arXiv research

Wild involutions found in 3D sphere's Sobolev space.

A new method shrinks a complex structure without much change.

New bounds on the wildness of Bing's involution.

We consider pairs (X,Y) where X is a compact, locally CAT(-1) space, and Y is a totally geodesic subspace. The inclusion induces an embedding of the boundaries at infinity of the universal covers; we focus on the case where these are spheres whose dimensions differ by 2. We show that if the embedding is tame, then it i…

We study (i) asymptotic behaviour of wild harmonic bundles, (ii) the relation between semisimple meromorphic flat connections and wild harmonic bundles, (iii) the relation between wild harmonic bundles and polarized wild pure twistor $D$-modules. As an application, we show the hard Lefschetz theorem for algebraic semis…

Constructs infinitely many non-equivalent wild knots in Menger sponge.

New method uses mosaics to study wild knots.

This paper constructs wild knots from beaded necklaces using a Schottky group.

Injectivity proven for measure homology of certain wild spaces.

Study of wild mapping class groups on complex reflection groups.

Study of wild mapping class groups and their cabled braids.

The Gauss-Bonnet formula for classical translation surfaces relates the cone angle of the singularities (geometry) to the genus of the surface (topology). When considering more general translation surfaces, we observe so-called wild singularities for which the notion of cone angle is not applicable any more. We study w…

LoD improves model safety by integrating unlabeled wild data, reducing OOD misclassification.

We will construct twisted versions of the wild character varieties.

In this paper we study kleinian groups of Schottky type whose limit set is a wild knot in the sense of Artin and Fox. We show that, if the ``original knot'' fibers over the circle then the wild knot $Λ$ also fibers over the circle. As a consequence, the universal covering of $\mathbb{S}^{3}-Λ$ is $\mathbb{R}^{3}$. We p…

WILDS 2.0 expands benchmark datasets for unsupervised adaptation.

Efficiently refits black box predictions with wild refitting method.

This is the next step of uncovering the relation between string theory and exotic smooth R^4. Exotic smoothness of R^4 is correlated with D6 brane charges in IIA string theory. We construct wild embeddings of spheres and relate them to a class of topological quantum Dp-branes as well to KK theory. These branes emerge w…

Using methods of descriptive theory it is shown that the classification problem for wild knots is strictly harder than that for countable structures.

Automatic understanding of human affect using visual signals is of great importance in everyday human-machine interactions. Appraising human emotional states, behaviors and reactions displayed in real-world settings, can be accomplished using latent continuous dimensions (e.g., the circumplex model of affect). Valence …

Proves correspondence between harmonic and Higgs bundles.

New method estimates model risk without knowing function class.

In this paper we prove that a wild knot $K$ which is the limit set of a Kleinian group acting conformally on the unit 3-sphere, with its standard metric, is homogeneous: given two points $p, q\in{K}$ there exists a homeomorphism $f$ of the sphere such that $f(K)=K$ and $f(p)=q$. We also show that if the wild knot is a …

We will give several descriptions of some basic examples of wild character varieties, including a discussion of links to work of Sibuya, Calabi and Euler, amongst others.

The Ooguri-Vafa space is linked to framed wild harmonic bundles via hyperkähler geometry.

New method refines model-free evaluation of complex machine learning models.

The paper revisits the investment simulation based on strategies exhibited by Generalized (m,2)-Zipf law to present an interesting characterization of the wildness in financial time series. The investigations of dominant strategies on each specific time series shows that longer words dominant in larger time scale exhib…

In this paper we construct infinitely many wild knots, $\mathbb{S}^{n}\hookrightarrow\mathbb{S}^{n+2}$, for $n=2,3,4$ and 5, each of which is a limit set of a geometrically finite Kleinian group. We also describe some of their properties

New embeddings show answer to Baker-Laidacker question can be yes or no.

A wild bootstrap method for nonparametric hypothesis tests based on kernel distribution embeddings is proposed. This bootstrap method is used to construct provably consistent tests that apply to random processes, for which the naive permutation-based bootstrap fails. It applies to a large group of kernel tests based on…

Classifies involutions on spherical 3-manifolds.

Project creates new dataset for 'in the wild' emotions recognition.

Study classifies Calabi-Yau threefolds with non-Gorenstein involutions.

The paper studies circular evolutes and involutes of framed curves in Euclidean space.

Paper presents a CNN-RNN method for multi-dimensional emotion recognition in-the-wild.

New formula for dual knots using involutions.

Every countable compact subset of sphere is tame.

The purpose of this paper is to construct an example of a 2-knot wildly embedded in $\mathbb{S}^{4}$ as the limit set of a Kleinian group. We find that this type of wild 2-knots has very interesting topological properties.

The study classifies involutions on del Pezzo surfaces.

Characterizes the Legendre involution on generic frontals.

Let $C$ and $D$ be a pair of crumpled $n$-cubes and $h$ a homeomorphism of $\text{Bd }C$ to $\text{Bd }D$ for which there exists a map $f_h: C\to D$ such that $f_h|\text{Bd }C =h$ and $f_{h}^{-1}(\text{Bd }D)=\text{Bd }C$. In our view the presence of such a triple $(C,D,h)$ suggests that $C$ is "at least as wild as" $D…

The paper defines conditions for good involutions in generalized Alexander quandles.

WILD-SCAV benchmarks AI in complex 3D FPS environments.

Study proves naturality and functoriality in a type of Heegaard Floer homology.

The paper develops a new theory for knots and 3-manifolds with involutions.

The study proves symplectic quandles cannot have good involutions.

Involution algebroids extend Lie algebroids to tangent categories.

Classifies dissecting involutions on symmetric spaces.