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Various widely-used mean-field type theories for a dilute Bose gas are critically examined in the light of the recent discovery of Bose-Einstein condensation of atomic gases in a confined geometry. By numerically solving the mean-field…
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
We propose a versatile variational method to investigate the spatio-temporal dynamics of one-dimensional magnetically-trapped Bose-condensed gases. To this end we employ a \emph{q}-Gaussian trial wave-function that interpolates between the…
We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law conservation law. When the…
We consider the inverse problem of recovering an isotropic electrical conductivity from interior knowledge of the magnitude of one current density field generated by applying current on a set of electrodes. The required interior data can be…
A procedure based on a Mixture Density Model for correcting experimental data for distortions due to finite resolution and limited detector acceptance is presented. Addressing the case that the solution is known to be non-negative, in the…
Motivated by the recent successes of particle models in capturing the precession and interactions of vortex structures in quasi-two-dimensional Bose-Einstein condensates, we revisit the relevant systems of ordinary differential equations.…
Density profiles are the most common measure of inhomogeneous structure in confined fluids, but their connection to transport coefficients is poorly understood. We explore via simulation how tuning particle-wall interactions to flatten or…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
We consider the problem of estimating a multivariate function $f_0$ of bounded variation (BV), from noisy observations $y_i = f_0(x_i) + z_i$ made at random design points $x_i \in \mathbb{R}^d$, $i=1,\ldots,n$. We study an estimator that…
We demonstrate theoretically and experimentally coherence-induced polarization changes in generic and higher-order vector vortex beams with polarization singularity. The prominent depolarization on decreasing transverse correlation-width in…
Elastic scattering probes directly the interaction potential. For weakly interacting condensates this potential is given by the condensate density. We investigate how the differential and total cross sections reflect the density. In…
Recovering a function from integrals over conical surfaces recently got significant interest. It is relevant for emission tomography with Compton cameras and other imaging applications. In this paper, we consider the weighted conical Radon…
We consider the phenomenon of Bose-Einstein condensation in a random growing directed network. The network grows by the addition of vertices and edges. At each time step the network gains a vertex with probabilty $p$ and an edge with…
The Thirring model and various generalizations of it are analyzed in detail. The four-Fermi interaction modifies the equation of state. Chemical potentials and twisted boundary conditions both result in complex fermionic determinants which…
Modern iterations of deep learning models contain millions (billions) of unique parameters, each represented by a b-bit number. Popular attempts at compressing neural networks (such as pruning and quantisation) have shown that many of the…
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…
The dynamics of interacting quantized vortex filaments in a rotating trapped Bose-Einstein condensate, which is in the Thomas-Fermi regime at zero temperature and described by the Gross-Pitaevskii equation, is considered in the hydrodynamic…
The dynamics of a two-dimensional Bose-Einstein condensate in a presence of quantum fluctuations is studied. The properties of localized density distributions, quantum droplets (QDs), are analyzed by means of the variational approach. It is…
We consider deformations of bounded complexes of modules for a profinite group G over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex…