arXiv research

Paper proposes a new method to improve clustering ensemble performance.

We study co-associative fibrations of G_{2}-manifolds. We propose that the adiabatic limit of this structure should be given locally by a maximal submanifold in a space of indefinite signature and set up global versions of the constructions.

In this paper, we solve a semi-supervised regression problem. Due to the lack of knowledge about the data structure and the presence of random noise, the considered data model is uncertain. We propose a method which combines graph Laplacian regularization and cluster ensemble methodologies. The co-association matrix of…

Study $SO(3)$-invariant $G_2$-cobordisms on 6-manifolds.

We introduce a homology theory whose Euler characteristics counts ASD bundles over four dimensional co-associative submanifolds in (almost) G_2 manifolds. As a TQFT, in relative situations, we have the Fukaya-Floer category of Lagrangians intersection in the moduli space of special Lagrangian submanifolds in CY threefo…

By analogy with associative and co-associative cases we introduce a class of three-dimensional non-orientable submanifolds, of almost $\mathrm{G}_2-$manifolds, modelled on planes lying in a special $\mathrm{G}_2-$orbit. An application of the Cartan-Kähler theory shows that some three-manifold can be presented in this w…

This article studies the geometry of moduli spaces of G2-manifolds, associative cycles, coassociative cycles and deformed Donaldson-Thomas bundles. We introduce natural symmetric cubic tensors and differential forms on these moduli spaces. They correspond to Yukawa couplings and correlation functions in M-theory. We ex…

Given a parallel calibration $φ\in Ω^p(M)$ on a Riemannian manifold $M$, I prove that the $φ$--critical submanifolds with nonzero critical value are minimal submanifolds. I also show that the $φ$--critical submanifolds are precisely the integral manifolds of a $\mathscr{C}^\infty(M)$--linear subspace $\sP \subset Ω^p(M…

We develop a unifed theory to study geometry of manifolds with different holonomy groups. They are classified by (1) real, complex, quaternion or octonion number they are defined over and (2) being special or not. Specialty is an orientation with respect to the corresponding normed algebra A. For example, special Riema…

Solves weakly supervised regression using low-rank approximations and manifold regularization.

Imaging genetic research has essentially focused on discovering unique and co-association effects, but typically ignoring to identify outliers or atypical objects in genetic as well as non-genetics variables. Identifying significant outliers is an essential and challenging issue for imaging genetics and multiple source…

The paper examines properties of deformed Donaldson-Thomas connections on G2-manifolds.

Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack theoretical guarantees, or depend heavily on their initialization. We present a novel …

The paper studies deformations of calibrated subbundles in special holonomy manifolds.

The paper studies deformations of Hermitian Yang-Mills and Donaldson-Thomas connections on $G_2$-manifolds.

Ensemble clustering has been a popular research topic in data mining and machine learning. Despite its significant progress in recent years, there are still two challenging issues in the current ensemble clustering research. First, most of the existing algorithms tend to investigate the ensemble information at the obje…

Defines a volume functional for Hermitian connections on manifolds, proving its properties and connections.