Alignment Errors Research Articles

Velocity-independent NMO correction based on multi-scale dynamic time warping

Normal moveout (NMO) correction is one of the common steps of seismic data processing. Conventional NMO correction is generally based on a velocity function, but velocity analysis is considered time-consuming and labor-intensive. Moreover, the field seismic data observed in complex areas can have low signal-to-noise ratio (SNR), resulting in inaccurate picked up velocity parameters and poor NMO correction. The conventional NMO correction has stretching issues, most significantly at shallow and large offset areas. To address these problems, a new multi-scale dynamic time warping (MSD) algorithm for velocity-independent stretch-free NMO correction is investigated. This algorithm has higher accuracy and stronger noise resistance, as our comparisons with other applications of DTW show. In our algorithm, the original seismic data is decomposed into multiple morphological scales (using mathematical morphology theory), and alignment errors are calculated separately at each scale, followed by further adaptive weighted summation. Accumulation and backtracking operations based on alignment errors produce time shift sequences for automatic flattening of the gathers. The effectiveness of the presented approach is tested on both synthetic and field data. The results demonstrate that compared with traditional velocity-based NMO correction methods, the proposed method can accurately flatten seismic gathers without the NMO stretch and is robust to strong noise.

Robustness of Divergence Time Estimation Despite Gene Tree Estimation Error: A Case Study of Fireflies (Coleoptera: Lampyridae).

Genomic data has become ubiquitous in phylogenomic studies, including divergence time estimation, but provide new challenges. These challenges include, amongst others, biological gene tree discordance, methodological gene tree estimation error, and computational limitations on performing full Bayesian inference under complex models. In this study, we use a recently published firefly (Coleoptera: Lampyridae) anchored hybrid enrichment dataset (AHE; 436 loci for 88 Lampyridae species and 10 outgroup species) as a case study to explore gene tree estimation error and the robustness of divergence time estimation. First, we explored the amount of model violation using posterior predictive simulations because model violations are likely to bias phylogenetic inferences and produce gene tree estimation error. We specifically focused on missing data (either uniformly distributed or systematically) and the distribution of highly variable and conserved sites (either uniformly distributed or clustered). Our assessment of model adequacy showed that standard phylogenetic substitution models are not adequate for any of the 436 AHE loci. We tested if the model violations and alignment errors resulted indeed in gene tree estimation error by comparing the observed gene tree discordance to simulated gene tree discordance under the multispecies coalescent model. Thus, we show that the inferred gene tree discordance is not only due to biological mechanism but primarily due to inference errors. Lastly, we explored if divergence time estimation is robust despite the observed gene tree estimation error. We selected four subsets of the full AHE dataset, concatenated each subset and performed a Bayesian relaxed clock divergence estimation in RevBayes. The estimated divergence times overlapped for all nodes that are shared between the topologies. Thus, divergence time estimation is robust using any well selected data subset as long as the topology inference is robust.

Design of a stagger‐tuned high‐power low‐stress capacitive wireless power transfer system

AbstractCapacitive power transfer (CPT) has emerged as a promising alternative to traditional inductive methods. CPT offers advantages like cost‐effectiveness, reduced weight and volume, and greater tolerance to alignment errors. However, the high‐Q resonant circuits used as matching networks can be susceptible to high voltage stress, especially when transmitting substantial power. Consequently, designing matching networks for CPT systems necessitates consideration of multiple parameters, including practical constraints such as component losses and breakdown thresholds. In this work an innovative algorithm is presented for designing practical matching networks in CPT systems. The algorithm conducts a methodical search of potential solutions, and converges on component values that maximize power transfer efficiency whilst also minimizing component voltage stress. The proposed algorithm is demonstrated theoretically and experimentally.

Novel analysis of alignment error on spherical Fizeau interferometer and uncertainty evaluation of sphericity calibration system based on random ball test

The National Metrology Institute of Japan (NMIJ) has developed a high-precision sphericity calibration system utilizing a Fizeau interferometer and conducted a thorough evaluation of the system's measurement uncertainty. Generally, there are two principal sources of uncertainty in the measurement outcomes when utilizing a spherical Fizeau interferometer. First, the accuracy of the system is significantly influenced by the prior knowledge of the reference sphere surface's absolute profile. To address this, the study established a straightforward yet effective calibration system for the reference sphere surface using a random ball test method. Second, the system's precision is affected by misalignment aberration, which occurs when there is any lateral or longitudinal displacement of the test sphere from the confocal position relative to the reference sphere. This misalignment can introduce both high-order shape errors (misalignment aberrations) and low-order shape errors (alignment errors). Through analytical consideration of an observation coordinate system on the camera plane, this study delves into misalignment aberrations, suggesting that the impact of misalignment should be determined experimentally for each reference sphere unit due to potential imperfections that may be revealed by misalignment. Furthermore, the study proposes that uncertainties related to misalignment aberrations are theoretically confirmed to be smaller than previous studies by conducting an in-depth uncertainty analysis of the misalignment, with a focus on the observation coordinate system on the camera plane. Notably, the research demonstrates that a measurement uncertainty level of λ/100 is achievable, maintaining a broader tolerance for misalignment than previously reported studies. The uncertainty of calibration of the reference sphere unit's absolute profile was 4.2 nm and the uncertainty of sample measurement was determined to be 4.6 nm with misalignment tolerance of ±λ/10. This advancement marks a stride toward improving the accuracy and reliability of sphericity measurements, offering potential for widespread application in precision engineering and metrology.

Refractive error and ocular alignment in school-aged children from low-income areas of São Paulo, Brazil

BackgroundUncorrected refractive errors and amblyopia are reported as the two main causes of childhood visual impairment and blindness worldwide. Our purpose was to evaluate refractive status, ocular alignment and effective refractive error coverage (eREC) of school-aged children from low-income areas of Sao Paulo city, Brazil.MethodsData from the “Ver na Escola” Project were used for the current study. Children enrolled in the selected schools had an ophthalmic exam including eye alignment assessed by cover test, automatized and subjective dynamic and static refraction. The associations of demographic variables with occurrence and magnitude of refractive errors and eREC were investigated by multiple logistic regressions and multilevel mixed effect models.ResultsA total of 17,973 children (51.12% females) with mean ± sd age 8.24 ± 3.54 years old examined from July 2018 to July 2019, were included in the study. Most of the participants (73%) showed orthoposition of the visual axis for both distance and near. Heterophoria was found in about 25% of participants (N = 4,498), with 71.7% of them (N= 3,222) classified as exophoria. Less than 2% (N = 232) showed strabismus, most of them (N = 160) esotropia. Overall, 1,370 (7.70%) of participants had myopia and 577 (3.24%) had hyperopia. Age was found to be significantly associated with increasing static subjective refraction spherical equivalent (Coefficient: -0.18; 95% Confidence Interval (CI): -0.21 to -0.16; p < 0.001). Female sex (Odds Ratio (OR) = 1.13; 95%CI: 1.01–1.27; p = 0.027) and older age (OR = 1.17; 95%CI: 1.16–1.19; p < 0,001) were significantly associated with myopia diagnosis. Older age decreased the odds of hyperopia (OR = 0.95; 95%CI: 0.93–0.98; p < 0.001). The overall effective refractive coverage was 51.76% and was significantly associated with age group, ranging from 32.25% in children aged 3 to 7 years to 61.35% in children aged 8 to 12 years.ConclusionsMost children have shown eye alignment for both distance and near assessments and no refractive error. Myopia was observed in 7.70% of the population and it was associated with older age and female sex. Hyperopia was observed in 3.24% and was associated with younger age. The overall eREC was 51.76%, significantly associated with age.

Prediction of refraction error after toric lens implantation with biometric input data uncertainties and power labelling tolerances.

The purpose of this study was to simulate the impact of biometric measure uncertainties, lens equivalent and toric power labelling tolerances and axis alignment errors on the refractive outcome after cataract surgery with toric lens implantation. In this retrospective non-randomised cross sectional Monte-Carlo simulation study we evaluated a dataset containing 7458 LenStar 900 preoperative biometric measurements. The biometric uncertainties from literature, lens power labelling according to ISO 11979, and axis alignment tolerances of a modern toric lens (Hoya Vivinex) were taken to be normally distributed and used in a Monte-Carlo simulation with 100 000 samples per eye. The target variable was the defocus equivalent (DEQ) derived using the Castrop (DEQC) and the Haigis (DEQH) formulae. Mean/median / 90% quantile DEQC was 0.22/0.21/0.36 D and DEQH was 0.20/0.19/0.32 D. Ignoring the variation in lens power labelling and toric axis alignment the respective DEQC was 0.20/0.19/0.32 D and DEQH was 0.18/0.17/0.29 D. DEQC and DEQH increased with shorter eyes, steeper corneas, equivalent lens power and highly with toric lens power. According to our simulation results, uncertainties in biometric measures, lens power labelling tolerances, and axis alignment errors are responsible for a significant part of the refraction prediction error after cataract surgery with toric lens implantation. Additional labelling of the exact equivalent and toric power on the lens package could be a step to improve postoperative results.

Implementation of an exact completing method of generation for face-milled spiral bevel gears with uniform depth taper

AbstractThis paper proposes an exact completing method of generation of face-milled spiral bevel gears with uniform depth taper. This method ensures localized bearing contact without kinematic transmission errors in both directions of rotation. Both sides of the tooth are generated simultaneously using the same set of basic machine tool settings. A tip relief on the tooth surfaces is the only required microgeometry modification to achieve a smooth transition of load between consecutive pairs of teeth. An analytical approach to determine the basic machine tool settings and select the grinding cutter parameters has been also developed. The selection of the nominal cutter radius follows the recommendations of Information Sheet AGMA 22849-A12. The basis for alignment error compensation has been also established. Tooth contact and stress analyses demonstrate the advantages and limitations of the proposed method, making it suitable for applications with higher power demands for the drive side than for the coast side.

Genuine Multipartite Entanglement Detection with Imperfect Measurements: Concept and Experiment.

Standard procedures for entanglement detection assume that experimenters can exactly implement specific quantum measurements. Here, we depart from such idealizations and investigate, in both theory and experiment, the detection of genuine multipartite entanglement when measurements are subject to small imperfections. For arbitrary qubits number n, we construct multipartite entanglement witnesses where the detrimental influence of the imperfection is independent of n. In a tabletop four-partite photonic experiment, we demonstrate first how a small amount of alignment error can undermine the conclusions drawn from standard entanglement witnesses and then perform the correction analysis. Furthermore, since we consider quantum devices that are trusted but not perfectly controlled, we showcase advantages in terms of noise resilience as compared to device-independent models.

Stochastic stability of random stacking of blocks

The paper explores the stability of a tower obtained by stacking identical rectangular blocks on top of each other with an inherent randomness due to slight positional offsets between successive blocks. With probabilistic modeling techniques, the diffusive behavior of the stacking process is studied and the collapse is seen as a first passage time problem. In the considered model, alignment errors are idealized as independent Gaussian random variables with zero mean and given standard deviation. We derive expressions for the joint probability density functions of block positions, and analyze their correlation. The study extends to the stochastic stability of a stack of given height, by exploring the statistical characteristics of the center of gravity of the part of tower above each block. Eventually, the probabilistic analysis of collapse is developed to quantify the statistics of the number of blocks that can be heaped up before the tower topples. Although this problem may initially appear playful, it offers an illustrated introduction to first passage problems on a non homogenous process. From a practical standpoint, this analysis offers a simple understanding of the influence of alignment errors on the overall stability of a stack, which may find several fields of application.

Deciphering the cleavage sites of 3C-like protease in Gammacoronaviruses and Deltacoronaviruses

Coronaviruses replicate by using the 3C-like protease (3CLpro) to cleave polyprotein precursors and host proteins. However, current tools for identifying 3CLpro cleavage sites are limited, particularly in Gammacoronaviruses (GammaCoV) and Deltacoronaviruses (DeltaCoV). This study aims to fill this gap by identifying 3CLpro cleavage sites in these viruses to provide deeper insights into their pathogenic mechanisms. By integrating sequence alignments and structural model comparisons, we developed a position-specific scoring matrix (PSSM) based on self-cleavage motifs, revealing specific preferences for each residue. Utilizing AlphaFold2's predicted alignment error (PAE) and predicted local distance difference test (pLDDT), we found that most cleavage sequences are located in regions with high PAE and low pLDDT values. KEGG pathway analysis showed that potential host protein cleavage targets are mainly concentrated in pathways related to nucleo-cytoplasmic transport and endocytosis. Through in vitro cleavage experiments and mutational analysis, we identified and validated three high-scoring proteins—nucleoporin 58 (NUP58), cell division cycle 73 (CDC73), and signal transducing adaptor molecule 2 (STAM2). These findings suggest that 3CLpro not only plays a vital role in viral replication but may also influence host cell functions by cleaving host proteins. This study provides an effective tool for identifying 3CLpro cleavage sites, revealing the pathogenic mechanisms of coronaviruses, and offering new insights for developing potential therapeutic targets.

Analyzing Alignment Error in Tibial Tuberosity–Trochlear Groove Distance in Clinical Scans Using 2D and 3D Methods

Background: Tibial tuberosity–trochlear groove distance (TT-TG) is often used as a primary metric for surgical decision-making in the treatment of patellofemoral instability (PFI), particularly when considering tibial tubercle transfer. Although TT-TG has high interrater reliability, it is prone to measurement differences caused by the alignment of the patient's leg in a scanner gantry, potentially influencing surgical decision-making. Quantification of this error within the clinical literature remains limited. Purpose: To quantify and specify the error in TT-TG caused by leg-scanner alignment by using detailed topographical landmarks and 3-dimensional (3D) analysis of computed tomography scans of patients with PFI. Study Design: Controlled laboratory study. Methods: Three-dimensional models of knees with PFI were created from computed tomography scans and used to identify TT-TG landmarks. TT-TG was measured using the established 2-dimensional (2D) and 3D methods. A model to estimate the differences between these 2 methods was created, and the orientation of the patients’ legs in relation to scanner longitudinal axis was measured to validate this model via linear regression. Interrater reliability was calculated via intraclass correlation coefficients (ICC). Results: A total of 44 knees of patients with PFI were analyzed. Differences between the 2D and 3D methods ranged from -4.0 to 14.7 mm (mean ± SD, 2.7 ± 4.1 mm) with a root mean square difference of 4.8 mm. The TT-TG distance of the 2D method (19.8 ± 7.2 mm) was significantly (P = .045) longer than that of the 3D method (17.1 ± 4.9 mm). The variance of the 2D method was significantly larger than that of the 3D method. In total, 13 (29.5%) of the knees had a difference of >5 mm between 2D and 3D TT-TG. The estimation model had an adjusted r2 value of 1.00 and a resulting root mean square difference of 0.21 mm. 3D TT-TGs interrater reliability was good to excellent (ICC, 0.94 [95 CI%, 0.81-0.98]). Conclusion: 3D TT-TG can be used to correct scanner-leg alignment errors, some of which are substantial when using only 2D TT-TG measurements. Clinical Relevance: The findings in this study suggest a need for caution and awareness of the potential effects of differences in alignment of the axes of the leg and scanner when using purely 2D TT-TG as a basis for surgical planning.

Artificial kinetochore beads establish a biorientation-like state in the spindle

Faithful chromosome segregation requires biorientation, where the pair of kinetochores on the chromosome establish bipolar microtubule attachment. The integrity of the kinetochore, a macromolecular complex built on centromeric DNA, is required for biorientation, but components sufficient for biorientation remain unknown. Here, we show that tethering the outer kinetochore heterodimer NDC80-NUF2 to the surface of apolar microbeads establishes their biorientation-like state in mouse cells. NDC80-NUF2 microbeads align at the spindle equator and self-correct alignment errors. The alignment is associated with stable bipolar microtubule attachment and is independent of the outer kinetochore proteins SPC24-SPC25, KNL1, the Mis12 complex, inner kinetochore proteins, and Aurora. Larger microbeads align more rapidly, suggesting a size-dependent biorientation mechanism. This study demonstrates a biohybrid kinetochore design for synthetic biorientation of microscale particles in cells.

Triple-Camera Rectification for Depth Estimation Sensor.

In this study, we propose a novel rectification method for three cameras using a single image for depth estimation. Stereo rectification serves as a fundamental preprocessing step for disparity estimation in stereoscopic cameras. However, off-the-shelf depth cameras often include an additional RGB camera for creating 3D point clouds. Existing rectification methods only align two cameras, necessitating an additional rectification and remapping process to align the third camera. Moreover, these methods require multiple reference checkerboard images for calibration and aim to minimize alignment errors, but often result in rotated images when there is significant misalignment between two cameras. In contrast, the proposed method simultaneously rectifies three cameras in a single shot without unnecessary rotation. To achieve this, we designed a lab environment with checkerboard settings and obtained multiple sample images from the cameras. The optimization function, designed specifically for rectification in stereo matching, enables the simultaneous alignment of all three cameras while ensuring performance comparable to traditional methods. Experimental results with real camera samples demonstrate the benefits of the proposed method and provide a detailed analysis of unnecessary rotations in the rectified images.

Research on Multi-Modal Music Score Alignment Model for Online Music Education

As music data storage becomes increasingly diverse in the era of big data, ensuring alignment of music works with the same semantics for online music education is crucial. To achieve this, a multi-modal music score alignment algorithm model based on deep learning was developed and optimized. Experimental results demonstrated that Note + DCO feature combination yielded the best MIDI input characteristics (mean value: 13.27 ms), whereas CQT feature comparison produced the best results for audio input (average: 12.85 ms). The ResNet-34 network was noted to have the most effective music score alignment effect with alignment errors averaging less than one frame. Compared with other algorithms, the proposed algorithm had the lowest average value of 9.28 ms, median value of 5.85 ms, and standard deviation of 20.17 ms. Actual music retrieval showed a Top-1 retrieval accuracy of 10.93% that was close to 11%. Overall, the proposed algorithm is significant for score alignment and music retrieval recognition in online music education.

Systematical and universal calibration scheme for division-of-aperture polarimetric camera

Division-of-aperture polarimetric (DoAP) camera has been widely used to obtain polarization images of scene owing to its feature in simultaneous acquisition of polarization information, real-time measurement and compact system. However, practical applications of DoAP imaging inevitably involve calibrating the camera from several aspects, which is very essential but the related reports are relatively lacking in current research. In this paper, we proposed a systematical and universal calibration scheme for the DoAP camera, which includes the lens distortion correction, the image registration, the polarization channel calibration and the Stokes parameters modification. Accordingly, a software for calibration and imaging processing, which consists of four modules, is designed to collectively facilitate the efficient and accurate execution of all calibration steps. In order to achieve real-time polarimetric imaging, the lens distortion correction and the image registration were done by means of lookup tables. Experimental results by using a full-Stokes DoAP camera we fabricated indicate that, via the lens distortion correction and the image registration, the alignment error between two images with a mean absolute error (MAE) less than 0.16 pixels can be obtained, resulting in the aligned images having an average increase of 64.53 % for the structural similarity index (SSIM) and that of 84.97 % for the peak signal to noise ratio (PSNR), respectively; and further via the polarization channel calibration and the Stokes parameters modification, the MAE of 0.0146 for the degree of polarization (DoP) and that of 0.3544° for the angle of polarization (AoP) are obtained, respectively. This proposed calibration scheme for DoAP camera is systematic, automatic and robust, which is benefit of improving the polarization detection accuracy, enhancing the camera calibration efficiency and thus promoting its polarimetric imaging performance.

High-efficiency hard X-ray blazed diffraction via refraction by nanometer-scale prism arrays

X-ray transmission gratings are widely utilized as wavelength dispersion elements in inertial confinement fusion and X-ray astronomy fields due to their high tolerance for alignment errors, light weight and compact size. However, the high transmittance of the grating bars in the hard X-ray range can lead to reduced efficiency of all other diffraction orders except for straight through zeroth order. We propose a novel blazed refraction grating design for the hard X-ray range that combines the advantages of transmission gratings and compound refraction lenses for the first time, demonstrating its superior performance in high broadband efficiency through compound refraction and diffraction from nanometer-scale periodic arrays of silicon prisms using beam propagation method and Fraunhofer diffraction simulation. This research develops blaze methods in gratings design and provides a new solution for compact and sensitive spectrum measurement in hard X-ray range.

Identification of Insertion and Deletion (InDel) Markers for Chickpea (Cicer arietinum L.) Based on Double-Digest Restriction Site-Associated DNA Sequencing.

Enhancing the marker repository and the development of breeder-friendly markers in chickpeas is important in relation to chickpea genomics-assisted breeding applications. Insertion-deletion (InDel) markers are widely distributed across genomes and easily observed with specifically designed primers, leading to less time, cost, and labor requirements. In light of this, the present study focused on the identification and development of InDel markers through the use of double-digest restriction site-associated DNA sequencing (ddRADSeq) data from 20 chickpea accessions. Bioinformatic analysis identified 20,700 InDel sites, including 15,031 (72.61%) deletions and 5669 (27.39%) insertions, among the chickpea accessions. The InDel markers ranged from 1 to 25 bp in length, while single-nucleotide-length InDel markers were found to represent the majority of the InDel sites and account for 79% of the total InDel markers. However, we focused on InDel markers wherein the length was greater than a single nucleotide to avoid any read or alignment errors. Among all of the InDel markers, 96.1% were less than 10 bp, 3.6% were between 10 and 20 bp, and 0.3% were more than 20 bp in length. We examined the InDel markers that were 10 bp and longer for the development of InDel markers based on a consideration of the genomic distribution and low-cost genotyping with agarose gels. A total of 29 InDel regions were selected, and primers were successfully designed to evaluate their efficiency. Annotation analysis of the InDel markers revealed them to be found with the highest frequency in the intergenic regions (82.76%), followed by the introns (6.90%), coding sequences (6.90%), and exons (3.45%). Genetic diversity analysis demonstrated that the polymorphic information content of the markers varied from 0.09 to 0.37, with an average of 0.20. Taken together, these results showed the efficiency of InDel marker development for chickpea genetic and genomic studies using the ddRADSeq method. The identified markers might prove valuable for chickpea breeders.

Adaptive remanufacturing for freeform surface parts based on linear laser scanner and robotic laser cladding

Freeform surface parts play a significant role in the aerospace industry, the mold- manufacturing industry and the automobile industry, and it is energy-saving, material-saving, time-saving and environmentally beneficial to remanufacture the damaged components to restore their functionality and performance. Due to the complex geometry of the freeform surface wear, the adaptive remanufacturing of freeform surface parts is confronted with challenges. In this paper, an adaptive remanufacturing method for freeform surface parts based on linear laser scanner and robotic laser cladding is proposed to realize the precise freeform surface measurement and optimized remanufacturing path generation. On the one hand, a systematic wear measurement and assessment method is proposed to precisely locate and quantify the wear. With the noncontact calibration of the laser scanner and industrial robot, the contour of the target surface is real-timely measured and the reverse model is efficiently constructed, which provides detailed 3D morphological information of the worn freeform surface for the latter wear analysis. Next, considering the considerable difference between the reverse model and the nominal model, a refined model aligning method weighted by surface wear segmentation is proposed to minimize the alignment error and, further, the difference entity to be additively manufactured is obtained by discrete model comparison. On the other hand, to cope with the unsatisfactory binding strength over the freeform surface basis and small fragments of the working path for the traditional plane or cylinder slicing method, a novel remanufacturing path generation method is proposed. Considering the curvature distribution of the freeform surface, an optimized equidistant freeform surface slicing method is especially proposed for the difference entity to realize the adaptive fitting to the freeform basin. Furthermore, based on the equivalent volume overlapping model of laser cladding, the cladding track filling method for the freeform surface slicing is designed with the optimized track-to-track distance, which can reduce surface waviness and improve remanufacturing efficiency. Finally, simulations and experiments for the remanufacturing scenario of the steam turbine blade are conducted to verify the validity and feasibility of the proposed adaptive remanufacturing method for freeform surface parts based on linear laser scanner and robotic laser cladding.

Full surface profile measurement of a small sized ball based on a stitching measurement method by reversal clamping

For the full surface profile measurement of a small sized ball, traditional measurement methods inevitably have blind measurement areas since clamping part cannot be directly measured. To address the challenge of measuring the full surface, this paper proposed a reversal clamping measurement method based on a bidirectional vacuum adsorption system. The position of the measuring part and the clamping part was exchanged by reversal clamping the workpiece, and the full surface was obtained by stitching two measurement results before and after reversal clamping process. Two visual sensors were used to monitor the reversal clamping processes, and the error model was established to separate the alignment and scanning errors. Experiments were performed with the measurement system and a ball with diameter of 4 mm, the feasibility of the full surface measurement was verified to be with a measuring accuracy of hundred nanometer-level.

Modeling the skeleton-language uncertainty for 3D action recognition

Human 3D skeleton-based action recognition has received increasing interest in recent years. Inspired by the excellent ability of the multi-modal model, some pioneer attempts to employ diverse modalities, i.e., skeleton and language, to construct the skeleton-language model and have shown compelling results. Yet, these attempts model the data representation as deterministic point estimation, ignoring a key issue that descriptions of similar motions are uncertain and ambiguous, which brings about restricted comprehension of complex concept hierarchies and impoverished cross-modal alignment reliability. To tackle this challenge, this paper proposes a new Uncertain Skeleton-Language Learning Framework (USLLF) to capture the semantic ambiguity among diverse modalities in a probabilistic manner for the first time. USLLF consists of both inter- and intra-modal uncertainties. Specifically, first, we integrate the language (text) generated by ChatGPT with the generic skeleton-based network and develop a deterministic multi-modal baseline, which can be easily achieved via any off-the-shelf skeleton and text encoders. Then, based on this baseline, we explicitly model the intra-modal (skeleton/language) uncertainties as the Gaussian distributions using the new uncertainty networks capable of learning the distributional embeddings of modalities. Following this, these embeddings are aligned and formulated as inter-modal (skeleton-language) uncertainty using both the contrastive and negative log-likelihood objectives to alleviate the cross-modal alignment error. Experimental results on NTU RGB+D, NTU RGB+D 120, and NW-UCLA datasets show that our approach outperforms the proposed baseline and achieves comparable performance with a high inference efficiency compared to the state-of-the-art methods. Besides, we also deliver insightful analyses on how learned uncertainty reduces the impact of uncertain and ambiguous data on model performance.