A method for automatically identifying single cell types based on a deep residual generation algorithm

Abstract

The application discloses a kind of based on deep residual generation algorithm automatic identification single cell type method, this method is based on the convolutional neural network in residual module, since convolution is connected with partial neural network, compared with the full connection mode in prior art, the problem of low efficiency is solved.Because using the convolution structure in residual module, local features of single cell transcriptome data can be captured, therefore the model improves the feature extraction capability, makes the inference of cell type more accurate.The residual structure used in the application can improve the degradation problem of neural network, and using this point to make the network layer become deeper, which is also conducive to further feature extraction of data.In addition, since semi-supervised learning can utilize original label and additional data to improve the bias of sample, the scRSSL proposed in the application can improve the imbalance problem of sample in single cell data set by using the characteristics of semi-supervised learning, and higher accuracy is obtained.

Description

Technical Field

[0001] This invention pertains to computer science methods (deep neural networks), and relates to the processing and analysis of biological information data using artificial intelligence, particularly a method for automatically identifying single-cell types based on a deep residual generation algorithm (scRSSL). Background Technology

[0002] The development of single-cell sequencing in recent years has had a tremendous impact on the field of biology because it allows researchers to study cellular heterogeneity at the individual cell level, something that previous tissue-based sequencing technologies could not do. Identifying the type of individual cells from a large amount of single-cell data is a crucial step in a complete study, often affecting downstream analysis results. Currently, unsupervised clustering is a common method for determining cell types. However, with the increasing volume of single-cell sequencing data, these traditional methods are becoming increasingly inapplicable, both in terms of rising costs and overall complexity. Current single-cell datasets often exhibit extremely high dimensionality, large sample sizes, high sparsity, and imbalanced distribution, posing significant challenges to research.

[0003] scANVI is the algorithm most similar to this invention, and it is also based on a semi-supervised deep model. See the article "Probabilistic harmonization and annotation of single-cell transcriptomics data with deep generative models" for details. scANVI mainly consists of a variational autoencoder (VAE) and a semi-supervised module based on a fully connected neural network. It reduces the dimensionality of the data using the VAE, then uses a fully connected neural network to infer cell types. During model training, both unlabeled and labeled data are used. After obtaining the low-dimensional representation of the data, a decoder neural network restores the data to its original distribution. The main focus of the scANVI algorithm is cell type inference and the integration of different data samples. Furthermore, it uses a fully connected neural network for single-cell type inference. This results in a large number of computational parameters, leading to low computational efficiency and less accurate results. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention provides a method for automatically identifying single-cell types based on a deep residual generation algorithm.

[0005] This method is based on a convolutional neural network within a residual module. Since convolution connects only a portion of the neural network, it overcomes the inefficiency problem of fully connected methods in previous techniques. Because the convolutional structure within the residual module captures local features from single-cell transcriptome data, the improved feature extraction capability of the model leads to more accurate cell type inference. The residual structure used in this invention can mitigate the degradation problem of neural networks, allowing for deeper network layers, which also facilitates further feature extraction from the data.

[0006] This invention is achieved through the following technical solution:

[0007] A method for automatically identifying single-cell types based on a deep residual generation algorithm, characterized by the following steps:

[0008] Step 1: Convert single-cell data and some labeled data into Anndata format; preprocess the single-cell data, filter out genes with less than 3 expression in each cell, and select the top 50% of differentially expressed genes;

[0009] Step 2: Input the preprocessed data from Step 1 into the model (VAE) for training.

[0010] The specific process of VAE is as follows: The variational autoencoder contains an original variable x and a latent variable z. Assuming that the prior p(z) is normally distributed, it is used in conjunction with the conditional distribution p... σ Let (x|z) be used to find the joint probability p. σ (x,z)=p(z)p σ (x|z), where p() represents the probability function, and σ is the probability of p. σ The parameters of (x|z), the joint probability p σ (x,z) represents its original distribution;

[0011] The variational autoencoder first uses Bayes' theorem to calculate Then calculate p. σ (x)=Ε z～p(z) [p σ (x|z)];

[0012] Among them, Ε z～p(z) Let p represent the expectation of z under p(z). σ The probability value of (x|z), where σ is the parameter value;

[0013] This maximizes the likelihood function p of the original variables. σ Since calculating p(z|x) is difficult, a parameterized q is introduced. ω We approximate it using (z|x), where the parameter ω refers to (μ, σ).2 The mean and variance are used to calculate a log-likelihood, also known as the Evidence Lower BOund (ELBO), which is calculated using the following formula:

[0014]

[0015] Here, log() represents the function that takes the logarithm. This means that z satisfies q. ω p obtained under the (z|x) distribution σ The probability of (x|z), σ and ω are parameter values, and KL() represents the distance function between the two distributions;

[0016] The general formula for variational autoencoders:

[0017]

[0018] Where F() represents the encoder function and p() represents the probability function. This means that z satisfies q. ω p obtained under the (z|x) distribution σ The probability of (x|z), log() represents the function of taking the logarithm, KL() represents the distance function between the two distributions, and σ and ω are parameter values.

[0019] Step 3: Input the data trained in Step 2 into the semi-supervised inference network for cell types. After the data is reduced to 100 dimensions, the model divides the labeled data and unlabeled data into two groups and uses the labeled data and unlabeled data together to generate the feature representation of the next layer.

[0020] The specific process is as follows: Data is generated from the continuous variable z and the categorical variable y obtained from the VAE latent space, and its definition is:

[0021] p(y)=Cat(y|π), p(z)=Ν(z|0,I),p θ (x|z,y)=f(x;y,z,θ)

[0022] Where p() represents the probability function, N(z|0,I) represents the standard normal distribution, 0,I represent the mean and variance, θ is the parameter of the likelihood function f(x; y,z,θ), and Cat(y|π) is the multinomial distribution; for unlabeled single cells, y is a latent type variable, and z is also a latent continuous variable p θ () represents probability;

[0023] All unlabeled single cells are integrated, and then a classification inference is performed by training a neural network, and the type of unlabeled cells is predicted from the inferred posterior distribution.

[0024] The specific inference process is as follows: optimize two objective functions for labeled data and unlabeled data respectively, denoted as L(x,y) and U(x), with the objective likelihood function as follows: Where p l and p u Let represent the distributions of the labeled and unlabeled datasets, respectively, and ∑ denotes summation;

[0025] To perform predictions, a classification loss term is added to the objective function J, which is:

[0026] The hyperparameter α controls the weights of the generative and discriminative models. The predicted cell type is obtained using the above formula.

[0027] Step 4: After training, we obtain the dimensionality-reduced data z and the unlabeled data y. z can be used for a series of other downstream research tasks, and y allows researchers to obtain cell types.

[0028] Furthermore, in step 2, when training the data obtained in step 1, the data is transformed into 128 dimensions after passing through a hidden layer of 128 neurons, and then passed through a hidden layer of 100 neurons, so that the original data is represented by 100 features.

[0029] Furthermore, in step 3, the hyperparameter α controls the weights of the generative model and the discriminative model, and is set to a default value of 0.1.

[0030] Furthermore, in step 3, when inferring cell type, a residual network module is used for label inference. When the data is located in the residual network hierarchy and the input is x, the learned feature is H(x). The residual function is defined as: F(x) = H(x) - x. The original function is: F(x) + x. Residual learning is used every few stacked modules, defined as: y = F(x, {W i})+x, at this point, x and F have the same dimension.

[0031] Where x represents the input vector, y represents the output vector, and F(x,{W i}) represents the residual mapping that needs to be learned. In module F = W2α(W1x), α represents the ReLU activation function, and F+x represents a shortcut connection method.

[0032] Furthermore, when the dimensions of x and F are not equal, a linear mapping W needs to be performed. s Perform dimensional matching on them: y = F(x, {Wi})+W s x.

[0033] Furthermore, in step 3, the residual network consists of 4 basic blocks, 1 convolutional layer, 1 batch normalization (BN) layer, 1 max pooling layer, 1 average pooling layer, and 1 fully connected layer. Each basic block consists of 4 convolutional layers, and the inputs and outputs of its 4 basic blocks are connected by the formulas described above.

[0034] Compared with the prior art, the advantages of the present invention are as follows:

[0035] 1. Since semi-supervised learning can improve sample bias by using original labels and additional data, the scRSSL proposed in this invention utilizes the characteristics of semi-supervised learning to improve the problem of sample imbalance in single-cell datasets; this invention achieves higher accuracy in predicting cell types compared to previous techniques (scANVI, Random Forest, SVM, KNN, etc.).

[0036] 2. The model scRSSL proposed in this invention is based on a semi-supervised residual network. It uses a neural network approach when inferring unknown labels, and sets the connection structure of the neural network to a residual network structure. Compared with fully connected neural networks, it has two advantages: First, the convolutional layers in the residual module can extract local features from single-cell data; Second, the residual structure can improve the degradation problem of neural networks. This can be used to make the number of network layers deeper, which is conducive to further feature abstraction of the data.

[0037] 3. With the emergence of large-scale single-cell datasets, data acquisition is relatively simple, but obtaining data labels is difficult. Previously, it was necessary to transfer existing label annotations to newly generated datasets. The scRSSL proposed in this invention can transfer labels from small datasets to large datasets using a semi-supervised learning approach.

[0038] 4. The scRSSL model proposed in this invention is scalable and can be extended to process large-scale single-cell datasets, such as single-cell datasets with more than one million samples. Attached Figure Description

[0039] The invention will now be further described with reference to the accompanying drawings.

[0040] Figure 1 This is a schematic diagram of the network connection method of the residual module of the present invention;

[0041] Figure 2 This is a flowchart illustrating the framework for single-cell data processing and analysis in this invention.

[0042] Figure 3This is a comparison chart of the evaluation of the model of this invention;

[0043] Figure 4 This is a comparison chart showing the effectiveness of the model of this invention on imbalanced datasets;

[0044] Figure 5 This is a comparison chart of ROC curves showing the effectiveness of this invention for imbalanced data. Detailed Implementation

[0045] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0046] Example 1

[0047] Step 1: Convert single-cell data and partially labeled data into Anndata format. Preprocess the single-cell data, filtering out genes expressed at less than 3 in each cell. Select the top 50% of differentially expressed genes.

[0048] Step 2: Input the data into the model (VAE) for training. The data is transformed into 128 dimensions after passing through a hidden layer with 128 neurons, and then passed through a hidden layer with 100 neurons, so that the original data is represented by 100 features.

[0049] The specific process of VAE is as follows: The variational autoencoder contains an initial variable x and a latent variable z. Assuming that the prior p(z) is normally distributed, it is used in conjunction with the conditional distribution p... σ Let (x|z) be used to find the joint probability p. σ (x,z)=p(z)p σ (x|z), where p() represents the probability function, and σ is the probability of p. σ The parameters of (x|z). This joint probability p σ (x, z) represents its original distribution. The data generation process can be understood as: using the low-dimensional feature z generated from the standard normal distribution as a condition for the original variable x.

[0050] The variational autoencoder first uses Bayes' theorem to calculate

[0051]

[0052] This allows us to obtain the latent variable z from the original variable x, and then calculate p. σ (x)=Ε z～p(z) [p σ [x|z)], where Ε z～p(z) Let p represent the expectation of z under p(z). σ The probability value of (x|z) is given by σ, which is a parameter value. This is used to maximize the likelihood function p of the original variables. σ(x). Since computing p(z|x) is difficult, a parameterized q is introduced. ω We approximate it using (z|x), where the parameter ω refers to (μ, σ). 2 The mean and variance are the base values. Then, a log-likelihood, or Evidence Lower BOund (ELBO), needs to be calculated. The formula is as follows:

[0053]

[0054] log() is a function that takes the logarithm of a function. This means that z satisfies q. ω p obtained under the (z|x) distribution σ The probability of (x|z), where σ and ω are parameter values, and KL() represents the distance function between the two distributions.

[0055] Maximizing ELBO is equivalent to simultaneously minimizing KL(q). ω (z|x)||p(z|x)). This also meets the requirement, that is, to let the introduced distribution q ω (z|x) is closest to p(z|x), and with the help of deep learning, this calculation is very convenient. Only two neural network structures need to be designed, with one encoder primarily responsible for optimizing q. ω The parameters of (z|x) are primarily handled by a decoder that optimizes p. σ The parameters of (x|z). It is worth noting that when the low-dimensional representation of the data introduces Gaussian noise into the latent space, a resampling technique is needed to make it differentiable, thus ensuring the continuity of training.

[0056] The general formula for variational autoencoders:

[0057]

[0058] F() represents the encoder function, and p() represents the probability function. This means that z satisfies q. ω p obtained under the (z|x) distribution σ The probability of (x|z), log() represents the function of taking the logarithm, KL() represents the distance function between the two distributions, and σ and ω are parameter values.

[0059] Step 3: Input the data obtained in Step 2 into the semi-supervised network for inferring cell types. After the data is reduced to 100 dimensions, the model separates the labeled and unlabeled data into two groups, and uses both the labeled and unlabeled data together to generate the feature representation for the next layer.

[0060] Specifically, such as Figure 2 The diagram illustrates the framework flowchart for single-cell data processing and analysis. As can be seen, the input data consists of partially labeled single-cell data. After a preprocessing step, the input data is fed into a neural network model. The input single cells pass through a hidden layer to obtain z1. z1 is then divided into two classes based on whether it has a label. For labeled data, its label and itself are used to generate the next representation feature z2. For unlabeled data, its label is inferred through a residual network, and then the next representation feature z2 is generated. z2 passes through a hidden layer and is then mapped back to the original data distribution.

[0061] The specific process is as follows: Data is generated from the continuous variable z and the categorical variable y obtained from the VAE latent space, and its definition is:

[0062] p(y)=Cat(y|π), p(z)=Ν(z|0,I),p θ (x|z,y)=f(x;y,z,θ)

[0063] Where p() represents the probability function, N(z|0,I) represents the standard normal distribution, 0,I represent the mean and variance, θ is the parameter of the likelihood function f(x;y,z,θ), and Cat(y|π) is the multinomial distribution.

[0064] For unlabeled single cells, y is a latent type variable, and z is a latent continuous variable. These latent variables are unentangled and can represent certain attributes used to distinguish single cells. f(x; y, z, θ) is the hypothesized likelihood function, which, considering the characteristics of single-cell data, is assumed to be a negative binomial distribution. It is obtained by nonlinear parameterization of the latent variables, implemented here through the decoder neural network in the model.

[0065] All unlabeled single cells are integrated, then a neural network is trained for classification inference, and the inferred posterior distribution p is used as the basis for classification. θ (y|x) predicts the type of unlabeled cells. θ () represents probability, y represents potential type variable, and x represents original data.

[0066] The inference process actually involves optimizing two objective functions, L(x,y) and U(x), for labeled and unlabeled data respectively. The objective likelihood functions are: Where p l and p u Let J represent the distributions of the labeled and unlabeled datasets, respectively, and ∑ denotes summation. For prediction, a classification loss term is added to the objective function J.

[0067] The objective function is:

[0068] The hyperparameter α controls the weights of the generative and discriminative models, and is set to a default value of 0.1. The predicted cell type can be obtained using the above formula.

[0069] Label inference is performed using residual network modules during semi-supervised training. When the data is located in the residual network hierarchy and the input is x, the learned feature is H(x). Assuming that multiple nonlinear layers can gradually approximate a complex function, they can also asymptotically approximate a residual function, i.e., H(x) - x, where the output and input dimensions are equal. The residual function is defined as: F(x) = H(x) - x, and the original function is: F(x) + x. The degradation problem illustrates that approximating the identity mapping using multiple nonlinear layers can be difficult.

[0070] In this process, residual learning is used every few stacked modules, defined as: y = F(x, {W i})+x. x represents the input vector, y represents the output vector, F(x,{W i}) represents the residual mapping that needs to be learned. In module F=W2α(W1x), α represents the ReLU activation function, and F+x represents a shortcut connection method.

[0071] It is important to note that the dimensions of x and F must be equal. If they are not equal, a linear mapping W needs to be performed. s Perform dimensional matching on them: y = F(x, {W i})+W s x. The residual network of this invention consists of four basic blocks, one convolutional layer, one batch normalization (BN) layer, one max pooling layer, one average pooling layer, and one fully connected layer. Each basic block consists of four convolutional layers, and the inputs and outputs of its four basic blocks are connected using the formula in the above equation. For details on the residual connection method of the basic blocks, please refer to... Figure 1 .

[0072] from Figure 1 As can be seen, after the original data passes through the hidden layer and activation function, it does not directly output the calculated value, but outputs a fitting residual. This residual represents the difference between the fitted value and the true value. This difference plus the original x is the output value of the residual network, which is also the input value of the next layer of the neural network.

[0073] The design follows a principle: whenever the size of the feature map is halved, the number of filters is doubled, so that the time complexity of each layer remains unchanged.

[0074] Step 4: After training, we obtain the dimensionality-reduced data z and the unlabeled data y. z can be used for a series of other downstream research tasks, and y allows researchers to obtain cell types.

[0075] Example 2

[0076] The specific parameters for implementing this invention are as follows:

[0077] scRSSL is implemented using PyTorch. For the variational autoencoder module, the dimensionality transformation is set to: input dimension - 128 - 100 - 128 - output dimension. That is, the latent space dimension is set to 100, the batch size during training is set to 128, and when the number of input samples exceeds 10,000, it is increased to 1024 to reduce training time. The Adam optimizer is chosen to optimize the model, with a learning rate of 0.001 and a training epoch of 100. The activation function is set to ReLU().

[0078] For the semi-supervised module, i.e., the residual network training module, the 100-dimensional data in the latent space is set to [batch size, 1, 10, 10]. The residual network consists of 20 convolutional layers, 1 max pooling layer, 1 average pooling layer, and 1 fully connected layer. It consists of a total of 8 residual modules. The last fully connected layer of the residual network module is set to [512, number of cell types]. The activation function in the module is ReLU(), and the last fully connected layer uses Sigmoid() as the activation function. All experiments in this invention were conducted on a Windows 10 Professional Edition system with an Intel(R) Core(TM) i9-10900K CPU @ 3.70GHz, 128GB of RAM, and a VIDIA GeForce RTX 3060 GPU (16GB).

[0079] Example 3

[0080] In this embodiment, a total of five single-cell datasets were used: Wang, Xin, Baron, Seger, and Muraro. The Wang dataset primarily comes from the article "Single-cell transcriptomics of the human endocrine pancreas," the Xin dataset primarily comes from the article "RNA sequencing of single human islet cells reveal type 2 diabetes genes," the Baron dataset primarily comes from the article "A single-cell transcriptomic map of the human and mouse pancreas reveals inter- and intra-cell population structure," the Seger dataset primarily comes from the article "Single-cell transcriptome profiling of human pancreatic islets in health and type 2 diabetes," and the Muraro dataset primarily comes from the article "A single-cell transcriptome atlas of the human pancreas." One dataset was selected as the training set each time, and the other four datasets were used as the test set, effectively performing a five-fold cross-validation to evaluate and compare the models. Seven methods were selected for comparison with scRSSL: RandomForest (RF), Support Vector Machine (SVM), K-Nearest Neighbor (KNN), AdaptiveBoosting (AdaBoost), Decision Tree (DT), Naive Bayes (NB), and scANVI. For example, in the first test (first row), we selected the Xin dataset as the training set and the other four datasets as the test sets, and evaluated each of the seven methods mentioned above.

[0081] like Figure 3 As shown in the results, the scRSSL algorithm of this invention maintains good performance even in some extreme cases, outperforming other algorithms. For example, when using the smallest single-cell dataset, Wang (457 cells), as the training set and the largest single-cell dataset, Baron (8569 cells), as the test set, scRSSL still achieves the highest score.

[0082] like Figure 4 The diagram shows a comparison of the model's effectiveness on imbalanced datasets. In each matrix, rows represent the true cell label values, columns represent the predicted single-cell labels, and the darkened portion above the diagonal represents the cell types correctly predicted by the model. We can see that the method scRSSL of this invention has a higher prediction accuracy compared to other methods.

[0083] like Figure 5 The figure shows a comparison of ROC curves for the effectiveness of imbalanced data. Each line represents a different model. It can be observed from the figure that the method scRSSL of this invention has the second largest ROC area, indicating the effectiveness of scRSSL. The reason it is slightly lower than KNN is likely because KNN uses optimal parameters.

[0084] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for automatically identifying single-cell types based on a deep residual generation algorithm, characterized in that: Includes the following steps: Step 1: Convert single-cell data and some labeled data into Anndata format; The single-cell data were preprocessed to filter out genes with less than 3 expression levels in each cell and select the top 50% of differentially expressed genes. Step 2: Input the preprocessed data from Step 1 into the VAE model for training. The specific process of VAE is as follows: The variational autoencoder contains a primitive variable. and a latent variable Under the assumption prior In the case of a normal distribution, use it in conjunction with the conditional distribution. To find the joint probability ,in Represents a probability function. yes Parameters, joint probability This represents its original distribution; The variational autoencoder first uses Bayes' theorem to calculate Then calculate ; in By representation exist Under the expectation The probability value, It is a parameter value; This maximizes the likelihood function of the original variables. Due to calculation It is difficult, so a parameterized one is introduced. To approximate it, the parameters here It refers to That is, the mean and variance, and then a log-likelihood, also known as Evidence Lower BOund ELBO, is calculated using the following formula: ； in, The function that takes the logarithm. express In compliance The distribution obtained The probability, and It is a parameter value. A distance function representing the distance between two distributions; The general formula for variational autoencoders: ， in, Represents the encoder function. Represents a probability function. express In compliance The distribution obtained The probability, The function that takes the logarithm. This represents the distance function between two distributions. and It is a parameter value; Step 3: Input the data trained in Step 2 into the semi-supervised inference network for cell types. After the data is reduced to 100 dimensions, the model divides the labeled data and unlabeled data into two groups and uses the labeled data and unlabeled data together to generate the feature representation of the next layer. The specific process is as follows: Data is generated from the continuous variable z and the categorical variable y obtained from the VAE latent space, and its definition is: ， in, Represents a probability function. Represents the standard normal distribution. Indicates the mean and variance. It is the likelihood function The parameters, It is a multinomial distribution; for unlabeled single cells, It is a potential type variable. It is also a potential continuous variable Represents probability; All unlabeled single cells are integrated, and then a classification inference is performed by training a neural network, and the type of unlabeled cells is predicted from the inferred posterior distribution. The specific inference process is as follows: optimize two objective functions for labeled data and unlabeled data respectively, denoted as […]. and Objective likelihood function: ,in and These represent the distributions of the labeled and unlabeled datasets, respectively. To express summation; In order to make predictions, in the objective function Add a classification loss term, and the objective function is: , in Hyperparameters control the weights of the generative and discriminative models, and the predicted values ​​for cell types are obtained using the above formulas. Step 4: Training completes, yielding dimensionality-reduced data. and unlabeled data ,in It can be used for a range of other downstream research tasks, allowing researchers to obtain cell types.

2. The method for automatically identifying single-cell types based on a deep residual generation algorithm according to claim 1, characterized in that: In step 2, when training the data obtained in step 1, the data is transformed into 128 dimensions after passing through a hidden layer of 128 neurons, and then passed through a hidden layer of 100 neurons, so that the original data is represented by 100 features.

3. The method for automatically identifying single-cell types based on a deep residual generation algorithm according to claim 1, characterized in that: In step 3, the hyperparameters Controls the weights of the generative and discriminative models, set to the default value of 0.

1.

4. The method for automatically identifying single-cell types based on a deep residual generation algorithm according to claim 1, characterized in that: In step 3, when inferring cell type, a residual network module is used for label inference. When the data is located in the residual network hierarchy, the input is... The features learned at that time are The residual function is defined as follows: The original function is: Residual learning is used every few stacked modules, defined as: ,at this time, and The dimensions are equal; in, Represents the input vector. Indicates the output vector. This represents the residual mapping that needs to be learned, and the module. middle Represents the activation function ReLU. This represents a quick connection method.

5. The method for automatically identifying single-cell types based on a deep residual generation algorithm according to claim 4, characterized in that: when and When the dimensions are not equal, a linear mapping needs to be performed. Perform dimensional matching on them: .

6. A method for automatically identifying single-cell types based on a deep residual generation algorithm according to claim 4 or 5, characterized in that: In step 3, the residual network consists of 4 basic blocks, 1 convolutional layer, 1 batch normalization (BN) layer, 1 max pooling layer, 1 average pooling layer, and 1 fully connected layer. Each basic block consists of 4 convolutional layers, and the inputs and outputs of its 4 basic blocks are connected by the formulas mentioned above.

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