This dissertation presents an exploration on solving traffic load balancing problems concentrating on the IP layer in hop-by-hop networks. The first part of the traffic load balancing research is focused on bandwidth-sensitive routing for premium class traffic in Differentiated Service (DiffServ) networks, where bandwidth usage of the premium class traffic is critical not only for the traffic i...

Crane and Frenkel proposed a notion of a Hopf category [2]. It was motivated by Lusztig’s approach to quantum groups – his theory of canonical bases. In particular, Lusztig obtains braided deformations Uqn+ of universal enveloping algebras Un+ for some nilpotent Lie algebras n+ together with canonical bases of these braided Hopf algebras [4, 5, 6]. The elements of the canonical basis are identi...

We start with some terminology from differential topology [1]. Let  be a circle and  ≥ 2 be an integer. An immersion  :  → R is a smooth function whose derivative never vanishes. An embedding  :  → R is an immersion that is oneto-one. It follows that () is a manifold but () need not be ( is only locally one-to-one, so consider the map that twists  into a figure eight). A knot is a s...

I. In this paper we state a splitting theorem for manifolds and describe some applications and consequences. We announced a weaker form of this result in August 1969 at the Georgia Topology Conference. Besides its immediate applications, especially in the classification of homotopy equivalent manifolds, it implies the existence of a Mayer-Vietoris sequence for surgery groups. Using this, many s...

Integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems, where a set of items has to be placed in multiple target locations. Herein a configuration describes a possible placement on one of the target locations, and the IP is used to chose suitable configurations covering the items. Configuration IPs ar...

We obtain the first nontrivial d.c.e. Turing approximation to the class of computably enumerable (c.e.) degrees. This depends on the following extension of the splitting theorem for the d.c.e. degrees: For any d.c.e. degree a, any c.e. degree b, if b < a, then there are d.c.e. degrees x0,x1 such that b < x0,x1 < a and a = x0 ∨ x1. The construction is unusual in that it is incompatible with uppe...

In this work, we introduce patchable indistinguishability obfuscation: our notion adapts the notion of indistinguishability obfuscation (iO) to a very general setting where obfuscated software evolves over time. We model this broadly by considering software patches P as arbitrary Turing Machines that take as input the description of a Turing Machine M , and output a new Turing Machine descripti...

Fast Fourier Transform (FFT) is an important technology in real-time signal processing system, which means the efficiency of FFT algorithm mapping to hardware system has very important significance. At first, we aim at the FFT execution process on processor. And then analyze the memory access process based on cache mechanism, and get that the cache hit directly affects FFT execution time. Hence...