear pair, which has been demonstrated to enhance the bearing capacity and transmission stability extension while also impacting the dynamic meshing performance.

Snapshot infrared Fourier transform imaging spectrometer for transient dynamic sensing

Imaging spectroscopy is an effective method for simultaneously acquiring the spatial information distribution and the spectral fingerprint characteristics of a target. Implementing dynamic target spectral mapping through optical scanning may lead to image artifacts and spectral interference. This paper proposes an innovative structure for a snapshot infrared Fourier transform Imaging spectrometer (SIFTIS), which utilizes a stepped micro-mirror and a lens array, combining the advantages of snapshot imaging spectroscopy and infrared spectral detection. The SIFTIS technology acquires a complete three-dimensional dataset within a single integration time, featuring good stability, strong real-time capability, and high spatiotemporal resolution. It has significant advantages in fields such as camouflage target recognition and harmful and pollutant gas measurement. Firstly, the optical field transmission model of SIFTIS was constructed, and the system's error propagation model was further deduced. The impact of the optical system and core optical components’ aberration residues and positional errors on spectral mapping were analyzed, providing design error tolerance. Subsequently, preliminary experiments combined with simulation analysis were used to calibrate and correct the spectral shifts caused by rotation, pitch, and roll component errors of the stepped micro-mirrors reflective surfaces at various levels. Finally, imaging spectral detection of dynamic plume targets was conducted to demonstrate the desired results and feasibility.

A Flat-Span Contrastive Learning Method for Nested Named Entity Recognition

In Natural Language Processing (NLP), it is common for one entity to contain another entity, i.e., nested entities. However, the most commonly used methods can only handle flat entities but not nested entities. To solve this problem, this paper proposes a flat-span contrastive learning method for nested Named Entity Recognition (NER), which consists of two sub-modules: a flat NER module and a candidate span classification module. The flat NER module is used to recognize the outermost entities, and we use star-transformer to capture the long-range dependencies of sentences, and the Conditional Random Field (CRF) to decode the outermost entity spans, contrastive learning is introduced, and the InfoNEC loss function is used to increase the difference between entity spans and nonentity spans. Finally, to improve the model performance and reduce error propagation, we jointly train the flat NER and candidate span classification modules through multi-task learning. Experimental results on the GENIA, GermEval2014, and JNLPBA datasets thoroughly verify the effectiveness of our model, and the ablation experiments further demonstrate the effectiveness of the model components. In the candidate span classification module, we generate all possible candidate spans based on the outermost entities by enumeration to better distinguish entity spans from nonentity.

An Arctic sea ice concentration data record on a 6.25 km polar stereographic grid from 3 years of Landsat-8 imagery

Abstract. The decline in Arctic sea ice in the global warming era has received much attention as a contributing factor to the changes in the weather and climate in the Arctic and beyond. The coverage of Arctic sea ice (i.e. sea ice concentration (SIC)) has been monitored since 1972 using satellite passive microwave (PMW) measurements because of their extensive coverage and all-weather capability. However, the fundamental basis of algorithms for estimating SIC has not improved much since the early days due to the lack of reference SIC data, leading to discrepancies between existing PMW SIC algorithms. To overcome this issue, this study aims to construct data records of reference SIC over Arctic sea ice using 30 m resolution imagery from the Operational Land Imager (OLI) on board Landsat-8. In order to collect relatively bright and clear scenes, thresholds of solar elevation >15° and cloud cover <10 % were applied in this study. Clouds in each Landsat-8 scene were masked using the cloud-masking array provided in Landsat data. Due to the poor accuracy of the cloud-masking array over ice-covered surface types, an additional step of visually inspecting the state of the cloud mask using the true-colour image was designated in this study. Each Landsat-8 scene was sorted into four categories depending on the state of the cloud mask. The normalized difference snow index and OLI band-5 reflectivity were used to differentiate between ice and open water within each selected Landsat-8 pixel. The classified data were projected onto a 6.25 km polar stereographic grid, and SIC for each grid cell was obtained by counting ice-classified pixels within the grid. SIC was only computed for grid cells where more than 99 % of their area was covered with Landsat-8 pixels to limit the uncertainty in SIC arising from grids that are not fully concentrated with Landsat-8 pixels. Uncertainty in the produced SIC was 1 %–4 %, inferred using the Gaussian error propagation method. Out of 15 286 collected Landsat-8 images, 14 297 images were translated into SIC maps, and a total of 2 934 399 Landsat-8 SIC grid cells were generated. Evaluation of Landsat-8 SIC with SIC from ice charts revealed a good linear relationship (correlation coefficient of 0.96) between the two products, as well as a mean negative bias which fell within the uncertainty range of Landsat-8 SIC. SIC based on Landsat-8 can be used as reference SIC to evaluate existing SIC products, and, thus, one can improve SIC products, as well as use the improved SIC for other applications such as data assimilation and retrieval studies. The vast amount of Landsat-8 SIC generated in this study may also be used to train deep-learning models for the estimation of Arctic SIC coverage. The Landsat-8 SIC dataset can be publicly accessed at https://doi.org/10.5281/zenodo.10973297 (Jung et al., 2024), and the Python codes for the production and evaluation of the Landsat-8 SIC dataset are accessible at https://doi.org/10.5281/zenodo.12754602 (Jung, 2024).

China Aerosol Raman Lidar Network (CARLNET)—Part I: Water Vapor Raman Channel Calibration and Quality Control

Water vapor is an active trace component in the troposphere and has a significant impact on meteorology and the atmospheric environment. In order to meet demands for high-precision water vapor and aerosol observations for numerical weather prediction (NWP), the China Meteorological Administration (CMA) deployed 49 Raman aerosol lidar systems and established the first Raman–Mie scattering lidar network in China (CARLNET) for routine measurements. In this paper, we focus on the water vapor measurement capabilities of the CARLNET. The uncertainty of the water vapor Raman channel calibration coefficient (Cw) is determined using an error propagation formula. The theoretical relationship between the uncertainty of the calibration coefficient and the water vapor mixing ratio (WVMR) is constructed based on least squares fitting. Based on the distribution of lidar in regions with different humidity conditions, the method of real-time calibration and quality control based on radiosonde data is established for the first time. Based on the uncertainty requirements of the World Meteorological Organization for water vapor in data assimilation, the calibration and quality control thresholds of the WVMR in regions with different humidity conditions are determined by fitting real-time lidar and radiosonde data. Lastly, based on the radiosonde results, the calibration algorithm established in this study is used to calibrate CARLNET data from October to December 2023. Compared with traditional calibration results, the results show that the stability and detection accuracy of the CARLNET significantly improved after calibration in regions with different humidity conditions. The deviation of the Cw decreased from 12.84~18.47% to 5.41~11.54%. The inversion error of the WVMR compared to radiosonde decreased from 1.05~0.46 g/kg to 0.82~0.34 g/kg. The reliability of the improved calibration algorithm and the CARLNET’s performance have been verified, enabling them to provide high-precision water vapor products for NWP.

An experimental approach for dimensional tolerance analysis using 3D printed parts

Abstract In 2D or 3D tolerance analysis, a dimension chain involves a complex propagation of random deviations from individual parts to the controlled assembly requirement. This can be calculated by setting up complex mathematical models, possibly with the help of CAD-based software tools. The paper studies the feasibility of an alternative approach, which uses measurements on assemblies of 3D printed parts to estimate the coefficients of a linearized error propagation model. The analysis is structured as a designed experiment, where each dimension is varied in two levels resulting in two different printed parts. The experimental plan consists of building assemblies from selected combinations of parts and measuring the assembly dimension on each combination. Among the possible designs of the plan, the paper compares two methods based on finite differences and least squares. The comparison includes both simulations with randomly generated dimension chains and physical tests on simple cases. The results show that a least squares plan allows a significant improvement in the accuracy on the estimation of model coefficients compared to a finite difference plan, with just a marginally higher number of assembly combinations. However, dimensional and geometric deviations in the 3D printing process are shown to play a critical role, and criteria are suggested to reduce or compensate them.

It's about time: moving away from statistical analysis of ecotoxicity data.

Environmental risk assessment of chemicals (ERA) relies on single-species laboratory testing to establish the toxic properties of a compound. However, ERA is not concerned with toxicity under laboratory conditions: it needs to assess the impacts of the compound in the real world. Data-driven statistical analyses (e.g., hypothesis testing and interpolation) are the common approaches for analysing toxicity data, but such approaches are the wrong tool for the job at hand. ERA does not need a statistical description of the effects in the toxicity test (at the end of the standardised test duration), it needs to extrapolate from the laboratory test to longer and time-varying exposure. Such extrapolation requires mechanistic process models, providing a simplified representation of the mechanisms underlying toxicity. Any useful model for the toxicity process should explicitly consider both dose (e.g., exposure concentration) and time. In the history of effects analysis for ERA, the factor of time does not get as much attention as the dose, hence common use of the term 'dose-response analysis'. However, this is a historical oversight: time is a crucial factor for understanding toxicity and thereby essential for meaningful extrapolation from laboratory to field. Mechanistic models for ecotoxicity, considering both dose and time, have been around for quite some time and are classified as toxicokinetic-toxicodynamic (TKTD) models. TKTD models are starting to find their way into pesticide ERA in Europe, next to the classical statistical approaches. In this opinion paper, I argue that it is about time to leave statistical analysis of toxicity data behind us. Statistics remains important for ERA's effects assessment, but its role lies in the definition of appropriate 'error models', explaining the deviations between model output and observations, which is essential for parameter estimation, uncertainty quantification, and error propagation. The 'process model', essential for extrapolation, firmly belongs to TKTD modelling.

Evaluation of the Linear Damage Assumption in JPCP Bottom-up Fatigue Cracking

Current pavement design methods for Jointed Plain Concrete Pavements assume that bottom-up fatigue cracking occurs at one critical location at the mid-slab edge and that damage accumulates linearly and can be described via S-N curves. More recently, experiments have shown that fatigue does not accumulate linearly. This assumption will lead to an accumulation of prediction error which depends on the sequence of applied loads. In this paper, a modified Paris fatigue equation is used to simulate mid-slab edge fatigue damage. The fatigue equation accounts for the transient and steady state stages of cracking in addition to the peak and stress range effects. An interpolation scheme was used to determine the pavement stresses at the bottom mid-slab edge. The interpolation scheme was constructed from a total of 35,000+ FEM runs in EVERFE. Intra-axle peak and valley stresses were accounted for so load history and R-ratio effects could be assessed simultaneously. Two different climatic regions were considered: Miami, FL and Lansing, MI. The results of this study suggest that the dominant stress and R ratio fall between 0 and 0.1 for both climates. In addition, it seems that although high stress ratios (0.7-0.9) occur infrequently (less than 1% for both cases), the life of the pavement is strongly correlated with high stress ratio events. Finally, it is shown that damage may be under-predicted using a linear damage rule because it does not account for the over-load effect. This under-prediction can be corrected by re-calibrating the percent slabs cracked equation.

Efficient Path Following Control Design for Tractor With Multiple Trailers Systems Utilizing Movement Rules and Passive Multi‐Steering Angles

ABSTRACTThis paper proposes a straightforward and robust control strategy for a tractor with multiple trailers system (TMTS, for short) to effectively follow identical paths. Hereto, the control design is structured into four steps for path‐tracking precision. Firstly, a suitable passive steering angle is assigned to each trailer, granting it some steering capability to follow the moving path of its direct leader. Secondly, movement rules of the TMTS with passive multi‐steering angles are explored in‐depth for the first time, facilitating the convenient deduction of kinematic and dynamic models. Thirdly, a desired movement task of the TMTS is reduced to a tracking control by the tractor through the implementation of suitable passive steering angles. Additionally, by virtue of a curvature tracking method, cumulative location errors could be greatly reduced by tracking the relative curvature. Fourthly, a combination of feedback linearization, optimal control, and integral sliding mode control methods is employed to design two driven torques for the tractor to precisely follow the geometric path. Consequently, both the tractor and all trailers are capable of simultaneously following an identical path. In the end, numerical simulations are presented to demonstrate the effectiveness, feasibility, and robustness of the resulting control strategy for practical applications.