Correct Errors Research Articles

Human vs machine: identifying ChatGPT-generated abstracts in Gynecology and Urogynecology

BackgroundChatGPT, a publicly available artificial intelligence (AI) large language model, has allowed for sophisticated AI technology on demand. Indeed, use of ChatGPT has already begun to make its way into medical research. However, the medical community has yet to understand the capabilities and ethical considerations of AI within this context, and unknowns exist regarding ChatGPT’s writing abilities, accuracy, and implications for authorship. ObjectivesWe hypothesize that human reviewers and AI detection software differ in their ability to correctly identify original published abstracts and AI-written abstracts in the subjects of Gynecology and Urogynecology. We additionally suspect that concrete differences in writing errors, readability, and perceived writing quality exist between original and AI-generated text. Study DesignTwenty-five articles published in high impact medical journals and a collection of Gynecology and Urogynecology journals were selected. ChatGPT was prompted to write 25 corresponding AI-generated abstracts, providing the abstract title, journal-dictated abstract requirements, and select original results. The original and AI-generated abstracts were reviewed by blinded Gynecology and Urogynecology faculty and fellows to identify the writing as original or AI-generated. All abstracts were analyzed by publicly available AI detection software GPTZero, Originality, and Copyleaks and were assessed for writing errors and quality by AI writing assistant Grammarly. ResultsOne hundred fifty-seven reviews of 25 original and 25 AI-generated abstracts were conducted by 26 faculty and 4 fellows. Fifty-seven percent of original abstracts and 42.3% of AI-generated abstracts were correctly identified for an average of 49.7% across all abstracts. All three AI detectors rated the original abstracts as less likely be AI-written than the ChatGPT-generated abstracts (GPTZero 5.8 vs 73.3%, p<0.001; Originality 10.9 vs 98.1%, p<0.001; Copyleaks 18.6 vs 58.2%, p<0.001). The performance of the three AI detection software differed when analyzing all abstracts (p=0.03), original abstracts (p<0.001), and AI-generated abstracts (p<0.001). Grammarly text analysis identified more writing issues and correctness errors in original than AI abstracts, including lower Grammarly score reflective of poorer writing quality (82.3 vs 88.1, p=0.006), more total writing issues (19.2 vs 12.8, p<0.001), critical issues (5.4 vs 1.3, p<0.001), confusing words (0.8 vs 0.1, p=0.006), misspelled words (1.7 vs 0.6, p=0.02), incorrect determiner use (1.2 vs 0.2, p=0.002), and comma misuse (0.3 vs 0.0, p=0.005). ConclusionsHuman reviewers are unable to detect the subtle differences between human and ChatGPT-generated scientific writing due to AI’s ability to generate tremendously realistic text. AI detection software improve identification of AI-generated writing but still lack complete accuracy and require programmatic improvements in order to achieve optimal detection. As reviewers and editors may be unable to reliably detect AI-generated pieces, clear guidelines for reporting AI use by authors and implementing AI detection software in the review process will need to be established as AI chatbots gain more widespread use.

Fireball symmetry and its influence on perspective error from thermography data

Thermography uses high-speed color cameras to perform two-color pyrometry for measuring spatially resolved surface temperatures of condensed phases. One application is to investigate the thermal evolution of particles within fireballs, but data analysis is affected by emissivity and optical density. Fireball dynamics exhibit large variations in both properties across space and time, while diagnostics measure the line-of-sight radius of a maturing fireball, raising the question: does thermography accurately represent temperature distributions regardless of spatial perspective? Here, fireballs are observed at two 90° perspectives. Every frame of data is categorized based on symmetry, then compared using the median temperature difference. Symmetric flame profiles show higher congruity in global median temperature, whereas asymmetric flames produce varying optical density profiles leading to larger differences between perspectives. Methods to correct perspective errors are discussed.

Leveraging the power of generative AI: a case study on feedback analysis of student evaluation in an undergraduate physiology practical course

Student surveys with Likert scales and open responses are key to gauging the student experience in educational institutions. However, the thematic analysis of open responses is time-consuming, delaying feedback. This study aims to evaluate the effcacy of ChatGPT-4, a generative AI large language model (LLM) to streamline thematic analysis of student perception surveys. We hypothesise that LLMs can expedite the process, however, human intervention remains essential. The study focused on a 2nd-year physiology course’s and evaluated comparing online vs face-to-face (F2F) delivery, to determine if practical classes could successfully be delivered to students online without compromising the delivery of the desired skills and learning outcomes. Data from six cohorts were included (2019-2022); three semesters online and three F2F. Overall grades, and grades from individual written assessments requiring data analysis and critical thinking showed no difference between the different delivery modes, indicating that major learning outcomes are maintained in online delivery. Student perception was analysed from an online cohort (Semester 2, 2022). Analysis of the Likert data from the student survey from an online cohort (response rate: 40/202) found that students strongly agreed that the class was enjoyable (83% agreement) and the online tools and software were easy to use (83% agreement). Thematic analysis was performed on the open text responses using a LLM (ChatGPT-4) guided by a structured thematic analysis framework and was conducted in three phases: coding responses, collating codes into themes, and visualizing these themes. Each phase required precise prompt engineering to ensure the outputs were accurate and relevant. Thematic analysis using ChatGPT-4 identified that students enjoyed the social aspects of the teamwork and collaboration. The students found the online and software tools easy to use due to rapid feedback from instructors. Altogether, this produced a positive experience in their online learning experiments. A significant advantage to using ChatGPT-4 is the rapid processing of the thematic analysis and alleviate the burdensome aspects of qualitative analysis. Thus, allowing for the timely extraction of nuanced findings provided by qualitative data, and ensuring that student feedback can be effectively addressed. While the results showed that ChatGPT-4 was largely successful in processing the qualitative data, human oversight was necessary to correct minor errors and ensure logical consistency. In addition, LLMs like ChatGPT-4 cannot operate in isolation; human involvement are imperative in making evaluative judgments and checking for hallucinations. Nevertheless, we present a framework for a collaborative human-LLM approach to qualitative analysis of student evaluations to provide more timely feedback and action. The increase rapidity in feedback will help alleviate the student believe that their feedback goes unread and unheeded, thereby improving student outcomes. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Material Characterization Augmented with Artificial Intelligence.

The present paper investigates the application of artificial intelligence to improve the results from simple, non-instrumented, tensile tests, performed with a desktop-size MaCh3D smart universal testing machine. Non-instrumented tensile tests, performed on any testing machine, are affected by both deterministic and random factors that introduce errors in the test results. Specific features of the MaChh3D tester minimize random factors effects on test results while introducing a larger effect of deterministic factors. Artificial intelligence is identified as a novel approach to correct errors in non-instrumented tensile test, capable of simulating a direct strain measure onto the test, replacing traditional contact or non-contact instrumentations (like strain-gages, extensometer and optical measures) that introduce complexity into test procedure and require time for setup. The resulting AI model implementation is described and its performance evaluated in comparison with instrumented tests, also comparing different training strategies. The developed AI-extensometer (artificial intelligence virtual extensometer), is capable of a precise mechanical properties evaluation, with errors from 0 to 10% depending on the specific parameter.

A family of permutationally invariant quantum codes

We construct a new family of permutationally invariant codes that correct t Pauli errors for any t&amp;#x2265;1. We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction contains some of the previously known permutationally invariant quantum codes as particular cases, which also admit transversal gates. In many cases, the codes in the new family are shorter than the best previously known explicit permutationally invariant codes for Pauli errors and deletions. Furthermore, our new code family includes a new ((4,2,2)) optimal single-deletion-correcting code. As a separate result, we generalize the conditions for permutationally invariant codes to correct t Pauli errors from the previously known results for t=1 to any number of errors. For small t, these conditions can be used to construct new examples of codes by computer.

Exploring Undergraduate Students’ Viewpoints on Corrective Feedback Implementations in Interpreting

Considering the importance of interpreting as an effective communication tool, the critical role of systematic error-treatment practices, which might ultimately enable the construction of more accurate renditions, is undeniable. However, the number of studies addressing the feedback mechanism, especially in the interpreter training domain, is quite low in the relevant literature. In this vein, the current research, based on a mixed-method research design, aims to portray the perceptions regarding the multidimensional characteristics of the error feedback process from the lens of interpreter candidates. The quantitative data were gathered with the participation of a total of 102 undergraduate-level students majoring in the Translation and Interpreting Department. In the data analysis procedure, firstly the Principal Components Analysis was conducted and 7 sub-dimensions based on the corrective error feedback were extracted. The qualitative data were collected with the participation of 10 students in the semi-structured interviews. The findings gathered with these two methods revealed that the participants had a favourable opinion of obtaining feedback regarding their performances. Notably, while most of the participants reported the highest endorsement on the explicit type of feedback and receiving corrective feedback oriented to all error types, they indicated the least agreement on peer and delayed feedback types. The resulting information may further broaden teachers’ insights into designing a learning environment congruent with students’ perspectives, eventually leading to more efficient learning outcomes.

TQRFormer: Tubelet query recollection transformer for action detection

Spatial and temporal action detection aims to precisely locate actions while predicting their respective categories. The existing solution, TubeR (Zhao et al., 2022), is designed to directly detect action tubes in videos by recognizing and localizing actions using a unified representation. However, a potential challenge arises during the decoding stage, leading to a gradual decrease in the model's performance in action detection, specifically in terms of the confidence associated with detected actions. In this paper, we propose TQRFormer: Tubelet Query Recollection Transformer, enabling the subsequent decoder to obtain information from the previous stage. Specifically, we designed Query Recollection Attention to correct errors and output the synthesized results, effectively breaking the limitations of sequential decoding. During the training stage, TubeR (Zhao et al., 2022) generates a limited number of positive sample queries through a one-to-one matching strategy, potentially impacting the effectiveness of training with positive samples. To enhance the quantity of positive samples, we propose a stage matching approach that combines both one-to-many matching and one-to-one matching without additional queries. This approach serves to boost the overall number of positive samples for improved training outcomes. We also propose a more elegant classification head that contains the start and end frames of the small tubes information, eliminating the necessity for a separate action switch. The performance of TQRFormer is superior to previous state-of-the-art technologies on public action detection datasets, including AVA, UCF101–24, JHMDB-21 and MultiSports. The code will available at https://github.com/ykyk000/TQRFormer.

Integral inequalities of Ostrowski type for two kinds of s-logarithmically convex functions

Abstract In the paper, the authors establish several integral inequalities of the Ostrowski type for s-logarithmically convex functions. These integral inequalities modify the conditions and correct errors in two main theorems of the paper [A. O. Akdemir and M. Tunç, Ostrowski type inequalities for s-logarithmically convex functions in the second sense with applications, Georgian Math. J. 22 (2015), no. 1, 1–7].

Tapping into the Pedagogical Potential of infinigoChatIC: Evidence from iWrite Scoring and Comments and Lu &amp; Ai’s Linguistic Complexity Analyzer

ChatGPT has drawn rapid interest among linguists and language teachers, with academics and industries rushing to tap into its potential. Yet the pedagogical potential of ChatGPT for L2 English writing remains to be further explored academically. This study aims to examine the effects of ChatGPT, or one of its Chinese versions called infinigoChatIC, in improving the quality of L2 writing and in facilitating the development of L2 proficiency among some postgraduate students learning an English reading and writing course in a prestigious university in Southwest China. Specifically, the main research questions focus on how infinigoChatIC-polished L2 English writings perform in comparison to L2 learner writings, and how the improvement of English writing is reflected in the changes of lexical and syntactic complexity, as evidenced by measured data and its pedagogical significance. A set of 24 English writings are collected as part of regular homework assignments, then this set of English writing is polished by the teacher researcher in the infinigoChatIC dialogue box with the prompt “please correct grammatical errors in the following English text so that it is grammatically accurate.” These two sets of writings are scored in iWrite automatic scoring system and then analyzed in Lu &amp; Ai’s web-interfaced linguistic complexity analyzer. The study finds that infinigoChatIC can effectively improve the quality of L2 English writing, with lexical complexity vastly improved and yet surprisingly overall syntactic complexity slightly reduced. Pedagogical implications are discussed.

What can writing-process data add to the assessment of spelling difficulties?

Spelling difficulties are commonly associated primarily with spelling errors. However, it is not uncommon for spelling challenges to transform the whole writing process into a formidable struggle. This paper delves into the exploration of whether and to what extent analyses of children’s writing processes can enhance our understanding of their difficulties, potentially contributing to the assessment of spelling challenges. We focused particularly on the degree of hesitation within words and the ability to detect and correct spelling errors among children with and without reading and spelling difficulties, as well as how these processes impact the quality and lexical diversity of their texts. Additionally, we sought to contribute to disentangling the influence of spelling and decoding abilities on these processes. A cohort of 47 children, aged 10–13, participated in the study, comprising 16 typically developing children, 16 with predominantly spelling difficulties, and 15 with both reading and spelling difficulties. Our analysis encompassed their spelling performance in both standardized tests and task-oriented writing samples, as well as an examination of their pausing and revision behaviour. As expected, we found robust correlations between the children’s spelling test scores and the proportions of spelling errors in their texts. Furthermore, our findings indicated that children encountering spelling difficulties exhibited a reduced ability to detect and correct errors compared to their peers without such challenges. Additionally, they displayed a slightly higher tendency to experience word-internal interruptions, aligning with prior research. The children who also had reading difficulties produced fewer words and processed words more slowly compared to children in both the other groups. Intriguingly, process data did not reliably predict text characteristics, suggesting that dysfluent writing may not significantly detriment the overall quality of the text, contrary to our initial expectations based on prevailing writing development models. Nevertheless, the study revealed considerable individual variation, with some participants demonstrating a high degree of struggling and dysfluency, resulting in poorer text outcomes, but also others whose struggling processes led to better outcomes. We posit that the crucial aspect lies in identifying these individuals within a classroom context and gaining insights into their processes to provide them with appropriate, formative feedback and adequate writing tools to facilitate their writing.

Stitching interferometry using alternating calibration of positioning and systematic errors

Stitching interferometry is an essential technique for the non-contact, high-precision measurement of large apertures or complex optical surfaces. However, the accuracy of full-aperture surface reconstruction is significantly compromised by subaperture positioning and systematic errors. To address this challenge, this study introduces a novel stitching interferometry method utilizing alternating calibration of positioning and systematic errors (SIAC). This method calibrates one type of error while maintaining the other constant, and alternates between these processes to effectively decouple the two errors, facilitating accurate phase stitching. Within this calibration framework, an iterative weighted phase stitching model employing vertical projection for estimating overlapping areas was developed to calibrate positioning errors. Additionally, the rotation measurements of a single subaperture, in conjunction with a global fitting approach, were employed to correct reference errors. Numerical simulations have confirmed the efficacy of SIAC in calibrating these errors. Moreover, experimental measurements were performed on both a plane mirror and gullwing aspheres, with the resulting stitched full-aperture phase distributions and cross-testing outcomes affirming the method's accuracy and practicality. This research provides a novel solution for stitching interferometry, enhancing the precision of optical surface measurements.

Comparative Analysis between Vietnamese Reduplicative Words with Hmong Language Reduplicative Ones to Propose Measures to Correct Mistakes in using Vietnamese Reduplicative Words for Hmong Primary School Pupils in Vietnam

Our article “Comparative analysis between Vietnamese reduplicative words with Hmong language reduplicative ones to propose measures to correct mistakes in using Vietnamese reduplicative words for Hmong primary school pupils in Vietnam.” Shows that the similarities and the differences in type, formation, meanings middle of the Vietnamese reduplicative word with the Hmong language reduplicative ones. These similarities and differences create linguistic interferences that help us correctly predict the errors in using Vietnamese reduplicative words of Hmong primary school pupils. To prove this prediction to be correct, we have surveyed, totaled up, and analyzed the causes of errors in using Vietnamese reduplicative words due to language interference of Hmong primary school pupils in Vietnam. From there, we propose and conduct effective experiments to prove the feasibility of measures to correct errors in using Vietnamese reduplicative words for the Hmong primary school pupils in Vietnam. This research has practical significance in language education is to contributes to improving the quality of Vietnamese language teaching for the Hmong primary school pupils in Vietnam.

Laboratory study of aberration calculation in underwater turbulence using Shack-Hartmann wavefront sensor and Zernike polynomials

This paper presents a laboratory study of the aberrations calculation in underwater turbulence using the Shack-Hartmann wavefront sensor. The wavefront decomposition method and Zernike polynomials determine the aberration parameters. In our experimental setup, the turbulent phase screen generator is located in two locations: near the transmitter and therefore far from the receiver, and near the receiver and consequently far from the transmitter. Additionally, we investigate the impact of aperture diameter on turbulence-induced aberrations in the optical receiver system. However, it is essential to note that the coefficients of Zernike polynomials obtained using this method are subject to errors caused by receiver sensor noise and correlation between the polynomials. To address this, we first calculate the coefficients in different arrangements and then correct measurement errors arising from sensor noise and polynomial coefficient correlation.

DiSTNet2D: Leveraging Long-Range Temporal Information for Efficient Segmentation and Tracking

Extracting long tracks and lineages from videomicroscopy requires an extremely low error rate, which is challenging on complex data sets of dense or deforming cells. Leveraging temporal context is key to overcoming this challenge. We propose DiSTNet2D, a new deep neural network architecture for two-dimensional (2D) cell segmentation and tracking that leverages both mid- and long-term temporal information. DiSTNet2D considers seven frames at the input and uses a postprocessing procedure that exploits information from the entire video to correct segmentation errors. DiSTNet2D outperforms two recent methods on two experimental data sets, one containing densely packed bacterial cells and the other containing eukaryotic cells. It is integrated into an ImageJ-based graphical user interface for 2D data visualization, curation, and training. Finally, we demonstrate the performance of DiSTNet2D on correlating the size and shape of cells with their transport properties over large statistics, for both bacterial and eukaryotic cells. Published by the American Physical Society 2024

E-PVT: enhanced position-velocity-time scheduler for computer-controlled optical finishing with comprehensive considerations of dynamics constraints, continuity and efficiency

Deterministic computer-controlled optical finishing is an essential approach for achieving high-quality optical surfaces. Its determinism and convergence rely heavily on precise and smooth motion control to guide the machine tool over an optical surface to correct residual errors. One widely supported and smooth motion control model is position-velocity-time (PVT), which employs piecewise cubic polynomials to describe positions. Our prior research introduced a PVT-based velocity scheduling method, demonstrating sub-nanometer level convergence in ion beam figuring (IBF) processes. However, three challenges remained. Firstly, this method relies on quadratic programming, resulting in computational intensiveness for dense tool paths. Secondly, the dynamics constraints and velocity and acceleration continuities are not comprehensively considered, limiting the full potential of PVT-based control. Thirdly, no compensation mechanism existed when dynamics constraints are exceeded. In this study, in response to these challenges, we proposed the Enhanced PVT (E-PVT) method, reducing the time complexity from O(n3) to O(n) while fully addressing dynamics constraints and continuities. A novel compensation method utilizing particle swarm optimization was proposed to address situations where dynamics constraints might be exceeded while maintaining the overall processing efficiency. Validation through simulation and experimentation confirmed the improved performance of E-PVT.

Scaling and merging macromolecular diffuse scattering with mdx2.

Diffuse scattering is a promising method to gain additional insight into protein dynamics from macromolecular crystallography experiments. Bragg intensities yield the average electron density, while the diffuse scattering can be processed to obtain a three-dimensional reciprocal-space map that is further analyzed todetermine correlated motion. To make diffuse scattering techniques more accessible, software for data processing called mdx2 has been created that is both convenient to use and simple to extend and modify. mdx2 is written in Python, and it interfaces with DIALS to implement self-contained data-reduction workflows. Data are stored in NeXus format for software interchange and convenient visualization. mdx2 can be run on the command line or imported as a package, for instance to encapsulate a complete workflow in a Jupyter notebook for reproducible computing and education. Here, mdx2 version 1.0 is described, a new release incorporating state-of-the-art techniques for data reduction. The implementation of a complete multi-crystal scaling and merging workflow is described, and the methods are tested using a high-redundancy data set from cubic insulin. It is shown that redundancy can be leveraged during scaling to correct systematic errors and obtain accurate and reproducible measurements of weak diffuse signals.

InAs quantum dots with a narrow photoluminescence linewidth for a lower threshold current density in 1.55 µm lasers: erratum

We address and correct errors identified in our previously published article [Opt. Mater. Express 14, 1074 (2024)10.1364/OME.521709]. The corrections necessitate modifications to the text of the original paper, leading to its rephrasing for clarity and accuracy.

Refractive Lens Exchange after Implanted Collamer Lens: A Case Report

Introduction: Myopia stands as a prevalent ametropic condition. Posing ongoing challenges for ophthalmologists. Surgery to correct refractive errors is a primary intervention for severe myopia, encompassing procedures like the removal of the crystalline lens coupled with the placement of an intraocular lens (IOL), and the insertion of phakic IOL. The Implantable Collamer Lens (ICL) is commonly utilized in the posterior chamber but carries potential risks including the disruption of the eye’s normal function, potentially leading to conditions like cataracts and glaucoma. Methods and Purpose: This case report explains a single case patient with ICL that includes previous clinical condition, current condition, steps of surgical procedure, and follow-up after procedure. Case Illustration: We present the case of a 66-year-old male patient who came to the hospital for refractive surgery due to a cataract with a history of implantable collamer lens (ICL) for high myopia. Cataract surgery was performed after an explanation of the ICL followed by an implanted capsular tension ring (CTR) and IOL. Discussion: Several cases of patients using ICL will have complications such as glaucoma and cataracts. Determining ICL design will influence the progression of these complications. An explanation procedure by tuck and pull method is needed for age-related cataract patients. Conclusion: ICL is a safe procedure for high myopia patients. Explanation of ICL can be performed by several medical conditions.

A Simple Statistical Postprocessing Scheme for Enhancing the Skill of Seasonal SST Predictions in the Tropics

Abstract Seasonal prediction systems are subject to systematic errors, including those introduced during the initialization procedure, that may degrade the forecast skill. Here we use a novel statistical postprocessing correction scheme that is based on canonical correlation analysis (CCA) to relate errors in ocean temperature arising during initialization with errors in the predicted sea surface temperature fields at 1–12-month lead time. In addition, the scheme uses CCA of simultaneous SST fields from the prediction and corresponding observations to correct pattern errors. Finally, simple scaling is used to mitigate systematic location and phasing errors as a function of lead time and calendar month. Applying this scheme to an ensemble of seven seasonal prediction models suggests that moderate improvement of prediction skill is achievable in the tropical Atlantic and, to a lesser extent, in the tropical Pacific and Indian Ocean. The scheme possesses several adjustable parameters, including the number of CCA modes retained, and the regions of the left and right CCA patterns. These parameters are selected using a simple tuning procedure based on the average of four skill metrics. The results of the present study indicate that errors in ocean temperature fields due to imperfect initialization and SST variability errors can have a sizable negative impact on SST prediction skill. Further development of prediction systems may be able to remedy these impacts to some extent. Significance Statement The prediction of year-to-year climate variability patterns, such as El Niño, offers potential benefits to society by aiding mitigation and adaptation efforts. Current prediction systems, however, may still have substantial room for improvement due to systematic model errors and due to imperfect initialization of the oceanic state at the start of predictions. Here we develop a statistical correction scheme to improve prediction skill after forecasts have been completed. The scheme shows some moderate success in improving the skill for predicting El Niño and similar climate patterns in seven prediction systems. Our results not only indicate a potential for improving prediction skill after the fact but also point to the importance of improving the way prediction systems are initialized.

Ionospheric corrections tailored to Galileo HAS: validation with single-epoch navigation

The Galileo high accuracy service (HAS) is a new capability of the European global navigation satellite system, currently providing satellite orbit and clock corrections and dispersive effects such as satellite instrumental biases for code and phase. In its full capability, Galileo HAS will also correct the ionospheric delay on a continental scale (initially over Europe). We analyze a real-time ionospheric correction system based on the fast precise point positioning (F-PPP), and its potential application to the Galileo HAS. The F-PPP ionospheric model is assessed through a 281-day campaign, confirming previously reported results, where the proof of concept was introduced. We introduce a novel real-time test that directly links the instantaneous position error with the error of the ionospheric corrections, a key point for a HAS. The test involved 15 GNSS receivers in Europe acting as user receivers at various latitudes, with distances to the nearest reference receivers ranging from tens to four hundred kilometers. In the position domain, the test results show that the 95th percentile of the instantaneous position error depends on the user-receiver distance, as expected, ranging in the horizontal and vertical components from 10 to 30 cm and from 20 to 50 cm, respectively. These figures not only meet Galileo HAS requirements but outperform them by achieving instantaneous positioning. Additionally, it is shown that formal errors of the ionospheric corrections, which are also transmitted, are typically at the decimeter level (1 sigma), protecting users against erroneous position by weighting its measurements in the navigation filter.