arXiv subjects

Jonas Flechsig

Publications and source records attributed to Jonas Flechsig.

5 recordsLinked to original sources

arXiv2025

Conformal prediction without knowledge of labeled calibration data

We extend the method of conformal prediction beyond the case relying on labeled calibration data. Replacing the calibration scores by suitable estimates, we identify conformity sets $C$ for classification and regression models that rely on unlabeled calibration data. Given a classification model with accuracy $1-\beta$, we prove that the conformity sets guarantee a coverage of $P(Y \in C) \geq 1-\alpha-\beta$ for an arbitrary parameter $\alpha \in (0,1)$. The same coverage guarantee also holds for regression models, if we replace the accuracy by a similar exactness measure. Finally, we describe how to use the theoretical results in practice.

stat.ME↗

arXiv2024

Asymptotic mapping class groups of Cantor manifolds and their finiteness properties

We prove that the infinite family of asymptotic mapping class groups of surfaces of defined by Funar--Kapoudjian and Aramayona--Funar are of type $F_\infty$, thus answering questions of Funar-Kapoudjian-Sergiescu and Aramayona-Vlamis. As it turns out, this result is a specific instance of a much more general theorem which allows to deduce that asymptotic mapping class groups of Cantor manifolds, also introduced in this paper, are of type $F_\infty$, provide the underlying manifolds satisfy some general hypotheses. As important examples, we will obtain $F_\infty$ asymptotical mapping class groups that contain, respectively, the mapping class group of every compact surface with non-empty boundary, the automorphism group of every free group of finite rank, or infinite families of arithmetic groups. In addition, for certain types of manifolds, the homology of our asymptotic mapping class groups coincides with the stable homology of the relevant mapping class groups, as studied by Harer and Hatcher--Wahl.

math.GT↗

arXiv2023

Orbifold braid groups and complex braid groups

A result of Allock [1](arXiv:math/9907194) states that certain orbifold braid groups contain Artin groups of type $D_n$, $\tilde{B}_n$ and $\tilde{D}_n$ as finite index subgroups. The underlying orbifolds have at most two cone points of order two. Based on [10](arXiv:2305.04273) and [12](arXiv:2305.04273), we generalize this result allowing cone points of arbitrary order. In these cases, the orbifold braid groups contain similar subgroups of finite index. We show that in many cases these subgroups can be identified as certain complex braid groups.

math.GR↗

arXiv2023

Mapping class groups for 2-orbifolds

We define orbifold mapping class groups (with marked points) and study them using their action on certain orbifold analogs of arcs and simple closed curves. Moreover, we establish a Birman exact sequence for suitable subgroups of orbifold mapping class groups. The short exact sequence allows us to deduce finite presentations of these groups. This is the basis for a similar discussion of orbifold braid groups in [6].

math.GT↗

arXiv2023

Braid groups and mapping class groups for 2-orbifolds

The main result of this article is that pure orbifold braid groups fit into an exact sequence $1\rightarrow K\rightarrowπ_1^{orb}(Σ_Γ(n-1+L))\xrightarrow{ι_{\textrm{PZ}_n}}\textrm{PZ}_n(Σ_Γ(L))\xrightarrow{π_{\textrm{PZ}_n}}\textrm{PZ}_{n-1}(Σ_Γ(L))\rightarrow1.$ In particular, we observe that the kernel $K$ of $ι_{\textrm{PZ}_n}$ is non-trivial. This corrects Theorem 2.14 in [12](arXiv:2006.07106). Moreover, we use the presentation of the pure orbifold mapping class group $\textrm{PMap}^{\textrm{id},orb}_n(Σ_Γ(L))$ from [8] to determine $K$. Comparing these orbifold mapping class groups with the orbifold braid groups, reveals a surprising behavior: in contrast to the classical case, the orbifold braid group is a proper quotient of the orbifold mapping class group. This yields a presentation of the pure orbifold braid group which allows us to read off the kernel $K$.

math.GT↗