相关论文: There exists a topologically mixing IET
Interchange theorems between minimization and integration are useful in optimization, especially in optimal control and in stochastic optimization. In this article, we establish a generalized minimization interchange theorem, where…
Topological conjugateness of one dimensional unimodal dynamical systems, which are generated by interval [0, 1] into itself maps are studied. We study the smoothness and differentiability of the conjugacy of symmetrical and non-symmetrical…
We construct a set of topological generators for the monoid of time-changes preserving the space of dynamical zeta functions.
In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a non empty set. Also we have used the idea of I-convergence of double sequences to…
We investigate substitution subshifts and tiling dynamical systems arising from the substitutions (1) \theta : 0 \rightarrow 001,1 \rightarrow 11001 and (2) \eta : 0 \rightarrow 001,1 \rightarrow 11100. We show that the substitution…
Motivated by the notion of intermediate dimensions introduced by Falconer et al., we introduce a continuum of topological entropies that are intermediate between the (Bowen) topological entropy and the lower and upper capacity topological…
Mixture of Experts (MoE) models based on Transformer architecture are pushing the boundaries of language and vision tasks. The allure of these models lies in their ability to substantially increase the parameter count without a…
A relationally exchangeable structure is a random combinatorial structure whose law is invariant with respect to relabeling its relations, as opposed to its elements. Aside from exchangeable random partitions, examples include edge…
A combinatorial substitution is a map over tilings which allows to define sets of tilings with a strong hierarchical structure. In this paper, we show that such sets of tilings are sofic, that is, can be enforced by finitely many local…
This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.
The aim of this paper is to prove an improved version of the bounded differences inequality for matrix valued functions, by developing the methods of Mackey et al.: "Matrix Concentration Inequalities via the Method of Exchangeable Pairs".…
A sequence of random variables is called exchangeable if the joint distribution of the sequence is unchanged by any permutation of the indices. De Finetti's theorem characterizes all $\{0,1\}$-valued exchangeable sequences as a "mixture" of…
Recent advances in experimental and computational techniques have allowed for an accurate description of the adsorption of ionic liquids on metallic electrodes. It is now well established that they adopt a multi-layered structure, and that…
Topological phases usually are unreachable in molecular solids, which are characteristic of weakly dispersed energy bands with a large gap, in contrast to topological materials. In this work, however, we propose that nontrivial electronic…
Analytical expressions for the exchange interaction between $J$-multiplets of interacting metallic centers are derived on the basis of a complete electronic model. A common belief that this interaction can be approximated by an isotropic…
For some full measure subset B of the set of iet's (i.e. interval exchange transformations) the following is satisfied: Let X be a $C^r$, $1\le r\le \infty$, vector field, with finitely many singularities, on a compact orientable surface M.…
Let $T\times X\rightarrow X, (t,x)\mapsto tx$, be a topological semiflow on a topological space $X$ with phase semigroup $T$. We introduce and discuss in this paper various transitivity dynamics of $(T,X)$.
Interval exchange transformations are typically uniquely ergodic maps and therefore have uniformly distributed orbits. Their degree of uniformity can be measured in terms of the star-discrepancy. Few examples of interval exchange…
Mechanical vibrations are being harnessed for a variety of purposes and at many length scales, from the macroscopic world down to the nanoscale. The considerable design freedom in mechanical structures allows to engineer new…
This paper considers the egodicity properties in iterated function systems. First, we will introduce chain mixing and chain transitive iterated function systems then some results and examples are presented to compare with these notions in…