Related papers: Unwrapping phase fluctuations in one dimension
We review connections between phase transitions in high-dimensional combinatorial geometry and phase transitions occurring in modern high-dimensional data analysis and signal processing. In data analysis, such transitions arise as abrupt…
Various phase transitions in models for coupled charge-density waves are investigated by means of the $\epsilon$-expansion, mean-field theory, and Monte Carlo simulations. At zero temperature the effective action for the system with…
In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
We demonstrate how one can construct renormalizable perturbative expansion in formally nonrenormalizable higher dimensional field theories. It is based on $1/N_f$-expansion and results in a logarithmically divergent perturbation theory in…
The refined composite multiscale-entropy algorithm was applied to the time-dependent behavior of the Weierstrass functions, colored noise, and Logistic map to provide fresh insight into the dynamics of these fluctuating phenomena. For the…
Band theory provides the foundation for understanding electronic structure in crystalline materials, but its reliance on exact translational symmetry limits its applicability to systems with defects, disorder, incommensurate modulations, or…
Effective field theories of two-dimensional lattice models of fluctuating loops are constructed by mapping them onto random surfaces whose large scale fluctuations are described by a Liouville field theory. This provides a geometrical view…
Non-equilibrium dynamics are present in many aspects of our lives, ranging from microscopic physical systems to the functioning of the brain. What characterizes stochastic models of non-equilibrium processes is the breaking of the…
Unfolding, in the context of high-energy particle physics, refers to the process of removing detector distortions in experimental data. The resulting unfolded measurements are straightforward to use for direct comparisons between…
We present a new four-dimensional phase unwrapping approach for time-lapse quantitative phase microscopy, which allows reconstruction of optically thick objects that are optically thin in a certain temporal point and angular view. We thus…
Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
A variant of coupled-cluster theory is described here, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction are…
Spatial, amplitude and phase variations in spatial functional data are confounded. Conclusions from the popular functional trace variogram, which quantifies spatial variation, can be misleading when analysing misaligned functional data with…
We investigate the zero-temperature quantum phases of a quasi-one-dimensional zigzag chain of dipoles that are polarized in a plane by an external electric field. Since the Hamiltonian contains nearest-neighbor (NN) and…
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
Microwave, submillimetre-wave, and far-infrared phased arrays are of considerable importance for astronomy. We consider the behaviour imaging phased arrays and interferometric phased arrays from a functional perspective. It is shown that…
Large-time correlation functions have a pivotal role in extracting particle masses from Euclidean lattice field theory calculations, however little is known about the statistical properties of these quantities. In this work, the asymptotic…