Quantitative analysis method for balance between occupation and compensation of cultivated land based on soil environment perception

Abstract

The application discloses a cultivated land occupation and compensation balance quantitative analysis method based on soil environment sensing, relates to the technical field of cultivated land data analysis, and comprises the following steps: collecting ground surface measurement data by means of a high-spectrum camera carried by a UAV to generate a soil-nutrient-vegetation comprehensive physical characteristic vector of each land plot at time t; establishing an adaptive yield-ecology prediction model based on the soil-nutrient-vegetation comprehensive physical characteristic vector in combination with a data driving component to obtain an initial adaptive weight and predict the yield of the land plot; when the initial adaptive weight does not belong to a set threshold interval, running an adaptive and migration learning strategy to update the adaptive weight and returning to the adaptive yield-ecology prediction model. The application solves the problem that agricultural production modes are different in different regions and affect the quality index and yield model of cultivated land.

Description

Technical Field

[0001] This invention relates to the field of arable land data analysis technology, specifically a quantitative analysis method for arable land occupation-compensation balance based on soil environment perception. Background Technology

[0002] While some progress has been made in the evaluation of farmland occupation and compensation, and the prediction of yield and ecological benefits, both domestically and internationally, there are still several key technical shortcomings. Existing methods mostly rely on single remote sensing indicators, statistical yearbooks, or sparse field survey data to assess yield and farmland quality. The remote sensing is affected by factors such as cloud cover, observation angle, and vegetation saturation, making it difficult to accurately characterize soil moisture, root zone nutrients, and underground processes.

[0003] For example, Chinese invention patent CN109214686B discloses a quantitative analysis method for arable land occupation-compensation balance, comprising: determining the analysis area for quantitative analysis; collecting analysis data within the analysis area; the analysis data including land use patch data, arable land quality grade patch data, and ground elevation raster data; after acquiring the analysis data, constructing a quantitative analysis model; and sequentially performing arable land occupation-compensation quantity and quality analysis, arable land occupation-compensation spatial heterogeneity analysis, and arable land occupation-compensation landscape pattern analysis based on the analysis model to obtain quantitative analysis results. This method can reduce the interference of human subjective factors in the analysis process, thereby obtaining more accurate information on the spatial morphology and landscape pattern of arable land.

[0004] Although the aforementioned patents use physical process models for quantitative analysis, they rely on a large number of parameters and are difficult to calibrate, making them prone to bias under complex management conditions. While purely data-driven methods are flexible, they are extremely sensitive to out-of-distribution samples and cross-regional extrapolation, and usually lack physical boundary constraints, resulting in unstable predictions when data is scarce or institutional differences are significant.

[0005] Furthermore, significant differences exist between regions in crop seasons, crop rotation practices, and irrigation and fertilization management. These institutional differences alter the response relationship between the same physical signal and yield. Most existing data models do not include crop structure and management practices as explicit input conditions, or lack domain adaptation strategies based on institutional hierarchy. This leads to a sharp decline in model performance when migrating from one domain to another, requiring extensive local annotation to restore performance.

[0006] Agricultural production patterns vary across different regions, affecting arable land quality indicators and yield models. Model migration often requires consideration of local crop structure and management practices; otherwise, it is difficult to accurately predict grain output and ecological benefits after land reclamation.

[0007] Therefore, this invention provides a quantitative analysis method for the balance of cultivated land occupation and replenishment based on soil environmental perception. Summary of the Invention

[0008] The purpose of this invention is to provide a quantitative analysis method for the balance of cultivated land occupation and compensation based on soil environmental perception, so as to solve the existing problems mentioned in the background art.

[0009] To achieve the above objectives, the present invention provides the following technical solution: a quantitative analysis method for farmland occupation-compensation balance based on soil environmental perception, comprising the following steps:

[0010] S1. Deploy soil moisture sensors, soil temperature sensors, soil conductivity sensors, and meteorological sensors on the plot and upload them to the spatiotemporal database through an edge gateway;

[0011] S2. Ground surface measurement data is collected by using a drone equipped with a hyperspectral camera, and RTK is embedded for spatiotemporal registration. The data is then fused with multiple sources to generate a comprehensive physical feature vector of soil-nutrients-vegetation for each plot at time t.

[0012] S3. Based on the integrated physical feature vector of soil-nutrients-vegetation combined with the data-driven component, establish an adaptive yield-ecological prediction model, obtain the initial adaptive weights, and predict the yield of the plot.

[0013] S4. When the initial adaptive weight does not belong to the set threshold range, proceed to S5;

[0014] S5. Establish an adaptive and transfer learning strategy. After achieving domain alignment at the edge, meta-learning small sample fine-tuning, and uncertainty-driven active sampling, update the adaptive weights and return to S3.

[0015] A further improvement of this invention is that the soil-nutrient-vegetation integrated physical feature vector in the adaptive yield-ecological prediction model includes a photosynthetically active radiation estimation module, a leaf area index time series module, and a water-nutrient response function module, which are manifested as follows:

[0016]

[0017] in, Indicates photosynthetically active radiation. This is expressed as crop light energy utilization efficiency. It is represented as a water-nutrient response function.

[0018] A further improvement of this invention lies in that the data-driven component of the adaptive yield-ecological prediction model combines a graph convolutional network and a long short-term memory network. It takes the normalized physical feature vector and the plot-level crop structure vector as input, learns the spatiotemporal dependency of plot adjacency based on the XGBoost model, and outputs a data yield estimate. and confidence interval The adjacency matrix of the graph convolutional network is constructed based on the centroid distance threshold of the plots.

[0019] A further improvement of this invention is that the adaptive yield-ecological prediction model further includes an adaptive data fusion strategy, which integrates the soil-nutrient-vegetation physical feature vector. With data output estimation Weighted fusion is performed to obtain the predicted output of the land parcels, where the data output estimate The weights are obtained through an initial adaptive weight function.

[0020] A further improvement of this invention is that the initial adaptive weighting function includes: calculating the relative confidence interval width. ,Will Mapped to confidence scores via linear truncation Secondly, calculate the sample size score. , Indicates the number of locally calibrated samples. This represents the set half-saturation constant; it scores the sample size. With confidence score The local reliability score is obtained by weighted summation, and the initial adaptive weights are obtained by Sigmoid mapping. .

[0021] A further improvement of this invention is that the adaptive and transfer learning strategy uses plot-level crop structure vectors. With management practice vector The implementation includes: the plot-level crop structure vector comprising single- and double-season identifiers, crop rotation sequence encoding, the proportion of each crop, and historical straw treatment methods; the management practice vector comprising irrigation regime, fertilization rate, tillage method, sowing density, and input intensity index; and the adaptive and transfer learning strategy specifically comprising:

[0022] An unsupervised domain alignment layer is used to reduce the difference in feature covariance between the source and target domains, and outputs the aligned features of the current land parcel. ;

[0023] A few-sample fast adaptation layer is used to localize model parameters in the target region with a limited number of calibrated samples, and outputs a fine-tuned fitness metric. ;

[0024] An online incremental fine-tuning layer is used for edge deployment to perform mini-batch updates using streaming local observation data;

[0025] An adaptive weight fusion layer is used to receive the updated model parameters from the online incremental fine-tuning layer and sum them with the initial adaptive weights to obtain the updated adaptive weights. .

[0026] A further improvement of this invention is that the unsupervised domain alignment layer groups vector samples according to institutional conditions based on the crop structure vector and management practice vector of the plot, and calculates the feature covariance matrix of the training data and the current plot for each group k. and By minimizing the conditional covariance difference, unsupervised distribution alignment based on conditions is achieved. The output domain reliability metric of the unsupervised domain alignment layer is expressed as... .

[0027] A further improvement of this invention is that the few-sample fast adaptation layer aligns the target domain features. Locally calibrated samples and training data model parameters As input, based on meta-learning, 1–K steps are performed locally to quickly adapt and generate initial localized parameters. And calculate the quantitative index of adaptability after fine-tuning. .

[0028] A further improvement of this invention is that the online incremental fine-tuning layer is deployed at the edge to receive streaming local observation data and perform incremental parameter updates in small batches, calculating and outputting local verification reliability in real time. Score with fine-tuned sample size and output the updated model parameters. , , .

[0029] A further improvement of this invention is that the predicted value of the adaptive yield-ecological prediction model is expressed as: .

[0030] Compared with the prior art, the beneficial effects of the present invention are:

[0031] 1. This invention first solves the problem of unreliability of a single model when facing cross-regional land parcels or scarce data by coupling physical priors and data-driven models and performing dynamic linear fusion with adaptive weights; when data is sufficient, it utilizes the advantages of data models, and when data is scarce or uncertain, it relies on physical models to ensure the rationality of boundaries, thereby making yield prediction more accurate and less prone to exceeding the limits.

[0032] 2. Secondly, by explicitly encoding block-level crop structure vectors and management practice vectors, which are used in adaptive units for conditional domain alignment, task partitioning, and meta-learning, the problem of model cross-regional transfer failure caused by differences in covariate distribution due to different agricultural systems is solved; system-aware alignment and hierarchical transfer can preserve essential differences and only adjust transferable components, thereby avoiding erroneous transfer.

[0033] 3. There is a risk that automatic fusion of adaptive and transfer learning strategies may be too aggressive or lead to incorrect decisions in abnormal situations; combining human prior knowledge with automatic judgment can balance adaptability and safety. Attached Figure Description

[0034] Figure 1 This is a flowchart of the quantitative analysis method for farmland occupation-compensation balance based on soil environmental perception, as proposed in this invention. Detailed Implementation

[0035] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0036] The term "and / or" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three cases: A exists alone, A and B exist simultaneously, and B exists alone.

[0037] Example 1

[0038] Figure 1 The flowchart of the quantitative analysis method for farmland occupation-compensation balance based on soil environmental perception disclosed in this embodiment is shown, and the steps are as follows:

[0039] S1. Deploy soil moisture sensors, soil temperature sensors, soil conductivity sensors, and meteorological sensors on the plot and upload them to the spatiotemporal database through an edge gateway;

[0040] S2. Ground surface measurement data is collected by using a drone equipped with a hyperspectral camera, and RTK is embedded for spatiotemporal registration. The data is then fused with multiple sources to generate a comprehensive physical feature vector of soil-nutrients-vegetation for each plot at time t.

[0041] S3. Based on the integrated physical feature vector of soil-nutrients-vegetation combined with the data-driven component, establish an adaptive yield-ecological prediction model, obtain the initial adaptive weights, and predict the yield of the plot.

[0042] The adaptive yield-ecological prediction model includes a soil-nutrient-vegetation integrated physical feature vector comprising a photosynthetically active radiation estimation module, a leaf area index time-series module, and a water-nutrient response function module, which are expressed as follows:

[0043]

[0044] in, This represents photosynthetically active radiation, obtained through inversion from remote sensing data. This is expressed as crop light energy utilization efficiency. It is represented as a water-nutrient response function.

[0045] The calculation formula is expressed as follows ,in Indicates the moisture content at the wilting point. Indicates the optimum moisture content. Representing real-time moisture content, using a saturated function can map soil moisture content from a physical level to crop response; A represents the plot area, and N represents the soil nitrogen concentration. Indicates the optimal soil nitrogen concentration;

[0046] Since farmland is not isolated, graph convolutional networks can incorporate the spatial relationships in which neighboring irrigation or topography affects water flow and microclimate into the model; and since crop yield is affected by historical dynamics, LSTM can capture the time dependence.

[0047] The adaptive yield-ecological prediction model uses a data-driven component that combines graph convolutional networks and long short-term memory networks. It takes normalized physical feature vectors and plot-level crop structure vectors as input, learns the spatiotemporal dependencies of plot adjacency based on the XGBoost model, and outputs a data yield estimate. and confidence interval The adjacency matrix of the graph convolutional network is constructed based on a centroid distance threshold. For example, for the adjacency matrix M, if plot i and plot j are sufficiently close, then based on the centroid distance threshold, It approaches 1, otherwise it approaches 0.

[0048] The adaptive yield-ecological prediction model also includes an adaptive data fusion strategy, which integrates the soil-nutrient-vegetation physical feature vector. With data output estimation Weighted fusion is performed to obtain the predicted output of the land parcels, where the data output estimate The weights are obtained through an initial adaptive weight function.

[0049] The initial adaptive weighting function includes: calculating the relative confidence interval width. ,Will Mapped to confidence scores via linear truncation Secondly, calculate the sample size score. , Indicates the number of locally calibrated samples. This represents the set half-saturation constant; since the model may be misled even with a small CI if there are large differences between plots, the sample size score is used. With confidence score The local reliability score is obtained by weighted summation, and the initial adaptive weights are obtained by Sigmoid mapping. .

[0050] At this point, the narrower the confidence interval, The smaller, then As the data model's predictions become more "certain," the weights shift towards the data model. An increase in the number of local samples leads to a higher sample size score, indicating sufficient local calibration and increasing confidence in data-driven results. The closer it is to 1, rise.

[0051] When there is a large amount of reliable data available in the region, the data model is usually more accurate. It should be larger; when data is scarce or unreliable, the physical model is more robust. Small strain. Hybrid energy combines the advantages of both, reducing extrapolation risk.

[0052] For example, if a certain area has only 3 ground calibration points and a wide confidence interval, the model will rely heavily on physical feature vectors. If there are 100 calibration points and the error is small, then the estimation relies more on data yield. .

[0053] S4. When the initial adaptive weight does not belong to the set threshold range, proceed to S5;

[0054] S5. Establish adaptive and transfer learning strategies;

[0055] In decision-making scenarios like the balance between land occupation and compensation, which requires weighing food output against ecological benefits, single-point forecast values ​​cannot reflect the level of risk and confidence. Most existing systems lack the quantification and utilization of forecast uncertainty, and cannot conduct proactive sampling, conservative decision-making, or risk control based on uncertainty, thereby increasing the uncertain legal and ecological risks of land occupation and compensation implementation.

[0056] After edge domain alignment, meta-learning few-sample fine-tuning, and uncertainty-driven active sampling, the adaptive weights are updated and returned to S3 to output the final plot yield and ecological indicators.

[0057] This is used to address the mismatch between the forecast and conversion factor migration of post-occupation and compensation yields due to different agricultural production models in different regions.

[0058] The adaptive and transfer learning strategy uses plot-level crop structure vectors. With management practice vector The implementation includes: the plot-level crop structure vector comprising single- and double-season identifiers, crop rotation sequence encoding, the proportion of each crop, and historical straw treatment methods; the management practice vector comprising irrigation regime, fertilization rate, tillage method, sowing density, and input intensity index; and the adaptive and transfer learning strategy specifically comprising:

[0059] The unsupervised domain alignment layer is used to reduce the difference in feature covariance between the source domain and the target domain. The unsupervised domain alignment layer groups the vector samples according to the system conditions based on the crop structure vector and management practice vector of the plot. This includes first dividing the samples into regular bins to obtain the seasonal irrigation layer, and then performing secondary clustering on the continuous management intensity and crop proportion within each seasonal irrigation layer to obtain the final group k.

[0060] For each group k, the feature covariance matrix between the training data and the current land parcel is calculated. and By minimizing the conditional covariance difference, it can be expressed as This achieves conditional unsupervised distribution alignment, where the output domain reliability metric of the unsupervised domain alignment layer is expressed as... Output the aligned features of the current land parcel In the unsupervised domain alignment layer, grouping by institutional conditions and aligning the feature covariance of each group can preserve the essential differences between different institutions while eliminating only the statistical differences in the transferable parts between the source and the target, thus improving the accuracy and security of alignment; it avoids flattening institutional differences that should not be aligned by global alignment (such as incorrectly aligning drought-resistant and high-input types), thereby reducing the risk of erroneous migration.

[0061] A few-sample fast adaptation layer is used to localize model parameters in the target region with a limited number of calibrated samples, and outputs a fine-tuned fitness metric. ;

[0062] The few-sample fast adaptation layer uses aligned target domain features. Locally calibrated samples and training data model parameters As input, based on meta-learning, 1–K steps are performed locally to quickly adapt and generate initial localized parameters. And calculate the quantitative index of adaptability after fine-tuning. , This represents all parameters (weights and biases) of the machine learning model.

[0063] The few-sample fast adaptation layer provides rapid, localized parameter adjustment capabilities through meta-learning or finite-step fine-tuning, enabling the model to achieve significant performance improvements even with very few calibration samples, reducing deployment and calibration costs and shortening time to go online; it solves the problem of difficulty in effectively training or fine-tuning the model when the target domain labeling is sparse, avoiding large-scale labeling for every new region.

[0064] An online incremental fine-tuning layer is deployed at the edge to perform mini-batch updates using streaming local observation data. This layer receives streaming local observation data and performs incremental parameter updates in mini-batches, where the data is divided into W small subsets, and only a small portion is used to update the parameters each time (e.g., w / W). The layer also calculates and outputs the local verification reliability in real time. Score with fine-tuned sample size and output the updated model parameters. , , .

[0065] The online incremental fine-tuning layer absorbs streaming observations in small batches at the edge and updates parameters in real time, which can continuously respond to dynamic changes in the environment / management, reduce the decay of model timeliness, and output instant reliability to support real-time decision-making; it solves the problem of performance degradation of static models due to environmental changes or implementation error accumulation during long-term operation, and provides online self-calibration capability to ensure long-term availability.

[0066] An adaptive weight fusion layer is used to receive the updated model parameters from the online incremental fine-tuning layer and sum them with the initial adaptive weights to obtain the updated adaptive weights. .

[0067] The predicted value of the adaptive yield-ecological prediction model is then expressed as: .

[0068] The threshold and weight settings can be set by default according to the present invention, or they can be set by those skilled in the art.

[0069] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0070] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0071] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0072] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0073] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A quantitative analysis method for farmland occupation-compensation balance based on soil environmental perception, characterized by: Includes the following steps: S1. Deploy soil moisture sensors, soil temperature sensors, soil conductivity sensors, and meteorological sensors on the plot and upload them to the spatiotemporal database through an edge gateway; S2. Ground surface measurement data is collected by using a drone equipped with a hyperspectral camera, and RTK is embedded for spatiotemporal registration. The data is then fused with multiple sources to generate a comprehensive physical feature vector of soil-nutrients-vegetation for each plot at time t. S3. Based on the integrated physical feature vector of soil-nutrients-vegetation combined with the data-driven component, establish an adaptive yield-ecological prediction model, obtain the initial adaptive weights, and predict the yield of the plot. S4. When the initial adaptive weight does not belong to the set threshold range, proceed to S5; S5. Establish an adaptive and transfer learning strategy. After achieving domain alignment at the edge, meta-learning small sample fine-tuning, and uncertainty-driven active sampling, update the adaptive weights and return to S3. The adaptive yield-ecological prediction model includes a soil-nutrient-vegetation integrated physical feature vector comprising a photosynthetically active radiation estimation module, a leaf area index time-series module, and a water-nutrient response function module, which are expressed as follows: in, Indicates photosynthetically active radiation. This is expressed as crop light energy utilization efficiency. Represented as a water-nutrient response function; The adaptive yield-ecological prediction model uses a data-driven component that combines graph convolutional networks and long short-term memory networks. It takes normalized physical feature vectors and plot-level crop structure vectors as input, learns the spatiotemporal dependencies of plot adjacency based on the XGBoost model, and outputs a data yield estimate. and confidence interval The adjacency matrix of the graph convolutional network is constructed based on the centroid distance threshold of the land parity. The initial adaptive weighting function includes: calculating the relative confidence interval width. ,Will Mapped to confidence scores via linear truncation Secondly, calculate the sample size score. , Indicates the number of locally calibrated samples. This represents the set half-saturation constant; it scores the sample size. With confidence score The local reliability score is obtained by weighted summation, and the initial adaptive weights are obtained by Sigmoid mapping. .

2. The quantitative analysis method for farmland occupation-compensation balance based on soil environmental perception according to claim 1, characterized in that: The adaptive yield-ecological prediction model also includes an adaptive data fusion strategy, which integrates the soil-nutrient-vegetation physical feature vector. With data output estimation Weighted fusion is performed to obtain the predicted output of the land parcels, where the data output estimate The weights are obtained through an initial adaptive weight function.

3. The quantitative analysis method for farmland occupation-compensation balance based on soil environmental perception according to claim 2, characterized in that: The adaptive and transfer learning strategy uses plot-level crop structure vectors. With management practice vector The implementation includes: the plot-level crop structure vector comprising single- and double-season identifiers, crop rotation sequence encoding, the proportion of each crop, and historical straw treatment methods; the management practice vector comprising irrigation regime, fertilization rate, tillage method, sowing density, and input intensity index; and the adaptive and transfer learning strategy specifically comprising: An unsupervised domain alignment layer is used to reduce the difference in feature covariance between the source and target domains, and outputs the aligned features of the current land parcel. ; A few-sample fast adaptation layer is used to localize model parameters in the target region with a limited number of calibrated samples, and outputs a fine-tuned fitness metric. ; An online incremental fine-tuning layer is used for edge deployment to perform mini-batch updates using streaming local observation data; An adaptive weight fusion layer is used to receive the updated model parameters from the online incremental fine-tuning layer and sum them with the initial adaptive weights to obtain the updated adaptive weights. .

4. The quantitative analysis method for farmland occupation-compensation balance based on soil environmental perception according to claim 3, characterized in that: The unsupervised domain alignment layer groups vector samples according to institutional conditions based on the crop structure vector and management practice vector of the plot, and calculates the feature covariance matrix between the training data and the current plot for each group k. and By minimizing the conditional covariance difference, unsupervised distribution alignment based on conditions is achieved. The output domain reliability metric of the unsupervised domain alignment layer is expressed as... .

5. The quantitative analysis method for farmland occupation-compensation balance based on soil environmental perception according to claim 4, characterized in that: The few-sample fast adaptation layer uses aligned target domain features. Locally calibrated samples and training data model parameters As input, based on meta-learning, 1–K steps are performed locally to quickly adapt and generate initial localized parameters. And calculate the quantitative index of adaptability after fine-tuning. .

6. The quantitative analysis method for farmland occupation-compensation balance based on soil environmental perception according to claim 5, characterized in that: The online incremental fine-tuning layer is deployed at the edge to receive streaming local observation data and perform incremental parameter updates in small batches, calculating and outputting local verification reliability in real time. Score with fine-tuned sample size and output the updated model parameters. 、 , .

7. The quantitative analysis method for farmland occupation-compensation balance based on soil environmental perception according to claim 6, characterized in that: The predicted values ​​of the adaptive yield-ecological prediction model are expressed as follows: .

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