arXiv research

Paper examines trading polarity to predict market crashes.

The availability of data on digital traces is growing to unprecedented sizes, but inferring actionable knowledge from large-scale data is far from being trivial. This is especially important for computational finance, where digital traces of human behavior offer a great potential to drive trading strategies. We contrib…

Consider a financial market in which an agent trades with utility-induced restrictions on wealth. By introducing a general convex-analytic framework which includes the class of umbrella wedges in certain Riesz spaces and faces of convex sets (consisting of probability measures), together with a duality theory for polar…

Paper evaluates and mitigates privacy risks in deep learning models.

Study predicts cryptocurrency price movements using Twitter sentiment analysis.

We classify the polar actions on the complex hyperbolic plane up to orbit equivalence. Apart from the trivial and transitive polar actions, there are five polar actions of cohomogeneity one and four polar actions of cohomogeneity two.

Uniform K-stability holds for close polarizations if original is canonical or anti-canonical.

Study polar actions on Damek-Ricci spaces, proving existence and finding examples.

The paper studies how Kähler polarizations degenerate to mixed polarizations on toric varieties.

Polarized and $G$-polarized CR manifolds are smooth manifolds endowed with a double structure: a real foliation $\Cal F$ (given by the action of a Lie group $G$ in the $G$-polarized case) and a transverse CR distribution $(E,J)$. Polarized means that $(E,J)$ is roughly speaking invariant by $\Cal F$. Both structures ar…

A polarity of a projective plane is a map, often assumed to be involutive, mapping a generic point to a generic line and reciprocally. The most classical polarity is the polarity with respect to a conic, but other exist: the harmonic polarity with respect to a triangle, the polarities with respect to high-degree algebr…

The generic fiber of a Lagrangian fibration on an irreducible holomorphic symplectic manifold is an abelian variety. Associate a polarization type to such Lagrangian fibrations coming from polarizations on a generic fiber. We prove that this polarization type is constant in families of Lagrangian fibrations. Further, w…

Financial markets provide an ideal frame for studying decision making in crowded environments. Both the amount and accuracy of the data allows to apply tools and concepts coming from physics that studies collective and emergent phenomena or self-organised and highly heterogeneous systems. We analyse the activity of 29,…

Paper uses ResUNet-CMB to reconstruct cosmic polarization rotation from CMB data.

New method polarizes anisotropic Heisenberg groups.

The study introduces polarization of generalized Nijenhuis torsions and their relevance in operator fields.

The study classifies Riemannian homogeneous spaces with polar isotropy actions.

Classifies polar foliations on symmetric spaces.

The paper studies polar normalizations of skew ruled surfaces in 3D space.

Classifies totally geodesic submanifolds and polar actions on Stiefel manifolds.

Classifies hexagonal circular 3-webs with cubic polar curves.

The main result of this paper is that a polar action on a compact irreducible homogeneous Kaehler manifold is coisotropic. This is then used to give new examples of polar actions and to classify coisotropic and polar actions on quadrics.

Consider a financial market in which an agent trades with utility-induced restrictions on wealth. For a utility function which satisfies the condition of reasonable asymptotic elasticity at $-\infty$ we prove that the utility-based super-replication price of an unbounded (but sufficiently integrable) contingent claim i…

POLAR framework interprets word embeddings using polar opposites.

Study empty polar varieties' impact on singular function-germs.

For complex projective manifolds we introduce polar homology groups, which are holomorphic analogues of the homology groups in topology. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the boundary operator is defined by taking the polar divisor and the Poincare residue …

Totally geodesic sections found in polar actions.

We prove a criterion for an isometric action of a Lie group on a Riemannian manifold to be polar. From this criterion, it follows that an action with a fixed point is polar if and only if the slice representation at the fixed point is polar and the section is the tangent space of an embedded totally geodesic submanifol…

Carnot groups can be polarized if they have specific coordinate systems.

Polar manifolds are Riemannian G-manifolds admitting a "section", i.e., a complete submanifold passing through every orbit and doing so orthogonally. We consider compact simply-connected polar manifolds and achieve an equivariantly diffeomorphic classification in dimensions 5 or less. As an application, we determine wh…

The paper bounds abnormal and Goh-abnormal sets for metabelian Lie groups with polarizations.

In this paper, we generalize the polar transforms of spacelike isothermic surfaces in $Q^4_1$ to n-dimensional pseudo-Riemannian space forms $Q^n_r$. We show that there exist $c-$polar spacelike isothermic surfaces derived from a spacelike isothermic surface in $Q^n_r$, which are into $S^{n+1}_r(c)$, $H^{n+1}_{r-1}(c)$…

Classifies polar actions on 3D homogeneous spaces.

Study shows horizontal diameter of unit spheres is π for specific foliations.

The paper introduces polarizations in symplectic and orthogonal settings.

We give a simple sufficient condition for K-stability of polarized del Pezzo surfaces and for the existence of a constant scalar curvature Kahler metric in the Kahler class corresponding to the polarization.

We classify infinitesimally polar actions on compact Riemannian symmetric spaces of rank one. We also prove that every polar action on one of those spaces has the same orbits as an asystatic action.

Investigates polar tangential angles of curves and their monotonicity.

Proved inequality for anti-self-polar polytopes.

New method shows unitarity in quantization for toric manifolds.

Classifies foliations on specific symmetric spaces.

In this paper, assuming that a polarized algebraic manifold $(X,L)$ is strongly K-stable, we shall show that the polarization class $c_1(L)$ admits a constant scalar curvature Kaehler metric.

This paper fine-tunes BERT for stock market sentiment analysis and improves trading performance.

Introduces Polar Depth for analyzing multivariate heavy-tailed data extremes.

The paper introduces a method to make neural networks more robust to adversarial attacks.

Paper uses polar field data to improve solar flare prediction accuracy.

We analyze polar actions on Hermitian and quaternion-Kähler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries concerning the geometry of these actions. The results are independent of the classificatio…

We relate the Lipschitz-Killing measures of a definable set $X \subset \mathbb{R}^n$ in an o-minimal structure to the volumes of generic polar images. For smooth submanifolds of $\mathbb{R}^n$, such results were established by Langevin and Shifrin.Then we give infinitesimal versions of these results. As a corollary, we…