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Transfer learning has emerged as a highly sought-after and actively pursued research area within the statistical community. The core concept of transfer learning involves leveraging insights and information from auxiliary datasets to…

We prove that every factor map between topological flows preserves the standard shadowing property if it is injective except for a closed orbit that shrinks to a singularity. As an application, we construct a $C^\infty$-flow on a…

This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generically (in topological sense) if the attractor of such a…

We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of increasing functions on the positive integers. Our results and…

We provide a simple description of asymptotic pairs in the subshift associated with an interval exchange transformation and show that, under reasonably general conditions, doubly asymptotic pairs do not occur.

The aim of this article is to analyze the asymptotic properties of the C-metric, using a general method specified in work of Tafel and coworkers, [1], [2], [3]. By finding an appropriate conformal factor $\Omega$, it allows the…

We investigate generic properties (i.e. properties corresponding to residual sets) in the space of subshifts with the Hausdorff metric. Our results deal with four spaces: the space $\mathbf{S}$ of all subshifts, the space…

Given an infinite iterated function system (IFS) $\mathcal{F}$, we define its dimension spectrum $D(\mathcal{F})$ to be the set of real numbers which can be realised as the dimension of some subsystem of $\mathcal{F}$. In the case where…

The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a…

Inspired by distributed applications that use consensus or other agreement protocols for global coordination, we define a new computational model for parameterized systems that is based on a general global synchronization primitive and…

We introduce a unified framework for studying persistence phenomena in commutative algebra via filtrations of ideals. For a filtration $\mathcal{F} = \{I_i\}_{i \in \mathbb{N}}$, we define $\mathcal{F}$-persistence and $\mathcal{F}$-strong…

We show that in a generalized Adams spectral sequence, the presence of a vanishing line of fixed slope (at some term of the spectral sequence, with some intercept) is a generic property.

Generalized likelihoods are commonly used to obtain consistent estimators with attractive computational and robustness properties. Formally, any generalized likelihood can be used to define a generalized posterior distribution, but an…

The signature of a path, as a fundamental object in Rough path theory, serves as a generating function for non-commutative monomials on path space. It transforms the path into a grouplike element in the tensor algebra space, summarising the…

We prove that a graph G is asymptotically isomorphic to the ray if and only if G is uniformly spherically bounded and is of bounded local degrees. This problem arouse in combinatorics and was posed in [3] (Problem 10.1).

We consider iterated function systems $\mathrm{IFS}(T_1,\dots,T_k)$ consisting of continuous self maps of a compact metric space $X$. We introduce the subset $S_{\mathrm{t}}$ of {\emph{weakly hyperbolic sequences}} $\xi=\xi_0\ldots\xi_n…

S-matrix elements exhibit universal factorization when multiple infrared photons are emitted in scattering processes. We explicitly show that the leading soft factorization of tree-level amplitudes with the emission of any number of soft…

This paper is partly an exposition, and partly an extension of our work [1] to the multiparameter case. We consider certain classes of parametrized dynamically defined measures. These are push-forwards, under the natural projection, of…

We establish an averaging principle on the real semi-axis for semi-linear equation \begin{equation}\label{eqAb1} x'=\varepsilon (\mathcal A x+f(t)+F(t,x))\nonumber \end{equation} with unbounded closed linear operator $\mathcal A$ and…

We prove the asymptotic normality of the standardized number of crossings of a centered stationary mixing Gaussian process when both the level and the time horizon go to infinity in such a way that the expected number of crossings also goes…