Immune optimization-based diatomic cluster structure optimization method and system, storage medium

Abstract

The application relates to the field of computational chemistry simulation, and particularly discloses a diatomic cluster structure optimization method and system based on immune optimization, and a storage medium, the method comprising the following steps: cluster structure initialization, cluster structure clone selection, cluster deformation variation mechanism, adaptive immune response, and memory cluster library updating. The variation strategies of large deformation and micro deformation guarantee the search ability of the algorithm, and the adaptive immune response strategy effectively solves the problems of rapid optimization of geometric isomers and position isomers, and improves the algorithm efficiency.

Description

Technical Field

[0001] This invention relates to the field of computational chemistry simulation, and more specifically to a method and system for optimizing diatomic cluster structures based on immune optimization, as well as a storage medium. Background Technology

[0002] Diatomic clusters, especially alloy clusters, possess unique and excellent catalytic, electromagnetic, and optical properties, making them a research hotspot in electrochemistry, materials science, and other fields with broad application prospects. Determining their stable structure is a prerequisite for studying the special properties of clusters; however, finding stable cluster structures requires theoretical calculations. Empirical potential energy functions are commonly used to describe the interactions between cluster atoms. Optimizing the stable structure of monatomic clusters involves finding the optimal geometric isomers from complex potential energy surfaces. However, for diatomic clusters, even with the same configuration, differences in the relative positions of different types of atoms result in positional isomers. Therefore, the coexistence of geometric and positional isomers exists in diatomic cluster structure optimization, significantly increasing the difficulty of optimization. Currently, popular methods for diatomic cluster structure optimization include improved genetic algorithms (GA), improved Basic-hopping algorithms (BH), and improved adaptive immune optimization algorithms (AIOA).

[0003] Existing diatomic cluster structure optimization algorithms struggle to simultaneously optimize both geometric and positional isomers. They often assume the geometric configuration before determining the optimal configuration at a given position, thus getting trapped in local maxima of the geometric potential well. Furthermore, existing algorithms have low mutation efficiency and struggle to quickly resolve positional isomerism issues after structural mutation. Summary of the Invention

[0004] The purpose of this invention is to overcome the problems existing in the prior art and provide a method, system and storage medium for optimizing diatomic cluster structures based on immune optimization, which can simultaneously solve the problem of rapid optimization of geometric isomers and positional isomers, and improve the efficiency of the algorithm.

[0005] To achieve the above objectives, the first aspect of the present invention provides a method for optimizing diatomic cluster structures based on immune optimization, comprising the following steps:

[0006] S1, Randomly generate multiple diatomic A atoms n B m Cluster structure coordinates, where the total number of atoms is the sum of the number of atoms of type A (n) and the number of atoms of type B (m), for M lib The structural coordinates are centered to form the initial memory cluster library. This is iterated k times to form the final memory cluster library. k is then set... max This represents the maximum number of iterations.

[0007] S2. A temporary cluster library is formed by selecting several cluster structures from the memory cluster library using the roulette wheel selection method.

[0008] S3. For each structure in the temporary cluster library, randomly select a mutation operation from the large deformation and micro deformation methods. The cluster structure after the mutation operation is X.

[0009] S4. Execute the binary dynamic grid search algorithm to achieve fast surface optimization of the diatomic cluster structure X. If the potential energy value of the structure does not decrease, end this step; otherwise, execute the first improved local search algorithm on the structure X' whose energy value has decreased to obtain the new structure X”. If the energy value of X” is lower than the energy value of X', replace structure X with the new structure X”; otherwise, replace X with X'.

[0010] S5. Compare the similarity between the structure of the temporary cluster library after step S4 and the structure in the memory cluster library. If the energy value of the structure in the temporary cluster library is lower than that of the most similar structure in the memory library, then replace the structure in the memory cluster library with that structure.

[0011] S6. Determine if k>k max If so, proceed to step S7; otherwise, k = k + 1, proceed to step S2.

[0012] S7: The structure with the lowest energy value in the memory cluster library is the diatomic A. n B m The globally optimal structure of a cluster.

[0013] Preferably, in step S3, the large deformation includes structural torsion and structural expansion / contraction.

[0014] The structural torsion operation is as follows: along the y-axis of the coordinate system, in the structural coordinate system, y... i >r max The atoms of / 2 are rotated 90 degrees clockwise, and in the structural coordinates 0.0≤y i ≤r max The atom of / 2 is rotated 45 degrees clockwise, in structural coordinates -r max / 2≤y i Atoms with a value <0.0 rotated 45 degrees counterclockwise in structural coordinates. i <-r max / 2 of the atoms rotate 90 degrees counterclockwise;

[0015] The structural scaling operation is as follows: along the y-axis of the coordinate system, the y-axis of the structural coordinate system... i >r max / 2 and y i <-r max The atoms of / 2 are translated r along the y-axis and -y-axis respectively. 0 Distance, rmax / 3 <y i ≤r max / 2 and -r max / 2 <y i ≤-r max The atoms of / 3 are translated r along the y-axis and -y-axis respectively. 0 / 2 distance, 0.0≤y i <r max / 3 and -r max / 3 <y i Atoms ≤0.0 are translated r along the x-axis and -x-axis towards the center of the structure. 0 / 2 distance;

[0016] Where, r max r is the farthest distance from the atom to the center of the structure in each cluster structure. 0 y represents the minimum nearest neighbor distance between atoms AA, BB, and AB. i Let y be the y-coordinate of the i-th atom.

[0017] Preferably, in step S3, the micro-deformation is a localized deformation of atoms with a low atomic connection number, and the micro-deformation operation is as follows:

[0018] The atoms with the highest potential energy in the structure are randomly moved to the atom with the highest remaining energy. 0 Within the radius.

[0019] Preferably, in step S5, the similarity comparison method is as follows: The number of atoms corresponding to coordination numbers j from 1 to 14 is counted and denoted as C(j), and the similarity is calculated using the following formula: Where u and v are the structures in the temporary cluster library and the corresponding structures in the memory cluster library, respectively.

[0020] Preferably, the coordination number is the number of atoms in a cluster structure that directly bond with each other. When the distance between two atoms of types AA, BB, and AB is less than 1.2 times... and Values ​​are considered as bonds; where, and These are the nearest neighbor distances between atoms AA, BB, and AB, respectively.

[0021] Preferably, in step S1, k max The value is set according to the optimization scale. Preferably, the total number of atoms is between 1 and 50 and is 10 and 15 respectively when it is greater than 50.

[0022] Preferably, in step S2, the cluster structures are selected based on their affinity. Cluster structures with high affinity will have more cloning opportunities. The affinity formula for each cluster structure is as follows:

[0023]

[0024] Among them, f i p represents the fitness value of each cluster. i The affinity of each cluster structure is represented by N, where N is the total number of atoms and i is the atom number.

[0025] A second aspect of the present invention provides an immune-optimized diatomic cluster structure optimization system, comprising:

[0026] Cluster structure initialization module: used to randomly generate multiple diatomic A atoms n B m Cluster structure coordinates, where the total number of atoms is the sum of the number of atoms of type A (n) and the number of atoms of type B (m), for M lib The structural coordinates are centered to form the initial memory cluster library. This is iterated k times to form the final memory cluster library. k is then set... max This represents the maximum number of iterations.

[0027] The cluster structure cloning selection module is used to select several cluster structures from the memory cluster library to form a temporary cluster library using a roulette wheel selection method;

[0028] The cluster deformation mutation mechanism module is used to randomly select a mutation operation from large deformation and micro deformation for each structure in the temporary cluster library. The cluster structure after the mutation operation is X.

[0029] The adaptive immune response module is used to execute a binary dynamic grid search algorithm to achieve rapid surface optimization of the diatomic cluster structure X. If the potential energy value of the structure does not decrease, this step ends; otherwise, the improved local search algorithm is executed again for the structure X' whose energy value has decreased to obtain a new structure X'". If the energy value of X' is lower than that of X', the new structure X' replaces the structure X; otherwise, X' replaces the structure X.

[0030] The memory cluster library module is updated to compare the similarity between the structure of the temporary cluster library processed by the adaptive immune response module and the structure in the memory cluster library. If the energy value of the structure in the temporary cluster library is lower than that of the most similar structure in the memory library, then the structure in the memory cluster library is replaced by that structure.

[0031] The judgment module is used to determine if k > k max If so, proceed to step S7; otherwise, k = k + 1, proceed to step S2.

[0032] The cluster structure optimization module is used to memorize the structure with the lowest energy value in the cluster library, which is the diatomic A. n B m The globally optimal structure of a cluster.

[0033] A third aspect of the present invention provides an immune-optimized dual-atom cluster structure optimization terminal device, including a processor, a memory, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the steps of the above method.

[0034] A fourth aspect of the present invention provides a machine-readable storage medium storing instructions that cause a machine to perform the steps of the method described above.

[0035] Through the above technical solutions, the present invention has the following beneficial effects: (1) The proposed mutation strategy of large deformation and micro deformation ensures the search capability of the algorithm; (2) The proposed adaptive immune response strategy effectively solves the problem of rapid optimization of geometric isomers and positional isomers, and improves the efficiency of the algorithm; (3) The proposed method of similarity detection of diatomic cluster structures gives full play to the function of the memory cluster library. Attached Figure Description

[0036] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0037] Figure 1 This is a flowchart illustrating the optimization process of the diatomic cluster structure based on immune optimization according to the present invention. Detailed Implementation

[0038] To further illustrate the features of the present invention, the technical solution of the present invention will be described in more detail below through specific embodiments. However, the present invention can be implemented in many places other than those described herein, and those skilled in the art can make similar improvements without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0039] This invention takes the optimization of binary Lennard-Jones potential function cluster structures as an example. The first aspect proposes a method for optimizing diatomic cluster structures based on immune optimization, such as... Figure 1 As shown, it includes the following steps:

[0040] S1: Cluster structure initialization: Randomly generate M lib diatomic A n B mThe cluster structure coordinates are given, where the total number of atoms N is the sum of the number of atoms of type A (n) and the number of atoms of type B (m). The interatomic interactions within the cluster structure are described using a potential energy function, whose energy value is the cluster's fitness value f. The potential energy values ​​of each initial structure are calculated using the binary Lennard-Jones cluster potential energy function, with the following formula:

[0041]

[0042] Where, r ij σ is the distance between atoms i and j in the cluster structure; ij σ represents the distance between the nuclei of atom i and atom j. For AB type clusters, exemplarily, σ AA =1.0, σ BB =1.3, σ AB =1.15; ε is the depth of the potential energy well, with a value of 1.0. To make the randomly generated discrete structure more stable, local optimization operations, such as a memory-constrained quasi-Newton method, can be used. Subsequently, all structure coordinates are centered. Then, this M... lib These structures constitute the initial (k=1) memory cluster library, where k is the number of iterations performed by the algorithm. max This represents the maximum number of iterations.

[0043] S2: Cluster Structure Cloning Selection: A roulette wheel selection method is used to select cluster structures from a memory cluster library. The affinity formula for each structure is as follows:

[0044]

[0045] In the formula f i Let M be the fitness value of the i-th cluster. Cloning is performed from the memory cluster library based on cluster affinity; clusters with high affinity will receive more cloning opportunities. Choose M. sel Each cluster structure forms a temporary cluster library;

[0046] S3: Cluster Deformation Mutation Mechanism: For each structure in the temporary cluster library, a mutation operation is randomly selected from large deformation and micro deformation modes. Large deformation includes structural torsion and structural stretching, while micro deformation involves local deformation of atoms with low atomic connectivity. The distance r from the farthest point of each atom in each cluster structure to the structure center is calculated. max r 0 The nearest neighbor distance between atoms AA, BB, and AB and The minimum value. The structural torsion operation is:

[0047] Along the y-axis of the coordinate system, the y-axis in the structural coordinates i >r max / 2 of the atoms rotate 90 degrees clockwise, 0.0≤y i ≤r max The atom of / 2 rotates 45 degrees clockwise, -r max / 2≤y i Atoms with a value less than 0.0 rotate 45 degrees counterclockwise. i <-r max The atoms of / 2 rotate 90 degrees counterclockwise.

[0048] The structural expansion and contraction operation is as follows:

[0049] Along the y-axis of the coordinate system, the y-axis in the structural coordinates i >r max / 2 and y i <-r max The atoms of / 2 are translated r along the y-axis and -y-axis respectively. 0 Distance, r max / 3 <y i ≤r max / 2 and -r max / 2 <y i ≤-r max The atoms of / 3 are translated r along the y-axis and -y-axis respectively. 0 / 2 distance, 0.0≤y i <r max / 3 and -r max / 3 <y i Atoms ≤0.0 are translated r along the x-axis and -x-axis towards the center of the structure. 0 / 2 distance.

[0050] Micro-deformation operations are as follows:

[0051] The atoms with the highest potential energy in the structure (preferably 3) are randomly moved to the atom with the highest remaining energy. 0 Within the radius.

[0052] S4: Adaptive Immune Response: The cluster structure X after mutation of the temporary cluster library is first executed using a binary dynamic grid search algorithm to achieve rapid surface optimization of the diatomic cluster structure. If the potential energy value of the structure does not decrease, this step ends; otherwise, the improved local search algorithm is executed again on the structure X' whose energy value has decreased to obtain a new structure X”. If the energy value of X” is lower than the energy value of X’, the new structure X” replaces the structure X; otherwise, X’ replaces X.

[0053] S5: Update the memory cluster library: Compare the structures in the temporary cluster library with those in the memory cluster library based on their similarity. If the energy value of a structure in the temporary cluster library is lower than that of the most similar structure in the memory library, then that structure replaces the structure in the memory library. The similarity comparison method is as follows: the coordination number is the number of atoms in a cluster structure that are directly bonded to each other. When the distance between two atoms in AA, BB, and AB types is less than 1.2 times... and The similarity value is used to determine if they are bonded. The number of atoms corresponding to coordination numbers j from 1 to 14 is counted and denoted as C(j). The similarity calculation formula is: Where u and v are the structures in the temporary cluster library and the memory cluster library, respectively.

[0054] At this point, k = k + 1;

[0055] S6: If k>k max If yes, proceed to step S7; otherwise, proceed to step S2.

[0056] S7: The structure with the lowest energy value in the memory bank is the diatomic A. n B m The globally optimal structure of a cluster.

[0057] The above algorithm is used to optimize the binary Lennard-Jones cluster structure, with parameter M set as an example. lib and M sel They are 8 and 6 respectively, k max When N is between 1 and 50 and greater than 50, the values ​​are 10 and 15 respectively. Once the optimal value in Table 1 is found, one optimization is completed. The optimization results are shown in Table 1.

[0058] Table 1

[0059]

[0060]

[0061] Table 1 shows the calculation results of 100 independent runs of the optimization of the stable structure of some binary Lennard-Jones clusters according to the embodiments of the present invention. As shown in Table 1, the method can search for the known optimal structure, and for diatomic clusters with N of 38 and 39, the success rate of optimization of other size structures is 100%, demonstrating excellent search performance.

[0062] This invention is based on the basic framework of an immune optimization algorithm. It proposes a mutation strategy for large and small deformations to ensure the algorithm's search capability, proposes an adaptive immune response strategy to effectively solve the problem of rapid optimization of geometric and positional isomers, and designs a diatomic cluster similarity detection method to update the memory cluster library, thereby improving the algorithm's efficiency.

[0063] Based on the same inventive concept, a second aspect of the present invention provides an immune-optimized diatomic cluster structure optimization system, comprising:

[0064] Cluster structure initialization module: used to randomly generate multiple diatomic A atoms n B m Cluster structure coordinates, where the total number of atoms is the sum of the number of atoms of type A (n) and the number of atoms of type B (m), for M lib The structural coordinates are centered to form the initial memory cluster library. This is iterated k times to form the final memory cluster library. k is then set... max This represents the maximum number of iterations.

[0065] The cluster structure cloning selection module is used to select several cluster structures from the memory cluster library to form a temporary cluster library using a roulette wheel selection method;

[0066] The cluster deformation mutation mechanism module is used to randomly select a mutation operation from large deformation and micro deformation for each structure in the temporary cluster library. The cluster structure after the mutation operation is X.

[0067] The adaptive immune response module is used to execute a binary dynamic grid search algorithm to achieve rapid surface optimization of the diatomic cluster structure X. If the potential energy value of the structure does not decrease, this step ends; otherwise, the improved local search algorithm is executed again for the structure X' whose energy value has decreased to obtain a new structure X'". If the energy value of X' is lower than that of X', the new structure X' replaces the structure X; otherwise, X' replaces the structure X.

[0068] The memory cluster library module is updated to compare the similarity between the structure of the temporary cluster library processed by the adaptive immune response module and the structure in the memory cluster library. If the energy value of the structure in the temporary cluster library is lower than that of the most similar structure in the memory library, then the structure in the memory cluster library is replaced by that structure.

[0069] The judgment module is used to determine if k > k max If so, proceed to step S7; otherwise, k = k + 1, proceed to step S2.

[0070] The cluster structure optimization module is used to memorize the structure with the lowest energy value in the cluster library, which is the diatomic A. n B m The globally optimal structure of a cluster.

[0071] Based on the same inventive concept, a third aspect of the present invention provides a terminal device for optimizing diatomic cluster structures based on immune optimization, including a processor, a memory, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the steps of the above-described method for optimizing diatomic cluster structures based on immune optimization.

[0072] A fourth aspect of the present invention provides a machine-readable storage medium storing instructions that cause a machine to perform the steps of the immune-optimized diatomic cluster structure optimization method described above.

[0073] In summary, through the above technical solutions, this invention has the following beneficial effects: the proposed mutation strategy for large and small deformations ensures the search capability of the algorithm; the proposed adaptive immune response strategy effectively solves the problem of rapid optimization of geometric and positional isomers, improving algorithm efficiency; the proposed method for detecting the similarity of diatomic cluster structures leverages the function of the memory cluster library; and it can simultaneously solve the problem of rapid optimization of geometric and positional isomers, improving algorithm efficiency.

[0074] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings; however, the present invention is not limited thereto. Within the scope of the inventive concept, various simple modifications can be made to the technical solutions of the present invention, including combinations of various specific technical features in any suitable manner. To avoid unnecessary repetition, the present invention will not describe the various possible combinations separately. However, these simple modifications and combinations should also be considered as the content disclosed in the present invention and are all within the protection scope of the present invention.

Claims

1. A method for optimizing the structure of diatomic clusters based on immune optimization, characterized in that, Includes the following steps: S1, Randomly generate multiple diatomic A atoms n B m Cluster structure coordinates, where the total number of atoms is the sum of the number of atoms of type A (n) and the number of atoms of type B (m), for M lib The structural coordinates are centered to form the initial memory cluster library. This is iterated k times to form the final memory cluster library. k is then set... max This represents the maximum number of iterations. S2. A temporary cluster library is formed by selecting several cluster structures from the memory cluster library using the roulette wheel selection method. S3. For each structure in the temporary cluster library, randomly select a mutation operation from the large deformation and micro deformation methods. The cluster structure after the mutation operation is X. S4. Execute the binary dynamic grid search algorithm to achieve fast surface optimization of the diatomic cluster structure X. If the potential energy value of the structure does not decrease, end this step; otherwise, execute the local search algorithm again for the structure X' whose energy value has decreased to obtain the new structure X''. If the energy value of X'' is lower than the energy value of X', replace structure X with the new structure X''; otherwise, replace X with X'. S5. Compare the similarity between the structure of the temporary cluster library after step S4 and the structure in the memory cluster library. If the energy value of the structure in the temporary cluster library is lower than that of the most similar structure in the memory library, then replace the structure in the memory cluster library with that structure. S6. Determine if k > k max If so, proceed to step S7; otherwise, k = k + 1, and proceed to step S2. S7. The structure with the lowest energy value in the memory cluster library is the diatomic A. n B m The globally optimal structure of a cluster; In step S3, the large deformation includes structural torsion and structural expansion / contraction; The structural torsion operation is as follows: along the y-axis of the coordinate system, in the structural coordinate system, y... i > r max Rotate the atom by 90 degrees clockwise, and in the structural coordinates, 0.0 ≤ y i ≤ r max The atom of / 2 is rotated 45 degrees clockwise, in structural coordinates -r max / 2≤ y i Atoms with a value less than 0.0 rotate 45 degrees counterclockwise; in structural coordinates, y... i < -r max / 2 of the atoms rotate 90 degrees counterclockwise; The structural scaling operation is as follows: along the y-axis of the coordinate system, the y-axis of the structural coordinate system... i > r max / 2 and y i < -r max The atoms of / 2 are translated along the y-axis and -y-axis respectively. Distance, r max / 3 < y i ≤ r max / 2 and -r max / 2 < y i ≤ -r max The atoms of / 3 are translated along the y-axis and -y-axis respectively. Distance, 0.0 ≤ y i < r max / 3 and -r max / 3 < y i Atoms ≤ 0.0 translate along the x-axis and -x-axis towards the center of the structure. distance; Where, r max The distance from the atom to the center of the structure for each cluster is the furthest point. y represents the minimum nearest neighbor distance between atoms AA, BB, and AB. i Let be the y-coordinate of the i-th atom; In step S3, the micro-deformation involves locally deforming the atoms with a low atomic connection number. The micro-deformation operation is as follows: The atoms with the highest potential energy in the structure are randomly moved to the atom with the highest remaining energy. Within the radius; In step S5, the similarity comparison method is as follows: The number of atoms corresponding to coordination numbers j from 1 to 14 is counted and denoted as C(j), and the similarity is calculated using the following formula: , where u and v are the structures in the temporary cluster library and the corresponding structures in the memory cluster library, respectively; The coordination number refers to the number of atoms in a cluster structure that are directly bonded to each other. For AA, BB, and AB types, the distance between two atoms is less than 1.2 times the number of atoms in the cluster. , and Values ​​are considered as bonds; where, , and These are the nearest neighbor distances between atoms AA, BB, and AB, respectively.

2. The method for optimizing diatomic cluster structures based on immune optimization according to claim 1, characterized in that, In step S1, k max The value is set according to the optimization scale, with values ​​of 10 and 15 for a total number of atoms between 1 and 50 and for a total number of atoms greater than 50.

3. The method for optimizing diatomic cluster structures based on immune optimization according to claim 1, characterized in that, In step S2, cluster structures are selected based on their affinity. Cluster structures with high affinity will have more cloning opportunities. The affinity formula for each cluster structure is as follows: ， Among them, f i The fitness value for each cluster is [value]. The affinity of each cluster structure is represented by N, where N is the total number of atoms and i is the atom number.

4. A diatomic cluster structure optimization system based on immune optimization, characterized in that, The system is used to perform the steps of the immune-optimized diatomic cluster structure optimization method according to any one of claims 1-3, the system comprising: Cluster structure initialization module: used to randomly generate multiple diatomic A atoms n B m Cluster structure coordinates, where the total number of atoms is the sum of the number of atoms of type A (n) and the number of atoms of type B (m), for M lib The structural coordinates are centered to form the initial memory cluster library. This is iterated k times to form the final memory cluster library. k is then set... max This represents the maximum number of iterations. The cluster structure cloning selection module is used to select several cluster structures from the memory cluster library to form a temporary cluster library using a roulette wheel selection method; The cluster deformation mutation mechanism module is used to randomly select a mutation operation from large deformation and micro deformation for each structure in the temporary cluster library. The cluster structure after the mutation operation is X. The adaptive immune response module is used to execute a binary dynamic grid search algorithm to achieve rapid surface optimization of the diatomic cluster structure X. If the potential energy value of the structure does not decrease, this step ends; otherwise, the improved local search algorithm is executed again for the structure X' whose energy value has decreased to obtain a new structure X''. If the energy value of X'' is lower than the energy value of X', the new structure X'' replaces the structure X; otherwise, X' replaces X. The memory cluster library module is updated to compare the similarity between the structure of the temporary cluster library processed by the adaptive immune response module and the structure in the memory cluster library. If the energy value of the structure in the temporary cluster library is lower than that of the most similar structure in the memory library, then the structure in the memory cluster library is replaced by that structure. The judgment module is used to determine if k > k max If so, proceed to step S7; otherwise, k = k + 1, and proceed to step S2. The cluster structure optimization module is used to memorize the structure with the lowest energy value in the cluster library, which is the diatomic A. n B m The globally optimal structure of a cluster.

5. A terminal device for optimizing the structure of diatomic clusters based on immune optimization, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the steps of any one of claims 1-3.

6. A machine-readable storage medium storing instructions that cause a machine to perform the steps of any one of the methods of claims 1-3 of this application.

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