Retinal encoder construction method, device, and terminal based on multimodal features

Abstract

The present invention belongs to the field of computer applications, and discloses a method, device, and terminal for constructing a retinal encoder based on multimodal features. The method for constructing a retinal encoder based on multimodal features includes: extracting and quantizing multimodal stimulation features of input videos; encoding feature sequences using basis functions with multidimensional time domain features to obtain an external input stimulation matrix of a computing unit; and training cascaded linear-nonlinear computing units to obtain a nonlinear retinal encoder that can adapt to complex environments. In order to compare and analyze the actual performance of the retinal encoder based on multimodal features proposed in the present invention, the present invention selects some neurons, and respectively calculates the likelihood function values ​​and mutual correlation coefficients of the encoder's predicted output and the target value for comparison. The results show that the retinal encoder proposed in the present invention has significantly improved performance in both likelihood function and mutual correlation coefficient compared with other methods.

Description

Technical Field

[0001] The present invention belongs to the field of computer application technology, and specifically relates to a method, device and terminal for constructing a retinal encoder based on multimodal features. Background Art

[0002] At present, retinal encoders, as a method of encoding visual signals, use nonlinear calculations to encode multimodal visual stimuli into a series of spike discharge sequences, with the goal of simulating the characteristics of retinal ganglion cells. Research on retinal encoders can not only deepen the understanding of nonlinear calculations in the retina, but also provide a theoretical basis for lightweight computer retinal encoding.

[0003] Although there are many retinal coding methods, the existing methods have the following problems: the retinal coding method based on biological structure simulates the biological characteristics of the retina through complex circuits. Its complex connections and large amount of calculations make this method only suitable for academic research and cannot be used to solve practical problems; the retinal coding model based on linear nonlinear models and generalized linear models is based on the retinal encoder method of neurons with multiple inputs and single output structures. Its simple structure and calculation mode make this type of model small in size and fast in calculation, but this type of method greatly simplifies the biological structure of the retina, resulting in its inability to simulate the complex nonlinear calculations in the retina; the retinal coding model based on convolutional neural network can better reproduce the spike discharge sequence generated by ganglion cells under artificial stimulation such as white noise by virtue of its local connection, weight sharing, and multi-layer network characteristics, but this method has a large amount of calculation and cannot be applied to terminals with weak computing power. Therefore, a new retinal encoder implementation method is urgently needed.

[0004] Through the above analysis, the problems and defects of the prior art are as follows:

[0005] (1) Existing retinal coding methods based on biological structures use complex circuits to simulate the biological characteristics of the retina. They are complex in structure and not very practical, and cannot be used to solve practical problems.

[0006] (2) Existing retinal coding models based on linear nonlinear models and generalized linear models greatly simplify the biological structure of the retina, resulting in their inability to simulate the complex nonlinear calculations within the retina.

[0007] (3) The existing retinal coding model based on convolutional neural network has a large amount of computation and cannot be applied to terminals with weaker computing power.

[0008] The difficulty in solving the above problems and defects is as follows: the retinal encoder model based on biological structure simulates the response of the retina to light stimulation through a large number of bionic circuits. How to remove redundant network structures and simplify complex calculations is a difficulty in the research; the retinal coding model based on convolutional neural network can effectively extract the features of the input white noise video by means of convolution operation, but the introduction of convolution operation leads to an increase in the amount of calculation. How to reduce the amount of calculation is another difficulty.

[0009] The significance of solving the above problems and defects is that the implementation method of retinal encoder not only deepens scholars' understanding of nonlinear calculations in the retina, but also provides a theoretical basis for lightweight computer retinal encoding. Summary of the invention

[0010] In view of the problems existing in the prior art, the present invention provides a method for implementing a retinal encoder based on multimodal features.

[0011] The present invention is implemented in this way: a method for constructing a retinal encoder based on multimodal features, the method for constructing a retinal encoder based on multimodal features comprising the following steps:

[0012] Step 1, extracting multimodal stimulus features of the input video;

[0013] Step 2, using a basis function with instantaneous extreme value and continuous effect characteristics to encode the feature sequence, and obtaining an external input stimulus matrix for retinal ganglion cells;

[0014] Step three, a nonlinear retinal encoder with multimodal stimulus input that can adapt to complex environments is obtained through nonlinear computing unit training.

[0015] Further, in step 1, the step of extracting multimodal stimulus features of the input video includes:

[0016] (1) Extract the visual input within the receptive field of the input video and obtain the light stimulation sequence of the target neuron within the video time. The input intensity of the light stimulation to neuron i is calculated as follows:

[0017]

[0018] Where V(x,y,t) represents the light intensity of the input video at point (x,y,t), x,y represent the spatial position coordinates of a frame on the video, and t represents the number of video frames;

[0019] (2) Based on the input light stimulation of ganglion i Extracting the light intensity instantaneous change stimulus sequence from the video The formula is as follows:

[0020]

[0021] (3) Perform three-dimensional Gaussian blur on the video. Each pixel is calculated by applying three-dimensional Gaussian blur to the pixel values ​​of the points nearby in space and the pixel values ​​of the previous and next frames. The formula is as follows:

[0022]

[0023] (4) Take the values ​​within a certain range in the three-dimensional space near the target pixel point, determine the weight coefficient according to the normal distribution density, and multiply them to obtain the processed pixel value of the target position, and obtain the two-frame picture motion input stimulation of the neuron The formula is as follows:

[0024]

[0025] Furthermore, in step 2, the method of encoding the feature sequence using a basis function having instantaneous extreme value and continuous effect characteristics to obtain an external input stimulation matrix for retinal ganglion cells includes:

[0026] (1) Construct a multimodal visual spatiotemporal stimulus input matrix for quickly extracting video data in the time domain and space domain. The formula is as follows:

[0027]

[0028] in, represents the stimulus basis matrix constructed by the ith method; by selecting a sequence of feature extraction methods suitable for the application scenario, the visual spatiotemporal features of interest to the target task are extracted;

[0029] (2) Construct the stimulus basis matrix, the formula is as follows:

[0030]

[0031] in, Represents the kth stimulus feature extracted by neuron i from the input video material.

[0032] Furthermore, in step 3, the multimodal stimulus input nonlinear retinal encoder that can adapt to complex environments is obtained through nonlinear computational model unit training, including:

[0033] (1) Establish a nonlinear retinal encoder model;

[0034] (2) Propose an optimization plan for the model.

[0035] Furthermore, in step (1), the establishment of a nonlinear retinal encoder includes:

[0036] 1) Using different feature weight vectors to perform linear calculations on the input stimulus to obtain the corresponding features contained therein;

[0037] 2) Using a pair of linear-nonlinear upstream filters to calculate the excitatory-inhibitory inputs of the input stimulus matrix;

[0038] 3) Integrate and activate the upstream features according to the pulse nonlinear function to obtain the firing rate of the neuron caused by the input stimulus.

[0039] Furthermore, in step (1), the step of establishing a nonlinear retinal encoder further includes:

[0040]

[0041] Among them, k i is the feature matrix X stim The i-th linear selection filter, f i (·) and ω i is the upstream nonlinear function and weight coefficient corresponding to the feature, x(t) represents the additional factor inside the neuron, and h is the linear filter acting on x.

[0042] Furthermore, in step (2), the proposed optimization scheme for the retinal encoder model includes:

[0043] 1) In this model, ω is fixed i is ±1, for the linear filter bank {k i The optimization of} is performed by calculating the likelihood function for each filter k i The gradient of is:

[0044]

[0045] in, F′[·] and f i ′(·) are F[·] and f i The derivative of (·); Stim m (t) is the value of the mth column in the input stimulus matrix at time t;

[0046] 2) After the linear filter is determined, the optimization of the upstream nonlinearity is performed in a parameter-free manner; a set of piecewise linear bases is used to transform the nonlinear function f i (·) is expressed as Piecewise linear basis It is expressed as follows:

[0047]

[0048] The piecewise linear basis function calculation only needs to be based on the grid point xk The determination of f can provide sufficient upstream nonlinearity; refer to i (·) parameter distribution to select grid points, that is, p(g i (t)), where g(t) = k i ·s(t), p means taking g i (t), or n equally divided points in the function value space; at the same time, use the linear constraint a ij To ensure that the nonlinear function f i (·) is monotonically increasing, so that the model output remains interpretable to the neural input;

[0049] 3) For the pulse nonlinear function F(·), the following formula is used for control calculation:

[0050] F(x)=αlog[1+exp(β(G(t)-γ))];

[0051] Among them, α controls the scale of F(·), β controls the shape of the curve, and γ is the translation control term. This function ensures that its function value is a convex function in the parameter space. The gradient descent method is used to calculate α, β, and γ to achieve the optimization of F(·);

[0052] 4) Based on the obtained neuron firing rate curve, a random Poisson process is used to generate a random pulse train output of the simulated neuron of the retinal encoder method in response to input stimulation.

[0053] Another object of the present invention is to provide a retinal encoder constructed by applying the method for constructing a retinal encoder based on multimodal features. Compared with other retinal encoders, the retinal encoder can more accurately simulate the spike discharge sequence generated by the retina under natural scene input, and realize the simulation of the encoding of the input video signal by the retinal ganglion cells based on hardware calculation.

[0054] Another object of the present invention is to provide a computer device, the computer device comprising a memory and a processor, the memory storing a computer program, and when the computer program is executed by the processor, the processor performs the following steps:

[0055] (1) Extract multimodal stimulus features from input videos;

[0056] (2) Using basis functions with instantaneous extreme value and lasting effect characteristics to encode the feature sequence, the external input stimulus matrix for retinal ganglion cells is obtained;

[0057] (3) Through nonlinear model training, a nonlinear retinal encoder with multimodal stimulus input that can adapt to complex environments is obtained.

[0058] Another object of the present invention is to provide an information data processing terminal, which is used to implement the retinal encoder based on multimodal features.

[0059] Combining all the above technical solutions, the advantages and positive effects of the present invention are as follows: In order to compare and analyze the actual performance of the retinal encoder based on multimodal features proposed by the present invention, the present invention selects some neurons and calculates the likelihood function value and mutual correlation coefficient of their predicted output and target value for comparison. Figure 4 It can be seen that the retinal encoder model proposed in the present invention has significantly improved performance in likelihood function and cross-correlation coefficient compared with other models. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0061] Figure 1 It is a flow chart of a method for constructing a retinal encoder based on multimodal features provided in an embodiment of the present invention.

[0062] Figure 2 It is a schematic diagram of a method for constructing a retinal encoder based on multimodal features provided in an embodiment of the present invention.

[0063] Figure 3 It is a schematic diagram of the encoding process of input video stimulation using different types of basis matrices provided by an embodiment of the present invention.

[0064] Figure 4 It is a schematic diagram of a practical effect comparison experiment provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0066] In view of the problems existing in the prior art, the present invention provides a method for constructing a retinal encoder based on multimodal features. The present invention is described in detail below in conjunction with the accompanying drawings.

[0067] like Figure 1 As shown, the method for constructing a retinal encoder based on multimodal features provided by an embodiment of the present invention includes the following steps:

[0068] S101, extracting multimodal stimulus features of input video;

[0069] S102, encoding the feature sequence using a basis function having instantaneous extreme value and continuous effect characteristics to obtain an external input stimulation matrix for retinal ganglion cells;

[0070] S103, a nonlinear retinal encoder with multimodal stimulus input that can adapt to complex environments is obtained through nonlinear model training.

[0071] The principle diagram of the construction method of the retinal encoder based on multimodal features provided by the embodiment of the present invention is as follows: Figure 2 shown.

[0072] The technical solution of the present invention is further described below in conjunction with embodiments.

[0073] Step 1: Extract external input features to ganglion cells;

[0074] Step 2: Encode the external multimodal features using the basis functions with instantaneous extreme value and duration effect characteristics to obtain the external input stimulation matrix for the retinal ganglion cells;

[0075] Step 3: Obtain the parameters in the nonlinear retinal encoder computing unit through nonlinear model training, and construct a retinal encoder based on the ganglion cell stimulation processing mechanism.

[0076] In specific implementation, the steps for extracting external input features are as follows:

[0077] (1) Extract the visual input within the receptive field of the input video and obtain the light stimulation sequence of the target neuron within the video time. For neuron i, the input intensity of its light stimulation is calculated as follows:

[0078]

[0079] Among them, V(x,y,t) represents the light intensity of the input video at point (x,y,t), x,y represent the spatial position coordinates of a frame in the video, and t represents the number of video frames. The video size in the experiment is 360*360, containing a total of 1600 video frames.

[0080] (2) Based on the input light stimulation of ganglion i Further extract the instantaneous change stimulus sequence of light intensity in the video The formula is as follows:

[0081]

[0082] (3) Perform three-dimensional Gaussian blur on the video. Each pixel is calculated by applying three-dimensional Gaussian blur to the pixel values ​​of the points nearby in space and the pixel values ​​of the previous and next frames. The formula is as follows:

[0083]

[0084] (4) Take the values ​​within a certain range in the three-dimensional space near the target pixel point, determine the weight coefficient according to the normal distribution density, and multiply them to obtain the processed pixel value of the target position. Finally, the two-frame motion input stimulation of the neuron is obtained. The formula is as follows:

[0085]

[0086] The specific steps of calculating the external input stimulus matrix for retinal ganglion cells in step 2 are as follows:

[0087] (1) Application Figure 3 The basis functions of different spatiotemporal characteristics encode the input stimulus feature sequence. The stimulus effects of different features are controlled by the basis function type and basis function morphology parameters. The formula is as follows:

[0088]

[0089] in, represents the k-th stimulus feature extracted from the input video data by neuron i, bs(·) represents the basis function construction function, and s, d, and nb control the stimulus basis function shape, duration, and number of stimulus basis sequences, respectively.

[0090] (2) Combining the encoding stimulus basis functions corresponding to multiple stimuli into a multimodal stimulus input external matrix X for the target computational neuron stim :

[0091]

[0092] Finally, the steps of training the retinal encoder model in step 3 of the present invention are as follows:

[0093] (1) Establish a nonlinear retinal coding model. The steps are as follows:

[0094] 1) extracting the stimulus information contained in the input multimodal external stimulus matrix through a set of filter vectors to obtain stimulus input to the computational neuron model;

[0095] 2) A pair of parallel linear-nonlinear upstream filters are used to extract the "excitation-inhibition" signals in the input stimulus respectively, and a linear control term is introduced to integrate additional information to obtain the excitation state of the neuron at the current moment;

[0096] 3) Use the downstream pulse nonlinear unit to activate the excitation state information obtained upstream to obtain the neuron's excitation rate curve r(t) for the target input, and generate random pulse output through a certain Poisson process.

[0097] The above process can be expressed as follows:

[0098]

[0099] Among them, {k i} is the feature matrix X stim The filter bank, f i (·) and ω i is the upstream nonlinear function and weight coefficient corresponding to the feature, x(t) represents the additional factors inside the neuron, such as historical excitation information, and h is the linear filter acting on x.

[0100] (2) The optimization scheme for the proposed model is as follows:

[0101] 1) For the linear filter bank {k i The optimization of} can be achieved by calculating the likelihood function for each filter {k i The gradient of} is:

[0102]

[0103] Where G(t) = ∑ i g i (t)=∑ i w i f i (k i ·s(t)), F′[·] and f i ′(·) are F[·] and f i The derivative of (·). Stim m (t) is the value of the mth column in the input stimulus matrix at time t.

[0104] 2) In this model, the present invention fixes ω i is ±1, and the linear filter bank {k i After} is determined, the subsequent nonlinear calculation optimization can be performed in a parameter-free manner. The present invention uses a set of piecewise linear bases to transform the nonlinear function f i (·) is expressed as Piecewise linear basis It can be expressed as follows:

[0105]

[0106] The piecewise linear basis function calculation only needs to be based on the grid point x kThe selection of these grid points can refer to f i (·) is chosen by the parameter distribution, that is, p(g i (t)), where g(t) = k i ·s(t), p means taking g i (t) is the nth quantile, or the nth equally divided point in the function value space. At the same time, in order to make the model of the present invention interpretable to the neural input, the present invention uses the linear constraint a ij To ensure that the nonlinear function f i (·) is monotonically increasing.

[0107] 3) For the pulse nonlinear function F[·], the present invention uses the following formula for control calculation:

[0108] F(x)=αlog[1+exp(β(G(t)-γ))]

[0109] Among them, α controls the scale of F[·], β controls the shape of the curve, and γ is the translation control term. This function ensures that its function value is a convex function in the parameter space. The optimization of F[·] is achieved by calculating and updating α, β, and γ using the gradient descent method.

[0110] Finally, based on the obtained neuronal firing rate curves, a random Poisson process was used to generate the random pulse train output of the retinal encoder neurons in response to the input stimulation.

[0111] like Figure 4 As shown in the figure, the actual performance of the retinal encoder based on multimodal features proposed by the present invention is compared and analyzed. The present invention selects some neurons and calculates the likelihood function value and the mutual correlation coefficient of their predicted output and target value for comparison. Figure 4 It can be seen that the retinal encoder proposed in the present invention has significantly improved performance in likelihood function and cross-correlation coefficient compared with other models.

[0112] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When the use is implemented in whole or in part in the form of a computer program product, the computer program product includes one or more computer instructions. When the computer program instructions are loaded or executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions may be transmitted from one website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL) or wireless (e.g., infrared, wireless, microwave, etc.) mode) to another website site, computer, server or data center. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state hard disk SolidState Disk (SSD)), etc.

[0113] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A method for constructing a retinal encoder based on multimodal features, characterized in that: First, the multimodal stimulation features of the input video are extracted; then the feature sequence is encoded using a basis function with multidimensional time domain effect characteristics to obtain the external input stimulation matrix for retinal neuron cells; finally, a multimodal stimulation input nonlinear retinal encoder that can adapt to complex environments is obtained through linear-nonlinear computing unit training; The step of extracting multimodal stimulus features of an input video comprises: (1) Extract the visual input within the receptive field of the input video and obtain the light stimulation sequence of the target neuron within the video time. The input intensity of the light stimulation to neuron i is calculated as follows: Among them, V(x,y,t) represents the light intensity of the input video at the point (x,y,t), x and y represent the spatial position coordinates of a frame in the video, and the video size in the experiment is 360*360; t represents the number of video frames, and the experimental video contains a total of 1600 frames of images; (2) Based on the input light stimulation of neuron i Extracting the light intensity instantaneous change stimulus sequence from the video The formula is as follows: (3) Perform three-dimensional Gaussian blur on the video. Each pixel is calculated by applying three-dimensional Gaussian blur to the pixel values ​​of the points nearby in space and the pixel values ​​of the previous and next frames. The formula is as follows: (4) Take the values ​​within a certain range in the three-dimensional space near the target pixel point, determine the weight coefficient according to the normal distribution density, and multiply them to obtain the processed pixel value of the target position, and obtain the two-frame picture motion input stimulation of the neuron The formula is as follows:

2. The method for constructing a retinal encoder based on multimodal features as claimed in claim 1, characterized in that: The method of encoding the characteristic sequence using a basis function having multi-dimensional time domain effect characteristics to obtain an external input stimulation matrix for retinal neuron cells includes: (1) Construct a multimodal visual spatiotemporal stimulus input matrix for quickly extracting video data in the time domain and space domain. The formula is as follows: in, represents the stimulus basis matrix constructed by the ith method; by selecting a sequence of feature extraction methods suitable for the application scenario, the visual spatiotemporal features of interest to the target task are extracted; (2) Construct the stimulus basis matrix, the formula is as follows: in, Represents the kth stimulus feature extracted by neuron i from the input video material.

3. The method for constructing a retinal encoder based on multimodal features as claimed in claim 1, characterized in that: The multi-modal input nonlinear retinal encoder that can adapt to complex environments is obtained by training the linear-nonlinear computing unit, including: (1) Establish a nonlinear retinal coding model; (2) Propose an optimization plan for the model.

4. The method for constructing a retinal encoder based on multimodal features as claimed in claim 3, characterized in that: In step (1), the establishment of a nonlinear retinal encoder comprises: 1) Using different feature weight vectors to perform linear calculations on the input stimulus to obtain the corresponding features contained therein; 2) Using a pair of linear-nonlinear upstream filters to calculate the excitatory-inhibitory inputs of the input stimulus matrix; 3) Integrate and activate the upstream features according to the pulse nonlinear function to obtain the firing rate of the neuron caused by the input stimulus.

5. The method for constructing a retinal encoder based on multimodal features as claimed in claim 3, characterized in that: In step (1), the establishment of a nonlinear retinal coding model further includes: Among them, k i is the feature matrix X stim The i-th linear selection filter, f i (·) and ω i is the upstream nonlinear function and weight coefficient corresponding to the feature, x(t) represents the additional factor inside the neuron, and h is the linear filter acting on x.

6. The method for constructing a retinal encoder based on multimodal features as claimed in claim 3, characterized in that: In step (2), the proposed optimization scheme for the retinal encoder model includes: 1) In this model, ω is fixed i is ±1, for the linear filter bank {k i The optimization of} is performed by calculating the likelihood function for each filter k i The gradient of is: Where G(t) = ∑ i g i (t)=∑ i w i f i (k i ·s(t)), F′[·] and f i ′(·) are F[·] and f i The derivative of (·); Stim m (t) is the value of the mth column in the input stimulus matrix at time t; 2) After the linear filter is determined, the optimization of the upstream nonlinearity is performed in a parameter-free manner; a set of piecewise linear bases is used to transform the nonlinear function f i (·) is expressed as Piecewise linear basis It is expressed as follows: The piecewise linear basis calculation only needs to be based on the grid point x k The determination of f can provide sufficient upstream nonlinearity; refer to i (·) parameter distribution to select grid points, that is, p(g i (t)), where g(t) = k i ·s(t), p means taking g i (t), or n equally divided points in the function value space; at the same time, use the linear constraint a ij To ensure that the nonlinear function f i (·) is monotonically increasing, making the model interpretable to the neural input; 3) For the pulse nonlinear function F(·), the following formula is used for control calculation: F(x)=αlog[1+exp(β(G(t)-γ))]; Among them, α controls the scale of F[·], β controls the shape of the curve, and γ is the translation control term. This function ensures that its function value is a convex function in the parameter space. The gradient descent method is used to calculate α, β, and γ to achieve the optimization of F[·]. 4) Based on the obtained neuron firing rate curve, a random Poisson process is used to generate a random pulse train output of the retinal encoder neuron in response to the input stimulus.

7. A retinal encoder constructed by implementing the method for constructing a retinal encoder based on multimodal features as described in any one of claims 1 to 6.

8. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the method for constructing a retinal encoder based on multimodal features according to any one of claims 1 to 6, comprising the following steps: (1) Extract multimodal stimulus features from input videos; (2) Using basis functions with multi-dimensional time domain effect characteristics to encode the feature sequence, the external input stimulus matrix for retinal neuron cells is obtained; (3) Through nonlinear model training, a retinal encoder based on multimodal features that can adapt to complex environments is obtained.

9. An information data processing terminal for encoding visual signals, characterized in that: The information data processing terminal for encoding visual signals is used to implement the retinal encoder based on multimodal features as described in claim 7.

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