Related papers: Renormalization Analysis of Resonance Structure in…
We propose a renormalization group (RG) approach to compare and collapse eigenvalue densities of random matrix models of complex systems across different system sizes. The approach is to fix a natural spectral scale by letting the model…
We show that artificial neural networks (ANNs) can, to high accuracy, determine the topological invariant of a disordered system given its two-dimensional real-space Hamiltonian. Furthermore, we describe a "renormalization-group" (RG)…
In the framework of semiclassical resonances, we make more precise the link between polynomial estimates of the extension of the resolvent and propagation of the singularities through the trapped set. This approach makes it possible to…
Our project is to define Radon-type transforms in symplectic geometry. The chosen framework consists of symplectic symmetric spaces whose canonical connection is of Ricci-type. They can be considered as symplectic analogues of the spaces of…
This survey paper addresses uniqueness questions for symplectic forms on closed manifolds, explains what is known in several examples, and reviews some open problems.
Renormalisation group (RG) equations in two-dimensional N=1 supersymmetric field theories with boundary are studied. It is explained how a manifestly N=1 supersymmetric scheme can be chosen, and within this scheme the RG equations are…
The Density Matrix Renormalization Group (DMRG) method scales exponentially in the system width for models in two dimensions, but remains one of the most powerful methods for studying 2D systems with a sign problem. Reviewing past…
In this article, we attempt to study the possible link between the dynamics of a circle map and the caustics of its iterations. The attention is on a geometrically defined off-center reflections, which, coincidentally, is also a…
In these memos, we define a pregeometry $\mathcal{T}_{\mathbb{S}} ^{alg}$ and a geometry $\mathcal{G}_{\mathbb{S}} ^{alg}$ which integrate symplectic manifolds with $E_{\infty}$-ring sheaves, enabling the construction of…
We consider orthogonal transformations of arbitrary square matrices to a form where all diagonal entries are equal. In our main results we treat the simultaneous transformation of two matrices and the symplectic orthogonal transformation of…
We study locally harmonic maps between a Riemann surface or Lorentz surface $M$ and a Riemann surface or Lorentz surface $N$. {All four cases are studied in a unified way}. All four cases are written using a unified formalism. Therefore…
We present a general analysis of the orbit structure of 2D potentials with self-similar elliptical equipotentials by applying the method of Lie transform normalization. We study the most relevant resonances and related bifurcations. We find…
The special structures that arise in symplectic topology (particularly Gromov--Witten invariants and quantum homology) place as yet rather poorly understood restrictions on the topological properties of symplectomorphism groups. This…
We use the numerical renormalization group method (NRG) to investigate a single-impurity Anderson model with a coupling of the impurity to a superconducting host. Analysis of the energy flow shows, in contrast to previous belief, that NRG…
In electrical impedance tomography, algorithms based on minimizing a linearized residual functional have been widely used due to their flexibility and good performance in practice. However, no rigorous convergence results have been…
In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…
We develop a renormalization theory of non-perturbative dissipative H\'enon-like maps with combinatorics of bounded type. The main novelty of our approach is the incorporation of Pesin theoretic ideas to the renormalization method, which…
Strong Disorder Renormalization is an energy-based renormalization that leads to a complicated renormalized topology for the surviving clusters as soon as $d>1$. In this paper, we propose to include Strong Disorder Renormalization ideas…
It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations are analyzed. The amplitude equations…
Analysis sparsity is a common prior in inverse problem or machine learning including special cases such as Total Variation regularization, Edge Lasso and Fused Lasso. We study the geometry of the solution set (a polyhedron) of the analysis…