Technology

Computer algebra systems such as Maple compute using mathematical formulae as well as numbers, mechanizing the mathematics used in education and research labs. This project focuses on the design and implementation of algorithms for these systems. Emphasis is placed on efficiency that allows large and complex problems of the type encountered in industrial settings to be solved. In the past year the team has made major advances in the core tools that are needed to solve these complex problems.

How quickly and effectively a designer can transform a mental concept into a digital object that is easy to refine and reuse is a central challenge in computer graphics. The focus of this project is, therefore, to develop new mathematical representations, or build upon existing ones, to capture the essence of shape as perceived by designers. In the past year, a freeware software program, Shapeshop, which was developed by the project team was released for download.

This project uses mathematical filtering theory to develop computer tractable real time solutions for incomplete, corrupted information problems. These techniques have proven to be beneficial in defence, communications, media effects, and manufacturing. In 2002-2003, Optovation Inc. was added as a new partner, Lockheed Martin Corp. filed for two new patents and we formed a spin-off company, Random Knowledge Inc. to commercialize our technology in the areas of Network Security, Fraud Detection, and Finance.

Route planning is a complex task which has many applications in the civilian and military worlds. This project seeks to develop planning tools to aid in planning search and rescue operations while taking into account uncertain factors such as weather, type of terrain, physical feasibility of search pattern, threat levels, desired coverage, risk and survivability considerations. The team will study the process of selecting a path for a vehicle to follow through friendly or unfriendly terrain based on multiple constraints and criteria.

Reactive Systems are formal systems that cause events in the physical world, in reaction to a set of monitored inputs. Examples include control systems for aircraft, medical devices, industrial processes, and consumer appliances. In many of these examples, safety (and often security) of the system is of paramount importance. To say anything at all about whether such a system is safe or secure, one has to be able to predict its behavior under the conditions that the system may encounter in use.

The management of transportation and production systems often requires solving a sequence of optimization problems, each problem optimizing the utilization of some resources: equipment, personnel, etc. For instance, transit authorities perform bus scheduling followed by daily and monthly driver scheduling; airlines perform aircraft scheduling followed by crew pairing and monthly crew scheduling; and manufacturing companies address manpower scheduling before production scheduling. Such a sequential approach for management was introduced a long time ago when solutions were computed manually.

The power of human vision to process wide ranges of intensities far exceeds the abilities of current imaging technology. Both cameras and displays are currently limited to a contrast, or dynamic range, of between 300:1 to 1,000:1, while humans can process a simultaneous dynamic range of 50,000:1 or more. As a result, there has been a push to develop high-dynamic range (HDR) display and camera hardware and the supporting algorithms. In the past year, the team has worked closely with industrial sponsor Dolby Canada on a range of topics in HDR imaging and display.

This project will explore new ways of customizing and translating the mass of daily information produced by Environment Canada (EC). This information in digital format is later transformed into weather and environmental forecasts, warnings and alerts that must be broadcast in real-time in at least two languages, in many different formats and in a way that takes location into account.

Algorithms for solving difficult computational problems play a key role in many applications, including scheduling, resource allocation, computer-aided design, and software verification. In many cases, heuristic methods are the key to solving these problems effectively. However, the design of effective heuristic algorithms, particularly algorithms for solving computationally hard problems, is a difficult task that requires considerable expertise.

In industrialized countries, the expansion of power systems has become very difficult. According to power utility consortiums such as CEATI and EPRI, only drastic changes to the current power grid architecture, together with the introduction of new technologies can prevent the high social costs associated with a reduction in reliability of energy supply. High temperature superconductors (HTS) are among the most promising technologies to achieve this goal.