We study capacitated network flow problems with demands defined on a countably infinite collection of nodes having finite degree. This class of network flow models includes, for example, all infinite horizon deterministic dynamic programs with finite action sets, because these are equivalent to the problem of finding a shortest path in an infinite directed network. We derive necessary and suffi...

Data Flow Analysis (DFA for short) is a basic technique to collect statical information on run-time behaviors of programs: it is essential in optimizing compilers and is also used in type inference problems [1]. When performing a DFA, the program to be analyzed is modeled by its Control Flow Graph (CFG) and by a set of transformation functions, one for each node in the graph. The set of program...

In this paper we obtain the c-function of noncommutative Yang-Mills theory from the boundary counter-terms in its supergravity dual. For all backgrounds we consider, the c-function is found to be monotonically decreasing towards the infrared fixed point, where it recovers the central charge of ordinary YangMills theory. For a background corresponding to finite temperature we find an overall red...

In four dimensional N = 1 supersymmetric field theory it is often the case that the U(1)R current that becomes part of the superconformal algebra at the infrared fixed point is conserved throughout the renormalization group (RG) flow. We show that when that happens, the central charge a decreases under RG flow. The main tool we employ is an extension of recent ideas on “a-maximization” away fro...

The “cone condition”, used in passing in many proofs of the existence of inertial manifolds, is examined in more detail. Invariant manifolds for dissipative flows can be obtained directly using no other dynamical information. After finding a condition for the exponential attraction of trajectories to such a manifold, a cone invariance property is used to show the existence of orbits on the mani...

From the Wilsonian point of view, renormalisable theories are understood as submanifolds in theory space emanating from a particular fixed point under renormalisation group evolution. We show how this picture precisely applies to their gravity duals. We investigate the Hamilton-Jacobi equation satisfied by the Wilson action and find the corresponding fixed points and their eigendeformations, wh...

Information leakage occurs when a system exposes its secret information to an unauthorised entity. Information flow analysis is concerned with tracking flows of information through systems to determine whether they process information securely or leak information. We present a novel information flow model that permits an arbitrary amount of secret and publicly-observable information to occur at...