arXiv research

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.

We prove the Kobayashi-Hitchin correspondence between good wild harmonic bundles and polystable good filtered $λ$-flat bundles satisfying a vanishing condition. We also study the correspondence for good wild harmonic bundles with the homogeneity with respect to a group action, which is expected to provide another way t…

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 …

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.

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…

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.

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…

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

Human affect recognition is an essential part of natural human-computer interaction. However, current methods are still in their infancy, especially for in-the-wild data. In this work, we introduce our submission to the Affective Behavior Analysis in-the-wild (ABAW) 2020 competition. We propose a two-stream aural-visua…

4-manifolds have special topological properties which can be used to get a different view on quantum mechanics. One important property (connected with exotic smoothness) is the natural appearance of 3-manifold wild embeddings (Alexanders horned sphere) which can be interpreted as quantum states. This relation can be co…

The paper constructs wild Cantor sets in high dimensions.

Algorithm describes Fourier transform of Stokes data at infinity.

Let $Σ$ be a connected, oriented surface with punctures and negative Euler characteristic. We introduce wild globally hyperbolic anti-de Sitter structures on $Σ\times \mathbb{R}$ and provide two parameterisations of their deformation space: as a quotient of the product of two copies of the Teichmüller space of crowned …

A new method shrinks a complex structure without much change.

The Ooguri-Vafa space is a 4-dimensional incomplete hyperkähler manifold, defined on the total space of a singular torus fibration with one singular nodal fiber. It has been proposed that the Ooguri-Vafa hyperkähler metric should be part of the local model of the hyperkähler metric of the Hitchin moduli spaces, near th…

Automatic understanding of human affect using visual signals is a problem that has attracted significant interest over the past 20 years. However, human emotional states are quite complex. To appraise such states displayed in real-world settings, we need expressive emotional descriptors that are capable of capturing an…

In this paper we consider the Kleinian groups acting conformally on the sphere $\mathbb{S}^{n+2}$ $(1\leq{n}\leq5)$ which have as limit sets wild spheres $K^n$ which were constructed in \cite{BHV} and prove that $K^n$ is ambient homogeneous. In other words, given two points $p,\,\,q\in{K}$ there exists a homeomorphism …

The extended Wild sums considered in this article generalize the classi- cal Wild sums of statistical physics. We first show how to obtain explicit solutions for the evolution equation of a large system where the interactions are given by a single, but general, interacting kernel which involves m components, for a fixe…

Study concordance of decompositions from defining sequences in 3-sphere.

Study detects synthetic tabular data across different tables.

Over the past few years many research efforts have been devoted to the field of affect analysis. Various approaches have been proposed for: i) discrete emotion recognition in terms of the primary facial expressions; ii) emotion analysis in terms of facial Action Units (AUs), assuming a fixed expression intensity; iii) …

In the context of HCI, building an automatic system to recognize affect of human facial expression in real-world condition is very crucial to make machine interact naturallisticaly with a man. However, existing facial emotion databases usually contain expression in the limited scenario under well-controlled condition. …

T. Mochizuki constructs a theory of variations of wild Hodge structure for which the underlying flat connection can have irregular singularities at infinity. He extends in this way the correspondence of Corlette and Simpson between irreducible flat bundles and stables Higgs bundles, taking into account objects with irr…

Study local wild mapping class groups for irregular connections on complex curves.

Emotions recognition is the task of recognizing people's emotions. Usually it is achieved by analyzing expression of peoples faces. There are two ways for representing emotions: The categorical approach and the dimensional approach by using valence and arousal values. Valence shows how negative or positive an emotion i…

Uniform convergence of isotopies implies ambient isotopy, aiding knot equivalence.

We consider flat surfaces and the points of their metric completions, particularly the singularities to which the flat structure of the surface does not extend. The local behavior near a singular point x can be partially described by a topological space L(x) which captures all the ways that x can be "approached linearl…