Related papers: A sparse approximation of the Lieb functional with…
In this work, we discuss the task of finding a direction of optimal descent for problems in Shape Optimisation and its relation to the dual problem in Optimal Transport. This link was first observed in a previous work which sought…
Many body localization (MBL) is a phenomena that allows for the preservation of quantum information for long times. We study a variation of the disordered-Heisenberg model, which is known to exhibit an MBL phase [5][6], known as the…
Lloyd's algorithm is an iterative method that solves the quantization problem, i.e. the approximation of a target probability measure by a discrete one, and is particularly used in digital applications. This algorithm can be interpreted as…
We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness…
This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…
Stochastic compositional optimization minimizes objectives of the form $\min_{\bm{x} \in \mathcal{X}} F(\bm{f}(\bm{x}), \bm{x})$, where $\bm{f}$ is accessible only through noisy stochastic queries. Existing methods for this problem assume…
L\'evy ratchets are minimal models of fluctuation-driven transport in the presence of L\'evy noise and periodic external potentials with broken spatial symmetry. In these systems, a net ratchet current can appear even in the absence of time…
We consider in this work the problem of minimizing the von Neumann entropy under the constraints that the density of particles, the current, and the kinetic energy of the system is fixed at each point of space. The unique minimizer is a…
Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and properties given. The relationship between…
The quadratically regularized optimal transport problem is empirically known to have sparse solutions: its optimal coupling $\pi_{\varepsilon}$ has sparse support for small regularization parameter $\varepsilon$, in contrast to entropic…
We applied a method of compressed sensing to the observation of quasi-particle interference (QPI) by scanning tunneling microscopy/spectroscopy to improve efficiency and save measurement time. To solve an ill-posed problem owing to the…
Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…
For single-carrier systems with frequency domain equalization, decision feedback equalization (DFE) performs better than linear equalization and has much lower computational complexity than sequence maximum likelihood detection. The main…
Charge transport in crystalline organic semiconductors is intrinsically limited by the presence of large thermal molecular motions, which are a direct consequence of the weak van der Waals inter-molecular interactions. These lead to an…
The intricate relationship between electrons and the crystal lattice is a linchpin in condensed matter, traditionally described by the Fr\"ohlich model encompassing the lowest-order lattice-electron coupling. Recently developed quantum…
Electronic transport properties for single-molecule junctions have been widely measured by several techniques, including mechanically controllable break junctions, electromigration break junctions or by means of scanning tunneling…
We prove the existence of generalised solutions of the Monge-Kantorovich equations with fractional $s$-gradient constraint, $0<s<1$, associated to a general, possibly degenerate, linear fractional operator of the type, \begin{equation*}…
The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…
Spatial coupling has recently emerged as a powerful paradigm to construct graphical models that work well under low-complexity message-passing algorithms. Although much progress has been made on the analysis of spatially coupled models…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…