Active Sampling-based Binary Verification of Dynamical Systems

Nonlinear, adaptive, or otherwise complex control techniques are increasingly relied upon to ensure the safety of systems operating in uncertain environments. However, the nonlinearity of the resulting closed-loop system complicates verification that the system does in fact satisfy those requirements at all possible operating conditions. While analytical proof-based techniques and finite abstractions can be used to provably verify the closed-loop system's response at different operating conditions, they often produce conservative approximations due to restrictive assumptions and are difficult to construct in many applications. In contrast, popular statistical verification techniques relax the restrictions and instead rely upon simulations to construct statistical or probabilistic guarantees. This work presents a data-driven statistical verification procedure that instead constructs statistical learning models from simulated training data to separate the set of possible perturbations into "safe" and "unsafe" subsets. Binary evaluations of closed-loop system requirement satisfaction at various realizations of the uncertainties are obtained through temporal logic robustness metrics, which are then used to construct predictive models of requirement satisfaction over the full set of possible uncertainties. As the accuracy of these predictive statistical models is inherently coupled to the quality of the training data, an active learning algorithm selects additional sample points in order to maximize the expected change in the data-driven model and thus, indirectly, minimize the prediction error. Various case studies demonstrate the closed-loop verification procedure and highlight improvements in prediction error over both existing analytical and statistical verification techniques.Comment: 23 page

Explicit approximate controllability of the Schr\"odinger equation with a polarizability term

We consider a controlled Schr\"odinger equation with a dipolar and a polarizability term, used when the dipolar approximation is not valid. The control is the amplitude of the external electric field, it acts non linearly on the state. We extend in this infinite dimensional framework previous techniques used by Coron, Grigoriu, Lefter and Turinici for stabilization in finite dimension. We consider a highly oscillating control and prove the semi-global weak $H^2$ stabilization of the averaged system using a Lyapunov function introduced by Nersesyan. Then it is proved that the solutions of the Schr\"odinger equation and of the averaged equation stay close on every finite time horizon provided that the control is oscillating enough. Combining these two results, we get approximate controllability to the ground state for the polarizability system

A Novel Method for Epileptic Seizure Detection Using Coupled Hidden Markov Models

We propose a novel Coupled Hidden Markov Model to detect epileptic seizures in multichannel electroencephalography (EEG) data. Our model defines a network of seizure propagation paths to capture both the temporal and spatial evolution of epileptic activity. To address the intractability introduced by the coupled interactions, we derive a variational inference procedure to efficiently infer the seizure evolution from spectral patterns in the EEG data. We validate our model on EEG aquired under clinical conditions in the Epilepsy Monitoring Unit of the Johns Hopkins Hospital. Using 5-fold cross validation, we demonstrate that our model outperforms three baseline approaches which rely on a classical detection framework. Our model also demonstrates the potential to localize seizure onset zones in focal epilepsy.Comment: To appear in MICCAI 2018 Proceeding

Machine Learning with Chaotic Strange Attractors

Machine learning studies need colossal power to process massive datasets and train neural networks to reach high accuracies, which have become gradually unsustainable. Limited by the von Neumann bottleneck, current computing architectures and methods fuel this high power consumption. Here, we present an analog computing method that harnesses chaotic nonlinear attractors to perform machine learning tasks with low power consumption. Inspired by neuromorphic computing, our model is a programmable, versatile, and generalized platform for machine learning tasks. Our mode provides exceptional performance in clustering by utilizing chaotic attractors' nonlinear mapping and sensitivity to initial conditions. When deployed as a simple analog device, it only requires milliwatt-scale power levels while being on par with current machine learning techniques. We demonstrate low errors and high accuracies with our model for regression and classification-based learning tasks.Comment: Manuscript is 13 pages, 4 figures. Supplementary Material is 6 pages, 3 figure

Some Advances in Nonlinear Speech Modeling Using Modulations, Fractals, and Chaos

In this paper we briefly summarize our on-going work on modeling nonlinear structures in speech signals, caused by modulation and turbulence phenomena, using the theories of modulation, fractals, and chaos as well as suitable nonlinear signal analysis methods. Further, we focus on two advances: i) AM-FM modeling of fricative sounds with random modulation signals of the 1/f-noise type and ii) improved methods for speech analysis and prediction on reconstructed multidimensional attractors. 1