On the Global Convergence of Continuous-Time Stochastic Heavy-Ball Method for Nonconvex Optimization

We study the convergence behavior of the stochastic heavy-ball method with a small stepsize. Under a change of time scale, we approximate the discrete method by a stochastic differential equation that models small random perturbations of a coupled system of nonlinear oscillators. We rigorously show that the perturbed system converges to a local minimum in a logarithmic time. This indicates that for the diffusion process that approximates the stochastic heavy-ball method, it takes (up to a logarithmic factor) only a linear time of the square root of the inverse stepsize to escape from all saddle points. This results may suggest a fast convergence of its discrete-time counterpart. Our theoretical results are validated by numerical experiments.Comment: accepted at IEEE International Conference on Big Data in 201

Vibration-induced mobilization of trapped non-aqueous phase liquids in porous media

Acoustic wave stimulation, such as vibration-induced mobilization, is a promising enhancement approach to remove trapped NAPLs (Non-Aqueous Phase Liquids) usually encountered in multiphase flows through porous media, especially the remediation of underground water contamination and incomplete petroleum recovery from oil reservoirs, with advantages of high efficiency, low cost and environmental safety relative to traditional mobilization methods;According to a simple hypothesized capillary-physics mechanism, specific predictions can be deduced that vibration will be the most effective in mobilizing trapped non-aqueous phase liquids with a comparative higher acceleration amplitude and lower vibration frequency;Quasi-two-dimensional glass micro-model experiments were carried out and it was shown that for fixed acceleration amplitude TCE (trichloroethylene), the trapped organic phase, was more quickly displaced as the vibration frequency decreased from 60 Hz to 10 Hz. And for fixed vibration frequency, TCE displacement became more and more efficient as the acceleration amplitude increased from 0.5 m/s2 to 5.0 m/s2;Moreover, numerical simulations were performed using FLUENT to investigate single droplet flow and the related stimulation effects of vibration. Implementing vibration was demonstrated to be more helpful and efficient to mobilize a trapped droplet in capillary tubes. For fixed acceleration amplitude, the efficiency increases as the vibration frequency decreases from 50 Hz to 10 Hz. For fixed vibration frequency, the average bulk flow rate increase and the time necessary to mobilize the trapped droplet decrease as the acceleration amplitude increase;In addition, analysis of droplet breakup in constricted capillary tubes driven by interfacial tension was performed. A criterion was derived to determine whether droplet breakup could be initiated in sinusoidally constricted tubes, and was further validated by simulations and published data. Droplet breakup was shown to be strongly dependent on the shape of the constriction, viscosity ratio, and interfacial tension, but not on density ratio;In all, the work together with the capillary physics mechanism can make it possible to understand the physics of the mobilization effect of low frequency vibration, which can then be applied to the predictions of the stimulation effect in the field after further full parameter space investigations are performed

On the fast convergence of random perturbations of the gradient flow

We consider in this work small random perturbations (of multiplicative noise type) of the gradient flow. We prove that under mild conditions, when the potential function is a Morse function with additional strong saddle condition, the perturbed gradient flow converges to the neighborhood of local minimizers in $O(\ln (\varepsilon^{-1}))$ time on the average, where $\varepsilon$ is the scale of the random perturbation. Under a change of time scale, this indicates that for the diffusion process that approximates the stochastic gradient method, it takes (up to logarithmic factor) only a linear time of inverse stepsize to evade from all saddle points. This can be regarded as a manifestation of fast convergence of the discrete-time stochastic gradient method, the latter being used heavily in modern statistical machine learning.Comment: Revise and Resubmit at Asymptotic Analysi

Comparison of N uptake and internal use efficiency in two tobacco varieties

AbstractTo explain the observation in field experiments that tobacco variety CB-1 was more nitrogen (N)-efficient than K326, the influence of two N levels on growth, N uptake and N flow within plants of the two tobacco varieties was studied. Xylem sap from the upper and lower leaves of both tobacco varieties cultured in quartz sand was collected by application of pressure to the root system. CB-1 took up more N with smaller roots at both high (HN, 10mmolL−1) and low (LN, 1mmolL−1) N levels, and built up more new tissues in upper leaves especially at LN level, than K326. Both varieties showed luxury N uptake, and CB-1 accumulated significantly less NO3− in new tissues than K326, when grown at the HN level. At both N levels, the amount of xylem-transported N and phloem-cycled N from shoot to root in K326 was greater than those in CB-1, indicating higher N use efficiency in CB-1 shoots than in K326 shoots. The major nitrogenous compound in the xylem sap was NO3− irrespective of N level and variety. Low N supply did not cause more NO3− reduction in the root. The results indicated that the N-efficient tobacco variety CB-1 was more efficient in both N uptake by smaller roots and N utilization in shoots, especially when grown at the LN level

Short-Term Traffic Forecasting Using High-Resolution Traffic Data

This paper develops a data-driven toolkit for traffic forecasting using high-resolution (a.k.a. event-based) traffic data. This is the raw data obtained from fixed sensors in urban roads. Time series of such raw data exhibit heavy fluctuations from one time step to the next (typically on the order of 0.1-1 second). Short-term forecasts (10-30 seconds into the future) of traffic conditions are critical for traffic operations applications (e.g., adaptive signal control). But traffic forecasting tools in the literature deal predominantly with 3-5 minute aggregated data, where the typical signal cycle is on the order of 2 minutes. This renders such forecasts useless at the operations level. To this end, we model the traffic forecasting problem as a matrix completion problem, where the forecasting inputs are mapped to a higher dimensional space using kernels. The formulation allows us to capture both nonlinear dependencies between forecasting inputs and outputs but also allows us to capture dependencies among the inputs. These dependencies correspond to correlations between different locations in the network. We further employ adaptive boosting to enhance the training accuracy and capture historical patterns in the data. The performance of the proposed methods is verified using high-resolution data obtained from a real-world traffic network in Abu Dhabi, UAE. Our experimental results show that the proposed method outperforms other state-of-the-art algorithms