A social media network topic heat evaluation method

Abstract

The application provides a social media network topic heat evaluation method, comprising the following steps: S1, obtaining user stickiness; S2, obtaining topic activity; S3, obtaining topic persistence; S4, obtaining topic freshness; S5, obtaining media attention of the topic; S6, obtaining heat and influence effectiveness evaluation model-energy value model of the topic according to the user stickiness, topic activity, topic persistence, topic freshness, media attention and topic heat decay ratio of the topic. The application comprehensively considers the user stickiness, topic activity, topic persistence, topic freshness, media attention and topic heat decay ratio, and constructs a more comprehensive and reasonable public opinion influence effectiveness evaluation model, so that the heat of the network topic in the social media platform can be better evaluated. Meanwhile, the topic concerned by people can be accurately found, and the hot topic can be screened.

Description

Technical Field

[0001] This invention relates to the technical field of acquiring original topic datasets and evaluating topic popularity, specifically to a method for evaluating the popularity of topics on social media networks. Background Technology

[0002] Due to the rapid development of information technology and the widespread use of the internet, people's primary ways of obtaining information have gradually changed. Social media is one of the most important information dissemination platforms in today's society, reflecting public concerns and values. Online topics are a special form of information on social media, typically composed of one or more keywords, capable of sparking discussion and interaction among netizens. Assessing the popularity of online topics is the process of quantifying and analyzing the influence and reach of online topics on social media. It helps us understand the formation mechanism, dissemination patterns, and social effects of online topics. For media and website administrators, assessing the popularity of online topics on social media allows for effective understanding of the migration of trending news, changes in internet user behavior, and the direction of public opinion. This facilitates media outlets in publishing news reports based on reader preferences and trending topics, guiding and controlling the development of public opinion online. Simultaneously, it allows website administrators to intervene and manage online content based on public opinion trends. For users, assessing the popularity of online topics on social media provides a more convenient and comprehensive way to access the most comprehensive content, helping them understand the ins and outs of an event, its entire development process, and the understanding and opinions of various parties involved. For governments and businesses, assessing the popularity of topics on social media allows them to promptly grasp public opinion, public sentiment, and market dynamics, enabling timely adjustments to public policies and marketing strategies. This strengthens communication and trust with the public, effectively enhancing the image and reputation of governments and businesses. Therefore, researching methods for assessing the popularity of topics on social media is essential.

[0003] Traditional methods for assessing influence primarily employ the TF-PDF trend analysis algorithm, which considers the impact of media attention on a topic. However, relying solely on this factor is insufficient. While later algorithms have improved trend analysis by incorporating user engagement with the topic, this approach remains unsuitable for all domains. Summary of the Invention

[0004] This invention aims to provide a method for evaluating the popularity of social media topics, in order to solve the above problems.

[0005] The technical solution of this invention is: a method for evaluating the popularity of social media network topics, comprising:

[0006] Step S1: Analyze user behavior data based on the number of reposts, comments, and likes of the topic to obtain user stickiness;

[0007] Step S2: Obtain the topic activity level based on the proportion of articles related to the topic to all articles on the topic, and the number of articles generated within a unit of time.

[0008] Step S3: Divide the discussion time into units, and obtain the topic persistence based on the total number of units in which the topic is discussed within a fixed time.

[0009] Step S4: Obtain the topic freshness based on the time unit difference between the current time and the time when the topic was first published on the social media platform;

[0010] Step S5: Gain media attention based on the frequency of media coverage of the topic;

[0011] Step S6: Based on the topic's user stickiness, topic activity, topic persistence, topic freshness, media attention, and the proportion of topic popularity decline, obtain the topic's popularity and influence effectiveness evaluation model, namely the energy value model.

[0012] Preferably, S1 obtains user engagement based on the number of likes, shares, and comments on a topic within a certain period of time:

[0013] The energy value function is constructed as follows:

[0014] (1)

[0015] In equation (1), Indicates the topic. , , Each represents a topic The number of likes, shares, and comments within a certain period of time. , , These represent the number of likes, shares, and comments for all topics during that period, respectively, where e is a natural constant.

[0016] Preferably, S2 obtains the topic activity level based on the proportion of topic-related articles to all topic articles and the number of articles generated within a unit of time, including:

[0017] The proportion of articles related to a specific topic out of all articles on that topic. The energy value is quantified by the number of articles produced per unit time, and the energy value function is:

[0018] (2)

[0019] in, This indicates the number of articles related to the topic. This represents the total number of articles across all topics. It indicates the duration of a topic, that is, the interval between the time when the topic was last discussed and the time when it was first discussed, and is the same unit as a time slice.

[0020] Preferably, S3 divides the discussion time into units, and obtains the topic persistence based on the total number of units in which the topic is discussed within a fixed time, including:

[0021] The energy value function is constructed as follows:

[0022] (3)

[0023] In the formula, This indicates the number of time units in which the topic was reported and discussed, in days. If the number of days is not 0 and the number of hours is less than 12, then the portion less than 12 hours is counted as 1 day. This represents the total number of time units into which the entire time period is divided.

[0024] Preferably, S4 obtains the topic freshness based on the time unit difference between the current time and the time the topic was first published on the social media platform, including:

[0025] Constructing the energy value function:

[0026] (4)

[0027] In the formula, It is the difference in time units between the current time and the time when the topic was first published, in days; The rate of decline is measured by the number of comments on the topic; that is, when the number of comments decreases, it indicates that the topic's popularity is declining more and more.

[0028] Preferably, S5 gains media attention based on the frequency of topic coverage in authoritative media, including:

[0029] Construct the energy value function:

[0030] (5)

[0031] In the formula, , This is the ratio of the number of reports on this topic to the total number of reports. The rate of decline.

[0032] Preferably, S6 obtains a topic popularity and influence effectiveness evaluation model, i.e., an energy value model, based on user stickiness, topic activity, topic persistence, topic freshness, media attention, and the proportion of topic popularity decline, including:

[0033] Define the natural decline of topic popularity using a decay function:

[0034] (6)

[0035] In the formula, The decay rate is given by e, the natural constant, and t, which is time.

[0036] Define user attention as Then we have:

[0037] (7)

[0038] in, Indicate topic The number of comments within a certain period of time The number of comments for all topics within that time period;

[0039] Since a higher user engagement level indicates more interested users, the decay rate... The smaller it will be, therefore The following two conditions must be met:

[0040] (1) It is about A decreasing function;

[0041] (2)

[0042] Therefore, let

[0043] (8)

[0044] The heat decay ratio function is:

[0045] (9)

[0046] If the time interval between topics is set to 1 day, then the heat energy value of topic j after day d is... It indicates the topic The generated from day 1 to day 2 The energy accumulated over the days decays to the [number]th [day]. The energy value of the day and the first The sum of the energy values ​​of the heavens;

[0047] Then we have:

[0048] (10)

[0049] In the formula:

[0050] :topic Total number of likes Total number of likes for all topics;

[0051] :topic Total number of reposts Total number of reposts for all topics;

[0052] :topic Total number of comments Total number of comments for all topics;

[0053] The number of articles related to the topic. : Total number of articles across all topics;

[0054] Topic persistence refers to the interval between the last time a topic is discussed and the first time it is discussed, and is measured in the same unit as a time slice.

[0055] : The number of time units in which the topic was reported and discussed;

[0056] The total number of time units into which the entire time period is divided;

[0057] : The difference in time units between the current time and the time the topic was first published;

[0058] .

[0059] The beneficial effects of this invention are as follows:

[0060] This invention integrates user engagement, topic activity, topic persistence, topic freshness, media attention, and the rate of topic popularity decline to construct a comprehensive and reasonable evaluation model for the effectiveness of public opinion influence. This allows for a better assessment of the popularity of online topics on social media platforms. Simultaneously, it can accurately identify topics that people are paying attention to and discussing, and filter trending topics. Therefore, it can quantify and analyze the influence and reach of online topics on social media, achieving the goal of monitoring online content. Attached Figure Description

[0061] Figure 1 A flowchart of a method for evaluating the popularity of social media network topics provided in an embodiment of the present invention;

[0062] Figure 2 A flowchart of an algorithm for evaluating the popularity of social media network topics provided in an embodiment of the present invention. Detailed Implementation

[0063] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. The embodiments of the present invention are not limited thereto.

[0064] This invention proposes a comprehensive method for evaluating the popularity of topics on social media networks, integrating user engagement, topic activity, topic persistence, topic freshness, media attention, and the rate of topic popularity decline. It also constructs a more comprehensive and reasonable model for evaluating the effectiveness of public opinion influence. This method and model address the following problem: While it's impossible for people to browse and read all topics, numerous topics are generated on the internet every moment. Users primarily want to see topics with high public attention and significant news value. The proposed method and model analyze multiple dimensions, quantifying them into different indicators and constructing energy value functions for each indicator. Finally, the total energy value of each topic is used to rank them; topics with higher scores are more likely to be currently trending topics. Firstly, the most direct indicator for assessing the level of attention a topic receives is the number of likes, shares, and comments on articles related to that topic. User engagement with the topic can be obtained through user behavior data. The more likes, shares, and comments users receive on articles related to that topic, the higher the user engagement, and the more likely the topic is to be a trending topic. If a topic generates a large number of articles and reports in a short period of time, and the proportion of articles related to that topic in the total number of articles continues to rise, it indicates that the topic's activity level is increasing. The higher the activity level of a topic at any given time, the greater its popularity. Therefore, topic activity level is also one of the indicators for assessing topic popularity. The longer users discuss and pay attention to a topic, the greater the public's interest in that topic, which also reflects its popularity. Furthermore, some topics are not discussed every day; they may have periods of time when discussion occurs. In such cases, the discussion time is divided into units, and the total number of time units in which the topic is discussed is used as an indicator of topic popularity. The longer users discuss a topic, the greater their contribution to its popularity. Topic freshness refers to whether a topic or event appears relatively recently, i.e., whether the topic or event has recently attracted public attention. The higher the topic freshness, the more timely and novel the topic is likely to be, attracting more attention. Hot topics have a life cycle, going through a process from "generation" to "extinction." As time goes by, old topics are gradually replaced by new ones, and new topics emerge. Therefore, the further removed a topic is from the present moment, the older it is, and the less impact it has on users, resulting in lower popularity. Conversely, newer topics tend to have higher activity levels and more related articles, attracting users and potentially becoming trending topics. Media attention has a significant impact on popularity assessment. Media attention directly reflects the social influence and level of attention an event or topic receives. Media reports can expand the reach of an event or topic, increase exposure, and thus stimulate more discussion and participation, thereby increasing its popularity.Trending topics have a life cycle, going through a process from "emergence" to "extinction." The popularity of a topic typically only lasts for a period of time, especially for specific events and current issues. After a while, people's focus quickly shifts to the next event or topic, and this decline in popularity also affects the assessment of its popularity.

[0065] In user engagement, "users" refers to those who use online social media. User participation refers to user actions such as browsing, liking, commenting, and sharing on a particular topic. This level of user participation reflects the topic's popularity, speed of dissemination, scope of spread, and degree of influence among the public. If users like a topic, they may express their support and emotions by liking it. Especially for controversial topics, the number of likes is an important indicator of popularity, showing whether most users support or oppose the topic. The number of comments is also a useful parameter for measuring topic popularity. This indicates that users are more willing to spend time participating in discussions and expressing their opinions, and have a greater voice. When content that users are interested in is shared on their personal pages and among their followers, it is more likely to spread and attract more people to participate in the discussion. Therefore, for a trending topic, the number of shares can reflect its engagement and popularity on social media. The number of participants is a powerful indicator of a topic's popularity. If a trending topic can attract a large number of users to share, comment, and like it, its influence will be more significant.

[0066] In Weibo's popularity and influence assessment, topic activity refers to the measurement of the scale and breadth of discussion about a topic within a specific time period. Generally speaking, the higher the activity of a topic, the more attention and discussion it has attracted on social media. If the number of articles related to a topic accounts for a larger proportion of the total number of articles, it indicates a greater influence of the topic. When one topic generates a large number of related articles in a short period, while another topic generates only a few, the former is more popular than the latter. When a topic generates a large number of articles, but these are distributed over a considerable period, the average number of articles per unit of time is small, and the topic's popularity is lower than other topics that generate a large number of articles. By monitoring and analyzing topic activity, we can better understand user sentiment and needs, thus providing a reference for brand marketing, public opinion management, and other fields. Therefore, the topic activity is obtained by calculating the proportion of articles related to a particular topic to all articles on all topics, and the number of articles generated per unit of time for that topic.

[0067] In topic popularity assessment, topic persistence refers to the length of time a topic continues to receive attention and discussion. It's also a crucial indicator of a topic's popularity. Topic persistence refers to the period from when a topic begins to spread widely until user attention begins to decline. The longer a topic is discussed and followed by users, the more interested they are. Furthermore, some topics aren't discussed daily; they may have periods of peak activity. Therefore, dividing discussion time into units, the total number of time units occupied by a topic determines its persistence. More units contribute more to the popularity score and may attract more user participation. Generally, if a topic continues to be discussed and shared by users, its popularity assessment will be higher. Conversely, if a topic is quickly forgotten by users, its popularity assessment will be lower. Therefore, topic persistence is one of the important factors in measuring a topic's popularity.

[0068] In the evaluation of topic popularity and influence, topic freshness refers to whether a topic or event has recently attracted public attention. Higher topic freshness indicates that the topic is likely to be timely and novel, thus attracting greater public attention. Topics go through a process of emergence, development, peak, decline, and demise in their life cycle. As time passes, old topics are gradually replaced by new ones, the number of articles related to old topics decreases, while the number of new topics increases. As old topics fade from memory, the public pays more attention to the development of new topics. Therefore, the further removed a topic is from the present moment, the smaller its impact on users and the lower its popularity value. Conversely, newer topics tend to have higher activity levels and more related articles, attracting users and potentially becoming trending topics.

[0069] In topic popularity assessment, "media attention" refers to the degree of exposure and frequency of reporting on a particular topic or event in authoritative media (such as news media). Media attention has a significant impact on popularity assessment. It directly reflects the social influence and level of attention garnered by an event or topic. Media reports can expand the reach of an event or topic, increase its exposure, and thus stimulate more discussion and participation, thereby increasing its popularity score.

[0070] The media in media attention refers to various mainstream media, such as Sina, Xinhua Net, Phoenix Net, People's Daily, etc. With the rapid development of the information age, people's ways of obtaining information have changed from the original letters and newspapers to television, computers and mobile phones. The content published by up-masters with a large number of fans and large news reporting websites generally has a higher popularity, and they can be reposted by each other. It is not necessarily all original. Ordinary users generally pay more attention to the content published by these up-masters, and the popularity will be higher.

[0071] On social media platforms like Weibo, the popularity of a topic typically lasts only a limited time, especially for specific events and current affairs. After a while, people's focus quickly shifts to the next event or topic. This decline in popularity can negatively impact the assessment of trending topics. Failing to consider the timeliness of a topic can lead to significant deviations in the assessment results. Therefore, in assessing the popularity of a topic, it is necessary to consider its timeliness and update relevant algorithm models promptly to more accurately evaluate its popularity and influence.

[0072] Example 1

[0073] like Figure 1 and Figure 2 The diagram shown is a flowchart and an algorithm flowchart of the present invention.

[0074] This invention is based on the current mainstream social networking media platform—Weibo platform—to conduct method research. The following content provides an embodiment of this invention to demonstrate the verification of this method.

[0075] I. Data Collection

[0076] The dataset used in this experiment was crawled from various bloggers on Weibo, specifically from three topics on Weibo from April 4th to April 11th, 2023. The crawled data included the dimensions required for the methodology, such as likes, comments, reposts, source, and author, totaling over ten thousand data points. The three topics were designated "Topic 1," "Topic 2," and "Topic 3." The relevant data was stored in a MySQL database. The data format in the database is as follows: Figure 2 As shown.

[0077] II. Experimental Procedure

[0078] 1. Calculate user stickiness

[0079] According to the description in algorithm a, after collecting the dataset, the relevant articles for each topic are clustered together, and the total number of likes, reposts and comments for each topic are calculated to obtain the energy value function of user stickiness.

[0080] 2. Calculate topic activity level

[0081] According to the description in algorithm b, the energy value of topic activity is quantified by the proportion of articles related to the topic to all articles and the number of articles per unit time.

[0082] 3. Calculate the persistence of the topic.

[0083] According to the description in algorithm c, the discussion time is divided into units, and the energy value function of the topic's persistence is obtained based on the total number of time units in which the topic is discussed and reported within a fixed time.

[0084] 4. Calculate the topic's freshness.

[0085] According to the description in algorithm d, the energy value function of the topic freshness is obtained based on the time unit difference between the current time and the time when the topic was first published on the social media platform.

[0086] 5. Calculate the media attention given to the topic.

[0087] According to the description in algorithm e, based on the frequency of reports on the social topic in authoritative media (such as news media), that is, the ratio of the number of articles reported on the topic to the total number of articles on all topics, the energy value function of the media attention of the topic is obtained.

[0088] 6. Calculate the total topic popularity value based on the popularity decay ratio function.

[0089] According to the description in algorithm f, the popularity of a topic at a certain moment will be affected by the influence of other moments on the current moment. The closer to the current moment, the greater the influence. Therefore, the popularity of a topic has a natural decline phenomenon. Based on the number of users paying attention, the decline ratio function of the topic popularity is calculated.

[0090] Finally, calculate the total energy value of the topic to obtain its current popularity.

[0091] Taking topic 1 as an example, the number of likes, reposts, comments, number of articles related to the topic, and the topic's publication time are shown in Table 1.

[0092] Table 1. Statistics of Original Topic Data

[0093] topic Hot topic names Top 10 Likes Topics are always forwarded Total comments on the topic Number of articles on the topic Topic posting time 1 Topic 1 1443216 26512 62132 312 04-04

[0094] III. Experimental Results and Analysis

[0095] The results of the algorithm model are shown in Table 2. Table 2 lists the topic names of the three collected topics, the topic popularity obtained through the algorithm model, and the change in popularity over seven days.

[0096] Table 2 Results of the Algorithm Model

[0097] topic Day 1 the next day Day 3 Day 4 Day 5 Day 6 Day 7 Topic 1 13.10 10.79 9.35 8.36 7.63 7.07 6.61 Topic 2 3.22 2.63 2.28 2.04 1.86 1.72 1.61 Topic 3 38.10 55.73 54.47 50.34 46.38 43.06 40.31

[0098] The topic popularity assessment proposed in this invention primarily evaluates topic popularity based on several dimensions, including user engagement, topic activity, topic persistence, topic freshness, media attention, and the rate of topic popularity decline. In the embodiments of this invention, three topics are involved. Over time, the popularity of topics 1 and 2 showed a downward trend and low popularity values, indicating that these two topics were gradually losing public attention. The popularity of topic 3 showed an upward trend in the first three days and a high popularity value, indicating that topic 3 was in the stage of public opinion fermentation at that time and was a topic of close public attention and discussion. All three topics conform to the actual state and trend of topic popularity at that time, demonstrating that the method and model in this invention accurately assessed the changes in the popularity of online topics. Therefore, based on all the data for each topic and the results of the method and model, the popularity assessment model and method proposed in this invention have a certain degree of effectiveness and accuracy.

[0099] In summary, the present invention provides a method for evaluating the popularity of social media topics, comprising: analyzing user behavior data based on the number of reposts, comments, and likes of a social topic on a social network to obtain user stickiness; obtaining the activity level of a topic based on the proportion of articles related to the topic to all articles on the topic, and the number of articles generated within a unit of time; dividing the discussion time into units and obtaining the persistence of the topic based on the total number of units discussed within a fixed time; obtaining the freshness of the topic based on the time unit difference between the current time and the time when the topic was first published on the social media platform; obtaining the media attention of the topic based on the frequency of reports on the social topic in authoritative media (such as news media); and obtaining a popularity and influence effectiveness analysis model—an energy value model—based on the above characteristic indicators of the topic and the popularity decline ratio of the topic. This method integrates user stickiness, topic activity, topic persistence, topic freshness, media attention, and the popularity decline ratio to construct a more comprehensive and reasonable public opinion influence effectiveness evaluation model, thereby better evaluating the popularity of online topics on social media platforms. At the same time, it can accurately identify the topics that people are concerned about and discussing, and filter the hot topics. Therefore, it can quantify and analyze the influence and spread of online topics on social media, so as to achieve the purpose of monitoring online content.

[0100] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the processes depicted in the drawings are not necessarily essential for implementing the present invention.

Claims

1. A method for evaluating the popularity of social media online topics, characterized in that, include: Step S1: Analyze user behavior data based on the number of reposts, comments, and likes of the topic to obtain user stickiness; Step S2: Obtain the topic activity level based on the proportion of articles related to the topic to all articles on the topic, and the number of articles generated within a unit of time. Step S3: Divide the discussion time into units, and obtain the topic persistence based on the total number of units in which the topic is discussed within a fixed time. Step S4: Obtain the topic freshness based on the time unit difference between the current time and the time when the topic was first published on the social media platform; Step S5: Gain media attention based on the frequency of media coverage of the topic; Step S6: Based on user engagement, activity level, persistence, freshness, media attention, and the rate of decline in popularity, obtain the topic's popularity and influence effectiveness evaluation model, i.e., the energy value model; where, S6 derives a topic's popularity and influence effectiveness evaluation model, or energy value model, based on user engagement, activity level, persistence, freshness, media attention, and the rate of decline in popularity. This model includes: Define the natural decline of topic popularity using a decay function: (6) In the formula, Let e ​​be the decay rate, t be the natural constant, and t be time, where t ≥ 0; Define user attention as Then we have: (7) in, Indicate topic The number of comments within a certain period of time The number of comments for all topics within that time period; Since a higher user engagement level indicates more interested users, the decay rate... The smaller it will be, therefore The following two conditions must be met: (1) It is about A decreasing function; (2) Therefore, let (8) The heat decay ratio function is: (9) If the time interval between topics is set to 1 day, then the heat energy value of topic j after day d is... It indicates the topic The generated from day 1 to day 2 The energy accumulated over the days decays to the [number]th [day]. The energy value of the day and the first The sum of the energy values ​​of each day, t≥0; Then we have: (10) In the formula: :topic Total number of likes Total number of likes for all topics; :topic Total number of reposts Total number of reposts for all topics; :topic Total number of comments Total number of comments for all topics; The number of articles related to the topic. : Total number of articles across all topics; Topic persistence refers to the interval between the last time a topic is discussed and the first time it is discussed, and is measured in the same unit as a time slice. : The number of time units in which the topic was reported and discussed; The total number of time units into which the entire time period is divided; : The difference in time units between the current time and the time the topic was first published; 。 2. The method for evaluating the popularity of social media online topics according to claim 1, characterized in that, S1 assesses user engagement based on the number of likes, shares, and comments a topic receives over a specific period. The energy value function is constructed as follows: (1) In equation (1), Indicates the topic. , , Each represents a topic The number of likes, shares, and comments within a certain period of time. , , These represent the number of likes, shares, and comments for all topics during that period, respectively, where e is a natural constant.

3. The method for evaluating the popularity of social media online topics according to claim 1, characterized in that, S2 calculates topic activity based on the proportion of topic-related articles to all topic articles, and the number of articles generated within a unit of time. This includes: The proportion of articles related to a specific topic out of all articles on that topic. The energy value is quantified by the number of articles produced per unit time, and the energy value function is: (2) in, This indicates the number of articles related to the topic. This represents the total number of articles across all topics. It indicates the duration of a topic, that is, the interval between the time when the topic was last discussed and the time when it was first discussed, and is the same unit as a time slice.

4. The method for evaluating the popularity of social media online topics according to claim 1, characterized in that, S3 divides discussion time into units and obtains topic persistence based on the total number of units in which a topic is discussed within a fixed time, including: The energy value function is constructed as follows: (3) In the formula, This indicates the number of time units in which the topic was reported and discussed, in days. If the number of days is not 0 and the number of hours is less than 12, then the portion less than 12 hours is counted as 1 day. This represents the total number of time units into which the entire time period is divided.

5. The method for evaluating the popularity of social media online topics according to claim 1, characterized in that, S4 calculates the topic's freshness based on the time difference between the current time and the time the topic was first posted on the social media platform, including: Constructing the energy value function: (4) In the formula, It is the difference in time units between the current time and the time when the topic was first published, in days; The rate of decline is measured by the number of comments on the topic; that is, when the number of comments decreases, it indicates that the topic's popularity is declining more and more.

6. The method for evaluating the popularity of social media online topics according to claim 1, characterized in that, S5 gains media attention based on the frequency of topic coverage in authoritative media outlets, including: Construct the energy value function: (5) In the formula, , This is the ratio of the number of reports on this topic to the total number of reports. The rate of decline.

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