arXiv research

Refines geometric center of mass analysis for Einstein field equations.

We extend the Lyapunov-Schmidt analysis of outlying stable CMC spheres in the work of S. Brendle and the second-named author to the "far-off-center" regime and to include general Schwarzschild asymptotics. We obtain sharp existence and non-existence results for large stable CMC spheres that depend very delicately on th…

Researchers find entire solutions to magnetic Ginzburg-Landau equations in 4D.

Study of large area-constrained Willmore surfaces in Schwarzschild-like manifolds.

Study local foliations of surfaces with constant mean curvature and constant expansion in space-time.

The paper proves the existence of stable spheres in asymptotically flat 3-manifolds.

From minimal surfaces such as Simons' cone and catenoids, using refined Lyapunov-Schmidt reduction method, we construct new solutions for a free boundary problem whose free boundary has two components. In dimension $8$, using variational arguments, we also obtain solutions which are global minimizers of the correspondi…

The conformal Willmore functional (which is conformal invariant in general Riemannian manifold $(M,g)$) is studied with a perturbative method: the Lyapunov-Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3, g_ε)$ -where $g_ε$ is a metric close and asymptotic to the euclidean o…

In this thesis we deal with two different classes of variational problems: 1) the problem of closed curves with prescribed curvature, or $H$-loop problem; 2) the study of the nodal solutions of the fractional Brezis-Nirenberg problem. In both cases we deal with nonlinear equations (an ODE system for problem 1, and an e…

The paper classifies noncollapsed translators in 4D space.

New cylindrical solutions found for Grushin-type problem.

In this paper we adopt an alternative, analytical approach to Arnol'd problem \cite{A1} about the existence of closed and embedded $K$-magnetic geodesics in the round $2$-sphere $\mathbb S^2$, where $K: \mathbb S^2 \rightarrow \mathbb R$ is a smooth scalar function. In particular, we use Lyapunov-Schmidt finite-dimensi…

We construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form $H(X)=1+{A}{|X|^{-γ}}$ for $|X|$ large, when $A<0$ and $γ\in(0,2)$. Such surfaces are close to sections of unduloids with small necksize, fold…

CR structure on S³ with non-compact solutions to CR Yamabe problem.

We consider the multi-bump solutions of the following fractional Nirenberg problem \begin{equation}\label{01} (-Δ)^s u=K(x)u^{\frac{n+2s}{n-2s}}, \;\;\;\;u>0\;\;\text{ in }\mathbb{R}^n, \end{equation} where $s\in (0,1)$ and $n>2+2s$. If $K$ is a periodic function in some $k$ variables with $1\leq k<\frac{n-2s}2$, we pr…

We are concerned with hypersurfaces of $\mathbb{R}^N$ with constant nonlocal (or fractional) mean curvature. This is the equation associated to critical points of the fractional perimeter under a volume constraint. Our results are twofold. First we prove the nonlocal analogue of the Alexandrov result characterizing sph…

We construct embedded Willmore tori with small area constraint in Riemannian three-manifolds under some curvature condition used to prevent Möbius degeneration. The construction relies on a Lyapunov-Schmidt reduction; to this aim we establish new geometric expansions of exponentiated small symmetric Clifford tori and a…

We associate to a parametrized family $f$ of nonlinear Fredholm maps possessing a trivial branch of zeroes an {\it index of bifurcation} $β(f)$ which provides an algebraic measure for the number of bifurcation points from the trivial branch. The index $β(f)$ is derived from the index bundle of the linearization of the …

This is the second of a series of two papers where we construct embedded Willmore tori with small area constraint in Riemannian three-manifolds. In both papers the construction relies on a Lyapunov-Schmidt reduction, the difficulty being the Möbius degeneration of the tori. In the first paper the construction was perfo…

Normal forms for equivariant maps in infinite dimensions established.

Constructs foliations of critical surfaces for Hawking energy in asymptotically flat initial data sets.

A local normal form theorem for smooth equivariant maps between Fréchet manifolds is established. Moreover, an elliptic version of this theorem is obtained. The proof these normal form results is inspired by the Lyapunov-Schmidt reduction for dynamical systems and by the Kuranishi method for moduli spaces, and uses a s…

Study on hemisphere threshold for Escobar functional on Riemannian manifolds, revealing mass and boundary invariant behaviors.

Efficient private matrix analysis algorithms for recent variants.

This paper introduces compositional data analysis for financial ratios, improving industry-level analysis.

In this dissertation, the main goal is visualisation of financial time series. We expect that visualisation of financial time series will be a useful auxiliary for technical analysis. Firstly, we review the technical analysis methods and test our trading rules, which are built by the essential concepts of technical ana…

Paper combines geometry and time-series analysis for spatiotemporal data.

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 …

This paper investigates to identify the requirement and the development of machine learning-based mobile big data analysis through discussing the insights of challenges in the mobile big data (MBD). Furthermore, it reviews the state-of-the-art applications of data analysis in the area of MBD. Firstly, we introduce the …

Interactive DR framework for comparing datasets.

Combines topological and geometric approaches to data analysis.

Proposes a multivariate regression model for better analysis of multiple datasets.

New method uses topological data analysis to study stock market crashes.

Analyzes stock trends and e-commerce user behavior using Twitter data.

Study analyzes Disney stock market performance using machine learning.

This study analyzes data science vocabulary changes over 13 years.

FinSphere improves stock analysis quality with AI and expert-curated data.

This study examines whether PCA can effectively identify nitrogen pollution sources in rivers.

Paper introduces probabilistic methods to approximate archetypal analysis, reducing complexity.

We present a unifying framework which reduces the construction of probabilistic component analysis techniques to a mere selection of the latent neighbourhood, thus providing an elegant and principled framework for creating novel component analysis models as well as constructing probabilistic equivalents of deterministi…

Deep learning techniques are rapidly advanced recently, and becoming a necessity component for widespread systems. However, the inference process of deep learning is black-box, and not very suitable to safety-critical systems which must exhibit high transparency. In this paper, to address this black-box limitation, we …

In this paper, we explore the effectiveness of dynamic analysis techniques for identifying malware, using Hidden Markov Models (HMMs) and Profile Hidden Markov Models (PHMMs), both trained on sequences of API calls. We contrast our results to static analysis using HMMs trained on sequences of opcodes, and show that dyn…

Improved LDA method for better classification and dimensionality reduction.

CDVI improves variational inference for survival analysis by considering censoring mechanisms.

The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on the kernel matrix defines an explicit nonlinear mapping of the input data represen…

Prototypal analysis is introduced to overcome two shortcomings of archetypal analysis: its sensitivity to outliers and its non-locality, which reduces its applicability as a learning tool. Same as archetypal analysis, prototypal analysis finds prototypes through convex combination of the data points and approximates th…

In this paper, we introduce a Deep Convolutional Analysis Dictionary Model (DeepCAM) by learning convolutional dictionaries instead of unstructured dictionaries as in the case of deep analysis dictionary model introduced in the companion paper. Convolutional dictionaries are more suitable for processing high-dimensiona…

Improved analysis of UCBVI algorithm with better empirical performance.