A spatial signature of sprawl: or the proportion and distribution of linear networkcircuits

This paper sets out to investigate whether the frequency distribution ofthe linear network circuits within a graph-based representation of aroad transportation system can be helpful in identifying sprawl and, inparticular, whether a 'spatial signature of sprawl' can be determined.This paper is based upon an earlier study on Peachtree City, Georgia and in particular of its dual transportation system (roads and golf cartpaths). In order to fully understand the effect that the dualtransportation system has upon Peachtree City, the frequencydistribution of its circuits are compared to three, supposed, 'suburban' areas and three, supposed, 'urban' districts. The conclusion of thispaper is that there is, unquestionably, a measurable continuum between 'suburbia' and 'urbanity' and that this is reflected in the frequency,length and distribution of the graph network circuits. The main sectionof this paper is concerned with the presentation and discussion ofalternative algorithms for calculating these circuits. This section isfollowed by an introduction of a selection of methods for interpretingthe resultant data. Finally, with respect to Peachtree City, this paperconcludes that the effect of the dual transportation system is to make it more 'urban' than it would otherwise be, although it remains adistinctly suburban environment

Group Testing with Probabilistic Tests: Theory, Design and Application

Identification of defective members of large populations has been widely studied in the statistics community under the name of group testing. It involves grouping subsets of items into different pools and detecting defective members based on the set of test results obtained for each pool. In a classical noiseless group testing setup, it is assumed that the sampling procedure is fully known to the reconstruction algorithm, in the sense that the existence of a defective member in a pool results in the test outcome of that pool to be positive. However, this may not be always a valid assumption in some cases of interest. In particular, we consider the case where the defective items in a pool can become independently inactive with a certain probability. Hence, one may obtain a negative test result in a pool despite containing some defective items. As a result, any sampling and reconstruction method should be able to cope with two different types of uncertainty, i.e., the unknown set of defective items and the partially unknown, probabilistic testing procedure. In this work, motivated by the application of detecting infected people in viral epidemics, we design non-adaptive sampling procedures that allow successful identification of the defective items through a set of probabilistic tests. Our design requires only a small number of tests to single out the defective items. In particular, for a population of size $N$ and at most $K$ defective items with activation probability $p$, our results show that $M = O(K^2\log{(N/K)}/p^3)$ tests is sufficient if the sampling procedure should work for all possible sets of defective items, while $M = O(K\log{(N)}/p^3)$ tests is enough to be successful for any single set of defective items. Moreover, we show that the defective members can be recovered using a simple reconstruction algorithm with complexity of $O(MN)$.Comment: Full version of the conference paper "Compressed Sensing with Probabilistic Measurements: A Group Testing Solution" appearing in proceedings of the 47th Annual Allerton Conference on Communication, Control, and Computing, 2009 (arXiv:0909.3508). To appear in IEEE Transactions on Information Theor

SLIQ: Simple Linear Inequalities for Efficient Contig Scaffolding

Scaffolding is an important subproblem in "de novo" genome assembly in which mate pair data are used to construct a linear sequence of contigs separated by gaps. Here we present SLIQ, a set of simple linear inequalities derived from the geometry of contigs on the line that can be used to predict the relative positions and orientations of contigs from individual mate pair reads and thus produce a contig digraph. The SLIQ inequalities can also filter out unreliable mate pairs and can be used as a preprocessing step for any scaffolding algorithm. We tested the SLIQ inequalities on five real data sets ranging in complexity from simple bacterial genomes to complex mammalian genomes and compared the results to the majority voting procedure used by many other scaffolding algorithms. SLIQ predicted the relative positions and orientations of the contigs with high accuracy in all cases and gave more accurate position predictions than majority voting for complex genomes, in particular the human genome. Finally, we present a simple scaffolding algorithm that produces linear scaffolds given a contig digraph. We show that our algorithm is very efficient compared to other scaffolding algorithms while maintaining high accuracy in predicting both contig positions and orientations for real data sets.Comment: 16 pages, 6 figures, 7 table

Multiple Fault Isolation in Redundant Systems

Fault diagnosis in large-scale systems that are products of modern technology present formidable challenges to manufacturers and users. This is due to large number of failure sources in such systems and the need to quickly isolate and rectify failures with minimal down time. In addition, for fault-tolerant systems and systems with infrequent opportunity for maintenance (e.g., Hubble telescope, space station), the assumption of at most a single fault in the system is unrealistic. In this project, we have developed novel block and sequential diagnostic strategies to isolate multiple faults in the shortest possible time without making the unrealistic single fault assumption

Multiple Fault Isolation in Redundant Systems

Fault diagnosis in large-scale systems that are products of modem technology present formidable challenges to manufacturers and users. This is due to large number of failure sources in such systems and the need to quickly isolate and rectify failures with minimal down time. In addition, for fault-tolerant systems and systems with infrequent opportunity for maintenance (e.g., Hubble telescope, space station), the assumption of at most a single fault in the system is unrealistic. In this project, we have developed novel block and sequential diagnostic strategies to isolate multiple faults in the shortest possible time without making the unrealistic single fault assumption

Computationally Tractable Algorithms for Finding a Subset of Non-defective Items from a Large Population

In the classical non-adaptive group testing setup, pools of items are tested together, and the main goal of a recovery algorithm is to identify the "complete defective set" given the outcomes of different group tests. In contrast, the main goal of a "non-defective subset recovery" algorithm is to identify a "subset" of non-defective items given the test outcomes. In this paper, we present a suite of computationally efficient and analytically tractable non-defective subset recovery algorithms. By analyzing the probability of error of the algorithms, we obtain bounds on the number of tests required for non-defective subset recovery with arbitrarily small probability of error. Our analysis accounts for the impact of both the additive noise (false positives) and dilution noise (false negatives). By comparing with the information theoretic lower bounds, we show that the upper bounds on the number of tests are order-wise tight up to a $\log^2K$ factor, where $K$ is the number of defective items. We also provide simulation results that compare the relative performance of the different algorithms and provide further insights into their practical utility. The proposed algorithms significantly outperform the straightforward approaches of testing items one-by-one, and of first identifying the defective set and then choosing the non-defective items from the complement set, in terms of the number of measurements required to ensure a given success rate.Comment: In this revision: Unified some proofs and reorganized the paper, corrected a small mistake in one of the proofs, added more reference