相关论文: Flow-Cut Dualities for Sheaves on Graphs
Flow-based methods for local graph clustering have received significant recent attention for their theoretical cut improvement and runtime guarantees. In this work we present two improvements for using flow-based methods in real-world…
We develop a new framework for investigating linear equivalence of divisors on graphs using a generalization of Gioan's cycle--cocycle reversal system for partial orientations. An oriented version of Dhar's burning algorithm is introduced…
We introduce the notion of a generalized flow on a graph with coefficients in a R-representation and show that the module of flows is isomorphic to the first derived functor of the colimit. We generalize Kirchhoff's laws and build an exact…
We propose a new algorithm to obtain max flow for the multicommodity flow. This algorithm utilizes the max-flow min-cut theorem and the well known labeling algorithm due to Ford and Fulkerson [1]. We proceed as follows: We select one…
Using the precursor map in AdS/CFT, the renormalization group cutoff function is mapped to the dual theory. The resulting flow equations on the two sides of the duality are compared.
On a real analytic manifold M, we construct the linear subanalytic Grothendieck topology Msal together with the natural morphism of sites $\rho$ from Msa to Msal, where Msa is the usual subanalytic site. Our first result is that the derived…
Let $M$ be a compact manifold equipped with a pair of complementary foliations, say horizontal $\mathcal{H}$ and vertical $\mathcal{V}$. In Melo, Morgado and Ruffino (Disc Cont Dyn Syst B, 2016, 21(9)) it is proved that if a semimartingale…
Multi-region segmentation algorithms often have the onus of incorporating complex anatomical knowledge representing spatial or geometric relationships between objects, and general-purpose methods of addressing this knowledge in an…
A standard approach to reduce the complexity of very large networks is to group together sets of nodes into clusters according to some criterion which reflects certain structural properties of the network. Beyond the well-known modularity…
The incorporation of region regularization into max-flow segmentation has traditionally focused on ordering and part-whole relationships. A side effect of the development of such models is that it constrained regularization only to those…
We show that the dualizing sheaves of reduced simple normal crossings pairs have a canonical weight filtration in a compatible way with the one on the corresponding mixed Hodge modules by calculating the extension classes between the…
One issue limiting the adaption of large-scale multi-region segmentation is the sometimes prohibitive memory requirements. This is especially troubling considering advances in massively parallel computing and commercial graphics processing…
We consider the graphical mean curvature flow of maps ${\bf f}:\mathbb{R}^m\to\mathbb{R}^n$, $m\ge 2$, and derive estimates on the growth rates of the evolved graphs, based on a new version of the maximum principle for properly immersed…
The aim of this article is to provide space level maps between configuration spaces of graphs that are predicted by algebraic manipulations of cellular chains. More explicitly, we consider edge contraction and half-edge deletion, and…
We investigate flows on graphs whose links have random capacities. For binary trees we derive the probability distribution for the maximal flow from the root to a leaf, and show that for infinite trees it vanishes beyond a certain threshold…
We analyse the topological (knot-theoretic) features of a certain codimension-one bifurcation of a partially hyperbolic fixed point in a flow on $\real^3$ originally described by Shil'nikov. By modifying how the invariant manifolds wrap…
Many of the tools developed for the theory of tree-decompositions of graphs do not work for directed graphs. In this paper we show that some of the most basic tools do work in the case where the model digraph is a directed path. Using these…
The max-flow and max-coflow problem on directed graphs is studied in the common generalization to regular spaces, i.e., to kernels or row spaces of totally unimodular matrices. Exhibiting a submodular structure of the family of paths within…
We recently introduced a formalism for the modeling of temporal networks, that we call stream graphs. It emphasizes the streaming nature of data and allows rigorous definitions of many important concepts generalizing classical graphs. This…
This paper presents new results for the modulus of families of walks on a graph---a discrete analog of the modulus of curve families due to Beurling and Ahlfors. Particular attention is paid to the dependence of the modulus on its…