相关论文: Multivariate Dynamical Sampling in $l^2(\mathbb{Z}…

This paper presents an overview of physical ideas and mathematical methods for implementing non-smooth and discontinuous substitutions in dynamical systems. General purpose of such substitutions is to bring the differential equations of…

We study the problem of learning a mixture of multiple linear dynamical systems (LDSs) from unlabeled short sample trajectories, each generated by one of the LDS models. Despite the wide applicability of mixture models for time-series data,…

In nature, signals often appear in the form of the superposition of multiple non-stationary signals. The overlap of signal components in the time-frequency domain poses a significant challenge for signal analysis. One approach to addressing…

We present a dynamical system formulation for inhomogeneous LRS-II spacetimes using the covariant 1+1+2 decomposition approach. Our approach describes the LRS-II dynamics from the point of view of a comoving observer. Promoting the…

We present a Lie-algebraic classification and detailed construction of the dynamical invariants, also known as Lewis-Riesenfeld invariants, of the four-level systems including two-qubit systems which are most relevant and sufficiently…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

Despite the successful application of convolutional neural networks (CNNs) in object detection tasks, their efficiency in detecting faults from freight train images remains inadequate for implementation in real-world engineering scenarios.…

Time-averaged two-point currents are derived and shown to be spatially invariant within domains of local translation or inversion symmetry for arbitrary time-periodic quantum systems in one dimension. These currents are shown to provide a…

We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such…

Let Y={f(i), Af(i),..., A^{li} f(i): i in Omega}, where A is a bounded operator on l^2(I). The problem under consideration is to find necessary and sufficient conditions on A, Omega, {l_i:i in Omega} in order to recover any f \in l^2(I)…

In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…

We develop a sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band-limited at $L$ using only $L^2$ samples. We obtain the optimal number of samples given by the…

This paper deals with variable selection in multivariate linear regression model when the data are observations on a spatial domain being a grid of sites in $\mathbb{Z}^d$ with $d\geqslant 2$. We use a criterion that allows to characterize…

Powerful deep learning tools, such as convolutional neural networks (CNN), are able to learn the input-output relationships of large complicated systems directly from data. Encoder-decoder deep CNNs are able to extract features directly…

The paper surveys variational approaches for image reconstruction in dynamic inverse problems. Emphasis is on methods that rely on parametrised temporal models. These are here encoded as diffeomorphic deformations with time dependent…

We consider the problem of spatiotemporal sampling in a discrete infinite dimensional spatially invariant evolutionary process $x^{(n)}=A^nx$ to recover an unknown convolution operator $A$ given by a filter $a \in \ell^1(\mathbb{Z})$ and an…

The problem of diagonalization of Hamiltonians of N-dimensional boson systems by means of time-dependent canonical transformations (CT) is considered, the case of quadratic Hamiltonians being treated in greater detail. The unitary generator…

Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…

We consider the two-dimensional defocusing nonlinear Schr\"odinger equation (NLS) on the unit disc in the plane with the Gibbs initial data under radial symmetry. By using a type of random averaging operator ansatz, we build a strong…

As a generalization of the two-dimensional Fourier transform (2D FT) and 2D fractional Fourier transform, the 2D nonseparable linear canonical transform (2D NsLCT) is useful in optics, signal and image processing. To reduce the digital…