CN113643748B - Grid cell space information decoding method and system - Google Patents
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Abstract
The invention discloses a grid cell space information decoding method and a grid cell space information decoding system, wherein the decoding method comprises the following steps: s1, simplifying an attractor model: replacing the attractor cell dynamics equation with a preset display mathematical function; s2, decoding grid cells: decoding the position of the rat by using the discharge activity of the cell population; s3, decoding the multi-space scale grid cells: based on the Fourier transform idea, the mesh cell neural plates with the preset number and the equal proportion reduced scale are used for combined decoding, and the accurate displacement unique solution is obtained. The beneficial effects are that: the method effectively solves the problem of large calculation amount of the attractor model, is favorable for algorithm instantaneity, decodes the position of the rat by utilizing the discharge activity of the grid cell population, and can effectively realize the decoding of the grid cells.
Description
Technical Field
The invention relates to the technical field of biological information decoding, in particular to a grid cell space information decoding method and system.
Background
In 2005, by rat experiments, hafting et al found that there was a nerve cell with strong periodic discharge characteristics in the olfactory cortex of the rat, and the discharge field of the cell had a hexagonal lattice shape and was spread over the whole active space, and this nerve cell was called as a lattice cell. The grid cell belongs to one cell in the brain of animals, exists in the inner olfactory cortex, has obvious space discharge characteristics and presents a grid pattern discharge structure. Its main function is to help animals and humans recognize the way.
For integration of the movement path accomplished by the grid cells, spatial information needs to be decoded to achieve expression on the location cells and guiding navigation to the target. The spatial periodicity of the grid cell discharge has been noted by experimental and theoretical neuroscientists and is considered to constitute a metric space. Whereas the grid cell discharges are discretely spaced, the displacement of animal motion can be estimated from the phase of discharge modality movement. The invention therefore proposes a decoding method that is biologically viable and at the same time can be calculated in real time embedded on a robotic system.
For the problems in the related art, no effective solution has been proposed at present.
Disclosure of Invention
Aiming at the problems in the related art, the invention provides a grid cell space information decoding method and a grid cell space information decoding system, so as to overcome the technical problems in the prior art.
For this purpose, the invention adopts the following specific technical scheme:
according to an aspect of the present invention, there is provided a grid cell space information decoding method including the steps of:
s1, simplifying an attractor model: replacing the attractor cell dynamics equation with a preset display mathematical function;
s2, decoding grid cells: decoding the position of the rat by using the discharge activity of the cell population;
s3, decoding the multi-space scale grid cells: based on the Fourier transform idea, the mesh cell neural plates with the preset number and the equal proportion reduced scale are used for combined decoding, and the accurate displacement unique solution is obtained.
Further, the replacing the attractor cell dynamics equation with the preset display mathematical function in S1 includes the following steps:
s101, fitting the discharge characteristics of the stripe cells by using a preset Von Mises function;
s102, constructing a periodic popularization function of the Gaussian function:
Ω j (x)＝n max ·exp{k[cos(2π(x-c j )/λ)-1]}；
wherein n is max Represents the maximum desired discharge rate, k represents the gain factor, c j Represents the spatially preferential phase of cell j, λ represents the spatial period of cell j, and x represents the displacement vector;
s103, superposing three fringe waves with included angles being preset angles by using a preset grid cell space discharge probability function;
s104, modeling the grid cells to obtain the data for describing the positionFunction of the mean discharge rate of the cells>Wherein the function->The formula of (2) is as follows:
wherein n is max Indicating the maximum desired discharge rate,representing wave vectors corresponding to stripe cells in all directions, k representing gain coefficients, w representing angular frequencies, and x representing displacement vectors;
s105, setting the characteristics of the hexagonal grid to be aligned with the x-axis, and obtaining wave vectors corresponding to each stripe cell asφ l ＝-π/6+lπ/3；
S106, useSubstitute->Obtaining two-dimensional space of grid cells jDischarge mode phase->
Further, the preset angle of the three included angles in S103 is 60 degrees.
Further, the decoding the location of the rat using the discharge activity of the cell population in S2 includes the following steps:
s201, recording the discharge rate n of the grid cell i at the current position i Obtaining response vectors of the neural plate population
S202, calculating the positionMean value of discharge rate per neuron>
S203, assuming discharge rate of grid cell jObeying poisson distribution, and each neuron is statistically independent;
s204, calculating the group discharge rate vector of the given M cells in phaseThe calculation formula is as follows:
s205, simplifying the joint probability density function of each cell as follows:
s206, obtaining maximum likelihood estimation according to the simplified joint probability density function of each cellMeter with a meter bodyWherein the method comprises the steps of
Further, the grid cells on each of the grid cell neuroplates have the same dimensions and different spatial phases.
Further, in the step S3, based on the fourier transform concept, the combination decoding is performed by using a preset number of mesh cell neural plates with scaled down scales, and the accurate displacement unique solution is obtained, which includes the following steps:
s301, the common space decoding is carried out on the nerve plates with M grid cells, and the nerve cell number M on each nerve plate m Is consistent with the grid direction;
s302, setting the maximum grid period as lambda 0 The period of the mth grid cell nerve plate is lambda 0 /s m ；
S303, respectively calculating a posterior probability and a maximum posterior probability solution, wherein the calculation formula of the posterior probability is as follows:
the calculation formula of the maximum posterior probability solution is as follows:
in the method, in the process of the invention,representing a positional decode on the mth grid cell neural plate, L representing the number of network neural plates;
s304, setting the cell number of each network neural plate to be equal, so as to enableSubstitution of s m ＝λ 0 /λ m Deriving maximum likelihood estimation values from the combination of L network nerve plates>
S305, calculating the maximum likelihood estimated value of the L+1th network neural plateThe calculation formula is as follows:
s306, iterating the grid cells according to a preset step, and mapping the grid cells to the position cells to obtain an accurate displacement unique solution.
Further, in the step S306, the step of iterating the grid cells according to the preset steps, mapping the grid cells to the position cells, and obtaining the accurate displacement unique solution includes the following steps:
s3061, dimension lambda from single period capable of covering active space 0 Starting decoding calculation, and calculating group vectors through the activation values of the cell groups to obtain initial displacement estimated values
S3062, using the estimated valueFor the center, calculate the next scale lambda 1 Relative offset value of cell population position estimates on grid cell neuroplates and multiplying the offset value by a weight ω 1 To correct the estimated value of the previous level to obtain a new estimated value of displacement +.>
S3063, calculating new displacement estimated values step by step until a final position estimated value is obtained, namely an accurate displacement unique solution.
According to another aspect of the present invention, there is provided a grid cell spatial information decoding system including an attractor model simplification module, a grid cell decoding module, and a multi-spatial scale grid cell decoding;
wherein the attractor model simplification module is used for replacing attractor cell dynamics equation by using a display mathematical function;
the grid cell decoding module is used for decoding the position of the rat by utilizing the discharge activity of the grid cell population;
the multi-space scale grid cell decoding is used for carrying out combined decoding by using a preset number of grid cell nerve plates with scaled down scales in equal proportion based on the Fourier transform thought, so as to obtain an accurate displacement unique solution.
The beneficial effects of the invention are as follows: the invention provides a grid cell space information decoding method, which is used for effectively solving the problem of large calculation amount of attractor model by using a display mathematical function to replace an attractor cell dynamics equation, is beneficial to algorithm instantaneity, can effectively realize grid cell decoding by decoding the position of a rat by using discharge activity of a grid cell population, can obtain a high-precision displacement unique solution by using a plurality of grid cell nerve plates with scaled down quantity and equal proportion for combined decoding based on a Fourier transform idea, and can be suitable for real-time calculation of biology and embedded into a robot system for real-time calculation.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a method for decoding space information of cells in a grid according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a multi-scale decoding neural calculation process in a method for decoding space information of grid cells according to an embodiment of the present invention.
Detailed Description
For the purpose of further illustrating the various embodiments, the present invention provides drawings that are a part of the present disclosure and are primarily intended to illustrate embodiments and to explain the principles of the embodiments in conjunction with the description related thereto, wherein, in conjunction with the description, one skilled in the art will appreciate other possible implementations and advantages of the present invention, components are not drawn to scale, and like reference numerals are often used to designate like components.
According to the embodiment of the invention, a grid cell space information decoding method and a grid cell space information decoding system are provided.
The present invention will be further described with reference to the accompanying drawings and detailed description, as shown in fig. 1-2, according to an embodiment of the present invention, there is provided a method for decoding cell space information, the decoding method including the steps of:
s1, simplifying an attractor model: replacing the attractor cell dynamics equation with a preset display mathematical function;
the continuous attractor model is a simulation model for simulating the electrophysiological principle of nerve cells, realizes accurate path integration of space, and simultaneously theoretically explains the phenomenon observed by biological experiments. However, the bionic cognitive algorithm model of the robot needs to be studied in consideration of being convenient for real-time operation on a computer. The calculation amount of the attractor model based on the nerve plate is large, and the real-time performance of the algorithm is not facilitated, so that the invention considers the use of an explicit mathematical function to replace the attractor cell dynamics equation in the decoding operation.
Specifically, the step S1 of replacing the attractor cell dynamics equation with a preset display mathematical function includes the following steps:
s101, fitting the discharge characteristics of the stripe cells by using a preset Von Mises function;
s102, constructing a periodic popularization function of the Gaussian function:
Ω j (x)＝n max ·exp{k[cos(2π(x-c j )/λ)-1]}；
wherein n is max Represents the maximum desired discharge rate, k represents the gain factor, c j Represents the spatially preferential phase of cell j, λ represents the spatial period of cell j, and x represents the displacement vector;
s103, superposing three fringe waves with included angles being preset angles by using a preset grid cell space discharge probability function; specifically, the preset angle of the three included angles in S103 is 60 degrees.
S104, modeling the grid cells to obtain the data for describing the positionFunction of the mean discharge rate of the cells>Wherein the function->The formula of (2) is as follows:
wherein n is max Indicating the maximum desired discharge rate,representing wave vectors corresponding to stripe cells in all directions, k representing gain coefficients, w representing angular frequencies, and x representing displacement vectors;
s105, setting the characteristics of the hexagonal grid to be aligned with the x-axis, and obtaining wave vectors corresponding to each stripe cell asφ l ＝-π/6+lπ/3；
S106, useSubstitute->Obtaining the discharge mode phase +.>
S2, decoding grid cells: decoding the position of the rat by using the discharge activity of the cell population;
specifically, the cells on each of the cell-grid nerve plates have the same dimensions, but have different spatial phases.
Wherein, in the step S2, the discharge activity of the grid cell population is utilized to decode the position of the rat, which comprises the following steps:
s201, recording the discharge rate n of the grid cell i at the current position i Obtaining response vectors of the neural plate population
S202, calculating the positionMean value of discharge rate per neuron>Specifically, the true number n j Scattered around this value;
s203, assuming discharge rate of grid cell jObeying poisson distribution, and each neuron is statistically independent;
s204, calculating the group discharge rate vector of the given M cells in phaseThe calculation formula is as follows:
s205 of uniformly covering the motion space in consideration of the tuning curve of the grid discharge,approximately constant, thus simplifying the individual cell joint probability density function as:
s206, obtaining maximum likelihood estimation according to the simplified joint probability density function of each cellWherein the method comprises the steps of
S3, decoding the multi-space scale grid cells: based on the Fourier transform idea, the mesh cell neural plates with the preset number and the equal proportion reduced scale are used for combined decoding, and the accurate displacement unique solution is obtained.
If the scale of a single grid period is relatively large and the movable range can be covered, a unique space position solution can be obtained according to the decoding method, but the uncertainty error of decoding is relatively large. While using smaller scale uncertainties may decrease, but multiple solutions may be generated periodically. The study found that the cell space discharge cycle of the rat was about 25cm to several meters. By taking the thought of Fourier transformation into consideration, the embodiment proposes a mode of decoding by using a plurality of grid cell nerve plates with scaled down geometric proportion to obtain a displacement unique solution with high precision. The principle is shown in fig. 2, the probability distribution of position decoding under each scale is combined into joint probability density, and the probability distribution of the obtained maximum likelihood solution is more approximate to true value.
Based on the fourier transform idea, the step S3 of performing combined decoding by using a preset number of mesh cell nerve plates with scaled down scale to obtain an accurate displacement unique solution includes the following steps:
s301, the common space decoding is carried out on the nerve plates with M grid cells, and the nerve cell number M on each nerve plate m Is consistent with the grid direction;
s302, setting the maximum grid period as lambda 0 The period of the mth grid cell nerve plate is lambda 0 /s m ；
S303, respectively calculating a posterior probability and a maximum posterior probability solution, wherein the calculation formula of the posterior probability is as follows:
the calculation formula of the maximum posterior probability solution is as follows:
in the method, in the process of the invention,representing a positional decode on the mth grid cell neural plate, L representing the number of network neural plates;
s304, setting the cell number of each network neural plate to be equal, so as to enableSubstitution of s m ＝λ 0 /λ m Deriving maximum likelihood estimation values from the combination of L network nerve plates>
S305, calculating the maximum likelihood estimated value of the L+1th network neural plateThe calculation formula is as follows:
s306, according to the recurrence formula, iterating the grid cells according to a preset step, and mapping the grid cells to the position cells to obtain an accurate displacement unique solution.
Specifically, in S306, the step of iterating the grid cells according to the preset steps, mapping the grid cells to the position cells, and obtaining the accurate displacement unique solution includes the following steps:
s3061, dimension lambda from single period capable of covering active space 0 Starting decoding calculation, and calculating group vectors through the activation values of the cell groups to obtain initial displacement estimated values
S3062, using the estimated valueFor the center, calculate the next scale lambda 1 Relative offset value of cell population position estimates on grid cell neuroplates and multiplying the offset value by a weight ω 1 To correct the estimated value of the previous level to obtain a new estimated value of displacement +.>
S3063, calculating new displacement estimated values step by step until a final position estimated value is obtained, namely an accurate displacement unique solution.
The multi-scale decoding calculation process in this embodiment can be regarded as a weighted summation process of the bias values, which can be realized physiologically by calculation of the synapses.
According to another embodiment of the present invention, there is provided a grid cell spatial information decoding system including an attractor model simplification module, a grid cell decoding module, and a multi-spatial scale grid cell decoding;
wherein the attractor model simplification module is used for replacing attractor cell dynamics equation by using a display mathematical function;
the grid cell decoding module is used for decoding the position of the rat by utilizing the discharge activity of the grid cell population;
the multi-space scale grid cell decoding is used for carrying out combined decoding by using a preset number of grid cell nerve plates with scaled down scales in equal proportion based on the Fourier transform thought, so as to obtain an accurate displacement unique solution.
In summary, by means of the above technical solution of the present invention, the present invention provides a method for decoding space information of grid cells, which effectively solves the problem of large calculation amount of an attractor model by using a display mathematical function to replace the attractor cell dynamics equation, is favorable for algorithm instantaneity, decodes the position of a rat by using the discharge activity of the grid cell population, can effectively realize the decoding of the grid cells, and can obtain a high-precision displacement unique solution by using a plurality of grid cell nerve plates with reduced scale in number and equal proportion for combined decoding based on the fourier transform idea.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (5)
1. A method for decoding cell space information, the method comprising the steps of:
s1, simplifying an attractor model: replacing the attractor cell dynamics equation with a preset display mathematical function;
s2, decoding grid cells: decoding the position of the rat by using the discharge activity of the cell population;
s3, decoding the multi-space scale grid cells: based on the Fourier transform idea, using a preset number of grid cell nerve plates with equal proportion reduced scale to perform combined decoding to obtain an accurate displacement unique solution;
the step S1 of replacing the attractor cell dynamics equation by using a preset display mathematical function comprises the following steps of:
s101, fitting the discharge characteristics of the stripe cells by using a preset Von Mises function;
s102, constructing a periodic popularization function of the Gaussian function:
Ω j (x)＝n max ·exp{k[cos(2π(x-c j )/λ)-1]}；
wherein n is max Represents the maximum desired discharge rate, k represents the gain factor, c j Represents the spatially preferential phase of cell j, λ represents the spatial period of cell j, and x represents the displacement vector;
s103, superposing three fringe waves with included angles being preset angles by using a preset grid cell space discharge probability function;
s104, modeling the grid cells to obtain the data for describing the positionFunction of average discharge rate of cells at timeWherein the function->The formula of (2) is as follows:
wherein n is max Indicating the maximum desired discharge rate,representing wave vectors corresponding to stripe cells in all directions, k representing gain coefficients, w representing angular frequencies, and x representing displacement vectors;
s105, setting the characteristics of the hexagonal grid to be aligned with the x-axis, and obtaining wave vectors corresponding to each stripe cell asφ l ＝-π/6+lπ/3；
S106, useSubstitute->Obtaining the discharge mode phase +.>
The decoding of the position of the rat by using the discharge activity of the cell population in S2 comprises the following steps:
s201, recording the discharge rate n of the grid cell i at the current position i Obtaining response vectors of the neural plate population
S202, calculating the positionMean value of discharge rate per neuron>
S203, assuming discharge rate of grid cell jObeying poisson distribution, and each neuron is statistically independent;
s204, calculating the group discharge rate vector of the given M cells in phaseThe calculation formula is as follows:
s205, simplifying the joint probability density function of each cell as follows:
s206, obtaining maximum likelihood estimation according to the simplified joint probability density function of each cellWherein the method comprises the steps of
Based on the fourier transform idea, the step S3 of performing combined decoding by using a preset number of mesh cell nerve plates with scaled down scale to obtain an accurate displacement unique solution includes the following steps:
s301, the common space decoding is carried out on the nerve plates with M grid cells, and the nerve cell number M on each nerve plate m Is consistent with the grid direction;
s302, setting the maximum grid period as lambda 0 The period of the mth grid cell nerve plate is lambda 0 /s m ；
S303, respectively calculating a posterior probability and a maximum posterior probability solution, wherein the calculation formula of the posterior probability is as follows:
the calculation formula of the maximum posterior probability solution is as follows:
in the method, in the process of the invention,indicating position decoding on mth grid cell neural plate, L tableShowing the number of network neural plates;
s304, setting the cell number of each network neural plate to be equal, so as to enableSubstitution of s m ＝λ 0 /λ m Deriving maximum likelihood estimation values from the combination of L network nerve plates>
S305, calculating the maximum likelihood estimated value of the L+1th network neural plateThe calculation formula is as follows:
s306, iterating the grid cells according to a preset step, and mapping the grid cells to the position cells to obtain an accurate displacement unique solution.
2. The method for decoding spatial information of cells according to claim 1, wherein the three included angles in S103 are 60 degrees.
3. The method of claim 1, wherein the cells on each of the cell nerve plates have the same dimensions and different spatial phases.
4. The method for decoding space information of cells according to claim 1, wherein the step of mapping cells of the grid to cells of the location in S306 according to a predetermined step iteration, and obtaining a unique solution of accurate displacement comprises the steps of:
s3061, dimension lambda from single period capable of covering active space 0 Starting decoding calculation, calculating group vector by using grid cell group activation value to obtain initial displacement estimated value
S3062, using the estimated valueFor the center, calculate the next scale lambda 1 Relative offset value of cell population position estimates on grid cell neuroplates and multiplying the offset value by a weight ω 1 Correcting the estimation value of the previous scale to obtain a new displacement estimation value +.>
S3063, calculating new displacement estimated values step by step until a final position estimated value is obtained, namely an accurate displacement unique solution.
5. A grid cell space information decoding system for implementing the steps of the grid cell space information decoding method according to any one of claims 1 to 4, characterized in that the system comprises an attractor model simplifying module, a grid cell decoding module and a multi-space scale grid cell decoding;
wherein the attractor model simplification module is used for replacing the attractor cell dynamics equation by using a display mathematical function;
the grid cell decoding module is used for decoding the position of the rat by utilizing the discharge activity of the grid cell population;
the multi-space scale grid cell decoding is used for carrying out combined decoding by using a preset number of grid cell nerve plates with scaled down scales based on the Fourier transform thought, so as to obtain an accurate displacement unique solution.
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