Related papers: Labeled and Non-labeled Extended Rauzy Classes

Rauzy Classes and Extended Rauzy Classes are equivalence classes of permutations that arise when studying Interval Exchange Transformations. In 2003, Kontsevich and Zorich classified Extended Rauzy Classes by using data from Translation…

We consider generalized interval exchange transformations, or briefly GIETs, that is bijections of the interval which are piecewise increasing homeomorphisms with finite branches. When all continuous branches are translations, such maps are…

We introduce a new concept of interval rearrangement ensembles (IRE), which is a generalization of interval exchange transformations (IET). This construction expands the space of IETs in accordance with the natural duality that we pinpoint.…

We study the group of all interval exchange transformations (IETs). We show that for every IET $S$, there exists a dense open set of admissible IETs that share a relation with $S$. This is an extension of a result published by Dahmani,…

In this paper, we compare two definitions of Rauzy classes. The first one was introduced by Rauzy and was in particular used by Veech to prove the ergodicity of the Teichm\"uller flow. The second one is more recent and uses a "labeling" of…

Rauzy-type dynamics are group actions on a collection of combinatorial objects. The first and best known example (the Rauzy dynamics) concerns an action on permutations, associated to interval exchange transformations (IET) for the…

In this paper we present a variant of message sequence diagrams called EETs Extended Event Traces We provide the graphical notation discuss the methodological use of EETs to describe behavior of object oriented business information systems…

We introduce a definition of admissibility for subintervals in interval exchange transformations. Using this notion, we prove a property of the natural codings of interval exchange transformations, namely that any derived set of a regular…

A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira. Recurrent train tracks with a single switch provide a subclass of linear involutions. We call such linear involutions…

A disjoint rotation map is an interval exchange transformation (IET) on the unit interval that acts by rotation on a finite number of invariant subintervals. It is currently unknown whether the group E of all IETs possesses any non-abelian…

The structure of a network is an unlabeled graph, yet graphs in most models of complex networks are labeled by meaningless random integers. Is the associated labeling noise always negligible, or can it overpower the network-structural…

Identifying latent representations or causal structures is important for good generalization and downstream task performance. However, both fields have been developed rather independently. We observe that several methods in both…

The label noise transition matrix $T$, reflecting the probabilities that true labels flip into noisy ones, is of vital importance to model label noise and design statistically consistent classifiers. The traditional transition matrix is…

Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…

Large language models (LLMs) exhibit impressive in-context learning (ICL) capabilities, yet the quality of their predictions is fundamentally limited by the few costly labeled demonstrations that can fit into a prompt. Meanwhile, there…

We develop a renormalization scheme which extends the classical Rauzy-Veech induction used to study interval exchange tranformations (IETs) and allows to study generalized interval exchange transformations (GIETs) $T: [0,1) \to [0,1)$ with…

Let $T$ be an $m$-interval exchange transformation. By the rank of $T$ we mean the dimension of the $\mathbb{Q}$-vector space spanned by the lengths of the exchanged intervals. We prove that if $T$ is minimal and the rank of $T$ is greater…

The incremental sequence labeling task involves continuously learning new classes over time while retaining knowledge of the previous ones. Our investigation identifies two significant semantic shifts: E2O (where the model mislabels an old…

Federated learning (FL) is a popular solution for distributed machine learning (ML). While FL has traditionally been studied for supervised ML tasks, in many applications, it is impractical to assume availability of labeled data across…

Recent research shows that in-context learning (ICL) can be effective even when demonstrations have missing or incorrect labels. To shed light on this capability, we examine a canonical setting where the demonstrations are drawn according…