相关论文: Coherence and uniqueness theorems for averaging pr…
Coherence phenomena appear in two different situations. In the context of category theory the term `coherence constraints' refers to a set of diagrams whose commutativity implies the commutativity of a larger class of diagrams. In the…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
Ensemble learning is traditionally justified as a variance-reduction strategy, explaining its strong performance for unstable predictors such as decision trees. This explanation, however, does not account for ensembles constructed from…
We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…
We consider three uniqueness theorems: one from the theory of meromorphic functions, another one from asymptotic combinatorics, and the third one about representations of the infinite symmetric group. The first theorem establishes the…
We study a specific family of symmetric norms on the algebra $\mathcal B(\mathcal H)$ of operators on a separable infinite-dimensional Hilbert space. With respect to each symmetric norm in this family the identity operator fails to attain…
We consider continuous $\mathrm{SL}(2,\mathbb{R})$ valued cocycles over general dynamical systems and discuss a variety of uniformity notions. In particular, we provide a description of uniform one-parameter families of continuous…
By the early 1960's advances in statistical physics had established the existence of universality classes for systems with second-order phase transitions and characterized these by critical exponents which are different to the classical…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
The operations of linear algebra, calculus, and statistics are routinely applied to measurement scales but certain mathematical conditions must be satisfied in order for these operations to be applicable. We call attention to the conditions…
A differential operator of weight $\lambda$ is the algebraic abstraction of the difference quotient $d_\lambda(f)(x):=\big(f(x+\lambda)-f(x)\big)/\lambda$, including both the derivation as $\lambda$ approaches to $0$ and the difference…
Estimating covariance matrices is a problem of fundamental importance in multivariate statistics. In practice it is increasingly frequent to work with data matrices $X$ of dimension $n\times p$, where $p$ and $n$ are both large. Results…
We establish two versions of a central theorem, the Family Colimit Theorem, for the coarse coherence property of metric spaces. This is a coarse geometric property and so is well-defined for finitely generated groups with word metrics. It…
We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the…
Considering a family of upper frequently hypercyclic operators we care about the existence of vectors which are upper frequently hypercyclic for any operator of this family. We establish sufficient conditions for a family of operators to…
Many iterative methods in optimization are fixed-point iterations with averaged operators. As such methods converge at an $\mathcal{O}(1/k)$ rate with the constant determined by the averagedness coefficient, establishing small averagedness…
On the vertex operator algebra associated with rank one lattice we derive a general formula for products of vertex operators in terms of generalized homogeneous symmetric functions. As an application we realize Jack symmetric functions of…
We introduce a family of generalized d'Alembertian operators in D-dimensional Minkowski spacetimes which are manifestly Lorentz-invariant, retarded, and non-local, the extent of the nonlocality being governed by a single parameter $\rho$.…
We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, homogeneous kernels of such operators are also studied. The…
The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators…