arXiv research

Paper presents a data preprocessing method for PHM models.

Paper shows mapping class groups are not extremely amenable except for specific cases.

Nowcasts consumption and investment from Turkish bank transactions for real-time GDP.

The paper shows how to create scalar flat metrics with very large ADM mass.

The paper develops AMP theory for sparse and robust regression with polynomial iterations.

Extends graph factor system to quasi-median graphs.

Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model complexity, representational capacity and overfitting. In this work, we propose …

A homology cylinder over a compact manifold is a homology cobordism between two copies of the manifold together with a boundary parametrization. We study abelian quotients of the homology cobordism group of homology cylinders. For homology cylinders over general surfaces, it was shown by Cha, Friedl and Kim that their …

Survey of tools for studying hierarchical hyperbolic spaces.

Since 2006, deep learning (DL) has become a rapidly growing research direction, redefining state-of-the-art performances in a wide range of areas such as object recognition, image segmentation, speech recognition and machine translation. In modern manufacturing systems, data-driven machine health monitoring is gaining …

The article constructs differential operators for parabolic geometries.

Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we establish a new framework that generalizes distance correlation --- a correlation mea…

The ability to generalize is an important feature of any intelligent agent. Not only because it may allow the agent to cope with large amounts of data, but also because in some environments, an agent with no generalization capabilities cannot learn. In this work we outline several criteria for generalization, and prese…

This is the second of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps. It contains two parts: (1) the construction of a set of algebraic invariants -- the homotopy groups, and (2) an analog o…

We use Beltrami's theorem as an excuse to present some arguments from parabolic differential geometry without any of the parabolic machinery.

New method connects CAT(0) spaces to hyperbolic spaces.

New theory proves representability of PDE solutions without complex machinery.

Abstract machinery finds obstructions to uniform positive scalar curvature.

Keywords: corporate finance, Wrocław University of Economics, net profit margin lub net sales profitability

In this short note, we formulate three problems relating to nonnegative scalar curvature (NNSC) fill-ins. Loosely speaking, the first two problems focus on: When are $(n-1)$-dimensional Bartnik data $\big(Σ_i ^{n-1}, γ_i, H_i\big)$, $i=1,2$, NNSC-cobordant? (i.e., there is an $n$-dimensional compact Riemannian manifold…

Accurately estimating the remaining useful life (RUL) of industrial machinery is beneficial in many real-world applications. Estimation techniques have mainly utilized linear models or neural network based approaches with a focus on short term time dependencies. This paper, introduces a system model that incorporates t…

For a real or complex semisimple Lie group $G$ and two nested parabolic subgroups $Q\subset P\subset G$, we study parabolic geometries of type $(G,Q)$. Associated to the group $P$, we introduce a class of relative natural bundles and relative tractor bundles and construct some basic invariant differential operators on …

We prove that the Casimir operator acting on sections of a homogeneous vector bundle over a generalized flag manifold naturally extends to an invariant differential operator on arbitrary parabolic geometries. We study some properties of the resulting invariant operators and compute their action on various special types…

New algorithm finds approximate stationary points faster under differential privacy constraints.

New method detects bearing faults using multivariate statistical process control.

New algorithm for private non-convex optimization with optimal rates.

In Part III of this study, we apply the price dynamical model with big buyers and big sellers developed in Part I of this paper to the daily closing prices of the top 20 banking and real estate stocks listed in the Hong Kong Stock Exchange. The basic idea is to estimate the strength parameters of the big buyers and the…

Big data sets must be carefully partitioned into statistically similar data subsets that can be used as representative samples for big data analysis tasks. In this paper, we propose the random sample partition (RSP) data model to represent a big data set as a set of non-overlapping data subsets, called RSP data blocks,…

In this paper we consider the large genus asymptotics for two classes of Siegel-Veech constants associated with an arbitrary connected stratum $\mathcal{H} (α)$ of Abelian differentials. The first is the saddle connection Siegel-Veech constant $c_{\text{sc}}^{m_i, m_j} \big( \mathcal{H} (α) \big)$ counting saddle conne…

Establishes Kobayashi-Hitchin correspondence for nef and big classes.

Given $(X,ω)$ compact Kähler manifold and $ψ\in\mathcal{M}^{+}\subset PSH(X,ω)$ a model type envelope with non-zero mass, i.e. a fixed potential determing some singularities such that $\int_{X}(ω+dd^{c}ψ)^{n}>0$, we prove that the $ψ-$relative finite energy class $\mathcal{E}^{1}(X,ω,ψ)$ becomes a complete metric space…

This article provides the role of big idea statisticians in future of Big Data Science. We describe the `United Statistical Algorithms' framework for comprehensive unification of traditional and novel statistical methods for modeling Small Data and Big Data, especially mixed data (discrete, continuous).

Geometric quantization extended to big line bundles.

Extends confining subset theory to describe hyperbolic actions of solvable groups with higher rank abelianizations.

New DP algorithms achieve near-optimal regret bounds for online learning problems.

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+\…

This note displays an interesting phenomenon for percentiles of independent but non-identical random variables. Let $X_1,\cdots,X_n$ be independent random variables obeying non-identical continuous distributions and $X^{(1)}\geq \cdots\geq X^{(n)}$ be the corresponding order statistics. For any $p\in(0,1)$, we investig…

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

Refines spinorial Sobolev inequality on sphere, proving stability and new properties of Killing spinors.

Study assesses 'big data' in materials science, highlighting challenges.

We prove the Chern-Gauss-Bonnet Theorem using sigma models whose source supermanifolds have super dimension 0|2. Along the way we develop machinery for understanding manifold invariants encoded by families of 0|n-dimensional Euclidean field theories and their quantization.

Uniform volume estimate for Kähler metrics in big cohomology classes.

Study convexity of Mabuchi functional in big cohomology classes.

Mobile big data contains vast statistical features in various dimensions, including spatial, temporal, and the underlying social domain. Understanding and exploiting the features of mobile data from a social network perspective will be extremely beneficial to wireless networks, from planning, operation, and maintenance…

Currently, the world is witnessing a mounting avalanche of data due to the increasing number of mobile network subscribers, Internet websites, and online services. This trend is continuing to develop in a quick and diverse manner in the form of big data. Big data analytics can process large amounts of raw data and extr…

Big data transforms accounting and auditing, enhancing insights but posing challenges.

Unified view on big bang singularities from initial data.

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…