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This paper provides both theoretical and algorithmic results for the `1-relaxation of the Cheeger cut problem. The `2-relaxation, known as spectral clustering, only loosely relates to the Cheegerâ€¦ (More)

Ideas from the image processing literature have recently motivated a new set of clustering algorithms that rely on the concept of total variation. While these algorithms perform well forâ€¦ (More)

Pairwise particle interactions arise in diverse physical systems ranging from insect swarms to self-assembly of nanoparticles. In the presence of long-range attraction and short-range repulsion, suchâ€¦ (More)

- Theodore Kolokolnikov, Hui Sun, David Uminsky, Andrea L. Bertozzi
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2011

Pairwise particle interactions arise in diverse physical systems ranging from insect swarms to self-assembly of nanoparticles. In the presence of long-range attraction and short-range repulsion, suchâ€¦ (More)

We propose an adaptive version of the total variation algorithm proposed in [3] for computing the balanced cut of a graph. The algorithm from [3] used a sequence of inner total variationâ€¦ (More)

Large systems of particles interacting pairwise in d dimensions give rise to extraordinarily rich patterns. These patterns generally occur in two types. On one hand, the particles may concentrate onâ€¦ (More)

- James H. von Brecht, David Uminsky
- J. Nonlinear Science
- 2012

The classical inverse statistical mechanics question involves inferring properties of pairwise interaction potentials from exhibited ground states. For patterns that concentrate near a sphere, theâ€¦ (More)

In this paper we study the pattern formation of a kinematic aggregation model for biological swarming in two dimensions. The swarm is represented by particles and the dynamics are driven by aâ€¦ (More)

- David Uminsky, Karen Yeats
- Electr. J. Comb.
- 2007

We study the properties of a logconcavity operator on a symmetric, unimodal subset of finite sequences. In doing so we are able to prove that there is a large unbounded region in this subset that isâ€¦ (More)

- Raymond J. Nagem, Guido V. H. Sandri, David Uminsky, C. Eugene Wayne
- SIAM J. Applied Dynamical Systems
- 2009

The two-dimensional Navier-Stokes equations are rewritten as a system of coupled nonlinear ordinary differential equations. These equations describe the evolution of the moments of an expansion ofâ€¦ (More)