Related papers: Multivariate phase space reconstruction by nearest…
In this study, a new extension of the Markov Renewal theory is introduced by allowing time to evolve in multiple dimensions. The resulting chains are referred to as multi-time Markov Renewal chains and since this extension is new, the state…
This note considers the multidimensional unstructured sparse recovery problems. Examples include Fourier inversion and sparse deconvolution. The eigenmatrix is a data-driven construction with desired approximate eigenvalues and eigenvectors…
We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for…
It is shown that the phase space path integral for a system with arbitrary second class constraints (primary, secondary ...) can be rewritten as a configuration space path integral of the exponent of the Lagrangian action with some local…
This paper presents a data structure that summarizes distances between configurations across a robot configuration space, using a binary space partition whose cells contain parameters used for a locally linear approximation of the distance…
Reconstruction of a dynamical system from a time series requires the selection of two parameters, the embedding dimension $d_e$ and the embedding lag $\tau$. Many competing criteria to select these parameters exist, and all are heuristic.…
Multivariate time-series have become abundant in recent years, as many data-acquisition systems record information through multiple sensors simultaneously. In this paper, we assume the variables pertain to some geometry and present an…
A recently introduced technique of topology sensitivity in method of moments is extended by the possibility of adding degrees-of-freedom (reconstruct) into underlying structure. The algebraic formulation is inversion-free, suitable for…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting phase model has…
In a number of astrophysical applications one tries to determine the two-dimensional or three-dimensional structure of an object from a time series of measurements. While most methods used for reconstruction assume that object is static,…
We target time-dependent partial differential equations (PDEs) with heterogeneous coefficients in space and time. To tackle these problems, we construct reduced basis/ multiscale ansatz functions defined in space that can be combined with…
Identifying the qualitative changes in time-series data provides insights into the dynamics associated with such data. Such qualitative changes can be detected through topological approaches, which first embed the data into a…
We consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature…
Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…
This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…
We present a simple choice of integration variables that can be used to exploit the near-integrable character of problems in celestial mechanics. The approach is based on the well-known principle of variation of parameters: instead of…
Location prediction forecasts a user's location based on historical user mobility traces. To tackle the intrinsic sparsity issue of real-world user mobility traces, spatiotemporal contexts have been shown as significantly useful. Existing…
Phase-locked loops (PLLs) are now widely used in communication systems and have been a classic system for more than 60 years. Well-known mathematical models of such systems are constructed in a number of approximations, so questions about…
Deep learning models have significantly improved the visual quality and accuracy on compressive sensing recovery. In this paper, we propose an algorithm for signal reconstruction from compressed measurements with image priors captured by a…