Feature detectors by autoencoders: Decomposition of input patterns into atomic features by neural networks

In this paper, we propose a feature detector for the neural network. Our feature detector aims to decompose input patterns into minimum constituents or atomic features. Atomic features are classified into features, common to all the input patterns and features, specific to each pattern. Thus, our feature detector is mainly composed of a common feature detector, distinctive feature detectors. The other two components are an information maximizer and an error minimizer. The distinctive feature detector is realized by the information maximizer, which increases the information, specific to each pattern as much as possible. The error minimizer is a device to minimize the difference between targets and outputs, that is, a usual neural network. We applied our feature detector to two problems: detection of vertical and horizontal bars and the phonological feature detection. In both cases, experimental results confirmed that distinctive features could clearly be extracted and that the common feature detector could extract features, as close as possible to the common features.     

Neural coding: higher-order temporal patterns in the neurostatistics of cell assemblies

Recent advances in the technology of multiunit recordings make it possible to test Hebb's hypothesis that neurons do not function in isolation but are organized in assemblies. This has created the need for statistical approaches to detecting the presence of spatiotemporal patterns of more than two neurons in neuron spike train data. We mention three possible measures for the presence of higher-order patterns of neural activation--coefficients of log-linear models, connected cumulants, and redundancies--and present arguments in favor of the coefficients of log-linear models. We present test statistics for detecting the presence of higher-order interactions in spike train data by parameterizing these interactions in terms of coefficients of log-linear models. We also present a Bayesian approach for inferring the existence or absence of interactions and estimating their strength. The two methods, the frequentist and the Bayesian one, are shown to be consistent in the sense that interactions that are detected by either method also tend to be detected by the other. A heuristic for the analysis of temporal patterns is also proposed. Finally, a Bayesian test is presented that establishes stochastic differences between recorded segments of data. The methods are applied to experimental data and synthetic data drawn from our statistical models. Our experimental data are drawn from multiunit recordings in the prefrontal cortex of behaving monkeys, the somatosensory cortex of anesthetized rats, and multiunit recordings in the visual cortex of behaving monkeys.     

Calculations and hypotheses relating to the input conductivity function of an infinite grid of similar nonlinear resistors

A formula for the input conductivity characteristic of an infinite grid of similar, weakly nonlinear resistors (conductors) measured between two nodes is obtained using a specific approximate representation of the grid. This formula is more precise than the corresponding formula given earlier by Gluskin. Some hypotheses concerning the analytical features of the input resistive (conductive) function, not necessarily associated with weak nonlinearity, and also related to circuits of other topologies, are considered. One of the hypotheses leads to a simplified method of calculation of the input conductivity, which has a reasonable engineering precision and may replace incomparably more difficult calculations. The derivations are given in detail.     

Global output feedback control of nonlinear time-delay systems with input matching uncertainty and unknown output function

This paper studies the problem of global output feedback control for nonlinear time-delay systems with input matching uncertainty and the unknown output function, whose nonlinearities are bounded by lower triangular linear unmeasured states multiplying the unknown constant, polynomial-of-output and polynomial-of-input growth rates. By constructing a new extended state observer and skillfully combining the dynamic gain method, backstepping method and Lyapunov–Krasovskii theorem, a delay-independent output feedback controller can be developed with only one dynamic gain. It is proved that all the signals of the closed-loop system are bounded, the states of the original system and the corresponding observer converge to zero, and the estimation of input matching uncertainty converges to its actual value. Two examples demonstrate the effectiveness of the control scheme.     

On the capabilities of higher-order neurons: a radial basis function approach

Higher-order neurons with k monomials in n variables are shown to have Vapnik-Chervonenkis (VC) dimension at least nk + 1. This result supersedes the previously known lower bound obtained via k-term monotone disjunctive normal form (DNF) formulas. Moreover, it implies that the VC dimension of higher-order neurons with k monomials is strictly larger than the VC dimension of k-term monotone DNF. The result is achieved by introducing an exponential approach that employs gaussian radial basis function neural networks for obtaining classifications of points in terms of higher-order neurons.     

Simultaneous estimation of the input and output frequencies of nonlinear systems

In this paper, the simultaneous estimation of the input and output frequencies of nonlinear systems is considered. As the output frequencies are generated from the input frequencies, and are integer combinations of these frequencies, it is shown in this paper that the simultaneous estimation of both the input and output frequencies can therefore be formulated as a constrained estimation problem. First, the constrained Cramér-Rao lower bound, an important general property of any unbiased estimator, is derived. The procedure and algorithm for estimating the input and output frequencies are devised based on the periodogram method. Numerical examples are presented to illustrate the performance and implementation of the proposed estimation procedure and algorithm.     

Linear and nonlinear mapping of patterns

Discrete Karhunen-Loeve-transform and a newly developed nonlinear mapping are used to obtain a structure-preserving mapping of high-dimensional data to a plane. It seems that the potential power of nonlinear mappings is needed only for artificial data.     

Barrier function based finite-time tracking control for a class of uncertain nonlinear systems with input saturation

In this article, a novel robust finite-time tracking control scheme is proposed for a class of uncertain nonlinear systems subject to the model uncertainty, external disturbance, and input saturation. A barrier function based disturbance observer (BFDO) with finite-time convergence performance is developed to estimate the non-smooth nonlinear compound disturbance, which includes the uncertainty, disturbance of system and input saturation. In addition, an adaptive continuous nonsingular terminal sliding mode controller, based on the barrier function and the estimate of the BFDO is developed. The Lyapunov stability and finite-time convergence of the proposed control scheme are proved. The effectiveness and performance advantage of the proposed control scheme is demonstrated by numerical simulations and comparison with existing works.     

Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation

This article addresses a novel technique for the simultaneous design of a robust nonlinear controller and static anti‐windup compensator (AWC) for uncertain nonlinear systems under actuator saturation and exogenous bounded input. The system is presumed to have locally Lipschitz nonlinearities, time‐varying uncertainties (appearing both in the linear as well as nonlinear dynamics and both in the state in addition to the output equations), and external norm‐bounded inputs both in the state and the output equations. Several bilinear matrix inequality–based conditions are derived to simultaneously design the robust nonlinear controller and AWC gains for uncertain nonlinear systems by employing the Lyapunov functional, reformulated Lipschitz property, uncertainty bounds, linear parameter‐varying approach, modified local and global sector conditions, iterative linear matrix inequality algorithm, convex optimization procedure, and gain minimization. The proposed multiobjective AWC‐based dynamic robust nonlinear controller guarantees the mitigation of saturation effects, robustness against time‐varying parametric norm‐bounded uncertainties, the asymptotic stability of the closed‐loop nonlinear system under zero external disturbances, and the attenuation of disturbance effects under nonzero external disturbances. The effectiveness of the proposed AWC‐based dynamic robust nonlinear controller synthesis scheme is illustrated by simulation examples.     

Simultaneous compensation of input and state delays for nonlinear systems

The problem of compensation of arbitrary large input delay for nonlinear systems was solved recently with the introduction of the nonlinear predictor feedback. In this paper we solve the problem of compensation of input delay for nonlinear systems with simultaneous input and state delays of arbitrary length. The key challenge, in contrast to the case of only input delay, is that the input delay-free system (on which the design and stability proof of the closed-loop system under predictor feedback are based) is infinite-dimensional. We resolve this challenge and we design the predictor feedback law that compensates the input delay. We prove global asymptotic stability of the closed-loop system using two different techniques—one based on the construction of a Lyapunov functional, and one using estimates on solutions. We present two examples, one of a nonlinear delay system in the feedforward form with input delay, and one of a scalar, linear system with simultaneous input and state delays.     

Online adaptive decision trees: pattern classification and function approximation

Recently we have shown that decision trees can be trained in the online adaptive (OADT) mode (Basak, 2004), leading to better generalization score. OADTs were bottlenecked by the fact that they are able to handle only two-class classification tasks with a given structure. In this article, we provide an architecture based on OADT, ExOADT, which can handle multiclass classification tasks and is able to perform function approximation. ExOADT is structurally similar to OADT extended with a regression layer. We also show that ExOADT is capable not only of adapting the local decision hyperplanes in the nonterminal nodes but also has the potential of smoothly changing the structure of the tree depending on the data samples. We provide the learning rules based on steepest gradient descent for the new model ExOADT. Experimentally we demonstrate the effectiveness of ExOADT in the pattern classification and function approximation tasks. Finally, we briefly discuss the relationship of ExOADT with other classification models.     

非线性减震器的多脉冲轨道和同宿树研究

针对一类非线性减震器,应用能量相位法研究了减震器系统在1∶0内共振,第一阶主共振情形下系统的多脉冲轨道和同宿树.首先,将系统的无量纲动力学控制方程转化为近可积哈密顿系统的标准形式.其次,研究了该系统的未扰动力学行为和扰动动力学行为,分析了耗散因子及相位漂移角对多脉冲轨道脉冲数和层半径的影响,揭示了这类非线性减震器能量从高频模态向低频模态转移的动力学机理.     

State and input simultaneous estimation for a class of nonlinear systems

This paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems. Here, the systems nonlinear part comprises a Lipschitz nonlinear function with respect to the state and input, and a state-dependent unknown function including additive disturbance as well as uncertain/nonlinear/time-varying terms. Upon satisfying some conditions, the observer design problem can be solved via a Riccati inequality or a LMI-based technique with asymptotic estimation guaranteed. A numerical example is included for illustration.     

考虑重要输入变量选择的非线性系统模糊辨识

针对有数百个可能输入的复杂非线性动态系统模糊建模问题,本文提出一种新的考虑重要输入变量选择的模糊辨识方法.首先采用两阶段模糊曲线方法(TSFC)从大量可选择的输入变量中给出各输入变量与输出之间的关联度权重,根据输入变量指标快速选择出重要的输入变量,然后采用模糊聚类(FCM)和高斯(Gaussian)型隶属函数确定模糊模...     

Control for the synchronization of Chen system via a single nonlinear input

This paper addresses control for the synchronization of Chen chaotic systems via sector nonlinear inputs. Feedback control, adaptive control, fast sliding mode and robust control approaches based on single state feedback controller are investigated. In these cases, sufficient conditions for the synchronization are obtained analytically. Numerical simulations verify the control performances.     

Branching rates and growth functions in the outgrowth of dendritic branching patterns

The outgrowth of dendritic branching patterns proceeds by neurite elongation and branching. These actions are supported by growth cones, specialized dynamic structures at the tips of outgrowing neurites, in response to a multitude of intracellular and extracellular signals and mechanisms. Branching rates of growth cones and their temporal patterns thus reflect the extent and changes in these responses. The present study outlines a model framework to relate branching rates of individual growth cones with the growth rate of the entire dendritic tree. The branching rate of an individual growth cone is assumed to depend on the total number of growth cones at any given moment (representing competition between growth cones), on its position along the dendrite, and on a baseline component representing all other factors. Four different strategies are discussed for determining quantitatively these components from experimental data. The methods are applied in the analysis of dendritic trees of Wistar rat multipolar non-pyramidal neurons, quantitatively reconstructed at several developmental stages (Parnavelas J G and Uylings H B M 1980 Brain Res. 193 373-82, Uylings H B M, Parnavelas J G, Walg H and Veltman W A M 1980 Mikroskopie 37 220-4). It is shown that the baseline branching rate is a rapidly decreasing function of time, indicating the largest baseline drive for branching in the early days of outgrowth.     

Control for the synchronization of Chen system via a single nonlinear input

This paper addresses control for the synchronization of Chen chaotic systems via sector nonlinear inputs. Feedback control, adaptive control, fast sliding mode and robust control approaches based on single state feedback controller are investigated. In these cases, sufficient conditions for the synchronization are obtained analytically. Numerical simulations verify the control performances.     

Adaptive control of nonlinear systems with severe uncertainties in the input powers

In this study,we discuss global adaptive stabilization for a class of uncertain nonlinear systems.The input powers of the system are unknown,and the upper bound...     

Composite nonlinear feedback control for linear systems with input saturation: theory and an application

We study in this paper the theory and applications of a nonlinear control technique, i.e., the so-called composite nonlinear feedback control, for a class of linear systems with actuator nonlinearities. It consists of a linear feedback law and a nonlinear feedback law without any switching element. The linear feedback part is designed to yield a closed-loop system with a small damping ratio for a quick response, while at the same time not exceeding the actuator limits for the desired command input levels. The nonlinear feedback law is used to increase the damping ratio of the closed-loop system as the system output approaches the target reference to reduce the overshoot caused by the linear part. It is shown that the proposed technique is capable of beating the well-known time-optimal control in the asymptotic tracking situations. The application of such a new technique to an actual hard disk drive servo system shows that it outperforms the conventional method by more than 30%. The technique can be applied to design servo systems that deal with "point-and-shoot" fast targeting.     

Mining unexpected patterns using decision trees and interestingness measures: a case study of endometriosis

Because clinical research is carried out in complex environments, prior domain knowledge, constraints, and expert knowledge can enhance the capabilities and performance of data mining. In this paper we propose an unexpected pattern mining model that uses decision trees to compare recovery rates of two different treatments, and to find patterns that contrast with the prior knowledge of domain users. In the proposed model we define interestingness measures to determine whether the patterns found are interesting to the domain. By applying the concept of domain-driven data mining, we repeatedly utilize decision trees and interestingness measures in a closed-loop, in-depth mining process to find unexpected and interesting patterns. We use retrospective data from transvaginal ultrasound-guided aspirations to show that the proposed model can successfully compare different treatments using a decision tree, which is a new usage of that tool. We believe that unexpected, interesting patterns may provide clinical researchers with different perspectives for future research.