In order to extend the dynamical clustering algorithm to interval data sets, we define the prototype of a cluster by optimization of a classical adequacy criterion based on Hausdorff distance. Once this class prototype properly defined we give a simple and converging algorithm for this new type of interval data.

Noise-induced escape from a metastable state of a dynamical system is studied close to a saddle-node bifurcation point, but in the region where the system remains underdamped. The activation energy of escape scales as a power of the distance to the bifurcation point. We find two types of scaling and the corresponding critical exponents.

The string-dominated universe locally resembles an open universe, and fits dynamical measures of power spectra, cluster abundances, redshift distortions, lensing constraints, luminosity and angular diameter distance relations and microwave background observations. We show examples of networks which might give rise to recent string-domination without requiring any fine-tuned parameters. We discu...

A brief review of Rayleigh–Bénard studies performed all along the twentieth century is presented, with an emphasis on the transition to turbulence and the appropriate theoretical framework, relying on the strength of confinement effects and the distance to threshold, either dynamical systems for temporal chaos in the strongly confined case, or models of space-time chaos when confinement effects...

Kinetics of folding of a protein held in a force clamp are compared to an unconstrained folding. The comparison is made within a simple topology-based dynamical model of ubiquitin. We demonstrate that the experimentally observed variations in the end-to-end distance reflect microscopic events during folding. However, the folding scenarios in and out of the force clamp are distinct.

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to...

Small sample is an acute problem in many application domains, which may be partially addressed by feature selection or dimensionality reduction. For the purpose of distance learning, we describe a method for feature selection using equivalence constraints between pairs of datapoints. The method is based on L1 regularization and optimization. Feature selection is then incorporated into an existi...

The metric structure of bosonic scale-free networks and fermionic Cayley-tree networks is analyzed, focusing on the directed distance of nodes from the origin. The topology of the networks strongly depends on the dynamical parameter T, called the temperature. At T= infinity we show analytically that the two networks have a similar behavior: the distance of a generic node from the origin of the ...

It is possible to consider stochastic models of sequence evolution in phylogenetics in the context of a dynamical tensor description inspired from physics. Approaching the problem in this framework allows for the well developed methods of mathematical physics to be exploited in the biological arena. We present the tensor description of the homogeneous continuous time Markov chain model of phylo...