Related papers: On embedding of repetitive Meyer multiple sets int…

Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…

Embedding of large but redundant data, such as images or text, in a hierarchy of lower-dimensional spaces is one of the key features of representation learning approaches, which nowadays provide state-of-the-art solutions to problems once…

According to the method, suggested in our previous work (nlin/0509012) and based on the consideration of the specially coupled systems, the possibility of physical realization of the phenomena of complex analytic dynamics (such as…

We discuss the dependence of set-valued dynamical systems on parameters. Under mild assumptions which are often satisfied for random dynamical systems with bounded noise and control systems, we establish the fact that topological…

We extend the classical Mercer theorem to reproducing kernel Hilbert spaces whose elements are functions from a measurable space $X$into $\mathbb C^n$. Given a finite measure $\mu$ on $X$, we represent the reproducing kernel $K$ as…

We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…

The article presents a new perspective on the isomorphism problem for non-ergodic measure-preserving dynamical systems with discrete spectrum which is based on the connection between ergodic theory and topological dynamics constituted by…

The Krieger generator theorem says that every invertible ergodic measure-preserving system with finite measure-theoretic entropy can be embedded into a full shift with strictly greater topological entropy. We extend Krieger's theorem to…

If an automorphism f of a structure M is such that fix(f^k) = fix(f) for all positive k, then M|fix(f) is a substructure of M. The possible isomorphism types of such M|fix(f) are characterized when M is countable and arithmetically…

We extend the proof of automatic continuity for homeomorphism groups of manifolds to non-compact manifolds and manifolds with marked points and their mapping class groups. Specifically, we show that, for any manifold $M$ homeomorphic to the…

Let M be a compact manifold, possibly with boundary. We show that the group of homeomorphisms of M has the automatic continuity property: any homomorphism from Homeo(M) to any separable group is necessarily continuous. This answers a…

Word embedding models offer continuous vector representations that can capture rich contextual semantics based on their word co-occurrence patterns. While these word vectors can provide very effective features used in many NLP tasks such as…

A recent paper by Zapletal arXiv:2404.10612 discusses permutation models of set theory which arise from dynamical ideals and highlights properties of the dynamical ideal which relate to fragments of choice in the permutation model. In this…

A random group contains many subgroups which are isomorphic to the fundamental group of a compact hyperbolic 3-manifold with totally geodesic boundary. These subgroups can be taken to be quasi-isometrically embedded. This is true both in…

We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two topological properties for set-valued functions and…

For any dynamical system $T:X\rightarrow X$ of a compact metric space $X$ with $g-$almost product property and uniform separation property, under the assumptions that the periodic points are dense in $X$ and the periodic measures are dense…

This paper studies recurrence phenomena in iterative holomorphic dynamics of certain multi-valued maps. In particular, we prove an analogue of the Poincar\'e recurrence theorem for meromorphic correspondences with respect to certain…

We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…

Periodic surface homemorphisms (diffeomorphisms) play a significant role in the the Nielsen-Thurston classification of surface homeomorphisms. Periodic surface homeomorphisms can be described (up to conjugacy) by using data sets which are…

It is a consequence of the Jacobi Inversion Theorem that a line bundle over a Riemann surface M of genus g has a meromorphic section having at most g poles, or equivalently, the divisor class of a divisor D over M contains a divisor having…