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Optimal transport - Harmonic approximation

Harmonic approximation The proof of the non-existence of stationary, locally optimal matchings in 2d is based on a tool, which is called harmonic approximation. It says that optimal transportation…

Optimal transport - Optimal matchings in 2d

Optimal matchings in 2d Note that the optimal matching problem as described in (1) can be seen as a special case of optimal transportation problems where the original and final distributions are…

Optimal transport

An illustration of such a matching, where both \(\{x_i\}\) and \(\{y_i\}\) are distributed uniformly in a square, is given in Figure 1. By a simple heuristic argument [21], we expect…

Optimal transport - ... and optimal matching

... and optimal matching A common problem in these applications is to have two sets of data points \({\{x_i\}}\) and \({\{y_i\}}\) and to seek a matching \(T:\{x_i\} \rightarrow \{y_i\}\),…

Optimal transport - Optimal transportation

Optimal transportation Optimal transportation describes the problem of finding the most efficient way to move distribution of materials \(\mu\) to the consumers \(\lambda\), given that to move one…

Optimal transport - Optimal transport

Optimal transport Research Topic

Tropical Geometry - The tropical Grassmannian

The tropical Grassmannian The classical algebraic Grassmannian is a standard example of a parameter space: A point in the Grassmannian ${\rm Gr}(k,n)$  is a linear subspace of $K^n$ of…

Tropical Geometry - Bergman fans

Bergman fans Tropical varieties come in all shapes and forms, but locally they always look like Bergman fans. This is reminiscent to manifolds, where locally they look like linear spaces. So what…

Tropical Geometry - Tropical differential algebra

Tropical differential algebra An algebraic (ordinary) differential equation is an equation given as the vanishing of a polynomial in the variables $x,x',x^{(2)}, x^{(3)} \dots$. As an example, the…

Tropical Geometry

The tropical moduli spaces are closely connected to the classical algebraic moduli spaces $\mathcal{M}_{g,n}$ of curves of genus $g$ with $n$ marked points. In fact, the rational homology of…
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