Testing Uniformity of Stationary Distribution

A random walk on a directed graph gives a Markov chain on the vertices of the graph. An important question that arises often in the context of Markov chain is whether the uniform distribution on the vertices of the graph is a stationary distribution of the Markov chain. Stationary distribution of a Markov chain is a global property of the graph. In this paper, we prove that for a regular directed graph whether the uniform distribution on the vertices of the graph is a stationary distribution, depends on a local property of the graph, namely if (u,v) is an directed edge then outdegree(u) is equal to indegree(v). This result also has an application to the problem of testing whether a given distribution is uniform or "far" from being uniform. This is a well studied problem in property testing and statistics. If the distribution is the stationary distribution of the lazy random walk on a directed graph and the graph is given as an input, then how many bits of the input graph do one need to query in order to decide whether the distribution is uniform or "far" from it? This is a problem of graph property testing and we consider this problem in the orientation model (introduced by Halevy et al.). We reduce this problem to test (in the orientation model) whether a directed graph is Eulerian. And using result of Fischer et al. on query complexity of testing (in the orientation model) whether a graph is Eulerian, we obtain bounds on the query complexity for testing whether the stationary distribution is uniform

Asymptotic properties of a goodness-of-fit test based on maximum correlations

We study the efficiency properties of the goodness-of-fit test based on the Qn statistic introduced in Fortiana and Grané (2003) using the concepts of Bahadur asymptotic relative efficiency and Bahadur asymptotic optimality. We compare the test based on this statistic with those based on the Kolmogorov-Smirnov, the Cramér-von Mises and the Anderson-Darling statistics. We also describe the distribution families for which the test based on Qn is asymptotically optimal in the Bahadur sense and, as an application, we use this test to detect the presence of hidden periodicities in a stationary time series.Bahadur asymptotic relative efficiency, Goodness-of-fit, Local asymptotic optimality, L-statistics, Maximum correlation

Materials and Mix Optimization Procedures for PCC Pavements;TR-484, March 2006

Severe environmental conditions, coupled with the routine use of deicing chemicals and increasing traffic volume, tend to place extreme demands on portland cement concrete (PCC) pavements. In most instances, engineers have been able to specify and build PCC pavements that met these challenges. However, there have also been reports of premature deterioration that could not be specifically attributed to a single cause. Modern concrete mixtures have evolved to become very complex chemical systems. The complexity can be attributed to both the number of ingredients used in any given mixture and the various types and sources of the ingredients supplied to any given project. Local environmental conditions can also influence the outcome of paving projects. This research project investigated important variables that impact the homogeneity and rheology of concrete mixtures. The project consisted of a field study and a laboratory study. The field study collected information from six different projects in Iowa. The information that was collected during the field study documented cementitious material properties, plastic concrete properties, and hardened concrete properties. The laboratory study was used to develop baseline mixture variability information for the field study. It also investigated plastic concrete properties using various new devices to evaluate rheology and mixing efficiency. In addition, the lab study evaluated a strategy for the optimization of mortar and concrete mixtures containing supplementary cementitious materials. The results of the field studies indicated that the quality management concrete (QMC) mixtures being placed in the state generally exhibited good uniformity and good to excellent workability. Hardened concrete properties (compressive strength and hardened air content) were also satisfactory. The uniformity of the raw cementitious materials that were used on the projects could not be monitored as closely as was desired by the investigators; however, the information that was gathered indicated that the bulk chemical composition of most materials streams was reasonably uniform. Specific minerals phases in the cementitious materials were less uniform than the bulk chemical composition. The results of the laboratory study indicated that ternary mixtures show significant promise for improving the performance of concrete mixtures. The lab study also verified the results from prior projects that have indicated that bassanite is typically the major sulfate phase that is present in Iowa cements. This causes the cements to exhibit premature stiffening problems (false set) in laboratory testing. Fly ash helps to reduce the impact of premature stiffening because it behaves like a low-range water reducer in most instances. The premature stiffening problem can also be alleviated by increasing the water–cement ratio of the mixture and providing a remix cycle for the mixture