Small World Network of Athletes--论文代写范文精选

日益增长的复杂网络，发现了很多有趣的模式和统计特性,对于主要跨学科研究，已被广泛接受,网络的系统分析和信息提取，可以用于进一步的见解和揭示。下面的paper代写范文进一步详述。

Abstract 
  The paper proposes an alternative way to observe and extract the multiple matches games of sports, i.e.: tennis tournament in the Athlete’s Historical Relative Performance Index and its representation as graph. The finding of the small world topology is elaborated along with further statistical patterns in the fashion of the weighted and directed network. The explanation of the sport tournament system as a highly optimized system is hypothetically proposed. Finally, some elaborations regarding to further directions of the usability of the proposed methodology is discussed. 
  Keywords: small‐world network, sports and tournaments, historical relative performance index of athletes

 Introduction 
  The role of network analysis has been somewhat becoming a very interesting topics, since this method allows us to see the circumstances of observed phenomena in a whole view (cf. Barabási, 2003). Network analysis has been employed to observe the interconnectedness of many things in our life where we can represent elements of the system as nodes and the connections between them as the edges. The growing works of complex network has discovered a lot of interesting patterns and statistical properties that invites major interdisciplinary researches (Albert & Barabási, 2002). It has been broadly accepted that network representation of system analysis and information extraction from wide varieties of data can be useful for further insights and to reveal complexities beneath the system.

  There have been a lot of application of this nature of analytical works observing social system, e.g.: stock market network visualizations (Situngkir, 2005), network of business and innovation (Khanafiah & Situngkir, 2006), political parties relations and inter‐ connection representation (Situngkir, 2004), and even more.   One of the most interesting fields with abundant data is the world of sports. Sports now cannot be separated with the modern life: not only for its use to keep us health and as good fields for learning about fairness and honesty, moreover, modern life has treated sports as a media of entertainment and even an important symbol of national pride of which citizens achieving high grade of international stage of sports.   

  The task represents in this report is an alternative to extract useful information in the world of sport with multiple matches and head‐to‐head game plays important role. The games in professional tennis is an interesting discourse with abundant availability of data and interesting statistics. In this short paper, we extract some of them1 , i.e.: the games of head‐to‐head games in Professional Tennis Tournament of Grand Slams held yearly with four games of tournaments (United States Open, Australian Open, Wimbledon, and French Open), all of them represents specifically different tennis court yard: the hard‐court, grass‐ court, and clay‐court respectively2 .   

  The paper is structured in the fashion of step‐by‐step observation of the matches in each tournaments in all of the sets of the games in the graph representation of un‐weighted and un‐directed, un‐weighted and directed, and eventually the weighted and directed graphs. In the next section, we describe the complex network of the interconnectedness of the world tennis players that interestingly reveals the so‐called small world topology. The next sections we analyze the statistical properties of the network and discuss things related to the tournament system and its highly optimizations that exhibits the power law distributions on some aspects in the professional tennis tournaments. The paper ends with some discussions on possible further directions to the analysis of games of sport and tournaments, and eventually to possible gain fruits from the proposed methodology.  

 The Topology of the Network of Athletes 
  In each tournament played, professional tennis players meet in the head to head game in the nature of the applied competition system. There is somehow a kind of path must be won by an athlete to the top of the rank. The score of each set of game, however, reflect the dynamics within the game: the way in which each opposing sides try to beat each other. As it will be described later in the next section, we build the athlete’s network by using the sum of all performance of all athletes in series of tournaments in the proposed historical performance index. The better a player perform relative to her opponents, the better values of the index she has in the global view. In this perspective, however, winning is not always representing the whole thing within a game: as a weaker player could resist in a tight game, it would interestingly resist her performance index relative to other athletes. First of first, our network of athletes would be in the term of whether or not a player ever met with other players. 

  A player is considered to be connected to other player if they have ever met in a game of tournament. The improvement and development of any tournament systems in the world of sports aims to preserve sets of the game that would only let the best player turns out to be the champion. There has been a lot of sports tournament system available and applicable today regarding to many constraints, e.g.: the length of the tournament season, etc (cf. Coakley, 1999). Most of the competitive system does not afford to let all players meet all other players, therefore from series of games in various tournaments, only the best players are connected to most numbers of other players.   For example, as the world professional tennis champion, Andre Agassi (USA) must have met large numbers of other players from around the world whose various skills and performances in order to be able to arrive at the grand final sessions and become the champion by winning the peak of the game in all of those tournaments.    

  Thus, the more connected athletes are the most likely to be the best players. However, qualitatively speaking this is plausible for their performance in the large numbers of internationally recognized games consequently give positive feedback to enhance their maturity in other games. The famous term of “the richer gets richer” somehow entitles another meaning by representation of the word “rich” as the “richness in experience” by performance in the official games of sport. We realize this by understanding that game of sports is a complex thing in the perspective of athlete. 

  The performance of sport is not merely calculable from the performance while in the training sessions but also dependent to their psychological circumstances as well as physiological ones. A good player is not only good at training field, but also in the middle of (must be faced) stress in the well‐recognized sport events. The best players perform the best respect to all intertwining aspects. However, this grows the interesting part of the world sport tournaments and become the complex sources of the uncertainty of the game result.   Our observation to this kind of network structure could bring us to two analytical parts: the global topology of the emerging network and the representation of the nodes and links in the graph. 

  If we consider the graph of athletes in a lot of tournaments, ΩS , as defined by (, ) Ω =S SS A E , where s , (i N =1, 2,..., ) is the set of N players and { } E ij = e is the connections between players who has ever met in one of a game in the series of tournaments. Here, we have a certain function (, ) ij i j e faa = , (, ) 0 i j faa ≠ indicates that there is a link between player i a and j a , and vice versa. We will discuss later about this function since in this section, our focus right now is on the topology of the players’ interconnectedness. In this simplistic case, the two connected players are adjacent and thedegree of a given player is the number of edges that connects it other players. We do the observation on the head‐to‐head game among world professional tennis male and female players in the Grand Slam from the year of 1980‐2006 and 1995‐2006 respectively. 

  Here, the Grand Slam world tennis championship are made by four once in a year tournaments, the Australia Open, Wimbledon Championship, French Open, and the US Open. Interestingly, from the glance view, we can see (fig. 1) that the yielded graph is highly clustered and likely short average paths between two players in the network. These two properties are well‐ known as the Small World graph topology.   Small world topology has been discovered in the representation of various complex network of the real world. Interdisciplinary works have revealed the similar network topology in biological and chemical networks (Alon, et. al., 1999), human language and the use of words in sentences (Cancho & Solé, 2001), scientific collaborative networks (Newman, 2001), transportation networks (Li & Cai, 2007), power grids (Watts & Strogatz, 1998), the world wide web (Albert, et. al., 1999), biological metabolism (Fell & Wagner, 2000), ecological and food‐web networks (Dunne, et. al., 2002), movie star collaborations (Amaral, et. al., 2000), web of human sexual contacts (Liljeros, et. al. 2001), and even more networks representations of the real world systems (Barabási, 2003).(paper代写)

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