Graph theory, irreducibility, and structural analysis of differential-algebraic equation systems

The $\Sigma$-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of a system Jacobian is derived. This pattern implies a block-triangular form (BTF) of the DAE that can be exploited to speed up numerical solution. The paper compares this fine BTF with the usually coarser BTF derived from the sparsity pattern of the \sigmx. It defines a Fine-Block Graph with weighted edges, which gives insight into the relation between coarse and fine blocks, and the permitted ordering of blocks to achieve BTF. It also illuminates the structure of the set of normalised offset vectors of the DAE, e.g.\ this set is finite if and only if there is just one coarse block

How AD Can Help Solve Differential-Algebraic Equations

A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical solution. This is often done with the help of a computer algebra system. We show in two significant cases that it can be done efficiently by pure algorithmic differentiation. The first is the Dummy Derivatives method, here we give a mainly theoretical description, with tutorial examples. The second is the solution of a mechanical system directly from its Lagrangian formulation. Here we outline the theory and show several non-trivial examples of using the "Lagrangian facility" of the Nedialkov-Pryce initial-value solver DAETS, namely: a spring-mass-multipendulum system, a prescribed-trajectory control problem, and long-time integration of a model of the outer planets of the solar system, taken from the DETEST testing package for ODE solvers

Tip Allocation: A Compliance Study tor Restaurants

Survey research of the commercial food service industry with regard to tips and tip allocation revealed that 50 percent of restaurateurs require that employees report a minimum amount or percentage of sales and over 50 percent which allocate tips report them as employee income. The authors discuss these results and point out other problems

Ammonia emission abatement does not fully control reduced forms of nitrogen deposition

Human activities and population growth have increased the natural burden of reactive nitrogen (N) in the environment. Excessive N deposition on Earth’s surface leads to adverse feedbacks on ecosystems and humans. Similar to that of air pollution, emission control is recognized as an efficient means to control acid deposition. Control of nitrogen oxides (NO_x = NO + NO₂) emissions has led to reduction in deposition of oxidized nitrogen (NO_y, the sum of all oxidized nitrogen species, except nitrous oxide [N₂O]). Reduced forms of nitrogen (NH_x = ammonia [NH₃] + ammonium [NH₄⁺]) deposition have, otherwise, increased, offsetting the benefit of reduction in NO_y deposition. Stringent control of NH₃ emissions is being considered. In this study, we assess the response of N deposition to N emission control on continental regions. We show that significant reduction of NHx deposition is unlikely to be achieved at the early stages of implementing NH₃ emission abatement. Per-unit NH₃ emission abatement is shown to result in only 60–80% reduction in NH_x deposition, which is significantly lower than the demonstrated 80–120% benefit of controlling NO_x emissions on NO_y deposition. This 60–80% effectiveness of NH_x deposition reduction per unit NH₃ emission abatement reflects, in part, the effects of simultaneous reductions in NO_x and SO₂ emissions

Decentralized Data Fusion and Active Sensing with Mobile Sensors for Modeling and Predicting Spatiotemporal Traffic Phenomena

The problem of modeling and predicting spatiotemporal traffic phenomena over an urban road network is important to many traffic applications such as detecting and forecasting congestion hotspots. This paper presents a decentralized data fusion and active sensing (D2FAS) algorithm for mobile sensors to actively explore the road network to gather and assimilate the most informative data for predicting the traffic phenomenon. We analyze the time and communication complexity of D2FAS and demonstrate that it can scale well with a large number of observations and sensors. We provide a theoretical guarantee on its predictive performance to be equivalent to that of a sophisticated centralized sparse approximation for the Gaussian process (GP) model: The computation of such a sparse approximate GP model can thus be parallelized and distributed among the mobile sensors (in a Google-like MapReduce paradigm), thereby achieving efficient and scalable prediction. We also theoretically guarantee its active sensing performance that improves under various practical environmental conditions. Empirical evaluation on real-world urban road network data shows that our D2FAS algorithm is significantly more time-efficient and scalable than state-of-the-art centralized algorithms while achieving comparable predictive performance.Comment: 28th Conference on Uncertainty in Artificial Intelligence (UAI 2012), Extended version with proofs, 13 page