We study the growth of product sets in some finite three-dimensional matrix groups. In particular, we prove two results about the group of $2\times 2$ upper triangular matrices over arbitrary finite fields: a product set estimate using techniques from multiplicative combinatorics and an energy estimate using incidence geometry. The energy method gives better quantitative results but only applies to small sets. We also prove an energy result for the Heisenberg group.

In recent years, there has been increasing interest in the US Department of Defense to build an on-demand airborne network for communications relay utilizing high-capacity, long-range military radio systems. While these systems operate well in a network of homogeneous systems, platforms generally employ multiple heterogeneous radio systems making internetworking difficult due to varying radio characteristics and lack of interoperability. Although simulations and emulation tests can provide a baseline for how systems will perform in a controlled environment, field tests are crucial to demonstrate capabilities in real-world operating environments. In this paper, we present measurement results from a field test involving two airborne platforms forming a dynamically routed aerial IP backbone over 200 nautical miles with various radio systems as part of the C4ISR on-the-move 2010 exercise. We present measurement results on per link performance, radio-to-router interface performance, and multihop network performance results with prototype software on open source platforms. Additionally, key lessons learned and recommendations are given.

The desire to increase bandwidth efficiency in an all-IP infrastructure in the presence of reduced spectrum and increasing demand for connectivity has led to several developments in IP header compression techniques. In recent years, there have been several IP header compression schemes developed in industry specifically for wireless networks including RObust Header Compression (ROHC) and IP Header Compression (RFC 2507). ROHC and IPHC (RFC 2507) have been adopted by several commercial cellular networks and military networks as one of the techniques for implementing IP header compression. In addition to ROHC and IPHC which were designed primarily for one-hop wireless networks, MANET IP Header Compression (MIPHC) was defined to help bridge the gap to multi-hop MANETs. To evaluate the effectiveness of IP header compression schemes on multi-hop MANETs and other networks, we implement simulation models of ROHC, IPHC, and MIPHC and evaluate their performance under various conditions in a mobile ad hoc network. The results show that although ROHC was designed specifically for one-hop cellular networks and context is required to be maintained per hop per IP flow, its performance is fairly good in multi-hop MANETs.

The current generation of long-range, high capacity, military radios are stove-piped systems that work well in a homogeneous environment, but lack interoperability with other radio systems. Each radio provides a subset of disparate link information in non-standard interfaces and has built-in home-grown routers running different routing protocols. In a heterogeneous radio system airborne environment, wireless link characteristics change rapidly, often requiring direct link feedback from the radio to make routing decisions. In recent years, much work has been done in developing a common radio-to-router interface (R2RI) that standardizes a subset of per-link information to pass to the network layer for use in dynamic MANET routing. While simulations and emulation tests can provide a baseline for how systems might perform, field-tests are crucial to demonstrate capabilities in real-world operating environments. In this paper, we present measurement results from a field test involving several air and ground assets with various radio systems that test an implementation of RFC4938, a radio-to-router interface protocol, and its interaction with a dynamic MANET routing protocol. The assets formed a high capacity, dynamically routed aerial IP backbone made of heterogeneous radio technologies over 250 nautical miles (Nm), allowing the passing of military traffic.

This paper describes the design and construction of the first hardware running a generalised type-2 fuzzy logic system. A rationale for the design is given and hardware representations are discussed. An integrated development environment, also developed as part of this project, for type-2 fuzzy system is described along with the software which links this IDE to the novel hardware. The performance of the novel type-2 development board is tested under two scenarios.

In electrical impedance tomography, currents are applied to the body through electrodes that are attached to the surface and the corresponding surface voltages are measured. Based on these boundary measurements, the internal admittivity distribution of the body can be reconstructed. In order to improve the image quality it is necessary and useful to apply physiologically meaningful prior information into the image reconstruction. Such prior information usually can be obtained from other sources. For example, information on the object's boundary shape and internal structure can be obtained from computed tomography and magnetic resonance imaging scan. However, this type of prior information may change from time to time and from person to person. As these changes are limited anatomically and physiologically, the prior information including the possible changes can be presented in a number of variational forms. The aim of this paper is to find which form of prior information is more compatible for a specific imaged object at the time of imaging. This paper proposes a new method for selecting the most appropriate form of prior information, through the procedure of iterative image reconstruction by using the information obtained from boundary measurements. The method is based on the principle that incompatible prior information causes errors which are able to affect the image reconstruction's convergence behavior. In this method, according to the various forms of prior information available, several image reconstruction configurations are designed. Then, through monitoring the convergence behavior in an iterative image reconstruction, the configuration with compatible prior information can be found among those different configurations. As an example, the prior information regarding the imaged object's boundary shape and internal structure was studied by computer simulation. Results were shown and discussed.