Piecewise Linear Transfer Research Articles

Achieving signal power amplification using energetically passive devices

This article discusses some fundamental properties of electronic amplifiers and the associated implications. When defining the passivity of a multi-port circuit in the sense of net power consumption (rather than the ability to amplify signals), devices such as transistors, which are commonly described as “active”, have to be considered passive, which is referred to as “energetically passive” to avoid confusion with other definitions. It is shown that, when using such energetically passive devices to achieve signal power amplification, the amplifier circuit necessarily has to feature a non-linear transfer function. The article discusses how two common concepts (class A and B amplifiers) to achieve signal power amplification with such devices can be fundamentally related to Poynting’s theorem and that both of these concepts allow the realization of at least piecewise linear transfer functions in spite of the necessary non-linearity.

Nonlinear dynamics in an optoelectronic feedback delay oscillator with piecewise linear transfer functions from the laser diode and photodiode.

We investigate the nonlinear dynamics of a recent architecture of an optoelectronic oscillator, where the emitting laser and the receiving diode are connected in a head-to-tail configuration via an optical fiber delay line. The resulting nonlinear transfer function is a piecewise linear profile, and its interplay with the delay leads to many complex behaviors such as relaxation oscillations and deterministic chaos. This system belongs to a recent class of optoelectronic oscillators where the nonlinearity does not originate from the sinusoidal transfer function of an imbalanced interferometer, and, in particular, it is a simple optoelectronic oscillator configuration that is capable of displaying a chaotic behavior. The results of the analytic study are confirmed by numerical simulations and experimental measurements.

Deep learning based spectral extrapolation for dual-source, dual-energy x-ray computed tomography.

Data completion is commonly employed in dual-source, dual-energy computed tomography (CT) when physical or hardware constraints limit the field of view (FoV) covered by one of two imaging chains. Practically, dual-energy data completion is accomplished by estimating missing projection data based on the imaging chain with the full FoV and then by appropriately truncating the analytical reconstruction of the data with the smaller FoV. While this approach works well in many clinical applications, there are applications which would benefit from spectral contrast estimates over the larger FoV (spectral extrapolation)-e.g. model-based iterative reconstruction, contrast-enhanced abdominal imaging of large patients, interior tomography, and combined temporal and spectral imaging. To document the fidelity of spectral extrapolation and to prototype a deep learning algorithm to perform it, we assembled a data set of 50 dual-source, dual-energy abdominal x-ray CT scans (acquired at Duke University Medical Center with 5 Siemens Flash scanners; chain A: 50cm FoV, 100kV; chain B: 33cm FoV, 140kV+Sn; helical pitch: 0.8). Data sets were reconstructed using ReconCT (v14.1, Siemens Healthineers): 768×768pixels per slice, 50cm FoV, 0.75mm slice thickness, "Dual-Energy - WFBP" reconstruction mode with dual-source data completion. A hybrid architecture consisting of a learned piecewise linear transfer function (PLTF) and a convolutional neural network (CNN) was trained using 40 scans (five scans reserved for validation, five for testing). The PLTF learned to map chain A spectral contrast to chain B spectral contrast voxel-wise, performing an image domain analog of dual-source data completion with approximate spectral reweighting. The CNN with its U-net structure then learned to improve the accuracy of chain B contrast estimates by copying chain A structural information, by encoding prior chain A, chain B contrast relationships, and by generalizing feature-contrast associations. Training was supervised, using data from within the 33-cm chain B FoV to optimize and assess network performance. Extrapolation performance on the testing data confirmed our network's robustness and ability to generalize to unseen data from different patients, yielding maximum extrapolation errors of 26HU following the PLTF and 7.5HU following the CNN (averaged per target organ). Degradation of network performance when applied to a geometrically simple phantom confirmed our method's reliance on feature-contrast relationships in correctly inferring spectral contrast. Integrating our image domain spectral extrapolation network into a standard dual-source, dual-energy processing pipeline for Siemens Flash scanner data yielded spectral CT data with adequate fidelity for the generation of both 50keV monochromatic images and material decomposition images over a 30-cm FoV for chain B when only 20cm of chain B data were available for spectral extrapolation. Even with a moderate amount of training data, deep learning methods are capable of robustly inferring spectral contrast from feature-contrast relationships in spectral CT data, leading to spectral extrapolation performance well beyond what may be expected at face value. Future work reconciling spectral extrapolation results with original projection data is expected to further improve results in outlying and pathological cases.

The Solution of Backward Heat Conduction Problem with Piecewise Linear Heat Transfer Coefficient

In the fields of continuous casting and the roll stepped cooling, the heat transfer coefficient is piecewise linear. However, few papers discuss the solution of the backward heat conduction problem in this situation. Therefore, the aim of this paper is to solve the backward heat conduction problem, which has the piecewise linear heat transfer coefficient. Firstly, the ill-posed of this problem is discussed and the truncated regularized optimization scheme is introduced to solve this problem. Secondly, because the regularization parameter is the key factor for the regularization method, this paper presents an improved method for choosing the regularization parameter to reduce the iterative number and proves the fourth-order convergence of this method. Furthermore, the numerical simulation experiments show that, compared with other methods, the improved method of fourth-order convergence effectively reduces the iterative number. Finally, the truncated regularized optimization scheme is used to estimate the initial temperature, and the results of numerical simulation experiments illustrate that the inverse values match the exact values very well.

OTRA Based Piece-Wise Linear VTC Generators and Their Application in High-Frequency Sinusoid Generation

This paper proposes methods to generate various types of Linear Voltage Transfer Curves (VTC) using Operational Trans-Resistance Amplifier (OTRA) as the active block. It further goes on to propose methods to multiplex various individual Linear VTCs to obtain any form of Piece-Wise Linear Voltage Transfer Curves (PWL), which find many applications in the world of circuitry. One particular application has been highlighted, i.e. generation of High-Frequency Sinusoids. Simulations of the Circuits proposed via Cadence Virtuoso, using TowerJazz’s 180 nm Technology Node have been reported, which satisfy the aim behind its development.

A piecewise linear transverse shear transfer model for bolted side-plated beams

The performance of bolted side-plated (BSP) beams is affected by the degree of transverse partial interaction, which is a result of the interfacial slip caused by transverse shear transfer between the bolted steel plates and the reinforced concrete beams. However, explicit formulae for the transverse shear transfer profile have yet to be derived. In this paper, a simplified piecewise linear shear transfer model was proposed based on force superposition principle and simplification of shear transfer profiles derived from a previous numerical study. The magnitude of shear transfer was determined by force equilibrium and displacement compatibility condition. A set of design formulae for BSP beams under several basic load cases was also derived. Then the model was verified by test results. A worked example was also provided to illustrate the application of the proposed design formulae. This paper sheds some light on the shear force transfer mechanism of anchor bolts in BSP beams, and offers a practical method to evaluate the influence of transverse partial interaction in strengthening design.

Hydrographic variations in deep ocean temperature over the mid-Pleistocene transition

During the mid-Pleistocene transition the dominant 41 ka periodicity of glacial cycles transitioned to a quasi-100 ka periodicity for reasons not yet known. This study investigates the potential role of deep ocean hydrography by examining oxygen isotope ratios in benthic foraminifera. Oxygen isotope records from the Atlantic, Pacific and Indian Ocean basins are separated into their ice volume and local temperature/hydrography components using a piece-wise linear transfer function and a temperature calibration. Although our method has certain limitations, the deep ocean hydrography reconstructions show that glacial deep ocean temperatures approached freezing point as the mid-Pleistocene transition progressed. Further analysis suggests that water mass reorganisation could have been responsible for these temperature changes, leading to such stable conditions in the deep ocean that some obliquity cycles were skipped until precessional forcing triggered deglaciation, creating the apparent quasi-100 ka pattern. This study supports previous work that suggests multiples of obliquity cycles dominate the quasi-100 ka glacial cycles with precession components driving deglaciations.

Selectable and Unselectable Sets of Neurons in Recurrent Neural Networks With Saturated Piecewise Linear Transfer Function

The concepts of selectable and unselectable sets are proposed to describe some interesting dynamical properties of a class of recurrent neural networks (RNNs) with saturated piecewise linear transfer function. A set of neurons is said to be selectable if it can be co-unsaturated at a stable equilibrium point by some external input. A set of neurons is said to be unselectable if it is not selectable, i.e., such set of neurons can never be co-unsaturated at any stable equilibrium point regardless of what the input is. The importance of such concepts is that they enable a new perspective of the memory in RNNs. Necessary and sufficient conditions for the existence of selectable and unselectable sets of neurons are obtained. As an application, the problem of group selection is discussed by using such concepts. It shows that, under some conditions, each group is a selectable set, and each selectable set is contained in some group. Thus, groups are indicated by selectable sets of the RNNs and can be selected by external inputs. Simulations are carried out to further illustrate the theory.

Some multistability properties of bidirectional associative memory recurrent neural networks with unsaturating piecewise linear transfer functions

Multistability is an important dynamical property in neural networks in order to enable certain applications where monostable networks could be computationally restrictive. This paper studies some multistability properties for a class of bidirectional associative memory recurrent neural networks with unsaturating piecewise linear transfer functions. Based on local inhibition, conditions for globally exponential attractivity are established. These conditions allow coexistence of stable and unstable equilibrium points. By constructing some energy-like functions, complete convergence is studied.

Piecewise linear-in-dB variable gain amplifier to enhance integral nonlinearity

A new technique to improve the integral nonlinearity of the “linear-in-dB” variable gain amplifier (VGA) by adopting a piecewise linear transfer curve rather than a single curve is presented. The conventional single curve which is the first-order approximation of the exponential function yields bigger deviation errors as the gain control code advances. The integral nonlinearity (INL) of the proposed piecewise linear curve can be managed to be smaller because one of divisional curves moves to another before the deviation becomes prominent. A generic circuit schematic without chip size overhead is suggested with its future expansion in mind, and a design in a 0.35µm CMOS process under 3.3V supply is proposed and verified.

Multiperiodicity and Attractivity of Delayed Recurrent Neural Networks With Unsaturating Piecewise Linear Transfer Functions

This paper studies multiperiodicity and attractivity for a class of recurrent neural networks (RNNs) with unsaturating piecewise linear transfer functions and variable delays. Using local inhibition, conditions for boundedness and global attractivity are established. These conditions allow coexistence of stable and unstable trajectories. Moreover, multiperiodicity of the network is investigated by using local invariant sets. It shows that under some interesting conditions, there exists one periodic trajectory in each invariant set which exponentially attracts all trajectories in that region correspondingly. Simulations are carried out to illustrate the theories.

Switched-current 3-bit CMOS 4.0-MHz wideband random signal generator

The paper presents a switched-current circuit implementation of a chaotic algorithm to generate a white noise. A 3-bit digital normalizer is utilized to adjust the coefficients in the piecewise-linear transfer function such that the probability of the generated numbers will be very close to a uniform distribution. A 1.0-GHz linear track-and-hold circuit is applied in the random number generator (RNG) to achieve a wide output bandwidth. TSMC 0.25-/spl mu/m one-poly five-metal CMOS process is adopted to carry out the proposed design to verify the wideband performance. When the operating clock is 10.0 MHz, the measured bandwidth of the generated noise is 4.0 MHz.

Multistability analysis for recurrent neural networks with unsaturating piecewise linear transfer functions.

Multistability is a property necessary in neural networks in order to enable certain applications (e.g., decision making), where monostable networks can be computationally restrictive. This article focuses on the analysis of multistability for a class of recurrent neural networks with unsaturating piecewise linear transfer functions. It deals fully with the three basic properties of a multistable network: boundedness, global attractivity, and complete convergence. This article makes the following contributions: conditions based on local inhibition are derived that guarantee boundedness of some multistable networks, conditions are established for global attractivity, bounds on global attractive sets are obtained, complete convergence conditions for the network are developed using novel energy-like functions, and simulation examples are employed to illustrate the theory thus developed.

Dynamical stability conditions for recurrent neural networks with unsaturating piecewise linear transfer functions.

We establish two conditions that ensure the nondivergence of additive recurrent networks with unsaturating piecewise linear transfer functions, also called linear threshold or semilinear transfer functions. As Hahnloser, Sarpeshkar, Mahowald, Douglas, and Seung (2000) showed, networks of this type can be efficiently built in silicon and exhibit the coexistence of digital selection and analog amplification in a single circuit. To obtain this behavior, the network must be multistable and nondivergent, and our conditions allow determining the regimes where this can be achieved with maximal recurrent amplification. The first condition can be applied to nonsymmetric networks and has a simple interpretation of requiring that the strength of local inhibition match the sum over excitatory weights converging onto a neuron. The second condition is restricted to symmetric networks, but can also take into account the stabilizing effect of nonlocal inhibitory interactions. We demonstrate the application of the conditions on a simple example and the orientation-selectivity model of Ben-Yishai, Lev Bar-Or, and Sompolinsky (1995). We show that the conditions can be used to identify in their model regions of maximal orientation-selective amplification and symmetry breaking.

Current Mode Circuit Implementations of PWL Functions

Current-mode techniques have been used to realize improved basic building blocks of elementary piecewise linear (PWL) functions. These alternative circuit implementations, used for synthesis of precision PWL transfer characteristics, are described and compared in performance. In this paper, two optional topologies of the PWL function building blocks are proposed, based on the regulated cascode current mirror, current sources, Schottky “prebiased” diodes, and improved CMOS class AB “prebiased diodes.” The comparison of DC and high frequency performances is based on HSPICE simulation results and shows very good DC accuracy and transient time response of the proposed building blocks.

Numerical solution of a calculus of variations problem using the feedforward neural network architecture

It is demonstrated, through theory and numerical example, how it is possible to construct directly and noniteratively a feedforward neural network to solve a calculus of variations problem. The method, using the piecewise linear and cubic sigmoid transfer functions, is linear in storage and processing time. The L 2 norm of the network approximation error decreases quadratically with the piecewise linear transfer function and quartically with the piecewise cubic sigmoid as the number of hidden layer neurons increases. The construction requires imposing certain constraints on the values of the input, bias, and output weights, and the attribution of certain roles to each of these parameters. All results presented used the piecewise linear and cubic sigmoid transfer functions. However, the noniterative approach should also be applicable to the use of hyperbolic tangents and radial basis functions.

Modelling the effects of spatial variability in rainfall on catchment response. 2. Experiments with distributed and lumped models

Computational experiments are carried out with the rainfall field model described in Part 1 of this paper and a physically based distributed modelling system, the Système Hydrologique Européen (SHE), to explore the interaction between spatial variability in rainfall and other factors controlling catchment response; both models have been calibrated for the small upland Wye catchment (area 10.55 km 2). Simulated rainfall fields are used to provide fully distributed rainfall inputs to the SHE; the corresponding ‘true’ catchment responses are then compared with those derived from incomplete sampling of the rainfall fields. The differences in simulated peak discharges and runoff volumes are assessed as a function of antecedent catchment conditions, network density and the level of spatial correlation in the rainfall input. A piecewise linear transfer function model with an averaged rainfall input is used to approximate SHE responses to fully distributed rainfall inputs, to provide insight into simple lumped model performance.

Equalization technique to reduce clipping-induced nonlinear distortion in subcarrier-multiplexed lightwave systems

A pretransmission compression and postdetection decompression scheme is proposed to reduce the clipping-induced nonlinear distortion (NLD) in subcarrier-multiplexed lightwave systems. In an AM-VSB CATV system, compression using a two-segment, piecewise-linear transfer characteristic promises to yield a 3.2-dB gain in carrier-to-noise ratio (CNR), or a 110% increase in the number of transmitted channels.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Bidirectional Subminiature Thermistor Sensor for Analog Control by Breath Flow

A subminiature airflow sensor is described, which can discriminate between exhalation and inhalation, has good linearity and stability, and is small enough to fit inside the stoma button of a laryngectomee. The system employs two fast-response self-heated thermistors placed on opposing sides of an aerodynamic obstacle inside a tube; flow polarity discrimination is based on differences between the heat exchange patterns under laminar vs. turbulent flow. An output proportional to airflow is achieved by the connection of a circuit with a piecewise-linear transfer characteristic in cascade with the thermistors. Developed in-house, this circuit may be adjusted to create an arbitrary range of input-output characteristics. Applications are suggested for an input device for various handicapped aids, for medical diagnostics and in industrial control.

Synthesis of piecewise-linear networks

Systematic methods for synthesising nonlinear networks having a prescribed scalar or multidimensional piecewise-linear function are described. In the scalar case, precision active-circuit building blocks using operational amplifiers, transistors, diodes, and resistors are given for realising piecewise-linear drivingpoint and transfer characteristic plots. In the multidimensional case, methods are given for realising a multiterminal nonlinear network having a multidimensional piecewise-linear transfer function. Finally, these methods are generalised for synthesising nonlinear n-ports having a prescribed multidimensional piecewiselinear driving-point function. Although most of the basic building blocks are grounded active networks, convertor networks are developed for transforming such grounded networks into floating networks having the same properties. By slight modifications of these convertor networks, other useful conversion properties are also presented