Nonlinear Function Generation Research Articles

EO nonlinear function generator.

An electro-optical programmable nonlinear function generator (PNFG) is developed on a multimode waveguide with four parallel thermal electrodes. The current on one electrode is chosen as the input, while the rest serve as function-defining units to modulate the multimode interference. The electro-thermo-optical effects are analyzed step by step and the impact on the eigenmode properties is derived. It shows that the optical output power variation by altered interference, in response to the input current, manifests as a complex ensemble of functions in general. The PNFG aims to find the special setting under which such relation can be simplified into some basic functions. Through an optimization program, a variety of such functions are found, including Sigmoid, SiLU, and Gaussian. Furthermore, the shape of these functions can be adjusted by finetuning the defining units. This device may be integrated in a large-scale photonic computing network that can tackle complex problems with nonlinear function adaptability.

VTAE: Variational Transformer Autoencoder with Manifolds Learning.

Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables and these models use a non-linear function (generator) to map latent samples into the data space. On the other hand, the non-linearity of the generator implies that the latent space shows an unsatisfactory projection of the data space, which results in poor representation learning. This weak projection, however, can be addressed by a Riemannian metric, and we show that geodesics computation and accurate interpolations between data samples on the Riemannian manifold can substantially improve the performance of deep generative models. In this paper, a Variational spatial-Transformer AutoEncoder (VTAE) is proposed to minimize geodesics on a Riemannian manifold and improve representation learning. In particular, we carefully design the variational autoencoder with an encoded spatial-Transformer to explicitly expand the latent variable model to data on a Riemannian manifold, and obtain global context modelling. Moreover, to have smooth and plausible interpolations while traversing between two different objects' latent representations, we propose a geodesic interpolation network different from the existing models that use linear interpolation with inferior performance. Experiments on benchmarks show that our proposed model can improve predictive accuracy and versatility over a range of computer vision tasks, including image interpolations, and reconstructions.

MM-FSM: A High-Efficiency General Nonlinear Function Generator for Stochastic Computation

AbstractNonlinear function calculation is widely used in numerous science and technology fields. Stochastic computation is a novel high-efficiency value representation and calculation scheme for information and signal processing. The main challenges of stochastic computation based nonlinear function implementation lie on poor generalization, low accuracy and high latency. In this paper, we propose a multiple driving and multiple dimension finite state machine (MM-FSM) to realize major single variable nonlinear functions used in information and signal processing areas on common platforms with low complexity and latency. We provide corresponding synthesis method of the activation parameters and conditional parameters of MM-FSM. In order to improve the calculation accuracy, we further propose an adaptive scaling algorithm for MM-FSM. The most salient feature of MM-FSM is that we can configure different types of nonlinear functions with the same MM-FSM structure. Thus, MM-FSM can be used in a wide range of stochastic based applications. Compared with the traditional stochastic scheme and Coordinate Rotation Digital Computer (CORDIC) algorithm, simulation results show that the proposed MM-FSM nonlinear function generator has significantly lower complexity while guaranteeing the calculation accuracy.

Fast spatial beam shaping by acousto-optic diffraction for 3D non-linear microscopy.

Acousto-optic deflection (AOD) devices offer unprecedented fast control of the entire spatial structure of light beams, most notably their phase. AOD light modulation of ultra-short laser pulses, however, is not straightforward to implement because of intrinsic chromatic dispersion and non-stationarity of acousto-optic diffraction. While schemes exist to compensate chromatic dispersion, non-stationarity remains an obstacle. In this work we demonstrate an efficient AOD light modulator for stable phase modulation using time-locked generation of frequency-modulated acoustic waves at the full repetition rate of a high power laser pulse amplifier of 80 kHz. We establish the non-local relationship between the optical phase and the generating acoustic frequency function and verify the system for temporal stability, phase accuracy and generation of non-linear two-dimensional phase functions.

NON LINEAR FEEDBACK STREAM CIPHER

The main aim of this paper is to develop a new generation and innovative security software for applications. We proposed new stream cipher called NLFS. NLFS means Non-linear feedback stream cipher, which is a fast and secure stream cipher for egovernance applications. This stream cipher uses AES secure non-linear function and AES key generation. NLFS uses primitive polynomial generated S-boxes in byte substitution step. NLFS uses two similar AES round functions and these two proceed parallelly to produce key-stream. Non-linear *function of NLFS has AES nonlinear function steps (add-round key, byte substitution, mix column, shift rows) and it extra includes value-based rotation step. In value based rotation step it rotates each 8-bit word by its first 3-bit (decimal) value.NLFS have two modes basic mode that is synchronous mode and self synchronous mode. In synchronous mode key stream is independent of plain text and cipher text. In selfsynchronous mode key stream generation depending on cipher text. In self synchronous mode generated keystream update first 512-bit buffer and cipher text update the second buffer.

Linearization of Gamma Energy Spectra in Scintillator-Based Commercial Instruments

This paper presents a novel technique developed for linearizing the energy spectra of radiation detectors in commercial radioisotope identification devices. Based on few spectrum measurements with standard radio-nuclide sources, this method allows generation of individual nonlinear calibration functions at minimum expense in the routine instrument setup. Instead of fitting peak positions, the measured raw data are compared with simulated spectrum templates, and local gain factors providing the best correspondence are taken as reference points for the calibration function. This approach avoids the problem of fitting multiple peaks with intensity ratios influenced by absorbing layers and assures an accuracy of 1% in the energy range of 30 keV to 3 MeV.

Neural Network Applications in Power Electronics and Motor Drives—An Introduction and Perspective

Artificial intelligence (AI) techniques, particularly the neural networks, are recently having significant impact on power electronics and motor drives. Neural networks have created a new and advancing frontier in power electronics, which is already a complex and multidisciplinary technology that is going through dynamic evolution in the recent years. This paper gives a comprehensive introduction and perspective of neural network applications in the intelligent control and estimation for power electronics and motor drives area. The principal topologies of neural networks that are currently most relevant for applications in power electronics have been reviewed including the detailed description of their properties. Both feedforward and feedback or recurrent architectures have been covered in the description. The application examples that are discussed in this paper include nonlinear function generation, delayless filtering and waveform processing, feedback signal processing of vector drive, space vector PWM of two-level and multilevel inverters, adaptive flux vector estimation, and some of their combination for vector-controlled ac drive. Additional selected applications in the literature are included in the references. From the current trend of the technology, it appears that neural networks will find widespread applications in power electronics and motor drives in future

Nonlinear function generators and chaotic signal generators using a pulse-width modulation method

A new approach for making arbitrary nonlinear transfer function generator circuits is proposed. Arbitrary non-monotone functions can be made by combining plural pulse-width modulation (PWM) circuits. Chaotic signal generators can be made by using these circuits. This approach is useful for implementing large-scale nonlinear circuit systems.

A New Nonlinear Function Generation Technique for Sine Wave Synthesis

A new nonlinear function generation technique for sine wave synthesis, using operational amplifiers and the field effect transistor characteristics, is presented with symmetrical triangular wave as...

High resolution CMOS current comparators: design and applications to current-mode function generation

This paper uses fundamental models to derive design conditions for maximum speed and resolution in CMOS transimpedance comparators. We distinguish two basic comparator architectures depending on whether the input sensing node is resistive or capacitive, and show that each type yields advantages for different ranges of input current. Then, we introduce a class of current comparator structures which use nonlinear sensing and/or feedback to combine the advantages of capacitive-input and resistive-input architectures. Two members of this class are presented demonstrating resolution levels (measured on silicon prototypes) in the range of pAs. They exhibit complementary functional features: one, the current steering comparator, displays better transient response in the very comparison function, while operation of the other, the current switch comparator, is easily extended to support systematic generation of nonlinear transfer functions in current domain. The paper explores also this latter extension, and presents current-mode circuit blocks for systematic generation of nonlinear functions based on piecewise-linear (PWL) approximation. Proposals made in the paper are demonstrated via CMOS prototypes in two single-poly CMOS n-well technologies: 2μm and 1.6μm. These prototypes show measured input current comparison range of 140 dB, resolution and offset below 10 pA, and operation speed two orders of magnitude better than that of conventional resistive-input circuits. Also, measurements from the PWL prototypes show excellent rectification properties (down to a few pAs) and small linearity errors (down to 0.13%).

Self-electro-optic effect device in waveguiding configuration as optical switch and power discriminator

The authors report the room temperature operation of an InGaAs/InP based Wannier-Stark modulator in a waveguide configuration as a self-electro-optic effect device for the generation of various nonlinear optical transfer functions for TE polarised light at 1.55 µm. Optical bistability has been achieved and the application of the device as an optical power discriminator is demonstrated.

Nonlinear function generation apparatus, and musical tone synthesis apparatus utilizing the same

A nonlinear function generation apparatus and a musical tone synthesis apparatus are disclosed. The nonlinear function generation apparatus comprises hysteresis and nonhysteresis function generators for generating hysteresis and nonhysteresis functions using an input signal as a variable respectively, and a multiplier for synthesizing the functions outputted from the generators. The musical tone synthesis apparatus comprises a closed loop including delay circuits, and the nonlinear function generation apparatus.

Dynamic Nuclear Power Plant Simulations Using Single-Board Peripheral Array Processors

The application of a host/ coprocessor system, consisting of an IBM PC/AT and a Marinco peripheral array proc essor, to the simulation of nuclear power plant transients is described. The simulation algorithm employs a multistep, multirate integration method. Rapidly varying transients were implemented on the array processor, while the slow components of the system dynamics were handled by the host computer. The generation of nonlinear functions of dependent variables using table lookup techniques was also implemented on the array processor. A simplified model of a pressurized water reactor was employed as a benchmark. Flow rate and power transients using a variety of integration formulas are presented along with data showing the speed up achieved through the use of the peripheral processor.

Algorithmic styles for nonlinear function generation in lumped-parameter systems

Within the simulation community, it is often believed that integration is the limiting factor to program performance and run-time efficiency when simulating large-scale continuous feedback systems. Much attention is given to selection of the best approximation technique (e.g., Euler, Runge-Kutta, Adams-Bashforth). However, performance is shown to be up to six times more sensitive to impact on nonlinear function generation due to computational complexities associated with one- and two-dimensional table-look-up algorithms. Such algorithms utilize linear interpolation and sequential search that when combined, produce a number of approaches to algorithm construction. Algorithms and associated data structures have been formulated in contrasting general-purpose languages to illustrate stylistic differences and for direct application in nonlinear simulation of lumped-parameter systems.

On Identification of Nonlinear Nonparametric Control Systems

Nonlinear nonparametric identification of stochastic control systems is treated here as a problem of determining the dependence of its input and output signals. A new measure of dependence between random processes, a quasi-maximal correlation function, coincides with the ordinary correlation function of these processes. It is proved that for the class of quasi-independent random processes which are defined herein a quasi-maximal correlation function is consistent The markovian processes and those of transforming the Gaussian signal in a system consisting of a linear dynamic plant and nonlinear memoryless function generator linked in series, are proved to belong to the same class. Examples of function calculations for real and model control systems are given.

Memory scanning: A comparison of the dynamic stack and exhaustive serial scan models, with an extension of the latter

Sternberg (1966) introduced a paradigm which allowed him to examine the relation between recognition latency and the size of a set of targets. He obtained linear plots of latency against set size, and explained these by a model for the item recognition task which included a process of exhaustive serial scanning of the list of positive items. Theios (1973) offered an alternative explanation for these data. In his model positive and negative items are stochastically ordered in a dynamic stack, and subjected to serial, self-terminating search. The present paper derives alternative predictions from these two theories and tests them. Experimental results are reported which are not compatible with either model. On the basis of these results, the dynamic stack model is rejected, and a theory is put forward that preserves Sternberg's (1966) principle of serial exhaustive search, but adds to this strategies directed at speed and accuracy maximisation. The theory allows memory scans to be repeated. It provides a new account of the generation of nonlinear latency functions which is consistent with serial exhaustive search. It allows differences to arise between the slopes of positive and negative set size functions even though the search process is exhaustive and not self-terminating. It also predicts speed-accuracy trade-off data of the form obtained by Reed (1976).

A hybrid computer technique for nonlinear function generation

The simulation of a physical system on an analog computer often requires the use of one or more nonlinear function generators. This paper describes a means by which a dig ital computer can be used to simulate the diode function generators of the analog computer in a closed-loop system. The digital computer program utilizes a table-lookup procedure to transform x into f(x). The table is previously prepared by the machine through linear interpolation be tween breakpoints. The breakpoints are the input data for the program. Many simulation problems need a nonlinear function generator as an element in a feedback loop. The digital computer introduces delay into the loop, rendering the simulation inaccurate and perhaps even unstable. A phase- advancing network must be included to compensate for the delay in the hybrid system. A simple and inexpensive technique for accomplishing the phase advance is analyzed and experimentally verified; the derivative of the incom ing waveform is used to predict the wave's value at some later instant of time. Advantages of the digital function generator include rapid setting, perfect reproducibility of functions, no limit on breakpoints, and an effective increase of the analog facility's nonlinear standby capability.

A trainable nonlinear function generator

Trainable threshold logic elements have been used in the adaptive pattern recognition field to design linear classifiers for patterns of binary variables. This paper shows how one of these trainable linear devices can be used to implement a trainable non-linear function generator. A trainable function generator is similar in function to the spatial function generators found in analog computers except that the coefficients of its function are set in an iterative "training" procedure instead of being predetermined in the design stage. The primary application of the trainable function generator, to date, has been in the real-time design of nonlinear pattern classification devices, therefore, the use of the trainable function generator as a nonlinear discriminant function in pattern classification is emphasized. It is demonstrated that in the implementation of the trainable function generator it is highly advantageous to use what has been defined as a linearly independent code to represent the analog pattern parameters as binary patterns for the threshold element. When a linearly independent code is used, a linear threshold element in a trainable function generator can be used to "learn" nonlinear discriminant functions just as it is used to learn linear discriminant functions.

A hybrid computer technique for nonlinear function generation

A hybrid computer technique for nonlinear function generation

Microprogramming for Data Acquisition and Control

The paper describes a different approach to the control of experimental apparatus in which control is performed by a microprogram controlling a very general register configuration and a single logical element. The basic concepts of microprogram control are described, including how program sequencing is accomplished and used to permit a variety of control capabilities including the generation of non-linear functions within a single system. A short discussion of presently available components will provide some perspective as to the performance levels that may be achieved and system availability. As an example, a possible microprogram controller for the PEPR film scanning system will be described in some detail and its potential performance outlined.