Related papers: SVD, discrepancy, and regular structure of conting…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a…
This survey reviews a clustering method based on solving a convex optimization problem. Despite the plethora of existing clustering methods, convex clustering has several uncommon features that distinguish it from prior art. The…
This article deals with the regularity of the entropy solutions of scalar conservation laws with discontinuous flux. It is well-known [Adimurthi et al., Comm. Pure Appl. Math. 2011] that the entropy solution for such equation does not admit…
This paper establishes the consistency of a family of graph-cut-based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on…
This paper is devoted to the study of a discrepancy-type characteristic -- the fixed volume discrepancy -- of the Fibonacci point set in the unit square. It was observed recently that this new characteristic allows us to obtain optimal rate…
Suppose that you add rigid bars between points in the plane, and suppose that a constant fraction $q$ of the points moves freely in the whole plane; the remaining fraction is constrained to move on fixed lines called sliders. When does a…
We investigate the singularities and boundedness of a special kind of algebraic varieties so-called stable minimal models, which are constructed and studied by Birkar. Given a klt stable minimal model with bounded relative volume, if we fix…
Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…
Clustering algorithms for large networks typically use modularity values to test which partitions of the vertex set better represent structure in the data. The modularity of a graph is the maximum modularity of a partition. We consider the…
Motivated by applications to perverse sheaves, we study combinatorics of two cell decompositions of the symmetric product of the complex line, refining the complex stratification by multiplicities. Contingency matrices, appearing in…
Temperature time traces are obtained in turbulent thermal convection at high Rayleigh numbers. Measurements are made in the midplane of the apparatus, near the sidewall but outside the boundary layer. A telegraph approximation for…
Coherent structures created through turbulent cascades play a key role in energy dissipation and particle acceleration. In this work, we investigate both current and vorticity sheets in 3D particle-in-cell simulations of decaying…
The statistics of random-matrix spectra can be very sensitive to the unfolding procedure that separates global from local properties. In order to avoid the introduction of possible artifacts, recently it has been applied to ergodic…
Spectral clustering is a widely used algorithm to find clusters in networks. Several researchers have studied the stability of spectral clustering under local differential privacy with the additional assumption that the underlying networks…
The vertical distribution of suspended sediment concentration (SSC) remains a subject of active research given its relevance to a plethora of problems in hydraulics, hydrology, ecology, and water quality control. Much of the classical…
Biclustering is a class of techniques that simultaneously clusters the rows and columns of a matrix to sort heterogeneous data into homogeneous blocks. Although many algorithms have been proposed to find biclusters, existing methods suffer…
Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the…
Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…