相关论文: Weak Separation, Pure Domains and Cluster Distance

We discuss the notion of a dense cluster with respect to the information distance and prove that all such clusters have an extractable core that represents the mutual information shared by the objects in the cluster.

We present the science case for mapping several thousand galaxy (proto)clusters at z=1-10 with a large aperture single dish sub-mm facility, producing a high-redshift counterpart to local large surveys of rich clusters like the well-studied…

We present a weak lensing and multi-wavelength analysis of three galaxy clusters: A115, A2219, and A2261. Weak lensing is performed using shape measurements made in short 60s exposure images obtained using WIYN-ODI. Forced measurement is…

The Solow--Polasky diversity indicator (or magnitude) is a classical measure of diversity based on pairwise distances. It has applications in ecology, conservation planning, and, more recently, in algorithmic subset selection and diversity…

Let $\mathfrak{i}$ denote the minimal cardinality of a maximal independent family and let $\mathfrak{a}_T$ denote the minimal cardinality of a maximal family of pairwise almost disjoint subtrees of $2^{<\omega}$. Using a countable support…

We develop a stability theory for minimal projective resolutions of $\mathbf{P}$-modules, where $\mathbf{P}$ is a finite metric poset. We use the G\"ulen-McCleary distance on $\mathbf{P}$-modules together with a new complex matching…

We study how small is the set of critical values of the distance function from a compact (resp. closed) set in the plane or in a connected complete two-dimensional Riemannian manifold. We show that for a compact set, the set of critical…

We present a detailed analysis of the baryonic and dark matter distribution in the lensing cluster Abell 611 (z=0.288), with the goal of determining the dark matter profile over an unprecedented range of cluster-centric distance. By…

As the main theorem, it is proved that a collection of minimal $PI$-flows with a common phase group and satisfying a certain algebraic condition is multiply disjoint if and only if the collection of the associated maximal equicontinuous…

Cluster abundance measurements are among the most sensitive probes of the amplitude of matter fluctuations in the universe, which in turn can help constrain other cosmological parameters, like the dark energy equation of state or neutrino…

Cluster number counts can constrain the properties of dark energy if and only if the evolution in the relationship between observable quantities and the cluster mass can be calibrated. Next generation surveys with ~10000 clusters will have…

We consider Bernoulli percolation on a locally finite quasi-transitive unimodular graph and prove that two infinite clusters cannot have infinitely many pairs of vertices at distance 1 from one another or, in other words, that such graphs…

Mixture models and topic models generate each observation from a single cluster, but standard variational posteriors for each observation assign positive probability to all possible clusters. This requires dense storage and runtime costs…

Cluster mass profiles are tests of models of structure formation. Only two current observational methods of determining the mass profile, gravitational lensing and the caustic technique, are independent of the assumption of dynamical…

Metric clustering is fundamental in areas ranging from Combinatorial Optimization and Data Mining, to Machine Learning and Operations Research. However, in a variety of situations we may have additional requirements or knowledge, distinct…

In \cite{FKW} Katznelson and Weiss establish that all sufficiently large distances can always be attained between pairs of points from any given measurable subset of $\mathbb{R}^2$ of positive upper (Banach) density. A second proof of this…

Single-cell omics enable the profiles of cells, which contain large numbers of biological features, to be quantified. Cluster analysis, a dimensionality reduction process, is used to reduce the dimensions of the data to make it…

A new clustering accuracy measure is proposed to determine the unknown number of clusters and to assess the quality of clustering of a data set given in any dimensional space. Our validity index applies the classical nonparametric…

Evolution in the mass function of galaxy clusters sensitively traces both the expansion history of the Universe and cosmological structure formation. Robust cluster mass determinations are a key ingredient for a reliable measurement of this…

We prove that the algebraic set of pairs of matrices with a diagonal commutator over a field of positive prime characteristic, its irreducible components, and their intersection are $F$-pure when the size of matrices is equal to 3.…