Simple Gradient Algorithm Research Articles

Axial displacement calibration and tracking of optically trapped beads

High-precision axial displacement tracking of trapped beads is an indispensable feature of optical tweezers in advanced single-molecule studies. Here, we demonstrate an alternative method that enables axial calibration and tracking to be carried out on the same sample to avoid unnecessary errors. This method works by applying a dynamic force balance on a bead trapped between a piezoelectrically driven glass slide and an optical trap; in this configuration, the bead can be stopped precisely in different positions and imaged by a camera. A simple gradient algorithm is used to process the images into calibration data. After optimization of the calibration method and samples, our method exhibited better than 5 nm experimental axial resolution, with a measurement range of +/-500 nm around the objective focus at video speed. Moreover, for the first time, the deviation of the focusing plane in dual-trap optical tweezers was measured. We confirmed the axial deviation between two optical traps in our setup to be ~10 nm, corresponding to a force spectroscopy gage error of ~1 pN. This approach offers a favorable solution for in-use setup updating, as it can be seamlessly integrated into any optical tweezers system without requiring new hardware updates.

Rate-optimal denoising with deep neural networks

Abstract Deep neural networks provide state-of-the-art performance for image denoising, where the goal is to recover a near noise-free image from a noisy observation. The underlying principle is that neural networks trained on large data sets have empirically been shown to be able to generate natural images well from a low-dimensional latent representation of the image. Given such a generator network, a noisy image can be denoised by (i) finding the closest image in the range of the generator or by (ii) passing it through an encoder-generator architecture (known as an autoencoder). However, there is little theory to justify this success, let alone to predict the denoising performance as a function of the network parameters. In this paper, we consider the problem of denoising an image from additive Gaussian noise using the two generator-based approaches. In both cases, we assume the image is well described by a deep neural network with ReLU activations functions, mapping a $k$-dimensional code to an $n$-dimensional image. In the case of the autoencoder, we show that the feedforward network reduces noise energy by a factor of $O(k/n)$. In the case of optimizing over the range of a generative model, we state and analyze a simple gradient algorithm that minimizes a non-convex loss function and provably reduces noise energy by a factor of $O(k/n)$. We also demonstrate in numerical experiments that this denoising performance is, indeed, achieved by generative priors learned from data.

A new T-S fuzzy model predictive control for nonlinear processes

A new Takagi-Sugeno system based Kernel ridge regression (TS-KRR) was proposed.The TS-KRR strategy is implemented for both adaptive and offline identification.The TS-KRR was integrated with the GPC to control discrete-time nonlinear systems.The proposed controller showed good results in TS fuzzy GPC with offline modeling.The adaptive TS fuzzy GPC showed good results in dealing with disturbances. In this paper, a novel fuzzy Generalized Predictive Control (GPC) is proposed for discrete-time nonlinear systems via Takagi-Sugeno system based Kernel Ridge Regression (TS-KRR). The TS-KRR strategy approximates the unknown nonlinear systems by learning the Takagi-Sugeno (TS) fuzzy parameters from the input-output data. Two main steps are required to construct the TS-KRR: the first step is to use a clustering algorithm such as the clustering based Particle Swarm Optimization (PSO) algorithm that separates the input data into clusters and obtains the antecedent TS fuzzy model parameters. In the second step, the consequent TS fuzzy parameters are obtained using a Kernel ridge regression algorithm. Furthermore, the TS based predictive control is created by integrating the TS-KRR into the Generalized Predictive Controller. Next, an adaptive, online, version of TS-KRR is proposed and integrated with the GPC controller resulting an efficient adaptive fuzzy generalized predictive control methodology that can deal with most of the industrial plants and has the ability to deal with disturbances and variations of the model parameters. In the adaptive TS-KRR algorithm, the antecedent parameters are initialized with a simple K-means algorithm and updated using a simple gradient algorithm. Then, the consequent parameters are obtained using the sliding-window Kernel Recursive Least squares (KRLS) algorithm. Finally, two nonlinear systems: A surge tank and Continuous Stirred Tank Reactor (CSTR) systems were used to investigate the performance of the new adaptive TS-KRR GPC controller. Furthermore, the results obtained by the adaptive TS-KRR GPC controller were compared with two other controllers. The numerical results demonstrate the reliability of the proposed adaptive TS-KRR GPC method for discrete-time nonlinear systems.

1A2-U07 運転行動予測型支援制御系における支援量最適化計算の連続変形法を用いた高速化(人間機械協調(2))

This paper presents a personalized driver assisting system that makes use of the driver's behavior model. First, a PrARX model that describes the driver's vehicle following skill on expressways is identified using a simple gradient algorithm from actual driving data collected on a driving simulator. The obtained PrARX model describes the driver's logical decision making as well as continuous maneuver in a uniform manner. Second, the optimization of the assisting output is formulated by Homotopy method using the identified driver model, and computed online in the model predictive control framework. Thirdly, the proposed as siting system is tested in driving simulator and the usefulness is verified. Finally, the high speed of the calculation by Homotopy method is proved by comparing to the conventional method(MILP).

ALGORITHM FOR MODEL STUDY OF OFF-LATTICE PROTEIN FOLDING

A three-dimensional AB off-lattice protein model, which involves two species of residues interacting through simplified backbone and modified Lennard-Jones potentials, is studied. Incorporating an extra energy contribution into the original potential energy function, we develop and study a simple gradient algorithm for finding the lowest energy states of this protein model. The performance of our algorithm is tested on the Fibonacci sequences of lengths ranging from 13 to 55 residues previously studied by Hsu et al. Computational performance and behavior of our algorithm are also discussed.

Self-Orthogonalizing Adaptive Equalization Algorithms

A comparison is made of several self-orthogonalizing adjustment algorithms for linear tapped delay line equalizers. These adaptive algorithms accelerate the rate of convergence of the equalizer tap weights to those which minimize the output mean-squared error of a data transmission system. Accelerated convergence of the estimated gradient algorithm is effected by premultiplying the correction term in the algorithm by a matrix which is an estimate of the inverse of the channel correlation matrix. The various algorithms differ in the manner in which this estimate is sequentially computed. Depending on the degree of complexity available, the equalizer convergence time may be reduced more than an order of magnitude from that required by the simple gradient algorithm.