arXiv research

Proves conjecture on deformation invariance of big fundamental groups.

Uniform volume estimate for Kähler metrics in big cohomology classes.

Study proves stability of big bang singularity in complex system.

Estimates Kaehler metrics' diameter in big cohomology classes.

Explosive growth in data and availability of cheap computing resources have sparked increasing interest in Big learning, an emerging subfield that studies scalable machine learning algorithms, systems, and applications with Big Data. Bayesian methods represent one important class of statistic methods for machine learni…

Study foundational aspects of degenerate para-CR structures and their PDE systems.

Paper optimizes a big data and ML risk monitoring system for financial markets.

New algorithm learns halfspaces with adversarial noise efficiently.

New insights into spectral statistics of sample covariance matrix for stable linear systems.

One of the key technologies for future large-scale location-aware services covering a complex of multi-story buildings --- e.g., a big shopping mall and a university campus --- is a scalable indoor localization technique. In this paper, we report the current status of our investigation on the use of deep neural network…

As a non-parametric Bayesian model which produces informative predictive distribution, Gaussian process (GP) has been widely used in various fields, like regression, classification and optimization. The cubic complexity of standard GP however leads to poor scalability, which poses challenges in the era of big data. Hen…

The paper discusses scalable learning for wireless data-driven systems.

Localized big bang singularities found without background solutions.

Paper presents a data preprocessing method for PHM models.

We consider model-free reinforcement learning for infinite-horizon discounted Markov Decision Processes (MDPs) with a continuous state space and unknown transition kernel, when only a single sample path under an arbitrary policy of the system is available. We consider the Nearest Neighbor Q-Learning (NNQL) algorithm to…

The paper proves boundedness of envelopes in complex manifolds.

The recent trend for acquiring big data assumes that possessing quantitatively more and qualitatively finer data necessarily provides an advantage that may be critical in competitive situations. Using a model complex adaptive system where agents compete for a limited resource using information coarse-grained to differe…

Let $X$ be a smooth projective complex variety of maximal Albanese dimension, and let $L \to X$ be a big line bundle. We prove that the moving Seshadri constants of the pull-backs of $L$ to suitable finite abelian étale covers of $X$ are arbitrarily large. As an application, given any integer $k\geq 1$, there exists an…

New methods prove controllability of non-linear systems, extending classical results.

Improves EM algorithm for better local optima in mixture models.

We prove a $C^{1,1}$ estimate for solutions of complex Monge-Ampère equations on compact Kähler manifolds with possibly nonempty boundary, in a degenerate cohomology class. This strengthens previous estimates of Phong-Sturm. As applications we deduce the local $C^{1,1}$ regularity of geodesic rays in the space of Kähle…

The goal of this work is to prove the regularity of certain quasi-plurisubharmonic upper envelopes. Such envelopes appear in a natural way in the construction of hermitian metrics with minimal singularities on a big line bundle over a compact complex manifold. We prove that the complex Hessian forms of these envelopes …

FS&P uses birth-death process to ensure global convergence of stochastic conic particle gradient descent.

We study the local equivalence problem for real-analytic ($\mathcal{C}^ω$) hypersurfaces $M^5 \subset \mathbb{C}^3$ which, in coordinates $(z_1, z_2, w) \in \mathbb{C}^3$ with $w = u+i\, v$, are rigid: \[ u \,=\, F\big(z_1,z_2,\overline{z}_1,\overline{z}_2\big), \] with $F$ independent of $v$. Specifically, we study th…

The study finds conditions for a third rank Killing tensor field on a 2D Riemannian torus.

This work is devoted to a systematic study of symplectic convexity for integrable Hamiltonian systems with elliptic and focus-focus singularities. A distinctive feature of these systems is that their base spaces are still smooth manifolds (with boundary and corners), similarly to the toric case, but their associated in…

The rise of Big Data has led to new demands for Machine Learning (ML) systems to learn complex models with millions to billions of parameters, that promise adequate capacity to digest massive datasets and offer powerful predictive analytics thereupon. In order to run ML algorithms at such scales, on a distributed clust…

GT-SARAH optimizes decentralized non-convex problems with recursive variance reduction.

Interpretability has always been a major concern for fuzzy rule-based classifiers. The usage of human-readable models allows them to explain the reasoning behind their predictions and decisions. However, when it comes to Big Data classification problems, fuzzy rule-based classifiers have not been able to maintain the g…

This paper uses information theory to improve risk modeling in big data.

Proves left-orderability of mapping class groups of infinite-type surfaces.

A method to select important experts for Gaussian processes to balance computational efficiency and uncertainty quantification.

Let $G/H$ be a contractible homogeneous Sasaki manifold. A compact locally homogeneous aspherical Sasaki manifold $Γ\big\backslash G/H$ is by definition a quotient of $G/H$ by a discrete uniform subgroup $Γ\leq G$. We show that a compact locally homogeneous aspherical Sasaki manifold is always quasi-regular, that is, $…

Improved algorithm reduces stochastic gradient complexity for large-scale learning problems.

We establish various stability results for solutions of complex Monge-Ampère equations in big cohomology classes, generalizing results that were known to hold in the context of Kähler classes.

In this survey, we remind some fibrations structure theorems (also called Milnor's fibrations) recently proved in the real and complex case, in the local and global settings. We give several Poincaré-Hopf type formulae which relates the Euler-Poincaré characteristic of these fibers (also called Milnor's fibers) and ind…

Sharp constants in curl-Sobolev inequalities on spheres determined.

New method improves likelihood-free parameter estimation in complex models.

Efficiently learns sparse halfspaces with noisy labels.

Let $\big(M,g^{TM}\big)$ be a noncompact complete spin Riemannian manifold of even dimension $n$, with $k^{TM}$ denote the associated scalar curvature. Let $f\colon M\rightarrow S^{n}(1)$ be a smooth area decreasing map, which is locally constant near infinity and of nonzero degree. We show that if $k^{TM}\geq n(n-1)$ …

The paper tackles machine unlearning by designing efficient algorithms for adaptive query classes.

The paper studies positivity properties of cotangent bundles in complex hyperbolic manifolds with cusps.

Proves properties of complex algebraic varieties and local systems.

Agent-based modeling is a powerful simulation technique to understand the collective behavior and microscopic interaction in complex financial systems. Recently, the concept for determining the key parameters of the agent-based models from empirical data instead of setting them artificially was suggested. We first revi…

Characterizes and analyzes the large scale geometry of big mapping class groups of surfaces.

Continuity of complex Monge-Ampère potentials on Kähler manifolds.

The world is witnessing an unprecedented growth of cyber-physical systems (CPS), which are foreseen to revolutionize our world {via} creating new services and applications in a variety of sectors such as environmental monitoring, mobile-health systems, intelligent transportation systems and so on. The {information and …

The following problem is addressed: A $3$-manifold $M$ is endowed with a triple $Ω= \big(Ω^1,Ω^2,Ω^3\big)$ of closed $2$-forms. One wants to construct a coframing $ω= \big(ω^1,ω^2,ω^3\big)$ of $M$ such that, first, ${\rm d}ω^i = Ω^i$ for $i=1,2,3$, and, second, the Riemannian metric $g=\big(ω^1\big)^2+\big(ω^2\big)^2+\…