Related papers: Applications of joinings to sparse equidistributio…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
Complex Langevin dynamics can be used to perform numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is…
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…
Patterns in reaction-diffusion systems near primary bifurcations can be studied locally and classified by means of amplitude equations. This is not possible for excitable reaction-diffusion systems. In this Letter we propose a global…
We consider a dynamical system consisting of subsystems indexed by a lattice. Each subsystem has one conserved degree of freedom ("energy") the rest being uniformly hyperbolic. The subsystems are weakly coupled together so that the sum of…
We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs. Heterogeneity means that some equations receive many inputs whereas most of the equations are given only with a few connections. Starting from…
Granular segregation is ubiquitous in industrial, geological or daily-life context, but there is still no unifying theoretical approach. In this review, we examine two examples of granular segregation -- shallow rapid flows and rotating…
A class of splitting alternating algorithms is proposed for finding the sparse solution of linear systems with concatenated orthogonal matrices. Depending on the number of matrices concatenated, the proposed algorithms are classified into…
This study addresses the challenge of predicting network dynamics, such as forecasting disease spread in social networks or estimating species populations in predator-prey networks. Accurate predictions in large networks are difficult due…
The paper develops a general framework for constrained clustering which is based on the close connection of geometric clustering and diagrams. Various new structural and algorithmic results are proved (and known results generalized and…
We develop novel tools for computing the likelihood correspondence of an arrangement of hypersurfaces in a projective space. This uses the module of logarithmic derivations. This object is well-studied in the linear case, when the…
Extremes of information combining inequalities play an important role in the analysis of sparse-graph codes under message-passing decoding. We introduce new tools for the derivation of such inequalities, and show by means of a concrete…
This paper presents the current possible applications of Dynamical Systems in Engineering. The applications of chaos, fractals have proven to be an exciting and fruitful endeavor. These applications are highly diverse ranging over such…
We study linear difference equations with variable coefficients in a ring using a new nonlinear method. In a ring with identity, if the homogeneous part of the linear equation has a solution in the unit group of the ring (i.e., a unitary…
Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic…
We consider synchronization of coupled dynamical systems when different types of interactions are simultaneously present. We assume that a set of dynamical systems are coupled through the connections of two or more distinct networks (each…
This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which describe the macroscopic dynamics of a variety of large systems of interacting particles.…
In this paper we propose a mixture model, SparseMix, for clustering of sparse high dimensional binary data, which connects model-based with centroid-based clustering. Every group is described by a representative and a probability…
We quantify nonlinear interactions between coupled complex processes, when the system is subject to noise and not all its components are measurable. Our method is applicable even when the system cannot be continuously monitored over time,…
Using information theory we derive a thermodynamics for systems evolving under a collective motion, i.e. under a time-odd constraint. An illustration within the Lattice gas Model is given for two model cases: a collision between two complex…