The uncertainty is fundamentally epistemic, includes incertitude, in the sense of lack of certainty about the parameter. The model bias becomes an equivalent of the Jensen gap (the difference between the two sides of Jensen's inequality), typically p
Dec 29, 2015 - In Section 3, we will discuss how to infer such a probability distribution for both binary and real-valued data matrices. Problem Statement Given a multi-relational dataset, a bicluster chain across multiple relations de- scribes a pro
Dec 29, 2015 - Abstract. Modern visual analytic tools promote human-in-the-loop analysis but are limited in their ability to direct the user toward interesting and promising directions of study. This problem is especially acute when the analysis task
SIMPLE FIT OF DATA RELATING SUPERMASSIVE BLACK HOLE MASS TO. GALAXY PITCH ANGLE. Harry I. Ringermacher. General Electric Global Research Center, Schenectady, NY 12309. AND. Lawrence R. Mead. Dept. of Physics and Astronomy, University of Southern Miss
Sep 4, 2008 - DSS. IC 342. SABcd. 33 Â± 3. < 5.0 Ã 105. (5). 37.â¦1 Â± 1.â¦3. R. DSS. NGC 1068. SAb. 151. (2.0 Â± 1.0) Ã 107. (6). 17.â¦3 Â± 2.â¦2. R. LCO 2.5-m. NGC 3227. SABb. 128 .... been determined from the bulge central velocity dispersio
between unrelated sets of entity sets of structured data sources. Gowri Shankar ... Linking data within structured data sources i.e. relational tables relies on referential integrity constraints introduced during the design. But less has been thought
Jan 31, 2014 - (12.755, 0.152). An IPython Notebook and raw Python file of all examples is included in Supporting Information. ... PDFs require binning of the data, and when presenting a PDF on logarithmic axes the bins should have .... in neuroscien
Jul 15, 2014 - employees of any business are responsible for 80% of productive output or 20% of all people own 80% of all wealth. .... xi xmin. ] â1. (6) where xi are the observed data values and xi â¥ xmin (Muniruzzaman, 1957). The discrete. MLE
(2000) and it was identified as a possible coun- terrotator by ..... Noeske, K. G., Papaderos, P., CairÃ³s, L. M., & Fricke, K. J. 2003, A&A, submitted. Silich, S. A. ...
Feb 5, 2018 - 3Cornell Center for Astrophysics and Planetary Science and Department of Astronomy, Cornell University, Ithaca, NY 14853, USA. 4Dept. of Physics and .... Green Bank Telescope to observe PSR J1946+2052 at. 820 MHz using GUPPI ... To prop
We present spectra of QSOs 1343+266A, B, covering Ly to C IV emission at 2 A res- olution, and nd further evidence that this system is not gravitationally lensed.
being performed, and the specific epistemological criteria being brought to bear . From these works we can plausibly ..... internal energy plus work minus heat.â The interviewer asks if this was ..... the physics task prompt from the worksheet
Â¶Present address: Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia,. V6T 1Z1 Canada. #Present address: ...
Sep 15, 2010 - 1Spitzer Science Center, California Institute of Technology, Mail Code 220-6, 1200 East California Blvd., ... We call these stars WMD47â and WMD48â, after their designations in Wachter et al. (2010); they corre- spond to stars 2MAS
Mar 20, 2013 - In our derivation, we first determine sensitivity in terms of a number of counts (analogous to S0) and then ..... ison of an upcoming experiment with previously reported experimental limits. The average-limit ... however, we cannot con
Nov 23, 2015 - Optically bright, wide separation double (gravitationally lensed) quasars can be easily mon- itored, leading to light curves of great importance in determining the Hubble constant and other cosmological parameters, as well as the struc
Oct 17, 2017 - neutrinoless double beta (0Î½Î²Î²) decay in 136Xe with a target half-life sensitivity of approximately. 1028 years using 5 Ã 103 kg of ..... save computing time, a subset of daughters of the 238U and 232Th chains are simulated ..... 1
May 21, 2010 - 1, DAVID L. KAPLAN. 2,3 , AVI SHPORER. 1,4, LARS BILDSTEN. 1,2, AND STEVE B. ..... 900. 30. 60. R. Vel. (km/s). Error Bar. 0. 200. 400. Radial. V elo city. (km/sec). 2010-02-02. 2010-02-04. Error Bar. â0.2. 0.0. 0.2. 0.4. 0.6. 0.8. 1
Nov 14, 2013 - and a digital spectrometer provided a bandwidth and res- olution of 1 GHz and 61 kHz, which ..... by the Besancon model. The simulated colorâmagnitude diagrams are in excel- lent agreement with the IRSF ..... centers is a common sign
Aug 21, 2012 - Department of Physics and Astronomy, Camosun College, Victoria, British Columbia & Interna- tional Statistics and Research Corporation, Brentwood Bay, British Columbia, Canada. A. Kunder. Cerro Tololo Inter-American Observatory, La Ser
were introduced to solve this problem. Among related works, one idea used Genetic Algorithms (GA) to design constant weight codes. , another one used GA for searching the minimum distance of. BCH code . Lacan et al.  introduced Genetic algor
Jan 14, 2013 - upcoming Planck data, has deep implications on the discovery of the nature of neutrinos. In particular, the ... opportunity to observe Î²Î²0Î½ events, and their combined discovery potential is quite large. The next ..... collaboration
Oct 17, 2017 - The resulting PDF normal- izations ..... In the post-simulation reconstruction code, energy res- olution is applied through ..... fSS j . These parameters are fit, rather than being fixed, to accommodate the uncertainty the final nEXO
Feb 22, 2014 - we call this generator of Z/n by Ï. Then there exists a bijective ... of Ï (an integer by which the center of GLmn(C) which is CÃ operates on Ï), and if zi are the central characters of Ïi, then we ..... at San Diego hosted by Wee
Clarifying the Role of Distance in Friendships on Twitter: Discovery of a Double Power-Law Relationship Won-Yong Shin, Jaehee Cho, and Andr´e M. Everett
arXiv:1510.05763v1 [cs.SI] 20 Oct 2015
Abstract This study analyzes friendships in online social networks involving geographic distance with a geo-referenced Twitter dataset, which provides the exact distance between corresponding users. We start by introducing a strong definition of “friend” on Twitter, requiring bidirectional communication. Next, by utilizing geo-tagged mentions delivered by users to determine their locations, we introduce a two-stage distance estimation algorithm. As our main contribution, our study provides the following newly-discovered friendship degree related to the issue of space: The number of friends according to distance follows a double power-law (i.e., a double Pareto law) distribution, indicating that the probability of befriending a particular Twitter user is significantly reduced beyond a certain geographic distance between users, termed the separation point. Our analysis provides much more fine-grained social ties in space, compared to the conventional results showing a homogeneous power-law with distance. Index Terms Befriend, Bidirectional Friendship, Double Power-Law, Geo-Tagged Mention, Separation Point, Twitter
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2054577). W.-Y. Shin is with the Department of Computer Science and Engineering, Dankook University, Yongin 448-701, Republic of Korea (E-mail: [email protected]). J. Cho is with the Department of Business Administration, Kwangwoon University, Seoul 139-701, Republic of Korea (E-mail: [email protected]) A. M. Everett is with the Department of Management, University of Otago, Dunedin 9054, New Zealand (E-mail: [email protected]).
I. I NTRODUCTION To understand the nature of friendships online with respect to geographic distance, some efforts have originally focused on users’ online profiles that include their city of residence. In , experimental results based on the LiveJournal social network demonstrated a close relationship between geographic distance and probability distribution of friendship, where the probability of befriending a particular user on LiveJournal is inversely proportional to the positive power of the number of closer users. However, the geographic location points only to the location of users at a city scale. For this reason, the friendship degree distribution contains a background probability that is independent of geography due to the city-scale resolution. As follow-up studies, using the data collected from Facebook  and three popular online location-based social networks (LBSNs) , it was found that the probability distribution of friendship as a function of distance also closely follows a single power-law but represents some heterogeneous features. More precisely, it is observed in  that the corresponding curve has two regions according to the population density, indicating that it is flatter at shorter distances—a small fraction of Facebook users who entered their home addresses were used. In , the probability of friendship with distance was shown to present noisy patterns such as an almost flatness in a certain range—the home location of each user was defined as the place with the largest number of check-ins. Contrary to –, based on the data collected from the Tuenti social network, it was found in  that social interactions online are only weakly affected by spatial proximity, with other factors dominating. Alternatively, there is extensive and growing interest among researchers to understand a variety of social behaviors through geo-tagged tweets –. The volume of geo-located Twitter has grown constantly and now forms an invaluable register for understanding human behavior and modelling the way people interact in space. In , along with geo-locations for collected tweets, analysis included how geo-related factors such as physical distance, frequency of air travel, national boundaries, and language differences affect formation of social ties on Twitter. In , it was found that the geo-locations of Twitter users across different countries considerably impact their participation in Twitter and their connectivity with other users. New approaches based on geo-tagged tweets were also proposed to find top vacation spots for a particular holiday by applying indexing, spatio-temporal querying, and machine learning techniques  and to detect unusual geo-social events by measuring geographical regularities of crowd behaviors . Additionally, owing to the location information from geotagged tweets, there has been a steady push to understand individual human mobility , , which is of fundamental importance for many applications. Recent effort has focused on the studies of human mobility using tracking technologies such as mobile phones, GPS receivers, WiFi logging, Bluetooth, and RFID devices as well as LBSN check-in data , but these technologies involve privacy concerns or data access restrictions. On the other hand, geo-tagged tweets can capture much richer features of human mobility , . In our work, we utilize geo-tagged mentions on Twitter, sent by users, to identify their exact location information. A ‘mention’ in Twitter consists of inclusion of “@username” anywhere in the body of tweets. From the fact that we tend to interact offline with people living very near to us, we derive as a natural extension the question whether geography and social relationships are inextricably intertwined on Twitter. Our research is interested in how a pair of users interacts through geo-tagged mentions. As people normally spend a substantial amount of time online, data regarding these two dimensions (i.e., geography and online social relationships) are becoming increasingly precise, thus motivating us to build more reliable models to describe social interactions –. This paper goes beyond past research to determine how friendship patterns are geographically
represented by Twitter, analyzing a single-source dataset that contains a huge number of geo-tagged mentions from users in i) the state of California in the United States (US) and Los Angeles (the most populous city in the state) and ii) the United Kingdom (UK) and London (the most populous city in the UK). These two location sets were selected as demographically comparable, yet distinct and geographically separated, leading adopters of Twitter with sufficient data to enable meaningful comparative analysis for our intentionally exploratory study. We propose and apply the following framework, which establishes a much more accurate friendship degree on Twitter, and a method to enable analysis based on geographic distance: • To fully take into account the intensity of communication between users, we start our analysis by introducing a rather strong definition of “friend” on Twitter, i.e., a definition of bidirectional friendship, instead of na¨ıvely considering the set of followers and followees (unidirectional terms). This definition requires bidirectional communication within a designated time frame or creating a friendship. • By showing that almost all Twitter users are likely to post consecutive tweets in the static mode (i.e., no movement mode), we propose a two-stage distance estimation method, where the geographic distance between two befriended users based on our definition of bidirectional friendship is estimated by sequentially measuring the two senders’ locations. We would like to synthetically analyze how the geographic distance between Twitter users affects their interaction, based on our new framework. Our main results are summarized as follows: • We characterize a newly-discovered probability distribution of the number of friends according to geographic distance, which does not follow a homogenous power-law but, instead, a double power-law (i.e., a double Pareto law). • From this new finding, we identify not only two fundamentally separate regimes, which are characterized by two different power-laws in the distribution, but also the separation point between these regimes. We refer to our full paper  for more detailed description and all the rigorous steps. II. DATASET We use a dataset collected via Twitter Streaming API. The dataset consists of a huge amount of geo-tagged mentions recorded from Twitter users from September 22, 2014 to October 23, 2014 (about one month) in the following four regions: California, Los Angeles, UK, and London. Note that this short-term (one month) dataset is sufficient to examine how closely one user has recently interacted with another online. In this dataset, each mention record has a geo-tag and a timestamp indicating from where, when, and by whom the mention was sent. Based on this information, we are able to construct a user’s location history denoted by a sequence L = (xki , yki , ti ), where xki and yki are the x− and y− coordinates of User k at time ti , respectively. The location information provided by the geo-tag is denoted by latitude and longitude, which are measured in degrees, minutes, and seconds. Each mention on Twitter contains a number of entities that are distinguished by their attributed fields. For data analysis, we adopted the following five essential fields from the metadata of mentions: • user id str: string representation of the sender ID • in reply to user id str: string representation of the receiver ID • lat: latitude of the sender • lon: longitude of the sender • created at: UTC/GMT time when the mention is delivered, i.e., the timestamp
III. R ESEARCH M ETHODOLOGY We start by introducing the following definition of “bidirectional friendship” on Twitter. Definition 1: If two users send/receive mentions to/from each other (i.e., bidirectional personal communication occurs) within a designated amount of time, then they form a bidirectional friendship with each other. Note that our definition differs from the conventional definition of “friend” on Twitter, which is referred to as a followee and thus represents a unidirectional relation. This strong definition enables exclusion of inactive friends who have been out of contact online for a long designated amount of time (e.g., about one month in our work) and to count the number of active friends who have recently communicated with each other. Now, let us characterize the friendship degree of individuals regarding geography by analyzing their sequences L = (xki , yki , ti ) of geo-tagged mentions, where only the senders’ location information is recorded. We propose a two-stage distance estimation method, where the geographic distance between two befriended users is estimated by sequentially measuring the two senders’ locations. We first focus on the time interval between the following two events for a befriended pair: a mention and its replied mention at the next closest time. We count only the events with a time duration between a mention and its replied mention, or inter-mention interval, of less than one hour to exclude certain inaccurate location information that may occur due to users’ movements. We next consider the instance for which User u, originally placed at (xu0 , yu0, t0 ), sent a mention to User v at (xv0 , yv0 , t0 ), and then received a replied mention at the location (xu1 , yu1 , t1 ) from User v placed at (xv1 , yv1 , t1 ). From these two consecutive mention events, it is possible to estimate the geographic distance based on the two sequences (xu0 , yu0, t0 ) and (xv1 , yv1 , t1 ). In our framework, by assuming that the Earth is spherical, we deal with the shortest path between two users’ locations measured along the surface of the Earth. Then, the distance between two locations on the Earth’s surface can be computed according to the spherical law of cosines, which gives a well-conditioned result of the estimated distance down to distances as small as around 1 meter. The estimated distance for one pair is finally obtained by taking the average of all distance values computed over the available inter-mention intervals, each of which is less than one hour. While the estimated distance may differ from the actual distance between Users u and v at time t1 , it is worth noting that people tend to send/receive multiple consecutive tweets from the same location to convey a series of ideas . Our supplementary experiments also demonstrate that most of the Twitter users (approximately 90%) in the four regions under consideration are likely to post consecutive tweets in the static mode whose average velocity ranges from 0 to 2 km/h. Although the inter-tweet interval may show a different pattern from that of the inter-mention interval, we believe that our demonstration is sufficient to support our analysis methodology. IV. A NALYSIS R ESULTS Using bidirectional mentions in Section III, we characterize the probability distribution PD (D = d) of the number of friends according to the distance d, where d [km] is the geographic distance between a user and his/her friend. Unlike the earlier work in –, the heterogeneous shape of PD (D = d) for the entire interval cannot be captured by a single commonly-used statistical function such as a homogeneous power-law using the approach of parametric fitting. Interestingly, we observe that for the distance d ∈ [dmin , dmax ], PD (D = d) can be described as a double power-law distribution, which is given below: −γ d 1 if dmin ≤ d < ds (intra-city regime) PD (D = d) ∼ d−γ2 if ds ≤ d ≤ dmax (inter-city regime),
(b) Los Angeles
3 /.,- #$ 2 !" 67 ' 5 4 & % +*() 0 1
(c) UK Fig. 1.
Probability distribution PD (D = d) of the number of friends with respect to distance (log-log plot).
where γ1 and γ2 denote the exponents for each individual power-law and ds is the separation point. This finding indicates that the friendship degree can be composed of two separate regimes characterized by two different power-laws, termed the intra-city and intercity regimes. Figure 1 shows the log-log plot of the distribution PD (D = d) from empirical data, logarithmically binned data, and fitting function, where the fitting is applied to the binned data. As depicted in the figure, statistical noise exists in the tail for large d, which can be eliminated by applying logarithmic binning.1 We use the traditional least squares estimation to obtain the fitting function.2 Unlike the earlier studies that do not capture the friendship patterns in the intra-city regime, our analysis exhibits two distinguishable features with respect to distance. More specifically, in each regime, the following interesting observations are made: • In the intra-city regime, PD (D = d) decays slowly with distance d, which means that geographic proximity weakly affects the number of intra-city friends with which one user interacts. That is, in this regime, the geographic distance is less relevant for determining the number of friends. This finding reveals that more active Twitter users tend to preferentially interact over short-distance connections. 1
It is verified that this binning procedure does not fundamentally change the underlying power-law exponent of PD (D =
Using maximum likelihood estimation to fit a mixture function (e.g., a double power-law function) is not easy to implement and the performance of a mixture function has not been well understood.
In the inter-city regime, PD (D = d) depends strongly on the geographic distance, where there exists a sharp transition in the distribution PD (D = d) beyond the separation point ds . Thus, long-distance communication is made occasionally. The above argument stems from the fact that the separation point ds is closely related to the length and width of the city in which a user resides. From these observations, we may conclude that, within a given period, the individual is much more likely to contact online mostly friends who are in location-based communities that range from the local neighborhood, suburb, village, or town up to the city level. In addition, the following interesting comparisons are performed according to types of regions: • Comparison between the city-scale and state-scale/country-scale results: We observe that ds in populous metropolitan areas is greater than that in larger regions that include local small towns (such as at the state or country level). For example, from Figures 1(a) and 1(b), we see that ds is 8 km and 22 km in California and Los Angeles, respectively. From Figures 1(c) and 1(d), the same trend is observed by comparing the results for the UK and London (18 km and 21 km, respectively). This finding reveals that Twitter users in populous metropolitan areas (e.g., Los Angeles and London) have a stronger tendency to contact friends on Twitter who are geographically away from their location (i.e., interacting over long-distance connections). This is because the average size (referred to as the land area) of the considered metropolitan cities is relatively bigger than that of larger regions including small towns. It is also seen that the exponent in the inter-city regimes (i.e., γ2 ) in metropolitan areas is significantly higher than that in larger regions. Unlike the state-scale/country-scale results, this finding implies that PD (D = d) sharply drops off beyond ds in huge metropolitan areas. • Comparison between the results in the two cities: From Figures 1(b) and 1(d), one can see that γ1 is 0.60 and 0.38 and γ2 is 6.23 and 7.13 in Los Angeles and London, respectively. Thus, in the intra-city regime, the geographic distance is less relevant in London for determining the number of friends. However, in the inter-city regime, PD (D = d) in London shows a bit steeper decline. •
R EFERENCES  D. Liben-Nowell, J. Novak, R. Kumar, P. Raghavan, and A. Tomkins. Geographic routing in social networks. Proceedings of the National Academy of Sciences of the United States of America (PNAS), 102(33):11623–11628, August 2005.  L. Backstrom, E. Sun, and C. Marlow. Find me if you can: Improving geographical prediction with social and spatial proximity. In Proceedings of the 19th International World Wide Web Conference (WWW2010), pages 61–70, April 2010.  S. Scellato, A. Noulas, R. Lambiotte, and C. Mascolo. Social-spatial properties of online location-based social network. In Proceedings of the 5th International AAAI Conference on Weblogs and Social Media (ICWSM-11), pages 329–336, July 2011.  A. Kaltenbrunner, S. Scellato, Y. Volkovich, D. Laniado, D. Currie, E. J. Jutemar, and C. Mascolo. Far from the eyes, close on the web: Impact of geographic distance on online social interactions. In Proceedings of the 5th ACM Workshop on Online Social Networks (WOSN’12), pages 19–24, August 2012.  Y. Takhteyev, A. Gruzd, and B. Wellman. Geography of Twitter networks. Social Networks, 34(1):73–81, January 2012.  J. Kulshrestha, F. Kooti, A. Nikravesh, and K. P. Gummadi. Geographic dissection of the Twitter network. In Proceedings of the 6th International AAAI Conference on Weblogs and Social Media (ICWSM-12), pages 202–209, June 2012.  J. S. Alowibdi, S. Ghani, and M. F. Mokbel. VacationFinder: A tool for collecting, analyzing, and visualizing geotagged Twitter data to find top vacation spots. In Proceedings of the 6th ACM SIGSPATIAL International Workshop on Location-Based Social Networks (LBSN2014), November 2014.  R. Lee and K. Sumiya. Measuring geographical regularities of crowd behaviors for Twitter-based geo-social event detection. In Proceedings of the 2nd ACM SIGSPATIAL International Workshop on Location-Based Social Networks (LBSN2010), pages 1–10, November 2010.
 B. Hawelka, I. Sitko, E. Beinat, S. Sobolevsky, P. Kazakopoulos, and C. Ratti. Geo-located Twitter as proxy for global mobility patterns. Cartography and Geographic Information Science (CaGIS), 41(3):260–271, 2014.  R. Jurdak, K. Zhao, J. Liu, M. AbouJaoude, M. Cameron, amd D. Newth. Understanding human mobility from Twitter. PLoS ONE, 10(7):1–15, July 2015.  E. Cho, S. A. Myers, and J. Leskovec. Friendship and mobility: User movement in location-based social networks. In Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD2011), pages 1082–1090, August 2011.  W.-Y. Shin, J. Cho, and A. M. Everett. A new understanding of friendships in space: Complex networks meet Twitter. Journal of Information Science, 41(6), December 2015 (to appear).