Bio-inspired (biomimetic) materials, which are inspired by living organisms, offer exciting opportunities for the development of advanced functionalities. Among them, bio-inspired superhydrophobic surfaces have attracted considerable interest due to their potential applications in self-cleaning surfaces and reducing fluid resistance. Although the mechanism of superhydrophobicity is understood to be the free energy barrier between the Cassie and Wenzel states, the solid-surface technology to control the free energy barrier is still unclear. Therefore, previous studies have fabricated solid surfaces with desired properties through trial and error by measuring contact angles. In contrast, our study directly evaluates the free energy barrier using molecular simulations and attempts to relate it to solid-surface parameters. Through a series of simulations, we explore the behavior of water droplets on surfaces with varying values of surface pillar spacing and surface pillar height. The results show that the free energy barrier increases significantly as the pillar spacing decreases and/or as the pillar height increases. Our study goes beyond traditional approaches by exploring the relationship between free energy barriers, surface parameters, and hydrophobicity, providing a more direct and quantified method to evaluate surface hydrophobicity. This knowledge contributes significantly to material design by providing valuable insights into the relationship between surface parameters, free energy barriers, and hydrophilicity/hydrophobicity. Bio-inspired materials, which are inspired by living organisms, have emerged as a promising avenue for the development of advanced functions in various scientific disciplines ,2,3. AmoA thorough understanding of the Wenzel  and CassLeroy and Müller-Plathe’s pioneering work proposed that surface hydrophilicity/ hydrophobicity could be tuned by controlling the length and depth of the roughness pattern . Their r surface . For hyd surface . The cur surface . As a re surface . Their wHowever, as mentioned above, while the free energy barrier is the essence of the phenomenon, it is also a quantity that is difficult to measure directly. In recent years, there have been numerous instances of employing molecular simulations to investigate droplet behavior on surfaces ,19,20,21This innovative approach allows more direct determination of the free energy barrier on the surface parameter and provides a deeper understanding of how to optimize materials for desired hydrophilic/hydrophobic properties, thereby streamlining material design processes.We employed the many-body dissipative particle dynamics (MDPD) method ,23,24 toHere, m, and the energy T denotes the temperature and In the current report, we utilize reduced units for the cutoff radius w) of the pillars and heights (h) of the pillars, as shown in In this study, the mosquito eye model, which is well-known for its superhydrophobic properties, was employed as a solid surface model for the nanostructured bio-inspired surfaces. We prepared ten wall models with different center-to-center distances  increases, particularly when the pillar height exceeds the radius of the droplet. This indicates that increasing the pillar height effectively increases the free energy barrier. Based on According to Extrand’s theory, the surface forces should exceed gravity (or other body forces) and act in an upward direction. In addition, the surface columns must be high enough to prevent the liquid from coming into contact with the bottom of the surface, which could cause the liquid to be pulled down and can lead to collapse. w and h influence the magnitude of the free energy barrier. In the study by Burton and Bharat [The results show that both d Bharat , it is od Bharat  demonstrh, to match the diameter of the droplet. We have calculated the relationship between the droplet center coordinates with time in An intermediate state, more typical in nature, becomes increasingly likely when we adjust the surface pillar height, Our conjecture regarding the energy landscape of this transition state is illustrated in w–G and h–G into a three-dimensional coordinate system depending on the function (x- and y-axes representing the ratios of w and h to z-axis representing We attempted to integrate the functions function , with thHere, A unique aspect of our study is the ability to calculate the free energy barrier based solely on surface parameters. In previous research, surface experiments have typically been carried out to measure the contact angle of droplets on the surface, allowing an assessment of the hydrophilic or hydrophobic nature of the surface. In contrast, our study focuses on calculating the magnitude of the free energy barrier using only surface parameters, eliminating the need for experimental measurements. This provides significant convenience for material design, as it allows the direct determination of surface hydrophilicity or hydrophobicity based on the free energy barrier and without the need to perform experiments.The magnitude of the free energy barrier serves as an indicator of the hydrophilicity/hydrophobicity of the surface. In general, higher free energy barriers correspond to more hydrophobic surfaces, while lower free energy barriers correspond to more hydrophilic surfaces.When considering the physical properties alone without taking into account the surface chemistry, we observed that increasing the distance between the surface pillars results in a lower free energy barrier.Similarly, when considering only the physical properties and not the surface chemistry, we found that higher surface pillar heights lead to higher free energy barriers.The We performed coarse-grained molecular simulations to investigate the effects of droplets on solid surfaces with bio-inspired nanostructures with the aim of contributing to the advancement of solid-surface engineering. Our primary aim was to gain a deeper insight into the properties of these surfaces, focusing in particular on the nanostructure inspired by the compound eyes of mosquitoes, known as the mosquito eye structure. Through this investigation, we aimed to explore the influence of the physical properties of this nanostructure on the free energy barrier. Our results can be summarized as follows:Our study provides valuable insights into the behavior of droplets hitting solid surfaces with bio-inspired nanostructures. By considering the physical properties of the nanostructure, we gain a better understanding of how these surfaces affect the free energy barrier. These findings have implications for the field of solid-surface engineering and offer potential applications in the design of surfaces with specific hydrophilic or hydrophobic properties.


The clinical success of vascular interventional surgery relies heavily on a surgeon’s catheter/guidewire manipulation skills and strategies. An objective and accurate assessment method plays a critical role in evaluating the surgeon’s technical manipulation skill level. Most of the existing evaluation methods incorporate the use of information technology to find more objective assessment models based on various metrics. However, in these models, sensors are often attached to the surgeon’s hands or to interventional devices for data collection, which constrains the surgeon’s operational movements or exerts an influence on the motion trajectory of interventional devices. In this paper, an image information-based assessment method is proposed for the evaluation of the surgeon’s manipulation skills without the requirement of attaching sensors to the surgeon or catheters/guidewires. Surgeons are allowed to use their natural bedside manipulation skills during the data collection process. Their manipulation features during different catheterization tasks are derived from the motion analysis of the catheter/guidewire in video sequences. Notably, data relating to the number of speed peaks, slope variations, and the number of collisions are included in the assessment. Furthermore, the contact forces, resulting from interactions between the catheter/guidewire and the vascular model, are sensed by a 6-DoF F/T sensor. A support vector machine (SVM) classification framework is developed to discriminate the surgeon’s catheterization skill levels. The experimental results demonstrate that the proposed SVM-based assessment method can obtain an accuracy of 97.02% to distinguish between the expert and novice manipulations, which is higher than that of other existing research achievements. The proposed method has great potential to facilitate skill assessment and training of novice surgeons in vascular interventional surgery. Minimally invasive intravascular interventions have been widely adopted to diagnose and treat a variety of vascular diseases, such as stenosis, aneurysms, atherosclerosis, and thrombosis ,2,3. DurHowever, though intravascular interventions have brought many benefits and are being adopted worldwide, they are still associated with several challenges wherein steep learning curves for training surgeons in catheterization skills are of great concern ,9,10,11.Traditionally, written/oral examinations and case logs are employed to assess trainees’ surgical judgment and cognitive knowledge . AdditioIn recent years, research efforts have been conducted to explore more objective and accurate approaches to evaluating vascular interventional skills with the aid of information technology. Some studies have explored objective evaluation techniques by analyzing the motions of catheters/guidewires during vascular interventional procedures. Rolls et al.  developeHowever, most of the existing objective assessment techniques are highly dependent on EM sensors, accelerometers, and EMG sensors. These sensors are required to be fixed to intravascular instruments  and the surgeon’s upper limbs , which may influence the motion trajectory of intravascular tools and constrain the surgeon’s manipulations. In addition, incorrectly or inappropriately positioned sensors may affect the accuracy of data collection for skill evaluation.Motivated by the above-mentioned drawbacks, we have developed a novel assessment framework to evaluate the surgeon’s manipulation skills. Nine objective performance metrics, including procedure time (PT), number of collisions between intravascular tools and vasculature (CN), path length (PL), number of speed peaks (SPN), slope variations of tool tip displacement (SV), vascular difficulty (VD), maximum force (MF), and mean force values (MFV), are proposed to assess the surgeon’s intravascular interventional skills, taking into consideration the traditional expert observation–based evaluation criterion. PT, CN, PL, SPN, SV, and VD are extracted and calculated from video sequences. MF and MFV are analyzed based on a 6-Dof force/torque sensor mounted under the vascular model. An SVM-based classification model is trained and used to discriminate the intravascular interventional skill levels of surgeons based on the above-mentioned performance metrics. The main contributions of this paper are as follows: (1) The proposed assessment framework disposes of the need to attach any sensors to the surgeon’s upper limbs and intravascular instruments. (2) During the data collection process, surgeons are allowed to drive the catheters/guidewires within the vascular model with the same manipulation skills that they utilize in real intravascular interventions. (3) Nine objective performance metrics are investigated for technical skill evaluation, in which the number of collisions, slope variations, and the number of speed peaks, to the best of our knowledge, have rarely been exploited.The assessment framework is designed to accurately acquire the motion data of intravascular instruments from the vascular model, contact force data between instruments and the vascular model, and the manipulation data from the surgeon’s performance, as illustrated in A remote-controlled vascular interventional surgical (VIS) robot ,46 is usSix intravascular surgeons were recruited during data collection. Participants were divided into two groups, the expert group and the novice group, based on their experience in vascular interventional surgery. The expert group involved three expert surgeons who have performed more than 200 intravascular interventional procedures and the novice group included three novice surgeons who have performed fewer than 20 interventions. All the surgeons who participated in this study had the right dominant hand. Prior to data collection, surgeons were trained to familiarize themselves with the operation of the master controller and the catheterization tasks in advance. After the data collection started, the surgeon’s manipulations were allowed to proceed without intervention.The focus of this study is the interventional procedure of delivering the medical guidewire from the descending aorta, passing through the aorta arch to the brachiocephalic artery, left common carotid artery, and left subclavian artery, respectively. This procedure is a highly demanding test of the surgeon’s familiarity with the anatomical structures of the vessels and the surgeon’s skills in guidewire manipulation. Varying levels of intravascular interventional skills often result in varying surgical outcomes. Thus, five tasks were designed to evaluate the surgeon’s guidewire manipulation skills. As illustrated in To evaluate the trajectory of the input guidewire in a quantitative way, an image processing algorithm based on the OpenCV library in Python is proposed to automatically detect and track the guidewire tip frame by frame within the vascular model. This algorithm provides the 2D position, in pixel coordinates, of the catheter tip within the recorded videos. Each frame of the video is converted into a binary image using a cut-off threshold to extract the shape of the guidewire. Pixels with a greyscale value below the threshold are assigned the value ‘0′, while those above are assigned the value ‘1’. The shape of the guidewire is delineated by the white pixels in the resulting binary image  and (6):Vascular difficulty is the degree of surgical difficulty in terms of the impact of the vascular structure on the surgeon’s operation. It depends on the complexity of the physiological structure of the blood vessels. A higher degree of vascular difficulty indicates a more complex vascular structure that is difficult to treat during vascular interventional surgery. In the GRS for intravascular interventional surgery, the degree of difficulty was considered to be a measurable scale . Vasculap-value less than 0.05 was considered statistically significant. The results of the significant difference analysis are shown in Statistical analysis was performed to analyze the contribution of the proposed performance measures to the intravascular skill assessment model. The t test, an inferential statistic used to determine whether there is a significant difference, was used to test the significance of the differences between the manipulation data for each indicator obtained from the same skill group at different vascular difficulty levels. A For experienced surgeons, there were significant differences in the number of collisions between the guidewire and the vascular model and the variation of the slope in the vertical direction when performing intravascular interventions within vessel branches with different vascular difficulties. On the other hand, the variability was not significant for the metrics of the procedure time, the maximum and mean force applied to the vascular model, and the number of speed peaks. The variability of the manipulation data for these metrics is not significant because experienced surgeons are able to control the contact force between the guidewire and the vascular model well and are more familiar with the anatomical structure of the vasculature, even when performing on different vessels with different vascular difficulties. For novice surgeons, there were significant differences in the slope variations in both the horizontal and vertical directions, which were used as two performance metrics of trajectory smoothness when performing on different vessels with different vascular difficulties.Similarly, we also verified the variability between the manipulation data of different skill groups for the same vascular difficulty, and the results are shown in I represent the vectors including nine feature values, and class labels indicate whether the surgeons are from the expert group or the novice group. The binary SVM classifier with radial basis function (RBF) kernel was used to classify the manipulations performed by novice and expert surgeons. The nine features based on the performance metrics during the intravascular interventional tasks were extracted to construct the feature space for the binary SVM classification. The feature vectors, combined with the corresponding class labels, were used to train the SVM classifier, as shown in (7):Proper training is a critical step in supervised machine-learning modeling. The SVM classification maps the input feature vectors into a higher dimensional space in a nonlinear way and determines a separating hyperplane with the maximum margin between the two classes using an optimization step. The performance of the SVM-based assessment model was evaluated using the k-fold cross-validation method. The data set was divided into a training set containing 65% of the total number of data samples, while the remaining 35% was used to test the model. After dividing the data into the training set and the verification set, the SVM model was trained and the classification accuracy was calculated. To obtain the optimal model, the parameters for the SVM model training should be adjusted in real time. Among these parameters, the kernel function and the regularization parameter have a significant impact on the model. The bigger the regularization parameter, the more penalty SVM gets when it makes a misclassification. Setting a small regularization parameter value can reduce penalties for misclassification and allows for fault tolerance owing to strong generalization capabilities. The complexity of the model would be altered by adjusting the regularization parameter. The radial basis function kernel, which is suitable for moderate sample sizes and small numbers of features, was used to map the sample space to infinite dimensional space after parameter adjustment. After several training sessions, the regularization parameter was adjusted to 0.8 and the gamma was adjusted to 20 to obtain higher accuracy. The SVM-based assessment model based on nine performance metrics can achieve an accuracy of 97.02% in discriminating expert and novice manipulations.Assessment of surgical skills is an important part of the surgeon’s professional development. Moreover, in light of major surgical errors, the maintenance of surgical competence has been a matter of great public concern. However, there is currently no standardized way of assessing vascular interventional skills. Traditionally, the trainee to be assessed performs a series of predefined procedures while being supervised by experts in the field. The supervising experts subjectively assess performance on the basis of the trainee’s manipulation in accordance with the GRS and checklists. The need for reliable and objective techniques to assess the surgeon’s intravascular skills, especially during complex interventional procedures involved in vascular interventional surgery, has become one of the main priorities of the surgical community. Motion sensors attached to the tip of intravascular instruments or the surgeon’s upper limbs have been the most commonly used approach to collect data to objectively differentiate surgical skill levels during intravascular procedures. However, the added sensors may influence the physical properties of intravascular tools and constrain the surgeon’s manipulations. Additionally, incorrectly or inappropriately positioned sensors may influence the accuracy of data collection for skill evaluation. To overcome these drawbacks, we developed a novel assessment method to evaluate the surgeon’s manipulation skills based on nine objective performance metrics. During the data collection process, surgeons are allowed to manipulate the catheters/guidewires within the vascular model with the same manipulation skills that they use during real intravascular interventions, without the need to attach any sensors. An SVM-based assessment model is proposed to discriminate between expert and novice manipulation, with a classification accuracy of 97.02%, which is higher than other existing research results. In this study, we have not split the data by participant. In our future work, more surgeons will be recruited for data collection and some other algorithms  and multiple validation methods will be investigated.


In several regions across the globe, snow has a significant impact on hydrology. The amounts of water that infiltrate the ground and flow as runoff are driven by the melting of snow. Therefore, it is crucial to study the magnitude and effect of snowmelt. Snow droughts, resulting from reduced snow storage, can drastically impact the water supplies in basins where snow predominates, such as in the western United States. Hence, it is important to detect the time and severity of snow droughts efficiently. We propose the Snow Drought Response Index or SnoDRI, a novel indicator that could be used to identify and quantify snow drought occurrences. Our index is calculated using cutting-edge ML algorithms from various snow-related variables. The self-supervised learning of an autoencoder is combined with mutual information in the model. In this study, we use Random Forests for feature extraction for SnoDRI and assess the importance of each variable. We use reanalysis data (NLDAS-2) from 1981 to 2021 for the Pacific United States to study the efficacy of the new snow drought index. We evaluate the index by confirming the coincidence of its interpretation and the actual snow drought incidents. Recently, it has led to a broad discussion on the association between droughts and snow, along with the emergence of several studies focusing on “snow drought,” indicative of lower-than-normal snow conditions9. However, a consistent way of characterizing snow droughts is missing in these past studies, resulting in the absence of a solid framework to detect snow droughts.In many regions worldwide, snow has a vital contribution to drought occurrence1. Another study argued that defining snow droughts just in terms of SWE might not be sufficient, and it referred to snow drought as a combination of general droughts and shortages in snow storage, reflecting both the lack of winter precipitation and SWE5. Subsequently, Hatchett & McEvoy (2018) defined different types of snow droughts based on the origination, persistence, and termination of below-normal snow accumulations. Later, several studies expressed snow droughts in terms of threshold percentiles, which is essentially subjective10. Some of these studies used the median SWE (of the cooler months in the entire time period) to identify snow droughts, whereas others used maximum SWE10. Although we need an index to study and predict snow droughts, the lack of coherence in the characterization of snow droughts potentially questions the reliability of a snow drought index based on strict definitions. Therefore, we need a framework to calculate a snow drought index independent of such definitions, which, at the same time, can also capture the signals of a snow drought, considering factors connected to snow accumulation and ablation.Different authors defined snow droughts differently, making the analysis of these droughts conditioned upon and potentially sensitive to the definitions. For example, a recent study assessing the global snow drought hotspots and characteristics considered a snow drought event as a deficit of snow water equivalent (SWE)1. Keyantash and Dracup11 developed the aggregated drought index (ADI) based on rainfall, evapotranspiration, streamflow, reservoir storage, soil moisture, and snow water content variables. Here, a principal component analysis (PCA) was employed to reduce the dimensionality and explain the key variabilities represented by the selected variables. Staudinger et al.12 developed an extension to the Standardized Precipitation Index (SPI) named Standardized Snow Melt and Rain Index (SMRI), where they used the sum of rainfall and snowmelt variables instead of precipitation. Qiu13 modified the standard Palmer Drought Severity Index  by including degree day factor (DDF), an empirical threshold temperature-based snowmelt model, to account for snow processes. This modification improved the drought monitoring capabilities in several snow-dominated regions15. However, these indices often depend upon in-situ observations, which might not be readily available in many regions, and the problem is exacerbated in ungauged or sparsely gauged regions. This calls for an index that can leverage remote sensing datasets and bypass the need for extensive in-situ observation networks.To date, only a limited number of studies have been conducted on snow drought indices. The recently developed Standardized Snow Water Equivalent Index (SWEI) is obtained through the inverse standard normal distribution of probabilities associated with SWE integrated over three months19. Thus, we can use ML techniques to infer the influence of hydroclimatic variables on snow droughts. Apart from this, information theory-based methods can manifest the relative influence of variables and their causal connections22. Mutual Information (MI), a measure of how much information about one random variable is contained in another random variable, has been widely applied in feature selection problems24.Merging and extracting necessary information on snow droughts from a wide range of variables present in remote sensing datasets can be challenging since not all variables are equally related to the formation of snow droughts. However, we need to identify important variables so that they can be merged to form one single index. Machine learning (ML)-based feature selection algorithms are promising in this regard since they can filter our variables based on their importanceIn this study, we introduce a new snow drought index, the Snow Drought Response Index (SnoDRI), and a novel drought index estimation approach using a combination of ML techniques and MI. Our framework is advantageous for multiple reasons: (1) our index is not based on any specific variable, instead, it aggregates information from multiple variables, (2) we do not require any in-situ observations, thus enabling snow drought detection in ungauged basins, (3) our framework is explainable, i.e., it can provide insights into crucial features impacting the occurrence of snow drought. Our results show that SnoDRI could successfully detect the signals of a historical snow drought event.1. Snow plays a significant role in the hydrology of the Western United States. The maximum annual SWE accumulation in the region is 1176 mm (elevation 2835 m) at Mammoth Pass, California25. During spring or early summer, discharge in the high-elevation watersheds that drain through mountains contains a substantial amount of water as a result of warming snowpacks and snowmelt27. Recent events have shown that the water resources and management in this region are hugely influenced by snow droughts5. Therefore, this study focuses on three states (Pacific Coast States) in the western USA: Washington, California, and Oregon  forcing data, which provides a total of eleven variables, given in Table 35. We might inhibit the model from learning crucial information using only snowfall. Here, in our framework, the idea is to provide available data, which might or might not be important in drought stress formation, and let the model figure out the key information.The North American Land Data Assimilation System (NLDAS) is a multi-institutional partnership project intended to develop land-surface model datasets from observations and reanalysis with quality control that is coherent across space and time36. The SPI is obtained by mapping the actual probability distribution of precipitation to a normal distribution. A zero SPI indicates normal conditions. The positive values of SPI represent wet conditions, whereas the negative values represent dry conditions. The larger the negative value of SPI, the higher the severity of drought conditions. We calculate SPIs at three timescales  and provide them as inputs for the SnoDRI because they provide a combined measure of precipitation over multiple time scales. The SPI at 3, 4, and 6 months timescales are chosen because the snow processes and the impact of reduced winter precipitation generally occur at these timescales. These SPIs can reflect the reduced snowpack and discharge from snowmelt. For the same reason, SPIs at longer timescales (such as SPI-12 and 60) are potentially unimportant for snow droughts. Therefore, we have also fed the model with SPI-12 and SPI-60 as a sanity check to see whether the model can discard irrelevant information, which is confirmed by our results (see Sect. “The Standardized Precipitation Index (SPI) is an index widely used for quantifying precipitation anomalies38 from the National Snow and Ice Data Center (NSIDC). This data provides daily SWE and snow depth at a spatial resolution of 4 km x 4 km for the conterminous United States (CONUS). We collected the SWE data from 1982 to 2020, spatially aggregated them for the study basins, and converted them to monthly time series.We use snow water equivalent (SWE) as an indicator variable for the snow drought case used for validation. SWE is the target variable for the Random Forest model (discussed in a later section) used in selecting the input features for our index. We obtained SWE data and snow depth from assimilated in-situ and modeled data over the conterminous US, Version 140. These basins are least affected by human actions40. The dataset contains different categories of basin attributes: topography, climate, streamflow, land cover, soil, and geology40. We use the basin shapefiles provided in the dataset and filtered basins  belonging to the Pacific Coast states. The gridded datasets are aggregated to the basin scale using these shapefiles.Catchment Attributes and MEteorology for Large-sample Studies (CAMELS) provide the time series of meteorological forcings and attributes of 671 basins across the CONUS41.The discharge data for these basins were collected from the US Geological Survey’s (USGS) streamflow measurements provided in the CAMELS dataset. USGS collects, monitors, and analyzes existing resource conditions across the different sites in the US. USGS stations measure velocity through a current meter or acoustic Doppler current profiler. The discharge is computed by multiplying the cross-sectional area by the estimated velocity. For this study, daily data were obtained from 1979 through 2020. The daily flow records for USGS gage stations provide the value of mean discharge for each day of the water yearIn this work, as shown in Fig. 42. Since every regression tree inside the Random Forest identifies an order of variables to classify the training dataset, we can leverage the random forest regression algorithm to find the feature importance of training variables in predicting the target variable. In this study, we use Random Forest regression to select the important variables to develop SnoDRI. We aggregated the NLDAS-2 variables for 85 CAMELS basins in the Western US and regressed it against SWE and discharge within the basins. This yields two sets of feature importance corresponding to SWE and discharges for each basin. Then, by taking the mean of all basins, the average feature importance of variables for the Western US is calculated. The union of the top three variables in average feature importance for predicting SWE and discharge is used to compute SnoDRI. Note that both SWE and discharge variables are in effect only during the Random Forest feature selection. The idea here is to use available measured variables, which potentially indicate droughts, to filter variables accounted for the index calculation for the region. Once we obtain the filtered variables and their weights (discussed in a later section), they can be transferred to other ungauged basins in the region for calculating the index, which enables us to calculate the index for ungauged basins.Random Forests are a collection of decision trees. Each tree in a Random Forest is built based on a random subset of variables from bootstrapped data, which can be used for classification and regression problems43. During the learning process, autoencoders “discard” the insignificant information present in the dataset. An autoencoder consists of an input layer, an encoder with hidden layers, a bottleneck layer, a decoder with hidden layers, and an output layer that tries to reconstruct the input data (self-supervised learning). The NLDAS-2 variables identified through Random Forest regression , is calculated using Eq.  of the model, which is a single time series since the bottleneck consists of only one node. Our framework calculates the Mutual Information (MI) between the bottleneck output and each input variable, which is used as their weights . MI is a measure of how much information, on average, can one random variable tell us about another random variableX (x) and PY (y) are marginal probabilities, and PXY is the joint probability. As shown in Fig. Here PA valid question here is why we cannot directly use the weights of the trained autoencoder. To explain this, referring to Fig. 47 proposed. The wet bulb temperature is calculated from air temperature, specific humidity, and surface pressure from the NLDAS-2 dataset.We also use snow fraction as an input into the model. In the modeling realm, there are different rain-snow partitioning schemes based on which precipitation variable is used as the forcing is separated into snow and rainfall. Classifying rain and snow based on a threshold temperature is the most straightforward scheme. This method is susceptible to the choice of threshold temperature. In another scheme proposed by Jordan (1991), the snow percent is calculated as a linear stepwise function of air temperature. In this study, we estimate the snow fraction based on a sigmoid function of wet bulb temperature, as Wang et al.There is no single framework for validating a drought index. Based on the purpose of the new index, one must examine whether the index follows the drought indicators, such as the scarcity of relevant environmental variables. This study uses the anomaly in SWE as an indicator variable. A negative anomaly represents the lack of snow accumulation compared to normal and vice versa. The lower the anomaly, the more severe the snow drought. The discharge co-occurring with SWE is another indicator variable. Reduced discharge due to low meltwater contribution can be a potential impact of the snow drought. A lower discharge following a lower SWE is a prime case of snow drought.8 and Harpold and Dettinger5 reported a snow drought in this region during the winter (Jan to Apr) of 2014 and 2015. A lower SWE, along with a lower discharge, is taken as a signal of snow drought in the basin. We check if these signals correspond to a lower value of SnoDRI. Meanwhile, the index should not give a false positive forecast.We compare the novel SnoDRI with patterns of SWE and discharge in the Upper Tuolumne basin of California. Hatchett et al.49. After temperature, the downward shortwave radiation affects the SWE most. Since the primary source of energy that drives the atmospheric process is the incoming shortwave radiation, we can expect that the formation and accumulation of snow are highly dependent on shortwave radiation. Specific humidity is the third most crucial variable for SWE as obtained from Random Forest regression. Specific humidity (the measure of water content in the atmosphere) could have a significant effect on the formation of snow.Through Random Forest regressions for 85 CAMELS basins, we obtained the average feature importance of NLDAS-2 variables for the Pacific Coast States of the US in predicting SWE and discharge. This method gives a sense of the relative significance of each variable in generating SWE or discharge. Figure Figure From both cases, Random Forest regression targeting SWE and discharge, we identified the top three variables having the highest average feature importance for our study area. In the case of SWE, the top three variables are TMP, DSWRF, and SPFH Fig. a. Wherea12. Our result suggests further investigating the direct and indirect association between downward shortwave radiation and snow droughts. The model also identifies shorter-scale SPIs  as significant. Since SPIs represent the lack of precipitation in the case of drought, they can be a proxy for lower snowfall and snowpack conditions. Following this, the model assigns more weight to temperature, complying with the fact that temperature drives snow processes from the formation of snow to the melting of snow. Snow fraction, another variable with considerable weight, can be directly related to the amount of snowpack. The lower the snow fraction, the lower the snowfall, leading to snow drought conditions. Interestingly, the model identifies that precipitation as such does not have a severe influence. The reason could be that the SPIs, which are the precipitation mapped to a normal distribution, already contain the information of precipitation. This can also be attributed to the ability of the model to dismiss redundant information. The lowermost weights are assigned to the SPI-12 and 60, two variables presupposed to be irrelevant for snow droughts, additionally confirming the aforementioned ability of the model.The MI between the compressed bottleneck output and each input variable measured the relative importance of the corresponding variable in the compressed data (bottleneck output). Figure With the newly developed snow drought index, SnoDRI, we analyzed the conditions of snow drought in the Upper Tuolumne River basin from February 2013 to May 2019. This period is included in the evaluation period. In other words, the model has never seen the input dataset of this duration throughout its training. Over this evaluation period, the new index shows a good performance in capturing snow drought events. Figure In addition, we place SnoDRI and the potential signals of the snow drought in juxtaposition. Comparing SnoDRI with the anomaly in SWE, SnoDRI shows lower (more negative) values when the SWE anomaly is shallow. For instance, in 2014, 2015, and 2018, the Upper Tuolumne Basin showed a negative anomaly in SWE Fig. . During Given the ability of SnoDRI to capture snow droughts, we can implement the following steps to apply our new framework for a selected basin (in Pacific states) in a selected year: (1) obtain the filtered NLDAS-2 variables for the year of interest and aggregate them over the basin of interest, (2) calculate the SPIs and snow fraction, (3) derive the monthly time series and standardize them, (4) multiply the pre-calculated weights see Fig.  with eac12. Thirdly, our framework, besides calculating the index, can give insights into what factors drive snow drought conditions, as represented by the weights from the autoencoder with MI. Typically, studies investigating snow droughts calculate the index based on the abnormal variations in snow variables. Fourthly, regardless of several model inputs that possess multicollinearity, a common issue while using multiple predictor variables, we can see that the SnoDRI framework could eliminate redundant information to a certain extent. For instance, the model gave a lower weight to specific humidity, a variable used along with temperature to calculate snow fraction. Finally, unlike SPI or Palmer Drought Severity Index , the proposed ML-based framework is not sensitive to the time series length. Once the model is trained, its weights are fixed and can be applied to a new dataset, no matter the range of time. Moreover, since ML models are known for their capacity to learn complex patterns, we can relax the assumption of stationarity. However, the efficacy of SnoDRI in capturing multi-scale  droughts needs to be explored in greater depth. The abovementioned capabilities of the framework highlight the competence of ML and information theory metrics in assessing snow droughts .Generally, this study proposes a new framework to calculate SnoDRI, an index that can measure snow droughts. The framework could be advantageous due to the multiple strengths that we identified. Firstly, it can be applied in ungauged basins. Since we use only the selected features from NLDAS-2 forcings, a gridded dataset integrating satellite observation with measurement gauges and radars, we do not need to rely on any ground-measured variables to calculate SnoDRI. Several basins worldwide are still ungauged, especially in developing countries, leading to a lack of an efficient drought monitoring system. Our framework can act as an alternative snow drought indication framework in such regions. Note that while NLDAS-2 integrates ground-based observations in their reanalysis process, it does not impede the applicability of the index over ungauged basins, as the gridded data extends over these areas. Secondly, our framework reduces the subjectivity in choosing the input variables by using Random Forest models to select important features. Previous studies examined snow droughts with definitions based on a handful of variables  selected based on expert knowledge and assumptions, which add subjectivity to the analysis50. Generally, the researchers compare a new index with some of the reported drought events to validate the index53. Nevertheless, this does not show exclusively the ability of an index to capture all the drought events. Some studies validate their index by checking its congruency with the US Drought Monitor54. There is vast room for research in developing an established framework for validating drought indices. A possible way to create a validation framework is to verify the closeness of the distributions of relevant variables with that of the index. The closeness of different distributions can be quantified with statistical methods.Formulating the framework for drought index calculation came with several challenges. Most importantly, the absence of a target variable to train and test the ML model. It is not straightforward to establish the performance of the index with a statistical metric . Rather, we had to compare and contrast the indicator variables with the index to see whether it was able to capture the signals of drought. This gave rise to another challenge: the lack of characterization of snow droughts in the present literature. Despite the ongoing interest in the topic, researchers have not reached an established definition of snow drought. Although our framework can overcome this issue since it is independent of a definition based on a single variable, more detailed investigation on snow drought characterization can better help assess their presence. Our framework, using the autoencoder, calculates the stress in the combined effect of hydrometeorological variables instead of looking at a single variable. However, validating this ability of the index can be tricky given the lack of understanding of the snow drought mechanism and the availability of observed data. This limits the validation process to be solely based on available records of indicator variables—another challenge in this study. It is a common problem in all drought index development studies57. The effects of incorporating such methods, which could potentially further the feature selection component of the new framework, need to be explored. Although we only considered the NLDAS-2 variables in calculating SnoDRI, the framework can be applied to any set of time series input variables. For example, the ERA5-Land dataset, which provides a larger number of variables with a more extended period58, and the data from Land Information System (LIS) simulations. In spite of the high computational cost, it would be interesting to see the performance of the framework with ERA-5 or LIS variables. We have executed the framework at a basin scale in the western US. Future efforts can be directed towards establishing the framework in a gridded manner at continental or global scales.We acknowledge that, to some extent, the index is susceptible to the group of input variables we start with before the Random Forest feature selection. The importance of any variable obtained from the Random Forest feature selection depends on the whole set of input variables. In other words, adding more variables or choosing a different dataset might produce a different order of feature importance. Several studies have employed a feature selection strategy based on sensitivity analysis Although we focus on snow droughts, this framework can be applied to identify any type of drought, given the appropriate input variables and feature selection. We select variables by regressing Random Forests against SWE and discharge. Training the Random Forests against different target variables relevant to the interested drought type would give another set of input variables. These can be transformed into an index by following the steps in our framework. Thus, by design, our framework is transferrable. We can set up the framework for any region of interest by training the Random Forest (for feature selection) and autoencoder (for estimating the weights of selected features through MI scores) with the data of that region. It should be noted that, for different regions, the model might assign different weights to variables depending on the hydroclimatic characteristics of the region. For instance, in the regions where temperature variability has greater influence, temperature is most likely to control the compressed bottleneck information inside the autoencoder, leading to a higher MI score for temperature (with bottleneck information). This aspect of our framework can be used to get insights about the impact of each variable on droughts.We developed a framework to calculate a new index, SnoDRI, that can be used to identify snow droughts. We trained Random Forest models for 85 basins across the West Coast to select the input features for the index calculation. Our novel framework showed the capability of combining autoencoders  with MI  to estimate the importance of input variables in the occurrence of snow droughts. We found that the downward shortwave radiation, SPIs, temperature, and snow fraction considerably influence snow droughts. In validation, SnoDRI successfully captured the reported snow drought events and their signals in the Upper Tuolumne Basin in the Sierra Nevada region. The framework demonstrated the potential to eliminate redundant information in the dataset. The novelty of our framework is that it can be applied to ungauged basins since it does not use any ground measurements. The framework can be adapted to other types of droughts and to different regions around the world.


Convolutional neural networks (CNNs) have been successfully applied to chest x-ray (CXR) images. Moreover, annotated bounding boxes have been shown to improve the interpretability of a CNN in terms of localizing abnormalities. However, only a few relatively small CXR datasets containing bounding boxes are available, and collecting them is very costly. Opportunely, eye-tracking (ET) data can be collected during the clinical workflow of a radiologist. We use ET data recorded from radiologists while dictating CXR reports to train CNNs. We extract snippets from the ET data by associating them with the dictation of keywords and use them to supervise the localization of specific abnormalities. We show that this method can improve a model’s interpretability without impacting its image-level classification. The intCXRs are the most common medical imaging exam in the United States . This ty•developing knowledge of the complexities of the use of eye-tracking data for annotation in radiology, including the proposed method of considering the lag between a radiologist’s gaze and dictation for accumulating ET data specific for each abnormality label; and•informing about expected relative value between ET data and manual annotations for the decision of starting future more comprehensive eye-tracking studies.We propose to use ET data with timestamped dictations of radiology reports to identify when the presence of specific abnormalities was dictated, identify the times when radiologists would have visually attended to such abnormality, and extract the associated gaze locations. The extracted information can be used as label-specific annotation for supervising models to highlight abnormalities spatially. The localization supervision is performed using a combination of a multiple instance learning loss over the last spatial layer of a convolutional neural network (CNN)  and a mu2.2.1.We designed a pipeline to extract disease locations from ET data. This pipeline has two main parts: extracting label mentions in reports and generating an ET heatmap for a given detected label. A representation of the pipeline is shown in 2.1.1.To extract labels from reports, we adopted a modified version of the CheXpert labeler , which u2.1.2.•for the first moments after being shown a CXR, radiologists looked all over the image without dictating anything;•when dictating, radiologists usually looked at regions corresponding to the content of the current sentence or the following sentence (when near the end of the dictation of the current sentence).From these two observations, we decided to generate ET heatmaps for detected labels from the fixations of the sentences where the label was mentioned, the previous sentence, and the pause between sentences. We accumulated fixations within a limit of 1.5 s previous to the start of the mentioning sentence and up to the last mention in the mentioning sentence. An illustration of the method for choosing which fixations were included in the heatmaps is given in From observing the gaze of radiologists on a few examples, we noticed patterns that seemed to be in common for all radiologists:2.1.3.Heatmaps were generated by placing Gaussians over each fixation location with a standard deviation of one degree of visual angle, following Le Meur et al. . Fixatio2.2.OR function, assigning a positive image-level label when at least one of the grid cells was found to contain that class.We used the multiple instance learning loss term from Li et al.  to trainDuring training, the loss function depended on the presence of a localization annotation. For images annotated with localization ,•MAX,•MAX,•start of first report sentence,•start of the previous sentence,•end of the previous sentence,•start of mention sentence,•start of the recording of data for that CXR,where TIME is a time delay assuming the values of 2.5 s, 5.0 s, and 7.5 s. The end times we considered were:•start of mention sentence,•end of mention sentence,•end of the first mention,•end of the last mention.We tested all combinations between starting times and end times with a duration of 0 s or more. We compared the extracted heatmaps with the validation hand-annotated ellipses using the IoU metric with a validated threshold. After this validation, we finetuned, as a second stage of validation, the time delay by testing more times .We tested several methods for extracting label-specific localization of abnormalities from the eye-tracking data. All methods involved the accumulation of fixations into heatmaps, with different starting and ending accumulation times, after extracting the label’s mention time from the dictation. For a first stage of validation, the starting times we considered were:2.9.For our experiments,Unannotated) and a model trained with data annotated by the drawn ground truth (GT) truth ellipses (Ellipse). The ellipses were represented by binary heatmaps and were processed in the same way as the ET heatmaps. The loss function, CNN architecture, and training hyperparameters were the same for all methods. We did not include a cross-entropy classification loss baseline because it achieved lower scores than the presented methods. The best epoch for each method was chosen using the average AUC on the validation set. The best model heatmap threshold for each method and label was calculated using the average validation intersection over union (IoU) over the five seeds, considering the full range of thresholds.As baselines, we evaluated a model trained without the annotated data (ET model) and the two baselines by calculating the test AUC for image-level labels of the MIMIC-CXR-JPG dataset and the test IoU for localization of abnormalities, compared against the drawn GT ellipses. IoU was calculated individually per positive label for all images with a positive label. We calculated three heatmaps for each label and input image: the output of decoder Ellipse and ET model using the output of decoder Unannotated model using the spatial activations. The heatmaps for each method were upscaled to the resolution of the GT ellipses using nearest-neighbor interpolation.We evaluated our model  and ET model , shown in Furthermore, we evaluated the impact of the quality of the label mention extraction, performed using the modified version of the CheXpert labeler. To check how IoU scores change with respect to the quality of the labeler, we intentionally lowered the quality of Pleural Abnormality label extraction, for which both recall and precision were high in 4.Other studies have applied ET data for localizing abnormalities and improving the localization of models. Stember et al.  showed tContrary to other works, such as Karargyris et al.  and Li eUnannotated model. There are several reasons why the method might not be generalizable to the other dataset, including:•It is possible that the method choices were only well-adapted to some of the five radiologists in the REFLACX dataset and not generic for all radiologists, including the single one in the other dataset.•Some of the method choices might have only been well-adapted to the characteristics of the ET data of the REFLACX dataset. The other dataset, for example, has data collected at 60 Hz instead of 1,000 Hz and has two cases with the first fixations happening after the first mention of an abnormality.•The size of the other dataset might be too small, or the distribution of cases might be different from the validation set of the REFLACX dataset, which we used to evaluate performance. For example, the dataset shared by Karargyris et al.  includesThe method we proposed for producing label-specific localization annotations from ET data and for training models to produce heatmaps that match the annotation improved the interpretability of deep learning models for CXRs, as measured by comparing produced heatmaps against hand-annotated localization of abnormalities. From the IoU achieved by training the model with 15% of the available bounding boxes, we showed that, in our setup, around seven CXRs with ET data provide the same level of efficacy in localization supervision as one CXR with expert-annotated ellipses, showing the possible value of using this type of data for scaling up annotations. This relative value might be used in calculations involving the costs and benefits of each data collection method when deciding on how to get annotations. As shown by our ablation study, the use of label-specific annotations was essential to the added value of using the ET data. We also showed in the ablation study that the performance of the label extraction algorithm has a corresponding impact on the improvements over IoU. These results show that there is an opportunity for improvement of the IoU results for labels that had a low recall and/or precision on We tried to apply the same method to train localization with the 1,064 images from the dataset shared by Karargyris et al. . HoweverThe ET data were relatively noisy, and the achieved IoU for our label-specific training heatmaps was relatively low, limiting the achieved IoU for our proposed method of using ET data for training. In future work, we will investigate other methods of extracting the localization information to reduce the noise in the data, including methods of unsupervised alignment.


The tracking of lineage frequencies via DNA barcode sequencing enables the quantification of microbial fitness. However, experimental noise coming from biotic and abiotic sources complicates the computation of a reliable inference. We present a Bayesian pipeline to infer relative microbial fitness from high-throughput lineage tracking assays. Our model accounts for multiple sources of noise and propagates uncertainties throughout all parameters in a systematic way. Furthermore, using modern variational inference methods based on automatic differentiation, we are able to scale the inference to a large number of unique barcodes. We extend this core model to analyze multi-environment assays, replicate experiments, and barcodes linked to genotypes. On simulations, our method recovers known parameters within posterior credible intervals. This work provides a generalizable Bayesian framework to analyze lineage tracking experiments. The accompanying open-source software library enables the adoption of principled statistical methods in experimental evolution. These experimental efforts rely on our ability to reliably infer the relative fitness of an ensemble of diverse genotypes. Moreover, inferring these fitness values over an ensemble of environmental conditions can help us determine the phenotypic diversity of a rapid adaptation process4.The advent of DNA barcoding—the ability to uniquely identify cell lineages with DNA sequences integrated at a specific locus—and high-throughput sequencing has opened new venues for understanding microbial evolutionary dynamics with an unprecedented level of temporal resolution5. This, combined with the development of modern Markov Chain Monte Carlo sampling algorithms6 and approximate variational approaches7 have boosted a resurgence of Bayesian methods in different fields8.As with any other sequencing-based quantification, tracking lineages via DNA barcode sequencing is inexorably accompanied by noise sources coming from experimental manipulation of the microbial cultures, DNA extraction, and sequencing library preparation that involves multiple rounds of PCR amplification, and the sequencing process itself. Thus, accounting for the uncertainty when inferring the relevant parameters from the data is a crucial step to draw reliable conclusions. Bayesian statistics presents a paradigm by which one can account for all known sources of uncertainty in a principled way4. We present a Bayesian inference pipeline to quantify the uncertainty about the parametric information we can extract from high-throughput competitive fitness assays given a model of the data generation process and experimental data. In these assays, the fitness of an ensemble of genotypes is determined relative to a reference genotypeFor all the model variations presented in this paper, we benchmark the ability of our pipeline to infer relative fitness parameters against synthetic data generated from logistic growth simulations with added random noise. A Julia package accompanies the present method to readily implement the inference pipeline with state-of-the-art scientific computing software.4. In these competition assays, an ensemble of genotypes is pooled together with an unlabeled reference strain that, initially, represents the vast majority (≥ 90%) of the cells in the culture . The rest of the culture is left for the ensemble of genotypes of interest.The present work is designed to analyze time-series data of relative abundance of multiple microbial lineages uniquely identified by a DNA barcodeS. cerevisiae and to Ascensao et al. [E. coli. neutral lineages, genetically equivalent to the untagged ancestor strain that initially dominates the culture. These spiked-in neutral lineages simplify the inference problem since the fitness metric of all relevant barcodes is quantified with respect to these barcodes—thus referred to as relative fitness.To determine the relative fitness of the ensemble of genotypes, a series of growth-dilution cycles are performed on either a single or multiple environments. In other words, the cultures are grown for some time; then, an aliquot is inoculated into fresh media for the next growth cycle. This process is repeated for roughly 4–7 cycles, depending on the initial abundances of the mutants and their relative growth rates. The DNA barcodes are sequenced at the end of each growth cycle to quantify the relative abundance of each of the barcodes. We point the reader to Kinsler et al. [o et al.  for equiBefore jumping directly into the Bayesian inference pipeline, let us establish the mathematical notation used throughout this paper. We define (column) vectors as underlined lowercase symbols such asIn the same way, we define matrices as double-underline uppercase symbols such as4Empirically, each barcode frequency trajectory follows an exponential function of the formThe presence of the neutral lineages facilitates the determination of the population mean fitness value Therefore, we can use the data from these reference barcodes to directly infer the value of the population mean fitness.number of cells  of the formIt is important to notice that the frequencies This is the frequency Our ultimate objective is to infer the relative fitness Uncertainty in the determination of frequencies. Our model relates frequencies between adjacent growth-dilution cycles to the fitness of the corresponding strain. However, we do not directly measure frequencies. Instead, our data for each barcode consists of a length Uncertainty in the value of the population mean fitness. We define neutral lineages to have fitness Uncertainty in each of the mutants’ fitness values.To account for all these sources of uncertainty in a principled way, in the next section, we develop a Bayesian inference pipeline.As defined in Section, our ultimate objective is to infer the vector of relative fitness valuesOur objective is to compute the joint probability distribution for all relative fitness values given our data. We can express this joint posterior distribution using Bayes theorem asHowever, when implementing the model computationally, the normalization constant on the right-hand side of Although To recover the marginal distribution over the non-neutral barcodes relative fitness values, we can numerically integrate out all nuisance parameters, i.e.,The left-hand side of Written in this form, 6, the dimensionality of the problem in One of the technical challenges to the adoption of Bayesian methods is the analytical intractability of integrals such as that of 7. Briefly, when performing ADVI, our target posterior distribution 9—equivalent to minimizing the variational free energy10—is mathematically equivalent to performing the optimization prescribed by To overcome this computational limitation, we rely on the recent development of the automatic differentiation variational inference algorithm (ADVI)11.This work is accompanied by the Julia library BarBay.jl that makes use of the implementation of both MCMC-based integration as well as ADVI optimization to numerically approximate the solution of To assess the inference pipeline performance, we applied it to a simulated dataset with known ground truth relative fitness values (See Section for details on simulation). X% credible region is the interval where we expect the true parameter value to lie with X% probability.To visualize the performance of our inference pipeline in fitting our fitness model to the observed data, we compute the so-called posterior predictive checks (PPC). In short, the PPC consists of repeatedly generating synthetic datasets in agreement with the results from the inference results. In other words, we use the resulting parameter values from the ADVI inference to generate possible datasets in agreement with the inferred values (See Section for further details on these computations). X% credible region indeed captures the region of parameter space where we expect with X% probability the actual value of the parameter lies given our statistical model, our prior information, and the observed experimental data. A common mistake in the literature is interpreting frequentist confidence intervals as Bayesian credible regions when they are not equivalent12. Frequentist confidence intervals and Bayesian credible regions are based on fundamentally different philosophical approaches to statistics. Frequentist confidence intervals represent the range of values that would contain the true population parameter with a certain probability if the experiment was repeated many times. The confidence interval does not represent the probability that the interval contains the true value. According to a specific model and prior information, Bayesian credible regions represent the range of values that contain the parameter with a certain posterior probability. The credible region directly represents the probability that the region contains the true value. So, frequentist confidence intervals cannot be interpreted as Bayesian credible regions because they have fundamentally different meanings. Treating an X% confidence interval like an X% credible region is fallacious since confidence intervals do not represent probabilistic coverage of the true value like credible regions. The intervals are generated through entirely different procedures.The main advantage of our method is this natural interpretability of these credible regions where an To capture the global performance of the model, The fitness model in This natural error propagation can help us with the experimental design schematized in 13. Briefly, when accounting for multiple repeated measurements of the same phenomena, there are two extreme cases one can use to perform the data analysis: On the one hand, we can treat each measurement as entirely independent, losing the power to utilize multiple measurements when trying to learn a single parameter. This can negatively impact the inference since, in principle, the value of our parameter of interest should not depend on the particular experimental replicate in question. However, this approach does not allow us to properly “combine” the uncertainties in both experiments when performing the inference. On the other hand, we can pool all data together and treat our different experiments as a single measurement with higher coverage. This loses the subtle differences due to biotic and abiotic batch effects, effectively halving the data that goes into our inference problem.Our inference pipeline can be extended to account for multiple experimental replicates via Bayesian hierarchical modelshyper-parameters, that capture the parametric inference we are interested in—for this inference problem, we have a hyper-fitness value local fitness value Hierarchical models present a middle ground between these extremes. First, hierarchical models rely on the definition of so-called To test the performance of this model, we simulated two experimental replicates with 1000 unique barcodes see -C) whereAs shown in Hierarchical models can also capture another experimental design in which multiple barcodes map to the same or an equivalent genotype. As we will show, this many-to-one mapping can improve the inference compared to the extreme cases of inferring the fitness of each barcode independently or pooling the data of all barcodes mapping to a single genotype. As schematized in 14. From questions related to the optimal fine-tuning of gene expression programs15, to the dimensionality, geometry, and accessibility of the adaptive fitness landscape explored by these rapidly adapting populations16, to the emergence of eco-evolutionary dynamics in a long-term evolution experiment17; for all of these and other cases, the microbial experimental platform combined with high-throughput sequencing has been essential to tackling these questions with empirical data. This exciting research area promises to improve as new culturing technologies18 as well as more complex lineage barcoding schemes19, are adopted.Experimental evolution of microbial systems has dramatically advanced our understanding of the basic principles of biological evolution20. Moreover, Bayesian analysis offers a more natural way to interpret the role that probability theory plays when performing data analysis compared to the often-misinterpreted frequentist methods21. Nevertheless, the technical challenges associated with Bayesian analysis has limited its application. This is set to change as recognition of the misuse of frequentist concepts such as the p-value is receiving more attention22. Moreover, advances in numerical methods such as Hamiltonian Monte Carlo6 and variational inference7 allows for complex Bayesian models to be fit to empirical data.For this data-heavy field, properly accounting for the uncertainty in parameters inferred from experiments is vital to ensure the conclusions drawn are reliable. Bayesian statistics presents a principled way to quantify this uncertainty systematically4. The proposed model accounts for multiple sources of uncertainty with proper error propagation intrinsic to Bayesian methods. To scale the inference pipeline to large datasets with > 10, 000 barcodes, we use the ADVI algorithm7 to fit a variational posterior distribution. The main difference between our method and previous inference pipelines, such as Li et al. [In this paper, we present a computational pipeline to analyze lineage-tracking time-series data for massive-parallel competition assays. More specifically, we fit a Bayesian model to infer the fitness of multiple genotypes relative to a referencei et al. , is that24. Our model gets around this issue by assuming that the frequency of any barcode cannot be, but still can get arbitrarily close to, zero. Therefore, we implicitly assume that no lineage goes extinct during the experiment. Moreover, the statistical model directly accounts for the uncertainty associated with having zero barcode counts, increasing the corresponding uncertainty. Third, the models presented in this paper require the existence of a labeled sub-population of barcoded reference strains. These barcodes help determine the fitness baseline, as every fitness is quantified with respect to this reference genotype. This experimental design constraint facilitates the inference of the population mean fitness since most of the culture—the unlabeled reference genotype—is not tracked. Finally, the presented statistical model assumes that relative fitness is solely a constant of the environment and the genotype. Future directions of this work could extend the fitness model to properly analyze data with time-varying or frequency-dependent fitness values.It is important to highlight some of the consequences of the general experimental design and the implicit assumptions within the proposed statistical model to analyze the resulting data. First, the composition of the population is such that the initial fraction of the population occupied by the barcoded genotypes is small—usually >90% of the initial population is the non-labeled reference strain. This constraint is important as the fitness model used to fit the time series data assumes that the tracked frequencies are In total, the statistical model presented in this work and the software package accompanying the paper allow for a principled way of quantifying the accuracy with which we can extract relevant parametric information from large-scale multiplexed fitness competition assays. Furthermore, the implementation of Bayesian models and their fitting via automatic differentiation approaches opens the gate to extend this type of formal analysis to the data-rich literature in experimental evolution and other high-throughput technologies applications.Supplement 1


Gearboxes are one of the most widely used speed and power transfer elements in rotating machinery. Highly accurate compound fault diagnosis of gearboxes is of great significance for the safe and reliable operation of rotating machinery systems. However, traditional compound fault diagnosis methods treat compound faults as an independent fault mode in the diagnosis process and cannot decouple them into multiple single faults. To address this problem, this paper proposes a gearbox compound fault diagnosis method. First, a multiscale convolutional neural network (MSCNN) is used as a feature learning model, which can effectively mine the compound fault information from vibration signals. Then, an improved hybrid attention module, named the channel–space attention module (CSAM), is proposed. It is embedded into the MSCNN to assign weights to multiscale features for enhancing the feature differentiation processing ability of the MSCNN. The new neural network is named CSAM-MSCNN. Finally, a multilabel classifier is used to output single or multiple labels for recognizing single or compound faults. The effectiveness of the method was verified with two gearbox datasets. The results show that the method possesses higher accuracy and stability than other models for gearbox compound fault diagnosis. Gearboxes are one of the most widely used speed and power transfer elements in rotating machinery and play a vital role in the manufacturing industry. Gearbox failures can lead to unplanned shutdowns, causing substantial economic losses and even significant casualties. Therefore, in order to prevent accidents and ensure the efficient operation of mechanical systems, it is essential to carry out fault diagnosis of gearboxes ,2.Among the gearbox fault diagnosis methods, intelligent fault diagnosis is one of the most widely used methods. Hajnayeb et al.  designedDriven by artificial intelligence technology, deep learning is also widely used in fault diagnosis. Compared with traditional intelligent fault methods, deep learning-based methods are free from reliance on expert knowledge and signal pre-processing methods and have obvious advantages in the face of massive data. Zhang et al.  proposedIn recent years, some scholars have attempted to construct multiscale convolutional neural network models for capturing the multiscale features of vibration signals. Chen et al.  combinedAttention mechanisms consider weighting effects, i.e., mapping relationships between inputs and outputs, which can enhance critical features and weaken redundant components ,21. Ther(1) For spatial attention, the information interaction between channels is ignored because the features of each channel are treated equally. Similarly, channel attention is directly global to the information within the channel and tends to ignore the information interactions in space .(2) In the face of compound faults, conventional classifiers can only output one label instead of multiple labels, meaning it is impossible to classify compound faults into two or more single faults. Compound faults are considered a special independent failure mode in fault diagnosis . For sinlt forms . The incThe main contributions of this paper are as follows:(1) A channel–space attention module (CSAM) is proposed to solve the side effects of the bottleneck structure in hybrid attention. Then a CSAM-MSCNN is designed based on the CSAM and multiscale convolutional neural network (MSCNN), which can effectively solve the feature redundancy problem brought by multiscale feature fusion. In addition, the CSAM-MSCNN also takes into account the interaction of channel information and the interaction of spatial information.(2) For solving the deficiency of a traditional fault diagnosis mode in a compound fault, a gearbox compound fault diagnosis method is proposed by combining a multilabel classifier and CSAM-MSCNN, which can decouple the compound fault into multiple single faults.(3) Two gearbox datasets are leveraged to validate the compound fault diagnosis capability of the proposed method. The experimental results show that the proposed method has higher prediction accuracy for compound fault than the classical diagnosis methods.The rest of the paper is organized as follows: A CNN, a supervised deep learning method, has achieved excellence in speech recognition, image classification, and target detection. Typically, CNNs contain a convolutional layer, an activation layer, a pooling layer, a classification layer, and some techniques to improve the model’s generalization ability, such as batch normalization.The convolutional layer is the core component of the CNN model, enabling local connectivity and weight sharing through convolutional kernels. The convolution kernel slides along the input feature map and performs convolution operations with the data in the perceptual field to achieve feature extraction. The specific arithmetic formula is as follows:Batch normalization (BN) is used to reduce the internal covariance bias and accelerate the training of deep neural networks. The BN layer is usually added after the convolutional or fully connected layer and before the activation function. The mathematical formula for the BN layer is as follows:The activation function enables the network to gain nonlinear representation capability, enhances the feature representation of the model, and maps otherwise linearly indistinguishable multidimensional features to another space, making the learned features easier to distinguish. In recent years, rectified linear units (ReLU) have been widely used as activation functions to accelerate the convergence of neural networks. The ReLU is calculated as follows:The pooling layer is usually placed after the convolutional layer to reduce the number of feature dimensions and parameters and to prevent network overfitting. A typical pooling layer includes maximum pooling and average pooling with the following operations:After multiple convolutional and pooling layers, a few fully connected layers are usually secured and used to integrate the extracted features. The activation function in the fully connected layer usually uses the ReLU function. For a one-dimensional input The SoftMax classifier (SC) is trained using a cross-entropy loss function and is widely used in multiclassification tasks. Given a training set The cross-entropy loss function has a more vital global optimization ability and faster convergence than other loss functions. It is widely used in deep convolutional neural networks with the following equation:Since the traditional SC cannot handle the multilabel problem, some changes are made in the output layer activation function, loss function, and labels. First, the Sigmoid function is chosen as the activation function for the last fully connected layer. Similarly, given the training set Then, in multiclassification, a sample has only one label, while a sample in multilabel classification may contain more than one label. The multilabel classification problem is usually converted into an Finally, a class-unique thermal coding is used for the labels, i.e., the number of all single-fault types is used as the length of the label vector, and the compound fault is considered as a combination of multiple single faults so that its label exists as one at various indices.The SC takes out the fault type with the highest confidence probability as its prediction label by the argmax function. The multilabel classifier (MLC) filters the confidence probabilities by a threshold The differences between SC and MLC are shown in The convolutional block attention module (CBAM)  is a typInspired by the spatial attention module structure in the CBAM, an improved channel attention mechanism was proposed using a one-dimensional convolution instead of the original shared fully connected layer. The side effects of bottleneck structures were avoided while ensuring cross-channel information interaction and reducing model complexity. The design of the specific improved channel attention module is shown in The channel attention module in the CSAM was processed as follows: First, the input feature map The spatial attention module in the CSAM handles the process as follows: First, the feature map The network architecture constructed in this paper is shown in The feature extraction layer performed feature extraction on the input sample To solve the feature redundancy problem caused by feature fusion, the CSAM assigned different weights to the fused features. Attention-corrected features were obtained by enhancing critical fault information and suppressing useless information. Finally, the feature map was downscaled by global average pooling to get the feature map The main advantages of the CSAM-MSCNN proposed in this paper are as follows: (1) The feature extraction layer of the network can significantly enrich the fault feature information obtained by feature extraction of the input fault samples from three different scales. (2) Using the hybrid channel–space attention mechanism, the large amount of fault feature information extracted from the multiscale structure is weight mapped to enhance key features and weaken redundant CSAM, effectively solving the feature redundancy problem caused by multiscale feature fusion and improving the efficiency of fault diagnosis. (3) CSAM optimizes the bottleneck structure of the channel attention module in CBAM. While ensuring cross-channel information interaction, the side effects of the bottleneck structure are avoided, and the model complexity is also reduced. (4) The CSAM-MSCNN uses a Sigmoid function with a binary cross-entropy loss, which provides independent probabilities for each class and an unrestricted sum of possibilities for all classes, solving the problem that traditional intelligent fault diagnosis cannot classify compound faults into two or more single faults.The CSAM-MSCNN proposed in this paper consisted of three gearbox compound fault diagnosis parts. The first part was to collect the gearbox vibration signal using the digital acquisition system, sample it and divide the dataset. The second part was to train the CSAM-MSCNN model. The third part was the performance test evaluation of the completed training model to realize the compound fault diagnosis of the gearbox. In this method, there was no need to extract and select features manually. The original vibration signal could be used directly to achieve fault diagnosis in an end-to-end manner. (1) Acquisition of gearbox vibration signals using acceleration sensors.(2) The sample dataset is constructed by the overlapping sampling of the original vibration signals, and the training set, validation set, and test set are divided randomly in proportion.(3) Construct the CSAM-MSCNN model, set the network hyperparameters such as learning rate, sample batch size, and the number of training iterations, and initialize the network weights.(4) The CSAM-MSCNN is trained using the training set samples, and the error between the network output and the sample labels is calculated using the binary cross-entropy loss function. The error is back-propagated according to the Adam gradient descent algorithm, and the network weight parameters are updated up to the set number of training iterations. The network is evaluated using the validation set for each training round, but backpropagation of errors and network weight updates are not performed.(5) Performance test evaluation of the completed trained CSAM-MSCNN using the test set. The network prediction labels of the test set samples are compared with the sample labels to obtain the test set sample accuracy.To verify the effectiveness and superiority of the method in this paper, we used SQI’s wind turbine drive system fault diagnosis test bench to conduct compound fault diagnosis experiments and collect relevant fault data. The structure of the test bench is shown in The experimental data were collected at a gearbox with 0 loads and a fixed speed of 1500 rpm. The sensor used to collect the data was a piezoelectric triaxial acceleration sensor. The sensor’s sensitivity was 95.8 mV/g, and the output bias was 10.9 VDC. The gearbox failure parts used in the experiment are shown in The gearbox vibration signal was collected by an acceleration sensor placed on the secondary parallel shaft gearbox, with a sampling frequency of 20,480 Hz and a sampling time of 8 s. For each gearbox state, the data sample contained 163,840 points. Two thousand and forty-eight points were selected as the sampling window, with five hundred overlapping points between adjacent samples. Nine hundred samples were obtained for each state sampling, and their time domain plots are shown in To verify the effectiveness of the improved attention module CSAM proposed in this paper, the CSAM-MSCNN was compared with the CBAM-MSCNN, convolutional neural network (CNN) , fully-cTo supplement the effectiveness of the proposed method, simulation data were used to test the diagnostic performance of the proposed model. The structure of the gearbox simulation model is shown in The output layer dimension of the network was changed to three, and the rest of the model parameters are shown in The data for this experiment originated from the 2009 PHM Challenge, which are representative of general industrial gearbox data. The gearbox contained three shafts: the input shaft; the idler shaft; and the output shaft. It also included six bearings and four gears, divided into spur and helical gears. In this paper, the data of the spiral gear set was selected, and only the first channel of the vibration signal was used. A sketch of the gearbox structure is shown in The experimental dataset was collected from the gearbox at low load and 30, 40, and 50 Hz speed and contained six different health states. The six states of the gearbox are shown in To further show the superiority of the method in this paper for composite fault diagnosis, it was compared with the CBAM-MSCNN, CNN, FNN, SVM, RF, and WT-MLCNN. The detailed network parameters of the CSAM-MSCNN are shown in Ten parallel experiments were conducted to avoid specificity and chance, and the experimental results are shown in To demonstrate the advantages of the proposed CSAM-MSCNN more intuitively, feature visualization was implemented using t-SNE. The features extracted at the first scale, the features extracted at the second scale, the features extracted at the third scale, the features obtained by feature fusion, the features corrected by the attention module, and the last fully connected layer features of the output layer were mapped to two-dimensional space, in the model. The output features of each network layer are shown in Analysis of the above experimental results led to the following:(1) In (2) Comparing the results of the 10 parallel experiments of the CSAM-MSCNN and CBAM-MSCNN in (3) The advantages of the proposed method in terms of diagnostic accuracy and stability can be visualized in (4) As seen from the plots (a), (b), and (c) in This paper proposed a new gearbox composite fault diagnosis method, CSAM-MSCNN. The technique combined an improved channel–space attention module, a multiscale network structure, and a multilabel classifier, which can take full advantage of the feature extraction capability of the multiscale system, the feature enhancement capability of the attention mechanism, and the edges of the multilabel classifier in handling compound faults. The proposed method’s validity was verified using gearbox data collected in the laboratory and the data from the 2009 PHM Challenge. In Experiment 1, the average accuracy of the CSAM-MSCNN was 99.79%, with a standard deviation of only 0.13%. In Experiment 2, the average accuracy of the CSAM-MSCNN was 99.61%, with a standard deviation of only 0.13%. In two experiments, the proposed method in this paper effectively diagnosed compound faults in gearboxes and showed a more competitive fault diagnosis performance than other models. The method proposed in this paper is mainly used for severe gearbox failures. The intention is to apply the method to early faint fault diagnosis in future research.


Scientific Reports 10.1038/s41598-021-94450-8, published online 29 July 2021Retraction of: The Editors have retracted this Article.Following publication, concerns were raised about the rationale for the approach presented, the assumptions and approximations used and the validity of its application to cardiology. A post-publication review of the Authors' mathematical arguments revealed a lack of clarity in the terms presented and inferences that are not adequately justified. The main concerns are that the model is based on circular reasoning which makes it non-predictive, that it assumes that blood behaves as an ideal gas, and hypothesizes that quasi-sonic flow velocities exist in the cardiovascular system while all experimental evidence shows that cardiovascular flow velocities are orders of magnitude lower than the speed of sound and do not involve any compressibility effects. The Editors therefore no longer have confidence in the conclusions presented.None of the Authors has responded to correspondence from the Editors about this retraction.