88 research outputs found
Derivative-variable correlation reveals the structure of dynamical networks
We propose a conceptually novel method of reconstructing the topology of
dynamical networks. By examining the correlation between the variable of one
node and the derivative of another node, we derive a simple matrix equation
yielding the network adjacency matrix. Our assumptions are the possession of
time series describing the network dynamics, and the precise knowledge of the
interaction functions. Our method involves a tunable parameter, allowing for
the reconstruction precision to be optimized within the constraints of given
dynamical data. The method is illustrated on a simple example, and the
dependence of the reconstruction precision on the dynamical properties of time
series is discussed. Our theory is in principle applicable to any weighted or
directed network whose internal interaction functions are known.Comment: Submitted to EPJ
Stability and chaos in coupled two-dimensional maps on Gene Regulatory Network of bacterium E.Coli
The collective dynamics of coupled two-dimensional chaotic maps on complex
networks is known to exhibit a rich variety of emergent properties which
crucially depend on the underlying network topology. We investigate the
collective motion of Chirikov standard maps interacting with time delay through
directed links of Gene Regulatory Network of bacterium Escherichia Coli.
Departures from strongly chaotic behavior of the isolated maps are studied in
relation to different coupling forms and strengths. At smaller coupling
intensities the network induces stable and coherent emergent dynamics. The
unstable behavior appearing with increase of coupling strength remains confined
within a connected sub-network. For the appropriate coupling, network exhibits
statistically robust self-organized dynamics in a weakly chaotic regime
Chaotic dephasing in a double-slit scattering experiment
We design a computational experiment in which a quantum particle tunnels into
a billiard of variable shape and scatters out of it through a double-slit
opening on the billiard's base. The interference patterns produced by the
scattered probability currents for a range of energies are investigated in
relation to the billiard's geometry which is connected to its classical
integrability. Four billiards with hierarchical integrability levels are
considered: integrable, pseudo-integrable, weak-mixing and strongly chaotic. In
agreement with the earlier result by Casati and Prosen [1], we find the
billiard's integrability to have a crucial influence on the properties of the
interference patterns. In the integrable case most experiment outcomes are
found to be consistent with the constructive interference occurring in the
usual double-slit experiment. In contrast to this, non-integrable billiards
typically display asymmetric interference patterns of smaller visibility
characterized by weakly correlated wave function values at the two slits. Our
findings indicate an intrinsic connection between the classical integrability
and the quantum dephasing, responsible for the destruction of interference
Diffusion maps for changing data
Graph Laplacians and related nonlinear mappings into low dimensional spaces
have been shown to be powerful tools for organizing high dimensional data. Here
we consider a data set X in which the graph associated with it changes
depending on some set of parameters. We analyze this type of data in terms of
the diffusion distance and the corresponding diffusion map. As the data changes
over the parameter space, the low dimensional embedding changes as well. We
give a way to go between these embeddings, and furthermore, map them all into a
common space, allowing one to track the evolution of X in its intrinsic
geometry. A global diffusion distance is also defined, which gives a measure of
the global behavior of the data over the parameter space. Approximation
theorems in terms of randomly sampled data are presented, as are potential
applications.Comment: 38 pages. 9 figures. To appear in Applied and Computational Harmonic
Analysis. v2: Several minor changes beyond just typos. v3: Minor typo
corrected, added DO
Quantifying the consistency of scientific databases
Science is a social process with far-reaching impact on our modern society.
In the recent years, for the first time we are able to scientifically study the
science itself. This is enabled by massive amounts of data on scientific
publications that is increasingly becoming available. The data is contained in
several databases such as Web of Science or PubMed, maintained by various
public and private entities. Unfortunately, these databases are not always
consistent, which considerably hinders this study. Relying on the powerful
framework of complex networks, we conduct a systematic analysis of the
consistency among six major scientific databases. We found that identifying a
single "best" database is far from easy. Nevertheless, our results indicate
appreciable differences in mutual consistency of different databases, which we
interpret as recipes for future bibliometric studies.Comment: 20 pages, 5 figures, 4 table
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