This study proposes a new approach to determine phenomenological or physical relations between microstructure features and the mechanical behavior of metals bridging advanced statistics and materials science in a study of the effect of hard precipitates on the hardening of metal alloys. Synthetic microstructures were created using multi-level Voronoi diagrams in order to control microstructure variability and then were used as samples for virtual tensile tests in a full-field crystal plasticity solver. A data-driven model based on Functional Principal Component Analysis (FPCA) was confronted with the classical Voce law for the description of uniaxial tensile curves of synthetic AISI 420 steel microstructures consisting of a ferritic matrix and increasing volume fractions of  Describing mechanical properties of macroscopic materials in relation to their microstructural features has been the focus of many studies. Multiple attempts to formulate physics-based and phenomenological models can be found in the literature ,3,4,5,6.The high number of microstructural parameters, the interrelation among them, and external factors, such as measurement accuracy and limited experimental control, make the identification of a clear relation between microstructure features and mechanical properties, such as material strengthening, very hard to achieve. Accounting for multiple physical factors increases reliability but often results in complex models requiring a trustworthy acquisition of parameters. Phenomenological models are popular due to their simplicity, but they typically lack a clear physics-based interpretation of their parameters. These parameters can be related to microstructure features by designing appropriate experiments that isolate the effect of specific variables. However, controlling microstructures to identify certain relations is a very ambitious goal in real experiments.The relationship between the volume fraction of carbides and the flow stress has been the subject of several studies ,8,9,10. As a proof of concept, this technique was applied to the analysis of the effect of The first step is the synthetic generation of microstructures. An appropriate model for representing steel microstructures needs to be selected. The advantage of the generation of model microstructure is the possibility of building microstructures with a complete control of their morphology that will allow the identification of specific relations between the microstructure features and the mechanical behavior of the material. In , a very In the present work, the synthetic generation of microstructures was based on matching  statistical and stereological parameters of the real microstructures .Methods like Voronoi tessellations , cellulaSeventy synthetic microstructures with an increasing carbide volume fraction and different texture were generated. More specifically, ten different randomly generated crystallographic textures were considered, and, for each of these configurations, seven microstructures with identical geometrical properties but different carbide volume fractions were generated. The idea behind this computational design, called a randomized block design, is to prevent the rise of “spurious relations” due to the well known influence of the orientation on the strain development . After tIn material strengthening simulations, via uniaxal tensile testing, the main results are stress–strain curves, in this case corresponding to microstructures with different carbide volume fractions and textures. For understanding the influence of these microstructural parameters on the stress–strain curve, two different approaches were considered. The first is to study the influence of the microstructural features on the parameters of the Voce model . The VocFor interpretation purposes, a modified version of the classical approach was proposed: the functions are not centered on the mean of all curves but on the expected stress–strain curve one would observe for a microstructure without carbides.For both approaches, the dependence of the model parameters on the carbides volume fraction is explained using linear mixed-effects models . The advFinally, the validity of the results was evaluated qualitatively comparing the approaches.The article outline is the following. In After introducing the crystal plasticity software and the advantages of using simulations, the results of the simulated mechanical behaviour of the different microstructures obtained via DAMASK are shown in This section describes the generation of synthetic microstructures containing geometrical, physical, and mechanical information in agreement with the microstructure features of the materials to study. The synthetic microstructures generated in this work aim to represent typical annealed AISI 420 steel microstructures containing increasing volume fractions of coarse us study .For studying the influence of carbides volume fraction on work hardening, taking into account the variation caused by the texture, a randomized block experiment with two classification factors was set. During deformation the grains in a polycrystalline material tend to rotate in relation to the loading mode , and theFirst, the geometrical structure underlying the microstructure was created. The multi-level Voronoi diagram was selected as a model for representing the microstructures. As previously mentioned, the advantage of using multi-level Voronoi diagrams is the possibility of accounting for complex microstructures, including non-convex grains and different grain-size and shape distributions for grains of different phases or precipitates. The idea behind the construction of multi-level Voronoi diagrams is to stack layers of tessellation with decreasing intensity parameters of the generator points. Without loss of generality we introduce the multi-level Voronoi diagrams considering two tessellation layers.Consider two finite sets of distinct points in Here Loosely speaking, given the two point sets However, unlike the case of the tratidional (one-level) Poisson–Voronoi diagrams, there is not a single parameter (the intensity parameter of the underlying Poisson process) determining the distribution of the geometrical characteristics of the grains. In fact, at least two intensity parameters are now responsible for the resulting grain geometry and morphology. Taking values of For the construction of synthetic microstructures, the values of the intensity parameters of the first- and second-level cells are chosen to approximately match the experimental values of the volume fractions and of the mean grain size of the material under study. For representing the annealed AISI 420 stainless steel with For representing the two-phase nature of the material, the intensity parameter of the first-level tessellation needs to take into account the volume fractions of the ferrite grains and of the carbides. Therefore, the intensity of the first-level cells is decomposed as:and 0.11 ,34, seveThe geometry of the synthetic microstructures is shown in This exact same generation was repeated for each of the ten blocks given by the different textures; hence, in total, 70 microstructures were considered. Whereas the ferrite grain size was kept steady, not changing the value of the intensity of the second-level grains, the orientations of the grains were randomly assigned. The ten diverse randomly produced textures are shown in random texture. The maximum intensity value varied from approximately 3.5 to 8 random units. The deviation between these textures was assumed to be reasonable for the range of variation observed in real materials. M, calculated for each texture using a full-constraints (FC) Taylor model [More specifically, ree RVEs a. Althouor model . The Tayor model , which ia is a dimensionless parameter related to the material’s hardening.Once the synthetic microstructures are ready, the second step is to perform the virtual experiments. The uniaxial strain and stress development in the different synthetic microstructures is simulated integrating a crystal plasticity model and a spectral solver based on the Fast Fourier Transform (FFT) implemented in the DAMASK software . A thorA longitudinal strain rate of 0.0001 te phase . The infTwo approaches were proposed and assessed in this study to relate microstructure features of the artificial microstructures shown in The total strain E is called the elastic or Young’s modulus. However, there is no consensus on how to describe the plastic component K is the strength coefficient and n the strain hardening exponent. Equation εe=σ/relation :6)σ−σy=σ−σy=εe iL and q are material constants. However, this expression is found not to be appropriate for austenitic stainless steel [Another commonly used expression, proposed by Ludwik , is:(7)σss steel . A modifss steel , was pross steel :(8)σ=k1εquations  have alsquations ,44.extended Voce law takes the form:Voce also proposed a model to describe the plastic flow of metals . The VocIn the classical law, However, describing the stress response to strain deformation over the different stages of the tensile test and for a whole range of materials with a single expression is hardly possible ,47. In tFor estimating the parameters of the Voce model described in Equation , a nonliAlthough some small deviations were observed around a strain of In this section, the influence of the carbides volume fraction on the resulting stress–strain curves  is descrPrincipal Component Analysis and its functional extension have been successfully used for data complexity reduction and variability interpretation . The ideIn the conventional FPCA, found in . FPCA atfound in . In thisediction .j-th texture. In M.The first step for the modified FPCA approach is defining the mean stress–strain curve for microstructures without carbides. Using the stress–strain values obtained for the ten different microstructures corresponding to the ten different textures, the mean stress–strain curve for the microstructure without carbides is defined as:Secondly, the original stress–strain data are centered to the mean stress–strain curve for microstructures without carbides as shown in Then, we can perform the modified FPCA. The first two eigenfunctions are plotted in From the plot of the two FPCA scores, 1 and A2 , some adOne of the aims of FPCA is a reduction in the model complexity. Therefore, given that the first functional principal component explains more than 98% of the total variance around the expected stress–strain curve for the microstructure without carbides, the analysis was reduced to just this component see .The results of the model are shown in Fixed effects, which concern parameters associated with the levels of the experimental factor or of the explanatory variable whose effect needs to be primarily investigated;Random effects, which concern parameters associated with the levels of the blocking factor or better associated with individuals or groups drawn at random from a population.In this section, linear mixed-effects models are used for expressing the two different model parameters in terms of the carbide volume fraction and the texture. Mixed-effects models are a class of models especially used when the data present a clustered or grouped structure. They are employed to describe the relation between a response variable and the explanatory variables, giving a different role to the classification factors. Two effects were considered:i-th cluster, where Let Four different linear mixed models  were useUsing Equation , the fouj∼N0,3.54,i=1,…,70The same approach was used for giving a physical meaning to the functional principal component score Combining Equations  and 17)17), the Moreover, multiplying the coefficient of the linear mixed model by the eigenfunction valuated a,b.As a measure of goodness of fit of the two proposed models, the root mean square-error (RMSE) and the mean absolute error (MAE), the most commonly used scale-dependent metrics , were coThe RMSE is the square root of the mean of the square of all errors , were followed to understand the influence of carbide fraction on the development of the stress–strain curve controlled by the possible effect of the texture. The aim of this work was not finding the best fitting for the strain–stress curve but illustrating two different methods for obtaining insight into the mechanical behavior of the material using information on microstructure features. This was achieved by the application of a linear mixed model. Voce and other typical models used to describe the material strain–stress curve entail the assumption of a law and then the fitting of parameters. The FPCA approach has the advantage of not requiring any assumption, and it can directly evaluate the influence of an input parameter on the investigated mechanical behavior. In this respect, the approach based on FPCA allows to study the effect of the two microstructural variables, carbides’ volume fraction and texture, at any point of the stress–strain curve, highlighting differences in the intensity of the effect in the different stages of the tensile testing.The analysis of the linear-mixed model shows that in the Voce model, the carbide volume fraction strongly influences the parameters The interpretation of the results obtained from Voce and FPCA models are in line with experimental results on an AISI 420 steel with a 0.03 carbide fraction, in which it was demonstrated that the contribution of carbides (and grain boundaries) to the development of heterogeneous local strains decreases with macroscopic strain . It was o et al. . It is rAs pointed out previously, the reader should bear in mind that tensile curves have been created from the application of a phenomenological hardening law in a crystal plasticity model previously applied and validated in . This haThe design of a randomized-block experiment allows to study the contribution of the Multi-level Voronoi diagrams prove to be a flexible model that allow to represent the microstructure under analysis.The approach is simulation-based, and hence it is fully reproducible and tuneable for other microstructure-features and mechanical-properties investigation.The FPCA model is a flexible approach that does not require any physical assumption and that can be applied also for modeling the mechanical behavior, highlighting the effect of the different sources of variations given by the microstructural features.Linear mixed-effects models are able to give a clear interpretation of the model parameters of both the Voce and the FPCA model in terms of the carbide volume fraction and the textures.The presented research methodology can be applied to other alloys with different precipitates such as graphite in cast iron or intermetallics in superalloys.


Nowadays people are mostly focused on their work while ignoring their health which in turn is creating a drastic effect on their health in the long run. Remote health monitoring through telemedicine can help people discover potential health threats in time. In the COVID-19 pandemic, remote health monitoring can help obtain and analyze biomedical signals including human body temperature without direct body contact. This technique is of great significance to achieve safe and efficient health monitoring in the COVID-19 pandemic. Existing remote biomedical signal monitoring methods cannot effectively analyze the time series data. This paper designs a remote biomedical signal monitoring framework combining the Internet of Things (IoT), 5G communication and artificial intelligence techniques. In the constructed framework, IoT devices are used to collect biomedical signals at the perception layer. Subsequently, the biomedical signals are transmitted through the 5G network to the cloud server where the GRU-AE deep learning model is deployed. It is noteworthy that the proposed GRU-AE model can analyze multi-dimensional biomedical signals in time series. Finally, this paper conducts a 24-week monitoring experiment for 2000 subjects of different ages to obtain real data. Compared with the traditional biomedical signal monitoring method based on the AutoEncoder model, the GRU-AE model has better performance. The research has an important role in promoting the development of biomedical signal monitoring techniques, which can be effectively applied to some kinds of remote health monitoring scenario. Telemedicine is the use of electronic information and telecommunication technology to provide the health care that people need while practicing social distancing . The fieNowadays, remote health monitoring relies on artificial intelligence, the Internet of Things (IoT), cloud computing and other Internet technologies . There aIn order to solve the problems of existing remote biomedical signal monitoring methods, this paper introduces the IoT, 5G communication, artificial intelligence and other technologies and constructs a biomedical signal monitoring framework based on GRU-AE deep learning model, which realizes the automatic collection and intelligent analysis of multi-dimensional biomedical signals. The framework collects biomedical signals through IoT sensing devices, and then uses high-speed mobile communication networks to transmit them to the cloud server in real time. The GRU-AE model deals with the correlated biomedical signals based on time series to achieve more accurate and efficient intelligent health monitoring. The proposed framework has the strengths of fast response and high accuracy. It is especially suitable for the intelligent monitoring of biomedical signals such as body temperature under the COVID-19 pandemic.The structure of this paper is organized as follows. In In recent years, many remote health monitoring methods based on multi-techniques have emerged. Most monitoring frameworks are implemented using technologies such as the IoT and wireless sensor networks. Yang  designedFurthermore, artificial intelligence technology has also been widely used in the fields of medical health and biomedical signal processing . Guo 1616 autonoIn summary, artificial intelligence, IoT and other techniques have been applied in the field of biomedical signal monitoring and medical health. However, the current related research works have some limitations. Remote healthy monitoring through the IoT and cloud computing is simple collection. Biomedical signals are simply recorded or reminded that they exceed the normal range. Most biomedical signal processing methods lack analysis of biomedical signal data in time series. They cannot process multi-dimensional biomedical signal data in parallel . At presThe proposed biomedical signal monitoring framework consists of four layers including: (1) Biomedical signal perception layer, (2) Network layer, (3) Intelligent monitoring layer and (4) Application layer, shown in (1)The biomedical signal perception layer is the sensing device layer. In this layer, IoT devices  are widely used to collect different biomedical signals from users.(2)The network layer is responsible for transmitting the data collected by perception layer. The network connection between this layer and the perception layer usually relies on a wireless sensor network, such as Wi-Fi, Bluetooth, etc. The data transmission is based on various communication networks such as LAN, wired broadband and mobile communication networks.(3)The intelligent monitoring layer is the most critical part of this framework. The deep learning model is deployed here. It generally has three main steps: (1) data processing, (2) deep learning model training, (3) real-time monitoring. This layer is generally deployed in the cloud. It can even be deployed in the edge cloud . In the (4)The application layer is used to deploy applications suitable for this framework. At present, the main application proposed in this paper is health monitoring. It can also provide some other health data statistical analysis applications for biomedical signal data, such as health state assessment and prediction.The workflow of the entire framework is shown in The actual application scenario of the biomedical signal monitoring framework is shown in The intelligent biomedical signal monitoring model is deployed in the intelligent monitoring layer . BiomediAutoEncoder is an unsupervised artificial neural network that is used to efficiently compress and encode data to achieve the goal of dimensionality reduction. The schematic diagram of AutoEncoder model is shown in AutoEncoder consists of three layers including an input layer, a hidden layer, and the output layer. Input and output layers have an equal number of nodes in AutoEncoder. This is because the purpose of the AutoEncoder is to initialize the hidden layer parameters that will reconstruct the multidimensional input data. Encoding is the process between the input layer and the hidden layer. The encoder is usually used to reduce multidimensional data to low-dimensional data (compressed representation), whereas it may allow different representations of equal dimension and higher dimensional data (sparse representation) to be obtained. The decoding constructs the process of the output using hidden layer output weights between the hidden layer and the output layer. Decoding aims to reconstruct the input data by using the sparse or compressed representations into preferred dimensionality. In monitoring applications, the output data need to be as close to the original data as possible. The monitoring function is realized by evaluating the difference between the output data and the original data. The encoding and decoding process are shown in the following formulas.l. It is shown in the following formula.The objective function is when the difference between input and output is the smallest. It means the loss is the smallest After the model has been trained, if the Loss exceed the threshold, it indicates that the data is abnormal.LSTM has a complex structure, and the model is shown in x and the hidden layer output In addition to the sample feature The update formula of the memory cell is as follows.The update formula of the hidden cell is as follows.The final output y is calculated by the deformation of the h.Among them, the excitation function σ is the sigmoid function.GRU is mainly proposed to solve the problem of gradient disappearance in standard recurrent neural networks. Since GRU and LSTM are very similar, GRU can also be regarded as a variant of LSTM. The GRU only has an update gate and a reset gate. These two gate vectors determine which information should be passed to the output. Therefore, there are fewer parameters and calculations in GRU. It is easier to converge and has higher efficiency. However, when the data set is large, LSTM expression performance is better.σ represents the sigmoid function. In order to describe the GRU message transfer process in detail, the specific GRU unit structure is shown in W, the product of U should be obtained. Then the product of reset gate The GRU model can use the reset gate to store past information. Firstly, the product of the input m types of biomedical signal data. Each unit represents a single LSTM unit or GRU unit in Both GRU and LSTM are models related to time series. The state of the previous moment is used as the input of the current moment. The memory is selected according to the gate. The state of the model in time is shown in Biomedical signal data monitoring must meet the requirements of both monitoring function and time series. This paper combines the AutoEncoder model and the GRU model, using the GRU unit as the node of the AutoEncoder. It constructs a three-layer GRU-AutoEncoder (GRU-AE) model. A fully connected layer is added to the output layer. This can make the dimensionality of the output data consistent with the input data. The entire model is shown in The input data of the model is biomedical signal data. The feature dimension of the input data is determined by the classes of the biomedical signals. The first layer of the model is the same as the ordinary GRU model. The number of GRU units is reduced in the second layer. The output of the previous layer is used as the input of this layer. The third layer has the same number of units as the first layer to achieve decoding. At the same time, each layer takes t, which are composed of n kinds of biomedical signal, as shown in the formula (14).The input of the first layer is that the collected biomedical signal data are k-th layer is represented by the superscript on the right. Then, the relationship between the input and output of the first layer at time t is:Each GRU unit has two inputs and one output, which is a function of binary independent variables. The g represents a series of function combinations of the GRU model introduced earlier.The function The input of the second layer becomes the output of the previous layer. The input and output relationships of the second and third layers are respectively:After going through the fully connected layer:In general, supervised learning is to find the minimum value of the objective function MSE, as shown in formula (19). Its role is to make the output of the model approximate the label value.t is:The Autoencoder is to find the minimum loss between output and input. Its goal is to make the output as close to the input as possible. The loss function at a certain time The loss at all moments is:Therefore, the ultimate goal is to make loss tend to 0. Each parameter is obtained by the back propagation principle of a neural network. According to the gradient descent iterative update principle of back propagation, combining the input-related functions in back propagation, the update of some parameters in the coding layer is shown in the following formula:Through the GRU-AE model, multiple biomedical signals can be correlated in time series. The model uses a variety of biomedical signals and historical states as the basis for monitoring health. Such standards are more scientific and accurate than other monitoring models, and even human judgments. In addition, the GRU-AE model only needs biomedical signals of the health state for training.After the GRU-AE model has been trained, it can start to monitor health. The flowchart of the monitoring process is shown in The experimental platform built in this paper collected a variety of biomedical signals from the subjects, and analyzed them with heart rate and body temperature as examples. In the COVID-19 pandemic prevention and control scenario, body temperature is the main monitored parameter. When there is an issue with human health, body temperature and heart rate are usually abnormal, rising or falling. Doctors often judge whether there are health issues according to the abnormal body temperature and heart rate . HoweverIn answering to the feasibility and credibility of the experiment, this study selected subjects of different age and gender who could be easily tracked. This paper selects 2000 subjects between the ages of 18–50 and the duration is 24 weeks. Specifically, there were 978 male and 1022 female who are evenly distributed in the range of 18–50. The males accounted for 48.9% of the total subjects. In addition, all 2000 subjects had no special diseases and were healthy in the month before the tracking test.In this experiment, a variety of biomedical signals were collected by wearable IoT sensor devices. Biomedical signal data were collected every hour, and a total of 8,064,000 sets of biomedical signal data were obtained. Among them, 613 subjects had health issues  during the experiment period.In order to verify the performance of the model, this paper divided the acquired data into a train set and a test set. More specifically, based on the time series characteristics of biomedical signals, we selected the data from week 1 to week 20 as the training set, including 2000 subjects containing 6,720,000 data. The data from week 21 to week 24 were the test set, including 2000 subjects containing 1,344,000 data. For each subject, there were a total of 672 sets of biomedical signal data in the 4 weeks of the test set. In this paper, a 20-year-old male subject and a 50-year-old female subject are taken as examples to analyze and elaborate the experimental results. The data of the former are defined as test set 1, and the data of the latter are defined as test set 2, shown in MAE) measures the average magnitude of the errors in a set of forecasts, without considering their direction. It measures accuracy for continuous variables. The root mean squared error (RMSE) is a quadratic scoring rule which measures the average magnitude of the error. The MAE and the RMSE can be used together to diagnose the variation in the errors in a set of forecasts. The formulas of MAE and RMSE can be expressed as follows.The mean absolute error  is shown in the following formula:When the test set data are input to the trained model, if the output result is very close to the input, it means that the data are a healthy biomedical signal. When the model output differs greatly from the input, it means that biomedical signal is unhealthy. Therefore, the difference can be used to determine whether there is an unhealthy state. The size of the threshold determines the performance of the model. Similar to most classification models, this paper evaluates the accuracy of model by constructing a confusion matrix. FPR) is shown in the following formula:The false positive rate , and multi-dimensional biomedical signal data need to be fused and analyzed from a horizontal perspective.AUC metrics. Meanwhile we introduced the ratio of RMSE to MAE to diagnose the variation in the errors in a set of forecasts. Compared with the traditional AutoEncoder model, shown in AUC metric, the results in AUC increased by 15.9%). These results reveal that our proposed model significantly improves the accuracy of health monitoring. The increment in accuracy also indicates a better precision in health issue judgement. It can be seen that the improvement of monitoring accuracy can benefit from combining the effective analysis of time series data and multi-dimensional data fusion analysis.In our remote biomedical signal monitoring framework, we deployed IoT devices, 5G communications and a novel GRU-AE deep learning model to enable the process of time series data and the fusion analysis of the multi-dimensional data. In order to benchmark the performance (the ability to solve the above issues) of our proposed model, we introduced health issues’ overall accuracy and Compared to existing studies, such as the studies of ,19,22, rA biomedical signal monitoring framework based on deep learning is proposed. It can collect, transmit and intelligently analyze multi-dimensional biomedical signals in real time to realize remote health intelligent monitoring.A GRU-AE biomedical signal monitoring model is proposed, which addresses the time series biomedical signals data to realize personalized intelligent analysis.The experimental platform of biomedical signal monitoring framework based on deep learning is built. The experiment collected the biomedical signal data of 2000 subjects, and successfully realized remote health monitoring. The experimental results show that GRU-AE outperforms the traditional AutoEncoder model.This paper proposes a biomedical signal monitoring framework based on deep learning in combination with the IoT, 5G communication, and artificial intelligence technique. The main contributions are summarized as follows:Considering the COVID-19 pandemic scenario, remote health monitoring can obtain and analyze human body temperature or other biomedical signals while avoiding direct body contact. Furthermore, it can reduce the risk of transmission and labor costs, and improve monitoring efficiency and accuracy. In future work, this framework will be applied to remote health monitoring of the COVID-19 pandemic, such as quarantining people. In addition, the framework can also carry out intelligent remote health monitoring for the elderly and those in a recovery period.


We present Annealed Mutational approximated Landscape (AMaLa), a new method to infer fitness landscapes from Directed Evolution experiments sequencing data. Such experiments typically start from a single wild-type sequence, which undergoes Darwinian in vitro evolution via multiple rounds of mutation and selection for a target phenotype. In the last years, Directed Evolution is emerging as a powerful instrument to probe fitness landscapes under controlled experimental conditions and as a relevant testing ground to develop accurate statistical models and inference algorithms (thanks to high-throughput screening and sequencing). Fitness landscape modeling either uses the enrichment of variants abundances as input, thus requiring the observation of the same variants at different rounds or assuming the last sequenced round as being sampled from an equilibrium distribution. AMaLa aims at effectively leveraging the information encoded in the whole time evolution. To do so, while assuming statistical sampling independence between sequenced rounds, the possible trajectories in sequence space are gauged with a time-dependent statistical weight consisting of two contributions: (i) an energy term accounting for the selection process and (ii) a generalized Jukes–Cantor model for the purely mutational step. This simple scheme enables accurately describing the Directed Evolution dynamics and inferring a fitness landscape that correctly reproduces the measures of the phenotype under selection , notably outperforming widely used inference strategies. In addition, we assess the reliability of AMaLa by showing how the inferred statistical model could be used to predict relevant structural properties of the wild-type sequence. Over the last few years, the development of increasingly accurate high-throughput biochemical assays with massive parallel sequencing techniques has established large-scale genetic screening as a fundamental tool for the investigation of the relationship between evolution, fitness and other important biological concepts that were behind the experimental research ,25,26,27These experiments that simultaneously screen up to millions of variants of a given protein come in two main flavors. Deep Mutational Scanning (DMS) experiments , where aRecently, high-throughput screening experiments have been used to predict the folded three-dimensional structure ,29. It hBesides the motivation to predict the protein structure, we argue that Directed Evolution experimental data can be employed to infer a global genotype-to-phenotype mapping, or in other words, a comprehensive fitness landscape. Indeed, such experiments allow us to extensively explore the sequence space around the wild-type sequence, thanks to the continuous generation of new variants. At the same time, these variants are bound to be functional since they are subjected to a selection screening. Another typical goal of DE experiments is in fact the production of one or more specific variants that are optimal with respect to the selection process. We point out how this is conceptually different from measuring the effect of single-point mutations on fitness. In this case, no statistical model is learned, and instead, an accurate fitness score is associated to a limited pool of sequences as in ,7). None. None7])As more high-throughput sequencing data of screened libraries are available, new computational methods for accurate statistical modeling of the genotype–phenotype association are actively developed. Most of the computational strategies developed so far rely on two approaches: (i) DCA-inspired models of phylogenetically related sequences used to describe local fitness landscapes ,43,44,45More recently, alternative unsupervised strategies have been proposed ,53 to coIn this paper, we propose Annealed Mutational approximated Landscape analysis (AMaLa), a new unsupervised inference framework that effectively takes into account the mutational aspects of Directed Evolution experiments in terms of a global likelihood to observe a time series of variants’ abundances. AMaLa specifically aims to model the whole in vitro evolutionary trajectory in contrast to the DCA approach that only considers the last sequenced round. The ultimate purpose of the method is to infer a global genotype-to-phenotype mapping, defined in terms of a multivariate Potts-like Hamiltonian with both additive contributions from individual residues and pairwise epistatic interactions. Such a mapping assigns a score that is a proxy for functionality to all possible protein sequences. We remark that the method does not require computing an enrichment ratio of the variants population.We use the AMaLa inference scheme to analyze three Directed Evolution high-throughput experiments ,29. OnceAnnealed Mutational approximated Landscape (AMaLa) uses the sequencing samples of rounds of Directed Evolution experiments to learn a map between the protein amino acid sequence and the fitness associated with the selection process, generically indicated as the fitness landscape. Typically, fitness in these experiments is related to the binding affinity to a certain target or to more complex phenotypic traits, such as antibiotic resistance in bacterial strains.t in the following form:t, a at round t. We will implement a maximum likelihood estimate of We consider the probability of observing a generic sequence at a certain time (or round) ing form:P(t)(S)=equation  is related to the fitness of the sequence in a selection process. In analogy with standard DCA analysis, we choose to parameterize the energy function as a generalized Potts model:To describe the selection term, we introduce a statistical energy ractions . The amil to k over a time interval t. In Directed Evolution experiments, the starting point is typically a single sequence, the wild-ype, that undergoes several rounds of error-prone PCR to create the initial library to be screened. Under the hypothesis that mutation is a site-independent process, we can express the probability of observing a sequence t through Equation μ=n matrix:Wl→k(t)μ=The normalization factor is t as:Combining the Jukes–Cantor mutational model with the selection process term, we obtain the Hamiltonian expression and thus the probability of finding a sequence Comparing Equation  to the cEquation  to obtaiEquation , one asst is proportional to t rounds of selection to be observed at round t. In this simple case, the inverse temperature t. Temperature decreases with subsequent rounds, and in the theoretical limit of an infinite number of selection rounds, the only surviving sequence is the ground state of the Hamiltonian E, i.e., the sequence with the larger probability according to the model.The The likelihood of the whole experiment outcome is obtained by substituting Equation  into Equrameters ,57. See We tested AMaLa on three recently published Directed Evolution experiments: two are described in  and one We used two strategies to test the inferred fitness landscape: (i) by direct comparison of the predicted fitness with experimental measures of the phenotype under selection in the Directed Evolution experiment for a set of variants; (ii) through indirect assessment of the predicted 3D structure of the protein using the inferred epistatic interaction of the learned model . The fiHigh-throughput measurements ampicillin resistance (viz. the same phenotypic trait under selective pressure in ) of singented in . The fitented in  , whereas the second, not surprisingly considering the extremely long time-scale involved in the evolutionary process, shows a remarkably high degree of variability (average sequence identity of 19%). Both can be used to learn a statistical model  through a model that explicitly  takes into account both mutation and selection steps could, in principle, generate a more accurate model of the selection process, providing at the same time better structural information.We assessed the quality of the DCA scores derived from AMaLa and PlmDCA  by cIn complete analogy with what was already observed in , when thInterestingly, in , the autAs a further check, we decided to employ PlmDCA to infer the energy landscape not only on the last round but on all the available ones. The results in terms of contact prediction on  data arep and (ii) the strength of the selective pressure The results on AAC6, PSE-1 and TEM-1 clearly indicate how different experimental conditions (in particular the choice of the mutation rate and the selective pressure) impact the ability of the inference algorithm to predict either functional and structural properties. In particular, the interplay between the mutation rate and the selective pressure determines the different dynamical regimes where the assumptions at the basis of our inference method could be more or less verified. To understand the limits of AMaLa, we simulated in silico Directed Evolution experiments at different ranges of selection and mutation rates (see details in wild-type sequence (or more precisely the ground truth energy of such sequence) fixed. We used a subset of variable sizes among the total simulated rounds . The performance of the inference is assessed in terms of the correlation between teacher and student energies computed over a test set of sequences not used to train the model.In all experiments, we keep the teacher energy parameters and the initial In Unfortunately, we do not have access experimentally to a quantitative assessment of the strength of the selective pressure, making a direct comparison with other experiments difficult. The method works at intermediate selective pressure as the selection tends to undermine the method assumptions see . Indeed,Equation  an inaccIn Directed Evolution experiments, one of the limiting factors is the number of selection rounds that can be sequenced (and that therefore can be used for the inference). In the following, we will assume we can afford only between two and five rounds of sequencing, and we ask which rounds bring the larger information content.As shown in Furthermore, the in silico experiments can be used to investigate the generalization power of the learned fitness landscape beyond the local region of sequence space probed by the experiment. More specifically, how far from the wild-type an inference strategy is still able to predict the fitness? To answer this question, we trained both AMaLa and PlmDCA on rounds . Then, we tested the teacher–student energy correlation over randomly extracted sequences at a Hamming distance up to the whole sequence length . More refined data can be found at BioSNS site: http://laborator- iobiologia.sns.it/supplementary-mbe-2019/. Raw data related to [https://github.com/sanderlab/3Dseq. Both datasets were downloaded on 12 June 2020.Raw data related to experiment  are availated to  can alsoThe abundances of the sequenced variants are used to compute the normalized weights Equation . To learhe Model , we maxihe Model  using a he Model  is conveEquation , thus pei and j, the Frobenius norm over all possible amino acid combinations of the interaction parameters F matrix: To compute an epistatic score associated with each pair of residues, we used the Frobenius norm with APC correction . Two residues are in contact if at least two heavy atoms have a distance less than a present at the round t for To simulate a Directed Evolution experiment, we define a dynamical process that mimics the mutation and selection steps occurring in a real experiment. We define p . The parameter The energy function Equation  and giveFrom the set of variants produced by the mutation process, which we identify as Finally, the population of clones that survived the selection step is amplified up to a fixed number In addition, we randomly sample In The parameters setup of the simulation was chosen with the aim to be as close as possible to a real experiment and to not introduce unnecessary artificial features. The teacher model for the ground truth fitness landscape is obtained by the inference of a Potts model on a Deep Mutational Scan (DMS) experiment . The infWhile finalizing this work, we became aware of a similar approach described in . Their sEquation  may be chistory of the experiment in terms of all sequenced rounds of selection. By doing so, we are able to infer a better statistical model both in terms of the ability to predict functional phenotypes and structural properties of the protein.In this work, we presented AMaLa, a new inference strategy for modeling Directed Evolution experiments. At the heart of our algorithm, there is an effective model of the two main ingredients of Directed Evolution experiments: mutation and selection. Other competing algorithms’ computational strategies typically use data from the last sequenced round, whereas our model leverages all the available As Directed Evolution is becoming a very relevant instrument to test different evolutionary theories on a controlled ground, as well as an invaluable tool to find optimal target phenotype sequences with pharmaceutical and/or biotechnological interest, we believe that a reliable statistical modeling of the experiment has two-fold interest: on the one hand, we show how our model can quantitatively predict the trait under selection of variants that have not been used in the training data, suggesting that our model could, in principle, be used to propose sequences and/or libraries of sequences of improved biological activity. On the other hand, our statistical model could be used to optimally set the experimental control parameters. In particular, we were able to stress how relevant the trade-off between mutation and selection is in different experiments. Our findings are also corroborated by extensive in silico Directed Evolution experiments, where the modification of these two parameters can easily be taken into consideration in limits that would otherwise be experimentally inaccessible.AMaLa, of course, is a first attempt at modeling evolutionary trajectories under fixed selection pressure, although some interesting attempts have been recently published in  in the s


There has been a growing interest in the non-invasive stimulation of specific brain tissues, while reducing unintended stimulation in surrounding regions, for the medical treatment of brain disorders. Traditional methods for non-invasive brain stimulation, such as transcranial direct current stimulation (tDCS) or transcranial magnetic stimulation (TMS), can stimulate brain regions, but they also simultaneously stimulate the brain and non-brain regions that lie between the target and the stimulation site of the source. Temporal interference (TI) stimulation has been suggested to selectively stimulate brain regions by superposing two alternating currents with slightly different frequencies injected through electrodes attached to the scalp. Previous studies have reported promising results for TI applied to the motor area in mice, but the mechanisms are yet to be clarified. As computational techniques can help reveal different aspects of TI, in this study, we computationally investigated TI stimulation using a multiscale model that computes the generated interference current pattern effects in a neural cortical model of a mouse head. The results indicated that the threshold increased with the carrier frequency and that the beat frequency did not influence the threshold. It was also found that the intensity ratio between the alternating currents changed the location of the responding nerve, which is in agreement with previous experiments. Moreover, particular characteristics of the envelope were investigated to predict the stimulation region intuitively. It was found that regions with high modulation depth  and low minimum envelope (near zero) corresponded with the activation region obtained via neural computation. There has been increasing interest in the non-invasive electrostimulation of specific parts of the brain. Recently, as one of the topics in this field, stimulation of the deep brain region has gained attention . In convTemporal interference (TI) stimulation has attracted significant attention as it may achieve stimulation of specific cortical or deep brain regions without activation of superficial parts . TI makeIn the non-invasive brain stimulation studies, the electric current, as a physical agent, is computed using a volume conductor model, in which the human head (not only the brain) is considered as an inhomogeneous conductor without considering the neural model . Here, tHere, we present multiscale computational modeling to explore the effects of interferential stimulation on the mouse motor cortex for first time based on experimental measurements. In addition, the characteristics of the generated envelope were explored to intuitively predict the stimulation region.The mouse model used in this study was developed using computer tomography . The modThe electric potential generated by the current injected from the electrodes attached to the rat scalp was computed using the scalar potential finite-difference method, with successive over-relaxation and multigrid methods  to solveVe and σ denote the scalar potential and tissue conductivity, respectively. Then, the electric field was obtained by dividing the potential between the two nodes along the edge of a cubic voxel (the minimum component of the model) by the length of the voxel edge. We assigned the electrical conductivity of tissue to each tissue based on the fourth order Cole–Cole model at 1 kHz and literature values  and nodes of Ranvier (ionic channels). The variable R = 0.5 × (Rn+Rn+1) denotes the intra-axonal resistance between the centers of two adjacent compartments (nodes and internodes). At the myelinated internodes, the leak conductance was modeled as a passive element. At the nodes of Ranvier, the ionic membrane current was formulated as a conductance-based voltage-gated model based on the Chiu–Ritchie–Rogart–Stagg–Sweeney model .The stimulation condition is shown in I1+I2), which is the mean value reported in In this study, we fixed the total current injected into the two electrodes as 0.776 mA (I1 and I2 as the experiment.The effect of the frequency difference (beat frequency) and carrier frequency of the two injection currents on the stimulation was evaluated computationally and compared with the motor threshold reported in a previous study . The expAs shown in The effect of the amplitude ratio of the two injection currents on the stimulation was evaluated. The different characteristics of the generated modulated signals of the electric field and electric potential were explored. Specifically, estimations of neuronal stimulation related to the maximum, minimum, and depth of the envelope were evaluated see .In this study, we computationally investigated the effects of interference current patterns in a neural model embedded in a mouse brain using a multiscale model approach. To replicate the neuromodulation effects in the computational domain, we considered neural stimulation generated by interferential electric currents shaped by electrical and anatomical properties of the tissues in a realistic mouse head model for the first time. The model reproduced the experimental results by showing that that interferential stimulation acts on the neuronal axons. Also, this study showed which characteristics of the generated envelope can be used to predict the stimulation region to facilitate computational analysis intuitively.Multiscale modeling was applied to replicate the experiments conducted in We then explored the features of the generated envelope signal on the brain to determine which characteristics may serve as a physical metric of stimulation based on validated multiscale modeling. First, we observed that the maximum value of the generated electric field or electric potential envelope did not correspond to the exact activated nerve region given by the multiscale model. Instead, high values of the “depth” parameter  corresponded to better predictions of the activation region. We also noticed that the minimum value near zero (100% modulation) of the envelope may be used to determine the activated nerve region, which is the region in which both injection currents have the same intensity. Moreover, the combination of these metrics may help to better characterize the activated nerve region predicted using the multiscale model.A limitation of our computational model is summarized as follows: first, the mouse model did not consider the cerebrospinal fluid, whose conductivity is higher than those of the remaining tissues, altering the current direction. However, the medical images, in general, do not warrant a resolution of less than 0.1 mm, and thus, unlike humans, tissue segmentation is insufficient. Therefore, the current flow due to the complexity of the brain might not be well represented. Also, neural trajectories have a radial orientation of neuronal paths from the cortex in the mouse . Our assIn terms of validation where the experimental data is available , the motIn conclusion, we examined the effects of interferential stimulation on a neural model of the motor cortex. We considered the effects of the injection current on a realistic mouse head model. The results confirmed that varying the carrier frequency does not affect the threshold value, and the threshold value increases with an increase in the carrier frequency. The verified multiscale model for interferential stimulation was used to reveal the significant characteristics of the envelope generated by interferential stimulation to facilitate the estimation of the stimulation region. In particular, regions with a high modulation depth and low minimum envelope correspond to the activation region.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.AH and JG-T conceived and designed the study. JG-T developed the interferential multiscale model. AA conducted the simulation experiments. AA and JG-T processed the data. All authors analyzed the data, wrote the manuscript, and read and approved the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The skin barrier is provided by the organized multi-layer structure of epidermal cells, which is dynamically maintained by a continuous supply of cells from the basal layer. The epidermal homeostasis can be disrupted by various skin diseases, which often cause morphological changes not only in the epidermis but in the dermis. We present a three-dimensional agent-based computational model of the epidermis that takes into account the deformability of the dermis. Our model can produce a stable epidermal structure with well-organized layers. We show that its stability depends on the cell supply rate from the basal layer. Modeling the morphological change of the dermis also enables us to investigate how the stiffness of the dermis affects the structure and barrier functions of the epidermis. Besides, we show that our model can simulate the formation of a corn (clavus) by assuming hyperproliferation and rapid differentiation. We also provide experimental data for human corn, which supports the model assumptions and the simulation result. Stem cells in the basal layer continuously supply cells into suprabasal layers, consisting of the spinous, granular, and cornified layers from below. The cornified layer, the outermost part of the skin, consists of flat, regularly stacked cornified cells and the lipids filling the spaces between them, and its organized structure is responsible for epidermal barrier functions. Therefore, to understand epidermal homeostasis and its barrier function, one has to elucidate how the organized layer structure is maintained.Skin is a pivotal organ that prevents water loss and protects us from various external pathogens and stimuli6. One advantage of using agent-based models is that they can easily incorporate various features, such as stem cell dynamics, differentiation, lipid production and secretion, and cell morphology. Pathological states of the skin can also be easily created, enabling one to study wound healing9 and the development of psoriasis10. An integrated model of the epidermis that includes all features relevant to epidermal homeostasis would be desired to simulate various skin diseases and understand their mechanisms.Mathematical modeling is a valuable tool to investigate the emergence of epidermal homeostasis as a complex phenomenon. Among others, agent-based models have been widely adopted to study homeostatic properties of the epidermis18. Mathematical models were proposed for the calcium gradient in the epidermis20, as well as localized calcium excitation in cultured keratinocytes21, and the effect of the calcium layer on the epidermal structure was investigated23. The effect of calcium was further studied by using agent-based models25. By introducing an agent-based model of the epidermis, we suggested that the acceleration of differentiation due to calcium ions could stabilize the boundary between the granular and the cornified layers26.One factor that needs to be taken into account to have such an integrated model is a localized layer of calcium ions beneath the cornified layer, which could affect barrier functions27, which suggested that an increase of the surface area due to dermal undulations could lead to an increase of epidermal thickness; This effect has been supported by an experiment28. Dynamical processes of dermal deformation were also studied: We proposed an agent-based model with the deformable dermis, which successfully simulated upward protrusions of the dermis starting from a flat dermis29, as observed in real human epidermis. It is well known that growing tissues can develop a spatial structure due to the buckling instability38; our model has revealed that the structure could also affect the spatial patterning of stem cells.Another important factor is the shape of the dermis, which could affect the spatial patterns of cell supply from the basal layer. The effect of dermal shape on the thickness of the epidermis was studied using a rigid, undulating dermis26 has not taken into account deformability of the dermis; The dermal deformation model29 has taken into account only the dermis, the basement membrane, and the basal layer, disregarding the suprabasal layers. In this work, we integrate these two models into a unified model that can simulate epidermal homeostasis with the deformable dermis. This model includes important aspects for simulating the maintenance of the epidermis, such as cell division in the basal layer, calcium-dependent cell differentiation, flattening of cell shape during differentiation, secretion of lipids, desquamation, and the development of a spatial structure of the dermis due to cell division. By numerical simulations, we demonstrate that the model can produce a stable epidermis with well-organized layer structures. Extensive numerical investigations reveal that the stability of the layer structure depends on the supply rate of cells from the basal layer. Besides, by controlling the stiffness of the dermis, we show how the hardening of the dermis affects epidermal homeostasis. Finally, we show that our model can be used to simulate a skin disease that causes morphological changes in both the epidermis and the dermis, such as the corn (clavus). We also show an experimental result of the corn formation and compare it with the simulation result.Our two previous models mentioned above are complementary: the epidermal modelWe consider the system composed of the dermis, the basement membrane, and the epidermis. The dermis is a soft elastic substrate, which is modeled by particles adhesive to each other. The stiffness of the dermis is controlled by modifying the adhesion strength. The basement membrane is modeled by particles connected in the form of a triangular lattice. The lattice edges are assigned stretching and bending energies so that the membrane exhibits elasticity. Membrane particles are adhesive to dermal particles. Epidermal cells are represented by spheroids, whose flattening rate depends on differentiation.The basal layer is defined as a monolayer of basal cells, which are stem cells or transit-amplifying (TA) cell. Stem cells are strongly bound to the basement membrane, whereas TA cells are weakly bound. Cells passively move due to the pressure created by repeated cell division, which causes TA cells to leave the basement membrane. Stem cells divide an infinite number of times, whereas TA cells divide a finite number of times, A cell is assigned a state variable; it starts to increase when differentiated, with the increase accelerated by calcium ions and stimulants released by the cornified cells. Cell type changes as spinous, granular, or cornified in this order as the state variable increases. Lipids are produced inside granular cells and released when calcium ions increase, which typically occurs at cornification. After cornification, the cell undergoes desquamation, i.e., peels off from the bulk  controlled by corneodesmosomes, cell-junction structures specific to cornified cells.Hence, the model consists of equations of motion for dermal particles, membrane particles, and epidermal cells; cell division cycle; cell differentiation process; cell flattening during differentiation; lipid production; desquamation; and dynamics of calcium ions and stimulants. A schematic illustration is shown in Fig.  The scales of length and time in this model were determined so that the cell diameter is 10 In the real epidermis, the barrier function is often evaluated by transepidermal water loss, the loss of body water through the epidermis. It is known that the water loss is prevented by regularly stacked cornified cells and intercellular lipids filling the spaces between them. Therefore, the barrier function requires a well-organized layer structure and sufficient lipid content. Hence we first checked whether the present model could produce an epidermis serving as a barrier both in terms of the structure and the lipid production.We performed simulations with two different conditions by changing the maximum number of cell divisions mentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimH; the dispersion G, and the spatial variation of the thickness E. A schematic illustration of these measures is given in Fig. H is the thickness of the bulk; G expressed the largest vertical deviation of isolated cells from the bulk; and E represents the magnitude of modulations of the bulk thickness. These measures can capture different features: A cell layer with uniform thickness and a well-defined boundary with the adjacent cell layer should have small G and E.Then we investigated the effect of the cell supply rate on the epidermal structure and the lipid production more systematically by varying the parameters entclass1pt{minimaH is high and both the dispersion G and the spatial variation E  are small, indicating a spatially uniform, well-defined granular layer. On the other hand, in the upper-left region, where the cell supply rate is small , and spatial variations were more enhanced (larger E/H). The differences become small but still recognizable in the cornified layer [Fig. Next, to see how the structure and the barrier function would be affected by the deformability of the dermis, we performed a simulation by increasing the stiffness of the dermis and compared the result with the previous simulation in Fig. The stiffening of the dermis directly affected the dermal shape, as diminished dermal undulations observed in Fig. We wondered if our mathematical modeling could simulate human diseases by adjusting parameters. A corn  is a well-demarcated and painful callus and typically develops on the plantar skin where the repeated friction or pressure is applied. We hypothesized that modulation of one stem cell is sufficient for corn development. We performed a simulation with the following modifications: We selected one stem cell as an abnormal cell; Those cells produced from this abnormal stem cell would divide twice as fast in the basal layer and differentiate twice as fast in the suprabasal layer as those produced from a normal stem cell. The system size was made larger than the previous simulations. As shown in Fig. 39 [Fig. Then we asked if the human corn reproduces the dynamics of proliferation and differentiation seen in the mathematical model Fig. . We anal26 and the cell supply dependence of the stability of the suprabasal layer40. Also, the shape of the dermis, as well as the spatial distribution pattern of stem cells, is qualitatively the same as in the dermal deformation model29. These features are preserved in the present integrated model. The reduction of undulation magnitude in the dermis by stiffening is also consistent with the previous model29. More importantly, the present integrated model has also revealed that the stiffness could affect the suprabasal layers, as shown in Fig. The numerical results presented above are compatible with our previous results: Using the previous model with a flat, rigid dermis, we have already reported both the stable epidermal structure as in Fig. 129, where it has been shown that a flat shape of the basement membrane destabilizes due to a buckling instability, and resulting upward protrusions and stem cell distributions are determined by differential adhesion of basal cells. This can be explained as follows: The basement membrane has stretching and bending elasticity. Since cells are adhesive to the basement membrane, cell division on the basement membrane exerts tangential forces on it, creating negative surface tension. Thus a flat shape becomes destabilized due to a buckling instability. To understand why protrusions direct upward and why stem cells are on the top of protrusions, we need to consider differential adhesion. When a cell strongly adhesive to the membrane divide, upward bending (a convex shape) would require a smaller energy cost  than downward bending (a concave shape). The same argument applies to a cell weakly adhesive to the membrane, but since it can also leave the basement membrane, it is energetically more preferable for strongly bound cells to occupy the place with upward protrusions. This scenario has been numerically confirmed29.How dermal protrusions arise has been studied in the previous work26. First, the previous model did not consider the shape change of cells during differentiation. By taking this into account, we have succeeded in producing columnar structures in granular and cornified cells, as shown in Fig. 42. We note that the flattening process was also introduced in a different model5. Second, in addition to calcium ions, we have assumed that a second factor is released from cells undergoing cornification. In the previous model, we have shown that a localized layer of calcium ions could maintain a well-defined boundary between cornified cells and granular cells. Both the previous and the present models assume that calcium ions released at the time of cornification accelerate cell differentiation, which causes stabilization of the boundary of the cell layer. How this mechanism works has been analytically confirmed by using a reaction-diffusion-advection model43. Since the previous model did not distinguish the granular and the spinous cells, however, an additional mechanism is needed to create another boundary between the granular and the spinous layers. Hence we introduced the second factor that can modify differentiation speed differently from calcium ions. The two factors work together to form two boundaries separating the spinous, granular, and cornified layers, as shown in Fig. We have made two major modifications to the previous epidermal model44, where a single population of basal cells can divide indefinitely and differentiate with a certain probability, would require a different model for the adhesion of basal cells to the basement membrane. There are studies using agent-based models on the comparison of different stem cell hypotheses4 and the mechanism for the maintenance of stem cell niche45. It is worth investigating to what degree these modifications to our model would change the stability of the epidermal homeostasis.In this work, we have modeled proliferative cells by stem cells and TA cells. In order that stem cells do not leave the basal layer, we have assumed that stem cells are bound to the basal layer more strongly than TA cells. Different cell division scenarios, such as a single progenitor compartment model46, accompanied by the decrease in the number and the activity of stem cells47. This phenomenon can be accounted for by our model: When the elasticity is lost in the dermis by photoaging, undulations in the basement membrane would be suppressed, with the surface area diminished. Then the cell supply would decrease, resulting in the thinning of the epidermis.Our result on the stiffness of the dermis Fig.  may shed26 and the dermal deformation model29. The previous epidermis model26 had already found applications in simulating a thick epidermis equivalent on an undulating substrate28 or the epidermal proliferation under the reduced adhesion of progenitor cells to the basement membrane48. In this work, by considering the deformation of the dermis, we could also simulate the formation of a corn, which was consistent with the experimental results. Furthermore, our model allows us to infer dynamics that the experiments could not directly observe, which is one of the major advantages of mathematical modeling. Our model is expected to be applied for simulating various diseases entailing structural changes of the dermis.In summary, we have presented an integrated framework for simulating epidermal homeostasis by combining the epidermal structure modelH&E staining and immunohistochemistry for formalin-fixed paraffin-embedded samples were performed on three human corn specimens. The following antibodies were used for immunohistochemistry: anti-K1 , anti-K6 , anti-K10 , anti-K14 , and anti-Ki-67 . Images of immunohistochemistry and H&E sections were captured with a BZ-9000 microscope . For quantification of Ki-67+ cells in the epidermis, the whole areas of the specimens were analyzed using ImageJ . The number of Ki-67+ cells was normalized by the length of the epidermis in each section. The institutional review board of the Hokkaido University Graduate School of Medicine approved all human studies described above (ID: 14-063). The study was conducted according to the Declaration of Helsinki Principles. Participants provided written informed consent.H, G, and E for the granular layer as follows (the same quantities are defined for the cornified layer in the same way). First, we divide the region i, j-subregions defined as i, j-subregion as the total (approximated) volume occupied by the cells divided by the area of the subregion:z direction is defined asz value of granular cells in the i, j-subregion, respectively. The mean thickness H and the dispersion G(t) of the whole cell group are given byWe define the measures E is defined as the standard deviation of The spatial modulation of the thickness Supplementary Information.


This study approaches the investigation of the simplification hypotheses in corpus-based translation studies from a syntactic complexity perspective. The research is based on two comparable corpora, the English monolingual part of COCE (Corpus of Chinese-English) and the native English corpus of FLOB (Freiburg-LOB Corpus of British English). Using the 13 syntactic complexity measures falling into five subconstructs , our results show that translation as a whole is less complex compared to non-translation, reflected most prominently in the amount of subordination and overall sentence complexity. Further pairwise comparison of the four subgenres of the corpora shows mixed results. Specifically, the translated news is homogenous to native news as evidenced by the complexity measures; the translated genres of general prose and academic writing are less complex compared to their native counterparts while translated fiction is more complex than non-translated fiction. It was found that mean sentence length always produced a significant effect on syntactic complexity, with higher syntactic complexity for longer sentence lengths in both corpora. ANOVA test shows a highly significant main effect of translation status, with higher syntactic complexity in the non-translated texts (FLOB) than the translated texts (COCE), which provides support for the simplification hypothesis in translation. It is also found that, apart from translation status, genre is an important variable in affecting the complexity level of translated texts. Our study offers new insights into the investigation of simplification hypothesis from the perspective of translation from English into Chinese. The quest for translation universals (TUs) using corpus-based translation methods spearheaded by Baker , 2 pavedBaker  defined Although corpus-based TUs research is still controversial as compared to other well-grounded and schematized corpus-based translation studies, TUs has been extensively and fruitfully investigated in the field of translation studies. In the field of translation studies, the concept of TUs has been questioned, scrutinized or even rejected by researchers , 16. ForThe development and controversies of the concept of TUs in translation research are reviewed here because simplification research has often been pursued under the umbrella term of TUs. Although theoretical and conceptual variations exist as to the scientific use of term, the TUs concept has motivated a number of corpus-based studies and greatly advanced translation research. The goal of the current study is not aimed at simply confirming or refuting the existence of simplification as a TUs candidate, instead, TUs is used as a starting point to probe into the complex nature of translational language especially when genre is brought into the picture. The paper is structured as follows. Section 1 is a general introduction providing the necessary background for the current study. Section 2 provides a review of relevant corpus-based studies on simplification, highlights some gaps in this line of research and presents the research questions. Section 3 examines the use of syntactic complexity in language and translation research. The design of the COCE corpus and the methodology of the study are described in Section 4. Section 5 reports the results and Section 6 attempts to interpret the results in relation to some previous studies on translational simplification. Lastly, Section 7 concludes by discussing the implications and caveats of our approach and outlining directions for future research.In the field of translation studies, TUs has been predominantly studied from a Eurocentric perspective , 19, 23.However, the most debated and widely discussed translational universal is perhaps simplification, which has attracted the attention of a number of scholars , 35. SimThe research on simplification has some methodological issues. First, this line of research predominantly focuses on lexical simplification while ignoring simplification at the syntactic or stylistic levels. Second, the measures chosen to study simplification are often randomly selected and more often than not to confirm the simplification hypothesis. Third, statistical methods have rarely been used to test whether the observed differences are statistically significant. In recent years, the use of the multivariate statistical methods in order to understand the phenomenon of TUs has received more attention , 44. TheFew studies have approached simplification by studying the syntactic complexity of translated versus non-translated texts. Although the term simplification has been frequently used and discussed in the field of translation studies, translated vs non-translated texts have seldom been evaluated using syntactic complexity measures. In fact, under the TUs framework, syntactic complexity is worthy of serious study because a methodical account of the syntactic features of translational language is vital to understand the important mechanism and values of the process of translation. A systematic study on syntactic complexity can provide significant insights into the simplification issue, and probe into the syntactic features of translation as opposed to non-translation.How are translated texts and non-translated texts different in terms of syntactic complexity?Does syntactic complexity differ between translated texts and non-translated texts within the same genre?Based on the above analysis, to what extent can the simplification universal be confirmed in translated texts?The purpose of the present study is to apply the complexity measures to study simplification in translated texts. We contend that syntactic complexity is an important construct for probing into simplification and knowing the real nature of the translation products. In order to investigate whether and to what extent translated English texts tend to be simpler than non-translated texts (Chinese into English translation), the study aims to addresses the following research questions:Syntactic complexity is manifest in second language writing in terms of how varied and sophisticated the production units or grammatical structures are, which has been considered an important construct in second language teaching and research . SyntactDue to the disparate development of second language acquisition and translation research, the field of translation studies has largely ignored the developments in second language acquisition. Such a situation may be related to the European tradition which attaches more importance to “direct translation” (translators work from a foreign language into their mother tongue) rather than “inverse translation” (translators work from their mother tongue into a foreign language). The opinion that translating from one’s own language does not have any but pedagogical purpose is deeply rooted in Europe, as evidenced by the widespread practice by international organizations which accept only the translation into the mother tongue . On the While there is considerable research devoted to the investigation of syntactic complexity in ESL and EFL settings, relatively little attention has been paid to the use of such measures by translation researchers despite their connection to simplification research. As far as simplification is concerned, translation researchers more often studied lexical simplification by using a number of isolated features (see Section 2). In view of the shared nature between translated language and second language output and the merits of syntactic complexity measures, corpus-based research on simplification would be remiss not to make use of such measures that have been proved effective in ESL and EFL context. A systematic study into the specific complexity patterns of translated language would yield more findings than previous research using traditional parameters.Therefore, in order to fill the existing gaps in simplification research, the current study adopts an interdisciplinary approach enlightened by similar research in ESL and EFL to probe into the translational simplification from the perspective of syntactic complexity. It is envisaged that the methods for measuring syntactic complexity in EFL can be effectively applied to translation studies to yield a scientific and systematic description of the unique features of translation. In order to get a complete understanding of syntactic complexity in translated and non-translated texts, the present study adopts the syntactic complexity measures generated by the L2 syntactic complexity analyzer (henceforth L2SCA) . The meaAs has been mentioned in the foregoing review, there remains gaps in corpus-based translation studies on simplification. With the aim of investigating the simplification features in translated texts, the current study was based on two corpora, namely, Corpus of Chinese into English (COCE) which was designed as a counterpart to the already existing corpus of Freiburg-LOB Corpus of British English (FLOB) . The comCOCE is a parallel balanced corpus that matches closely in size and composition as FLOB. The corpus contains two parts, i.e., Chinese source texts and the correspondent English translations. The current research is based on the English monolingual part of the corpus. Hu, Xiao and Hardie  used COTCOCE contains 500 text samples of around 2000 words covering 4 major genres and 15 subgenres.  As a parallel corpus designed to be comparable to FLOB in genre and size, COCE comprises news ; (2) general prose ; (3) academic writing ; and (4) fiction . Syntactic complexity is measured between translational and non-translational English as a whole and across all the four genres. The variation of genres in such a corpus design can provide a systematic analysis into the syntactic complexity of translational language, thus enabling us to get a better understanding of the simplification features.Corpus-based translation researchers have made use of different constructs and measures to study simplification features in translation. One of the reasons hampering previous research on simplification is the use of measures which are tied with individual linguistic features. The use of such measures cannot avoid the issue of “cherry picking”, i.e., intentionally selecting measures to support or reject the hypothesis based on the researcher’s standpoint. There is clearly a need for adopting holistic features to study translational simplification to answer the question of whether and in what specific areas translation tends to be simpler (or possibly more complex) than native language. In order to get a fuller picture of simplification vs complexity in translated texts, the present study adopted five subconstructs of syntactic complexity  from the L2 syntactic complexity analyzer (L2SCA) to study the syntactic complexity of translated and non-translated texts between two corpora  by translation status (translation vs. non-translation) and genres . Pairwise Mann-Whitney tests were computed to measure the differences between each translated and non-translated genre  using the 13 measures to obtain a fuller picture of the simplification features.There were four genres in our data: news, prose, academic writing, and fiction. For simplicity, we only included corpus as the independent variable of interest, together with mean sentence length as a co-variate see . As showWe next carried out separate analyses for each subconstruct of syntactic complexity, again using corpus as the independent variable of interest and mean sentence length as a co-variate. In the following, we compared translated with non-translated text for each genre using each of the 13 complexity measures. As we compared within each measure, we reverted back to their raw scores (instead of using z-scores as we did when we included different measures) and we used Mann-Whitney tests as a result of the data mostly being non-normal.In this paper, we studied the syntactic complexity between translated and non-translated texts, with the aim to probe into the simplification features in translation. For this purpose, we compared the English monolingual part of COCE, a Chinese-English corpus, with its non-translation counterpart FLOB using the 13 syntactic complexity measures (five subconstructs) generated by the L2SCA software . This tyAs can be seen from the current study, simplification has many levels and comprises a variety of linguistic features. Although the overall comparison between translation and non-translation as a whole has provided support for the simplification hypothesis, further comparisons of the four subgenres revealed mixed results. For example, the news genre shows similarities in syntactic complexity in both translated and non-translated corpora. As a non-literary genre, news writing emphasizes practicality and instantaneity and follows a rather rigid writing format, i.e. the inverted-pyramid structure. To a certain extent, such a genre would transcend the writing traditions of the source language socio-cultural norms. The ANOVA test has shown that genre plays an equally essential role as translation status in affecting the complexity level of texts. For many years, the translation field has prioritized the translation status in corpus-based investigations at the expense of other important variables such as genres. Based on the findings of the current research, we contend that genre should be treated as an important variable in the quest for simplification as well as other TUs candidates.Translation is both a cognitive endeavor carried out inside the mind of the translator and a social conduct cutting across languages and cultures . One widPreviously, most research on TUs seems to put a focus on the study of literary texts while ignoring the non-literary texts. This is also the case many studies using TEC  held at Manchester University which has been criticized as skewed towards the literary genre. Based on our research findings, we found that the quest for translation universals cannot be totally free from the source language or genre interference. Taking genre into account, the current research reveals some interesting findings that might otherwise remain hidden in corpus-based studies where genre is not taken into account. In a sense, the complexity level of texts is a combined effect of cognitive factors and translator’s decision-making process . Our resThis study was aimed at identifying the simplification features in translated texts using syntactic complexity measures to compare between translated English from Chinese and the non-translated native English writing. By systematically studying syntactic complexity in four major genres between the translated and non-translated texts, our study has lent some support for the simplification hypothesis; however, it also identifies that genre is an important variable contributing to the different profiling between translated and non-translated texts apart from translation status. Our study also shows the potential of using syntactic complexity measures for corpus-based investigations of simplification and possibly other TUs. However, the findings from the current research are only limited to Chinese-English translation. Previous research  has show