RESULTS: SSO demonstrated decreased wholebrain intrinsic connectivity compared to controls in left BA-39 and bilateral BA-7’s (p=0.071), which are the superior parietal lobules and the angular gyrus. UCS had significantly decreased intrinsic connectivity throughout the prefrontal cortex (PFC, p=0.031). On seed-based analysis, UCS had significantly increased connectivity between left BA-40 and b...

In the `-Component Order Connectivity problem (` ∈ N), we are given a graph G on n vertices, m edges and a non-negative integer k and asks whether there exists a set of vertices S ⊆ V (G) such that |S| ≤ k and the size of the largest connected component in G−S is at most `. In this paper, we give a kernel for `-Component Order Connectivity with at most 2`k vertices that takes nO(`) time for eve...

The SQuad data structure represents the connectivity of a triangle mesh by its “S table” of about 2 rpt (integer references per triangle). Yet it allows for a simple implementation of expected constant-time, random-access operators for traversing the mesh, including in-order traversal of the triangles incident upon a vertex. SQuad is more compact than the Corner Table (CT), which stores 6 rpt, ...

Motivated by challenges related to domination, connectivity, and information propagation in social and other networks, we initiate the study of the Vector Connectivity problem. This problem takes as input a graph G and an integer kv for every vertex v of G, and the objective is to find a vertex subset S of minimum cardinality such that every vertex v either belongs to S, or is connected to at l...

For a connected graphG= (V ,E), an edge set S ⊂ E is a k-restricted-edge-cut, ifG−S is disconnected and every component of G− S has at least k vertices. The k-restricted-edge-connectivity of G, denoted by k(G), is defined as the cardinality of a minimum k-restricted-edge-cut. The k-isoperimetric-edge-connectivity is defined as k(G)=min{|[U,U ]| : U ⊂ V, |U | k, |U | k}, where [U,U ] is the set ...

In the `-Component Order Connectivity problem (` ∈ N), we are given a graph G on n vertices, m edges and a non-negative integer k and asks whether there exists a set of vertices S ⊆ V (G) such that |S| ≤ k and the size of the largest connected component in G−S is at most `. In this paper, we give a kernel for `-Component Order Connectivity with at most 2`k vertices that takes nO(`) time for eve...

In this work we study linear secret sharing schemes for s-t connectivity in directed graphs. In such schemes the parties are edges of a complete directed graph, and a set of parties (i.e., edges) can reconstruct the secret if it contains a path from node s to node t. We prove that in every linear secret sharing scheme realizing the st-con function on a directed graph with n edges the total size...

In a standard f -connectivity network design problem, we are given an undirected graph G = (V,E), a cut-requirement function f : 2 → N, and non-negative costs c(e) for all e ∈ E. We are then asked to find a minimum-cost vector x ∈ N such that x(δ(S)) ≥ f(S) for all S ⊆ V . We focus on the class of such problems where f is a proper function. This encodes many well-studied NP-hard problems such a...

We give various characterizations of k-vertex connected graphs by geometric, algebraic, and "physical" properties. As an example, a graph G is k-connected ff and only if, specifying any k vertices of G, the vertices of G can be represented by points of R ~-a so that no k are on a hyper-. plane and each vertex is in the convex hull of its neighbors, except for the k specified vertices. The proof...

Writer's cramp (WC) is a focal task-specific dystonia characterized by sustained or intermittent muscle contractions while writing, particularly with the dominant hand. Since structural lesions rarely cause WC, it has been assumed that the disease might be caused by a functional maladaptation within the sensory-motor system. Therefore, our objective was to examine the differences between patien...