Related papers: Wavelet correlations in hierarchical branching pro…
Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for…
Speckle patterns are inherent features of coherent light propagation through complex media. As a result of interference, they are sensitive to multiple experimental parameters such as the configuration of disorder or the propagating…
Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can…
Temporal decorrelations in compressible isotropic turbulence are studied using the space-time correlation theory and direct numerical simulation. A swept-wave model is developed for dilatational components while the classic random sweeping…
In this paper, I outline several conceptual and methodological issues related to modeling individual and group processes embedded in clustered/hierarchical data structures. We position multilevel modeling techniques within a broader set of…
We derive a simple analytical expression for the level correlation function of an integrable system. It accounts for both the lack of correlations at smaller energy scales and for global rigidity (level number conservation) at larger…
Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can be used for a variety of…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
Class-labeled datasets, particularly those common in scientific domains, are rife with internal structure, yet current class-conditional diffusion models ignore these relationships and implicitly diffuse on all classes in a flat fashion. To…
The statistical properties of turbulent flows are fundamentally different from those of systems at equilibrium due to the presence of an energy flux from the scales of injection to those where energy is dissipated by the viscous forces: a…
Most of dynamic systems which exhibit chaotic behavior are also known to posses self-similarity and manifest strong fluctuations of all possible scales.The meaning of this terms is not always same. In present note we make an attempt to…
We investigate the self-organization of point-particles with short-range interactions modeled via simple 1D and 2D Hubbard-like models. We show how various properties emerge such as, boson-like ordering leading to topological structures in…
Binary mixtures of hard-spheres with different diameters and square-well attraction between different particles are studied by theory and Monte Carlo simulations. In our mesoscopic theory, local fluctuations of the volume fraction of the…
Modeling heterogeneous correlated time series requires the ability to learn hidden dynamic relationships between component time series with possibly varying periodicities and generative processes. To address this challenge, we formulate and…
We investigate wavelet-like localized solutions in nonlinear waveguides, enabled by complementary propagation constants embedded in domains of anomalous dispersion. They are carrier-envelope-phase stable and independent of fine details of…
We show that the correlation and entanglement dynamics of spin systems can be understood in terms of propagation of spin waves. This gives a simple, physical explanation of the behaviour seen in a number of recent works, in which a…
Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…
Controlling the spread of correlations in quantum many-body systems is a key challenge at the heart of quantum science and technology. Correlations are usually destroyed by dissipation arising from coupling between a system and its…
Relation of ultrametric analysis, wavelet theory and cascade models of turbulence is discussed. We construct the explicit solutions for the nonlinear ultrametric integral equation with quadratic nonlinearity. These solutions are built by…
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order…