Lumbar puncture (LP) is a commonly performed medical procedure in a wide range of indications. Virtual reality (VR) provides a stimulating, safe and efficient learning environment. We report the design and the evaluation of a three dimensions (3D) video for LP training.We recorded a stereoscopic 180-degrees 3D video from two LPs performed in clinical settings in Fernand Widal Lariboisière University Hospital, Paris, France. The video was administered to third-year medical students as well as to a residents and attendings group during LP simulation-based training sessions.P < 0.05). Trainees evaluated favorably the 3D feature and supported the development of similar tutorials for other medical procedures .On 168 participants , satisfaction after video exposure was high . No significant discomfort was reported (comfort score graded 4.5 ± 0.8 on 5). LP-naive students displayed higher satisfaction and perceived benefit than users with prior LP experience (overall, We report our experience with a 3D video for LP training. VR support could increase knowledge retention and skill acquisition in association to LP simulation training.The online version contains supplementary material available at 10.1186/s12909-022-03317-7. Lumbar puncture (LP) is an important diagnostic and therapeutic procedure performed in various clinical settings –3. LP isSimulation technology using LP simulators has shown efficiency in improving teaching and operator experience in technical gestures and has been developed in LP –11. It wVirtual reality (VR) is emerging as a new method of delivering simulation –15. VR rWe report the design and development of a prototype stereoscopic 180-degree video of LP in clinical settings and its evaluation in a pilot cohort.curriculum, with no prior LP experience. Each participant was provided a detailed overview of the study and informed consent was obtained.The study was conducted in Université de Paris, Paris, France, from October 2020 to June 2021. We included participants during LP simulation-based training sessions. The first cohort included residents and attendings, who had already performed LP at the time of training. The second cohort included third-year medical students undergoing LP training session in their regular Two LPs performed in clinical settings in the Cognitive Neurology Centre, Lariboisière Fernand Widal Hospital, using atraumatic needle (pencil-point needle) were recorded Fig. . PatientSoftware used for video treatment was: Insta 360 Studio 2019, Insta360 PR plug-in for Première Pro, Adobe Première Pro 2019 and 2020 for editing and Adobe Medias Encoder 2019 and 2020 for encoding and export. No stitching of the images was needed. Captions with explanation on each step of the procedure were added with the text placed in the operator view at zero degree .https://youtu.be/EqtrQUfKO9U.The final video lasted 5 min after editing and was administered through Gizmo VR Video Player, Gizmolite®, Cyprus Fig. . The VR The video was administered once to included subjects during a live 2-h simulation-based training session. Simulation training protocol was previously published . In brieWe performed a survey to evaluate comfort during viewing and satisfaction after the administration of the video . ParticiZ test and Chi-squared test for categorical variables. A p-value < 0.05 was considered significant with a confidence interval of 95% (CI = 95%).Analysis was performed using GraphPad Prism version 9.00 . Continuous variables were described as mean and standard deviation, median and interquartile range, with indication of data distribution using mode and kurtosis. Categorical variables were described as number of subjects and percentage. Differences between the first cohort  and the second cohort (attendings & residents group) were studied using Mann-Whiney test for continuous variables with The datasets analyzed during the current study are available from the corresponding author on a reasonable request.One hundred sixty-eight subjects were administered the video and completed the survey during simulation training sessions carried out at Université de Paris, on October 26 and 27, 2020 and June the 8, 9 and 11, 2021 . Analysis of the data showed that the distribution did not differ between groups .The overall level of satisfaction of the included subjects was high: M = 4.7 ± 0.6 rated on a 5-point scale Table . Satisfamedical students group = 108, NAttendings and residents = 60] =2641, z = − 1.971, p = 0.0338). Analysis of the data revealed that the distribution was negatively skewed and with excessive kurtosis in the medical student group  whereas the attendings and residents group sample was negatively skewed with negative curtosis .The interest of the video in addition of simulation training was perceived positively in the overall cohort . In both groups, the distribution was negatively skewed and with excessive kurtosis .The added value of the 3D 180-degree characteristic of video compared to a 2D video was quoted to M = 3.9 ± 1.1 on a 5-point scale and did not differ between groups . Distribution was negatively skewed and with excessive kurtosis in both sample .Participants believed that the extension of VR to other medical procedures would be of high interest with a mean score of 4.4 ± 0.9, with no difference between groups (U [N P < 0.0001).In addition, 73% of total participants were interested in being able to have the video in open access for repeated viewing. This interest was higher in the medical students cohort  on which the video has been charged is the only required material. Each group can perform the activity in any environment being provided with the VR headset. A large number of trainees can use this tool simultaneously and its viewing can be repeated as needed. There is no need for continuous supervision. On a practical level, it was easy to produce, compared to immersive VR where the production is time consuming and often requires a large production team. The video could be recorded and edited within a few days. The low cost is also a significant aspect when considering applying it into education especially for low-income settings. Finally, the video modality allows for remote teaching, which is very valuable in the current Covid pandemic context and the associated need to restrict physical contact .We made the choice of a VR 180-degree video . EvolvinOur study has several limitations. VR is a relatively new pedagogical technique, so there is no high-quality evidence on the effectiveness of VR – based teaching. Evaluation of the effect of the video training on the performance of LP for the first time on a patient will be the next step of assessment, as it was done for evaluation of simulation training . A betteWe could develop an innovative VR 180-degree video for LP training. We provide to the community a sample of lumbar puncture VR video that can be freely used for future teaching. In a pilot cohort, the video could be efficiently implemented and its perceived interest and added value to the simulation training was evaluated as high by medical students. A future study will be needed to confirm that our VR video adds value to already established LP simulation training and establish whether it is a valuable tool to improve student learning and LP performance in real-life.Additional file 1.


The initial video did not include the final result after reconstruction. The corrected final Video 2 file has been inserted to replace the incomplete version and is now available online.In the article by Lalonde et al, “Simple Effective Ways to Care for Skin Wounds and Incisions,” published as e2471 in the October 2019 compendium


To describe an unexpected sensory outcome in an adult male who is seeking ocular re-alignment for a psychosocially symptomatic large non-specific exotropia with suppression. The primary diagnosis was infant onset exodeviation of unclear diagnosis, was managed with bilateral strabismus surgery at two years of age, little memory of follow-up.Measurable binocular single vision (BSV) was demonstrable following surgery at 17 years of age, albeit slowly between two weeks and six months postoperatively and subsequently enhanced. His newly acquired sub-optimal BSV led to symptomatic occupation-associated asthenopia. Following two subsequent operations over a 15-year period, he has stable, symptom-free ocular realignment within three prism diopters of orthophoria and performing tasks that require extended periods of near-vision activity.Delayed high levels of stereovision were unexpectedly achieved in an adult with infant onset exotropia with pre-operative sensory suppression that was surgically aligned to near orthophoria. The re-establishment of BSV in such a clinical scenario has to attain a level that is robust enough to meet an individual’s social and occupational needs. The lack of a reliable history is all too common in childhood onset strabismus cases that re-present itself later in life to the adult motility service. This can present management and prognostic challenges in patients with infant onset exotropia, where the spectrum of sensorimotor outcomes following strabismus surgery in adulthood are not well reported, when compared to patients presenting with consecutive exotropia  or post-A 16-year-old male presented to the adult motility clinic with a psychosocially symptomatic constant exotropia, which had been troubling him, especially in photographs, for some years. He never experienced diplopia and requested surgical management of his strabismus. His past ophthalmic history included bilateral lateral rectus recessions for a left divergent squint age two-years. Hospital records of his previous strabismus surgery were not available. The duration of post-operative follow-up was thought to be brief but was otherwise unknown. His parents recall the exodeviation to be present in the first year of life but did not clearly recall whether it was intermittent or constant. He was otherwise fit and well with no medical history of note.Figure 1). Synoptophore measurements were negative for simultaneous perception while the Worth 4 Dot test (W4D) found alternating suppression at both near and distance. Peripheral testing was not performed.Corrected visual acuity was 0.0 Log MAR in either eye  with a stable refractive error during follow-up in our department. Slit lamp examination revealed conjunctival scarring over the right lateral rectus. An alternate prism and cover test (APCT) measured 45 prism diopters (PD) exotropia at six meters and 40 PD exotropia for near viewing. Ocular motility testing revealed bilateral minor adduction deficits . As no BSV potential had been demonstrated, simultaneous bilateral inferior oblique muscle weakening was not performed for the mild inferior oblique overaction and asymptomatic V-pattern.On the first day post-operatively, he was pleased with the outcome of reduced angle 4 PD exotropia for both near and distance. At the second post-operative visit at two-weeks, he had further improved and was able to momentarily control to an 8 PD exophoria for near and distance in primary position but was not able to demonstrate stereopsis, motor fusion or simultaneous perception.Figure 2). The patient could converge to 8 cm then either eye diverged without diplopia. His prism fusion range at near and distance was 4 PD base-out (BO) to 10 PD base-in (BI) with 55’’ (arc/second) stereopsis using the Frisby Stereo test.Six months post operatively, at the third post-operative visit, the patient remained pleased with the outcome. The angle in primary position was 14 PD exophoria at 6m and 10 PD exophoria for near .Over the next 15 years, he had two more surgeries (Operations 3 and 4) for recurring asthenopia symptoms (headaches and sometimes blurred vision and/or diplopia) related to sustained near-vision tasks whilst working long hours in the software industry. At age 28 years, these included bilateral 10 mm inferior oblique muscle recessions and left lateral rectus re-recession from 12.5 mm to 16 mms’ from the limbus (Operation 3) for a decompensating primary position exophoria associated with persistent symptom-producing mild bilateral overacting inferior oblique muscles and with an increase in the magnitude of the up-gaze exotropia. The rationale for symmetrical additional inferior oblique recessions was to collapse the pattern, thereby reducing the larger incomitant up-gaze exodeviation that could exceed his fusional convergence amplitudes. Following Operation 3 he could converge to 12–14 cm before the left eye diverged. At that time, a fusion range at 6 meters could not be measured as the patient decompensated on introduction of a prism. His asthenopia symptoms initially reduced, only to recur circa three years later. At age 32, he decided to proceed with further surgery, namely a 4 mm right medal rectus re-resection (Operation 4) for recurrent symptomatic decompensating exophoria during the course of his aforementioned work . Bagolini striated glasses showed a BSV response for near and distance in free space. Prism fusion range for near measured 14 PD BO to 4 PD BI. The W4D showed BSV for near and distance alternating at distance with right suppression. His stereopsis measured 55’’ arc (Frisby), and his convergence was binocular to 6 cm at the last recorded assessment. The small and increased post-operative right abduction underaction may have helped with this ongoing stability in his alignment and symptomatic improvement, albeit at the expense of a slight non-symptoms producing increase in right horizontal gaze incomitance .Following the three strabismus procedures in adulthood his documented stereopsis improved, the chronology of such stereoacuity and surgical intervention is presented in . Infantile XT in healthy children is far more uncommon than X(T) . Given tHunter et al.  found thMaturation of binocular sensory function is almost complete by 18-months of age , howeverAndalib et al.  performeKoc & Sefi-Yurdakul  looked sFigure 5). Fluctuations of stereo-acuity, even in those who are visually mature can occur and seemingly there is residual neural plasticity . However, Saunders & Trivedi  suggest asticity .Convergence fusional reserves are linked to control of X(T) . On initAlthough data is limited and mainly retrospective; a minority of patients with infant-onset exotropia, good visual acuities and no demonstratable pre-operative binocular single vision (BSV) potential can develop gross BSV or even measurable stereovision when managed surgically in adulthood. In our patient, this re-established itself gradually, between two weeks and six months post-operatively. The limited literature suggests that the prognosis is consistently better for the infantile onset intermittent exotropia group. Paradoxically, the successful alignment outcome of our particular patient’s psychosocially symptomatic exotropia latterly presented him with secondary asthenopia related BSV challenges largely precipitated by the specific requirements of his career. This necessitated further surgeries to achieve near orthophoria alignment and binocular convergence to 6 cm so as to enable his restored sub-optimal fusion to better meet the demands of his occupation.


In this paper, an optimized initialization by calculating posterior probabilities of received symbols is proposed for non-binary LDPC decoding on additive white Class A noise (AWAN) channel. To verify the performance of the proposed initialization, extensive experiments are performed in terms of convergence, validity, and robustness. Preliminary results demonstrate that the decoding algorithm with the optimized initialization for non-binary LDPC codes performs better than the competing methods and that of binary LDPC codes on AWAN channel.Modern navigation satellite communication has the characteristic of high transmitting rate. To avoid bit errors in data transmission, low density parity check (LDPC) codes are widely recognized as efficient ways for navigation communication. Conventionally, the LDPC decoding is applied for additive white Gaussian noise (AWGN) channel and degrades severely while facing the impulsive noise. However, navigation communication often suffers from impulsive interference due to the occurrence of high amplitude “spikes”. At this time, the conventional Gaussian noise assumption is inadequate. The impulsive component of interference has been found to be significant which influences the reliability of transmitted information. Therefore the LDPC decoding algorithms for AWGN channel are not suitable for impulsive noise environments. Consider that LDPC codes over GF( With the explosive development of communication technology, the new mobile communication systems, such as beyond fifth generation B5G) and sixth generation 6G) systems, will suffer from severe challenges imposed by the requirement for heavy connection density and high efficiency . EspeciaG and sixG systemsq) have been employed in encoding and decoding as important codes. With the rapid development of BeiDou Navigation Satellite System (BDS) 3, B1C signal and B2a signal have been utilized gradually. The B-CNAV1 navigation message is transmitted through B1C signal. Each frame of message consists of 3 sub frames, of which the second sub frame exploits LDPC codes  over GF(64) and the third sub frame leverages LDPC codes  over GF(64) for encoding Reviewers' comments:Reviewer's Responses to QuestionsComments to the Author1. Is the manuscript technically sound, and do the data support the conclusions?The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: YesReviewer #2: Yes**********2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: YesReviewer #2: No**********3. Have the authors made all data underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #1: YesReviewer #2: Yes**********4. Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1: YesReviewer #2: Yes**********5. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1: This is a good contribution, however, when you mention in the abstract: In this paper, an optimized initialization by calculating posterior probabilities of received symbols is proposed for non-binaryLDPC decoding over additive white Class A noise (AWAN) channel... the optimized initialization can be performed by applying different optimization technqiues? do you think that metaheuristics are a good option? can you detail this in the abstract?In the second paragraph: ...For current navigation system, LDPC codes over GF(q) is adopted in encodingand decoding. With the development of BeiDou Navigation Satellite System (BDS) 3,B1C signal and B2a signal have been utilized gradually. The B-CNAV1 navigationmessage is transmitted through B1C signal. Each frame of message consists of 3 subframes, of which the second sub frame exploits LDPC codes  over GF(64)and the third sub frame leverages LDPC codes  over GF(64) for encoding [7].Meanwhile, the B-CNAV2 navigation message is transmitted through B2a signal withLDPC codes  over GF(64). Nowadays, evaluation and analysis of LDPC codesover GF(q) for navigation satellite communication, especially in harsh environments,arouse attentions of researchers all over the world....When you conclude this paragraph, can you detail why in harsh environments,arouse attentions of researchers all over the world? are there especial circumstances to consider these LDPC and GF the state of the art?In section: Conventional Initialization in Decoding Process.. you conclude: And the initial messages of BP algorithm over GF(q) could be obtained by bring(8) into (5)...again, can you detail why BP is better thab GF?, in addition, it seems that GF is the reference to be improved,In section: An optimized initialization approach for bp decodingover gf(q) on awan channel, you describe step by step and include simulation results, but can you include a pseudocode? see examples of pseudocode in this paper : Optimizing the kaplan–yorke dimension of chaotic oscillators applying de and pso, 2019Can you discuss convergence issues on your optimization initialization? see for example a cese of study in this paper: Convergence rates of the efficient global optimization algorithm for improving the design of analog circuits, 2020Reviewer #2: 1. Results and findings can be improved further. Interesting to improve the conclusion section as well.2. Add some key references such as: Deep Transfer Learning based Classification Model for COVID-19 Disease, Classification of COVID-19 patients from chest CT images using multi-objective differential evolution--based convolutional neural networks, Efficient Prediction of Drug-drug interaction using Deep Learning Models, Multi-objective particle swarm optimization-based adaptive neuro-fuzzy inference system for benzene monitoring, Improved Particle Swarm Optimization Based Adaptive Neuro-Fuzzy Inference System for Benzene Detection, Fusion of medical images using deep belief networks3. Add a suitable diagrammatic flow of the proposed model4. Authors should add atleast 5 references, otherwise it seems out of scope of PLOS one journal.**********what does this mean?). If published, this will include your full peer review and any attached files.6. PLOS authors have the option to publish the peer review history of their article  digital diagnostic tool,  7 Aug 2020We would like to thank the Editor and the reviewers for their valuable comments and feedback that has helped us make improvements to this paper. We give the respond as an attachment "Response_to_Reviewers.doc".Reviewer#1, Concern # 1: This is a good contribution, however, when you mention in the abstract: In this paper, an optimized initialization by calculating posterior probabilities of received symbols is proposed for non-binary LDPC decoding over additive white Class A noise (AWAN) channel... the optimized initialization can be performed by applying different optimization techniques? Do you think that metaheuristics are a good option? Can you detail this in the abstract?Author response: Thanks for this comment. In our manuscript, we analyze problems of the existing decoding algorithms and focus on an optimized initialization by calculating posterior probabilities of received symbols or non-binary LDPC decoding on AWAN channel and. The authors agree that we should consider and discuss the metaheuristic as an alternative to make the article more complete. Metaheuristics are widely recognized as efficient approaches for optimization problems. However, as illustrated in [33], the successful application of metaheuristics requires to find a good initial parameter setting, which is a tedious and time consuming task. Moreover, the performance of metaheuristics deteriorates quickly as the dimensionality increases, nevertheless high-dimensional circumstances are extremely common in encoding and decoding. Therefore, in contrast to metaheuristics, the proposed optimized initialization shows superiority in dealing with decoding problems based on BP.Author action: We have reorganized the manuscript to make it more clearly. We updated by rewriting the manuscript and adding a new section (i.e. Section 2 “Related work”). And we have included the consideration of metaheuristics in details in Section 2 as follows:This paper is focused on the design of an optimized initialization for non-binary LDPC codes on AWAN channel. In contrast to metaheuristics, our optimized initialization is dedicated to deal with decoding problems based on BP. Generally, as the famous optimization techniques, metaheuristics are widely recognized as efficient approaches for optimization problems, such as particle swarm optimization (PSO)  and differential evolution (DE) [28]. Various metaheuristic methods have reported advantages in image segmentation [29], tuning hyper-parameters of deep neural networks , and benzene prediction model [32]. However, as illustrated in [33], the successful application of metaheuristics requires to find a good initial parameter setting, which is a tedious and time consuming task. Moreover, the performance of metaheuristics deteriorates quickly as the dimensionality increases, nevertheless high-dimensional circumstances are extremely common in encoding and decoding. Therefore, decoding algorithms based on BP are considered for non-binary LDPC codes on AWAN channel, and an optimized initialization by calculating posterior probabilities of received symbols is proposed.________________________________________Reviewer#1, Concern # 2: In the second paragraph: “...For current navigation system, LDPC codes over GF(q) is adopted in encoding and decoding. With the development of BeiDou Navigation Satellite System (BDS) 3, B1C signal and B2a signal have been utilized gradually. The B-CNAV1 navigation message is transmitted through B1C signal. Each frame of message consists of 3 sub frames, of which the second sub frame exploits LDPC codes  over GF(64) and the third sub frame leverages LDPC codes  over GF(64) for encoding [7]. Meanwhile, the B-CNAV2 navigation message is transmitted through B2a signal with LDPC codes  over GF(64). Nowadays, evaluation and analysis of LDPC codes over GF(q) for navigation satellite communication, especially in harsh environments, arouse attentions of researchers all over the world....”. When you conclude this paragraph, can you detail why in harsh environments,arouse attentions of researchers all over the world? Are there especial circumstances to consider these LDPC and GF the state of the art?Author response: Thanks for this comment. The authors agree that we should illustrate the especial circumstances to consider LDPC and GF the state of the art and describe why navigation communication arouses attentions of researchers in harsh environments.Author action: We have rewritten the Section 1 in our manuscript and added more descriptions about the above issues in the second and third paragraphs as follows:Non-binary LDPC codes have been recognized as a powerful technology to encode navigation information efficiently. With the continuous development of BDS 3 and the increasing demand for navigation, people hope to access precise navigation information in time. However, working in severe environments, such as underwater environment surrounded by acoustical noises or in the power industry, the decoder of non-binary LDPC codes is inevitably subject to impulsive interference, which causes poor reliability of transmitted information and even leads to communication failure. Therefore, nowadays, evaluation and analysis of LDPC codes over GF(q) for navigation satellite communication, especially in harsh environments, arouse attentions of researchers all over the world.Conventionally, the LDPC decoding algorithms are designed for AWGN channel. However, navigation satellite communication often suffers from irregular noises due to the occurrence of high amplitude “spikes”. For navigation satellite communication, such spikes can be generated in atmosphere where lightning discharges in the vicinity of the receiver, or underwater environment where the ambient acoustical noises includes impulses due to noisy aquatic animals such as snapping shrimp [8-11]. At this time, the original assumption that noises are the Gaussian noises is inadequate. Unfortunately, few attention has been given to decoding algorithms for LDPC codes over GF(q) in impulsive noise environments.________________________________________Reviewer#1, Concern # 3: In section: Conventional Initialization in Decoding Process. You conclude: And the initial messages of BP algorithm over GF(q) could be obtained by bring (8) into (5) ...again, can you detail why BP is better than GF? In addition, it seems that GF is the reference to be improved,Author response: Thanks for this comment. As illustrated in our manuscript, a significant amount of research has been concentrated on the design, encoding, decoding and performance analysis of LDPC codes over GF(q). And iterative decoding algorithm based on BP is an important soft decision decoding algorithm. In section “Conventional Initialization in Decoding Process”, we give the conventional initialization of BP decoding algorithm considering non-binary LDPC codes. Non-binary LDPC codes mean LDPC codes over GF(q). By adding (8) to (5), the initial messages of BP algorithm for non-binary LDPC codes could be obtained. Author action: We have enhanced the detailed description about why non-binary LDPC codes perform better compared to binary LDPC codes in Section 1 (the penultimate paragraph) and Section 3 as follows:Generally, compared with binary LDPC, LDPC codes over GF(q) show superior performance in resisting burst errors such as impulsive noises for the characteristic of inner interleaving , which makes non-binary LDPC codes more suitable for navigation communication. Furthermore, non-binary LDPC codes combined with q-ary modulation can increase transmission rate obviously . Although there is an increment of computational complexity by adopting LDPC codes over GF(q), with the development of terminal computation, non-binary LDPC codes have become a hot research topic and would become more prevalent and applicable. Therefore, we focus on non-binary LDPC codes decoding on additive white Class A noise (AWAN) channel and present an optimized initialization for decoding in this paper. With simulation experiments, we demonstrate the efficiency of the proposed algorithm.Non-binary LDPC codes can be considered as a kind of linear block codes which are the extension of binary LDPC codes over GF(q). The difference between non-binary LDPC codes and binary LDPC codes is that each non-zero element of sparse parity-check matrix needs to be obtained from GF(q). The Tanner graph of non-binary LDPC codes given by a sparse parity-check matrix over GF(q) is constructed in the same way as that of binary LDPC codes. Compared with binary LDPC codes, non-binary LDPC codes perform better in communication due to advantages in resisting burst error and high transmission rate [34-37].The GF(q) related references include .Also, we have enhanced the detailed description about BP decoding and initialization in Section 3 as:The conventional decoding methods degrade severely while facing the impulsive noise since those methods acquire the posterior probability of received symbols by making use of the transition probability on AWGN channel. To tackle this problem, based on the BP decoding algorithm, we present an optimized initialization for LDPC decoding over GF(q) on AWAN channel with series truncation.As mentioned above, the initialization is the crucial part of the BP decoding over GF(q) algorithm. The posterior probability of received symbols is considered as the initial message transmitted from the variable nodes to the check nodes. Thus, to evaluate the posterior probability of received symbols correctly is vital for decoding.During the initialization of conventional decoding process, we obtain the posterior probability of the received bits from the transition probability of the AWGN channel as equation (9), which suffers from degradation of the bit error rate (BER) in impulsive noise environments. Therefore, for LDPC decoding over GF(q) on AWAN channel, since the channel parameters are only leveraged in the decoding initialization, we need to improve the initialization of the iterative decoding process without changing the information transmission mode between variable nodes and check nodes. Under this circumstance, the optimized initialization can be applied to various traditional LDPC decoding algorithms over GF(q), such as FFT BP and EMS algorithm. Generally, the BP decoding algorithm with optimized initialization for LDPC codes over GF(q) on AWAN channel can be illustrated by the flow chart in Fig 1.In addition, Figure 1 has been redrawn as follows and new references related to BP  have been added:________________________________________Reviewer#1, Concern # 4: In section: An optimized initialization approach for BP decodingover GF(q) on AWAN channel, you describe step by step and include simulation results, but can you include a pseudocode? See examples of pseudocode in this paper: Optimizing the kaplan–yorke dimension of chaotic oscillators applying de and pso, 2019Author response: Thanks for this comment very much. The authors agree that the pseudocode of the proposed initialization is significantly important.Author action: The authors have read the paper “Optimizing the kaplan–yorke dimension of chaotic oscillators applying de and pso” carefully. The pseudocode in this paper seems very clear and powerful. Moreover, this paper introduces the optimization of the Kaplan-Yorke dimension of chaotic oscillators by applying metaheuristics such as DE and PSO algorithms, which is consistent with our discussion about metaheuristics in Section 2. We updated the manuscript by adding this paper as reference. And we have included the symbol description and pseudocode of FFT BP decoding with the proposed initialization for non-binary LDPC codes on AWAN channel instead of the original descriptions step by step in Section 4 as:FFT BP decoding with the proposed initialization  for non-binary LDPC codes on AWAN channel is illustrated in Algorithm 1, …..(in the 5-th paragraph in Section 4)And the correspond pseudocode is added as:________________________________________Reviewer#1, Concern # 5: Can you discuss convergence issues on your optimization initialization? See for example a case of study in this paper: Convergence rates of the efficient global optimization algorithm for improving the design of analog circuits, 2020.Author response: Thanks for this comment very much. The authors agree that there should be more discussions with respect to the convergence of the proposed algorithm. We have conducted researches on the recommended article “Convergence rates of the efficient global optimization algorithm for improving the design of analog circuits” and found that convergence rates and comparisons performed by this article were useful.Author action: We have conducted researches on the recommended articles and performed experiments with respect to the convergence. We have reorganized the manuscript and added a new subsection “Convergence comparison” in Section 5 “Results and discussion” as follows:Firstly, convergence issues have been considered as in [40] and performance of different initializations was evaluated utilizing the BER. To be specific, we compared the BER of the FFT BP decoding algorithm with the optimized initialization  with that of the conventional FFT BP algorithm (designed for AWGN channel) on AWAN channel. We should note that the difference between the two algorithms is the initialization. Therefore, the statistical evaluation was performed using the Wilcoxon rank test metric runs of both algorithms for QC LDPC codes  with the statistical significance value. The null hypothesis H0 is ‘The difference between obtained by the optimized FFT BP algorithm and the conventional FFT BP algorithm is identical with the same BER’. Meanwhile, the alternative hypothesis is set as ‘the optimized FFT BP algorithm is validated’. Table 1 presents the convergence comparisons of different initializations using the Wilcoxon Signed-Rank Test metric at different BER, where the ‘+’ indicates the cases when the algorithm acquires better coding gain. It clearly shows that the FFT BP algorithm with the proposed optimized initialization is statistically more superior.And results of convergence comparisons at different BER by utilizing Wilcoxon rank test is also added as Table 1.________________________________________Reviewer#2, Concern # 1: Results and findings can be improved further. Interesting to improve the conclusion section as well.Author response: Thanks for this comment very much. The authors agree that both section should be improved further. We have rewritten Section 5 “Results and discussion” and Section 6 “Conclusion” Author action: We have updated by rewriting all experimental results to make them clear and adding a new subsection (i.e. convergence comparison) in Section 5, which has been described in Reviewer#1, Concern # 5.Further, we have rewritten Section 6 “Conclusion” as:In this paper, we investigate LDPC decoding over GF(q) in impulsive noise environments for modern navigation satellite communication. By jointly considering the Class A noise model and the series truncation, we propose an optimized initialization for LDPC decoding over GF(q) on AWAN channel, which can be employed in BP-based iterative decoding algorithm. In addition, convergence, validity, robustness of the proposed initialization are analyzed and discussed with extensive experiments. Simulation results demonstrate that, the decoding algorithm with the optimized initialization achieves 12.2 dB coding gain at BER=10-5 compared to conventional methods on the assigned AWAN channel. Moreover, LDPC codes over GF(q) acquire 1.7 dB coding gain over binary LDPC codes at BER = 10-5 on AWAN channel. Robustness and the effect of channel parameters are confirmed by considering LDPC codes with different lengths and AWAN channel with parameters. Furthermore, by comparing the proposed method and the piecewise fitting method, experimental result verifies the feasibility of our method in practical applications. With the continues development of BDS-3, to employ the optimized initialization for LDPC decoding over GF(q) can achieve superior performance significantly in impulsive noise environments. In the future work, we will focus on studying LDPC decoding over GF(q) in a more complex noise environment.________________________________________Reviewer#2, Concern # 2: Add some key references such as: Deep Transfer Learning based Classification Model for COVID-19 Disease, Classification of COVID-19 patients from chest CT images using multi-objective differential evolution--based convolutional neural networks, Efficient Prediction of Drug-drug interaction using Deep Learning Models, Multi-objective particle swarm optimization-based adaptive neuro-fuzzy inference system for benzene monitoring, Improved Particle Swarm Optimization Based Adaptive Neuro-Fuzzy Inference System for Benzene Detection, Fusion of medical images using deep belief networksAuthor response: Thanks for this comment very much. The authors agree that there should be more related references in this manuscript. Since our manuscript introduces an optimized initialization, as the famous optimization techniques, the authors agree that the metaheuristic should be considered and discussed as an alternative to make the article more complete. We have conducted researches on the recommended articles and found that those excellent articles are closely related to our consideration of metaheuristic algorithms. “Classification of COVID-19 patients from chest CT images using multi-objective differential evolution--based convolutional neural networks” presents a CNN to classify the chest CT images as as infected (+ve) or not (-ve) and tunes the initial parameters of CNN with multi-objective differential evolution. “Deep Transfer Learning based Classification Model for COVID-19 Disease” and “Fusion of medical images using deep belief networks” combine deep learning with meta-heuristics and give a detailed description about tuning hyper-parameters of deep neural networks. “Improved Particle Swarm Optimization Based Adaptive Neuro-Fuzzy Inference System for Benzene Detection” extends the metaheuristic algorithm to benzene prediction model. “Multi-objective particle swarm optimization-based adaptive neuro-fuzzy inference system for benzene monitoring” employs the metaheuristic (PSO) to enhance the accuracy of ANFIS for runtime parameter.Author action: We have conducted researches on the recommended articles and included those excellent literature as our references. We updated by rewriting the manuscript and adding a new section (i.e. Section 2 “Related work”). We have included the consideration of metaheuristics in details with the recommended articles as important references in Section 2 as:Generally, receivers adopts parameters of the AWGN channel and conventional decoding methods for LDPC decoding, which results in serious degradation in impulsive noise environments. The impulsive component of interference has been found to be significant which influences the reliability of transmitted information.Various attempts have been made to develop models of impulsive noises that can be divided into empirical models and physical models. Class A noise model proposed by Middleton is a typical kind of physical models [23]. The statistical feature of Class A noise is much different from that of Gaussian noise, therefore the LDPC decoding algorithms for AWGN channel are not suitable for Class A noise environments. Maad et al. analyzed the performance of LDPC codes in heavy-tailed, symmetric alpha stable noise (SαS) channels [24]. Further, Nakagawa et al. proposed the sum-product decoding method for binary LDPC codes in Class A noise environment [25]. However, few researches have ever explored decoding algorithms for LDPC codes over GF(q) in Class A noise environments.This paper is focused on the design of an optimized initialization for non-binary LDPC codes on AWAN channel. In contrast to metaheuristics, our optimized initialization is dedicated to deal with decoding problems based on BP. Generally, as the famous optimization techniques, metaheuristics are widely recognized as efficient approaches for optimization problems, such as particle swarm optimization (PSO)  and differential evolution (DE) [28]. Various metaheuristic methods have reported advantages in image segmentation [29], tuning hyper-parameters of deep neural networks , and benzene prediction model [32]. However, as illustrated in [33], the successful application of metaheuristics requires to find a good initial parameter setting, which is a tedious and time consuming task. Moreover, the performance of metaheuristics deteriorates quickly as the dimensionality increases, nevertheless high-dimensional circumstances are extremely common in encoding and decoding. Therefore, decoding algorithms based on BP are considered for non-binary LDPC codes on AWAN channel, and an optimized initialization by calculating posterior probabilities of received symbols is proposed.________________________________________Reviewer#2, Concern # 3: Add a suitable diagrammatic flow of the proposed modelAuthor response: Thanks for this comment. The authors agree that the pseudocode of the proposed initialization is significantly important. Author action: We redrawn Fig. 1 (the flow chart of BP decoding for LDPC codes over GF(q) on AWAN channel) and added the pseudocode of the proposed model in our manuscript, which has been described in Reviewer#1, Concern # 4.Also, to make the manuscript more clear and complete, we have enhanced Section 1 with a detailed description of the contribution as follows:Therefore, we focus on non-binary LDPC codes decoding on additive white Class A noise (AWAN) channel and present an optimized initialization for decoding in this paper. With simulation experiments, we demonstrate the efficiency of the proposed algorithm. The main contributions are summarized as follows:1) We investigate the problem of LDPC decoding in impulsive noise environments for navigation communication and formalize the impulsive noise as the Class A noise model.2) We propose an optimized initialization by calculating posterior probabilities of received symbols for non-binary LDPC decoding on AWAN channel, which makes use of series truncation for computing effectively.3) Extensive experiments are conducted on convergence, validity, robustness. The experimental results reveal that the optimized initialization has a significant effect on the decoding performance for non-binary LDPC codes on AWAN channel.________________________________________Reviewer#2, Concern # 4: Authors should add at least 5 references, otherwise it seems out of scope of PLOS one journal.Author response: Thanks for this comment. The authors agree that there should be more related references in this manuscript. We have conducted researches on the recommended articles.Author action: We have conducted researches on the recommended articles and included those excellent literature as our references, which has been described in Reviewer#2, Concern # 2.________________________________________AttachmentResponse_to_Reviewers.docSubmitted filename: Click here for additional data file. 8 Apr 2021PONE-D-20-15556R1An optimized initialization for LDPC decoding over GF(q) in impulsive noise environmentsPLOS ONEDear Dr. Zhao,Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.plosone@plos.org. 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For instructions see: We look forward to receiving your revised manuscript.Kind regards,Lisu Yu, Ph.DNanchang University, ChinaAcademic EditorPLOS ONEJournal Requirements:Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.Additional Editor Comments (if provided):The paper seems to be revised well. All the comments are addressed. There is one minor revisions to be noticed. LDPC decoding is a very old technique, so please add some new backgroud and references for that, like 5G or 6G application related references. For example,[1] “Massively Distributed Antenna Systems With Nonideal Optical Fiber Fronthauls: A Promising Technology for 6G Wireless Communication Systems,” IEEE Vehicular Technology Magazine, Dec. 2020. [2] "What should 6G be?" Nature Electronics, Jan. 2020.and so.[Note: HTML markup is below. Please do not edit.]Reviewers' comments:Reviewer's Responses to QuestionsComments to the Author1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.Reviewer #1: All comments have been addressed**********2. Is the manuscript technically sound, and do the data support the conclusions?The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: Yes**********3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes**********4. Have the authors made all data underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #1: Yes**********5. Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1: Yes**********6. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1: the revised paper can be accepted now, the authors have addressed all recommendations of this reviewer**********what does this mean?). If published, this will include your full peer review and any attached files.7. PLOS authors have the option to publish the peer review history of their article  digital diagnostic tool,  14 Apr 2021Thanks editors. The experimental data involved in this manuscript have been uploaded as the Supporting Information files regarding to each experiment .Additional Editor Comments (if provided): The paper seems to be revised well. All the comments are addressed. There is one minor revisions to be noticed. LDPC decoding is a very old technique, so please add some new background and references for that, like 5G or 6G application related references. For example, [1] "Massively Distributed Antenna Systems with Nonideal Optical Fiber Fronthauls: A Promising Technology for 6G Wireless Communication Systems," IEEE Vehicular Technology Magazine, Dec. 2020, [2] "What should 6G be?" Nature Electronics, Jan. 2020; and so.Author response: Thanks for this comment very much. The authors agree that there should be more background and references related to 5G or 6G application in our manuscript. As LDPC decoding is an old technique, we hope to highlight the connection between this paper and the latest communication system.Author action: We have made the manuscript more clearly. We updated by including some new background in Section 1 “Introduction” and adding some related references to emphasize the 5G or 6G application as follows:With the explosive development of communication technology, the new mobile communication systems, such as beyond fifth generation (B5G) and sixth generation (6G) systems, will suffer from severe challenges imposed by the requirement for heavy connection density and high efficiency [1]. Especially for 6G, satellite communications play an important role in providing high quality communication services to achieve the worldwide connectivity [2]. As one of the critical components, …[1]. Yu L, Wu J, Zhou A, et al. Massively Distributed Antenna Systems With Nonideal Optical Fiber Fronthauls: A Promising Technology for 6G Wireless Communication Systems. IEEE Vehicular Technology Magazine. 2020; 15(4): 43-51.[2]. Dang S, Amin O, Shihada B, et al. What should 6G be?. Nature Electronics. 2020; 3(1): 20-29.Further, in Section 6 “Conclusion”, we have included the consideration of the next communication systems as follows:The optimized initialization proposed in this paper can be also extended to decoding process of other 5G or 6G applications. In the future work, we will focus on studying LDPC decoding over GF(q) in a more complex noise environment for B5G and 6G systemsAttachmentResponse_to_Reviewers.docSubmitted filename: Click here for additional data file. 19 Apr 2021An optimized initialization for LDPC decoding over GF(q) in impulsive noise environmentsPONE-D-20-15556R2Dear Dr. Zhao,We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.Within one week, you’ll receive an e-mail detailing the required amendments. 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For more information, please contact Kind regards,Lisu Yu, Ph.DNanchang UniversityAcademic EditorPLOS ONEAdditional Editor Comments :No more comments.Reviewers' comments:No more comments. 22 Apr 2021PONE-D-20-15556R2 An optimized initialization for LDPC decoding over GF(q) in impulsive noise environments Dear Dr. Zhao:I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department. onepress@plos.org.If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact plosone@plos.org. 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Microcystis are dominant components of many harmful algal blooms worldwide. Their pelagic–benthic life cycle helps them survive periods of adverse conditions and contributes greatly to their ecological success. Many studies on Microcystis overwintering have focused on benthic colonies and suggest that sediment serves as the major inoculum for subsequent summer blooms. However, the contemporaneous overwintering pelagic population may be important as well but is understudied. In this study, we investigated near-surface and near-bottom pelagic population dynamics of both microcystin-producing Microcystis and total Microcystis over six weeks in winter at Dog Lake . We quantified relative Microcystis concentrations using real-time PCR. Our results showed that the spatiotemporal distribution of overwintering pelagic Microcystis was depth dependent. The abundance of near-bottom pelagic Microcystis declined with increased depth with no influence of depth on near-surface Microcystis abundance. In the shallow region of the lake (<10 m), most pelagic Microcystis was found near the lake bottom (>90%). However, the proportion of near-surface Microcystis rose sharply to over 60% as the depth increased to approximately 18 m. The depth-dependent distribution pattern was found to be similar in both microcystin-producing Microcystis and total Microcystis. Our results suggest the top of the water column may be a more significant contributor of Microcystis recruitment inoculum than previously thought and merits more attention in early CHAB characterization and remediation.Cyanobacteria in the genus  Typically defined as a rapid increase in localized cyanobacterial biomass ,2, CHABstrations  and risitrations ,13,14,15trations . Howevertrations  and in Ltrations . Reducintions [2 ,20. Additions [2 . This reMicrocystis is a major cyanotoxin produced in temperate freshwater CHABs [Microcystis and other coccoid colony-forming cyanobacteria consists of a benthic, overwinter resting phase, a pelagic, planktonic phase, and a colonial, blooming phase [Microcystis colonies that settle in the water column in the fall after summer blooms [Microcystis seed stock in the water column across different depths is not well understood despite their high overwintering viability [Microcystis is potentially more significant as a source of inoculum than their biomass suggests [Microcystis present in deeper areas of a water body, ice and snow cover restricts light availability in all areas, and reduced photosynthetic activity, surface oxygenation, and water flow during the winter means that low dissolved oxygen conditions are probably similarly uniform. Wind-induced mixing and bioturbation after ice melt may have a greater role in the resuspension of overwintering Microcystis in the near-bottom and sediment than active buoyancy control [Microcystis populations in the near-bottom may be higher in areas with shallower lakebeds and lower in deeper, aphotic areas of a lake due to weaker passive recruitment processes and a lack of interaction with the photic zone. In these deeper areas of the lake, the uppermost pelagic Microcystis may be a more significant source of inoculum and have a higher relative population. Understanding this overwintering distribution of Microcystis aeruginosa has important implications for early bloom prediction and bioremediation, as overwintering survival is likely to be strongly correlated with early spring recruitment, biomass build up, and the formation of nascent cyanobacterial blooms.The genus er CHABs . The lifng phase ,24,25,26r blooms . There, r blooms ,28. The iability ,29,30. Wsuggests . Althoug control . Stratif control . TherefoMicrocystis viridis has been isolated and identified from frozen pieces of ice cover [Microcystis viridis colonies on agar plates was much higher than samples from the water column or sediment in Vasas’ study [Microcystis in the form of small colonies or single cells may also survive overwintering in the ice cover as a potential inoculum source in general. Therefore, we hypothesized that ice cover contains viable Microcystis aeruginosa, although in smaller quantities than in the water column.An additional potential source of inoculum that has rarely been considered in temperate lakes is ice cover. Although viable ce cover , the pots’ study . Freeze–s’ study ,34, and Factors that influence the toxicity of CHABs are not well understood. It is well established that cyanobacteria within a lake can exhibit high genetic diversity , and toxM. aeruginosa, the 16S rRNA and mcyE genes have long been used to detect and quantify populations of total and toxic strains [Environmental DNA (eDNA) is an emerging approach to biomonitoring that allows us to take a quantitative biodiversity snapshot of an ecosystem. Organisms leave traces of their genetic material as they move through their environment , often i strains ,44,45. T strains .M. aeruginosa 16S rRNA gene to compare the relative abundance of overwintering pelagic populations in the near-surface, near-bottom, and ice cover at sites of a temperate lake with different lakebed depth. We hypothesized that near-surface Microcystis is most abundant in shallow areas, while near-bottom Microcystis is more prevalent in deeper areas of the lake due to later ice cover formation and a more stable water column. Finally, ice samples have a viable population of Microcystis. Overall distribution of Microcystis should favor shallow areas due to greater recruitment success. We also quantified the relative proportion of toxic strains by comparing the M. aeruginosa mcyE and 16S rRNA genes. We hypothesized that the toxigenic potential of near-bottom overwintering Microcystis populations within a lake decreases as depth increases.Our study used qPCR on the Our study site was at Gilmour Point , a small peninsula with a public beach and boat launches at Dog Lake, South Frontenac County, ON, Canada . GilmourWe conducted weekly sampling from 7 February to 12 March of 2019, collecting a total of 153 water samples across 6 sampling days. We collected 69 of those samples from the top 0.5 m of the water column, which we designated as near-surface samples, 69 samples from the bottom 0.5 m of the water column, which we designated as near-bottom samples, and 15 samples from the ice cover . We alsoWe sampled across two transects, originating at 44.432104° N, 76.354408° W, and extending approximately 300 m from the beach towards the middle of the basin . After cMicrocystis cells range from 2–8 μm in diameter, this protocol captures all intact cells, but the filtration rate and pore size minimize DNA adsorption to the PCTE membrane filter. Therefore, eDNA captured by this technique should mostly originate from live, viable cyanobacteria. After filtration, we folded the filters with flame sterilized forceps and stored them in 500 μL of 2% (w/v) cetrimonium bromide extraction buffer (CTAB) in 2-mL conical microcentrifuge tubes . We stored all filters in a −20 °C freezer until DNA extraction.Our filtration protocol was adapted from Turner et al.  and FengWe extracted DNA using a chloroform/ethanol-based method modified from Deiner and Altermatt . We initM. aeruginosa, CPCC 124 and CPCC 300, purchased from the Canadian Phycological Culture Centre . CPCC 124 is a non-toxic strain isolated by J. Acreman in July of 1987 from Heart Lake, Ontario, Canada, while CPCC 300 is a toxic strain (producing 204 μgmicrocystin g−1 of dry weight) isolated by A. Lam from Pretzlaff Pond, Alberta, Canada [We made standards for qPCR using two strains of , Canada .M. aeruginosa in 80 mL of sterile cyanobacteria growth medium adapted from Ichimura [3 (50 mg L−1); KNO3 (100 mg L−1); Ca (NO3)2∙4H2O (50 mg L−1); Na2SO4 (40 mg L−1); MgCl2∙6H2O (50 mg L−1); Na2 b-glycerophosphate∙5H2O (50 mg L−1); Na2-EDTA (5 mg L−1); FeCl3∙6H2O (0.5 mg L−1); MnCl2∙4H2O (5 mg L−1); ZnCl2 (0.5 mg L−1); CoCl2∙6H2O (5 mg L−1); Na2MoO4∙2H2O (0.8 mg L−1); H3BO3 (20 mg L−1); and C6H13NO4 (500 mg L−1), with the pH adjusted to 8.6 with aqueous NaOH. We kept cultures under a 16/8 H day/night cycle at 400 μmol m−2 s−1. We replenished the growth medium monthly and examined cultures under microscopy for contamination.We maintained axenic cultures of Ichimura  in 120 m® Mini Plant kit  following the manufacturer’s instructions. We obtained a rough estimate of DNA quality and quantity using a Nanodrop ND1000 spectrophotometer  and amplicon size with gel electrophoresis and a 100-bp ladder  on a 1.5% agarose gel stained with RedSafe® . We stored extracted DNA in a −20 °C freezer.We extracted genomic DNA from the two reference stains using a DNeasyMicrocystis cultures, with axenic cultures of Anabaena, Chlorella, and Oscillatoria as negative controls. PCR with the Microcystis 16S rRNA gene primers on genomic DNA extracted from the Microcystis strain CPCC 124 yielded an amplicon of 220 bp, and PCR with the Microcystis mcyE gene primers yielded an amplicon of 120 bp. PCR with both primer sets on genomic DNA from Anabaena, Chlorella, and Oscillatoria yielded no amplicons. This confirmed specificity.We tested the primers from Microcystis 16S rRNA gene primers produced peak fluorescence at a qPCR melting temperature of 86 °C, while Microcystis mcyE gene primers produced peak fluorescence at a qPCR melting temperature of 78 °C. There was no evidence of primer dimers.We determined the melting temperatures of the two primer sets with a CFX96 TouchTM Real-Time PCR Detection System  through raising the temperature from 65 to 95 °C and quantifying the fluorescence in this range. ® PCR System 9700  on genomic DNA previously extracted from the two Microcystis reference strains. The PCR reactions contained 10 μL of 2× Taq FroggaMix , 2 μL of extracted genomic DNA, 0.8 μL of both forward and reverse primers , 10 μg of bovine serum albumin , and 5.9 μL of ddH2O. Our PCR amplification protocol was as follows: initial denaturation of 5 min at 98 °C, 40 cycles of denaturation at 98 °C for 30 s, annealing at 60 °C for 30 s, and extension at 72 °C for 60 s, a final extension at 72 °C for 10 min, and pause at 4 °C. We confirmed the presence of the PCR product through gel electrophoresis on a 1.5% agarose gel stained with RedSafe® nucleic acid staining solution. We extracted DNA from the gel with a QIAquick Gel Etraction Kit  and quantified the resulting product using a DeNovix dsDNA High Sensitivity Kit on a DeNovix QFX Fluorometer . We then calculated the molecular weights of the PCR products with the following equation, where M is the mass of amplicon in ng µL−1, BP is the length of the amplicon in base pairs, and 660 g mol−1 is the average molar mass of 1 base pair of double stranded DNA:To produce standards for our two gene fragments, we performed PCR using a GeneAmpMicrocystis 16S rRNA and 16S gene fragments. qPCR on the standards yielded an R2 value of over 0.998 between the log10 of the gene copies and threshold cycle (CT) values, indicating that the standards were valid and accurate.We performed seven 10-fold serial dilutions of the purified PCR product to generate standard curves for the M. aeruginosa through performing a SYBR Green-based qPCR assay for the previously mentioned Microcystis 16S rRNA gene fragment and mcyE gene fragment on our field samples. We performed qPCR reactions in a total volume of 20 μL, containing 10 μL 2× SensiFAST SYBR Green Master Mix , 2 μL of DNA from field samples or standards, 0.8 μL of each primer , 0.5 μL (containing 10 μg) of bovine serum albumin, and 5.9 μL of ddH2O. We plated reactions in triplicate on clear 96-well PCR plates  and used a CFX96 TouchTM Real-Time PCR Detection System. The qPCR amplification protocol for both the 16S rRNA gene fragment and mcyE gene fragment is as follows: initial denaturation of 3 min at 95 °C, 40 cycles of 5 s of denaturation at 95 °C, and 15 s of annealing/extension at 57 °C. We corrected qPCR gene copy concentrations by the volume filtered for each sample.We detected the quantity of total and potentially toxigenic 10 transformed concentration data of M. aeruginosa 16S rRNA and mcyE gene copies prior to the statistical analyses.We conducted statistical analyses using IBM SPSS Statistics 26 , and generated all maps in ArcGIS . We tested for normality of error distributions using Kolmogorov–Smirnov tests and logWe conducted an ANOVA, followed by Tukey’s HSD post hoc testing to test for significant differences in gene concentrations between samples collected from the near-surface, the near-bottom, and ice cover.Microcystis population was influenced by water column level , we applied univariate general linear models (GLM) using “sampling time” and “water column level” as factors. “Depth” (depth of each sampling site) was included as covariate, and concentrations of M. aeruginosa gene copies (16S rRNA or mcyE) were used as the dependent variable. All two-way interactions were initially included but were excluded from the final models if non-significant (p > 0.05). To test for the correlation between Microcystis concentration and lake depth in different parts of the water column, we created linear regressions between log10 transformed mcyE and 16S rRNA gene concentrations with lake depth. We did this separately for near-surface and near-bottom samples.To determine whether the vertical distribution of overwintering mcyE gene to the general 16S rRNA gene as a proxy for the ratio of potentially toxigenic Microcystis to overall Microcystis. We conducted linear regressions between the ratio of the log10 transformed mcyE to 16S rRNA gene concentrations with depth.We tested the ratio of the toxigenic For all regressions, we assessed heteroscedasticity and linearity through graphical assessment of residual statistics.Microcystis 16S rRNA gene ranged from 5.62 × 105 to 4.53 × 108 copies per liter of water sampled near the bottom of the water column, with a mean of 9.99 × 107 copies per liter. In samples near the top of the water column, concentrations of the 16S rRNA gene ranged from 5.49 ×104 to 1.81 × 107 copies per liter, with a mean of 3.29 × 106 copies per liter. 16S rRNA concentrations in ice cover samples ranged from 5.90 × 104 to 1.14 × 106 copies per liter, with a mean of 4.34 × 105 copies per liter. There was a statistically significant difference between 16S rRNA gene concentrations in the ice cover, near-surface, and near-bottom (ANOVA: F(147) = 140.884, p < 0.001). The assumption of homogeneity of variances was not violated. Post hoc analysis with Tukey’s HSD indicated that 16S rRNA concentration in the near-bottom was significantly higher than in both the near-surface (p < 0.001) and ice cover (p < 0.001), and 16S rRNA concentration in the near-surface was higher than in the ice cover (p < 0.001) (Concentration of the < 0.001) A.Microcystis mcyE gene ranged from 2.26 × 105 to 1.41 × 108 copies per liter of water sampled near the bottom of the water column, with a mean of 2.93 × 107 copies per liter. In near-surface samples, the concentration of the mcyE gene ranged from 1.94 × 104 to 4.11 × 106 copies per liter, with a mean of 8.49 × 105 copies per liter. mcyE concentrations in ice cover samples ranged from 2.30 × 104 to 3.65 × 105 copies per liter, with a mean of 1.29 × 105 copies per liter. There was a statistically significant difference between mcyE gene concentrations in the ice cover, near-surface, and near-bottom (ANOVA: F(147) = 144.517, p < 0.001). The assumption of homogeneity of variances was not violated. Post hoc analysis with Tukey’s HSD indicated that mcyE concentration in the near-bottom was significantly higher than in both the near-surface (p < 0.001) and in ice cover samples (p < 0.001), and mcyE concentration in the near-surface was higher than in the ice cover (p < 0.001) (The concentration of the < 0.001) B.Microcystis population was influenced by both the main effects , and the interaction effects , the interaction effect between “water column level × depth” had an F-value an order of magnitude greater than the other significant interaction term .Vertical distribution of the overwintering pelagic M. aeruginosa 16S gene concentration and depth , while a significant negative correlation was found between near-bottom M. aeruginosa 16S gene concentration and depth  and near-bottom mcyE gene concentration and depth  at each sampling site and plotted against depth. The logistic fitting curve showed that the ratio rose with increased water depth, from roughly 0% in the shallow region to approximately 60% when depth reached 18 m  = 9.758, p = 0.003, R2 = 0.129  = 0.335, p = 0.564, R2 = 0.005  dominate, compared to deeper areas dominated by pelagic invertebrates that cause less bioturbation, such as chironomids. Abiotic hydrological effects may also favor cyanobacterial recruitment from the near-bottom of shallow lakebed areas. Wind-induced mixing typically occurred through Langmuir circulation and was only significant in shallow lakebeds, up to a depth of 4–6 m [Microcystis did not have sufficient carbohydrate content to restore buoyancy during spring recruitment, and buoyancy state was instead largely the result of mixing and subsequent resuspension. Therefore, benthic recruitment may be primarily driven by processes such as wind-induced mixing and heavy precipitation events, which most strongly mix shallower areas of lakes.Not only does the lake bottom in deeper lakebed areas receive fewer the environmental cues that promote active buoyancy recovery and recruitment, the passive processes that mediate recruitment may also favor the lake bottom of shallow lakebed areas. Stahl–Delbanco and Hansson  found thof 4–6 m ,66. Versof 4–6 m  found thMicrocystis depended on lake depth. As the depth of the lakebed increased, we observed a shift from lake bottom to top Microcystis dominance in Dog Lake. The persistence of planktonic, vegetative Microcystis in low temperatures is supported by Ma et al. [Microcystis in other temperate, dimictic lakes with winter ice cover may also be primarily surface dominated close to the center of lake basins, and sources of inoculum depend on the hydrological and topographic characteristics of lakes.Water column distribution of a et al. , who fouMicrocystis predominated overall, cell density in different parts of the water column may not be indicative of their actual contribution to blooms. Verspagen et al. [Microcystis. They found that sediment recruitment occurred throughout the year and was counterbalanced by high sedimentation rates. Additionally, their findings suggested that there was horizontal transportation of sedimented Microcystis from shallow to deeper areas of the lake. Although the pelagic Microcystis population was much smaller in the spring, their model implicated it as a more significant contributor to summer blooms, indicating that controlling it may be key to effective management.Although lake bottom populations of n et al.  examinedMicrocystis in the ice cover. This was similar to the results of Vasas et al. [Microcystis viridis with high viability from a visible bloom frozen in ice cover. However, our study found Microcystis in ice cover from a wider area in a natural lake, and compared it with lake surface and bottom sources as well, further demonstrating the potential of ice cover as a previously unexpected inoculum source. Our results are supported by Park [Microcystis, Anabaena, Oscillatoria, and Aphanizomenon in both colonial and planktonic form had high viability after cryopreservation at −60 °C without a cryoprotectant after as long as two years. This indicates that these CHAB species in general are probably highly resistant to freezing, an inference supported by the lack of a spore or akinete form in these particular species. It is possible that the extracellular lipopolysaccharide/polysaccharide mucilage of colonial cyanobacteria has a cryoprotectant effect, which is common in other mucilage forming bacteria [In addition to the near-surface and near-bottom, we also found concentrations of s et al. , who fou by Park , who foubacteria .M. aeruginosa mcyE to 16S rRNA gene concentration to lakebed depth in the near-bottom, indicating potentially higher toxicity in near-bottom Microcystis overwintering close to the shoreline and in other shallower areas. However, no significant relationship was present in the top of the water column. As there was no significant difference between the mcyE to 16S rRNA ratio in the near-surface and the mcyE to 16S rRNA ratio in the near-bottom across all lakebed depths, it is unlikely that this was solely the result of difference in water column depth. This variation in genotypes was similar to the results of Otten et al. [mcyE to cpcA ratio of 36% ± 12% in the Microcystis of Lake Taihu, which was similar to the mean mcyE to 16S rRNA ratio of 30% ± 7% in Dog Lake over the previous 3 years [Microcystis has been positively correlated with light and temperature [We observed a weak but significant negative correlation between the ratio of n et al. , who fou 3 years . This neperature ,69,70. Pperature .Microcystis populations in different parts of the water column, we did not examine their relative contributions as sources of inoculum to summer blooms. Additional research is needed to determine rates of reproduction and photosynthetic activity of CHAB species at different areas of water bodies, particularly in the top of the water column of lakes during and after spring recruitment. The hydrological characteristics of temperate, shallow lakes, and therefore the mechanisms that influence recruitment remain poorly understood, particularly in terms of interactions between macrophytes and other biotic influences with stratification and mixing [Microcystis through quantification of the M. aeruginosa 16S rRNA and mcyE genes. Perakis et al. [Microcystis populations did not significantly increase in response to high inputs from benthic recruitment, while Anabaena, Aphanizomenon, and Coelosphaerium did, indicating that different sources of inoculum may be dominant between different CHAB genera. Therefore, other CHAB species, particularly filamentous genera that lack mucilage and gas vesicles, such as Anabaena and Aphanizomenon, may differ in their overwintering distributions.Although our study quantified and compared overwintering d mixing . The impd mixing . Furthers et al.  found thMicrocystis and other bloom-forming species may compose a greater portion of the overwintering cyanobacterial population than previously thought, particularly in deeper areas of lakes, and may be significant contributors of inoculum in the spring. The water column distribution of overwintering cyanobacteria may be dependent on lakebed depth. Efforts in early CHAB modeling should consider the top of the water column and ice cover of lakes in the spring, in addition to lake-bottom, sedimentary, and fluvial-inflow sources of inoculum.The results of our study have several implications for bloom monitoring and control strategies and for future. Near-surface and ice cover populations of