181 research outputs found
The problem of shot selection in basketball
In basketball, every time the offense produces a shot opportunity the player
with the ball must decide whether the shot is worth taking. In this paper, I
explore the question of when a team should shoot and when they should pass up
the shot by considering a simple theoretical model of the shot selection
process, in which the quality of shot opportunities generated by the offense is
assumed to fall randomly within a uniform distribution. I derive an answer to
the question "how likely must the shot be to go in before the player should
take it?", and show that this "lower cutoff" for shot quality depends
crucially on the number of shot opportunities remaining (say, before the
shot clock expires), with larger demanding that only higher-quality shots
should be taken. The function is also derived in the presence of a
finite turnover rate and used to predict the shooting rate of an
optimal-shooting team as a function of time. This prediction is compared to
observed shooting rates from the National Basketball Association (NBA), and the
comparison suggests that NBA players tend to wait too long before shooting and
undervalue the probability of committing a turnover.Comment: 7 pages, 2 figures; comparison to NBA data adde
Geographic constraints on social network groups
Social groups are fundamental building blocks of human societies. While our
social interactions have always been constrained by geography, it has been
impossible, due to practical difficulties, to evaluate the nature of this
restriction on social group structure. We construct a social network of
individuals whose most frequent geographical locations are also known. We also
classify the individuals into groups according to a community detection
algorithm. We study the variation of geographical span for social groups of
varying sizes, and explore the relationship between topological positions and
geographic positions of their members. We find that small social groups are
geographically very tight, but become much more clumped when the group size
exceeds about 30 members. Also, we find no correlation between the topological
positions and geographic positions of individuals within network communities.
These results suggest that spreading processes face distinct structural and
spatial constraints.Comment: 10 pages, 5 figure
Twitter-based analysis of the dynamics of collective attention to political parties
Large-scale data from social media have a significant potential to describe
complex phenomena in real world and to anticipate collective behaviors such as
information spreading and social trends. One specific case of study is
represented by the collective attention to the action of political parties. Not
surprisingly, researchers and stakeholders tried to correlate parties' presence
on social media with their performances in elections. Despite the many efforts,
results are still inconclusive since this kind of data is often very noisy and
significant signals could be covered by (largely unknown) statistical
fluctuations. In this paper we consider the number of tweets (tweet volume) of
a party as a proxy of collective attention to the party, identify the dynamics
of the volume, and show that this quantity has some information on the
elections outcome. We find that the distribution of the tweet volume for each
party follows a log-normal distribution with a positive autocorrelation of the
volume over short terms, which indicates the volume has large fluctuations of
the log-normal distribution yet with a short-term tendency. Furthermore, by
measuring the ratio of two consecutive daily tweet volumes, we find that the
evolution of the daily volume of a party can be described by means of a
geometric Brownian motion (i.e., the logarithm of the volume moves randomly
with a trend). Finally, we determine the optimal period of averaging tweet
volume for reducing fluctuations and extracting short-term tendencies. We
conclude that the tweet volume is a good indicator of parties' success in the
elections when considered over an optimal time window. Our study identifies the
statistical nature of collective attention to political issues and sheds light
on how to model the dynamics of collective attention in social media.Comment: 16 pages, 7 figures, 3 tables. Published in PLoS ON
Semi-Markov Graph Dynamics
In this paper, we outline a model of graph (or network) dynamics based on two
ingredients. The first ingredient is a Markov chain on the space of possible
graphs. The second ingredient is a semi-Markov counting process of renewal
type. The model consists in subordinating the Markov chain to the semi-Markov
counting process. In simple words, this means that the chain transitions occur
at random time instants called epochs. The model is quite rich and its possible
connections with algebraic geometry are briefly discussed. Moreover, for the
sake of simplicity, we focus on the space of undirected graphs with a fixed
number of nodes. However, in an example, we present an interbank market model
where it is meaningful to use directed graphs or even weighted graphs.Comment: 25 pages, 4 figures, submitted to PLoS-ON
Who is the best player ever? A complex network analysis of the history of professional tennis
We consider all matches played by professional tennis players between 1968
and 2010, and, on the basis of this data set, construct a directed and weighted
network of contacts. The resulting graph shows complex features, typical of
many real networked systems studied in literature. We develop a diffusion
algorithm and apply it to the tennis contact network in order to rank
professional players. Jimmy Connors is identified as the best player of the
history of tennis according to our ranking procedure. We perform a complete
analysis by determining the best players on specific playing surfaces as well
as the best ones in each of the years covered by the data set. The results of
our technique are compared to those of two other well established methods. In
general, we observe that our ranking method performs better: it has a higher
predictive power and does not require the arbitrary introduction of external
criteria for the correct assessment of the quality of players. The present work
provides a novel evidence of the utility of tools and methods of network theory
in real applications.Comment: 10 pages, 4 figures, 4 table
Emergence of scale-free leadership structure in social recommender systems
The study of the organization of social networks is important for
understanding of opinion formation, rumor spreading, and the emergence of
trends and fashion. This paper reports empirical analysis of networks extracted
from four leading sites with social functionality (Delicious, Flickr, Twitter
and YouTube) and shows that they all display a scale-free leadership structure.
To reproduce this feature, we propose an adaptive network model driven by
social recommending. Artificial agent-based simulations of this model highlight
a "good get richer" mechanism where users with broad interests and good
judgments are likely to become popular leaders for the others. Simulations also
indicate that the studied social recommendation mechanism can gradually improve
the user experience by adapting to tastes of its users. Finally we outline
implications for real online resource-sharing systems
Manin matrices and Talalaev's formula
We study special class of matrices with noncommutative entries and
demonstrate their various applications in integrable systems theory. They
appeared in Yu. Manin's works in 87-92 as linear homomorphisms between
polynomial rings; more explicitly they read: 1) elements in the same column
commute; 2) commutators of the cross terms are equal: (e.g. ). We claim
that such matrices behave almost as well as matrices with commutative elements.
Namely theorems of linear algebra (e.g., a natural definition of the
determinant, the Cayley-Hamilton theorem, the Newton identities and so on and
so forth) holds true for them.
On the other hand, we remark that such matrices are somewhat ubiquitous in
the theory of quantum integrability. For instance, Manin matrices (and their
q-analogs) include matrices satisfying the Yang-Baxter relation "RTT=TTR" and
the so--called Cartier-Foata matrices. Also, they enter Talalaev's
hep-th/0404153 remarkable formulas: ,
det(1-e^{-\p}T_{Yangian}(z)) for the "quantum spectral curve", etc. We show
that theorems of linear algebra, after being established for such matrices,
have various applications to quantum integrable systems and Lie algebras, e.g
in the construction of new generators in (and, in general,
in the construction of quantum conservation laws), in the
Knizhnik-Zamolodchikov equation, and in the problem of Wick ordering. We also
discuss applications to the separation of variables problem, new Capelli
identities and the Langlands correspondence.Comment: 40 pages, V2: exposition reorganized, some proofs added, misprints
e.g. in Newton id-s fixed, normal ordering convention turned to standard one,
refs. adde
Content Disputes in Wikipedia Reflect Geopolitical Instability
Indicators that rank countries according socioeconomic measurements are important tools for regional development and political reform. Those currently in widespread use are sometimes criticized for a lack of reproducibility or the inability to compare values over time, necessitating simple, fast and systematic measures. Here, we applied the ‘guilt by association’ principle often used in biological networks to the information network within the online encyclopedia Wikipedia to create an indicator quantifying the degree to which pages linked to a country are disputed by contributors. The indicator correlates with metrics of governance, political or economic stability about as well as they correlate with each other, and though faster and simpler, it is remarkably stable over time despite constant changes in the underlying disputes. For some countries, changes over a four year period appear to correlate with world events related to conflicts or economic problems
Inheritance patterns in citation networks reveal scientific memes
Memes are the cultural equivalent of genes that spread across human culture
by means of imitation. What makes a meme and what distinguishes it from other
forms of information, however, is still poorly understood. Our analysis of
memes in the scientific literature reveals that they are governed by a
surprisingly simple relationship between frequency of occurrence and the degree
to which they propagate along the citation graph. We propose a simple
formalization of this pattern and we validate it with data from close to 50
million publication records from the Web of Science, PubMed Central, and the
American Physical Society. Evaluations relying on human annotators, citation
network randomizations, and comparisons with several alternative approaches
confirm that our formula is accurate and effective, without a dependence on
linguistic or ontological knowledge and without the application of arbitrary
thresholds or filters.Comment: 8 two-column pages, 5 figures; accepted for publication in Physical
Review
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