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The Hubble constant problem is the discrepancy between different measurements of the Hubble constant in different scales. We show that this problem can be resolved within the general relativistic framework of the perturbation theory in the…
We study a multi-factor block model for variable clustering and connect it to regularized subspace clustering through a distributionally robust version of nodewise regression. To solve the latter problem, we derive a convex relaxation,…
We work in the density model of random groups. We prove that they satisfy an isoperimetric inequality with sharp constant $1-2d$ depending upon the density parameter $d$. This implies in particular a property generalizing the ordinary $C'$…
In 2013, Cuturi [Cut13] introduced the Sinkhorn algorithm for matrix scaling as a method to compute solutions to regularized optimal transport problems. In this paper, aiming at a better convergence rate for a high accuracy solution, we…
This paper develops the exact linear relationship between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix. We propose a method for approximating the leading eigenvector of the…
Turbulence is a crucial component of dynamics of astrophysical fluids dynamics, including those of ISM, clusters of galaxies and circumstellar regions. Doppler shifted spectral lines provide a unique source of information on turbulent…
We are interested in the clustering problem on graphs: it is known that if there are two underlying clusters, then the signs of the eigenvector corresponding to the second largest eigenvalue of the adjacency matrix can reliably reconstruct…
We propose a modified density estimation problem that is highly effective for detecting anomalies in tabular data. Our approach assumes that the density function is relatively stable (with lower variance) around normal samples. We have…
We discuss a new technique for studying astrophysical turbulence that utilizes the statistics of Doppler-broadened spectral lines. The technique relates the power Velocity Coordinate Spectrum (VCS), i.e. the spectrum of fluctuations…
Let $d\ge 3$ be a fixed integer. Let $y:= y(p)$ be the probability that the root of an infinite $d$-regular tree belongs to an infinite cluster after $p$-bond-percolation. We show that for every constants $b,\alpha>0$ and $1<\lambda< d-1$,…
As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust…
How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder…
We discuss the statistical properties of the volume of the nodal set of wave function for two paradigmatic model systems which we consider in arbitrary dimension $s\ge 2$: the cuboid as a paradigm for a regular shape with separable wave…
For a quiver with non-degenerate potential, we study the associated stability scattering diagram and how it changes under mutations. We show that under mutations the stability scattering diagram behaves like the cluster scattering diagram…
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…
Regularity results for minimal configurations of variational problems involving both bulk and surface energies and subject to a volume constraint are established. The bulk energies are convex functions with p-power growth, but are otherwise…
We study the problem of graph clustering under a broad class of objectives in which the quality of a cluster is defined based on the ratio between the number of edges in the cluster, and the total weight of vertices in the cluster. We show…
We study the hierarchy of communities in real-world networks under a generic stochastic block model, in which the connection probabilities are structured in a binary tree. Under such model, a standard recursive bi-partitioning algorithm is…
Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the…
Stochastic Structural Stability Theory (SSST) provides an autonomous, deterministic, nonlinear dynamical system for evolving the statistical mean state of a turbulent system. In this work SSST is applied to the problem of understanding the…