Sampled forms of functional PCA in reproducing kernel Hilbert spaces

We consider the sampling problem for functional PCA (fPCA), where the simplest example is the case of taking time samples of the underlying functional components. More generally, we model the sampling operation as a continuous linear map from $\mathcal{H}$ to $\mathbb{R}^m$, where the functional components to lie in some Hilbert subspace $\mathcal{H}$ of $L^2$, such as a reproducing kernel Hilbert space of smooth functions. This model includes time and frequency sampling as special cases. In contrast to classical approach in fPCA in which access to entire functions is assumed, having a limited number m of functional samples places limitations on the performance of statistical procedures. We study these effects by analyzing the rate of convergence of an M-estimator for the subspace spanned by the leading components in a multi-spiked covariance model. The estimator takes the form of regularized PCA, and hence is computationally attractive. We analyze the behavior of this estimator within a nonasymptotic framework, and provide bounds that hold with high probability as a function of the number of statistical samples n and the number of functional samples m. We also derive lower bounds showing that the rates obtained are minimax optimal.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1033 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Discrete Adaptive Second Order Sliding Mode Controller Design with Application to Automotive Control Systems with Model Uncertainties

Sliding mode control (SMC) is a robust and computationally efficient solution for tracking control problems of highly nonlinear systems with a great deal of uncertainty. High frequency oscillations due to chattering phenomena and sensitivity to data sampling imprecisions limit the digital implementation of conventional first order continuous-time SMC. Higher order discrete SMC is an effective solution to reduce the chattering during the controller software implementation, and also overcome imprecisions due to data sampling. In this paper, a new adaptive second order discrete sliding mode control (DSMC) formulation is presented to mitigate data sampling imprecisions and uncertainties within the modeled plant's dynamics. The adaptation mechanism is derived based on a Lyapunov stability argument which guarantees asymptotic stability of the closed-loop system. The proposed controller is designed and tested on a highly nonlinear combustion engine tracking control problem. The simulation test results show that the second order DSMC can improve the tracking performance up to 80% compared to a first order DSMC under sampling and model uncertainties.Comment: 6 pages, 6 figures, 2017 American Control Conferenc

Arbitrary Waveform Generator for Quantum Information Processing with Trapped Ions

Atomic ions confined in multi-electrode traps have been proposed as a basis for scalable quantum information processing. This scheme involves transporting ions between spatially distinct locations by use of time-varying electric potentials combined with laser or microwave pulses for quantum logic in specific locations. We report the development of a fast multi-channel arbitrary waveform generator for applying the time-varying electric potentials used for transport and for shaping quantum logic pulses. The generator is based on a field-programmable gate array controlled ensemble of 16-bit digital-to-analog converters with an update frequency of 50 MHz and an output range of $\pm$10 V. The update rate of the waveform generator is much faster than relevant motional frequencies of the confined ions in our experiments, allowing diabatic control of the ion motion. Numerous pre-loaded sets of time-varying voltages can be selected with 40 ns latency conditioned on real-time signals. Here we describe the device and demonstrate some of its uses in ion-based quantum information experiments, including speed-up of ion transport and the shaping of laser and microwave pulses

Evaluation of the inhibitory synergic effects of the Persian Gulf brittle star extract and taxol on ovarian cancer A2780cp

Paclitaxel is a current standard chemotherapeutic drug for ovarian cancer with several side effects. Recurrences of drug resistant clones have been considered the serious problem in the failure of chemotherapy. Medicinal marine natural products have been intensively proposed as diverse chemotherapeutic agents. Therefore there is an affinity to find efficient modality to overwhelm ovarian cancer chemo resistance complication. Here we examine whether brittle star extract as marine echinoderm natural resources can remarkably improve the cytotoxicity of paclitaxel in human ovarian cancer. MTT (dimethyl thiazol-2-yl]-2, 5-diphenyl tetrazolium bromide) assay, PI (Propodium Iodide) assay, DAPI (4', 6-diamidino-2-phenylindole) staining, Acridine orange staining, caspase-3 and caspase-9 were performed to investigate cytotoxic effect. We found that a combination of sub-toxic concentrations of brittle star methanolic extract (lower than IC_50) can significantly enhance ovarian cell growth inhibition and intrinsic apoptosis pathways induced by paclitaxel. Consequently a combination of paclitaxel and brittle star extract may offer novel innovative strategies for ovarian cancer chemotherapy

Comment on "Anderson transition in disordered graphene"

We comment on a recent letter by Amini et al. (EPL 87, 37002 (2009)) concerning the existence of a mobility edge in disordered graphene.Comment: 3 pages, 3 figure

Focusing a fountain of neutral cesium atoms with an electrostatic lens triplet

An electrostatic lens with three focusing elements in an alternating-gradient configuration is used to focus a fountain of cesium atoms in their ground (strong-field-seeking) state. The lens electrodes are shaped to produce only sextupole plus dipole equipotentials which avoids adding the unnecessary nonlinear forces present in cylindrical lenses. Defocusing between lenses is greatly reduced by having all of the main electric fields point in the same direction and be of nearly equal magnitude. The addition of the third lens gave us better control of the focusing strength in the two transverse planes and allowed focusing of the beam to half the image size in both planes. The beam envelope was calculated for lens voltages selected to produced specific focusing properties. The calculations, starting from first principles, were compared with measured beam sizes and found to be in good agreement. Application to fountain experiments, atomic clocks, and focusing polar molecules in strong-field-seeking states is discussed.Comment: 8 pages 10 figure

A comparison between heuristic and machine learning techniques in fall detection using Kinect v2

In this paper, two algorithms were tested on 11 healthy adults: one based on heuristic and another one on video tagging machine learning methods for automatic fall detection; both utilizing Microsoft Kinect v2. For our heuristic approach, we used skeletal data to detect falls based on a set of instructions and signal filtering methods. For the machine learning approach, we implemented a dataset utilizing the Adaptive Boosting Trigger (AdaBoostTrigger) algorithm via video tagging to enable fall detection. For each approach, each subject on average has performed six true positive and six false positive fall incidents in two different conditions: one with objects partially blocking the sensor's view and one with partial obstructed field of view. The accuracy of each approach has been compared against one another in different conditions. The result showed an average of 95.42 % accuracy in the heuristic approach and 88.33 % in machine learning technique. We conclude that heuristic approach performs more accurately for fall detection when there is a limited number of training dataset available. Nevertheless, as the gesture detection's complexity increases, the need for a machine learning technique is inevitable

Efficient Fiber Optic Detection of Trapped Ion Fluorescence

Integration of fiber optics may play a critical role in the development of quantum information processors based on trapped ions and atoms by enabling scalable collection and delivery of light and coupling trapped ions to optical microcavities. We trap 24Mg+ ions in a surface-electrode Paul trap that includes an integrated optical fiber for detecting 280-nm fluorescence photons. The collection numerical aperture is 0.37 and total collection efficiency is 2.1 %. The ion can be positioned between 80 \mum and 100 \mum from the tip of the fiber by use of an adjustable rf-pseudopotential.Comment: 4 pages, 3 figures