Controlled linear perturbation

We present an algorithmic solution to the robustness problem in computational geometry, called controlled linear perturbation, and demonstrate it on Minkowski sums of polyhedra. The robustness problem is how to implement real RAM algorithms accurately and efficiently using computer arithmetic. Approximate computation in floating point arithmetic is efficient but can assign incorrect signs to geometric predicates, which can cause combinatorial errors in the algorithm output. We make approximate computation accurate by performing small input perturbations, which we compute using differential calculus. This strategy supports fast, accurate Minkowski sum computation. The only prior robust implementation uses a less efficient algorithm, requires exact algebraic computation, and is far slower based on our extensive testing.     

Survivable millimeter-wave mesh networks

Millimeter-wave mesh networks have the potential to provide cost-effective high-bandwidth solutions to many current bandwidth-constrained networks including cellular backhaul. However, the availability of such networks is severely limited due to their susceptibility to weather, such as precipitation and humidity. In this paper, we present a rigorous approach to survivable millimeter-wave mesh networks based on experimentation, modeling, and simulation. Individual link performance is characterised using frame error-rate measurements from millimeter-wave transmissions on test links over a period of one year. A geometric model based on radar-reflectivity data is used to characterise rain storms and determine their impact on spatially correlated links of a mesh network. To mitigate the impact of link impairments on network services, we present two cross-layered routing protocols to route around the failures: P-WARP (predictive weather-assisted routing protocol) and XL-OSPF (cross-layered open shortest-path first). We conduct a performance analysis of the proposed mesh network under the presence of actual weather events as recorded by the US National Weather Service. Results show that the proposed approach yields the highest dependability when compared against existing routing methods.     

Designing a Controller for a Multi-Train Multi-Track System

The use of formal methods for analyzing and synthesizing a controller for a multi-train multi-track railway system is discussed. The research was motivated by a case study involving the Bay Area Rapid Transit (BART) system. The overall goal is to design a train acceleration control function that enables trains to be safely placed but also increases system throughput. The use of a modeling language for specifying safety properties and a control function is illustrated. The program transformation methodology supported in the HATS system is employed to generate an efficient implementation from a high-level specification of a controller. This implementation can then be used to simulate the controller behavior, thus further enhancing confidence in the design. Properties of optimization transformations can be verified using an rewrite-rule based induction theorem prover Rewrite Rule Laboratory (RRL).     

Filtered Jitter

Jitter is one popular way of generating samples for stochastic sampling in computer graphics. The Poisson disk distribution better approximates that of the human photomosaic. In this paper we examine the spatial and frequency space behaviour of a number of existing algorithms for generating stochastic samples and propose a new algorithm based on low pass filtering a jittered set of displacements. The distribution is at least as much like that of the human photomosaic as any existing algorithm, while being fast to compute.     

Interactive visualization and analysis of transitional flow

A stand-alone visualization application has been developed by a multi-disciplinary, collaborative team with the sole purpose of creating an interactive exploration environment allowing turbulent flow researchers to experiment and validate hypotheses using visualization. This system has specific optimizations made in data management, caching computations, and visualization allowing for the interactive exploration of datasets on the order of 1TB in size. Using this application, the user (co-author Calo) is able to interactively visualize and analyze all regions of a transitional flow volume, including the laminar, transitional and fully turbulent regions. The underlying goal of the visualizations produced from these transitional flow simulations is to localize turbulent spots in the laminar region of the boundary layer, determine under which conditions they form, and follow their evolution. The initiation of turbulent spots, which ultimately lead to full turbulence, was located via a proposed feature detection condition and verified by experimental results. The conditions under which these turbulent spots form and coalesce are validated and presented.     

Leveraging online communities in fostering adaptive schools

There has long been a call for schools to prepare students for the twenty-first century where skills and dispositions differ significantly from much of what has historically characterized formal education. The knowledge based economy calls for policy and pedagogical efforts that would transform schools. Schools are to foster communities of learners. This paper suggests that para-communities may be points of leverage in the fostering of adaptive schools. A critical analysis is done on the differences between para-communities (such as online communities) and schools; and an argument is made that they each serve differing goals and should be left distinct because they achieve different societal and economic demands.     

Verification of bounded Petri nets using integer programming

Model checking based on the causal partial order semantics of Petri nets is an approach widely applied to cope with the state space explosion problem. One of the ways to exploit such a semantics is to consider (finite prefixes of) net unfoldings—themselves a class of acyclic Petri nets—which contain enough information, albeit implicit, to reason about the reachable markings of the original Petri nets. In [19], a verification technique for net unfoldings was proposed, in which deadlock detection was reduced to a mixed integer linear programming problem. In this paper, we present a further development of this approach. The essence of the proposed modifications is to transfer the information about causality and conflicts between the events involved in an unfolding, into a relationship between the corresponding integer variables in the system of linear constraints. Moreover, we present some problem-specific optimisation rules, reducing the search space. To solve other verification problems, such as mutual exclusion or marking reachability and coverability, we adopt Contejean and Devie's algorithm for solving systems of linear constraints over the natural numbers domain and refine it, by taking advantage of the specific properties of systems of linear constraints to be solved. Another contribution of this paper is a method of re-formulating some problems specified in terms of Petri nets as problems defined for their unfoldings. Using this method, we obtain a memory efficient translation of a deadlock detection problem for a safe Petri net into an LP problem. We also propose an on-the-fly deadlock detection method. Experimental results demonstrate that the resulting algorithms can achieve significant speedups.

Group weighted finite transducers

We consider weighted finite transducers over arbitrary groups, that is finite transducers having a counter in which, at any step, a value of the group is stored but no information regarding the content of this counter is available until the computation is finished. The computation is valid if the counter value is the neutral element of the group. We generalize here some results from [8] and [17]. Received: 28 January 2001 / 5 June 2001