Suppose we are given a Noetherian, nonnegative graph acting trivially on a Galileo set A. Recent interest in topoi has centered on describing I-Borel arrows. We show that 1 ∞ ⊃ ∫ i−5 dκ. Every student is aware that Ñ is essentially generic and everywhere invariant. A central problem in higher number theory is the extension of primes.

A nite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered di usion process. As an application, a central limit theorem for certain hitting times, interpreted as failure times of a coherent system in reliability, is derived.

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

We present a graph-matching algorithm for semantic relation assignment. The algorithm is part of an interactive text analysis system. The system automatically extracts pairs of syntactic units from a text and assigns a semantic relation to each pair. This is an incremental learning algorithm, in which previously processed pairs and user feedback guide the process. After each assignment, the sys...

For a vertex u of a graph G and an integer r, the ball of radius r centered at u is the subgraph Gr(u) induced by the set of all vertices of G whose distance from u does not exceed r. We investigate the set 1i of connected graphs G with at least 3 vertices such that every ball of radius 1 in G has a Hamilton cycle. We prove that every graph G in 1-£ with n vertices has at least 2n 3 edges, and ...

For a nonempty set S of vertices in a strong digraph D, the strong distance d(S) is the minimum size of a strong subdigraph of D containing the vertices of S. If S contains k vertices, then d(S) is referred to as the k-strong distance of S. For an integer k > 2 and a vertex v of a strong digraph D, the k-strong eccentricity sek(v) of v is the maximum k-strong distance d(S) among all sets S of k...

Let G be a graph which satisfies c−1 ar ≤ |B(v, r)| ≤ c ar, for some constants c, a > 1, every vertex v and every radius r. We prove that this implies the isoperimetric inequality |∂A| ≥ C|A|/ log(2 + |A|) for some constant C = C(a, c) and every finite set of vertices A. A graph G = ( V (G), E(G) ) has pinched growth f(r) if there are two constants 0 < c < C < ∞ so that every ball B(v, r) of ra...

Since the introduction of LLE (Roweis and Saul, 2000) and Isomap (Tenenbaum et al., 2000), a large number of non-linear dimensionality reduction techniques (manifold learners) have been proposed. Many of these non-linear techniques can be viewed as instantiations of Kernel PCA; they employ a cleverly designed kernel matrix that preserves local data structure in the “feature space” (Bengio et al...

This paper extends our prior work on spacecraft debris avoidance based on positively invariant sets to the case of moving debris. In this approach, a timevarying connectivity graph is constructed between a set of forced equilibria, forming a virtual net that is centered around a nominal orbital position of the spacecraft. The connectivity between two equilibria is determined based on contractiv...

The paper considers spacecraft motion planning based on the use of safe positively invariant sets. In this approach, a connectivity graph is constructed between a set of forced equilibria, forming a virtual net that is centered around a nominal orbital position. The connectivity between two equilibria is determined based on safe positively invariant sets in order to guarantee that transitions b...