arXiv research

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

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

This paper deals with skew ruled surfaces in the Euclidean space $\mathbb{E}^{3}$ which are equipped with polar normalizations, that is, relative normalizations such that the relative normal at each point of the ruled surface lies on the corresponding polar plane. We determine the invariants of a such normalized ruled …

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

Neural network implementation of Brenier's polar factorization for vector fields.

The paper introduces polarizations in symplectic and orthogonal settings.

Develops a universal Hermitian projective calculus for complex hyperbolic two-space

Let $M$ be a closed manifold of Sasaki type. A polarization of $M$ is defined by a Reeb vector field, and for one such, we consider the set of all Sasakian metrics compatible with it. On this space, we study the functional given by the squared $L^2$-norm of the scalar curvature. We prove that its critical points, or ca…

Given a polarized complex manifold, projection of a torus-equivariant test configuration to holomorphic vector fields was introduced by G. Székelyhidi, as the limit of the associated $\mathbb{C}^*$-actions. We show that there actually holds the moment convergence of the weight distributions. Our analytic approach at th…

The complete invariant for gradient like Morse-Smale dynamical systems (vector fields and diffeomorphisms) on closed 4-manifolds are constructed. It is same as Kirby diagram in a case of polar vector field without fixed points of index 3.

Study of cosmic microwave background polarization using spin random fields.

Let (X,L) be a polarized Kähler manifold that admits an extremal Kähler metric in c1(L). We show that on a nearby polarized deformation that preserves the symmetry induced by the extremal vector field of (X,L), the modified K-energy is bounded from below. This generalizes a result of Chen, Székelyhidi and Tosatti to ex…

Novel fusion network combines polarization and radiomics features for liver cancer classification.

PolarBM models complex-valued audio signals in polar coordinates, improving over conventional methods.

Classifies limits of groups of involutions in SL(2,F) over local fields.

The vulnerability of deep neural networks to small, adversarially designed perturbations can be attributed to their "excessive linearity." In this paper, we propose a bottom-up strategy for attenuating adversarial perturbations using a nonlinear front end which polarizes and quantizes the data. We observe that ideal po…

We show that using the family of adapted Kähler polarizations of the phase space of a compact, simply connected, Riemannian symmetric space of rank-1, the obtained field $H^{corr}$ of quantum Hilbert spaces produced by geometric quantization including the half-form correction is flat if $M$ is the 3-dimensional sphere …

We show that the Einstein-Hilbert functional, as a functional on the space of Reeb vector fields, detects the vanishing Sasaki-Futaki invariant. In particular, this provides an obstruction to the existence of a constant scalar curvature Sasakian metric. As an application we prove that K-semistable polarized Sasaki mani…

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

The paper describes a fine representation of the Ricci tensor and Hessian on RCD spaces.

The imbalance of buying and selling functions profoundly in the formation of market trends, however, a fine-granularity investigation of the imbalance is still missing. This paper investigates a unique transaction dataset that enables us to inspect the imbalance of buying and selling on the man-times level at high freq…

Defines volume and Monge-Ampère energy on polarized affine varieties.

We survey physical models which capture the main concepts of double field theory on para-Hermitian manifolds. We show that the geometric theory of Lagrangian and Hamiltonian dynamical systems is an instance of para-Kahler geometry which extends to a natural example of a Born geometry. The corresponding phase space geom…

We show how a polar representation of a compact connected Lie group can be linearly determined from its dimension and isotropy subgroup data in the general reducible case.

Second paper in series solves Einstein vacuum equations for three impulsive waves.

POLAR optimizes treatment strategies in dynamic settings with statistical guarantees.

Formula for critical points of chi fields on manifolds.

Study describes limits of non-collapsing K3 surfaces using algebraic data.

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.

In the previous article (\cite{S}), we proved that slope stability of a holomorphic vector bundle $E$ over a polarized manifold $(X,L)$ implies Chow stability of $(\mathbb{P}E^*,\mathcal{O}_{\mathbb{P}E^*}(1)\otimes π^* L^k)$ for $k \gg 0$ if the base manifold has no nontrivial holomorphic vector field and admits a con…

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.

In this paper, we give a new construction of the adapted complex structure on a neighborhood of the zero section in the tangent bundle of a compact, real-analytic Riemannian manifold. Motivated by the "complexifier" approach of T. Thiemann as well as certain formulas of V. Guillemin and M. Stenzel, we obtain the polari…

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…

Method estimates treatment effect bounds in sample selection models.

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…

This paper introduces an acceleration structure for hyperbolic embeddings.

We establish an equivalence between conformally Einstein--Maxwell Kahler 4-manifolds (recently studied in many works) and extremal Kahler 4-manifolds (in the sense of Calabi) with nowhere vanishing scalar curvature. The corresponding pairs of Kahler metrics arise as transversal Kahler structures of Sasaki metrics compa…

Study on spin random fields using chaos decomposition for cosmic microwave background modeling.

POLAR learns efficient data acquisition policies using pretrained belief representations.

Classifies polar foliations on symmetric spaces.

The paper analyzes how multiple classifiers' disagreement and polarization affect overall accuracy.

Assume that a projective variety together with a polarization is uniformly K-stable. If the polarization is canonical or anti-canonical, then the projective variety is uniformly K-stable with respects to any polarization sufficiently close to the original polarization.

Uniqueness proven for a specific type of complex manifold's solitons.

Classifies totally geodesic submanifolds and polar actions on Stiefel manifolds.

Synthetic approach to pluripotential theory measures finite energy.

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.