Related papers: Multivariate phase space reconstruction by nearest…
We consider the problem of estimating the underlying edge probabilities of a time-varying network observed at multiple time points. The probability structure is represented by a time-varying graphon that satisfies temporal H\"older…
The reconstruction mechanisms built by the human auditory system during sound reconstruction are still a matter of debate. The purpose of this study is to propose a mathematical model of sound reconstruction based on the functional…
Chaotic systems pose fundamental challenges for data-driven dynamics discovery, as small modeling errors lead to exponentially growing trajectory discrepancies. Since exact long-term prediction is unattainable, it is natural to ask what a…
The theory of stationary spatially localized patterns in dissipative systems driven by time-independent forcing is well developed. With time-periodic forcing related but time-dependent structures may result. These may consist of breathing…
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…
We study the implementation of a weak multiple delayed feedback for controlling coherence of chaotic oscillations. The specific system we treat is the Lorenz system with classical set of parameters. There are two reasons behind the interest…
Some time series can be hierarchically organized into levels based on certain characteristics, such as geography or other attributes of interest. These series are referred to as hierarchical time series. Typically, forecasts are generated…
The phase retrieval from multi-frequency intensity (power) observations is considered. The object to be reconstructed is complex-valued. A novel algorithm is presented that accomplishes both the object phase (absolute phase) retrieval and…
A machine-learning approach called "reservoir computing" has been used successfully for short-term prediction and attractor reconstruction of chaotic dynamical systems from time series data. We present a theoretical framework that describes…
This paper presents novel strategies for spawning and fusing submaps within an elastic dense 3D reconstruction system. The proposed system uses spatial understanding of the scanned environment to control memory usage growth by fusing…
The problem of phase retrieval has been intriguing researchers for decades due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phase-less measurements.…
Dynamic mode decomposition (DMD) is a leading tool for equation-free analysis of high-dimensional dynamical systems from observations. In this work, we focus on a combination of delay-coordinates embedding and DMD, i.e., delay-coordinates…
In this paper, we study the problem of locating a predefined sequence of patterns in a time series. In particular, the studied scenario assumes a theoretical model is available that contains the expected locations of the patterns. This…
Iterative projection algorithms are successfully being used as a substitute of lenses to recombine, numerically rather than optically, light scattered by illuminated objects. Images obtained computationally allow aberration-free…
In a recent letter, Fisher et al. reported the phenomenon of zero-lag long range isochronous synchronization via dynamical relaying in systems with delay [Phys. Rev. Lett. bf 97, 123902 (2006)]. They reported that when one has two coupled…
We propose a novel method of reconstructing the topology and interaction functions for a general oscillator network. An ensemble of initial phases and the corresponding instantaneous frequencies is constructed by repeating random…
In this paper, stability analysis of time delay systems is considered based on decomposition of the systems to subsystems. The decomposition process needs matrices of these systems to be simultaneously block triangularize. We show that a…
Finding a reduction of complex, high-dimensional dynamics to its essential, low-dimensional "heart" remains a challenging yet necessary prerequisite for designing efficient numerical approaches. Machine learning methods have the potential…
One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples, the raw data can be interpreted as the modulus of the…
We study convex relaxation algorithms for phase retrieval on imaging problems. We show that structural assumptions on the signal and the observations, such as sparsity, smoothness or positivity, can be exploited to both speed-up convergence…