Regional risk measurement method and system for shrinking urban population loss

Abstract

The invention belongs to the related technical field of city management and risk prevention and control, and discloses a regional risk measurement method and system for shrinkage city population loss, and the method comprises the steps: constructing a population migration network of a target region based on the region range of the target region to which a target shrinkage city belongs and population statistical data, nodes of the network are cities in the target area, an edge is connected between two nodes with population migration, and the weight of the corresponding edge is determined according to the population migration amount between the two nodes; according to the population migration network, acquiring an aggregation coefficient of the target contracted city in the network; and measuring the regional risk of population loss of the target shrinkage city according to the aggregation coefficient. According to the method, the population migration network is constructed based on the population statistical data, the regional risk of population loss of the target shrinkage city is measured through the aggregation coefficient in the network by means of the network generation technology, and the accuracy and objectivity of risk measurement are effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to urban management and risk prevention and control. More specifically, it relates to a method and system for measuring the regional risk of population loss in shrinking cities. Background Art

[0002] Urban shrinkage is a new concept and topic in the field of current urban planning and management. Urban shrinkage is directly characterized by the loss of urban population. The loss of urban population will seriously affect the development of cities. Population is the basis of production and even more the basis of consumption. The loss of population will not only cause a decline in the labor force, but also lead to a series of negative problems such as urban economic recession, rising debts, vacant urban housing, and insufficient utilization of existing urban facilities such as public service facilities and municipal facilities. For the high-quality development of urban and regional economy and society, urban shrinkage is a new challenge and problem that needs to be directly faced, and a method for measuring the risk prevention and control of urban shrinkage should be explored as early as possible.

[0003] At present, most of the domestic and foreign research on the risk prevention and control of urban planning is in the theoretical research stage. The mainstream research methods usually rely on expert opinions, and there is less research on the measurement of the shrinkage risk of urban population loss. There is a lack of relatively accurate scientific methods and practical tools for measuring the shrinkage risk of cities. Summary of the Invention

[0004] In view of the above defects or improvement requirements of the prior art, the present invention provides a method and system for measuring the regional risk of population loss in shrinking cities, which is used to solve the problem that there is less research on the measurement of the shrinkage risk of urban population loss in the prior art and there is a lack of accurate and scientific measurement methods for urban shrinkage risk.

[0005] To achieve the above object, according to one aspect of the present invention, a method for measuring the regional risk of population loss in shrinking cities is provided, including:

[0006] Based on the regional scope of the target region to which the target shrinking city belongs and the population statistical data within the region, construct a population migration network of the target region. The nodes of the population migration network are the cities within the target region. Among them, there is an edge connected between two nodes with population migration, and the weight of the corresponding edge is determined according to the population migration volume between the two nodes;

[0007] According to the population migration network, obtain the clustering coefficient of the target shrinking city in the network;

[0008] Measure the regional risk of population loss of the target shrinking city according to the clustering coefficient.

[0009] According to the method for measuring the regional risk of population loss in shrinking cities provided by the present invention, the regional risk of population loss of the target shrinking city is measured according to the clustering coefficient, specifically including:

[0010] Construct a population migration network of the target region under different time sections, and obtain the clustering coefficients corresponding to the target shrinking city under different time sections;

[0011] The relative change rate of the clustering coefficients corresponding to the target shrinking city under different time sections is used to measure the degree of the regional risk of population loss of the target shrinking city.

[0012] According to the method for measuring the regional risk of population loss in shrinking cities provided by the present invention, the regional risk of population loss of the target shrinking city is measured according to the clustering coefficient, specifically including:

[0013] According to the population statistics data under different time sections, determine the initial time when the population of the target shrinking city starts to shrink;

[0014] Respectively obtain the clustering coefficients corresponding to the target shrinking city before and after the initial time, and use the relative change rate of the clustering coefficients before and after to measure the degree of the regional risk of population loss of the target shrinking city.

[0015] According to the method for measuring the regional risk of population loss in shrinking cities provided by the present invention, specifically including the following steps for determining the initial time when the population of the target shrinking city starts to shrink:

[0016] Calculate the difference between the population statistics data of the target shrinking city at the current time section and the previous time section. If the difference in population statistics data is less than zero, the current time section is the initial time.

[0017] According to the method for measuring the regional risk of population loss in shrinking cities provided by the present invention, the weight of the corresponding edge is determined according to the population migration volume between two nodes, specifically: using the normalized population migration volume as the weight of the edge in the network.

[0018] According to the method for measuring the regional risk of population loss in shrinking cities provided by the present invention, the population migration network G is G = G(V, E, W), where V is the node, E is the edge, and W is the weight;

[0019] The weight w of the edge between the nodes m and n with population migration mn Specifically:

[0020]

[0021] s mn =s m→n +s n→m ;

[0022] Among them, s mn is the population migration volume between node m and node n; s max is the maximum value of the population migration volume between all pairwise nodes within the target area; s m→n is the population migration number from node m to node n; s n→m is the population migration number from node n to node m; w mn ∈[0, 1].

[0023] According to the method for measuring the regional risk of population loss in shrinking cities provided by the present invention, the clustering coefficient C of the node i corresponding to the target shrinking city in the population migration network i is:

[0024]

[0025] w imn =(w im w mn w in ) 1 / 3 ;

[0026] Among them, k i is the number of nodes in the neighborhood N i ; the neighborhood N i is the set of other nodes connected to node i; among them, m ∈ N i , n ∈ N i , and m ≠ n; w imn is the geometric mean of the weights of the edges between node i and nodes m and n; w im is the weight corresponding to the edge between node i and node m; w in is the weight corresponding to the edge between node i and node n; w mn is the weight corresponding to the edge between nodes n and m.

[0027] According to the method for measuring the regional risk of population loss in shrinking cities provided by the present invention, the relative change rate of the clustering coefficient before and after is used to measure the degree of the regional risk of population loss in the target shrinking city, specifically including:

[0028] Taking the relative change rate of the clustering coefficient corresponding to the previous time section of the current time section and the initial appearance time as the regional risk of population loss of the target shrinking city at the current time section;

[0029] Among them, the regional risk of population loss j caused by the target shrinking city at the time section T relative to the previous time section of the initial appearance time

[0030]

[0031] Among them, is the clustering coefficient corresponding to the target shrinking city at the time section T j ; i is the node corresponding to the target shrinking city; is the clustering coefficient corresponding to the target shrinking city at the time section T s-1 ; T s-1 is the previous time section of the initial appearance time T s .

[0032] According to the method for measuring the regional risk of population loss in shrinking cities provided by the present invention, the relative change rate of the above-mentioned clustering coefficients is used to measure the degree of regional risk of population loss in the target shrinking city, which specifically includes:

[0033] Taking the relative change rate of the clustering coefficient corresponding to the current time section and any time section before the initial appearance time as the regional risk of population loss of the target shrinking city at the current time section;

[0034] Among them, the regional risk of population loss caused by the target shrinking city at the time section T j relative to any time section before the initial appearance time is:

[0035]

[0036] Among them, is the clustering coefficient corresponding to the target shrinking city at the time section T j ; i is the node corresponding to the target shrinking city; is the clustering coefficient corresponding to the target shrinking city at the time section T b ; T b is any time section before the initial appearance time T s .

[0037] According to another aspect of the present invention, a system for measuring the regional risk of population loss in shrinking cities is provided. The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the method for measuring the regional risk of population loss in shrinking cities described in any one of the above.

[0038] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the method and system for measuring the regional risk of population loss in shrinking cities provided by the present invention:

[0039] 1. Constructing a population migration network based on demographic data in the target area can reflect the population migration situation between cities within the target area. Then, by using the clustering coefficient of the target shrinking city node in the network to measure the regional risk of population loss in the target shrinking city, with the help of network generation technology, the risk degree brought by the population loss of shrinking cities to regional development can be measured scientifically and accurately, effectively improving the accuracy of analyzing the risk degree of urban population loss shrinkage, and having strong practicability, objectivity and scientificity;

[0040] 2. Specifically, measure the regional risk of population loss in shrinking cities through the relative change rate of the clustering coefficient corresponding to the target shrinking city, realizing the quantification of the risk. The results show that this method can scientifically and effectively measure the regional population loss risk caused by urban shrinkage, which helps to provide scientific, objective and accurate reference information for formulating policies related to urban and regional transformation and development, and promotes the high-quality development of the urban and regional economy and society;

[0041] 3. The specific construction method of the proposed population migration network and the specific calculation process of the clustering coefficient excavate the internal correlation between population migration behavior characteristics and urban shrinkage. This internal correlation conforms to natural laws and has rationality and scientificity, making the measurement of the regional population loss risk of urban shrinkage based on the clustering coefficient more reliable and accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a schematic flowchart of the method for measuring the regional risk of population loss in shrinking cities provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0043] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0044] Please refer to Figure 1 , this embodiment provides a method for measuring the regional risk of population loss in shrinking cities. The method for measuring the regional risk of population loss in shrinking cities includes:

[0045] Based on the regional scope of the target area to which the target shrinking city belongs and the demographic data within the area, construct the population migration network of the target area. The nodes of the population migration network are the cities within the target area. Among them, there is an edge connected between two nodes with population migration, and the weight of the corresponding edge is determined according to the population migration volume between the two nodes;

[0046] Obtain the clustering coefficient of the target shrinking city in the network according to the population migration network;

[0047] Measure the regional risk of population loss of the target shrinking city according to the clustering coefficient.

[0048] Based on the existing technology's demand for the method of measuring and controlling the risk of urban shrinkage, this embodiment proposes a technical means of using the population migration network to quantitatively measure the risk caused by urban shrinkage to the region. The measurement results can be used for the prevention and control of urban shrinkage risks. The population migration network is established based on the population statistics data between cities in the target region. Each node in the population migration network corresponds to each city in the target region. The connection edges between nodes correspond to the population migration between cities, and the weight of the edge corresponds to the specific magnitude of the population migration volume between the corresponding two cities. The greater the population migration volume between two cities, the greater the weight value of the corresponding edge.

[0049] Therefore, the clustering coefficient of the target shrinking city in the network can reflect the influence degree of the target shrinking city in terms of population migration in the target region. Furthermore, it is reasonable and scientific to measure the regional risk of population loss of the target shrinking city based on the clustering coefficient, which conforms to the natural objective law. For example, the population migration network of the target region can be constructed for different time sections respectively, and the clustering coefficients of the target shrinking city corresponding to different time sections can be obtained. The change of the clustering coefficient can be used to reflect the regional risk of population loss of the target shrinking city. A clustering coefficient threshold can also be set. The clustering coefficient corresponding to the target shrinking city can be continuously obtained with a preset time section as the cycle, and then the clustering coefficient is compared with the preset threshold. According to the comparison result, the regional risk of population loss of the target shrinking city can be quantitatively evaluated.

[0050] The target region is the region including the target shrinking city. The scope of the target region can be determined according to urban planning and specific requirements for risk prevention and control. For example, the target region can be an urban agglomeration region or an urban cluster region including the target shrinking city, or an economic belt region, etc. There is no specific limitation. The specific scope and the number of cities included in different types of regions can be determined according to the regional planning scope.

[0051] In some specific embodiments, measuring the regional risk of population loss of the target shrinking city according to the clustering coefficient specifically includes:

[0052] Construct the population migration network of the target region under different time sections, and obtain the clustering coefficients corresponding to the target shrinking city under different time sections respectively;

[0053] Measure the degree of the regional risk of population loss of the target shrinking city with the relative change rate of the clustering coefficients corresponding to the target shrinking city under different time sections.

[0054] Based on the above embodiments, the clustering coefficient can reflect the influence degree of the target shrinking city in terms of population migration in the target area. Furthermore, the relative change rate of the clustering coefficient that can be calculated is proposed, which can reflect the change of the influence degree of the target shrinking city in terms of population migration. If the influence degree decreases, that is, the clustering coefficient decreases, it indicates the risk of population loss. Furthermore, the degree of population loss risk can be reflected according to the degree of decrease of the clustering coefficient, that is, the relative change rate.

[0055] Furthermore, the regional risk of population loss of the target shrinking city is measured according to the clustering coefficient, which specifically includes:

[0056] According to the population statistics data under different time sections, determine the initial time when the population of the target shrinking city starts to shrink;

[0057] Respectively obtain the clustering coefficients corresponding to the target shrinking city before and after the initial time, and measure the regional risk degree of population loss of the target shrinking city with the relative change rate of the clustering coefficients before and after. Since the target shrinking city has shrinkage, that is, population loss, starting from the initial time, the change rate is calculated based on the clustering coefficient before the initial time, which can better reflect the population loss risk caused by the target shrinking city to the region compared with before the shrinkage, has better warning properties, and is conducive to better realizing risk prevention and control and urban planning.

[0058] In some specific embodiments, determining the initial time when the population of the target shrinking city starts to shrink specifically includes:

[0059] Calculate the difference between the population statistics data of the target shrinking city at the current time section and the previous time section. If the difference in population statistics data is less than zero, the current time section is the initial time.

[0060] Determine the initial year when the selected city starts to shrink specifically as: taking a single year as the time section T j , sort out the population statistics data P within the urban area of the city to be studied in this time section, and calculate the population change ΔP between adjacent time sections within the urban area of the city to be studied:

[0061]

[0062] If the population change ΔP between adjacent time sections < 0, that is, the population within the urban area of the city to be studied shows negative growth, then this time section T s is the initial time of urban shrinkage.

[0063] In some specific embodiments, determining the weight of the corresponding edge according to the population migration volume between two nodes specifically is: taking the normalized population migration volume as the weight of the edge in the network.

[0064] In some specific embodiments, demographic data is used to construct a population migration network among cities within the regional planning scope of the region to which the selected cities belong. The population migration network G is G = G(V, E, W), where V is the node, and the number of nodes V is the number of cities within the regional scope. E is the edge, and the method for determining the number of edges E is as follows: Assume that there is population migration between two cities within the regional scope, then there is an edge connecting these two cities. Otherwise, there is no connecting edge between these two cities.

[0065] W is the weight; the method for determining the weight W of the edge E is as follows: If there is population migration between city m and city n, then the weight w of the edge between nodes m and n with population migration mn Specifically:

[0066]

[0067] s mn = s m→n + s n→m ;

[0068] where s mn is the population migration volume between nodes m and n; s max is the maximum value of the population migration volumes between all pairs of nodes within the target regional scope; s m→n is the number of population migrations from node m to node n; s n→m is the number of population migrations from node n to node m; w mn ∈[0, 1].

[0069] The population migration volume s between two cities mn divided by the maximum value s of the population migration volumes between all pairs of cities within the regional scope max is the weight w of the edge connection between the two cities mn ; The weights of the edge connections between all pairs of cities can form the weight matrix W of the population movement network.

[0070] In this way, a population migration network G = G(V, E, W) among cities within the regional planning scope of the region to which the selected cities belong is constructed.

[0071] By analogy, taking a specific year as the time section, the population migration network G among cities at different time sections can be constructed T .

[0072] In some specific embodiments, for the selected target shrinking city i, the neighborhood N of this city i as node i in the population migration network i is defined as the set of other city nodes directly connected to it, and E i is the neighborhood N of node ii Set of mid-edge connections. The clustering coefficient C of the node i corresponding to the target shrinking city in the population migration network i is:

[0073]

[0074] w imn =(w im w mn w in ); 1 / 3 ;

[0075] where k i is the number of nodes in the neighborhood N i ; the neighborhood N i is the set of other nodes connected to node i; where, two urban nodes m and n are selected in sequence from the neighborhood N i , m ∈ N i , n ∈ N i , and m ≠ n; w imn is the geometric mean of the weights of the edges between node i and nodes m and n; w im is the weight corresponding to the edge between node i and node m; w in is the weight corresponding to the edge between node i and node n; w mn is the weight corresponding to the edge between node n and node m.

[0076] From the edge weights W of the population migration network, the weight w im corresponding to the edge connection between urban node i and urban node m can be found in sequence; the weight w in corresponding to the edge connection between urban node i and urban node n; the weight w mn corresponding to the edge connection between urban node n and urban node m; calculate their geometric mean w imn , and select the clustering coefficient between the selected city and other cities in the population migration network.

[0077] In some specific embodiments, the regional risk degree of population loss of the target shrinking city is measured by the relative change rate of the clustering coefficient before and after, specifically including:[[]]

[0078] Taking the relative change rate of the clustering coefficient corresponding to the previous time section of the current time section and the initial appearance time as the regional risk of population loss of the target shrinking city at the current time section;

[0079] where, the regional risk of population loss j caused by the target shrinking city at the time section T relative to the previous time section of the initial appearance time

[0080]

[0081] Among them, is the clustering coefficient corresponding to the target shrinking city at the time section T j ; i is the node corresponding to the target shrinking city; is the clustering coefficient corresponding to the target shrinking city at the time section T s-1 ; T s-1 is the previous time section of the emergence time T s .

[0082] That is, construct the population migration network G s between cities at a specific time section T j after a certain year T Tj of the emergence year, and calculate the clustering coefficient j of city i at this time section T according to the above method, and construct the population migration network G s between cities at the time section T s-1 one year before the emergence year T Ts-1 , and calculate the clustering coefficient s-1 of city i at this time section T Thus, obtain the regional risk of population loss caused by the previous time section of the target shrinking city at the time section T j relative to the emergence time

[0083] Similarly, the population migration network G s between cities at any time section T b before the emergence year T Tb can be constructed, and the clustering coefficient b of city i at this time section T can be calculated according to the above method, and then the regional risk of population loss j caused by the shrinking city i at the time section T b relative to any time section T of the emergence year can be measured. The specific quantitative index of the regional risk of population loss of the target shrinking city can be set according to actual needs, and is not specifically limited.

[0084] That is, in some other specific embodiments, the relative change rate of the above-mentioned clustering coefficients is used to measure the degree of the regional risk of population loss of the target shrinking city, specifically including:

[0085] Taking the relative change rate of the clustering coefficient corresponding to the current time section and any time section before the initial appearance time as the regional risk of population loss of the target shrinking city at the current time section;

[0086] wherein, the target shrinking city at time section T j The regional risk of population loss caused relative to any time section before the initial appearance time is:

[0087]

[0088] wherein, is the clustering coefficient corresponding to the target shrinking city at time section T j ; i is the node corresponding to the target shrinking city; is the clustering coefficient corresponding to the target shrinking city at time section T b ; T b is any time section before the initial appearance time T s .

[0089] Furthermore, an embodiment of the present invention also provides a system for measuring the regional risk of population loss in shrinking cities. The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the method for measuring the regional risk of population loss in shrinking cities described in any one of the above.

[0090] The present invention discloses a method and system for measuring the regional risk of population loss in shrinking cities. The method includes: determining the initial appearance year of the selected city shrinking based on the population statistics data of different time sections; constructing a population migration network between cities within the regional planning scope of the selected city's region based on the population statistics data, and using the normalized population migration volume as the weight of the edges in the network; calculating the clustering coefficients between the city and other cities in the network before and after the initial appearance time respectively, and using the relative change rate of the clustering coefficient values to measure the degree of the regional risk of population loss in the shrinking city. Through the above method, the risk brought by the population loss in the shrinking city to the regional development can be scientifically and accurately quantified.

[0091] Those skilled in the art can easily understand that the above is only a preferred embodiment of the present invention and is not used to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for measuring the regional risk of population loss in shrinking cities, characterized in that: include: Based on the area scope of the target area to which the target shrinking city belongs and the demographic data in the area, a population migration network of the target area is constructed, wherein the nodes of the population migration network are the cities in the target area, wherein an edge is connected between two nodes where there is population migration, and the weight of the corresponding edge is determined according to the population migration amount between the two nodes; According to the population migration network, obtaining the clustering coefficient of the target shrinking city in the network; The regional risk of population loss in the target shrinking city is measured according to the clustering coefficient.

2. The method for measuring regional risk of population loss in shrinking cities as claimed in claim 1, characterized in that: The regional risk of population loss in the target shrinking city is measured according to the clustering coefficient, specifically including: Constructing a population migration network of the target area at different time sections, and obtaining the clustering coefficients corresponding to the target shrinking cities at different time sections; The regional risk degree of population loss of the target shrinking city is measured by the relative change rate of the clustering coefficient corresponding to the target shrinking city at different time sections.

3. The method for measuring regional risk of population loss in shrinking cities as claimed in claim 2, characterized in that: The regional risk of population loss in the target shrinking city is measured according to the clustering coefficient, specifically including: Determine the starting time of population shrinkage in the target shrinking city based on demographic data at different time sections; The clustering coefficients corresponding to the target shrinking cities before and after the onset time are respectively obtained, and the regional risk degree of population loss of the target shrinking cities is measured by the relative change rate of the clustering coefficients before and after the onset time.

4. The method for measuring regional risk of population loss in shrinking cities as claimed in claim 3, characterized in that: Determining the starting time of population shrinkage in the target shrinking city specifically includes: The difference between the demographic data of the target shrinking city at the current time section and the previous time section is calculated. If the difference between the demographic data is less than zero, the current time section is the start time.

5. The method for measuring regional risk of population loss in shrinking cities according to any one of claims 1 to 4, characterized in that: The weight of the corresponding edge is determined according to the population migration amount between two nodes: the normalized population migration amount is used as the weight of the edge in the network.

6. The method for measuring regional risk of population loss in shrinking cities as claimed in claim 5, characterized in that: The population migration network G is G=G(V,E,W), where V is a node, E is an edge, and W is a weight; The weight w of the edge between node m and node n where there is population migration mn Specifically: s mn =s m→n +s n→m ; Among them, s mn is the population migration between node m and node n; s max is the maximum value of population migration between all pairs of nodes within the target area; s m→n is the number of population migrations from node m to node n; s n→m is the number of population migrations from node n to node m; w mn ∈[0,1].

7. The method for measuring regional risk of population loss in shrinking cities according to any one of claims 1 to 4, characterized in that: The clustering coefficient C of the node i corresponding to the target shrinking city in the population migration network i for: In imn =(in im In mn In in ) 1 / 3 ; Among them, k i is the neighborhood N i The number of nodes in the neighborhood N i is the set of other nodes connected to node i; where m∈N i ,n∈N i , and m≠n; w imn is the geometric mean of the weights of the edges between node i and node m and node n; w im is the weight of the edge between node i and node m; w in is the weight of the edge between node i and node n; w mn is the weight corresponding to the edge between node n and node m.

8. The method for measuring regional risk of population loss in shrinking cities as claimed in claim 3, characterized in that: The relative change rate of the clustering coefficient is used to measure the regional risk of population loss in the target shrinking city, specifically including: The relative change rate of the clustering coefficient corresponding to the current time section and the previous time section of the onset time is used as the regional risk of population loss of the target shrinking city at the current time section; Among them, the target shrinking city is in the time section T j The regional risk of population loss caused by the previous time section relative to the onset time for: in, To achieve the goal of shrinking the city in the time section T j The corresponding clustering coefficient is as follows; i is the node corresponding to the target shrinking city; To achieve the goal of shrinking the city in the time section T s-1 The corresponding clustering coefficient under T s-1 is the onset time T s The previous time section.

9. The method for measuring regional risk of population loss in shrinking cities as claimed in claim 3, characterized in that: The relative change rate of the clustering coefficient is used to measure the regional risk of population loss in the target shrinking city, specifically including: The relative change rate of the clustering coefficient corresponding to the current time section and any time section before the onset time is used as the regional risk of population loss of the target shrinking city at the current time section; Among them, the target shrinking city is in the time section T j The regional risk of population loss caused by any time section before the onset time for: in, To achieve the goal of shrinking the city in the time section T j The corresponding clustering coefficient is as follows; i is the node corresponding to the target shrinking city; To achieve the goal of shrinking the city in the time section T b The corresponding clustering coefficient under T b is the onset time T s Any previous time section.

10. A regional risk measurement system for population loss in shrinking cities, characterized in that: The system includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the method for measuring the regional risk of population loss in shrinking cities described in any one of claims 1 to 9 is executed.

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