1 Analyzing General Properties of Network Deconvolution 3 1.1 Network deconvolution algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Optimality analysis of network deconvolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Modeling assumptions and intuitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

A graph G is ramdomly H–decomposable if every family of edge disjoint subgraphs of G, each subgraph isomorphic to H , can be extended to an H–decomposition of G. Let Pk denote a path of length k. In this paper we characterize all ramdomly P3– decomposable graphs and ramdomly P4–decomposable graphs. We also characterize all ramdomly Pk–decomposable graphs of size 2k where all vertices have even ...

A tree is called k-decomposable if it has a spanning forest whose components are all of size k. Analogously, a tree is called T -decomposable for a fixed tree T if it has a spanning forest whose components are all isomorphic to T . In this paper, we use a generating functions approach to derive exact and asymptotic results on the number of k-decomposable and T -decomposable trees from a so-call...

For an arbitrary localic étale groupoid G we provide simple descriptions, in terms of modules over the quantale O(G) of the groupoid, of the continuous actions of G, including actions on open maps and sheaves. The category of G-actions is isomorphic to a corresponding category of O(G)-modules, and as a corollary we obtain a new quantale based representation of étendues.

Suppose G is a second countable, locally compact, Hausdorff, principal groupoid with a fixed left Haar system. We define a notion of integrability for groupoids, and show G is integrable if and only if the groupoid C∗-algebra C∗(G) has bounded trace.

In this paper, we provide two types of boundary path groupoids from a generalized Boolean dynamical system (B,L,θ,Iα). For the first groupoid, associate an inverse semigroup to and use tight spectrum T as unit space groupoid Γ(B,L,θ,Iα) that is isomorphic Gtight. The other one defined Renault-Deaconu Γ(∂E,σE) arising topological correspondence E associated with system. We then prove homeomorphi...