Related papers: Minimizing couplings in renormalization by preserv…
We analyze the renormalization of the nucleon--nucleon interaction at low energies in coordinate space for both one and two pion exchange chiral potentials. The singularity structure of the long range potential and the requirement of…
We study of the effect of weak noise on critical one dimensional maps; that is, maps with a renormalization theory. We establish a one dimensional central limit theorem for weak noises and obtain Berry--Esseen estimates for the rate of this…
The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior…
I review the theory of renormalization, as applied to weak-coupling perturbation theory in quantum field theories.
Low-rank structures play important role in recent advances of many problems in image science and data science. As a natural extension of low-rank structures for data with nonlinear structures, the concept of the low-dimensional manifold…
By adjusting the tunnelling couplings over longer than nearest neighbor distances it is possible in discrete lattice models to reproduce the properties of the lowest energy band of a real, continuous periodic potential. We propose to…
We study the problem of identifying correlations in multivariate data, under information constraints: Either on the amount of memory that can be used by the algorithm, or the amount of communication when the data is distributed across…
Small-world networks provide an interesting framework for studying the interplay between regular and random graphs, where links are located in a regular and random way, respectively. On one hand, the random links make the model to obey some…
We explore the impact of coarse quantization on low-rank matrix sensing in the extreme scenario of dithered one-bit sampling, where the high-resolution measurements are compared with random time-varying threshold levels. To recover the…
We explore the principles of many-body Hamiltonian complexity reduction via downfolding on an effective low-dimensional representation. We present a unique measure of fidelity between the effective (reduced-rank) description and the full…
Alignment algorithms usually rely on simplified models of gaps for computational efficiency. Based on an isomorphism between alignments and physical helix-coil models, we show in statistical mechanics that alignments with realistic laws for…
Geometric optimisation algorithms are developed that efficiently find the nearest low-rank correlation matrix. We show, in numerical tests, that our methods compare favourably to the existing methods in the literature. The connection with…
Lorenz maps are maps of the unit interval with one critical point of order rho>1, and a discontinuity at that point. They appear as return maps of leafs of sections of the geometric Lorenz flow. We construct real a priori bounds for…
A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…
This note demonstrates that we can stably recover all symmetric Toeplitz matrices $\pmb{X}_0\in\mathbb{R}^{n\times n}$ of rank at most $r$ from a number of rank-one subgaussian measurements on the order of $r\log^{2} n$ with an…
Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce…
We propose a new general framework for recovering low-rank structure in optimal transport using Schatten-$p$ norm regularization. Our approach extends existing methods that promote sparse and interpretable transport maps or plans, while…
Density-matrix renormalization group is used to study the pairing when both of electron-electron and electron-phonon interactions are strong in the Holstein-Hubbard model at half-filling in a region intermediate between the adiabatic…
It is demonstrated that decimation of the one dimensional Ising model, with periodic boundary conditions, results in a non-linear renormalisation transformation for the couplings which can lead to chaotic behaviour when the couplings are…
Here we present new joint reconstruction and regularization techniques inspired by ideas in microlocal analysis and lambda tomography, for the simultaneous reconstruction of the attenuation coefficient and electron density from X-ray…