Spatio-Temporal Event Model for Cyber-Physical Systems

The emerging Cyber-Physical Systems (CPSs) are envisioned to integrate computation, communication and control with the physical world. Therefore, CPS requires close interactions between the cyber and physical worlds both in time and space. These interactions are usually governed by events, which occur in the physical world and should autonomously be reflected in the cyber-world, and actions, which are taken by the CPS as a result of detection of events and certain decision mechanisms. Both event detection and action decision operations should be performed accurately and timely to guarantee temporal and spatial correctness. This calls for a flexible architecture and task representation framework to analyze CP operations. In this paper, we explore the temporal and spatial properties of events, define a novel CPS architecture, and develop a layered spatiotemporal event model for CPS. The event is represented as a function of attribute-based, temporal, and spatial event conditions. Moreover, logical operators are used to combine different types of event conditions to capture composite events. To the best of our knowledge, this is the first event model that captures the heterogeneous characteristics of CPS for formal temporal and spatial analysis.

Review of Applied Spatial Data Analysis with R by R. S. Bivand, E. J. Pebesma, and V. Gomez-Rubio

Most authors struggle to pick a title that adequately conveys all of the material covered in a book. When I first saw Applied Spatial Data Analysis with R, I expected a review of spatial statistical models and their applications in packages (libraries) from the CRAN site of R. The authors’ title is not misleading, but I was very pleasantly surprised by how deep the word “applied” is here. The first half of the book essentially covers how R handles spatial data. To some statisticians this may be boring. Do you want, or need, to know the difference between S3 and S4 classes, how spatial objects in R are organized, and how various methods work on the spatial objects? A few years ago I would have said “no,” especially to the “want” part. Just let me slap my EXCEL spreadsheet into R and run some spatial functions on it. Unfortunately, the world is not so simple, and ultimately we want to minimize effort to get all of our spatial analyses accomplished. The first half of this book certainly convinced me that some extra effort in organizing my data into certain spatial class structures makes the analysis easier and less subject to mistakes. I also admit that I found it very interesting and I learned a lot.

Spatial statistical models that use flow and stream distance

We develop spatial statistical models for stream networks that can estimate relationships between a response variable and other covariates, make predictions at unsampled locations, and predict an average or total for a stream or a stream segment. There have been very few attempts to develop valid spatial covariance models that incorporate flow, stream distance, or both. The application of typical spatial autocovariance functions based on Euclidean distance, such as the spherical covariance model, are not valid when using stream distance. In this paper we develop a large class of valid models that incorporate flow and stream distance by using spatial moving averages. These methods integrate a moving average function, or kernel, against a white noise process. By running the moving average function upstream from a location, we develop models that use flow, and by construction they are valid models based on stream distance. We show that with proper weighting, many of the usual spatial models based on Euclidean distance have a counterpart for stream networks. Using sulfate concentrations from an example data set, the Maryland Biological Stream Survey (MBSS), we show that models using flow may be more appropriate than models that only use stream distance. For the MBSS data set, we use restricted maximum likelihood to fit a valid covariance matrix that uses flow and stream distance, and then we use this covariance matrix to estimate fixed effects and make kriging and block kriging predictions.

Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling

Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises.