Related papers: Hairer's Reconstruction Theorem without Regularity…
A new approach to disintegration of measures is presented, allowing one to drop the usually taken separability assumption. The main tool is a result on fibers in the spectrum of algebra of essentially bounded functions established recently…
Hairer's regularity structures transformed the solution theory of singular stochastic partial differential equations. The notions of positive and negative renormalisation are central and the intricate interplay between these two…
Many researches have discussed the phenomenon and definition of sharing economy, but an understanding of sharing economy's reconstructions of the world remains elusive. We illustrate the mechanism of sharing economy's reconstructions of the…
In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…
We aim to reconstruct a monoid scheme $X$ from the category of quasi-coherent sheaves over it. This is much in the vein of Gabriel's original reconstruction theorem. Under some finiteness condition on a monoid schemes $X$, we show that the…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
At the core of the Robertson-Seymour theory of graph minors lies a powerful structure theorem which captures, for any fixed graph H, the common structural features of all the graphs not containing H as a minor. Robertson and Seymour prove…
This paper focuses on the problem of reconstructing a vector of rational functions given some evaluations, or more generally given their remainders modulo different polynomials. The special case of rational functions sharing the same…
A characterization of regular topological fundamental groups yields a `no retraction theorem' for spaces constructed in similar fashion to the Hawaiian earring.
This expository note presents a constructive proof of Wigner's theorem using only a few basic facts about Hilbert spaces, such as the existence of orthonormal bases and the Fourier decomposition of a vector. Our proof is based on a proof by…
A new renormalization scheme for theories with nontrivial internal symmetry is proposed. The scheme is regularization independent and respects the symmetry requirements.
What belongs to quantum theory is no more than what is needed for its derivation. We argue for an approach focusing on reconstruction rather than interpretation of quantum mechanics and analyze several examples of reconstruction. We submit…
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…
We generalize the structure theorem of Robertson and Seymour for graphs excluding a fixed graph $H$ as a minor to graphs excluding $H$ as a topological subgraph. We prove that for a fixed $H$, every graph excluding $H$ as a topological…
A cornerstone theorem in the Graph Minors series of Robertson and Seymour is the result that every graph $G$ with no minor isomorphic to a fixed graph $H$ has a certain structure. The structure can then be exploited to deduce far-reaching…
General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…
The Hairer-Kelly map has been introduced for establishing a correspondence between geometric and non-geometric rough paths. Recently, a new renormalisation on rough paths has been proposed in (arxiv 1810.12179), built on this map and the…
In this paper, we present an algorithm for effectively reconstructing an object from a set of its tomographic projections without any knowledge of the viewing directions or any prior structural information, in the presence of pathological…
We study the problem of stable reconstruction of the short-time Fourier transform from samples taken from trajectories in $\R^2$. We first consider the interplay between relative density of the trajectory and the reconstruction property.…
Reconstruction problems lie at the very heart of both mathematics and science, posing the enigmatic challenge: \emph{How does one resurrect a hidden structure from the shards of incomplete, fragmented, or distorted data?} In this paper, we…