Adaptive, locally-linear models of complex dynamics

The dynamics of complex systems generally include high-dimensional, non-stationary and non-linear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties we detail a new approach based on local linear models within windows determined adaptively from the data. While the dynamics within each window are simple, consisting of exponential decay, growth and oscillations, the collection of local parameters across all windows provides a principled characterization of the full time series. To explore the resulting model space, we develop a novel likelihood-based hierarchical clustering and we examine the eigenvalues of the linear dynamics. We demonstrate our analysis with the Lorenz system undergoing stable spiral dynamics and in the standard chaotic regime. Applied to the posture dynamics of the nematode $C. elegans$ our approach identifies fine-grained behavioral states and model dynamics which fluctuate close to an instability boundary, and we detail a bifurcation in a transition from forward to backward crawling. Finally, we analyze whole-brain imaging in $C. elegans$ and show that the stability of global brain states changes with oxygen concentration.Comment: 25 pages, 16 figure

Modeling Financial Time Series with Artificial Neural Networks

Financial time series convey the decisions and actions of a population of human actors over time. Econometric and regressive models have been developed in the past decades for analyzing these time series. More recently, biologically inspired artificial neural network models have been shown to overcome some of the main challenges of traditional techniques by better exploiting the non-linear, non-stationary, and oscillatory nature of noisy, chaotic human interactions. This review paper explores the options, benefits, and weaknesses of the various forms of artificial neural networks as compared with regression techniques in the field of financial time series analysis.CELEST, a National Science Foundation Science of Learning Center (SBE-0354378); SyNAPSE program of the Defense Advanced Research Project Agency (HR001109-03-0001

BSUV-Net: a fully-convolutional neural network for background subtraction of unseen videos

Background subtraction is a basic task in computer vision and video processing often applied as a pre-processing step for object tracking, people recognition, etc. Recently, a number of successful background-subtraction algorithms have been proposed, however nearly all of the top-performing ones are supervised. Crucially, their success relies upon the availability of some annotated frames of the test video during training. Consequently, their performance on completely “unseen” videos is undocumented in the literature. In this work, we propose a new, supervised, background subtraction algorithm for unseen videos (BSUV-Net) based on a fully-convolutional neural network. The input to our network consists of the current frame and two background frames captured at different time scales along with their semantic segmentation maps. In order to reduce the chance of overfitting, we also introduce a new data-augmentation technique which mitigates the impact of illumination difference between the background frames and the current frame. On the CDNet-2014 dataset, BSUV-Net outperforms stateof-the-art algorithms evaluated on unseen videos in terms of several metrics including F-measure, recall and precision.Accepted manuscrip