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In 1961 Herbert Simon and Albert Ando published the theory behind the long-term behavior of a dynamical system that can be described by a nearly uncoupled matrix. Over the past fifty years this theory has been used in a variety of contexts,…
Deterministic simulations of the rate equations governing cluster dynamics in materials are limited by the number of equations to integrate. Stochastic simulations are limited by the high frequency of certain events. We propose a coupling…
Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…
The emergence of nontrivial collective behavior in networks of coupled chaotic maps is investigated by means of a nonlinear mutual prediction method. The resulting prediction error is used to measure the amount of information that a local…
Clustering is a common technique for statistical data analysis, Clustering is the process of grouping the data into classes or clusters so that objects within a cluster have high similarity in comparison to one another, but are very…
Clustering of mixed-type datasets can be a particularly challenging task as it requires taking into account the associations between variables with different level of measurement, i.e., nominal, ordinal and/or interval. In some cases,…
We present a new method for locating unstable periodic points of one dimensional chaotic maps. This method is based on order statistics. The densities of various maxima of the iterates are discontinuous exactly at unstable periodic points…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
Collective behavior is studied in globally coupled maps with distributed nonlinearity. It is shown that the heterogeneity enhances regularity in the collective dynamics. Low-dimensional quasiperiodic motion is often found for the…
The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…
The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…
A model based clustering procedure for data of mixed type, clustMD, is developed using a latent variable model. It is proposed that a latent variable, following a mixture of Gaussian distributions, generates the observed data of mixed type.…
A model of interacting motile chaotic elements is proposed. The chaotic elements are distributed in space and interact with each other through interactions depending on their positions and their internal states. As the value of a governing…
We propose a novel method for multiple clustering that assumes a co-clustering structure (partitions in both rows and columns of the data matrix) in each view. The new method is applicable to high-dimensional data. It is based on a…
Coexistence of various ordered chaotic states in a Hamiltonian system is studied with the use of a symplectic coupled map lattice. Besides the clustered states for the attractive interaction, a novel chaotic ordered state is found for a…
Network models provide a powerful and flexible framework for analyzing a wide range of structured data sources. In many situations of interest, however, multiple networks can be constructed to capture different aspects of an underlying…
We study the dynamics of an ensemble of globally coupled chaotic logistic maps under the action of a learning algorithm aimed at driving the system from incoherent collective evolution to a state of spontaneous full synchronization.…
We study the synchronization of a coupled map lattice consisting of a one-dimensional chain of logistic maps. We consider global coupling with a time-delay that takes into account the finite velocity of propagation of interactions. We…
Clustering is a common technique for statistical data analysis, which is used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics. Clustering is the process of grouping similar…
A limitation of many clustering algorithms is the requirement to tune adjustable parameters for each application or even for each dataset. Some techniques require an \emph{a priori} estimate of the number of clusters while density-based…