Power-Law Distribution & Stock Markets

Basing their investigation on the hypothesis that trades made within large populations cause major fluctuations in the stock market investigators found, with the use of power laws, that they were able to closely analyze the fluctuations in stock prices, number of trades, and the size of the trades that occur. Interestingly, they found that the exponents  used to represent various types of markets were similar for all of those varying markets, even for those markets that are in other countries. Two of the many equations used in there investigation were to be applied to the US stock. However, they decided to use equations (2) and (3) for the Paris Bourse, the French stock exchange, and lead it them to some interesting conclusions.

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Initially they applied these equations to the evaluation of 35 million transactions within the 30 biggest stocks in the Paris Bourse between the years 1994 and 1999. They learned that the power laws that were specifically for the US stock market also held for a foreign market. It also showed that equations (2) and (3) could be Universal.

Additionally, they showed that the power laws used in the financial data came about when the trading was conducted in an optimal manner. They also demonstrated the relationship between fluctuations in prices and the number of trades performed.

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The graph above demonstrates the collective distributions of the returns from 1,000 of the largest countries between the period 1994-1995. You can see that this bared a slight resemblance to the graph for the power-law distribution of Web-page links, as it is linear and downward sloping.

Gabaix, Xavier, et al. “A theory of power-law distributions in financial market fluctuations.” Nature 423.6937 (2003): 267+. General OneFile. Web. 21 Apr. 2016.

Link to Source


Social Network Sites & Advertising


       Since the rise of social network sites, such as Facebook and Twitter the majority of the population communicate and interact through the internet. Although, the greater part of these social networks are free for the users these networks obtain almost all their revenue from allowing companies to advertise on their own sites. Social network advertising is effective because advertisers track the searches made by social network users prior to their purchase.

        Data collected by an offline survey of 200 university students exhibited the positive correlation between the pre-purchase searches made by these students and their reactions to social network advertising. The study also revealed that the positive viewpoint of social networks sway them to click on the ads they feature. Because these students practiced their ad-clicking behavior they proved the effectiveness of these ad banners. It was also shown that users depend on social network sites to obtain more information on an item they are interested in.

       It stands to reason that with the considerable use of social network sites companies seeking to improve their marketing should acquire deals with social networks as a place to display their ad banners. Having said that, this is where search engine companies like Google and Bing come in because they sells the advertising rights for various keywords to other businesses through auctions. For these search engines keyword-based advertising is how they, like social network sites, make their money. Search engines use base their auctions on second-price auctions, like the Vickrey-Clarke-Groves mechanism, as ways to set prices for keyword-based advertising. Ultimately, researchers hope to duplicate this study and look into the other demographics, other than young university students, to see if their findings still hold or if more can be learned about the relationship between social network sites and advertising.


A, Mir A. “Effects of Pre-Purchase Search Motivation on User Attitudes Toward Online Social Network Advertising: A Case of University Students.” Journal of Competitiveness 6.2 (2014)ProQuest. Web. 30 Mar. 2016.  

The Networks In Our Body

       A study investigating the naturally evolving networks within our bodies proposed that homophyly and kinship play a fundamental part in natural networks and their individual fitness.  The idea behind the homophyly and kinship principle is that a large network or natural community will share nodes with other natural communities. Homophily specifically, refers to the tendency for one to share characteristics with individuals they bond with. In these events nodes from one community acquire the chance to obtain benefits or information from those other natural networks.

      Basing their algorithm on the fitness of networks they found that networks of cells share the same characteristics. They determined various properties for these natural networks inside of our bodies some of which are leadership and external de-centrality. Leadership refers to the leading nodes within a community who have many connections to other nodes within the area. External de-centrality is the idea that neighbors from one community are at times found in different communities. This is similar to the concept of social affiliation networks, which are connections between nodes and social foli. In the case of the human body these social affiliation networks would be the interactions of proteins and the network of tissue cells.

     By using network theory concepts they were able to have an incredible breakthrough. They found that using their algorithm would allow them to decipher the unique gene set for every unit of cells within the network of tissue in our body. With this ability they could calculate the survival time or fitness of these cells and accurately recognize the functions of the natural networks. Their algorithm also passed the evaluation for the classification of cancers.



Smoking or Nonsmoking?

Previous research has been conducted investigating the correlation between Fraternity members and the influence of peers which, has lead to the development of negative habits such as alcohol consumption and cigarette smoking. The behavioral habits of Greek life participants are widely seen as normal despite the harmful effects and prevalence of their excessive ingestion of chemicals. One of the studies carried out focused on a group of 34 fraternity members at a University in the Southwestern area of the U.S. These members, through a longitudinal study, were asked various questions relating to their associations within the fraternity and their smoking habits. The inquiries about their habits mainly focused on the number of packs they smoked, the likelihood of quitting, and whether they were more likely to smoke among other smokers than if they were alone. The results of the study showed that in the first interval of questioning 52.9% of the members said that they were more likely to smoke when hanging with friends who also smoked, whereas the following interval showed an increase to 58.8%. The network graph below, labeled figure 1,was constructed by the investigators and shows the relationships between smoking and nonsmoking fraternity members. The Red squares represent the smokers of the group and the blue circles represent the nonsmokers. The network shows a cluster effect within the fraternity, generally smokers befriend smokers and nonsmokers befriend nonsmokers. However, one node in particular, node 20, represents a nonsmoker who, fascinatingly enough is very much connected to the main group of smokers within the fraternity. Despite that minor inconsistency this network supports the common conception that since smoking is normally a social activity people are more likely to associate themselves with people who share the same tendencies. Unfortunately, the more popular a member is within the fraternity the more likely they will be able to influence the other members with their behavior. By their actions these members promote the idea of smoking and set standards that lead to an increase in the number of smoking members. Nevertheless, the network analysis of these groups can provide us with a better idea of how social networks such as fraternities work and how we could counteract these negative habits.

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Figure 1. 



Phua, Joe. “The Influence of Peer Norms and Popularity on Smoking and Drinking Behavior Among College Fraternity Members: A Social Network Analysis.” Social Influence 6, no. 3 (2011): 153. Accessed January 19, 2016. doi:10.1080/15534510.2011.584445.