Related papers: Axial correlation revivals and number factorizatio…

Irreversible aggregation is revisited in view of recent work on renormalization of complex networks. Its scaling laws and phase transitions are related to percolation transitions seen in the latter. We illustrate our points by giving the…

A new method (NM) for filtering three-dimensional reconstructed densities is proposed. The algorithm is tested with simulated spectra and employed to study the electronic structure of the rare-earth compound LaB6. For this system, momentum…

The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The…

With the discovery of gravitational waves and fast radio bursts, wave optics has become increasingly relevant in astrophysics. This paper studies the behaviour of random gravitational and plasma lenses, presenting the refractive and…

Truncated Fourier, Gauss, Kummer and exponential sums can be used to factorize numbers: for a factor these sums equal unity in absolute value, whereas they nearly vanish for any other number. We show how this factorization algorithm can…

Recursive partitioning is the core of several statistical methods including CART, random forest, and boosted trees. Despite the popularity of tree based methods, to date, there did not exist methods for combining multiple trees into a…

Paraxial diffraction of monochromatic Gaussian beams by arbitrarily shaped polygonal apertures is analytically explored within the boundary diffraction wave theory framework. Exact closed-form expressions of the diffracted wavefield are…

We introduce a variational quantum computing approach for quantum state reconstruction within a discretized logical framework, using experimental measurement data as input. By mapping the reconstruction cost function onto an Ising model,…

We introduce a new product representation for general random binary fractal apertures defined by removing voids from Euclidean space, and use it to derive a simple closed-form expression for ensemble-averaged correlations. Power-law scaling…

The Particle Number Projected Generator Coordinate Method is formulated for the pairing Hamiltonian in a detailed way in the projection after variation and the variation after projection methods. The dependence of the wave functions on the…

In this paper, we extend the paraxial conical refraction model to the case of the partially coherent light using the unified optical coherence theory. We demonstrate the decomposition of conical refraction correlation functions into…

We present a detailed theoretical treatment of four-wave mixing (FWM) in a quantized paraxial framework, capturing the multi-spatial-mode nature of the biphoton state generated in the process. By analyzing the biphoton state both in…

In this work, we consider the inverse problem of reconstructing the internal structure of an object from limited x-ray projections. We use a Gaussian process prior to model the target function and estimate its (hyper)parameters from…

Spontaneous parametric down-conversion is a vital method for generating correlated photon pairs in the visible and near-infrared spectral regions; however, its extension to X-ray frequencies has faced substantial barriers. Here, we present…

Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…

We show that the time frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time domain analysis. This advantage is crucial in…

Fractional revival occurs between two vertices in a graph if a continuous-time quantum walk unitarily maps the characteristic vector of one vertex to a superposition of the characteristic vectors of the two vertices. This phenomenon is…

X-ray observations of bright AGNs in or behind galaxy clusters offer unique capabilities to constrain axion-like particles (ALPs). Existing analysis technique rely on measurements of the global goodness-of-fit. We develop a new analysis…

We study the spatial correlations of quantum fluctuations that can be observed in multi-mode spontaneous parametric down-conversion in the regime of high gain. A stochastic model has been solved numerically to obtain quantitative results…

We develop a method to infer log-normal random fields from measurement data affected by Gaussian noise. The log-normal model is well suited to describe strictly positive signals with fluctuations whose amplitude varies over several orders…