The introduction section is arguably one of the most critical elements of a written piece of research work, often setting the tone for the remainder of any dissertation or research article. The primary purpose of an introduction is to provide the reader with a clear understanding of the research question, in addition to the scope, rationale, aims and objectives of the study. This ensures the reader can more easily comprehend the context of the research, which will consequently help them better interpret and evaluate the study results. One could liken an introduction to a trailer for a movie, where the plot of the film (the research topic) is introduced by setting the scene (outlining the significance of the topic) and enticing you to watch the full movie (understanding the research and its importance).,Despite this, our experience suggests that students frequently pay insufficient attention to the introduction section of their dissertation or omit elements which we consider essential to address. This editorial aims to help researchers appreciate the importance of a comprehensive dissertation introduction in medical education research and learn how to effectively manage this key section of their work.  Although it focuses purely on the introduction section of a written research submission, readers interested in learning more about the other primary steps of the research process are encouraged to read AMEE Guide No. 90 Here we aim to provide the reader with a simple structure of how best to construct the introduction for a dissertation and recommend that this should typically include the following essential components and principles.The purpose of providing background information in an introduction is to supply the context and other essential information concerning the research topic, and thus allow the reader to understand the significance of the specific research question and where it sits within the broader field of study. This aids the reader to better understand how the research question contributes to the existing body of knowledge and why it is, necessary to investigate this specific aspect further. For example, suppose the study concerns the effectiveness of simulation-based training in medical education. In this case, the broader field of the study may include relevant areas such as medical simulation, medical education research, health care education, standardised patients, simulation-based training, and curriculum development based on simulation training. After providing the reader with an understanding of the context and relevance of the topic of interest, the researcher must then establish a theoretical or conceptual framework. This underpins the study topic in order that the reader can understand how any research questions and objectives are formulated. It is important to distinguish between these two frameworks. A theoretical framework describes the rationale for applying a particular theory to provide support and structure for the topic being studied. In the absence of an applicable theory, a conceptual framework substantiates the significance of a particular problem, context or phenomenon within a specific area of the study by illustrating its relevance and connection to research topic.When considering Social Cognitive Theory (SCT), one of the key constructs is self-efficacy, as described by Albert Bandura,A literature review is the process of critically evaluating existing research and utilising it to inform and guide the research proposal under investigation. Taking this approach enables researchers to ensure that their research is not only grounded in, but also contributes meaningfully to, any existing knowledge as a whole. Critically reviewing the literature provides evidence and justification for any research and is essential when formulating a hypothesis, question, or study objectives. In addition, and perhaps most importantly, it helps identify any gaps or inconsistencies in the existing knowledge base. Determining the knowledge gap is critical in justifying the necessity for our research and advancing knowledge. A comprehensive literature review also helps establish the theoretical or conceptual frameworks to ground any subsequent research, providing researchers with guidance and direction on how best to conduct their future studies. Understanding from the literature what has worked previously and what may pose challenges or limitations assists researchers when exploring the best methods and techniques for answering new research questions. To clarify, consider a hypothetical study in which researchers wish to examine the effectiveness of a specific educational intervention in medical students to improve patient safety. Based on the existing literature, let's assume that researchers learned that most studies had only focused on short-term outcomes rather than long-term ones. The long-term effects of any intervention in medical students on patient safety therefore remain uncertain. Researchers may therefore wish to consider conducting longitudinal studies months after interventions have been carried out, rather than simply repeating research based on short-term outcomes, in order to address the current knowledge gap. A review of existing literature may highlight hitherto previously unconsidered logistical difficulties in conducting longitudinal studies in this area that the researcher may need to be aware of.More than simply reporting the existing research, one of the key objectives in any literature review is to summarise and synthesise existing research on the intended topic in order to analyse the significance of the research in question. In this process, diverse ideas can be merged to form fresh new perspectives. Any gaps, limitations, or controversies in medical education can be identified, and potential future benefits and implications of the proposed research explained to the reader. Based on any potential impact or perceived importance, the introduction provides an excellent opportunity for the researcher to affirm the significance of the research study and why it should be conducted.By way of an example, the significance of a study concerning feedback given to examiners for Objective Structured Clinical Examinations (OSCEs) is used to illustrate this point further. The potential significance of this research lies in improving the validity and reliability of OSCE scores in medical education. As a result of reviewing different types of feedback given to examiners, the research may assist in identifying the most effective strategies for improving the quality of OSCEs in medical education. By providing new insights into how feedback can improve the reliability and validity of OSCE results, the research could also contribute to the broader knowledge of assessment in general. This may result in the development of more accurate and robust medical education assessments, which in turn may potentially enhance delivery of healthcare and improve patient outcomes and safety. It may also address the current challenges and gaps in medical education assessment by providing evidence-based approaches for improving OSCE quality.Researchers formulate research questions and objectives based on the topic they are seeking to address. As noted previously, these will have already been derived as a result of a comprehensive literature review of any existing knowledge and based on a theoretical or conceptual framework. Furthermore, in medical education, the literature review provides researchers with the opportunity to formulate new research questions or research objectives to address any gaps or limitations in the existing literature and add something new to the current body of knowledge. Research questions and objectives should be stated clearly, being both specific, and measurable. These should then guide the subsequent selection of appropriate research methods, data collection and any subsequent analytical process. Clear, focused, and rigorous research questions and objectives will ensure the study is well-designed and make a valuable contribution to the existing body of knowledge.Qualitative research questions should be open-ended and exploratory rather than focused on a specific hypothesis or proposition. It is common for qualitative studies to focus on understanding how and why certain phenomena occur, rather than simply describing what has occurred. These should be formulated to elicit rich, detailed, and context-specific data that can provide insights into the experiences, perspectives, and meanings of the participants. In contrast, quantitative research questions are more specific and are designed to test a particular hypothesis or relationship. In medical education, it is imperative to emphasise the importance of both qualitative and quantitative research questions when it comes to generating new knowledge. Combining both quantitative and qualitative research methods (mixed methods) can be particularly powerful in providing a more comprehensive understanding of any phenomena under study. Assume again that we are examining the effectiveness of feedback on the performance of medical students and adopt a mixed-methods approach using a combination of qualitative and quantitative research methods. A quantitative research question may be, what is the impact of feedback on the performance of medical students as measured by OSCE mark? How the experience of receiving feedback on performance contributes to the future professional development of medical students is a more qualitative research question. This combination of quantitative and qualitative research questions will provide an in depth understanding of the effectiveness of feedback on medical student performance. It is important to note that in qualitative research methods particularly, there can be a wide variety of research question types. For example, grounded theory researchers may ask so-called "process questions", such as 'how do students interpret and use the feedback they are given?' Phenomenologists, on the other hand, are concerned with lived experience of research subjects and frequently ask questions looking to understand the "meaning" of any such experience, often aiming to attribute feelings to this experience, for example, ‘how do students feel when they receive feedback?’ Ethnographers look to understand how culture contributes to an experience, and may ask more "descriptive questions"For ease of reference, the key points we recommended are considered in any dissertation introduction are summarised below:1.       Set the context for the research2.       Establish a theoretical or conceptual framework to support your study3.       Define key variables both conceptually and theoretically4.       Critically appraise relevant papers during the literature review5.       Review previous studies to identify and define the knowledge gap by assessing what has already been studied and what areas remain unexplored6.       Clearly articulate the rationale behind your study, emphasising its importance in the intended field7.       Clearly define your research objectives, questions, and hypothesesWhilst crafting a research introduction may seem a challenging and time-consuming task, it is well worth the effort to convey your research clearly and engage potential readers. Providing sufficient background information on the research topic, conducting a comprehensive review of the existing research, determining the knowledge gap, understanding any limitations or controversies in the topic of interest, before then exploring any theoretical or conceptual frameworks to develop the research concepts, research questions and methodology are fundamental steps. Articulating any conceptual and operational definitions of key concepts and clearly defining any key terms, including explanations of how these will be used in the study is also paramount to a good introduction. It is essential to clearly present the rationale behind the research and why this is significant, clarifying what it adds to the existing body of knowledge in medical education and exploring any potential future implications. Lastly, it is vital to ensure that any research questions are clearly stated and are open-ended and exploratory in the case of qualitative studies, or specific and measurable in the case of quantitative studies.We feel that observing these basic principles and adhering to these few simple steps will hopefully set the stage for a highly successful piece of research and will certainly go some way to achieving a favourable editorial outcome for possible subsequent publication of the work.The authors declare that they have no conflict of interest.


Glacial–interglacial cycles constitute large natural variations in Earth’s climate. The Mid-Pleistocene Transition (MPT) marks a shift of the dominant periodicity of these climate cycles from  Ever since Ice Ages were discovered in the nineteenth century, there has been discussion about their causes. Initially, explanations focused on the role of variations in the Earth’s orbit Croll . HoweverSeveral hypotheses have focused on the Northern hemisphere ice sheets. Clark and Pollard  suggesteGlacial–interglacial cycles are characterized not only by large climatic variations but also by shifts in the global carbon cycle. Both before and after the MPT, atmospheric COn et al.  applied n et al.  model. In et al.  describea et al.  showed ta et al. . Furthera et al. .Finally, some hypothesized explanations do not invoke specific physical, chemical, or biological mechanisms but rather the subtleties of nonlinear dynamics. One example is the Huybers  model thallows us to investigate these questions, because it generates sawtooth cycles without a threshold and exhibits frequency locking to external periodic forcing  and its impact on atmospheric COThe calcifier-alkalinity model , which bury CaCOI,  the calcifier population growing at rate kA,  and calcite sedimentation occurring at rate M. We follow the transformation performed in Omta et al.  of 14 kyr Fig. a. When tThe average duration is found using the same method as the internal period; namely, running the simulation for 100 million years and averaging the last 50 cycles. The plots of average duration as a function of internal period in Fig. The periodicity begins to lock noticeably onto multiples of the forcing period when the amplitude of the external forcing reaches 001 Fig. b. The laNyman and Ditlevsen  proposeditlevsen , we now Upon the sudden change in feedback strength, we noticed two different behaviors. As in Fig. What is the dynamical mechanism behind the delayed system response? One possibility is that after the shift in entclass1pt{minimaIn our investigation of the impact from a dynamically changing value of The MPT represents a change in the periodicity of the glacial–interglacial cycles around 1 Myr ago. Although the dominant spectral peak shifted from the occurrence of CaCOa linear proportionality between the length and amplitude of glacial–interglacial cycles. We tested this prediction using a correlation between the length/amplitude of glacial cycles and the magnitude of deglacial CaCOWithin the context of the calcifier-alkalinity model, the feedback term implies that there is an enhanced alkalinity input during glacial times and a decreased alkalinity input during interglacials. A potential mechanism behind such variations in alkalinity input is the exposure of continental shelves during glacial periods, which increases carbonate weathering (Gibbs and Kump As discussed in Sect. mentclass2pt{minimV and increased this parameter to produce an increase in the periodicity similar to the MPT. The reason why a positive feedback induces longer cycles in two such different models is that it brings the system further out of equilibrium. This increases the amplitude of the cycles, which in turn implies an increase in the average duration of the cycles due to the sawtooth geometry (Omta et al. That said, our conclusions about the potential role of a positive feedback in generating the MPT are likely not dependent on the specific feedback mechanism. For example, Verbitsky et al.  also fouSimilar to Nyman and Ditlevsen , we modeitlevsen  is an inWith regard to the results, a key difference between our simulations and Nyman and Ditlevsen  is the tThere has been a long-running debate about the relative importance of precession and obliquity in forcing the glacial–interglacial cycles. According to classical Milankovitch  theory, The Nyman and Ditlevsen  model shThe possibility of a delay between a parameter change and the resulting periodicity shift suggests that the fundamental change in the Earth system giving rise to the MPT may have occurred a significant time before the observed periodicity shift. Therefore, we believe that investigations into the cause of the MPT should not be limited to co-occurring changes in the system. Rather, changes that occurred a significant time before the MPT may also be considered. In particular, the strong increase in peak Northern hemisphere ice volume and surface area during the early Pleistocene could be of interest.


The mobile node location method can find unknown nodes in real time and capture the movement trajectory of unknown nodes in time, which has attracted more and more attention from researchers. Due to their advantages of simplicity and efficiency, intelligent optimization algorithms are receiving increasing attention. Compared with other algorithms, the black hole algorithm has fewer parameters and a simple structure, which is more suitable for node location in wireless sensor networks. To address the problems of weak merit-seeking ability and slow convergence of the black hole algorithm, this paper proposed an opposition-based learning black hole (OBH) algorithm and utilized it to improve the accuracy of the mobile wireless sensor network (MWSN) localization. To verify the performance of the proposed algorithm, this paper tests it on the CEC2013 test function set. The results indicate that among the several algorithms tested, the OBH algorithm performed the best. In this paper, several optimization algorithms are applied to the Monte Carlo localization algorithm, and the experimental results show that the OBH algorithm can achieve the best optimization effect in advance. The wireless sensor network (WSN) is a distributed sensor network in which the number of nodes can reach hundreds or thousands . DiffereThere are many algorithms to realize an unknown node location in WSN, such as the DV-Hop algorithm, the APIT algorithm, and the centroid algorithm. The DV-Hop algorithm was proposed by Niculescu et al. . The maiWith the gradual maturity of mobile terminal and mobile internet technology, the localization of mobile wireless sensor networks (MWSN) has become a new trend of current wireless sensor networks and a hot research field of WSN . The mosThe swarm intelligence algorithm  simulateMetaheuristic search algorithms  are diviMobile node localization problems usually involve searching for the location of object nodes in complex spaces, such as locating the location of moving objects in three-dimensional space. The search space can be very large and complex, and traditional exact search methods are often not suitable. The metaheuristic search algorithm can efficiently search in the complex search space by simulating the optimization process in nature. Mobile node localization problems are usually performed in dynamic environments, where the location of the target node may change with time and other factors. Metaheuristic search algorithms are usually adaptive and can adjust search strategies in real time in dynamic environments to adapt to changes in target locations. Metaheuristic search algorithms are generally robust and adaptable and can cope with various uncertainties and noises. In the mobile node localization problem due to the uncertainty of the environment and nodes, such as noise, sensor error, communication interruption, etc., metaheuristic search algorithms can usually find better solutions in these uncertainties.Heuristic algorithms usually search in the search space through the population to replace the solution process of the problem to be optimized. Individuals in the population represent candidate solutions to the problem to be optimized, and the performance of candidate solutions corresponds to fitness. Almost all heuristic algorithms simulate the behavior patterns of creatures in nature or this natural phenomenon. The main idea of the black hole algorithm is to find the optimal solution of the problem to be optimized in the search space by simulating the black hole to attract the moving side of stars.In this paper, we combine the BH algorithm and MCL algorithm to localize mobile nodes in 3D WSN. The principle of the BH algorithm is simple, and there are few parameters. Using it to optimize the positioning of wireless sensor networks will not cause a large burden on its memory. It is precisely because the BH algorithm only simulates the phenomenon that the black hole attracts stars to move and does not balance the exploration and development stages of the algorithm, resulting in weak optimization ability and slow convergence speed of the algorithm. In order to overcome the defect of BH algorithm, we propose an opposition-based learning black hole (OBH) algorithm. According to the evolution degree of the population, OBH divides the population’s evolution into four stages. It applies different opposite strategies to the population at different evolution stages. At the same time, this paper uses an adaptive strategy  to deterThis section describes the organizational structure of the article. The MCL  algorithThe localization of sensor nodes in MWSN differs significantly from that of mobile robots. First, the active terrain of the robot is known, while the sensor nodes work in the unknown terrain. Secondly, the robot can control its motion posture very well. The speed and direction of motion are known. However, the sensor nodes rarely or almost never control their movement, so it is difficult to obtain the speed and direction of movement. The third difference is that the landmark information observed by the robot in the process of moving is accurate, which can effectively assist the current robot in locating the position. The sensor node only knows that the landmark information observed is within its radio range, and the specific location information cannot be known. Finally, the computing power of the robot is much higher than that of the sensor node. Because of the delay control of the sensor network, the sensor node cannot perform large-scale complex computing.Although the difference between the computing power and ranging accuracy of sensor nodes and robot localization makes the positioning of sensor nodes more complex, the network scale of wireless sensor network mobile node positioning is more significant. Many nodes can share each other’s location information, which is beneficial to the mobile positioning of sensor nodes.Algorithm 1 Monte Carlo localization algorithm1:Initialization: Initialize the wireless sensor network. N is the node’s number, 2:Step: According to the node position 3:while (size(N) do4:end whileIn the localization of MWSN, the node leaves the previous location to reach the current location. For the convenience of prediction, this paper assumes that the time is discrete, and the node needs to be located in each time unit. Because the direction and speed of node’s movement are unknown, the previous location information becomes more and more inaccurate after the node moves. On the other hand, the observation value from the anchor node in the sensor network can help us filter some false predicted locations. The samples are independent of each other, and the weight of the samples is 0 or 1. Algorithm 1 shows the pseudocode of MCL.t; t; and t and then filter the impossible location according to N samples N samples Equation . p do3:    Calculate the fitness of the population on the test function set4:    Select black hole individuals according to fitness5:    Move individuals in the population according to the Equation 6:    If the fitness of individual after moving is better than that of the black hole, it will become a new generation of black holes7:    The star entering the radius of the black hole is swallowed by it, and the algorithm will randomly generate a new star.8:    t = t + 19:end whileA pseudocode of the BH algorithm is shown in Algorithm 2, which shows that the BH algorithm has a simple process and few parameters, which is more suitable for wireless sensor network localization applications.The OBL strategy  is to imx as an individual in the population. Assume that the upper and lower bounds of x are a and b, respectively. The reflective opposition of x is as follows:Define x, a, and b is shown in the The relationship between x, namely, x), x), and x), which are calculated by the following formula:Divide the interval in x on the interval Further observation of In the opposition strategy, parameter The evolution process of the population can be divided into four states, namely, exploration , exploitSince the population is divided into four states, determining the state of the population becomes very important. Obviously, the average distance between individuals in a population is a good criterion for judging the state. The average distance between all individuals and the D represents the dimension that the individual has, and K represents a certain dimension of the individual. The average distance between the globally optimal individual and the other individuals is the smallest under the convergence state because individuals in the population only surround the global optimal individual. The average distance is the largest when jumping out because the global optimal individual may be far away from other individuals in the population. This paper lets f judging the population state:Equations –16) des des16) df is at a significant value. As the iteration progresses, the population enters the exploitation stage, and f starts to decrease gradually until the population enters the convergence state, and f also reaches the minimum value. Once the algorithm finds a better individual in another location, the population enters the jumping state, and f increases sharply until the population enters the convergence state again. Many test results have proved a specific range of intersection between each interval. f describes the state of the population.During the iteration, the population is in the exploration stage, and f is currently in the crossing interval of f and then adopting different strategies for the population is also called an adaptive strategy.The transition rule between states is When the algorithm encounters a deceptive location, the global optimal individual will always hover at that location, making the algorithm always explore a worthless area, wasting much fitness evaluation times. In order to make the OBH algorithm take advantage of the optimization opportunities as much as possible and avoid the endless exploration and development in the worthless areas, this paper will use Levy flight to accelerate the particles to jump out of the local optimal. Levy flight is a unique random walk, meaning an individual can advance any distance. It can be seen that the Levy flight has a significant probability of being of a large step size. When an individual falls into a local optimum, the Levy flight can be used to let the individual jump out of the current position and find a new optimal position through a large step size. Moreover, the Levy flight not only helps individuals jump out of the local optimum but also allows individuals to move forward at a significant pace in the exploration stage and to find promising areas in the whole search space as soon as possible after exploration.In order to avoid the profound negative impact on the population caused by the elite individuals trapped in the local optimal, this paper introduces several elite individuals to the OBH algorithm. At the same time, we found that the BH algorithm did not fully use the achievements of previous generations of individuals in the search space, so we introduced the inertia weight k elite individuals in the population. In order to perform reverse operations on the remaining individuals, it is necessary to calculate the evolutionary state of the current population. Finally, according to Algorithm 3 OBH algorithm.1:Initialization: D, k2:while (t < MaxGeneration) do3:for do    4:        Calculate the fitness of the population on the test function set5:        Select black hole individuals according to fitness6:        Update the population location according to the Equation 7:        If the performance of an individual after moving is better than that of a black hole, it will become a new generation of black holes8:end for    9:k individuals    Sort the population after one iteration and keep the top 10:    Calculate the average distance according to the Equation 11:f according to the Equation  ,39, the On the 28 test functions of the CEC2013, the OBH algorithm outperformed BA on 21 functions and BWO on 27 test functions, and CLPSO outperformed OBH on only 10 test functions, but on the remaining 14 functions, CLPSO performed worse than the OBH algorithm. Compared with the FMO algorithm, the OBH algorithm performs better on 18 functions. The OBH algorithm performs better than SO on 17 functions and is inferior to SO on only ten.The OBH algorithm performs better than many excellent swarm intelligence algorithms, and the advantages of the OBL strategy will be further described in combination with the fitness curve.We selects nine functions in the test function set to demonstrate the convergence of the algorithm in This section applies the OBH algorithm to MCL and replaces the general algorithm in To further verify the performance of the OBH algorithm, the deployment area of the 3D experiment is further expanded to 400 m × 400 m × 400 m. As seen from The average positioning accuracy of seven algorithms optimizing MCL are shown in When the increase in the deployment area leads to a decrease in the density of anchor nodes, the available information transmitted by the anchor nodes in the network is very small, and OBH can use this small amount of useful information to be optimized in the search space. It can be seen that the approximate position of the unknown node obtained by MCL positioning is passed to seven optimization algorithms for optimization, and OBH can perform the best solution in the search space.The BH algorithm has a simple structure and fewer parameters, making it more suitable for wireless sensor network localization with limited memory and computing power. However, the traditional BH algorithm performs generally and cannot stand out among many swarm intelligence algorithms. In this paper, we combine the OBL strategy and BH algorithm, and the OBH algorithm is proposed.The OBH algorithm reduces the number of duplicate individuals as much as possible based on preserving the dominant individuals, fully uses the current population information, and avoids wasting valuable fitness evaluation time. At the same time, an adaptive strategy can accurately judge the evolution state of the population, formulate the best OBL strategy for the algorithm, and significantly improve the performance of the algorithm. To verify the improvement in the OBH algorithm, this paper compares five excellent swarm intelligence algorithms with OBH, and the results show that the OBH algorithm performs best among the six algorithms. Finally, this paper applies the OBH and the other six algorithms to MCL. The simulation results show that the MCL positioning accuracy optimized by OBH is the highest, which indicates that the performance of the OBH algorithm is first class.Compared with the BH algorithm, the performance improvement in the OBH algorithm is very obvious, but it comes at a price. At each iteration, the algorithm calculates the evolutionary state of the population and operates oppositely, which increases the runtime of the algorithm. In a certain period of time, there are populations and opposite populations in the algorithm at the same time, which also increases the demand for memory resources from the sensor nodes to a certain extent.It is inevitable that the opposite operation will increase the runtime of the algorithm, but we can reduce the memory resource requirements of the algorithm through the compact strategy. The compact strategy uses the probability distribution to simulate the population, so the algorithm only needs to maintain the parameters of the probability distribution, and the updating of the parameters replaces the updating of the population, which will greatly reduce the memory requirements of the algorithm. Therefore, if we want to reduce the burden of sensor node memory, using the compact strategy to improve will be the focus of future work.


We derive expressions for the evolution of the thickness of the condensation layer, and its impact on cough frequency, inflammatory marker secretion, cilia beat frequency and respiratory droplet generation. We compare our predictions with human clinical data from multiple published sources and highlight the damaging impact of mouth breathing, dry, dirty air and high minute volume on upper airway function. We predict the hypertonic (or hypotonic) saline mass required to reduce (or amplify) dysfunction by restoration (or deterioration) of the structure of ciliated and condensation water layers in the upper airways and compare these predictions with published human clinical data. Preserving water balance in the upper airways appears critical in light of contemporary respiratory health challenges posed by the breathing of dirty and dry air.Respiratory disease and breathing abnormalities worsen with dehydration of the upper airways. We find that humidification of inhaled air occurs by evaporation of water over mucus lining the upper airways in such a way as to deliver an osmotic force on mucus, displacing it towards the epithelium. This displacement thins the periciliary layer of water beneath mucus while thickening topical water that is partially condensed from humid air on exhalation. With the rapid mouth breathing of dry air, this condensation layer, not previously reported while common to transpiring hydrogels in nature, can deliver an osmotic compressive force of up to around 100 cm H The results of our research are reported here – along with a reflection on the implication of these results to recent discoveries of the nano- and micro-structural nature of respiratory gas and water exchange.We explored airway fluid structure and function in healthy human airways during normal tidal breathing and sustained strenuous exercise [high minute volume (100 l min*C:Π) created by the difference between Eqs. , notably  and even recede into the mucus, drying out mucus.Evaporation from the airways during normal tidal breathing promotes osmotic movement of water through the ALF towards the air surface by way of an imbalance of osmolytic solutes including deposited particles and salt ions  above and below the mucus layer. We find that this imbalance can be expressedC*:2)C*:(1)et al., DM with hypertonic (or hypotonic) salt ion concentration DC may raise (or lower) the tonicity of the ALF sufficiently to hydrate (or dehydrate) the PCL by osmotic water flux from epithelial cells. This mass can be estimated by a simple mass balance. With uniform deposition of a mass of droplets DM in the upper airways (nose and trachea), the osmotic displacement of the mucus osmd in the direction of the airway lumen can be approximated for salt concentrations up to ~10% tonicity and after many breaths on time average by Π) pressing down on the PCL reduces cilia motility  by a linear relationship between the secreted biomarker (B) and the osmotic force or mucus displacement distance . Here, Bα is a dimensional airway constant (cm2 mg−1) that can be directly determined as described below from published data of ATP secretion following the compression of ciliated epithelial cells in vitro .PCL thickness can be restored (or further thinned) by deposition of hypertonic (or hypotonic) saline on the surface of the ALF. Unlike the case of isotonic saline, for which deposition on the surface of ALF increases the condensation layer thickness without increasing PCL thickness and, therefore, is incapable of modulating dysfunction , moderate (T = 2 s) and slow (T = 5 s) breaths. Assuming a 1-s transition from inhalation to exhalation, these cases correspond to a range of 20 breaths per minute (T = 1 s) to 5–6 breaths per minute (T = 5 s). We also considered the case of mouth breathing during strenuous exercise . The results of our analysis are summarised in Supplementary Material).We sought to determine whether the enhancement of ATP [approximated by −1 and 100 μm s−1  , the thickening of the condensation layer reaches around 0.7 μm, which is equivalent to the distance of displacement of the mucus membrane towards the epithelium , the consequence of water evaporation from the upper ALF a is to sithelium . The salithelium b in all  et al., . In the  et al., a, and ineQ or ventilation rate. Cough reflex in asthmatics has also been shown to increase in a linear fashion with airway ATP levels  following compression (20-cm H2O) of cilia beneath a mucus mimetic gel  (coughs per minute) and mucus displacement [see et al., eQ (mg s−1), condensation factor χ (dimensionless) and inhalation time T (s):et al. , with the totality of coughs assumed to have occurred within 1 min post challenge. Cough incidence grows linearly as ATP levels grow  groups. Nasal CBF diminishes on exercise with dehydration within the range of the predications based on moderate (intermediate to slow and fast) tidal breathing rate. In the Cambridge study  amounting to an estimated 3 mg deposition in the larynx and trachea based on a mass-median droplet diameter of around 10 μm   through a semi-permeable membrane (the mucus and airway epithelium in our model) . We assume warm ambient air at 30°C. We assumed the gradient of temperature from the outside air to the carina to be such that outside ambient temperature exists up to the carina at which point the air temperature rises to 35°C. This gradient is approximately as has been observed in thermal mapping studies , trachea (and larynx) and bronchi (and bronchioles) and used upper airways dimensions as reported in the literature for human airways, whereas from the carina to the small airways, we assumed Weibel lung geometry , we assumed the ALF to be essentially flat and of ‘infinite’ lateral dimension, with the principal physics of water and ion transport occurring in one dimension . Fully h2 surface area), we assume relatively quiescent conditions over the majority of ALF surface area within the nose (approximately 160 cm2) over the course of inhalation on normal tidal breathing. Principal air velocity in the trachea (approximately 12-cm length from the larynx to the carina) being driven by the jet of air that emerges from the larynx , we assume an average velocity on inhalation in the trachea of around 1 m s−1. Finally, we assumed salt concentrations in hydrated ALF are approximately equivalent to blood concentrations, such that in the reference state (C0), osmolarity equilibrium has been obtained between the airways and surrounding epithelial cells and vascularised tissues. As principal air flow in the nasal cavity  occurs in the narrow air passage of the middle or inferior meatus . Each pore is identical to the other, and of an effective diameter deduced from the model by comparison of predictions with reports of experimentally measured ALF permeability values. The model shared in the Supplementary Material explicitly considers transport of salt ions together with deposited airborne particles. The model demonstrates that while restricted motion is far greater for nanoparticle than for salt diffusion within mucus, the high concentration of salts renders the net osmotic pressure by salt ions much greater than that of inhaled particles at least in conditions where cilia continue to beat. We speculate on the possibility of diminished water permeability within mucus owing to the breathing of dirty air and the roles this diminished permeation might have in the phenomena described in Supplementary Material for permeability, reflection coefficient and other transport characteristics.The pore-level model of transport in the mucus hydrogel summarised in the Table S1 in the Supplementary Material for a summary of central airway Weibel geometry), and we determined the unknown variable needed for the determination of the dysfunction parameters appearing Supplementary Material.We determined the values of the model parameters in  Comments to Author: I have examined with great interest the manuscript, “Breathing dry air promotes inflammation, activates neural pathways and disrupts clearance by osmotic stresses imparted on airway epithelia” because it claims to explain the rise of respiratory diseases which the authors attribute to climate change. This is attributed to chronic dehydration of the airways. To me, this is a bold claim. I do not find it supported by the evidence presented.So, let’s turn to what is evidence is presented. It is found that water evaporation from the upper airways delivers an osmotic force on airway mucus that drives it toward the epithelium with increasing amount as the dryness of inhaled air increases. That part of the manuscript seems valid and supported. The connection of air dryness with climate change is suspected in general but not established. That respiratory disease and breathing abnormalities have been increasing seems a fact but attribute this solely to climate change strikes me as not supportable. Humans spend so much time indoors rather than outdoors and the air indoors is not controlled simply by climate change, so I am reluctant to recommend publication of this manuscript in its present form. Comments to Author: The authors seem unaware of the existenceof the endothelial surface layer or of the glycocalyx or of their micro/nanostructure (references enclosed) .Essential for their problem seems to be the critical salt concentration for bubble-bubble (and nanobubble) fusion inhibition, in nanobubble stability and that gas transfer occurs viananobubbles of (N2/O2)and (CO2 /H2O) and that the structure of lung surfactants and the interaction of viruses and other pathogens are important.A number of their issues may go away or resolved if the authors take into account the effects of these things. For example, the cystic fibrosis discussion and that about their reference 68.Reviewer #1: I have examined with great interest the manuscript, “Breathing dry air promotes inflammation, activates neural pathways and disrupts clearance by osmotic stresses imparted on airway epithelia” because it claims to explain the rise of respiratory diseases which the authors attribute to climate change. This is attributed to chronic dehydration of the airways. To me, this is a bold claim. I do not find it supported by the evidence presented.So, let’s turn to what is evidence is presented. It is found that water evaporation from the upper airways delivers an osmotic force on airway mucus that drives it toward the epithelium with increasing amount as the dryness of inhaled air increases. That part of the manuscript seems valid and supported. The connection of air dryness with climate change is suspected in general but not established. That respiratory disease and breathing abnormalities have been increasing seems a fact but attribute this solely to climate change strikes me as not supportable. Humans spend so much time indoors rather than outdoors and the air indoors is not controlled simply by climate change, so I am reluctant to recommend publication of this manuscript in its present form. No accompanying comment.


Due to its importance in airborne disease transmission, especially because of the COVID-19 pandemic, much attention has recently been devoted by the scientific community to the analysis of dispersion of particle-laden air clouds ejected by humans during different respiratory activities. In spite of that, a lack of knowledge is still present particularly with regard to the velocity of the emitted particles, which could differ considerably from that of the air phase. The velocity of the particles is also expected to vary with their size. In this work, simultaneous measurements of size and velocity of particles emitted by humans while speaking have been performed by means of Interferometric Laser Imaging Droplet Sizing (ILIDS). This technique allowed us to detect emitted particles with size down to 2 µm as well as to quantify all three components of the velocity vector and the particle concentration. The outcomes of this work may be used as boundary conditions for numerical simulations of infected respiratory cloud transmission. The particle-laden air cloud ejected by humans during different respiratory activities has drawn the attention of the scientific community since the first half of the twentieth century as it is involved in airborne disease transmission. This problem has become of major importance in the past 2 years due to the COVID-19 pandemic. Even though numerous experiments and numerical models have recently been carried out to assess the dynamics of dispersed cloud ejection . To apply ILIDS to respiratory droplets and recognize particles with very small diameter, a large aperture optic, free from spherical aberration, must be designed. Finally, the estimation of the measurement volume and the related particle concentration is not an easy task using ILIDS in that it is not possible to fix the size of the measurement volume a priori. For this reason, the measurement volume and its variation with the particle size have been estimated in the present work based on droplet location along the direction normal to the laser sheet.To provide an experimental characterization of the particles ejected by humans during different respiratory activities—namely measuring the three velocity components and size of the particles—we adopt here the ILIDS technique, which has so far never been used for this purpose. ILIDS is an interferometric technique based on a laser sheet illumination and an out-of-focus image recording. It was originally developed for liquid spray by Glover et al.  based onThe paper is organized as follows: Section The ILIDS technique is based on the light scattering properties of transparent particles. As shown in Fig. mentclass2pt{minimd, can be determined in the scattering diagram from the angular spacing of the fringes, N and and R are the fringe number and the circle radius in out-of-focus image, respectively, while x, z) (S-polarization) to maximize the fringe contrast for the smallest droplets. Figure As mentioned in the former Section, the droplet diameter, entclass1pt{minimaentclass1pt{miniman. It also varies weakly with the collection angle  and vertical (z) coordinates are evaluated from the circle center displacement in the sensor plane, while the streamwise coordinate  is deduced from the circle size variation.As mentioned earlier, the setup used in this work allows us to measure all three components of the particle velocity vector. These are determined from the particle coordinate changes between two images recorded with time delay z-axis (or y-axis). The lens assembly is composed of two perfect thin lenses having the same focal length f and spaced at a distance e  is never perfectly sharp, so that the identification of the laser sheet edges is not trivial. Moreover, dealing with a large size distribution, the effective measurement volume actually depends on the particle size  is not constant along the laser sheet thickness, but it is rather characterized by a smooth Gaussian-like shape. The measurement volume decreases with the particle size since smaller particles can be detected only at the center of the laser sheet, where the light intensity is sufficiently high. Conversely, the largest particles can be detected even in the edges of the laser sheet, where the light intensity is smaller, leading to a greater measurement volume. Note however that the largest particles located in the center of the laser sheet may lead to sensor saturation. This would prevent fringe frequency measurement, therefore leading to a measurement volume split into two parts. Besides, one should also consider the variation with x of the circle radius in the out-of-focus image. For smaller circle radii, the same amount of energy collected by the lenses is contained in a smaller area (circular surface in the out-of-focus image). Therefore, the minimum laser light intensity for which a particle of a given size can be detected is lower when the particle is positioned further away from the lenses, i.e., when the circle radius in the image is smaller.ILIDS is based on a laser light sheet illumination that is supposed to delimit the measurement volume. However, the intensity of the laser sheet profile ize Fig. . Therefoa posteriori considering the actual x-coordinate variation observed for all the detected particles in a particle size class, d, through its standard deviation, d is then simply estimated as follows:S is the FOV area.The most reliable way to quantify the measurement volume for each particle size class is to deduce it s et al. . The meaTo measure size and velocity of the particles ejected while speaking, twenty volunteers have been recruited to speak following the same protocol. To simulate the speech, they counted ten times from “one” to “one hundred.”2A double pulse Nd:YAG laser  was synchronized with a double frame camera  by using a programmable timing unit. The acquisition frequency was set to 15 Hz . The time delay between two consecutive frames, A mask was used to allow volunteers to place their mouth close to the optical axis Fig. . The masSeveral calibrations are required to consider the deformations due to comatic aberrations and to calculate the two coefficients As described in Sects. Similar images of a point light source at different positions are used to estimate The proportionality between  see Eq.  has beenThe data consisted of A background image is calculated for each test. It consists of the minimum intensity value for each pixel over all the images. The background image is subtracted to each image of the set.Each image is deformed in order to compensate the aberrations as described in Sect. In the third step, all particles—both liquid and solid—are detected by means of a convolutive approach. A Gaussian filter is applied to filter out the interference patterns within the circles. The gradient of the image is then calculated, exhibiting the circle edges, and convoluted by synthetic ring images of different sizes to detect the circles and to measure their position and radius. The detected particles are removed from the image, and new particles are identified, until the correlation peak is above a fixed threshold. At the end of this step, radius and position of all detected particles are known.k are known).In the fourth step, the interference pattern within the circles is analyzed and the fringe frequency is measured. When the circles overlap, only the non-overlapped part of them is analyzed. It is worth noting here that solid particles are easily recognizable (and therefore rejectable) in that they do not show regular horizontal fringes. This is a strong point of ILIDS technique applied to droplet recognition as it makes unnecessary to filter out ambient air to remove dust. The size of the liquid particles is then calculated by means of Eq. Particle size and position and circle radius are known at the end of the fourth step. Then, the three components of the particle velocity can be calculated by means of Eqs. Once repeated the four steps for all the images, size and velocity distributions can be built. The measurement volume for each particle size class, and therefore the particle concentration, can be estimated from Eq. In order to show the potential of the ILIDS technique employed in this paper, some preliminary results concerning the speaking activity are presented.3. As expected, the measured laser light intensity profile shows an almost Gaussian shape  for the largest particles, probably due to their settling.To build the joint pdf maps, five size classes have been considered in order to have robust statistics for each size class. All three velocity components depend on the particle size. In particular, the normal-to-the-mouth velocity component, y and z is −1, corresponding to a displacement of 0.5 pixel in 700 µs. The minimum velocity detectable along the x-direction is slightly higher, −1 . The maximal detectable particle velocity is 7 ms−1. However, the maximum −1 and 2.5 ms−1, respectively. The maximal values of x-particle detection range within the thickness of the laser sheet. The latter is, indeed, estimated by measuring the standard deviation of x, but some particles could be detected at an x-position which exceeds the Note that the theoretical minimum detectable value of the velocity components along −1 for the smallest and the largest particles, respectively. For comparison, the mean particle velocity measured by Wang et al.  are shown in Fig. Particle direction can be determined once the three velocity components are known. The ratios between the velocity components, The droplet sizes are determined from the image circle radius and the fringes frequency measurements. The uncertainty on image radius is estimated to be 1-pixel. Given that the circles radius are of order 400 pixels, the relative uncertainty in droplet diameter is only 0.25%. The fringe frequency measurement relies on a sub-pixel determination. Considering an uncertainty of 0.5 pixel (probably overestimated), the resulting uncertainty depends on the fringe frequency itself and decreases linearly with the droplet diameter. For a 2 µm droplet, this relative uncertainty is about 15%, and it decreases to 1.5% for a 20 µm droplet. The droplet velocity in the x-direction is also deduced from the image circle radius in two consecutive images. Assuming a 1-pixel uncertainty on the image circle radius variation and given the 700 µs time lag between two frames, the relative uncertainty on the x-velocity is about 0.02 m/s . Velocities in the y- and z-direction are determined from the displacement of the image circle center. These locations are determined by detecting a sub-pixel maximum in a convolution map. Assuming a 0.5 pixel uncertainty, the uncertainty on z- and y-velocity is of order 0.005 m/s . Note that the uncertainties on velocity measurement can be easily reduced by a factor 2 or 4 by increasing the time lag between the frames by the same factor. Other factors that could potentially increase the measurement uncertainty are related to (i) the presence of droplet images not perfectly circular after image deformation, (ii) image circles partly cut at the edge of the image or (iii) background noise. These uncertainties are more difficult to assess individually. However, a global estimate of the droplet sizing uncertainty can be provided by the average difference between the droplet size measured in the two consecutive frames (as the same size should be measured for the same particle detected in the two frames). On average, the variation of the droplet size between the two frames,  is about 4%; considering each size class individually, a maximum variation of 8% is observed for droplet size in the range 20–24 µm.In this work, the Interferometric Laser Imaging Droplet Sizing (ILIDS) technique has been employed to determine size and velocity of particles emitted by humans while speaking. ILIDS made it possible to overcome some of the problems encountered in previous works, i.e., i. it is effective in measuring low particle concentrations, as in the case of humans’ emission; ii. it allows data collection close to the emission point and thus, it minimizes the effect of both dilution and evaporation; and iii solid irregular particles are easily recognized, so that the measures are not affected by dusts naturally present in the air (filtered-air chambers are not needed for the experiments). d = 2 µm and all three components of the particle velocity vector have been measured simultaneously. Besides, the variation of the measurement volume with particle size has been taken into account, making its estimation more reliable than that obtainable using more common measurement techniques based on light sheet illumination.Several improvements have been introduced over standard ILIDS in order to widen as much as possible the range of measurable diameters, in particular the smallest ones. In this way, particle diameters down to3 going from d = 2 to 10 µm; for bigger particles, it remains nearly constant.The measurement volume increases linearly from 0.2 to 0.4 cmThe particle size distribution—expressed as particle number concentration—shows that most of the detected particles lie in the range 2–4 µm in diameter; a relative maximum of particle number concentration occurs at The agreement between our data with the APS measurements carried out by Johnson et al.  via Dropn et al.  and by Dn et al.  are obse−1 for The joint probability density functions of particle diameter and velocity components show a clear dependence of the normal-to-the-mouth velocity component on the size, e.g., The emission of the particles from the mouth is far from being unidirectional.In spite of all its merits, the ILIDS technique has its drawbacks. For example, the size range of the ejected particles is not completely covered as particles smaller than 2 µm cannot be recognized. Some problems occur also for the larger particles, whose scattering diagram may differ from that expected theoretically due to possible inclusions of air (or other substances) or to their not perfectly spherical shape. Another limitation of ILIDS consists in the small field of view area needed to detect the smallest particles. Long measuring time is thus required in order to have robust statistics. The last aspect to be considered is that ILIDS does not work well in case of high droplet concentrations, which would lead to a more likely overlapping of their out-of-focus images. The overlapping of droplet (or irregular particles) images is considered by limiting the fringe analysis to the non-overlapping part of the images, but for images that overlap almost completely, the fringe analysis becomes impossible. In the case of speaking or breathing activities, the droplet concentrations are relatively low, so that droplet image overlapping occurs rarely and is easily managed. In case of coughing instead, the number of droplet images overlapping increases due to higher droplet concentration. Preliminary tests show that overlapping is still manageable, without changing the optical setup. In the case of sneezing, however, we estimate that the higher droplet concentration and the larger droplet sizes would require some adaptations of the setup, to reduce the laser sheet thickness, the out-of-focus level and possibly the collection angle. A development of the present work concerns the use of consolidated techniques and instruments such as FMPS (Fast Mobility Particle Sizer) and OPS , which could be employed to analyze the size range (but not the velocity) of particles not detectable with ILIDS. A partial superposition of the measured size range could be useful also to compare the results. Furthermore, the reliability of the technique to characterize other respiratory activities is worth to be evaluated.The main results that can be drawn from our experiments are:


Background: Theoretical studies of superradiant lasing on optical clock transitions predict a superb frequency accuracy and precision closely tied to the bare atomic linewidth. Such a superradiant laser is also robust against cavity fluctuations when the spectral width of the lasing mode is much larger than that of the atomic medium. Recent predictions suggest that this unique feature persists even for a hot and thus strongly broadened ensemble, provided the effective atom number is large enough.Methods: Here we use a second-order cumulant expansion approach to study the power, linewidth and lineshifts of such a superradiant laser as a function of the inhomogeneous width of the ensemble including variations of the spatial atom-field coupling within the resonator.Results: We present conditions on the atom numbers, the pump and coupling strengths required to reach the buildup of collective atomic coherence as well as scaling and limitations for the achievable laser linewidth.Conclusions: We show how sufficiently large numbers of atoms subject to strong optical pumping can induce synchronization of the atomic dipoles over a large bandwidth. This generates collective stimulated emission of light into the cavity mode leading to narrow-band laser emission at the average of the atomic frequency distribution. The linewidth is orders of magnitudes smaller than that of the cavity as well as the inhomogeneous gain broadening and exhibits reduced sensitivity to cavity frequency noise. Even very recently a large number of theoretical and experimental studies focused on continuous superradiance, aiming at the development of a superradiant laser. Such a superradiant laser typically operates in a bad-cavity regime, where the cavity mode is much broader than the natural linewidth of the atoms providing the gain. In the limit of low photon number operation the coherence necessary for frequency stability is stored in the atoms rather than the cavity field. This makes the laser frequency insensitive to thermal and mechanical fluctuations of the cavity, which is the main limitation for conventional good-cavity lasers. In recent years pulsed superradiance has been experimentally demonstrated and a number of new theoretical ideas have been proposed. However, the experimental realization of a continuous wave superradiant laser has not yet been achieved.Collective stimulated emission of coherent light by atoms inside an optical cavity is a fundamental phenomenon studied for decades in quantum opticsEffects such as frequency broadening in the gain medium are an inherent part of any experiment. Such processes are capable of disrupting the collective interaction between the atoms and the cavity field. In this work, we aim to offer a comprehensive study of these potentially detrimental effects. To this end, we study a model of a superradiant laser and focus on inhomogeneity among the atomic ensemble. The inhomogeneity is primarily associated with a distribution of the atomic resonance frequencies leading to stimulated emission into the cavity at a range of different frequencies. Similar differences in the atom-field coupling due to variation in the atomic positioning are also included in the system.We numerically investigate the dynamics of an atomic medium with a wide range of resonance frequencies and show how the intensity of the pumping rate can lead to cooperative effects among the atoms such that superradiant lasing is achieved. Furthermore, we consider atoms to have different coupling strengths to the cavity. We also study the laser sensitivity to cavity noise.N incoherently pumped two-level atoms inside a single mode optical cavity as shown inκ ≫ Γ), the system constitutes a generic model of a superradiant laser. Thei-th atom couples to the cavity field with the coupling strengthig and has a resonance frequencyiω which might be shifted from the unperturbed atomic transition frequencyωa. Assuming that the cavity is on resonance with the unperturbed atomic transition frequency, we describe the coherent dynamics of the system by the Tavis-Cummings Hamiltonian in the rotating frame of the cavity,We consider an ensemble ofi =cω −iω,† = |e〉i〈g|i denote the raising and lowering operators of thei-th atom, where |g〉 and |e〉 are the atomic ground and excited states, respectively, anda† (a) is the photon creation (annihilation) operator of the cavity mode. The dissipative processes of this system are described by the Liouvillian termsHere, Δκ, the spontaneous atomic decay with the single-atom spontaneous emission rate Γ, and the individual incoherent pumping with the pump strengthR. Thus, the full dynamics of the system is determined by the master equation for the density matrixρ in standard Lindblad formrepresenting the loss of photons through the cavity at the rateN ≫ 1, we use a cumulant expansion method. First, we write down the equations for operator averages describing our system, which for a given operatorreadsSince the exponential growth of the Hilbert space with the number of atoms renders the solution of the masterc]= (2c†c –c†c–c†c)/2. We note that in some cases (mentioned in the description of the results) we additionally include cavity dephasing and atomic dephasing described by the termsξ 〈[a†a]〉 andwhere. Note that this is equivalent toM = 5 frequency clusters each containing a single atom. At low excitation the resulting cavity output spectrum then consists of precisely five spectral lines at the frequency of each cluster. Basically, these are five independent lasers using the same cavity mode simultaneously. If we increaseN and set the number of atoms per cluster according to a Gaussian normal distribution with the standard deviationσ =κ, the structure of the spectrum inM = 201 until the output merges into a single broad emission line. Note that an increase of the collective coupling toFirst, we simulateSo far we limited investigations to weak incoherent pumping in order to avoid significant additional broadening of the atomic linewidth due to pumping. However, this broadening effect can actually aid the buildup of coherences between the clusters. When the pumping is strong enough such that the distinct spectral lines overlap, the discrete spectral lines of the clusters merge into a single central peak see. In othecR. This critical value strongly depends on the overall width of the frequency distribution, but shows almost no dependence on the number of subensemblesM and the total number of atomsN. The critical transition pump strength is shown for different standard deviationsσ of the atomic frequency distribution inN = 102 (red dots) andN = 104 (blue circles) atoms sampled byM = 31 clusters. For comparison, we also plot the linear (solid line) functionRc = 0.4σ. We calculate the critical pumping by computing the spectrum for differentR. We then determine the critical value of the pump strength as the value at which the spectrum has only a single local maximum, i.e. all separate peaks have merged into a single spectral line. We find a linear dependence for large inhomogeneously broadened ensembles while for narrow ensembles a significantly lower pump strength is required.The collapse of the emission spectrum into a single central line occurs at a critical pump strengthσ : 3σ] and Γ ≤ 3σ ≤κ.σ as the number of atoms increases. Note that we chose a pumping strength well above the critical value for a wide atomic frequency distribution (red line). The sharp decrease of the linewidth is accompanied by an increase in the average photon number as can be seen inOnce the laser is operating at a single distinct emission frequency, we can characterize the properties of the output light by the linewidth and the average photon number. The results for different distributions of atomic frequencies are shown ing(x) =g0 cos(kx), whereg0 is the coupling constant,k = 2π/λ is the cavity mode wave number andx represents the position of an atom. In order to describe the atom-field dynamics we use a similar cluster approach as before. We assume equidistant positions for different clustersmx ∈ . On this simple example we would like to introduce our concept to the readers, which we use throughout the whole paper. We model the continuous frequency distribution with the standard deviation σ by choosing equidistant cluster frequencies, with the number of atoms per cluster given by the Gaussian distribution with the standard deviationσ. We have slightly changed the text in order to make it straightforward. Here the Gaussian distribution is related to Figure 4(a)  in the original version), where we consider only five frequency clustersIn Fig. 4 perhaps it should be stated that what is shown is the normalized intensity (or max intensity is set to 1). The comment on this has been added to the figure caption.4 atoms. How does it change with the atom number? Is it approximately inversely proportional to N, for otherwise the same parameters?In Fig. 5, the critical value of the pumping rate vs inhomogeneous linewidth σ is shown for N=10N. For an arbitrary given number ofN the structure of the spectrum remains the same as in Fig. 5 . In a weak pumping regime, the number of atoms determines the linewidth of each individual line, while after merging it determines the linewidth of a single line. The critical value of pumping which distinguishes the discrete spectrum of clusters from a single line remains the same for anyN. In the revised version, we give a comparison of the results for2N=10 (red dots) and4N=10 (blue circles) atoms in Fig.6, which confirms our predictions. This result appears to be independent ofThe authors mention that inhomogeneous broadening of the atomic transition can originate from trapping within the cavity, motion, or optical pumping. It would be useful if the author could expand the discussion a bit and clarify these issues. Do they mean that, depending on the atom position in the trap, its transition frequency will be different? Or that atom motion leads to the Doppler frequency shift? How does optical pumping lead to different frequency shifts of different atoms? Here we mainly think of differential Stark shifts e.g. induced by an inhomogeneous trapping lattice or a pump laser with with a Gaussian profile. Actually several lasers are needed to implement an effective pump rate as we use here. We are currently quantitatively studying this effect in a separate effort, which we hope will be finished soon. Doppler shifts would have similar effects in ring cavities, whereas in a standing-wave cavity they would generate a time-dependent atom-field coupling which we do not consider here.The present manuscript did not explicitly consider high-density atomic ensembles, where the atomic collisions or dipole-dipole interactions would lead to increased coherence relaxation or collective broadening of the atomic transition. Would the authors be in a position to give some informed speculations as to whether the superradiant lasing with narrow line spectrum will still be possible in such situations, compensating thereby the detrimental broadening due to the interatomic interactions?et al. 2014 Optics express 22 (11), 13269-13279) and appear not too detrimental. Similarly, collisions could have even a positive effect for synchronization, but a quantitative guess is hard . We added those references and a comment. We are considering atoms at fixed positions here, so that direct collisions are left out. The effect of dipole-dipole interactions have been studied in a small scale, full quantum model before .   Superradiant lasing in inhomogeneously broadened ensembles with spatially varying coupling”, the authors numerically study superradiant lasing from an incoherently pumped two-level atomic ensemble coupled to a bad cavity. The authors employ second-order mean-field theory and investigate the effect of various noise sources, inhomogeneous broadening, and variable coupling strengths. After a brief introduction and description of the model, the authors describe the second-order cumulant expansion approach which is followed by the results for a single atomic ensemble in the absence of inhomogeneous broadening but with non-zero cavity and atomic dephasing. Finally, the authors introduce inhomogeneous broadening and variable light-matter coupling in their system and study the emission properties.In the paper “Since the manuscript emphasizes on various noise sources, I think it would be helpful to include a color plot for the linewidth of the emission where cavity and atomic dephasing is varied along x and y axis with other parameters remaining the same in Fig.2.  This would highlight the tolerance of the linewidth on the two noise sources. In addition, the two paragraphs above Fig. 2 where the authors describe the figures was a bit confusing to me, mostly because all the figures were not labelled (a)-(h) and all figures were not described. For example, the authors write- “In Figure 2(c), we scan the linewidth over the coupling strength g ….”, which is actually the lower panel of Fig. 2(c). So I would recommend that a proper labelling of all the figures would make it easy for the readers.Next, the authors introduce inhomogeneous broadening and show that the atoms synchronize beyond a critical pump strength and for a weak pumping the spectrum reveals a single broad peak for sufficiently large M. It would be interesting to know the cross correlations between atoms in different clusters (let’s say between cluster number 1 and 201) as a function of the pump strength. The correlations should be easily available from the second moment equations. I would expect the cross correlations to grow in the synchronized regime, but what about in the regime where the emission reveals a single broad spectrum. Can the authors comment on this?In Fig.4(c), the authors take into account overall atom-number fluctuations. Did the authors introduce another equation for the atom number like dN/dt which models the loss of atoms from the trap? It might be helpful for the readers to add a few lines about how this was done numerically.c= 0.4σ derived by fitting the data points? The authors may add a comment on that for clarity. The equation is independent of M, but what about N? Can the authors make an intuitive comment about it?Was the equation RThe authors model the inhomogeneous broadening and varying light-matter coupling with M=11 and K=5 clusters. Does this mean it is a 2D grid of 11 x 5 dimensions? I think the results are interesting and is of interest to both theoretical and experimental groups working on superradiant lasing using ultra-cold atoms. In addition, a detailed study of various noise sources and inhomogeneous light-matter coupling as considered in this manuscript was not taken into account in Ref. [11] and [31], so the manuscript definitely fills that gap. I have some minor comments which I believe will improve the clarity of the manuscript. ħ in Eq.1 is no longer present in any of the later equations.A minus sign is missing in Eq.4In Eq.8, the correlation terms with superscript “st” is not defined in the text.On page 6, first paragraph last line. I guess the authors meant gain “medium”. Few typographical errors-Is the study design appropriate and does the work have academic merit?YesIs the work clearly and accurately presented and does it cite the current literature?YesIf applicable, is the statistical analysis and its interpretation appropriate?Not applicableAre all the source data underlying the results available to ensure full reproducibility?YesAre the conclusions drawn adequately supported by the results?YesAre sufficient details of methods and analysis provided to allow replication by others?YesReviewer Expertise:Quantum opticsI confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. Since the manuscript emphasizes on various noise sources, I think it would be helpful to include a color plot for the linewidth of the emission where cavity and atomic dephasing is varied along x and y axis with other parameters remaining the same in Fig 2. This would highlight the tolerance of the linewidth on the two noise sources. Thank you for the valuable suggestion - in the revised version we have included an additional figure  illustrating the influence of both cavity and atomic dephasing on the linewidth.In addition, the two paragraphs above Fig. 2 where the authors describe the figures was a bit confusing to me, mostly because all the figures were not labelled (a)-(h) and all figures were not described. For example, the authors write- “In Figure 2(c), we scan the linewidth over the coupling strength g ….”, which is actually the lower panel of Fig. 2(c). So I would recommend that a proper labelling of all the figures would make it easy for the readers.2. We agree that the labels in Fig. 2 could be misleading. In the revised version, all plots in Fig. 2 are labeled (a)-(h).Next, the authors introduce inhomogeneous broadening and show that the atoms synchronize beyond a critical pump strength and for a weak pumping the spectrum reveals a single broad peak for sufficiently large M. It would be interesting to know the cross correlations between atoms in different clusters (let’s say between cluster number 1 and 201) as a function of the pump strength. The correlations should be easily available from the second moment equations. I would expect the cross correlations to grow in the synchronized regime, but what about in the regime where the emission reveals a single broad spectrum. Can the authors comment on this? This is indeed a question which was interesting to us as well. In the revised version, we decided to include an appendix regarding the cross-correlations between atoms in different clusters. We considered the cross-correlations between the first and the central clusters in Figure 5(a)  as a function of the pumping strength. In a weak pumping regime, the correlations are zero and grow with the pumping strength, as shown in Figure 9 in the appendix. The function reaches its maximal value when the ensemble is fully synchronized. However, as pumping continues to grow the correlations decrease due-to growing dephasing imposed by pumping.In Fig.4(c), the authors take into account overall atom-number fluctuations. Did the authors introduce another equation for the atom number like dN/dt which models the loss of atoms from the trap? It might be helpful for the readers to add a few lines about how this was done numerically. The total number of atoms always remains constant and equal to N, so there is no loss of atoms form the trap. The particle number fluctuations simply were added in the cluster's atom numbers as small random deviations from a Gaussian distribution in a way that keeps the total number of atoms constant. The comment on this has been added in the text.c=0.4σ derived by fitting the data points? The authors may add a comment on that for clarity. The equation is independent of M, but what about N? Can the authors make an intuitive comment about it?Was the equation R Yes, the function c=0.4σR was found as the best linear fit to the data points.N. For an arbitrary given number ofN the structure of the spectrum remains the same as in Fig. 5 . In a weak pumping regime, the number of atoms determines the linewidth of each individual line, while after merging it determines the linewidth of a single line. The critical value of pumping which distinguishes the discrete spectrum of clusters from a single line remains the same for anyN. In the revised version, we give a comparison of the results forN=102 (red dots) and N=104 (blue circles) atoms in Fig.6, which confirms our predictions. The comment on this has been added to the figure caption. This result appears to be independent of5. The authors model the inhomogeneous broadening and varying light-matter coupling with M=11 and K=5 clusters. Does this mean it is a 2D grid of 11 x 5 dimensions? This is correct. The overall number of clusters in the model is equal toMxK clusters of atoms.Few typographical errors-ħ in Eq.1 is no longer present in any of the later equations.A minus sign is missing in Eq.4In Eq.8, the correlation terms with superscript “st” is not defined in the text.On page 6, first paragraph last line. I guess the authors meant gain “medium”. Thank you for the helpful remarks. We agree and corrected the errors, except Eq. 4 which is correct, for a reference see, for example, Eq.(94) in Jacobs K, Steck DA. A straightforward introduction to continuous quantum measurement. Contemporary Physics 47(5):279-303 (2006).Dear Dr. Debnath, First, we would like to thank you for a thorough reading of the manuscript and your constructive comments, which helped us to improve our work. Below, we respond to your comments point by point by using a different font.