arXiv research

New phenomenon found in Gothen components' boundary.

In this paper, we derive a maximum principle for a type of elliptic systems and apply it to analyze the Hitchin equation for cyclic Higgs bundles. We show several domination results on the pullback metric of the (possibly branched) minimal immersion $f$ associated to cyclic Higgs bundles. Also, we obtain a lower and up…

Maximal representations into $\mathrm{SO}_0(2,3)$ have bounded volume.

We classify the connected components of the space of representations of the fundamental group of a closed oriented surface of genus $\geq 2$ in $Sp(4,{\mathbf R})$. We prove that this is equivalent to classifying the connected components of the moduli space of representations (which consists of conjugacy classes of red…

Harmonic metrics on Higgs bundles over non-compact hyperbolic surfaces are studied.

We show that a surface group of high genus contained in a classical simple Lie group can be deformed to become Zariski dense, unless the Lie group is $SU(p,q)$ (resp. $SO^* (2n)$, $n$ odd) and the surface group is maximal in some $S(U(p,p)\times U(q-p))\subset SU(p,q)$ (resp. $SO^* (2n-2)\times SO(2)\subset SO^* (2n)$)…

We study holomorphic $(n+1)$-chains $E_n\to E_{n-1} \to >... \to E_0$ consisting of holomorphic vector bundles over a compact Riemann surface and homomorphisms between them. A notion of stability depending on $n$ real parameters was introduced in the work of the first two authors and moduli spaces were constructed by t…

Study finite group actions on Higgs bundle moduli spaces.

We develop the theory of maximal representations of the fundamental group of a compact connected oriented surface with boundary, into a group of Hermitian type. For any such representation we define the Toledo invariant, for which we establish properties such as uniform boundedness on the representation variety, additi…

Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model identifiability. Linear non-Gaussian component analysis (LNGCA) generalizes the ICA model t…

In links with two components there are three different types of crossings: self-crossings in the first component, self crossings in the second component, and crossings between components. In this paper we examine the minimum number of crossing changes needed to unlink without changing the crossings between components. …

Innovates a three-component link homotopy invariant.

This note proves properties of surface-links with trivial components.

A fast method estimates Gaussian mixture components without iterative fitting.

In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined, and its properties are developed. It is shown that modularity component analysis …

The paper shows infinitely many components in Floer Hessians space.

New concept of quasi-ribbon surface-links simplifies complex surface-links.

New simulations advise caution in choosing principal components for multivariate functional data.

Research has shown that widely used deep neural networks are vulnerable to carefully crafted adversarial perturbations. Moreover, these adversarial perturbations often transfer across models. We hypothesize that adversarial weakness is composed of three sources of bias: architecture, dataset, and random initialization.…

We construct links of arbitrarily many components each component of which is slice and yet are not concordant to any link with even one unknotted component. The only tool we use comes from the Alexander modules.

Uniform bounds found for Sierpinski carpet hyperbolic components.

The object of this paper is to study GL(2,R) orbit closures in hyperelliptic components of strata of abelian differentials. The main result is that all higher rank affine invariant submanifolds in hyperelliptic components are branched covering constructions, i.e. every translation surface in the affine invariant subman…

We develop a mean-field theory for multi-component ICA in high dimensions.

Research examines the distribution of curve components in random multicurves.

FMM fails to accurately determine the number of components even with consistent posterior.

msPCA solves sparse PCA for multiple components efficiently.

Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from only explanatory variables and not considered with the response variable. To addre…

Bayesian approach learns nonparametric mixture components from heterogeneous data.

System learns to combine multiple model components for personalized text generation.

Found a new connected component in symplectic structures.

The paper proposes reusable network components by making them compatible across tasks.

New invariants lift Milnor invariants for 3-component links.

We construct a graph G such that any embedding of G into R^{3} contains a nonsplit link of two components, where at least one of the components is a nontrivial knot. Further, for any m < n we produce a graph H so that every embedding of H contains a nonsplit n component link, where at least m of the components are nont…

The paper introduces COAR to estimate component attributions and enable model editing.

Study topological components of surface group representations into SL(2,R) and PSL(2,R).

Identifying components and estimating mixing weights in unlabeled finite mixtures under marginal independence.

A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to neighborhood homotopy by the elementary divisor of a linking matrix with respect to th…

We propose a penalized orthogonal-components regression (POCRE) for large p small n data. Orthogonal components are sequentially constructed to maximize, upon standardization, their correlation to the response residuals. A new penalization framework, implemented via empirical Bayes thresholding, is presented to effecti…

Essential principal components simplify spectral analysis with minimal training data.

Survey on Higgs bundle moduli spaces and their connected components.

Derives Fredholm criteria for isotypical components from a Simonenko principle.

In this paper, we study connected components of strata of the space of quadratic differentials lying over $\T_g$. We use certain general properties of sections of line bundles to put a upper bound on the number of connected components, and a generalized version of the Gauss map as an invariant to put a lower bound on t…

Classifies connected components of meromorphic differentials with residue conditions.

PCHAL and PCHAR use principal components to speed up HAL and HAR methods.

Identifies Anosov representations of hyperbolic triangle groups in SL(3,R).

Efficient private matrix analysis algorithms for recent variants.

QAPCA uses quantum annealing for robust PCA.

Clustering of data sets is a standard problem in many areas of science and engineering. The method of spectral clustering is based on embedding the data set using a kernel function, and using the top eigenvectors of the normalized Laplacian to recover the connected components. We study the performance of spectral clust…