Parallel computation of large-scale network equilibria and variational inequalities.

Equilibrium of a network is obtained when each user who competes to optimize his utility can not improve his utility any further. Equilibrium problems governed by distinct equilibrium concepts can be formulated in one general framework--that of variational inequalities. The synthesis of variational inequalities and networks induces the creation of highly efficient algorithms which are especially suited for the large-scale equilibrium problems. Motivated by the recent technological advances in parallel computing architectures, parallel algorithms of large-scale equilibrium problems were developed using the theory of variational inequalities. In the case where the feasible constraint set of a network equilibrium problem can be expressed as a Cartesian product of subsets, the application of variational inequality decomposition algorithms for the parallel computation becomes possible. A new spatial price equilibrium model, which is not based on the path flows, but, rather, on the link flows to allow the decomposition by time periods, was developed and used as a prototype of large-scale network equilibrium problems. The variational inequality formulations were decomposed first by commodities, then by time periods, and, subsequently, by markets. The coarse grain parallel architectures used were the IBM 3090-600E and the IBM 3090-600J at the Cornell Theory Center with six processors each. The maximum speed-ups obtained were 1.93 for two processors, 3.74 for four processors, and 5.15 for six processors. The market subproblems were further decomposed by links, resulting in a fine grain parallel implementation. The Thinking Machine\u27s Connection Machine, CM-2, with 32,768 processors was used for the numerical experimentation. The fine grain parallel algorithm solved input/output matrix problems more than 20 times faster, when compared to the results on the IBM 3090-600J. It is expected that further enhancements to parallel languages and parallel architectures will make even more efficient implementations realizable, and that parallel computing and the theory of variational inequalities can be successfully applied to solve more efficiently other large-scale problems with an underlying network structure, such as traffic equilibrium problems, general economic equilibrium problems, and financial equilibrium problems

Parallel Computation of Large-Scale Nonlinear Network Problems in the Social and Economic Sciences

In this paper we focus on the parallel computation of large - scale equilibrium and optimization problems arising in the social and economic sciences. In particular, we consider problems which can be visualized and conceptualized as nonlinear network flow problems. The underlying network structure is then exploited in the development of parallel decomposition algorithms. We first consider market equilibrium problems, both dynamic and static, which are formulated as variational inequality problems, and for which we propose parallel decomposition algorithms by time period and by commodity, respectively. We then turn to the parallel computation of large-scale constrained matrix problems which are formulated as optimization problems and discuss the results of parallel decomposition by row/column

Parallel Computation of Large-Scale Dynamic Market Network Equilibria via Time Period Decomposition

In this paper we consider a dynamic market equilibrium problem over a finite time horizon in which a commodity is produced, consumed, traded, and inventoried over space and time. We first formulate the problem as a network equilibrium problem and derive the variational inequality formulation of the problem. We then propose a parallel decomposition algorithm which decomposes the large-scale problem into T + 1 subproblems, where T denotes the number of time periods. Each of these subproblems can then be solved simultaneously, that is, in parallel, on distinct processors. We provide computational results on linear separable problems and on nonlinear asymmetric problems when the algorithm is implemented in a serial and then in a parallel environment. The numerical results establish that the algorithm is linear in the number of time periods. This research demonstrates that this new formulation of dynamic market problems and decomposition procedure considerably expands the size of problems that are now feasible to solve

15-04 Travel Behavior of Blind Individuals before and after Receiving Orientation and Mobility Training

In this pilot study, we devised, tested, and refined a protocol for evaluating the travel behavior of blind individuals. Preliminary analyses of our pilot study data suggest that our new method involving Global Positioning Systems (GPS), accelerometers, and Geographic Information Systems (GIS), will enable us to collect objective, quantitative, and valid measures of blind individuals’ travel behavior and Orientation and Mobility (O&M) training’s effectiveness. Preliminary analysis results from a small sample of blind travelers describe the individuals’ trip distances, trip frequencies, trip destinations, trip modes, travel times, whether assisted or not, and perceived ability to get around. With the completion of the full-scale study (proposed for FY 2016-18), we may be able to recommend changes to current O&M training to allow more active, confident, and safe travel by blind individuals in their communities. We may also discover characteristics of the physical environment that inhibit access by blind pedestrians and are more amenable to mitigation through good transportation planning (e.g., geometric design of intersections) than through O&M training

A Comparison of Hemodynamic and Neural Responses in Cat Visual Cortex Using Complex Stimuli

We compare fMRI-BOLD responses in anesthetized cats with local field potentials (LFPs), aggregate high-frequency responses (analog-Mua) and spiking activity recorded in primary and higher visual cortex of alert animals. The similarity of the activations in these electrophysiological signals to those in the BOLD is quantified by counting recording sites where different stimuli elicit the same relative activation as in the imaging experiments. Using artificial stimuli, a comparison of BOLD and LFP strongly depends on the frequency range used. Stimulating with complex or natural stimuli reduces this frequency dependence and yields a good match of LFP and BOLD. In general, this match is best between 20 and 50 Hz. The measures of high-frequency activity behave qualitatively different: the responses of the analog-Mua match those of the LFP; the spiking activity shows a low concordance with the BOLD signal. This dissociation of BOLD and spiking activity is most prominent upon stimulation with natural stimul

14-11 Travel in Adverse Winter Weather Conditions by Blind Pedestrians

Winter weather creates many orientation and mobility (O&M) challenges for people who are visually impaired. Getting the cane tip stuck is one of the noticeable challenges when traveling in snow, particularly when the walking surface is covered in deep snow. We compared four different cane tips: 1) metal glide, 2) marshmallow roller, 3) roller ball, and 4) bundu bahser. There was a statistically significant difference in frequency of sticking among the different cane tips. Post hoc analyses revealed that the sticking frequency for the metal glide tip was significantly higher than that for the roller ball tip, for the bundu basher tip, and for the marshmallow roller tip. In addition, there was a statistically significant difference in sticking frequency between the marshmallow roller tip and the roller ball tip. Cane tip shape appears to have contributed to differences in sticking frequency. For example, the metal glide tip, being the smallest and more sharply angled among the four cane tips, tended to get stuck on snow more often than more rounded and larger cane tips. Differences in sticking frequency among the cane tips observed in this study appear to be large enough to be practically significant for cane users and practitioners