arXiv research

CoCP optimizes prediction intervals by jointly learning center and radius, improving efficiency and coverage.

Gradient-based clustering method for various cost functions.

We compute the fundamental group of various spaces of Desargues configurations in complex projective spaces: planar and non-planar configurations, with a fixed center and also with an arbitrary center.

Anosov flow found in specific partially hyperbolic systems.

The paper explores uniform perfectness and centers in Morse boundaries.

The paper discusses fairness in bank stress tests, comparing various methods to address institutional differences.

We study the fixed point set in the ideal boundary of a parabolic isometry of a proper CAT(0)-space. We show that the radius of the fixed point set is at most pi/2, and study its centers. As a consequence, we prove that the set of fixed points is contractible with respect to the Tits topology.

MDCN improves treatment effect estimation in multicenter observational studies.

Let $α$ be a Morse closed $1$-form of a smooth $n$-dimensional manifold $M$. The zeroes of $α$ of index $0$ or $n$ are called \emph{centers}. It is known that every non-vanishing de Rham cohomology class $u$ contains a Morse representative without centers. The result of this paper is the one-parameter analogue of the l…

Study evaluates the impact of academic support center's face-to-face assistance on student performance.

This article briefly introduced Arthur and Vassilvitshii's work on \textbf{k-means++} algorithm and further generalized the center initialization process. It is found that choosing the most distant sample point from the nearest center as new center can mostly have the same effect as the center initialization process in…

New distributed clustering algorithms show resilience to initialization issues.

The paper studies geometric structures of polynomial spaces.

New features for quantum calculations learn N-center Hamiltonian matrix elements.

Characterizes curves for minimal surfaces in de Sitter space.

Let $QI(\mathbb{R})$ denote the group of all quasi-isometries $f:\mathbb{R}\to \mathbb{R}.$ Let $Q_+( \text{and}~ Q_-)$ denote the subgroup of $QI(\mathbb{R})$ consisting of elements which are identity near $-\infty$ (resp. $+\infty$). We denote by $QI^+(\mathbb R)$ the index $2$ subgroup of $QI(\mathbb R)$ that fixes …

With the inflation of the data, clustering analysis, as a branch of unsupervised learning, lacks unified understanding and application of its mathematical law. Based on the view of fixed point, this paper restates the model-based clustering and proposes a unified clustering framework. In order to find fixed points as c…

Study sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces.

The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first consider the similarity of elements in the data as the connectivity of nodes in an…

Proposes a new clustering method based on expectiles for non-spherical clusters.

We consider a high-dimensional mixture of two Gaussians in the noisy regime where even an oracle knowing the centers of the clusters misclassifies a small but finite fraction of the points. We provide a rigorous analysis of the generalization error of regularized convex classifiers, including ridge, hinge and logistic …

Unified theory linking atom-centered and message-passing models for molecular properties.

Fix two parallel circles in $\mathbb{R}^3$ centered about a common axis. Among surfaces of revolution immersed in $\mathbb{R}^3$ whose boundary is given by these circles, there is one which maximizes the first Dirichlet eigenvalue. If the circles are sufficiently close together, then this surface is unique.

This paper is concerned with fixed-point free $S^1$-actions (smooth or locally linear) on orientable 4-manifolds. We show that the fundamental group plays a predominant role in the equivariant classification of such 4-manifolds. In particular, it is shown that for any finitely presented group with infinite center, ther…

Valuable training data is often owned by independent organizations and located in multiple data centers. Most deep learning approaches require to centralize the multi-datacenter data for performance purpose. In practice, however, it is often infeasible to transfer all data to a centralized data center due to not only b…

We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum equal to any preassigned values measured with respect to a fixed affine frame at infinity. This is in contrast to the axisym…

Offline k-means clustering was studied extensively, and algorithms with a constant approximation are available. However, online clustering is still uncharted. New factors come into play: the ordering of the dataset and whether the number of points, n, is known in advance or not. Their exact effects are unknown. In this…

A centered innovation MA is equivalent to a digamma-link DARMA for bank-asset shares.

Proposes DR-ME test for interpretable distributional treatment effects.

One key use of k-means clustering is to identify cluster prototypes which can serve as representative points for a dataset. However, a drawback of using k-means cluster centers as representative points is that such points distort the distribution of the underlying data. This can be highly disadvantageous in problems wh…

Recently, Awasthi et al. introduced an SDP relaxation of the $k$-means problem in $\mathbb R^m$. In this work, we consider a random model for the data points in which $k$ balls of unit radius are deterministically distributed throughout $\mathbb R^m$, and then in each ball, $n$ points are drawn according to a common ro…

The oloid is the convex hull of two circles with equal radius in perpendicular planes so that the center of each circle lies on the other circle. We calculate the mean width of the oloid in two ways, first via the integral of mean curvature, and then directly. Using this result, the surface area and the volume of the p…

New approach estimates treatment effects from decentralized data.

Proposes a framework for energy-efficient AIGC workload scheduling in cloud data centers.

New method for better initial centers in clustering with improved accuracy and privacy.

Causalfe estimates treatment effects in panel data with fixed effects.

Improved spatial prediction for massive datasets using SME model.

We prove that, among the polygons in a punctured disc with fixed angles, the perimeter is minimized by the polygon with an inscribed horocycle centered at the puncture. We generalize this to a disc with a cone point and to an annulus with a geodesic boundary component and a complete end. Then we apply this result to de…

We study a parsimonious but non-trivial model of the latent limit order book where orders get placed with a fixed displacement from a center price process, i.e.\ some process in-between best bid and best ask, and get executed whenever this center price reaches their level. This mechanism corresponds to the fundamental …

It is known that every nonorientable surface $Σ$ has an orientable double cover $\tildeΣ$. The covering map induces an involution on the moduli space $\tilde{\M}$ of gauge equivalence classes of flat $G$-connections on $\tildeΣ$. We identify the relation between the moduli space $\M$ and the fixed point set of the modu…

A new method for network regression using optimal transport.

A simple Ising spin model which can describe the mechanism of advertising in a duopoly market is proposed. In contrast to other agent-based models, the influence does not flow inward from the surrounding neighbors to the center site, but spreads outward from the center to the neighbors. The model thus describes the spr…

ClovaCall introduces a new Korean call speech corpus for contact centers.

Let $P$ be a principal U(1)-bundle over a closed manifold $M$. On $P$, one can define a modified version of the Ricci flow called the Ricci Yang-Mills flow, due to these equations being a coupling of Ricci flow and the Yang-Mills heat flow. We use maximal regularity theory and ideas of Simonett concerning the asymptoti…

Many scientific and engineering challenges -- ranging from personalized medicine to customized marketing recommendations -- require an understanding of treatment effect heterogeneity. In this paper, we develop a non-parametric causal forest for estimating heterogeneous treatment effects that extends Breiman's widely us…

The paper develops a method for self-normalized inference in adaptive experiments.

Time dilation $\frac{1}{\sqrt{1-v^2}}$ and relative velocity $v$ are observationally indistinguishable in the special theory of relativity, a duality that carries over into the general theory under Fermi coordinates along a curve (in coordinate-independent language, in the tangent Minkowski space along the curve). For …

Study finds cherry-picking load shaping strategies outperforms others in reducing grid CO2 emissions.