Within the smooth category, an intertwining is exhibited between the global rigidity of irreducible higher-rank Z Anosov actions on T and the classification of equilibrium-free flows on T that possess nontrivial generalized symmetries.

Following the works by Wiegmann–Zabrodin, Elbau–Felder, Hedenmalm–Makarov, and others, we consider the normal matrix model with an arbitrary potential function, and explain how the problem of finding the support domain for the asymptotic eigenvalue density of such matrices (when the size of the matrices goes to infinity) is related to the problem of Hele-Shaw flows on curved surfaces, considere...

We introduce a gain-scaling technique for the generalized maximum ow problem. Using this technique, we present three simple and intuitive polynomial-time combinatorial algorithms for the problem. Truemper's augmenting path algorithm is one of the simplest combinatorial algorithms for the problem, but runs in exponential-time. Our rst algorithm is a polynomial-time variant of Truemper's algorith...

A mathematical definition of classical causality over discrete spacetime dynamics is formulated. The approach is background free and permits a definition of causality in a precise way whenever the spacetime dynamics permits. It gives a natural meaning to the concepts of cosmic time, spacelike hypersurfaces and timelike or lightlike flows without assuming the notion of a background metric. The c...

It is well-known how to use maximum flow to decide when a flow problem with demands, lower bounds, and upper bounds is infeasible. Less well-known is how to compute a flow that is least infeasible. This paper considers many possible ways to define “least infeasible” and shows how to compute optimal flows for each definition. For each definition it also gives a dual characterization in terms of ...

This paper defines an incremental version of the maximum flow problem. In this model, the capacities increase over time and the resulting solution is a sequence of flows that build on each other incrementally. Thus far, incremental problems considered in the literature have been built on NP-complete problems. To the best of our knowledge, our results are the first to find a polynomial time prob...

In this work we present a way of accelerating a column generation algorithm for the linear minimum cost multicommodity flow problem. We use a new model that, besides the usual variables corresponding to flows on paths, has a polynomial number of extra variables, corresponding to flows on circuits. Those extra variables are explicitly considered in the restricted master problem, from the beginni...

Hop constraint is associated with modern communication network flows. We consider the problem of designing an optimal undirected network with integer-valued edge-capacities that meets a given set of single-commodity, hop-constrained network flow value requirements. We present a strongly polynomial, combinatorial algorithm for the problem with value of hop-parameter equal to three when values of...

We present a variant of the stable flow problem. Instead of the traditional flow problem that obeys Kirchhoff’s law, for each vertex, the outflow is monotone and piecewise linear to the inflow. In a directed and capacitated network, each vertex has strict preference over their incident edges. A stable flow assignment does not allow a group of vertices to benefit from privately rerouting along a...

Our main concern is the following variant of the image segmentation problem: given a weighted grid graph and a set of vertical and/or horizontal base lines crossing through the grid, compute a maximum-weight object which can be decomposed into based rectilinear convex objects with respect to the base lines. Our polynomial-time algorithm reduces the problem to solving a polynomial number of inst...