Related papers: Topological phase estimation method for reparamete…
We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…
The periodic modulation of an oscillator's frequency can lead to so-called parametric oscillations at half the driving frequency, which display bistability between two states whose phases differ by \pi. Such phase-locking bistability is at…
Phase resetting is a common experimental approach to investigating the behaviour of oscillating neurons. Assuming repeated spiking or bursting, a phase reset amounts to a brief perturbation that causes a shift in the phase of this periodic…
In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…
Classical reconstruction methods for phase-contrast tomography consist of two stages: phase retrieval and tomographic reconstruction. A novel algebraic method combining the two was suggested by Kostenko et al. (Opt. Express, 21, 12185,…
We introduce "state space persistence analysis" for deducing the symbolic dynamics of time series data obtained from high-dimensional chaotic attractors. To this end, we adapt a topological data analysis technique known as persistent…
Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by…
We introduce and test several novel approaches for periodicity detection in unevenly-spaced sparse datasets. Specifically, we examine five different kinds of periodicity metrics, which are based on non-parametric measures of serial…
Phase recovery of modified spectrograms is a major issue in audio signal processing applications, such as source separation. This paper introduces a novel technique for estimating the phases of components in complex mixtures within onset…
We develop a methodology to learn finitely generated random iterated function systems from time-series of partial observations using delay embeddings. We obtain a minimal model representation for the observed dynamics, using a hidden…
Periodic and semi periodic patterns are very common in nature. In this paper we introduce a topological toolbox aiming in detecting and quantifying periodicity. The presented technique is of a general nature and may be employed wherever…
Machine-learning driven models have proven to be powerful tools for the identification of phases of matter. In particular, unsupervised methods hold the promise to help discover new phases of matter without the need for any prior…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
The knowledge of receiver beam shapes is essential for accurate radio interferometric imaging. Traditionally, this information is obtained by holographic techniques or by numerical simulation. However, such methods are not feasible for an…
The parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case,…
We study the problem of sampling and reconstruction of bandlimited graph signals where the objective is to select a node subset of prescribed cardinality that ensures interpolation of the original signal with the lowest reconstruction…
Controlling rhythmic systems, typically modeled as limit-cycle oscillators, is an important subject in real-world problems. Phase reduction theory, which simplifies the multidimensional oscillator state under weak input to a single phase…
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…
The problem of phase-noise compensation for correlated phase noise in coded multichannel optical transmission is investigated. To that end, a simple multichannel phase-noise model is considered and the maximum a posteriori detector for this…
We consider the problem of estimating a signal subspace in the presence of interference that contaminates some proportion of the received observations. Our emphasis is on detecting the contaminated observations so that the signal subspace…