181 research outputs found
Quantifying Self-Organization with Optimal Predictors
Despite broad interest in self-organizing systems, there are few
quantitative, experimentally-applicable criteria for self-organization. The
existing criteria all give counter-intuitive results for important cases. In
this Letter, we propose a new criterion, namely an internally-generated
increase in the statistical complexity, the amount of information required for
optimal prediction of the system's dynamics. We precisely define this
complexity for spatially-extended dynamical systems, using the probabilistic
ideas of mutual information and minimal sufficient statistics. This leads to a
general method for predicting such systems, and a simple algorithm for
estimating statistical complexity. The results of applying this algorithm to a
class of models of excitable media (cyclic cellular automata) strongly support
our proposal.Comment: Four pages, two color figure
Quantifying the complexity of random Boolean networks
We study two measures of the complexity of heterogeneous extended systems,
taking random Boolean networks as prototypical cases. A measure defined by
Shalizi et al. for cellular automata, based on a criterion for optimal
statistical prediction [Shalizi et al., Phys. Rev. Lett. 93, 118701 (2004)],
does not distinguish between the spatial inhomogeneity of the ordered phase and
the dynamical inhomogeneity of the disordered phase. A modification in which
complexities of individual nodes are calculated yields vanishing complexity
values for networks in the ordered and critical regimes and for highly
disordered networks, peaking somewhere in the disordered regime. Individual
nodes with high complexity are the ones that pass the most information from the
past to the future, a quantity that depends in a nontrivial way on both the
Boolean function of a given node and its location within the network.Comment: 8 pages, 4 figure
Hawkes process as a model of social interactions: a view on video dynamics
We study by computer simulation the "Hawkes process" that was proposed in a
recent paper by Crane and Sornette (Proc. Nat. Acad. Sci. USA 105, 15649
(2008)) as a plausible model for the dynamics of YouTube video viewing numbers.
We test the claims made there that robust identification is possible for
classes of dynamic response following activity bursts. Our simulated timeseries
for the Hawkes process indeed fall into the different categories predicted by
Crane and Sornette. However the Hawkes process gives a much narrower spread of
decay exponents than the YouTube data, suggesting limits to the universality of
the Hawkes-based analysis.Comment: Added errors to parameter estimates and further description. IOP
style, 13 pages, 5 figure
Dynamic communities in multichannel data: An application to the foreign exchange market during the 2007--2008 credit crisis
We study the cluster dynamics of multichannel (multivariate) time series by
representing their correlations as time-dependent networks and investigating
the evolution of network communities. We employ a node-centric approach that
allows us to track the effects of the community evolution on the functional
roles of individual nodes without having to track entire communities. As an
example, we consider a foreign exchange market network in which each node
represents an exchange rate and each edge represents a time-dependent
correlation between the rates. We study the period 2005-2008, which includes
the recent credit and liquidity crisis. Using dynamical community detection, we
find that exchange rates that are strongly attached to their community are
persistently grouped with the same set of rates, whereas exchange rates that
are important for the transfer of information tend to be positioned on the
edges of communities. Our analysis successfully uncovers major trading changes
that occurred in the market during the credit crisis.Comment: 8 pages, 6 figures, accepted for publication in Chao
The Visibility Graph: a new method for estimating the Hurst exponent of fractional Brownian motion
Fractional Brownian motion (fBm) has been used as a theoretical framework to
study real time series appearing in diverse scientific fields. Because its
intrinsic non-stationarity and long range dependence, its characterization via
the Hurst parameter H requires sophisticated techniques that often yield
ambiguous results. In this work we show that fBm series map into a scale free
visibility graph whose degree distribution is a function of H. Concretely, it
is shown that the exponent of the power law degree distribution depends
linearly on H. This also applies to fractional Gaussian noises (fGn) and
generic f^(-b) noises. Taking advantage of these facts, we propose a brand new
methodology to quantify long range dependence in these series. Its reliability
is confirmed with extensive numerical simulations and analytical developments.
Finally, we illustrate this method quantifying the persistent behavior of human
gait dynamics.Comment: 5 pages, submitted for publicatio
Concentrating tripartite quantum information
We introduce the concentrated information of tripartite quantum states. For three parties Alice, Bob, and Charlie, it is defined as the maximal mutual information achievable between Alice and Charlie via local operations and classical communication performed by Charlie and Bob. We derive upper and lower bounds to the concentrated information, and obtain a closed expression for it on several classes of states including arbitrary pure tripartite states in the asymptotic setting. We show that distillable entanglement, entanglement of assistance, and quantum discord can all be expressed in terms of the concentrated information, thus revealing its role as a unifying informational primitive. We finally investigate quantum state merging of mixed states with and without additional entanglement. The gap between classical and quantum concentrated information is proven to be an operational figure of merit for mixed state merging in absence of additional entanglement. Contrary to pure state merging, our analysis shows that classical communication in both directions can provide advantage for merging of mixed states
Homophily and Contagion Are Generically Confounded in Observational Social Network Studies
We consider processes on social networks that can potentially involve three
factors: homophily, or the formation of social ties due to matching individual
traits; social contagion, also known as social influence; and the causal effect
of an individual's covariates on their behavior or other measurable responses.
We show that, generically, all of these are confounded with each other.
Distinguishing them from one another requires strong assumptions on the
parametrization of the social process or on the adequacy of the covariates used
(or both). In particular we demonstrate, with simple examples, that asymmetries
in regression coefficients cannot identify causal effects, and that very simple
models of imitation (a form of social contagion) can produce substantial
correlations between an individual's enduring traits and their choices, even
when there is no intrinsic affinity between them. We also suggest some possible
constructive responses to these results.Comment: 27 pages, 9 figures. V2: Revised in response to referees. V3: Ditt
On Hilberg's Law and Its Links with Guiraud's Law
Hilberg (1990) supposed that finite-order excess entropy of a random human
text is proportional to the square root of the text length. Assuming that
Hilberg's hypothesis is true, we derive Guiraud's law, which states that the
number of word types in a text is greater than proportional to the square root
of the text length. Our derivation is based on some mathematical conjecture in
coding theory and on several experiments suggesting that words can be defined
approximately as the nonterminals of the shortest context-free grammar for the
text. Such operational definition of words can be applied even to texts
deprived of spaces, which do not allow for Mandelbrot's ``intermittent
silence'' explanation of Zipf's and Guiraud's laws. In contrast to
Mandelbrot's, our model assumes some probabilistic long-memory effects in human
narration and might be capable of explaining Menzerath's law.Comment: To appear in Journal of Quantitative Linguistic
Reductions of Hidden Information Sources
In all but special circumstances, measurements of time-dependent processes
reflect internal structures and correlations only indirectly. Building
predictive models of such hidden information sources requires discovering, in
some way, the internal states and mechanisms. Unfortunately, there are often
many possible models that are observationally equivalent. Here we show that the
situation is not as arbitrary as one would think. We show that generators of
hidden stochastic processes can be reduced to a minimal form and compare this
reduced representation to that provided by computational mechanics--the
epsilon-machine. On the way to developing deeper, measure-theoretic foundations
for the latter, we introduce a new two-step reduction process. The first step
(internal-event reduction) produces the smallest observationally equivalent
sigma-algebra and the second (internal-state reduction) removes sigma-algebra
components that are redundant for optimal prediction. For several classes of
stochastic dynamical systems these reductions produce representations that are
equivalent to epsilon-machines.Comment: 12 pages, 4 figures; 30 citations; Updates at
http://www.santafe.edu/~cm
Complex temporal patterns in molecular dynamics:a direct measure of the phase-space exploration by the trajectory at macroscopic time scales
Computer simulated trajectories of bulk water molecules form complex spatiotemporal structures at the picosecond time scale. This intrinsic complexity, which underlies the formation of molecular structures at longer time scales, has been quantified using a measure of statistical complexity. The method estimates the information contained in the molecular trajectory by detecting and quantifying temporal patterns present in the simulated data (velocity time series). Two types of temporal patterns are found. The first, defined by the short-time correlations corresponding to the velocity autocorrelation decay times (ââ°0.1ââŹps), remains asymptotically stable for time intervals longer than several tens of nanoseconds. The second is caused by previously unknown longer-time correlations (found at longer than the nanoseconds time scales) leading to a value of statistical complexity that slowly increases with time. A direct measure based on the notion of statistical complexity that describes how the trajectory explores the phase space and independent from the particular molecular signal used as the observed time series is introduced
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