Continuous-time Implementation Research Articles

Simulating the contact process in heterogeneous environments

The one-dimensional contact process (CP) in a heterogeneous environment-a binary chain consisting of two types of site with different recovery rates-is investigated. It is argued that the commonly used random-sequential Monte Carlo simulation method which employs a discrete notion of time is not faithful to the rates of the contact process in a heterogeneous environment. Therefore, a modification of this algorithm along with two alternative continuous-time implementations are analyzed. The latter two are an adapted version of the n -fold way used in Ising model simulations and a method based on a modified priority queue. It is demonstrated that the commonly used (but incorrect as we believe) discrete-time method yields a different critical threshold from all other algorithms considered. Finite-size scaling of the lowest gap in the spectrum of the Liouville time-evolution operator for the CP gives an estimate of the critical rate which supports these findings. Further, a performance test indicates an advantage in using the continuous-time methods in systems with heterogeneous rates. This result promises to help in the analysis of the CP in disordered systems with heterogeneous rates in which simulation is a challenging task due to very long relaxation times.

Discrete vs. continuous time implementation of a ring car following model in which overtaking is allowed

Car following models seek to describe the interactions between individual vehicles as they move along a stretch of road where the behaviour of each vehicle is dependent on the motion of the vehicle directly in front and overtaking is typically not permitted. In this work we study a modified version of the traditional car following model in which the vehicles are travelling on a closed loop and the ‘no overtaking’ restriction has been removed. The resulting model is described firstly in terms of a set of coupled continuous time delay differential equations and then in terms of their discrete time equivalents and both forms of the model are then solved numerically to analyse their post transient behaviour under a periodic perturbation. For certain parameter choices both the continuous and discrete forms of the model can exhibit chaotic behaviour but a comparison of the behaviour of the two models over a wide range of parameter values shows that the discretization can dramatically affect the type of post transient behaviour exhibited. This becomes increasingly evident as the time step used in the discrete time model is increased.

The valuation of a firm’s investment opportunities: a reduced form credit risk perspective

This paper develops a valuation model for a firm’s investment opportunities. Given standard market imperfections, we show that maximizing the firm’s equity value is consistent with the need to include a capital charge for an investment specific to a firm’s capital structure and in excess of the investment’s market determined risk. A reduced form credit risk perspective is taken to enable a continuous time implementation. This continuous time implementation is illustrated within the paper.

Common-input models for multiple neural spike-train data

Recent developments in multi-electrode recordings enable the simultaneous measurement of the spiking activity of many neurons. Analysis of such multineuronal data is one of the key challenge in computational neuroscience today. In this work, we develop a multivariate point-process model in which the observed activity of a network of neurons depends on three terms: (1) the experimentally-controlled stimulus; (2) the spiking history of the observed neurons; and (3) a hidden term that corresponds, for example, to common input from an unobserved population of neurons that is presynaptic to two or more cells in the observed population. We consider two models for the network firing-rates, one of which is computationally and analytically tractable but can lead to unrealistically high firing-rates, while the other with reasonable firing-rates imposes a greater computational burden. We develop an expectation-maximization algorithm for fitting the parameters of both the models. For the analytically tractable model the expectation step is based on a continuous-time implementation of the extended Kalman smoother, and the maximization step involves two concave maximization problems which may be solved in parallel. The other model that we consider necessitates the use of Monte Carlo methods for the expectation as well as maximization step. We discuss the trade-off involved in choosing between the two models and the associated methods. The techniques developed allow us to solve a variety of inference problems in a straightforward, computationally efficient fashion; for example, we may use the model to predict network activity given an arbitrary stimulus, infer a neuron's ring rate given the stimulus and the activity of the other observed neurons, and perform optimal stimulus decoding and prediction. We present several detailed simulation studies which explore the strengths and limitations of our approach.

0.18-/spl mu/m CMOS equalization techniques for 10-Gb/s fiber optical communication links

Limitations in data transmission caused by modal dispersion in fiber-optic links can be significantly improved using equalization techniques. In this paper, two different equalizer implementation approaches are proposed to extend the transmission capacities of existing fiber-optic links. The building blocks of the equalizer including a multiplier cell, a delay line, and an output buffer stage are fully integrated on a 0.18-/spl mu/m CMOS process. For the continuous-time tap-delay implementation, a passive LC delay line and an active inductance peaking delay line are compared for performance against process variation, as well as power consumption. In addition, a delay-locked loop is proposed to counter delay variations caused by changes in the process corner. A 10-Gb/s nonreturn-to-zero signal is received after transmission through a 500-m multimode-fiber channel, and the signal impairment due to the differential modal delay is successfully compensated using both feed-forward equalizers.

High-speed high-precision CMOS analog rank order filter with O(n) complexity

A continuous-time implementation of a voltage-mode analog rank order filter is presented. The proposed circuit features high speed, high precision, and simple circuit implementation. The overall architecture exhibits linear increase of complexity with the number of inputs (O(n)), at the rate of seven transistors per input. Rank is easily programmable with the tail current for all rank order values from the Max to the Min case, and the programmed function is accurate for a wide range of tail currents. Moreover, unlike previously reported rank order structures the precision of the proposed circuit does not rely on perfect matching of all input transistors. Simulations as well as experimental results are presented that verify the functionality and performance of the proposed circuit.

Invariant and Periodic Filters for Helicopter Vibration Attenuation

The class of Higher Harmonic Control (HHC) algorithms for helicopter vibration reduction is analysed, and a derivation of the continuous-time, state space form for such compensators is derived, both in the time-invariant and time-periodic cases. Finally, the results of a simulation study are presented, aiming at assessing the relative merits of the discrete and continuous-time implementations of HHC controllers.

Effects of a random noisy oracle on search algorithm complexity

Grover's algorithm provides a quadratic speed-up over classical algorithms for unstructured database or library searches. This paper examines the robustness of Grover's search algorithm to a random phase error in the oracle and analyzes the complexity of the search process as a function of the scaling of the oracle error with database or library size. Both the discrete- and continuous-time implementations of the search algorithm are investigated. It is shown that unless the oracle phase error scales as O(N^(-1/4)), neither the discrete- nor the continuous-time implementation of Grover's algorithm is scalably robust to this error in the absence of error correction.

Continuous time quadrature band-pass ΔΣ modulator with input mixers

A continuous time quadrature band-pass ΔΣ modulator preceded by input mixers is presented. Complex band-pass ΔΣ modulators provide better performance than band-pass ΔΣ modulators in digitising complex signals due to more efficient noise shaping (Yantzi et al., 1997). Continuous time implementation of the second-order ΔΣ noise shaping loop filter is preferred to a switched capacitor structure (van der Zwan and Dijkmans, 1996). Through the integration of mixers in the AD converter, RF input signals in the range 0.3–1.6 GHz can be down-converted to a digital I and Q output stream at a clock rate of 128 MHz. It is designed as a front-end for a low power receiver with a 2 MHz IF bandwidth centred around 4 MHz and attains a signal-to-noise ratio higher than 60 dB. The ΔΣ ADC and mixer are integrated in a 0.25 μm CMOS technology and consume 14 mW from a 2 V supply

Effect of random permutations applied to random sequences and related applications

This paper presents random permutations and their effects when they are applied to a random sequence. Random permutations are the digital implementation of continuous time “Periodic Clock Changes”. Continuous periodic clock changes have been already applied for multiple access and modulation purposes. It is shown that a random permutation applied to an input sequence with band-limited power spectrum can give a spreaded sequence with white power spectrum. Closed forms of the power spectral density of the interleaved sequences are given and simulations are presented. When the length of the permutation is large, it is shown that the new interleaved sequence power spectrum converges towards a white noise except for the null frequency, where the power spectrum remains the same as the input sequence. These results have an application to interleaving (random or deterministic), chip interleaving and more generally in spread spectrum techniques.

Exact ART: A Complete Implementation of an ART Network

In this article we introduce a continuous time implementation of adaptive resonance theory (ART). ART designed by Grossberg concerns neural networks that self-organize stable pattern recognition categories of arbitrary sequences of input patterns. In contrast to the current implementations of ART we introduce a complete implementation of an ART network, including all regulatory and logical functions, as a system of ordinary differential equations capable of stand-alone running in real time. This means that transient behavior is kept in tact. This implementation of ART is based on ART 2 and is called Exact ART. Exact ART includes an implementation of a gated dipole field and an implementation of the orienting sub-system. The most important features of Exact ART, which are the design principles of ART 2, are proven mathematically. Also simulation studies show that Exact ART self-organizes stable recognition codes that agree with the classification behavior of ART 2. © 1997 Elsevier Science Ltd.

A new field-oriented discrete-time controller for current-fed induction motors

Proving the stability of a discrete-time implementation of the standard field-oriented control (FOC) of induction motors is an open problem of great practical and theoretical significance. In a recent paper a modification to the FOC was introduced, to rigorously establish global asymptotic speed regulation and rotor flux norm tracking for current-fed machines. In this short note the properties of this new controller are further investigated. In particular it is shown that the main, and far from obvious, effect of discretization is that the tasks of flux and torque regulation have to be shared between the two control channels, as opposed to a continuous-time implementation where they can be decoupled. A consequence of this coupled control approach is an enhancement in rotor flux-tracking performance. Some experimental results that illustrate this and other features of the scheme are also presented.

Analogue system for eigenvalue computation and sorting based on an isospectral matrix flow

An analogue system for the computation of the eigenvalues of symmetric matrices and for sorting lists is described. The computation is based on an isospectral matrix flow. A fully parallel continuous time implementation of the equations is presented. The implementation was simulated using PSPICE, and the results of the simulation are described.

Predictive PI controller

A Predictive Proportional + Integral (PPI) controller with improved performance over standard PI and PID controllers is proposed. This controller consists of two parts: a standard PI controller and a predictive term with which its dynamics depend on the system time delay. The controller is realized by a continuous time implementation; i.e. a numerical solution of differential equations rather than a transformation to the Z-domain. The performance of this controller is compared with that of the PID controller tuned by Zeigler and Nichols and three other recent methods of tuning PID controllers. The conditions for stability are derived and the sensitivity of the new controller to process parameter changes is analysed by Monte-Carlo evaluation.

Full analog CMOS integration of very large time constants for synaptic transfer in neural networks

A method for the full on-chip analog implementation of large time constants in a CMOS technology is presented. These time constants are used for delayed synaptic transfer in neural networks for signal processing. For real-time speech recognition time constants from 1 to 500 ms are necessary, that vary logarithmically with a 4-bit digital code. An RC-type circuit is used to make a continuous time implementation. A modified operational transconductance amplifier (OTA) in a negative feedback configuration is used as a resistor and a gate-oxide capacitor is used as load. The output current of the OTA is divided by current dividers to obtain an electronic multiplication of the time constant. An adapted current mirror design is applied. Much attention is paid to offset-voltage reduction. This new multiplication scheme has several important advantages compared to other schemes. A global area minimization procedure is explained. The total active are of a 3-μm CMOS chip for a 500-ms time constant is 0.5 mm2. The realized circuit has a typical measured offset voltage of 130 mV. The area efficiency and the offset sensitivity are shown to be one order of magnitude better than in other designs.

Sampled Data Implementation of Eigenstructure Assignment Technique

A discrete time implementation of the eigenstructure assignment technique for diagonalizable systems is presented. Good agreement with continuous time implementations is demonstrated with sample rates as low as twice the Nyquist frequency.

Continuous-time implementation of optimal-aim controls

A modified optimal-aim control strategy for special classes of nonlinear systems is presented, and a theorem leading to an explicit, continuous-time implementation of the strategy is given.

Error-Free Recovery of Signals from Irregularly Spaced Samples

Error free recovery of signals from irregularly spaced samples in terms of completeness of sets of nonharmonic exponentials