Related papers: Dynamic Light Spanners in Doubling Metrics
An $f(d)$-spanner of an unweighted $n$-vertex graph $G=(V,E)$ is a subgraph $H$ satisfying that $dist_H(u, v)$ is at most $f(dist_G(u, v))$ for every $u,v \in V$. We present new spanner constructions that achieve a nearly optimal stretch of…
We present a new efficient localized algorithm to construct, for any given quasi-unit disk graph G=(V,E) and any e > 0, a (1+e)-spanner for G of maximum degree O(1) and total weight O(w(MST)), where w(MST) denotes the weight of a minimum…
The process of momentum and energy transfer between a massive body and a background medium it is moving through is known as dynamical friction (DF). It is key to our understanding of many astrophysical systems. We present a series of…
Let $C_b(K)$ be the set of all bounded continuous (real or complex) functions on a complete metric space $K$ and $A$ a closed subspace of $C_b(K)$. Using the variational method, it is shown that the set of all strong peak functions in $A$…
In this paper we consider the \emph{fully-dynamic} All-Pairs Effective Resistance problem, where the goal is to maintain effective resistances on a graph $G$ among any pair of query vertices under an intermixed sequence of edge insertions…
This work is concerned with the continuum limit of a graph-based data visualization technique called the t-Distributed Stochastic Neighbor Embedding (t-SNE), which is widely used for visualizing data in a variety of applications, but is…
A $\mathcal{PT}$-symmetric nonlinear Schr\"odinger dimer is a two-site discrete nonlinear Schr\"odinger equation with one site losing and the other one gaining energy at the same rate. In this paper, two four-parameter families of cubic…
In a graph $G$, we define a set of vertices to be a \emph{strong hub set} if for any two vertices in $G$, we can find a path between them whose internal vertices are all in this set. We define the \emph{strong hub cover pebbling number} of…
Consider a multidimensional SDE of the form $X_t = x+\int_{0}^{t} b(X_{s-})ds+\int{0}^{t} f(X_{s-})dZ_s$ where $(Z_s)_{s\ge 0}$ is a symmetric stable process. Under suitable assumptions on the coefficients the unique strong solution of the…
Recently, MLP-based vision backbones have achieved promising performance in several visual recognition tasks. However, the existing MLP-based methods directly aggregate tokens with static weights, leaving the adaptability to different…
Quantifying the parameters and corresponding uncertainties of hundreds of strongly lensed quasar systems holds the key to resolving one of the most important scientific questions: the Hubble constant ($H_{0}$) tension. The commonly used…
This paper studies multivariate nonparametric change point localization and inference problems. The data consists of a multivariate time series with potentially short range dependence. The distribution of this data is assumed to be…
This paper studies the N-dimensional FENE dumbbell model without velocity dissipation, focusing on the stability and decay of perturbations near the steady solution $(0,\pin)$. Due to the lack of velocity dissipation, the above problems are…
We describe a new method called t-ETE for finding a low-dimensional embedding of a set of objects in Euclidean space. We formulate the embedding problem as a joint ranking problem over a set of triplets, where each triplet captures the…
In quasi-two-dimensional experiments with photoelastic particles confined to an annular region, an intruder constrained to move in a circular path halfway between the annular walls experiences stick-slip dynamics. We discuss the response of…
We present a dynamic self-balancing octree data structure that enables efficient neighborhood maintenance in evolving metric spaces, a key challenge in modern machine learning systems. Many learning and generative models operate as…
Given a set P of n points in |R^d, an eps-kernel K subset P approximates the directional width of P in every direction within a relative (1-eps) factor. In this paper we study the stability of eps-kernels under dynamic insertion and…
In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results…
Recent years have witnessed a surge of biological interest in the minimum spanning tree (MST) problem for its relevance to automatic model construction using the distances between data points. Despite the increasing use of MST algorithms…
This paper makes a deep study of regular two-distance sets. A set of unit vectors $X$ in Euclidean space $\RR^n$ is said to be regular two-distance set if the inner product of any pair of its vectors is either $\alpha$ or $\beta$, and the…