arXiv research

Developed causal chambers for AI validation, providing real-world data.

We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.

The paper studies chambered invariants of real Cauchy-Riemann operators on Riemann surfaces.

The paper studies proper discontinuity of actions on Weyl chamber flow spaces.

Modular curves $X_{1}(N)$ parametrize elliptic curves with a point of order $N$. They can be identified with connected components of projectivized strata $\mathbb{P}\mathcal{H}(a,-a)$ of meromorphic differentials. As strata of meromorphic differentials, they have a canonical walls-and-chambers structure defined by the …

New compactification for character varieties with good topological properties.

In this paper we set up the family Seiberg-Witten theory. It can be applied to the counting of nodal pseudo-holomorphic curves in a symplectic 4-manifold (especially a Kahler surface). A new feature in this theory is that the chamber structure plays a more prominent role. We derive some wall crossing formulas measuring…

We investigate the geometry in a real Euclidean building X of type A2 of some simple configurations in the associated projective plane at infinity P, seen as ideal configurations in X, and relate it with the projective invariants (from the cross ratio on P). In particular we establish a geometric classification of gene…

We study the space $\nua{m}{d}$ of clouds in $\bbr^d$ (ordered sets of $m$ points modulo the action of the group of affine isometries). We show that $\nua{m}{d}$ is a smooth space, stratified over a certain hyperplane arrangement in $\bbr^m$. We give an algorithm to list all the chambers and other strata (this is indep…

The radius of the star-shaped set need not have been continuous.

The generalized soap bubble problem seeks the least perimeter way to enclose and separate n given volumes in R^m. We study the possible configurations for perimeter minimizing bubble complexes enclosing more than two regions. We prove that perimeter minimizing planar bubble complexes with equal pressure regions and wit…

We investigate discrete groups $G$ of isometries of a complete connected Riemannian manifold $M$ which are generated by reflections, in particular those generated by disecting reflections. We show that these are Coxeter groups, and that the the orbit space $M/G$ is isometric to a Weyl chamber $C$ which is a Riemannian …

The paper proves an infinite double bubble theorem in higher dimensions.

The paper characterizes when numerical criteria for PDE solvability fail and provides effective criteria for existence.

The paper studies HYM connections on stable vector bundles over Kähler manifolds.

We present an explicit construction of the moduli spaces of rank 2 stable parabolic bundles of parabolic degree 0 over the Riemann sphere, corresponding to "optimum" open weight chambers of parabolic weights in the weight polytope. The complexity of the different moduli space' weight chambers is understood in terms of …

In this paper we present a topological way of building a compactification of a symmetric space from a compactification of a Weyl Chamber.

New framework models echo chamber learning, proving tight bounds on algorithm performance.

Machine learning is used extensively in recommender systems deployed in products. The decisions made by these systems can influence user beliefs and preferences which in turn affect the feedback the learning system receives - thus creating a feedback loop. This phenomenon can give rise to the so-called "echo chambers" …

The automatic reconstruction of three-dimensional particle tracks from Active Target Time Projection Chambers data can be a challenging task, especially in the presence of noise. In this article, we propose a non-parametric algorithm that is based on the idea of clustering point triplets instead of the original points.…

BCAE-2D compresses 3D data from a time projection chamber at high speed.

We study arrangements of $m$ hyperplanes in the $n$-dimensional real projective space, with a special focus on $m=n+3$ and $n=3$ or $n=4$.

New resonance theory for Anosov flows connects spectral properties to mixing measures.

We consider the family of harmonic measures on a lamination $\mathcal{L}$ of a compact space $X$ by locally symmetric spaces $L$ of noncompact type, i.e. $L\simeq Γ_L\backslash G/K$. We establish a natural bijection between these measures and the measures on an associated lamination foliated by $G$-orbits, $\hat{\mathc…

Characterizes solutions to Z-critical equations on surfaces using effective conditions.

Study convex hulls of orbits for compact groups, defining new invariants related to polynomial degrees.

We present the Bayesian Echo Chamber, a new Bayesian generative model for social interaction data. By modeling the evolution of people's language usage over time, this model discovers latent influence relationships between them. Unlike previous work on inferring influence, which has primarily focused on simple temporal…

Model financial markets with social media influences using hierarchical networks.

Survey on hyperplane arrangements and their topology.

There is a well known link between (maximal) polar representations and isotropy representations of symmetric spaces provided by Dadok. Moreover, the theory by Tits and Burns-Spatzier provides a link between irreducible symmetric spaces of non-compact type of rank at least three and irreducible topological spherical bui…

Closed geodesics found on specific non-compact manifolds.

We compute the Moore-Witten regularized u-plane integral on CP^1 x CP^1 directly in a chamber where the elliptic unfolding technique fails to work. This allows us to determine explicit formulas for its SU(2) and SO(3)-Donaldson invariants in terms of Mock modular forms.

We introduce \textcolor{red}{general} new techniques for computing the geometric index of a link $L$ in the interior of a solid torus $T$. These techniques simplify and unify previous ad hoc methods used to compute the geometric index in specific examples \textcolor{red}{ and allow the simple computation of geometric i…

Symmetrizes 4d and 3d BPS quivers for Argyres-Douglas theories.

Model clusters authors and topics in short texts like social media posts.

StructureBoost improves gradient boosting for complex categorical variables efficiently.

We study the Weyl chamber length boundary both of the Hitchin and of the maximal character varieties and determine therein an open set of discontinuity for the action of the mapping class group. This result is obtained as consequence of a canonical decomposition of a geodesic current on a surface of finite type arising…

Categorical bundles provide a natural framework for gauge theories involving multiple gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality, and hence also of local triviality, for categorical bundles. We study categorical principal bundles that are product bundles in the categor…

New method constructs multi-monopoles on mapping tori.

The purpose of this paper is applying minimality of hyperplane arrangements to local system cohomology groups. It is well known that twisted cohomology groups with coefficients in a generic rank one local system vanish except in the top degree, and bounded chambers form a basis of the remaining cohomology group. We det…

Bayesian model improves categorization of explosions from sparse data.

UNTIE learns representations of coupled categorical data.

Paper introduces Categorical Normalizing Flows for better handling of categorical data.

This paper proposes a method to reduce complexity in GLMs with categorical predictors.

In this paper we describe the Seiberg-Witten invariants, which have been introduced by Witten, for manifolds with $b_+=1$. In this case the invariants depend on a chamber structure, and there exists a universal wall crossing formula. For every Kähler surface with $p_g=0$ and $q$=0, these invariants are non-trivial for …

The paper shows how integrating categorical semantics can enhance unsupervised domain translation.

Categorical variables are a natural choice for representing discrete structure in the world. However, stochastic neural networks rarely use categorical latent variables due to the inability to backpropagate through samples. In this work, we present an efficient gradient estimator that replaces the non-differentiable sa…

Study categorizes mutual funds using natural language processing from unstructured data.