Related papers: Remarks on ``Coloring Random Triangulation''
In this paper, we study the reconstruction of a bivariate function from weighted integrals along the edges of a triangular mesh, a problem of central importance in tomography, computer vision, and numerical approximation. Our approach…
We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…
Finite dimensional matrices having more columns than rows have no left inverses while those having more rows than columns have no right inverses. We give generalizations of these simple facts to bi--infinite matrices and use those to obtain…
An accurate method for warping images is presented. Differently from most commonly used techniques, this method guarantees the conservation of the intensity of the transformed image, evaluated as the sum of its pixel values over the whole…
The density matrix renormalization group (DMRG) has been extended to study quantum phase transitions on random graphs of fixed connectivity. As a relevant example, we have analysed the random Ising model in a transverse field. If the…
White's density matrix renormalization group ({DMRG}) method has been applied to the one-dimensional Ising model in a transverse field ({ITF}), in order to study the accuracy of the numerical algorithm. Due to the exact solubility of the…
Thimble regularization as a solution to the sign problem has been successfully put at work for a few toy models. Given the non trivial nature of the method (also from the algorithmic point of view) it is compelling to provide evidence that…
We consider a system of two equations that can be used to describe nonlinear chromatography and produce a coherent explanation and description of the unbounded solutions (singular shocks) that appear in M. Mazzotti's model. We use the…
We introduce a dually-weighted multi-matrix model that for a suitable choice of weights reproduce two-dimensional Causal Dynamical Triangulations (CDT) coupled to the Ising model. When Ising degrees of freedom are removed, this model…
This paper examines a broadly applicable triangular normal form for x-flat control-affine systems with two inputs. First, we show that this triangular form encompasses a wide range of established normal forms. Next, we prove that any x-flat…
A procedure for unfolding the true distribution from experimental data is presented. Machine learning methods are applied for simultaneous identification of an apparatus function and solving of an inverse problem. A priori information about…
Using Monte Carlo method we study a two-dimensional model with infinitely many absorbing states. Our estimation of the critical exponent beta=0.273(5) suggests that the model belongs to the (1+1) rather than (2+1) directed-percolation…
I give a brief review of results obtained recently at Ecole Normale on the depinning transition of interfaces and contact lines using a variety of approaches: non-local Monte Carlo algorithms, dynamical renormalization group calculations to…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different…
Despite the growing demand for accurate surface normal estimation models, existing methods use general-purpose dense prediction models, adopting the same inductive biases as other tasks. In this paper, we discuss the inductive biases needed…
Matrix reordering is a task to permute the rows and columns of a given observed matrix such that the resulting reordered matrix shows meaningful or interpretable structural patterns. Most existing matrix reordering techniques share the…
Causal modeling has been recognized as a potential solution to many challenging problems in machine learning (ML). Here, we describe how a recently proposed counterfactual approach developed to deconfound linear structural causal models can…
Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge $ c\leq 1, $ or not understood. It would be useful to devise an approximate scheme which would be reasonable for the known cases and could be…
We develop a scattering-matrix formalism to numerically study the resonant scattering of light on generic assemblies of atoms. Protocols to eliminate the artifacts of the method and extract physical information from the numerical data are…