Leveraging spatial abstraction in traffic analysis and forecasting with visual analytics

By applying spatio-temporal aggregation to traffic data consisting of vehicle trajectories, we generate a spatially abstracted transportation network, which is a directed graph where nodes stand for territory compartments (areas in geographic space) and links (edges) are abstractions of the possible paths between neighboring areas. From time series of traffic characteristics obtained for the links, we reconstruct mathematical models of the interdependencies between the traffic intensity (a.k.a. traffic flow or flux) and mean velocity. Graphical representations of these interdependencies have the same shape as the fundamental diagram of traffic flow through a physical street segment, which is known in transportation science. This key finding substantiates our approach to traffic analysis, forecasting, and simulation leveraging spatial abstraction. We present the process of data-driven generation of traffic forecasting and simulation models, in which each step is supported by visual analytics techniques

APPROXIMATE STOCHASTIC TECHNIQUES FOR DIVERSE ENGINEERING DYNAMICS APPLICATIONS

Generally, deterministic approaches are used in practice to analyze dynamic systems. Variations in loading conditions and material properties are taken into account by either selecting high, low or average values. Consequently, the uncertainty inherent in almost every dynamic analysis is considered just intuitively. To realistically capture the behavior of a dynamic system the intrinsic randomness must be appropriately modeled requiring concepts and methods of mathematical statistics and probability theory, as well as, random vibration theory. Undeniably, stochastic dynamics based approaches provide a more realistic modeling of the dynamic response of engineered systems allowing for enhanced design solutions. The prevailing approach used in the industry is the Monte Carlo simulation method. However, a well-known shortcoming of the method is the extensive computational cost required. Further, the class of problems of nonlinear random vibrations that lend themselves to exact solutions (e.g., via the associated Fokker-Planck-Kolmogorov equation) is extremely limited. Therefore, approximate approaches are desired for solving nonlinear stochastic dynamics problems. The current thesis seeks to exploit approximate stochastic dynamics tools to solve engineering dynamics problems encountered in practice. In particular, the primary focus is directed towards the recently developed Wiener path integral technique, which has been shown to poses certain advantages over alternative well-established solution methodologies, namely, computational efficiency and accuracy. Two applications are investigated: the stochastic response of nonlinear vibratory energy harvesters, and, the depth determination of ice gouging events. The accuracy/reliability of the approximate approaches is demonstrated via comparisons with pertinent Monte Carlo simulation data

New Approaches To Photometric Redshift Prediction Via Gaussian Process Regression In The Sloan Digital Sky Survey

Expanding upon the work of Way and Srivastava 2006 we demonstrate how the use of training sets of comparable size continue to make Gaussian process regression (GPR) a competitive approach to that of neural networks and other least-squares fitting methods. This is possible via new large size matrix inversion techniques developed for Gaussian processes (GPs) that do not require that the kernel matrix be sparse. This development, combined with a neural-network kernel function appears to give superior results for this problem. Our best fit results for the Sloan Digital Sky Survey (SDSS) Main Galaxy Sample using u,g,r,i,z filters gives an rms error of 0.0201 while our results for the same filters in the luminous red galaxy sample yield 0.0220. We also demonstrate that there appears to be a minimum number of training-set galaxies needed to obtain the optimal fit when using our GPR rank-reduction methods. We find that morphological information included with many photometric surveys appears, for the most part, to make the photometric redshift evaluation slightly worse rather than better. This would indicate that most morphological information simply adds noise from the GP point of view in the data used herein. In addition, we show that cross-match catalog results involving combinations of the Two Micron All Sky Survey, SDSS, and Galaxy Evolution Explorer have to be evaluated in the context of the resulting cross-match magnitude and redshift distribution. Otherwise one may be misled into overly optimistic conclusions.Comment: 32 pages, ApJ in Press, 2 new figures, 1 new table of comparison methods, updated discussion, references and typos to reflect version in Pres

Solar cycle effects in planetary geomagnetic activity: Analysis of 36‐year long OMNI dataset

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94796/1/grl13462.pd

A Gas Leak Rate Measurement System for the ATLAS MUON BIS-Monitored Drift Tubes

A low-cost, reliable and precise system developed for the gas leak rate measurement of the BIS-Monitored Drift Tubes (MDTs) for the ATLAS Muon Spectrometer is presented. In order to meet the BIS-MDT mass production rate, a total number of 100 tubes are tested simultaneously in this setup. The pressure drop of each one of the MDT is measured, within a typical time interval of 48 hours, via a differential manometer comparing with the pressure of a gas tight reference tube. The precision of the method implemented is based on the system temperature homogeneity, with accuracy of ÄT = 0.3 oC. For this reason, two thermally isolated boxes are used testing 50 tubes each of them, to achieve high degree of temperature uniformity and stability. After measuring several thousands of the MDTs, the developed system is confirmed to be appropriate within the specifications for testing the MDTs during the mass production

Macroscopic traffic models from microscopic car-following models

We present a method to derive macroscopic fluid-dynamic models from microscopic car-following models via a coarse-graining procedure. The method is first demonstrated for the optimal velocity model. The derived macroscopic model consists of a conservation equation and a momentum equation, and the latter contains a relaxation term, an anticipation term, and a diffusion term. Properties of the resulting macroscopic model are compared with those of the optimal velocity model through numerical simulations, and reasonable agreement is found although there are deviations in the quantitative level. The derivation is also extended to general car-following models.Comment: 12 pages, 4 figures; to appear in Phys. Rev.

Generalized Force Model of Traffic Dynamics

Floating car data of car-following behavior in cities were compared to existing microsimulation models, after their parameters had been calibrated to the experimental data. With these parameter values, additional simulations have been carried out, e.g. of a moving car which approaches a stopped car. It turned out that, in order to manage such kinds of situations without producing accidents, improved traffic models are needed. Good results have been obtained with the proposed generalized force model.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry

The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest elasticity tensor of the specified symmetry. Solutions are presented for three distance functions, with particular attention to the Riemannian and log-Euclidean distances. These yield solutions that are invariant under inversion, i.e., the same whether elastic stiffness or compliance are considered. The Frobenius distance function, which corresponds to common notions of Euclidean length, is not invariant although it is simple to apply using projection operators. A complete description of the Euclidean projection method is presented. The three metrics are considered at a level of detail far greater than heretofore, as we develop the general framework to best fit a given set of moduli onto higher elastic symmetries. The procedures for finding the closest elasticity tensor are illustrated by application to a set of 21 moduli with no underlying symmetry.Comment: 48 pages, 1 figur