Related papers: Layers and stability
Saliency maps are widely used in the computer vision community for interpreting neural network classifiers. However, due to the randomness of training samples and optimization algorithms, the resulting saliency maps suffer from a…
Density Based Clustering are a type of Clustering methods using in data mining for extracting previously unknown patterns from data sets. There are a number of density based clustering methods such as DBSCAN, OPTICS, DENCLUE, VDBSCAN,…
Multiplex networks are networks composed of multiple layers such that the number of nodes in all layers is the same and the adjacency matrices between the layers are diagonal. We consider the special class of multiplex networks where the…
Clusters of galaxies have a huge mass which can act as gravitational lenses. Galaxies behind clusters can be distorted to form arcs in images by the lenses. Herein a search was done for giant lensed arcs by galaxy clusters using the SDSS…
We prove a sharp representation stability result for graph complexes with a distinguished vertex, and prove that the chains realizing this sharp bound pass to non-trivial families of graph homology classes. This result may be interpreted as…
We consider the set of points chosen randomly, independently and uniformly in the $d$-dimensional spherical layer. A set of points is called $1$-convex if all its points are vertices of the convex hull of this set. In \cite{3} an estimate…
In this paper, we take an axiomatic approach to defining a population hierarchical clustering for piecewise constant densities, and in a similar manner to Lebesgue integration, extend this definition to more general densities. When the…
Stability landscapes are useful for understanding the properties of dynamical systems. These landscapes can be calculated from the system's dynamical equations using the physical concept of scalar potential. Unfortunately, for most…
We propose a new hierarchical method which uses dynamical arguments to find and describe substructures in galaxy clusters. This method (hereafter h--method or h--analysis) uses a hierarchical clustering analysis to determine the…
This review summarizes some aspects of the central kiloparsec scale structure of galaxies, and in particular spiral galaxies, elliptical galaxies and merger remnants. The focus is on results from optical and near-IR imaging and…
Galaxies are not uniformly distributed in space. On large scales the Universe displays coherent structure, with galaxies residing in groups and clusters on scales of ~1-3 Mpc/h, which lie at the intersections of long filaments of galaxies…
We discuss implications of the fundamental plane parameters of clusters of galaxies derived from combined optical and X-ray data of a sample of 78 nearby clusters. In particular, we investigate the dependence of these parameters on the…
Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…
Crystal orientation mapping experiments typically measure orientations that are similar within grains and misorientations that are similar along grain boundaries. Such (mis)orientation data will cluster in (mis)orientation space and…
Hierarchical clustering is an effective and efficient approach widely used for classical image segmentation methods. However, many existing methods using neural networks generate segmentation masks directly from per-pixel features,…
This note presents a summary and review of various conditions and characterizations for matrix stability (in particular diagonal matrix stability) and matrix stabilizability.
Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a…
Differences in clustering properties between galaxy subpopulations complicate the cosmological interpretation of the galaxy power spectrum, but can also provide insights about the physics underlying galaxy formation. To study the nature of…
In this review, I discuss just three aspects of the stability and evolution of galactic discs. (1) I first review our understanding of the bar instability and how it can be controlled. Disc galaxies in which the orbital speed does not…
Many set theorists point to the linearity phenomenon in the hierarchy of consistency strength, by which natural theories tend to be linearly ordered and indeed well ordered by consistency strength. Why should it be linear? In this paper I…