The brain tumor segmentation task with different domains remains a major challenge because tumors of different grades and severities may show different distributions, limiting the ability of a single segmentation model to label such tumors. Semi-supervised models  are strong unsupervised domain-adaptation learners. However, one of the main drawbacks of using a mean teacher is that given a large number of iterations, the teacher model weights converge to those of the student model, and any biased and unstable predictions are carried over to the student. In this article, we proposed a novel unsupervised domain-adaptation framework for the brain tumor segmentation task, which uses dual student and adversarial training techniques to effectively tackle domain shift with MR images. In this study, the adversarial strategy and consistency constraint for each student can align the feature representation on the source and target domains. Furthermore, we introduced the cross-coordination constraint for the target domain data to constrain the models to produce more confident predictions. We validated our framework on the cross-subtype and cross-modality tasks in brain tumor segmentation and achieved better performance than the current unsupervised domain-adaptation and semi-supervised frameworks. Accurate automatic brain segmentation is key to the accurate delineation of brain tumor regions on neuroimaging, which is required to formulate useful clinical practice guidelines and understand the disease and its clinical challenges. However, despite the tireless efforts of researchers, accurate automatic brain tumor segmentation on medical images has remained a technical challenge due to domain heterogeneity issues, domain shifts, costly and time-consuming labeling, low-contrast imaging, and data imbalance.With the promising progress made in medical image-segmentation models , severalNumerous UDA methods have been proposed in the literature, with a growing emphasis on learning to map representations of the source domain to those of the target domain while minimizing the distribution discrepancy . In addiFor medical image segmentation, In this study, we propose a combined framework that uses discriminators for aligning feature spaces, namely dual student models to break the limits of the consistency constraint instead of coupling the weights. We demonstrate the performance of our method on the Brain Tumor Segmentation 2019 (BraTS 2019) dataset. Specifically, we applied our method to perform the following two tasks:Cross-subtype task: We used images of HGGs as the source domain and those of LGGs as the target domain for HGG-to-LGG domain adaptation.Cross-modality task: Because the whole tumor was annotated using T2-weighted images in clinical practice, the tumor region and peritumoral edema were highlighted on fluid-attenuated inversion recovery (FLAIR) images and T2-weighted images, and the core tumor region without peritumoral edema was more visible on T1-weighted and contrast-enhanced T1-weighted (T1ce) images. We used the T2-weighted and FLAIR images as the labeled source domain and the T1-weighted and T1ce images as the target domain, which provided complementary information for the different subregions of brain tumors and a larger domain shift than that present in the cross-subtype task.To the best of our knowledge, our study is the first to use the combination of a dual student model and adversarial learning for brain tumor domain adaptation. Furthermore, we did not need an additional source-domain network or class-ratio priors  based on2.2.1.Unsupervised domain adaptation has become an important technique to alleviate the problem of highly variable data sources and costly labeling in a new domain because UDA does not rely on labeled training samples from the desired target domain. For the segmentation of white-matter hyperintensities, 2.2.In consistency-based methods, the following two roles are commonly created, either explicitly or implicitly: a teacher model and a student model . The teacher can be summarized as being generated by an exponential moving average (EMA) of the student. 2.3.In the case of UDA, adversarial training is the most common and explored approach for semantic segmentation. The objective behind this is to adapt the segmentation network to be invariant to variations between the source and target. 3.In this section, we present our proposed framework for UDA on the BraTS 2019 dataset . Our mod3.1.Our UDA framework consists of the two modules as shown in 3.2. as a one-hot vector. H, W, and D are the height, width, and depth, respectively, of the image and label. Let A robust model is the basis of source and target-domain training. Our models were trained with a supervised loss on the source domain. Formally, we set wherewhere 3.3.We combined adversarial learning with the dual student  to defin3.4.If the outputs of the two student models vary widely, directly applying the consistency constraint will cause collapse due to the exchange of wrong knowledge. The EMA teacher does not suffer from this type of problem owing to the coupling effect. For good performance of the dual student, each of the student models must be able to reliably extract knowledge and effectively exchange knowledge with the other model.As the BraTS 2019 dataset remains a significant challenge owing to the inclusion of multimodal data and domain-shift data, we put considerable effort into dealing with densely but inaccurately unlabeled target data. First, according to the smoothness assumption, a small perturbation must not affect the prediction of the samples. Therefore, we augmented the unlabeled images using operations such as random rotation/flip/reflection, contrast transformation, and noise perturbation. The transformed images were inputted into the two models to output the predictions condition}, followed by the method described by x. For student i, the condition outputs one when it is true, and zero otherwise, as follows:In addition to the abovementioned training details, to ensure that our dual adversarial student structure was trainable, we imposed the cross-coordination constraint on reliable samples from two independent models and introduced a Boolean function {wherex. x and i.x is considered to be far from the decision boundary of the ground truth, i.e., this sample has a high probability for the predicted label. We also used the Euclidean distance to measure the prediction consistency as shown:x. In addition to measuring the reliability of x from one model, the distance measurement between the predictions of students i and j was key to calculating the cross-coordination constraint. Their distance was measured by i on sample x was written as follows:Smaller distances indicate a more reliable x stems from unlabeled target data and not from the training data. For student j, we calculated the cross-coordination constraint in the same manner and marked it as Notably, 3.5.i and j, we formulated the final loss function for the domain-adaptation task as follows:With the proposed framework for training the student models 3.6.Segmentation network: We used U-Net  as the input and resampled them to a spatial size of 128 × 128 × 128 before the network training. We used the images of the HGG patients to test the performance of our framework. Our training set included the labeled T2-weighted + FLAIR MR images of 259 HGG patients as the source domain and the unlabeled T1 + T1ce MR images of 210 HGG patients as the target domain. The unlabeled T1 + T1ce MR images of the remaining 19 and 30 HGG patients were used as the validation and test sets, respectively.For the T1 + T1ce to T2 + FLAIR task, the preprocessing steps were the same as the cross-modality task described earlier. Our training set contained the labeled T1 + T1ce MR images of 259 HGG patients as the source domain and the unlabeled T2 + FLAIR MR images of 210 HGG patients as the target domain. The unlabeled T2 + FLAIR MR images of the remaining 19 and 30 HGG patients were used as the validation and test sets, respectively.4.2.4.2.1.For a fair comparison and analysis, we employed previous mainstream methods and our proposed framework to perform the same iterations with the same set of parameters for optimizers and learning rate decay. All training steps used a batch size of 2. We applied the poly learning rate, where the learning rate was multiplied by : Training the segmentation network (with no domain adaptation) on the combined source and target data and validating and testing on the holdout target dataset.(super-source): Training the segmentation network (with no domain adaptation) on source data alone and validating and testing on target data.(da-mt): Domain adaptation using only mean teacher . Trainin(da-entropy-mini): Domain adaptation using only entropy minimization .(da-adv): Domain adaptation using only adversarial training .(da-ds): Domain adaptation using the dual student model .(Ours): Proposed domain-adaptation framework using both dual student and adversarial training.4.2.2.For the evaluation of the segmentation models, we adopted two metrics: the dice similarity coefficient (DSC) and Hausdorff distance (HD). The DSC measures the general overlap rate and the similarity between two sets of image data As a boundary-based metric, the HD is more sensitive than the DSC in terms of the segmentation boundary. The HD between two point sets is defined by the sum of all minimum distances from all points of a point set to another, divided by the number of points in a point set. The point sets represent our segmentation results and the ground truth, such that the maximum HD can indicate the maximum distance of the labeled and the predicted boundary.4.3.4.3.1.HGGs and LGGs have different sizes and position distributions in terms of tumor regions. We trained all experiments for 15,000 iterations with HGG images as the source-domain and LGG images as the target domain. The networks were trained with four-channel 3D MRI volumes with a spatial size of 128 × 128 × 128 to perform four-class segmentation . The evaluation was implemented in the testing set consisting of LGG images. The performance scores for all experiments of the cross-subtype task are presented in 4.3.2.Multimodal images have abundant information that is effectively complemented, which improves the accuracy of segmentation but also increases its difficulty to a certain extent. Multimodal image information includes a large amount of unnecessary information, making the segmentation problem more difficult. We started our experiment using tumor image slices from different imaging modalities. To ensure the rigor of the controlled experiment, we used only the images of the HGG subjects for the experiment.The quantitative evaluation results of the T2 + FLAIR to T1 + T1ce and T1 + T1ce to T2 + FLAIR tasks in the cross-modality UDA task are presented in 5.We have presented a novel UDA framework based on semi-supervised methods for the tumor severity domain shift and cross-modality domain-adaptation tasks. Unlike other UDA methods that construct networks based on the characteristics of data from different domains, we did not work on designing the network but rather focused on establishing connections between the source-domain labels and the target-domain data. Despite the costly labeling, we had abundant biomedical images to utilize and could propose novel methods using source labels and the target-domain data to address UDA difficulties and alleviate the domain gap. Using a semi-supervised framework to solve the difficulties of UDA is a good research direction, and the purpose of our research in this study is also to try to utilize the advantages of semi-supervised approaches and achieve good performance on the BraTS 2019 dataset. Therefore, our framework has the potential to be applied to segmentation models that are stable in a source domain with the target-domain data from a range of clinical devices, in order to combat the problem of domain shift.6.We have presented a novel approach to multi-modality and cross-modality domain adaptations by using the dual student model and adversarial training. We evaluated our model on the BraTS 2019 dataset, which has multimodal images and includes HGG and LGG patients, to address the cross-modality and tumor severity domain shifts. The results showed an improved segmentation performance in both tasks. The superior performance in both types of domain shifts validates the efficiency and accuracy of our proposed model. We plan to extend our method to other biomedical image-segmentation datasets to overcome domain-shift problems and improve the domain application. Future studies will include extensive hyperparameter tuning for medical image segmentation and UDA.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.Ethics review and approval were not required for this study of images of human participants in accordance with the local legislation and institutional requirements. This research study was conducted retrospectively, using human subject data made available through the open-access dataset BraTS 2019.CQ, WL, and BZ designed the framework for brain tumor segmentation. BZ and JZ designed the experiments and analyzed the results. WZ and XZ analyzed the experimental datasets. CQ and WL were the major contributors to writing and editing the manuscript. JZ and CQ edited the manuscript. All authors contributed to the article and approved the submitted version.This study was supported by the NSFC (no. 61771347), the Special Project in Key Areas of Artificial Intelligence in Guangdong Universities (no. 2019KZDZX1017), the Guangdong Basic and Applied Basic Research Foundation (no. 2021A1515011576), the Basic Research and Applied Basic Research Key Project in General Colleges and Universities of Guangdong Province (no. 2021ZDZX1032), and the 2022 Guangdong Provincial Education Department Graduate Education Innovation Project (Guangdong Education and Research Letter [2022] no. 1).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.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


This contribution discusses surrogate models that emulate the solution field(s) in the entire simulation domain. The surrogate uses the most characteristic modes of the solution field(s), in combination with neural networks to emulate the coefficients of each mode. This type of surrogate is well known to rapidly emulate flow simulations, but rather new for simulations of elastoplastic solids. The surrogate avoids the iterative process of constructing and solving the linearized governing equations of rate-independent elastoplasticity, as necessary for direct numerical simulations or (hyper-)reduced-order-models. Instead, the new plastic variables are computed only once per increment, resulting in substantial time savings. The surrogate uses a recurrent neural network to treat the path dependency of rate-independent elastoplasticity within the neural network itself. Because only a few of these surrogates have been developed for elastoplastic simulations, their potential and limitations are not yet well studied. The aim of this contribution is to shed more light on their numerical capabilities in the context of elastoplasticity. Although more widely applicable, the investigation focuses on a representative volume element, because these surrogates have the ability to both emulate the macroscale stress-deformation relation , as well as to recover all microstructural quantities within each representative volume element. Rate-independent elastoplasticity is ‘path-dependent’, i.e. ‘history-dependent’. This means that the current stress state does not only depend on the current deformation, but also on ‘all previous deformations’—i.e. the ‘history’, the ‘path’, or the ‘trajectory’ of the deformation. The specification ‘rate-independent’ entails that the path of the deformation is of influence, but not at which rate the (load) path was taken.Rate-independent elastoplasticity uses plastic variables to quantify its history  variables’). The number of plastic variables depends on the constitutive model and the number of spatial dimensions considered, but not on the complexity of the history. In other words, the number of plastic variables does not increase as the deformation history complexifies.recurrent NNs, instead of feed-forward neural networks1. The reason is that recurrent NNs (RNNs) not only emulate the quantity of current interest, they also emulate auxiliary quantities, whose sole purpose is to quantify the RNN’s history. These auxiliary quantities are used by the RNN to affect its next prediction (i.e. the prediction for the next time increment). Hence, the auxiliary quantities, called ‘hidden states’ or ‘hidden variables’ in RNN terminology, play the same role for the RNN as the plastic variables for elastoplasticity. Similar to the number of plastic variables elastoplasticity, the number of hidden states does not increase as the RNN’s history grows.Most recent studies that investigate and develop neural networks (NNs) to rapidly emulate rate-independent elastoplastic behaviours focus on feed-forward NNs (FNNs) for elastoplasticity, this is not intended. FNNs, as investigated for elastoplasticity in pioneering studies5 but also recently6, are for instance useful if the entire load path is known in advance. In this case, the input of the FNN is the entire load path and its output is the quantity of interest for the entire load path . FNNs can also be used for each time step independently, if the load path is (close to) monotonically increasing.Although the previous paragraph may seem to argue against the use of 7 have included the path-dependence of elastoplasticity in an FNN by incorporating the entire load path up to the current time increment as input. In that way, the FNN’s output remains limited to the current time step.Often however, the load path is not known in advance and/or the load path is more complex than monotonically increasing. Alternatively, Huang et al.Currently, RNNs seem more popular than FNNs for the emulation of elastoplastic behaviours. Recent investigations of RNNs for elastoplasticity may be classified in different branches.16 investigates RNNs to emulate the computations of new stress states, as well as the sensitivity of the new stress state to the deformation . This accelerates mechanical simulations by rapidly emulating the construction of the linearized governing equations. It also provides a large degree of flexibility .The main branch14.A major application of interest to this branch is the data-driven discovery of macroscopic stress-deformation relations governed by representative volume elements (RVE) computations, in order to rapidly emulate time-consuming multiscale simulations13.It is worth noting that several of these works do not simply exploit RNNs, but incorporate knowledge of elastoplastic constitutive theory in order to improve their accuracyAnother  branch aims to rapidly emulate the entire displacement field of an elastoplastic simulation (for each time increment of the simulation). The only issue that remains to be computed in such emulators is the field of new plastic variables (once per increment). The primary and quintessential advantage over the approach of the previous paragraphs (when applied to an RVE) is that all microstructural quantities remain available.The disadvantage is a reduced flexibility, because the geometry and the mesh must remain the same. Hence, the RNN is generally restricted to only treat variations of the mechanical parameters and variations of the load path .17. Their framework regards a wide variety of loading states for which three variables are required to parametrize the currently imposed loading on a 2D elastoplastic RVE . The elastoplastic constitutive model furthermore accounts for large deformations and rotations, which also occur in their numerical tests.Wu and Noels investigated a similar approach17 is that the quantity of interest is not the primary solution field (i.e. the displacement field), but the fields of the plastic multiplier and the von Mises stress. The advantage is that these fields are indeed available in an instant, but the disadvantage for true multiscale simulations is that the macroscale stress-deformation response (that drives the simulation) is not available. Thus, the framework17 can only be used in combination with another RNN that emulates the macroscale stress-deformation relation (which was indeed published two years prior9).The issue with the study of Wu and NoelsA framework that emulates the displacement field once per increment, as is the focus of the current contribution, provides the flexibility to both emulate the macroscale stress-deformation relation that drives the multiscale simulation, as well as any microstructural quantity inside each RVE.However, if the RNN’s output is the entire displacement field (for each increment), the number of output variables is substantial; the RNN must emulate the displacement vector of each finite element node (besides the hidden states). This yields complex RNNs, with long training times.In order to keep an RNN’s architecture relatively simple, its number of outputs may be restricted. This can be achieved by first calculating a number of  displacements fields (i.e. ‘modes’) that are most characteristic for the displacement fields that were previously predicted by some training simulations. The RNN then only has to emulate the coefficient of each mode.23, but only three were developed for elastoplastic simulations26, to the best of the authors’ knowledge.These types of surrogates  have been developed for a wide variety of engineering simulations29, but in other domains it is known as principal-component analysis or the Karhunen–Loève expansion.The modes (which together form a basis) are obtained by first performing numerous direct numerical simulations (DNS), and storing the predicted displacement fields. One then applies singular value decomposition (SVD) to these displacement fields, in order to retrieve the modes that are most characteristic for all displacement fields. In model-order-reduction terminology, this approach is called ‘proper-orthogonal-decomposition’ (POD)31, but this is not considered in the current contribution (nor in the previous RNN-POD frameworks26).In case of (non-linear) elastic simulations, only a few POD modes are necessary to accurately represent the displacement fields, but many more modes must be incorporated in case of elastoplastic simulations to achieve a similar accuracy as for elastic simulations - albeit this depends amongst others on the amount of elastoplastic deformation that occurs. To reduce the number of modes for elastoplastic analyses, the modes may be adaptively changed during the course of a reduced-order-model simulation26 in which the modes do not evolve during the course of a simulation/emulation (but only the coefficients), it may be concluded that their capabilities and limitations are not yet fully investigated .Returning to the few RNN-POD surrogates24 and Freitag et al.25 strongly focus on the application of mechanical tunnelling, making it hard to distinguish (1) if large (plastic) deformations and rotations are considered, (2) if substantial plasticity-induced localizations occur, if these localizations occur at different locations throughout the domain for different scenarios, and (3) the range of variations for which the framework was trained. Predecessors to these studies25, e.g. Nagel et al.32, also did not reveal these points.For instance, the studies of Cao et al.26 clearly mentions the limitation to small deformations and rotations. Furthermore, plasticity-induced localization only appears at one or a few location(s) that do not change during the course of the simulations. Moreover, the applied boundary conditions seem to be limited to a single (history-dependent) ‘variable’ . The numerical limitations of the investigation26 are furthermore characterized by the fact that only eight modes suffice to obtain highly accurate results.On the other hand, the recent study of Im et al.the entire, current displacement field as the output of interest,a relatively simple RNN , sandwiched between two layers of conventional neurons),large deformations with plasticity-induced localizations at several locations in the domain, as well as large variations of the imposed deformations, andthe application to RVE computations with periodic boundary conditions in order to serve multiscale analyses.However, embedding the RNN-POD framework in a multiscale simulation is not considered yet. Also, the accuracy of the consistent tangent moduli is not quantatively considered yet—only the accuracy of the macroscale stress-deformation response, and the accuracy of the microstructural field of the plastic multiplier.The aim of the current contribution is to numerically reveal the capabilities and limitations of RNN-POD frameworks, by considering: The remainder of this paper is organized as follows. The next section concisely discusses how to efficiently train the surrugate for an RVE, by removing the rigid body rotations from the macroscale deformation gradient tensor (which is imposed on the boundaries of the RVE). The direct numerical simulations are concisely discussed in section "Surrogate models based on neural networks require a substantial amount of training data. The rather slow, conventional POD-based ROM , must generate this large amount of data. Therefore, it is convenient if the amount of training data can be restricted as much as possible.without rigid body rotations) can be rapidly transformed into the actual macroscale stress-deformation relation (with rigid body rotations).In the case of RVE computations, which are governed by an applied macroscopic deformation, it is more efficient to train the emulator for ‘pure’ macroscopic deformations (meaning that rigid body rotations are extracted from the macroscopic deformation) than for the actual macroscopic deformations. Extracting the rigid body rotations from the macroscale deformation reduces the number of inputs of the RNN-POD emulator from four to three in 2D (and from nine to six in 3D). The current section shows that the ‘pure’ macroscale stress-deformation relation , which is obtained from microstructural RVE simulations (with its modelling domain at the size of the microstructure). The macroscale deformation gradient tensor at time t, First-order multiscale  rotation tensor, The issue of interest here is that macroscale deformation gradient tensor T denotes the transpose, superscript Consequently, if a pure macroscopic deformation, mentclass2pt{minimThis indicates that if the RVE is exposed to macroscale deformations without rigid body rotations, the resulting macroscale stress tensor (as well as its sensitivity) can straightforwardly be related to the relevant macroscale stress tensor (as well as its sensitivity) that is affected by rigid body rotations.In the current section, we discuss the RVE simulations. The RVE simulations are the direct numerical simulations (DNS) which the POD-based ROM, and particularly the RNN-POD emulator must mimic.M in the previous section) is completely neglected. Thus, unless specified otherwise, all quantities discussed in the current section are microstructural quantities, but superscript The DNS are 2D RVE computations with stiff, elastic particles embedded in an elastoplastic matrix see Fig. . In relaF-bar method is utilized to alleviate locking due to the incompressibility of the plastic deformation. Within the F-bar framework, the volume change of the deformation at a quadrature point is replaced with the volume change at the center of the element. Thus, the deformation gradient tensor that is considered for the constitutive model in each quadrature point, We consider plane strain conditions and employ isoparametric bilinear quadrilateral finite elements with four quadrature points. An e) and a plastic (subscript p) deformation gradient tensor:E and The deformation gradient tensor that is used in the actual constitutive model, h and m denote the initial yield stress, the hardening modulus and an exponential hardening parameter, respectively. Furthermore, In order to assess if plastic yielding occurs, we first relate the The evolution of the plastic multiplier is linked to the evolution of the plastic deformation according to the following associated flow rule:t, not a single Because we are interested in RVE simulations, the boundary conditions are dictated by the ‘pure’ macroscale deformation, a) is linked to the displacement of a node on the top boundary (node b) according to:The current boundary conditions of the RVE simulations are governed by the current, ‘pure’ deformation gradient tensor, mentclass2pt{minimIn the RVE simulations, the left bottom node obtains displacement boundary conditions of zero. This entails that the displacements of the other corner nodes are known and can thus also be prescribed using displacement boundary conditions. However, the displacements of the remaining nodes on the boundaries, are not known in advance and hence, the aforementioned constraint must be included as an actual constraint . We have chosen to enforce the constraints using Lagrange multipliers.After linearization, the DNS implies that the following system of linear equations must be constructed and solved for each iteration, for each time increment:Now that the DNS are discussed, we continue the current section with the reduced-order model (ROM). The ROM is not the end goal; it only serves to reduce the number of output variables that will be emulated by the final framework, i.e. the RNN-POD surrogate.Projection-based model-order-reduction (MOR) projects the original In the method of proper-orthogonal-decomposition (POD), modes In RVE simulations, the modes are not directly extracted from the training solutions (computed by the DNS). Rather, each solution field is first decomposed into a homogeneous (i.e. affine) field, According to Eqs.  and 18)18), the The decomposition generates modes that are themselves periodic and hence, periodicity does not need to be actively enforced in the ROM (nor in the RNN-POD surrogate). Consequently, the system of linear equations that needs to be solved in terms of update 30 and Daniel et al.31 adaptively change the modes during the course of an elastoplastic ROM simulation in order to reduce the number of modes  for (non-linear) elastic simulations to obtain a good accuracy, but a substantially larger number of modes for elastoplastic simulations. In fact, studies as those of Zhang et al.solving the systems of linear equations is faster . HoweveIn this section, we discuss the recurrent neural network (RNN) that rapidly emulates the model coefficients, (see Eq. ). Howeve9. It consists of a gated recurrent unit (GRU), sandwiched between two feed-forward neural networks (FNNs). The input, i.e. the three independent components of t, is fed to FNNThe overall architecture of the employed RNN is graphically presented in Fig. Thus, the RNN outputs are evaluated from the problem inputs  must be identified (i.e. ‘learned’ or ‘trained’ in NN terminology). The number of parameters is substantial, because FNNi indicates the training simulation number and subscript t refers to the time increment number. The RNN must replicate these coefficients. To this purpose, one could minimize the following least square error:For the ease of the notation, we store all parameters of the RNN in column 40 to identify (i.e. ‘train’ or ‘learn’) the weights and biases  gradient determines in which direction the RNN’s parameter values are updated. On the other hand, the step size (‘learning rate’ in NN terminology), which governs how much the RNN’s parameter values are updated in the direction of the (stochastic) gradient, are determined by the first moment and second moment estimates of the root mean square part of ADAM.Now all methodologies are discussed, the current section explains the setup of the DNS, as well as the generation of the training data. The previous sections have already mentioned that two types of training data are required for the RNN-POD emulator: the training of the ROM requires solution fields computed by the DNS, and the training of the RNN requires modal coefficients computed by the ROM. However, the RNN requires substantially more training data than the ROM.The RVE of interest see Fig.  consistsBecause the matrix deforms mostly plastically and plastic deformation is isochoric, and because the particles deform only minimally relative to the matrix (due to the ratio of Young’s moduli), we only apply isochoric macroscale deformations  require some more explanation, because they are not entirely random . Of these ROM simulations, 350 cyclic loading simulations and 10,000 random loading simulations are used for the actual training .Finally, we summarize the hyperparameters for the ADAM optimizer. Each mini-batch considers approximately 1% of the training data. In the ADAM optimizer, we set the initial learning rate to 0.001 (i.e. ‘We now investigate the accuracy of the RNN for (i) different numbers of layers in FFNWe investigate the accuracy of the 64 RNNs after they are trained for 60,000 epochs. After 60,000 epochs, the RNN with the smallest loss function is then assumed to be the best possible RNN from the available options. We train this final RNN for a total of 450,000 epochs after which we have observed that its loss function does not reduce further.The loss functions of the 64 possible RNNs after 60,000 epochs are presented as bar charts in Fig. The evolution of the loss function of this final RNN when trained for 450,000 epochs is presented on the left of Fig. The average error of the final RNN after training (defined in the same way as Eq. ) is \docAlthough the previous section has demonstrated the capabilities of the RNN, this does not automatically entail that the overall accuracy of the emulator is the same. In this section, the mechanical results of the RNN-POD surrogate are investigated and compared to those of the DNS and the conventional ROM. The comparison focuses on the macroscopic stress-deformation responses, but for the cyclic loading path, we also compare the microstructural field of the plastic multiplier at the end of the simulation/emulation .Nevertheless, it is interesting to investigate scenarios for which the RNN is not trained. The reason is that we have assumed that training for random loading and cylic loading will make the RNN capable to emulate any scenario . The erOne could argue that the emulated stress-deformation curves Fig.  are so p9.This leads to the conclusion that training the surrogate for random loading and cyclic loading scenarios (two scenarios on opposite sides of the spectrum of possible loading scenarios) does not mean that other loading scenarios will be adequately emulated by the surrogate. As mentioned before, this contrasts previous observationsSo far we have only discussed accuracy and have ignored speed up. Table Though the data preparation and training the RNN required a total of two weeks of computational time, Table The difference in time savings of the surrogate for cyclic and random loading are because the DNS and conventional MOR require more iterations for random loading than for cyclic loading. The reasons are that (1) the loading paths for cyclic loading are substantially shorter than those for random loading whilst the same number of increments is employed, and (2) the previous plastic state is assumed at the start of each increment of a cyclic loading simulation  in order to increase the speed of the cyclic loading simulations.An RNN-POD surrogate model is investigated that emulates the displacement field of each increment of a rate-independent elastoplastic simulation. A recurrent neural network (RNN) in the surrogate is responsible for the emulation. In order to reduce the number of output variables of the RNN, proper-orthogonal-decomposition (POD) is exploited to efficiently reconstruct each displacement field as the sum  of orthogonal modes, each multiplied by a single coefficient. Consequently, the RNN only has to emulate the coefficient of each mode (instead of the displacement vector of each finite element node).14 aim to rapidly emulate the homogenized stress-deformation of an RVE , they lose all microstructural information. The RNN-POD surrogate has the potential to both drive multiscale simulations, as well as to recover any microstructural field of interest.We have applied the framework to an elastoplastic RVE. Whereas many neural networksBecause the surrogate emulates the displacement field in the entire RVE domain, the non-linear governing equations of the RVE simulations do not need to be constructed, nor solved. Instead, only the new plastic variables must be computed once per increment (together with any other quantity of interest). The time savings are thus substantial and we report a maximum acceleration factor of 100 relative to the direct numerical simulations.Instead of a conventional feed-forward neural network (FNN), an RNN is used in the surrogate. The reason is that RNNs predict both the primary output of interest, as well as hidden states, which affect the RNN’s next prediction. Thus, the role of hidden states in RNNs imitates the role of plastic variables in elastoplastic finite element simulations.Although we report acceleration factors of up to 100, the accuracy of the surrogate leaves much to be desired. The reconstruction of the displacement field using the POD modes definitely reduces the accuracy , but the macroscale stress-deformation relations predicted by the conventional ROM seem to be just as smooth as those of the DNS. Hence, we believe that the inaccuracy introduced by the POD modes would not affect the convergence of a multiscale simulation.9, in which the same RNN was used to only emulate the macroscale stress-deformation curves. Apparently, an RNN that mimics an elastoplastic constitutive response may not be sufficient to emulate the modal coefficients of an elastoplastic ROM.On the other hand, the RNN introduces both a substantial inaccuracy in the macroscale stress-deformation curves, as well as a substantial reduction of the smoothness of the macroscale stress-deformation curves. Only the macroscopic stress-deformation curves for the cyclic load case are accurate (but lack smoothness). We want to emphasize that this is in contrast to the results of Wu et al.drive multiscale simulations. Potential avenues to accomplish this aim are:A wider variety of load paths and of incremental step sizes of the macroscale deformation may be incorporated in the training data of the RNN.26 uses two long-short-term-memory (LSTM) units in parallel (whereas we have only used a single GRU) Another possible avenue are the RNNs of Liu et al.15 and Bhattacharya et al.16. In contrast to our GRU and the LSTM of Liu et al.26 in which the quantity of current interest and the updated hidden states are one and the same, the output of current interest and the updated hidden states are truly separate in the RNNs of Liu et al.15 and Bhattacharya et al.16, potentially increasing the accuracy.Another type of RNN may increase the accuracy. For instance, the RNN-POD framework of Im et al.In order to drive multiscale simulations, the sensitivity of the macroscale stress-deformation relation must be sufficiently smooth. The presented results have revealed that the RNN emulation (and not the POD construction of the displacement field in the ROM) is responsible for the lack of smoothness. A potential avenue may therefore be to not only train the RNN to emulate the displacement field itself, but also to train the RNN’s sensitivity according to the sensitivity of the macroscale stress-deformation relation.Finally, it is worth to mention that the accuracy of our conventional ROM was also not great, although 100 modes were employed. To overcome this problem, one may use non-linear MOR31. If non-linear MOR is used in combination with the RNN emulation of the model coefficients however, the RNN must not only be able to treat the ‘elastoplasticity’ in its emulation (as in the current contribution), but it must also be able to treat the evolution of the POD modes during the course of a simulation/emulation.In conclusion, we can state that the RNN-POD surrogate, as presented here, cannot emulate the microstructural fields sufficiently accurate to truly


Neurosporacrassa (Nc). The NcCARR-domain revealed activity for N-acetylcysteaminethioester (S-(2-acetamidoethyl) benzothioate), which mimics the phosphopantetheinylacyl-intermediateand can be anticipated as the minimal substrate for thioester reductionby CARs. The determined crystal structure of the NcCAR R-domain reveals a tunnel that putatively harbors the phosphopantetheinylacyl-intermediate,which is in good agreement with docking experiments performed withthe minimal substrate. In vitro studies were performedwith this highly purified R-domain and NADPH, demonstrating carbonylreduction activity. The R-domain was able to accept not only a simplearomatic ketone but also benzaldehyde and octanal, which are typicallyconsidered to be the final product of carboxylic acid reduction byCAR. Also, the full-length NcCAR reduced aldehydesto primary alcohols. In conclusion, aldehyde overreduction can nolonger be attributed exclusively to the host background.The synthesis of aldehydes from carboxylic acids has long beena challenge in chemistry. In contrast to the harsh chemically drivenreduction, enzymes such as carboxylic acid reductases (CARs) are consideredappealing biocatalysts for aldehyde production. Although structuresof single- and didomains of microbial CARs have been reported, todate no full-length protein structure has been elucidated. In thisstudy, we aimed to obtain structural and functional information regardingthe reductase (R) domain of a CAR from the fungus  The aldehyde functionalityis a valuable chemical moiety to make a variety of products, and CARsare becoming standard tools for this transformation.3 CARs consist of functional domains thatare each responsible for a respective step, namely the adenylationof the acid (A-domain), its transthiolation using a phosphopantetheinemoiety (T-domain or peptidyl carrier protein (PCP)-domain), and finallythe reduction of the enzyme-bound thioester intermediate to the aldehydein the reductase domain (R-domain). The substrate is shuttled as covalentthioester 1 from domain to domain through large-scaledomain movements.4 This intrinsic flexibilityof full-length CARs makes them challenging targets for structuralcharacterization. However, some mechanistic and structural insightwas deduced from crystallized single and didomains of bacterial CARs.4 CARs can be divided into five clans: The groupof bacterial CARs belongs to type I, while type III consists of CARsfrom Ascomycetes, type IV of CARs from Basidiomycetes and type IIrepresents a mixed group of fungal origin.5 The fifth type of enzymes of similar domain architecture is specializedin reducing aromatic amino acids.6 Sequencesimilarity between different CAR types is low,7 hence the structural insight from one clan is of limited value forthe others. In particular, the selectivity of the R-domain for two-electronreduction  CAR8 reductiondomain were first derived from proteolytic cleavage of heterologouslyexpressed full-length NcCAR equipped with WELQutcleavage sites at domain boundaries. Subsequently, the R-domain (NcCARΔ1–649) was produced via atruncated open reading frame to increase protein yield. Based on thecrystal structure of NcCARΔ1–649, activity assays with alternative substrates and docking experiments,we postulate how the enzyme-thioester intermediate is reduced. Weidentified the crucial part of the phosphopantetheinyl arm that leadsto the productive mode. Free thioesters are not accepted as substratesby the enzyme, due to the lack of N-acylcysteamine.We devised an approach for crystallizing single domains of a fungalCAR (type III). Crystals of the 4 To understand the mechanism underlyingthe strict two-electron reduction of thioesters and the substratespecificity of fungal CARs we have solved the crystal structure ofthe NcCAR reductase domain12 (PDB-code 8AEP). The respectiveconstruct that was crystallized in this work consists of the R-domainsubunit (residues 684–1052) and a linker (residues 649–683)that connects the R-domain to the PCP-domain of 0.178 indicates no biological relevance of this dimerization event.The residues Asp1002-Thr1006 form an antiparallel beta-sheet withtheir respective counterparts  is the R-domain from Segniliparusrugosus, SrCAR (PDB-code 5MSP).4 Both enzymes were found to be NADPH-dependent,and the key residues for cofactor binding are highly conserved. Therefore,the respective NADPH binding mode in NcCAR was modeledas observed in SrCAR and visualized  forms a putative sulfate or phosphate binding site.14The siteSI, . In contSorghumbicolor.14The hydride transfer from the NADPH is facilitated from its C4position to a given substrate. To achieve a productive binding mode,the substrate must be located close to the C4 and activated by theenzyme. Substrate activation is facilitated by a proton relay systemformed by Tyr844, Lys848 and putatively the ribityl backbone of theNADPH, as already described for other related short chain alcoholdehydrogenases like the cinnamoyl-CoA reductase 1 from 1a  benzothioate]}).This compound was readily reduced to 2a (43% conversion),leading to the conclusion that the amide functionality connected viaa C2 linker is the key to evoke substrate affinity  at the thioester moiety 1B. In ca1a 1—was modtersSI, .15 This ateof 1 1, benzoyaffinity 3. No 2a in silico modeling. To reduce the thioester, a ternary complex consistingof the enzyme, NADPH, and 4a must be formed. To analyzeputative productive binding modes that we have determined as minimalthioester-derived substrate, docking studies of 4a to NcCAR:NADPH were performed .s buried4A, indic4a and the model of phosphopantetheine in the tunnel are ingood agreement. This indicates that a productive ternary complex forthioester reduction can be formed by NADPH entering the active sitefrom one direction while the 1a-intermediate enters fromthe opposite direction and occupies the tunnel  to the SrCAR PCP-R-didomain (PDB-code 5MSP_A) as a representativeof a type I CAR that was reported to catalyze two-electron reductionof carboxylic acids  aredepicted in the SI, NcCAR active site with attached tunnel forthe phosphopantetheine linker (SrCAR. The differing active site shapes of NcCAR and SrCAR R-domains are shown in CARs are divided in five types (I–V).cids SI, . A coreoops SI, . Especiae linker 4, a broaNcCAR and SrCAR does differ to some extent. The catalytic residuesin SrCAR and NcCAR are largely conserved and the simple aromatic ketone acetophenone (5a) to cell-free extract (CFE) of NcCARΔ1–649 producing E. coli. NcCARΔ1–649 was indeed able to reduce 5a (73% conversion) to the secondary alcohol 6a, while the A-domain alone (NcCARΔ550–1052) and a full-length NcCAR variant with inactivatedreductase domain (NcCARY844A)17 were not  was investigated with 0.4 mg·mL–1 of highly pure NcCARΔ1–649 and 1 mg·mL–1 of full-length enzymes in orderto apply equimolar amounts of R-domain. Both the isolated R-domainand wild-type full-length NcCAR catalyzed the reductionof aldehyde to alcohol, whereas inactivated reductase domain variant NcCARY844A did not. 32% of 2a and54% of 2b was reduced by the R-domain alone . The grade of conservation and the proposed role ofthe residues within the first shell of the active site of the NcCAR, an evolutionary conservation score was projected onto the full-lengthmodel generated by AlphaFold 2 24 activities for aldehyde reduction amounted to16% and 66% of benzoic acid and octanoic acid reduction, respectively as an enzymeengineering strategy.7 and creates a basisfor rational enzyme engineering. Substrate recognition in this subdomainis based on the presence of the acetyl-cysteamine moiety and not onthe presence of a thioester in the putative substrate. The presenceof the acetyl-cysteamine moiety is essential for substrate recognitionin thioester reduction, as it mimics the phosphopantetheine arm, whichis the natural prosthetic group of CARs. Other thioesters lackingthis group were not accepted as substrates for thioester reductionto aldehyde. We identified a tunnel in the R-domain that putativelyharbors the PPT arm, which is in good agreement with docking experimentsconducted with the minimal substrate 4a. These resultsindicate that CARs do not rely on the ATP-dependent activation ofa substrate but that this step can be circumvented by employing SNAC-esters.This strategy proved to be a versatile tool for biotransformationswith non-ribosomal peptidesynthases.28We determined the first experimental structure of a reductase domainfrom a fungal CAR and evaluated its activity on a range of putativesubstrates. This structure is valuable for building more reliablemodels of fungal CARsSubstrate screening experiments revealed that the presence of theacetyl-cysteamine moiety is strictly necessary for the reduction ofthioesters to aldehydes, while it is not required for the reductionof carbonyl compounds like benzaldehyde or benzophenone to the respectivealcohols. This aldehyde over-reduction was previously attributed tothe host strain background, but our results indicate that alcoholformation is an intrinsic side activity of CAR R-domains. Ultimately,aldehyde overreduction cannot be attributed exclusively to the hostbackground and its extent is substrate dependent.


The High Speed High Pressure Torsion (HSHPT) is the severe plastic deformation method (SPD) designed for the grain refinement of hard-to-deform alloys, and it is able to produce large, rotationally complex shells. In this paper, the new bulk nanostructured Ti-Nb-Zr-Ta-Fe-O Gum metal was investigated using HSHPT. The biomaterial in the as-cast state was simultaneously compressed up to 1 GPa and torsion was applied with friction at a temperature that rose as a pulse in less than 15 s. The interaction between the compression, the torsion, and the intense friction that generates heat requires accurate 3D finite element simulation. Simufact Forming was employed to simulate severe plastic deformation of a shell blank for orthopedic implants using the advancing Patran Tetra elements and adaptable global meshing. The simulation was conducted by applying to the lower anvil a displacement of 4.2 mm in the z-direction and applying a rotational speed of 900 rpm to the upper anvil. The calculations show that the HSHPT accumulated a large plastic deformation strain in a very short time, leading to the desired shape and grain refinement. In addition, the technology is able to produce shells and larger disks that cannot be achieved in conventional High Pressure Torsion. Very few papers have reported results on severe-plastic-deformed low modulus Gum metal [Severe plastic deformation (SPD) is a deformation process in large plastic strains that are able to induce in bulk  fundamenum metal ,27,28 anum metal , copper um metal , magnesium metal , titaniuum metal . The mai2) [Withal, the purpose of the work was also to examine the possibility of obtaining not only disks but compression staples, which are left blank for HSHPT severe plastic deformation to be applied directly onto the multidirectional compression staples, a technique that provides a nanostructured Ti-Nb-Ta-Zr-O beta-type Gum alloy. In our previous paper , we exam2) . Moreove2) . The sevTypically, alloys used for staple applications are stainless steel and super-elastic NiTi alloys . Ti-baseAs-cast ingots of Ti-Nb-Zr-Ta-Fe-O gum alloys were produced by levitation melting in a cold crucible MP25 induction furnace , with the chemical composition given in 2 rpm).The HSHPT technique a is a hoA great amount of heat is generated by friction in a few seconds and hot severe plastic deformation occurs in the bulk material. This is the key observation showing why this method may process brittle materials in their as-cast states or materials that are very hard to deform.The recrystallization problem is solved by observing two things: the SPD time is very short and the samples, which are usually thin disks or shells, have a large diameter–thickness ratio. This means that in the HSHPT process, the material is fast-flowing in the cold areas of the anvils, thus losing heat by conduction. The radiation or convection is limited due to fast severe plastic deformation and the low exposed-area outside tools.To perform the severe plastic deformations (SPD), a process simulation, the anvils, and the workpiece were modelled using Inventor software, before being exported as solid geometry files to the Simufact Forming finite element software. The superior anvil and also the inferior one were modelled as rigid bodies. The workpiece was assumed to be a deformable body. Experimental processing data were used to set simulation parameters as follows: a constant inferior punch velocity of 0.525 mm/s and the revolution velocity of the superior punch at 900 rpm. At the beginning of the analysis, all three bodies had been in contact and, at increment zero, the rigid bodies did not have any loads (distributed or point) applied initially.The determination of contact was done automatically by software according to efficient algorithms. This is a major problem with these types of analyses due to the large number of nodes and elements in the model, and the adaptive meshing process.The model, as shown in The large strain parameter was included in the “parameter section” to deal with deformations. The deformations and rotations were large enough to invalidate the theory of infinitesimal deformations. In this case, the undeformed and deformed configurations of the model were significantly different, requiring a clear distinction between them. This is usually the case for plastic-deformed materials.Considered material is isotropic;Heat transfer between bodies in this simulation was done by conduction;2/°C;Heat transfer coefficient between the sample and punch as well as between sample and die was set to 450 W/mHeat transfer was assumed to occur in all three directions ;Mechanical and physical material properties  vary witThe friction conditions between the surfaces of the sample and the dies were considered to be shear with a coefficient of 0.1;The assumptions assigned for the simulation were the following:The variation of the Young modulus, the thermal conductivity, and the specific heat capacity with temperature is presented in The three bodies in contact were defined by a Coulomb friction model that was used with a friction coefficient of 0.1. Both anvils were treated as rigid bodies with an initial temperature of 20 °C. The contact table option had been used to indicate that there was no self-contact. The lower punch had a prescribed translated velocity in the negative z-direction of 0.42 mm/s and the revolution velocity of upper punch was 900 rpm.At the beginning of the analysis, the bodies were in contact, and as the punch was moved in the negative z-direction, it penetrated the deformable sample, changing its shape with the help of the die.The “adapt global” option was set to indicate that a new mesh was to be generated when the element distortion was based upon a change of strain of 40%. The advancing Patran Tetra elements, with a target number of 10,000 elements, were used.In manufacturing simulations, the objective is to deform the workpiece from an initial (simple) shape to a final (complex) one. This deformation of the material results in mesh distortion, and for this reason, it is necessary to perform a remeshing step. At this point, a new mesh has been created; the current state of deformation, strains, and stresses has been transferred to the new mesh; and the analysis has been continued.If a contact tolerance has not been defined, a new one is calculated, based on the new mesh, but this distance can be smaller than the previously calculated tolerance, leading to more iterations.k is a constant.For a compressible, deformable plastic material that meets the yield criterion, we have the equation :(1)σ¯2=1The effective stress depends on the strain rate as can be seen:The equivalent strain rate The functional Φ of a strain rate for a sensitive material is given by,TS. For a value of The Simufact Forming post-file contains the results for both the deformable and rigid bodies. When performing a contact analysis, three types of results can be obtained. The first type are the conventional results from the deformable body. This includes the deformation, strains, stresses, and measures of inelastic behaviors such as plastic and creep strains. Besides the reaction forces at conventional boundary conditions, it can be obtained through the contact and friction forces imparted on the body by rigid or other deformable bodies.Force variation is presented in The variation of the torque, the rotation speed of the upper anvil, and the displacement of the lower anvil confirm that the HSHPT started at 44 s and ended at 51 s. One second after the HSHPT process finished, the measured temperature was 522 °C.Pressure variation was often used to monitor the evolution of the process. In this case, the severe plastic deformation of the sample occurred at pressures higher than 1 GPa. This can be seen in In The convection and radiation phenomena are insignificant in the Bridgman cell. The maximum temperature value (542 °C) was validated by the experimental data .The temperature variation provided valuable information about the progress of severe plastic deformation and it can be used to optimize process parameters to achieve the desired material properties. However, it is important to note that excessive temperatures at the end of HSHPT lead to recrystallization. Therefore, temperature control during the severe plastic deformation process is essential to achieve the desired material properties.Initially, in the early stages of deformation, the Von Mises stress distribution may be relatively uniform on the upper surface of the workpiece. However, as the deformation process continues, the Von Mises stress distribution may become more localized, with areas of high-stress concentration in the regions where the material undergoes the greatest deformation.In the later stages of the deformation process, the Von Mises stress distribution be-comes more complex, with multiple zones of stress concentration developing on the upper surface of the part. These stress-concentration zones can provide information about the underlying deformation mechanisms, such as the formation of deformation bands or the initiation of shear localization.Monitoring the Von Mises stress distribution at several points located within the tool radius on the upper surface of the workpiece can provide valuable information about the deformation behavior of the material during severe plastic deformation. This information can be used to optimize process parameters and achieve desired material properties.The effective plastic strain variation is presented in The maximum strain predicted by FEA modeling is 3.09. It tends to be the optimum for the shape of the shell blank used for implantable multiaxial compression staples . The comWithal, the HSHPT technique combines high hydrostatic compressive stresses with the torsion of the superior punch by rotation, which leads to heating from the friction of the shell. The grain-size refinement takes place in just a few seconds. The finishing temperature of the blanks are well controlled. Consequently, the amorphization is highly improbable.A finite element model was developed for the simulation of the severe plastic deformation process based on the following hypotheses: the base material was considered isotropic and its physical characteristics depended on temperature;In the simulation of the deformation process, the total analysis time was considered as the time recorded during the physical HSHPT process;The variations of the Von Mises stress and the total equivalent strain in five points during the deformation process were plotted;The variations of the Von Mises stress and of the deformations along some curves on the surface of the workpiece were drawn at different time intervals.Following the modelling of High Speed High Pressure Torsion process performed within the present work, the following can be concluded:The FEA result is consistent with the experimental one that indicated the accuracy of the computer simulation. In addition, it shows that the implemented boundary conditions in the simulation were as close as those in experiments.


In this paper, the development law of residual deformation of coal gangue subgrade filler is analyzed through large scale triaxial test, and the residual deformation model of coal gangue mainly sandstone and limestone is established. The purpose is to provide research basis for the applicability of coal gangue as subgrade filler. The results show that the deformation of coal gangue filler increases first and then tends to be constant under cyclic load of multiple vibration times. It is found that the Shenzhujiang residual deformation model cannot accurately predict the deformation law, and the corresponding modification is made to the residual deformation model of coal gangue filling body. Finally, according to the calculation of grey correlation degree, the influence degree of main factors of coal gangue filler on its residual deformation is sorted. Combined with the actual engineering situation represented by these main factors, it can be analyzed that the effect of packing particle density on residual deformation is greater than that of packing particle size composition. Excessive accumulation of coal gangue will cause serious environmental problems4. At present, the coal gangue is mainly used as concrete coarse aggregate or fine aggregate filling material, to ensure the performance of concrete under the premise of improving the recycling rate of coal gangue8. In addition, when it reaches a higher density, it has excellent engineering characteristics such as strong bearing capacity, high structural stability and less prone to excessive deformation9, combined with these characteristics, the use of gangue as a subgrade filler can effectively achieve the purpose of recycling. Considering that the subgrade filler will produce residual deformation under the action of circulating load13, the residual deformation will lead to safety hazards when the residual deformation is too large. Therefore, the residual deformation of gangue is one of the key points of its research on the dynamic characteristics when used as a subgrade filler.Gangue refers to waste rock discharged during coal mine construction, coal mining, etc15, or vibration-residual deformation models determined directly from the residual deformation curve 18. Compared with the dynamic stress-residual deformation model, the vibration-residual deformation model  can not only describe the volume residual deformation caused by the shear characteristics of the granular materials, such as subgrade filler, but also can effectively avoid the influence of interpolation error19. However, the Shenzhujiang residual deformation model cannot accurately describe the residual deformation law of subgrade filler under some specific influencing factors, for example, when studying the vibration residual deformation characteristics of rockfill materials. Wang et al.20 found that the data fitted by Shen Zhujiang residual deformation model had greater discreteness; He et al.21 found that the actual lg (1 + N) (vibration) residual deformation curve of pile material showed obvious nonlinearity, especially under high stress conditions.The study of residual deformation of subgrade filler generally includes the establishment of residual deformation model and the investigation of the influencing factors of residual deformation. Residual deformation models are generally divided into two categories, namely dynamic stress-residual deformation models that describe the relationship between a certain vibration under dynamic stress and residual strain28. Among them, Liu et al.27 pointed out that the residual deformation of the rockfill materials under the action of cyclic load is mainly due to the rearrangement of particles of the rockfill materials and the fragmentation of the edges angles of the particles of the rockfill materials, which are closely related to the compactness of the rockfill materials. In the indoor test, the confining pressure and compaction of the specimen affect its compactness. For example, scholars29 have also found that the confining pressure has an effect on the shear residual deformation and volume residual deformation of coarse-grained soil. At the same time, particle gradation also affects the degree of fragmentation of particles27. In addition, the secondary crushing of coal gangue also greatly affects the residual deformation of coal gangue36. Zheng et al.31 found that the main influencing factor of particle breakage of coarse-grained soil is particle shape. This particle breakage is divided into three stages, namely void filling, skeleton failure and final stability, affecting the cumulative deformation of coarse-grained soil.In view of the research on the influencing factors of residual deformation of the granular materials, such as subgrade filler, scholars have found that the influencing factors are diverse, including the selection of filler materials, the granule gradation of fillers, the compaction of fillers, the frequency of cyclic loads, the cyclic stress ratio, and the confining pressure of the sample38. Then it investigate the degree of correlation between different factors, which has been widely used in engineering experiments40. In the previous studies, the small triaxial or medium triaxial tests were generally used41. Since the grain size of coal gangue subgrade filling specimen is above 60 mm, the use of minor triaxial will not only cause the grain size of the specimen to be larger than the event size, but also cause large errors due to the size effect.In order to explore the degree of association between multivariates and residual deformation, the gray correlation method is used in this paper. The method is a statistical analysis method used to compare different factors affecting the development and change of a certain parameterTherefore, in this paper, the experimental method is different from the small triaxial or medium triaxial tests, using large triaxial test; in terms of the number of load vibrations, different from the situation where the number of previous vibrations is small, the number of load cycles is set to 30,000 times to simulate the actual working conditions of subgrade filling. On this basis, combined with the main factors affecting the subgrade filling, this paper establishes the residual deformation model of coal gangue subgrade filling, analyzes the influence of various factors on its residual deformation. It aims to predict the settlement of coal gangue subgrade filling in practical work.42 remove the particles of more than 60 mm. The filler sample is shown in Fig. The experimental filler sample studied in this paper, is taken from Xiangtan Tangjiashan coal mine. It is identified that the coal gangue mainly contains sandstone, limestone, shale and mudstone. The filler particle size range is large, the uniformity is poor, the particles are scattered, including more than 10 cm and less than 0.5 mm particles. Large particles have obvious edge corner, irregular shape and medium hardness. Affected by weathering, as the particle size decreases, the particles are more blurred and the texture is softer. The liquid limit of the fine-grained material of the coal gangue roadbed filler is 31.46, the plastic limit is 20.57, and the plastic index is 10.89. According to the standard (JTG D30-2015)43:In this paper, the gradation control equation proposed by Talbot according to fractal theory is used to value the gradation parametersdi is the cumulative percentage content of particles smaller than the mass l of particle size in the specimen; i is the percentage of the total mass of particles with a particle size of less than one size; lmax is the maximum particle size, this test takes 60.0 mm, A is the graded parameter. This test selects three gradations, A = 0.63,0.87,1.11. Considering that the inhomogeneity coefficient Cu = d60/d10 > 5 and the curvature coefficient Cc = d302/(d60·d10) = 1–3 are good graded, the A value is 0.3691–1.1133. The particle gradation distribution is shown in Fig. Among this, Before the large three-axis test, it is necessary to determine the density of the subgrade filler body under the maximum pressure compaction according to the standard JTG D30-2015), through the surface vibration compaction test, as shown in Fig. 0-2015, tAccording to the Code for the Design of Highway Subgrades (JTG D30-2015), the test was loaded with 3–5 layers of compaction to simulate the filling process of subgrade packing in actual engineering. In the test, the compaction hammer is divided into 5 layers of compacted samples in this test, as shown in Fig. This study adopts the DJSZ-150 dynamic and static triaxial test system developed by Chengdu Donghua Excellence Technology Co., Ltd. and the West China Geotechnical Instrument Research Institute of Sichuan University, as shown in Fig. 44. The specimen belongs to the subgrade filler of the gravel type with good gradation, which belongs to the partial drainage material in the actual project. So, it is tested under drainage conditions. The basic test parameters in this article are shown in Table According to the standard JTG D30-2015), the compaction degree of roadbed filler must reach 93%. Therefore, the compaction levels used in this test are 90%, 93% and 95%, simulating under compaction, standard compaction and over compaction, respectively. The isobaric consolidation is used to consolidate the subgrade filler of the specimen. The cyclic load is based on the ratio of the general vehicle speed and length, and the load frequency f is 1 Hz, and the load waveform is a semi-sine wave015, the Considering the long-term nature of the traffic load action, when simulating the traffic load, the number of cyclic load vibrations is determined to be 30,000 times, a single stage of loading. One sample was selected to control the confining pressure of 50 kPa, a compaction degree of 93%, and a grading parameter A = 0.63. The specimen number was AY01. On this basis, the three influencing factors of confining pressure, compaction degree and gradation parameters were changed. At the same time, the other two groups of influencing factors were fixed for comparative test. Among them, AP01 and AP02 changed the confining pressure size, AC01 and AC02 changed the compaction size, and AG01 and AG02 changed the particle gradation, as shown in Table According to the residual deformation test scheme designed in this paper, due to the large amount of residual deformation test data, in order to facilitate comparison and calculation, combined with the characteristics of experimental data, the residual deformation is divided into three stages to take data points. The 1st to 1000th vibration is the rapid development stage of deformation (the first stage), at which the residual deformation is developed rapidly. Therefore, 1 point is extracted from every 20 points in the first stage. The 1000th to 5000th vibration is the deformation slowdown (the first stage), at which deformation gradually is slowed down. Therefore, considering the extraction of 1 point every 100 points in the second stage. In the range of 5000 to 30,000 vibration (the third stage), the deformation is almost flattened. Therefore, it is considered to extract 1 point every 500 points in the third stage. According to the development law of residual deformation of coal gangue subgrade filler, it can be found that the first and second stages are not suitable to characterize the long-term working state of the filler because the deformation is not stable. When the residual deformation develops to the third stage, the residual deformation is stable. Therefore, multiple vibration times are suitable for exploring the residual deformation of coal gangue when it is used as subgrade filler.The residual deformation is an irreparable deformation, so the residual deformation is the irreparable deformation of the specimen under cyclic load, the typical residual strain is shown in Fig. εd and volume residual strain εvd under different confining pressures were extracted. Then the axial, volumetric residual strain and vibration N relationship curves εd-N and εvd-N were plotted, respectively, as shown in Figs. The axial residual strain According to Figs. 45.The reason for this phenomenon is that as the number of vibrations increases, the subgrade filler of the specimen is gradually compacted and the stiffness gradually becomes larger, resulting in a larger growth in the initial stage of deformation, and then gradually slows down. The larger the confining pressure, the greater the compaction effect, the faster the stiffness increase, the smaller the residual deformation increment and residual deformation. In actual engineering, the confining pressure of coal gangue filler is smaller in shallow layer and larger in deep layer, so, the residual deformation of the gangue subgrade filler is larger when buried in the shallow layer. The larger the burial depth, the smaller the cumulative deformationεd and volume residual strain εvd under different degrees of compaction. We drew the axial, volumetric residual strain and vibration N relationship curves εd-N and εvd-N, as shown in Figs. Extract the axial residual strain εd-N and εvd-N relationship curve of each specimen is also the initial growth is larger, and then gradually slows down. The higher the compaction, the smaller the residual deformation of the specimen. According to the standard (JTG D30-2015), the compactness of subgrade filling needs to reach 93%. When the compactness of filling is less than 93%, the axial residual deformation will increase. The compaction degree is equal to 95%, which will significantly reduce the deformation of the gangue subgrade filler.It can be found from Figs. From Figs. εd and volume residual strain εvd under different gradations were extracted. Then the axial, volumetric residual strain and vibration N relationship curves εd-N and εvd-N were plotted, as shown in Figs. The axial residual strain 46. When the coarse particle content reaches a certain value, the impact on the axial residual strain is small. The reason for this phenomenon is attributed to: when there are more fine particles in the specimen, the water permeability inside the specimen will be reduced, thereby increasing the internal pore pressure at the beginning of the specimen loading, resulting in a rapid increase in the axial residual strain, while when there are more coarse particles, the pore water can be discharged in time, reducing the cumulative deformation at the beginning of the loading, thereby reducing the final axial residual deformation. In addition, during the loading process, the coarse particles will be broken twice, and the newly generated small particles will fill the particle voids, causing the increase of the overall stiffness and the decrease of the deformation.It can be seen from Figs. 19 on the large-scale triaxial test of the stone pile with multi-stage and small number of cycle loads. It was found that the residual deformation was proposed with the increase of the vibratile frequency in line with the semi-logarithmic law. The model takes into account the effects of confining pressure, pre-vibratile shear stress levels and vibratile frequency, and its expression is:The Shenzhujiang residual deformation model was originally used to analyze the residual deformation of earth-rock dams and has been widely used in China. The model was carried out by Shengεvd is the volume residual strain; γd is shear residual strain; N is the time of the shock; cvd and cd are the slope of the volume and shear residual deformation-vibratile correlation curves, is calculated by the empirical formula of Eqs. ;;εvd is t21. Therefore, it is necessary to modify the linear relationship in the Shenzhujiang residual deformation model model into a nonlinear relationship.Although the Shenzhujiang residual deformation model can take into account the shear ability of the subgrade filler and obtain the relationship between the volume residual strain and the vibratile degree. However, scholars found that the follow-up stress ratio increased, and the semi-logarithmic relationship curve of the residual strain-vibratile frequency showed obvious nonlinearityIn the past, the Shenzhujiang residual deformation model and its improved model was mostly a multi-stage, small vibration times of dynamic experiments (within 200 vibrations). Considering the engineering background of gangue as a subgrade filler, this paper performs a large Vibration times of single-stage loading of gangue filler samples. Combined with the experimental results of “vd is the Poisson ratio. The dynamic Poisson's ratio belongs to the characteristics of granular material, such as the Coal gangue subgrade filler, under dynamic load, which is a fixed value. In this paper, the dynamic Poisson 's ratio of coarse-grained filler is 0.33, which follows the previous research21.Since the DJSZ-150 dynamic and static triaxial test system can only collect axial displacement, it is necessary to convert the axial residual strain into shear residual strain, according to the study of ShenZhujiang's axial residual strain and shear residual strain as a linear relationship, according to formula  for conv48 and added Figs. The number of vibration has been logarithmically converted. The shear residual strain-vibration pattern diagram and the volume residual strain-vibration relationship diagram are drawn separately, and they are re-divided into the residual strain-vibration pattern of 0–200 vibration times, and the residual strain-vibration correlation diagram of 201–10,000 vibration, as shown in Figs. N). When the confining pressure is smaller, the compacting degree is lower, the coarse content is lower, the nonlinear is more obvious. This has a certain error with the Shenzhujiang residual deformation model, but it is highly matched with the improved Shenzhujiang residual deformation model such as Gong Siyi47. From 201 to 10,000 vibrations, the shear residual strain increased with the logarithmic vibration lg(1 + N), which was more in line with the prediction results of the Shenzhujiang residual deformation model. But the volume residual strain increased with the logarithmic vibration lg(1 + N), which had a certain nonlinearity and was in line with the logarithmic relationship.According to the data collation of Figs. N* = lg(1 + N), the fitted model is shown in Table According to the above analysis, the data are fitted so that According to the fitting parameters and fitting degree of the residual deformation model in Table Sl through static triaxial test. This test focuses on the residual deformation of coal gangue subgrade filling under dynamic conditions. At the same time, as a subgrade filler, considering dynamic environment is also the key research content. Therefore, the specific fitting of model parameters will be carried out in the follow-up research.In order to further analyze the relationship between the parameters of the model and the physical quantity of the test, the model parameters are analyzed. Under the premise of determining compaction degree and grading parameters, when confining pressure increases, oth Eqs.  and 5)  \documen49. The essence of this method is to analyze the degree of influence of each influencing factor on the affected object. Then identify the primary and secondary factors50. Therefore, the grey correlation analysis of coal gangue dynamic large-scale triaxial test is carried out to analyze the data. The correlation degree of each factor can be found out, that is, the influence degree on the deformation of gangue filler, so as to put forward guiding opinions for practical engineering.The grey correlation analysis method focuses on macro analysis and basic situation between various factors. The grey correlation analysis method does not require complex and rich information51:In terms of mathematical expression, the gray association analysis method adopts the degree of influence of the gray correlation degree characterization factor on the main behavior. Its calculation method is summarized as followsY0, where:There is a system feature number column (main behavior), denoted as Yi, i = 1,2,3, …, m (m is the number of factors in the series of comparisons):There is also a series of systematic factors, denoted as Then normalize the logarithm according to the formula , that isows Eqs.  and 11)9\documenl(1 ≦ l ≦ n)52:ξi(l) is the correlation coefficient of Yi to Y0 in l sample;The correlation coefficient between sequence max is the maximum absolute value of the difference between the total sequence and the corresponding time of the reference sequence at all moments as follows:Δmin is the minimum absolute value of the difference between the time of all sequences and the reference series at all moments as follows:Δi(k) is the absolute value of the difference between the k-time and the reference series corresponding to the time is calculated as follows49:ρ is the resolution coefficient, usually empirically based on ρ value, take ρ = 0.553.Δξi(l) only represents the degree of association between the sample data, because it has the characteristics of dispersion and not easy to compare, therefore, the introduction of the concept of correlation degree, that is, the average of the correlation coefficient, can be most of the correlation coefficients can be pooled into a value for centralized treatment. The correlation degree is calculated as follows:The correlation coefficient ri represents the degree to which factor Yi influences the main behavior Y0, for l,j ∈ , when Yl > Yk, then the system factor sequence Yl is considered to be superior to Yk, or has a higher correlation with the main behavior sequence.The degree of association εd and the final volume residual strain εvd as the residual deformation values after 30,000 times of dynamic load loading, and set them as reference sequences, Y0 and Z0, respectively, and set the confining pressure σ3, compaction degree η, graded parameters A and vibration N as factor sequences, including confining pressure series X1, compaction degree series X2,and cascading parameter series X3. According to the numerical value of the factor sequence, the corresponding reference sequence is selected, and the following results are obtained through the calculation in “In order to consider the degree of correlation between the influencing factors on the residual deformation of the specimen under large vibration times, this paper sets the values of the final axial residual strain According to the basic concept of gray correlation, it can be seen that the reference sequence representing the residual strain in this paper is positively correlated with the degree of correlation between the coefficient sequences, that is, the greater the degree of correlation, the greater the degree of influence, and vice versa.X1, compaction X2, and gradation X3. Considering, the confining pressure and compaction degree both indicate the compactness of the gangue test piece, and the particle gradation represents the particle composition of the sample. Reflected in the actual project, considering that the material quality of gangue is general, the quality fluctuation is large, and the natural grading is difficult to achieve good grading. According to the results of the gray correlation analysis, the degree of compaction should be appropriately increased to make the filler more compact, so as to reduce the residual strain under large vibrations.From Table εd and εvd of coal gangue subgrade filling gradually slows down with the increase of load vibration times. The residual deformation of coal gangue subgrade filler under different influencing factors is as follows the greater the confining pressure, the smaller the residual deformation of the sample; the higher the degree of compaction, the smaller the residual deformation of the sample; the increase of coarse grain content will make the cumulative deformation of the sample smaller.According to the test results, the deformation growth rate of N* = lg(1 + N). In 0–200 vibrations, (N*)2 is used instead of N* to fit the relationship between shear, volume residual strain and vibration displacement, and ln(N*) is used instead of N* to fit the relationship between volume residual strain and vibration frequency in 201–10,000 vibrations. This provides an idea for the analysis of residual deformation model of coarse-grained filler, gravel and other subgrade fillers under large cyclic loading.The actual residual deformation of gangue filler changes nonlinearly in semi-logarithmic coordinates with the development of vibration. Define According to the grey correlation degree between the influencing factors and the final residual deformation value of coal gangue filler, it can be found that the compactness of the sample can affect the residual deformation of the filler more than the particle composition of the sample.In this paper, the residual deformation development law of gangue subgrade filler was explored by using a large-scale triaxial experiment, and the correlation degree between different confining pressure, compaction degree, gradation parameters and vibration and the residual deformation value of gangue subgrade filler was analyzed based on the gray correlation analysis method, and the following conclusions were obtained.


Adolescence is a period of copious neural development, particularly in the ‘reward’ circuitry of the brain, and reward-related behavioral development, including social development. One neurodevelopmental mechanism that appears to be common across brain regions and developmental periods is the requirement for synaptic pruning to produce mature neural communication and circuits. We published that microglia-C3-mediated synaptic pruning also occurs in the nucleus accumbens (NAc) reward region during adolescence to mediate social development in male and female rats. However, both the adolescent stage in which microglial pruning occurred, and the synaptic pruning target, were sex specific. NAc pruning occurred between early and mid-adolescence in male rats to eliminate dopamine D1 receptors (D1rs), and between pre- and early adolescence in female rats (P20–30) to eliminate an unknown, non-D1r target. In this report, we sought to better understand the proteomic consequences of microglial pruning in the NAc, and what the female pruning target might be. To do this, we inhibited microglial pruning in the NAc during each sex’s pruning period and collected tissue for mass spectrometry proteomic analysis and ELISA validation. We found that the proteomic consequences of inhibiting microglial pruning in the NAc were inversely proportional between the sexes, and a novel, female-specific pruning target may be Lynx1.Please note, if this preprint will be pushed further to publication it will not be by me (AMK), as I am leaving academia. So, I’m going to write more conversationally. In this report, we sought to determine (1) whether the consequences of microglial pruning in the NAc, were, in fact, sexually divergent, and (2) what the female pruning target might be. To do this, we inhibited microglial pruning in the NAc during each sex’s pruning period and collected tissue for mass spectrometry proteomic analysis and ELISA validation. We found that the proteomic consequences of inhibiting microglial pruning in the NAc were inversely proportional between the sexes, and a novel, female-specific pruning target may be Lynx1.Social behaviors are integral to health and wellness across the lifespan. Adolescence is a period of copious neural development, particularly in the ‘reward’ circuitry of the brain, and reward-related behavioral development, including social development –3. One nAdult male and female Sprague-Dawley rats were purchased to be breeding pairs (Harlan/Envigo). Litters were culled to a maximum of 12 pups between postnatal day (P)2–5, and pups were weaned into same-sex housing in pairs or triplets at P21. At least 3 litters were represented in each experimental group. For Novel Social Interaction and Social Choice tests, rats were purchased from Harlan/Envigo to act as conspecifics. Rats were housed in conventional cages on cellulose bedding with ad libitum access to food and water. Colonies were maintained on a 12:12 light:dark cycle (lights on a 07:00) in a temperature- (20–24°C) and humidity- (35–55 RH) controlled room. Cages were changed twice weekly. All experiments were approved by the Institutional Animal Care and Use Committee at Albany Medical College.Rats underwent surgical intervention at either P22  or P30  according to our previously published sex-specific NAc pruning periods . Rats wehttps://www.creative-proteomics.com/).Rats were euthanized 8 days after surgery, a time point we have published that molecular and behavioral effects of NIF treatment are evident in both sexes , and per200μg protein per sample was precipitated with cold acetone. Pellets were dissolved in 2M urea and denatured with 10mM DTT for 1hr at 56°C followed by alkylation with 50nM IAA for 1hr at room temperature in the dark. Ammonium bicarbonate was added to a final concentration of 50mM, pH 7.8, and trypsin was added to the sample for digestion for 15 hrs at 37°C. Peptides were purified with a C18 SPE column and lyophilized to near dryness. Peptides were resuspended in 20μL of 0.1% formic acid before LC-MS/MS analysis. 1μg of sample was loaded onto a nanoLC-MS/MS platform. The full scan was performed between 300–1650 m/z at a resolution of 60,000 at 200 m/z. The gain was set to 3e6. The MS/MS scan operated in Top 20 mode with 15,000 at 200 m/z resolution, 1e5 automatic gain control target, 19ms maximum injection time, 28% normalized collision energy, 1.4 Th isolation window, unassigned, 1, >6 charge state exclusion, and 30 sec dynamic exclusion. Raw MS files were aligned with the rat protein database using Maxquant (1.6.1.14). Protein modifications were carbamidomethylation (fixed), oxidation (variable), the enzyme specificity was set to trypsin, the maximum missed cleavage was set to 2, the precursor ion mass tolerance was set to 10 ppm, and the MS/MS tolerance was 0.5 Da.t-tests were performed between NIF and Vehicle groups for each sex. In the case of duplicate protein IDs, the ID corresponding to the smallest p-value was retained and the others were excluded from analysis. Protein groups that were significantly changed by NIF treatment  were assessed for global proteomic summary, including Pearson’s correlation of NIF-induced changes in all proteins between the sexes (mybiosource.com (#MBS9902329), NAChR ELISA was purchased from LSBio (#LS-F37436), and D1r ELISA was purchased from Novus Biologicals (NBP2–67935). ELISA data were analyzed with t-tests for each sex. There were no outliers detected via Grubb’s test (α=0.05). For all analyses, statistical significance is defined as p<0.05. All statistics were performed in GraphPad Prism 9.5.1.Data from Creative Proteomics were quality controlled in-house: any proteins that had more than one sample in which they were not detected (0 intensity) within the group of 3–4 total samples was excluded from analysis. In proteins with just one non-detected sampled, the average of the other 2–3 samples was used to replace the 0. he sexes . Benjamihe sexes . ProteinBecause the male and female NAc pruning period is sex-specific , we perfr=−0.1697, p<0.001; In total, 3610 and 3687 total proteins were identified via label free mass spectrometry in NIF- and Vehicle-treated male and female NAc tissue, respectively. Of these, there were 278 differentially expressed proteins  in males and 207 DEPs in females. Only 7 of these proteins were differentially expressed in both sexes, and of the 7 only one was regulated in the same direction . A heatmboth sexes, 6 of which were regulated in different directions between the sexes. To better understand the unique consequences of NAc pruning in each sex, we conducted Benjamini-Hochberg adjustment for multiple comparisons, which revealed 4 DEPs in males and 7 DEPS in females that were still significantly regulated by NIF treatment. In males, these included the upregulation of Ncbp1, Fh, Gnaz, and Atp5b. In females, these included the upregulation of Lynx1 and Fras1 and the downregulation of Manf, Sept9, Dpysl2, Tnpo3, and Ggh. There was no meaningful pathway enrichment for either sex using either corrected or uncorrected DEP lists at the α = 0.05 level (data not shown).As discussed in t(14)=1.225, p=0.241,; females: t(12)=2.647, p=0.021; t(9)=2.138, p=0.061; females: t(10)=0.522, p=0.613; n=3–5/sex/group), we did see an increase in D1r levels in NIF-treated males, but not females  and were synaptically-localized. In the female dataset, only Lynx1 fits this criteria via its close association with nicotinic acetylcholine receptors (NAChRs). Neither NAChr nor D1r, the known male pruning target , was ide females , consistIn this set of studies, we determined how microglia-mediated synaptic pruning in the NAc impacts the NAc proteomic landscape in male and female rats. We observed that despite manipulating the same developmental mechanism, synaptic pruning, the global proteomic outcome in the NAc was inversely related between males and females, and the sets of DEPs regulated by pruning were unique to each sex. Finally, we identify Lynx1 as a putative female-specific NAc pruning target.the same developmental mechanism, C3-CR3 -mediated synaptic pruning, is engaged in the adolescent NAc to mediate largely the same social development outcomes in both sexes. But the details are very different. Inverse, in fact! The same proteins that are upregulated by NAc pruning in males are more likely to be downregulated by NAc pruning in females, and vice versa. I don’t think that is a consequence of microglia just nibbling off different synaptic protein in males vs. females to induce downstream proteomic consequences in the pruning target’s respective signaling cascade. I think this is a mechanism that can sex-specifically reprogram the NAc, similar to the highly sex-divergent effects microglial pruning has on the amygdala [Sex differences of varying levels are now being reported in virtually every neural and behavioral outcome. Some sex differences are easily identifiable, e.g. a large change in behavior, while others are more subtle . Our datamygdala  and preoamygdala . And if amygdala . Althougamygdala , 9. We dbound Lynx1 might equal less ‘free’, antibody-friendly Lynx1 for ELISAs. More validation will need to be performed, but it is worthwhile venturing down the Lynx1 as a female-specific pruning target path, as I think it could be quite impactful.The proteomic data and ELISA validation identified Lynx1 as protein that was significantly regulated by microglial pruning in the NAc, specifically in females. However, (surprise!) the proteomic data indicated Lynx1 was increased by NIF treatment and the ELISA data indicated Lynx1 was decreased by NIF treatment. There are a number of reasons the data would not agree between these measurements. Mass spectrometry requires digestion of proteins into short peptides that are read and matched in a database. ELISAs measure native proteins using antibodies. It is very possible that a protein might be bound to other proteins in such a way that an antibody would not be able to bind. Lynx1 is an accessory protein that physically associates with NAChRs to modulate receptor function with very high efficiency . If LynxLynx1 binding of NAChRs promotes receptor desensitization and slower recovery from desensitization . Lynx1 hSupplement 1