Approximation of non-autonomous dynamic systems by continuous time recurrent neural networks

This work provides a framework for the approximation of a dynamic system of the form x˙=f(x)+g(x)u by dynamic recurrent neural network. This extends previous work in which approximate realisation of autonomous dynamic systems was proven. Given certain conditions, the first p output neural units of a dynamic n-dimensional neural model approximate at a desired proximity a p-dimensional dynamic system with n>p. The neural architecture studied is then successfully implemented in a nonlinear multivariable system identification case study.

Discrete time representation of continuous time ARMA processes

This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.

On variational data assimilation in continuous time

Variational data assimilation in continuous time is revisited. The central techniques applied in this paper are in part adopted from the theory of optimal nonlinear control. Alternatively, the investigated approach can be considered as a continuous time generalization of what is known as weakly constrained four-dimensional variational assimilation (4D-Var) in the geosciences. The technique allows to assimilate trajectories in the case of partial observations and in the presence of model error. Several mathematical aspects of the approach are studied. Computationally, it amounts to solving a two-point boundary value problem. For imperfect models, the trade-off between small dynamical error (i.e. the trajectory obeys the model dynamics) and small observational error (i.e. the trajectory closely follows the observations) is investigated. This trade-off turns out to be trivial if the model is perfect. However, even in this situation, allowing for minute deviations from the perfect model is shown to have positive effects, namely to regularize the problem. The presented formalism is dynamical in character. No statistical assumptions on dynamical or observational noise are imposed.

Sensitivity and out-of-sample error in continuous time data assimilation

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time–tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade-off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade-off. A relation between the sensitivity and the out-of-sample error is established, which allows the latter to be calculated under operational conditions. A minimum out-of-sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade-off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, also known as synchronization. Numerical examples demonstrate the feasibility of the approach.

The phytocannabinoid Delta(9)-tetrahydrocannabivarin modulates inhibitory neurotransmission in the cerebellum

Background and purposeThe phytocannabinoid Delta(9)-tetrahydrocannabivarin (Delta(9)-THCV) has been reported to exhibit a diverse pharmacology; here, we investigate functional effects of Delta(9)-THCV, extracted from Cannabis sativa, using electrophysiological techniques to define its mechanism of action in the CNS.Experimental approachEffects of Delta(9)-THCV and synthetic cannabinoid agents on inhibitory neurotransmission at interneurone-Purkinje cell (IN-PC) synapses were correlated with effects on spontaneous PC output using single-cell and multi-electrode array (MEA) electrophysiological recordings respectively, in mouse cerebellar brain slices in vitro.Key resultsThe cannabinoid receptor agonist WIN 55,212-2 (WIN55) decreased miniature inhibitory postsynaptic current (mIPSC) frequency at IN-PC synapses. WIN55-induced inhibition was reversed by Delta(9)-THCV, and also by the CB(1) receptor antagonist AM251; Delta(9)-THCV or AM251 acted to increase mIPSC frequency beyond basal values. When applied alone, Delta(9)-THCV, AM251 or rimonabant increased mIPSC frequency. Pre-incubation with Delta(9)-THCV blocked WIN55-induced inhibition. In MEA recordings, WIN55 increased PC spike firing rate; Delta(9)-THCV and AM251 acted in the opposite direction to decrease spike firing. The effects of Delta(9)-THCV and WIN55 were attenuated by the GABA(A) receptor antagonist bicuculline methiodide.Conclusions and implicationsWe show for the first time that Delta(9)-THCV acts as a functional CB(1) receptor antagonist in the CNS to modulate inhibitory neurotransmission at IN-PC synapses and spontaneous PC output. Delta(9)-THCV- and AM251-induced increases in mIPSC frequency beyond basal levels were consistent with basal CB(1) receptor activity. WIN55-induced increases in PC spike firing rate were consistent with synaptic disinhibition; whilst Delta(9)-THCV- and AM251-induced decreases in spike firing suggest a mechanism of PC inhibition.British Journal of Pharmacology advance online publication, 3 March 2008; doi:10.1038/bjp.2008.57.

Estimating detailed soil water profile records from point measurements

Temporal and spatial patterns of soil water content affect many soil processes including evaporation, infiltration, ground water recharge, erosion and vegetation distribution. This paper describes the analysis of a soil moisture dataset comprising a combination of continuous time series of measurements at a few depths and locations, and occasional roving measurements at a large number of depths and locations. The objectives of the paper are: (i) to develop a technique for combining continuous measurements of soil water contents at a limited number of depths within a soil profile with occasional measurements at a large number of depths, to enable accurate estimation of the soil moisture vertical pattern and the integrated profile water content; and (ii) to estimate time series of soil moisture content at locations where there are just occasional soil water measurements available and some continuous records from nearby locations. The vertical interpolation technique presented here can strongly reduce errors in the estimation of profile soil water and its changes with time. On the other hand, the temporal interpolation technique is tested for different sampling strategies in space and time, and the errors generated in each case are compared.

A simple variance formula for population size estimators by conditioning

This note considers the variance estimation for population size estimators based on capture–recapture experiments. Whereas a diversity of estimators of the population size has been suggested, the question of estimating the associated variances is less frequently addressed. This note points out that the technique of conditioning can be applied here successfully which also allows us to identify sources of variation: the variance due to estimation of the model parameters and the binomial variance due to sampling n units from a population of size N. It is applied to estimators typically used in capture–recapture experiments in continuous time including the estimators of Zelterman and Chao and improves upon previously used variance estimators. In addition, knowledge of the variances associated with the estimators by Zelterman and Chao allows the suggestion of a new estimator as the weighted sum of the two. The decomposition of the variance into the two sources allows also a new understanding of how resampling techniques like the Bootstrap could be used appropriately. Finally, the sample size question for capture–recapture experiments is addressed. Since the variance of population size estimators increases with the sample size, it is suggested to use relative measures such as the observed-to-hidden ratio or the completeness of identification proportion for approaching the question of sample size choice.

A simple variance formula for population size estimators by conditioning

This note considers the variance estimation for population size estimators based on capture–recapture experiments. Whereas a diversity of estimators of the population size has been suggested, the question of estimating the associated variances is less frequently addressed. This note points out that the technique of conditioning can be applied here successfully which also allows us to identify sources of variation: the variance due to estimation of the model parameters and the binomial variance due to sampling n units from a population of size N. It is applied to estimators typically used in capture–recapture experiments in continuous time including the estimators of Zelterman and Chao and improves upon previously used variance estimators. In addition, knowledge of the variances associated with the estimators by Zelterman and Chao allows the suggestion of a new estimator as the weighted sum of the two. The decomposition of the variance into the two sources allows also a new understanding of how resampling techniques like the Bootstrap could be used appropriately. Finally, the sample size question for capture–recapture experiments is addressed. Since the variance of population size estimators increases with the sample size, it is suggested to use relative measures such as the observed-to-hidden ratio or the completeness of identification proportion for approaching the question of sample size choice.

Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo

We describe a Bayesian method for investigating correlated evolution of discrete binary traits on phylogenetic trees. The method fits a continuous-time Markov model to a pair of traits, seeking the best fitting models that describe their joint evolution on a phylogeny. We employ the methodology of reversible-jump ( RJ) Markov chain Monte Carlo to search among the large number of possible models, some of which conform to independent evolution of the two traits, others to correlated evolution. The RJ Markov chain visits these models in proportion to their posterior probabilities, thereby directly estimating the support for the hypothesis of correlated evolution. In addition, the RJ Markov chain simultaneously estimates the posterior distributions of the rate parameters of the model of trait evolution. These posterior distributions can be used to test among alternative evolutionary scenarios to explain the observed data. All results are integrated over a sample of phylogenetic trees to account for phylogenetic uncertainty. We implement the method in a program called RJ Discrete and illustrate it by analyzing the question of whether mating system and advertisement of estrus by females have coevolved in the Old World monkeys and great apes.

The phytocannabinoid Δ9-tetrahydrocannabivarin modulates inhibitory neurotransmission in the cerebellum

Background and purpose: The phytocannabinoid Delta(9)-tetrahydrocannabivarin (Delta(9)-THCV) has been reported to exhibit a diverse pharmacology; here, we investigate functional effects of Delta(9)-THCV, extracted from Cannabis sativa, using electrophysiological techniques to define its mechanism of action in the CNS. Experimental approach: Effects of Delta(9)-THCV and synthetic cannabinoid agents on inhibitory neurotransmission at interneurone-Purkinje cell (IN-PC) synapses were correlated with effects on spontaneous PC output using single-cell and multi-electrode array (MEA) electrophysiological recordings respectively, in mouse cerebellar brain slices in vitro. Key results: The cannabinoid receptor agonist WIN 55,212-2 (WIN55) decreased miniature inhibitory postsynaptic current (mIPSC) frequency at IN-PC synapses. WIN55-induced inhibition was reversed by Delta(9)-THCV, and also by the CB1 receptor antagonist AM251; Delta(9)-THCV or AM251 acted to increase mIPSC frequency beyond basal values. When applied alone, Delta(9)-THCV, AM251 or rimonabant increased mIPSC frequency. Pre-incubation with Delta(9)-THCV blocked WIN55-induced inhibition. In MEA recordings, WIN55 increased PC spike firing rate; Delta(9)-THCV and AM251 acted in the opposite direction to decrease spike firing. The effects of Delta(9)-THCV and WIN55 were attenuated by the GABA(A) receptor antagonist bicuculline methiodide. Conclusions and implications: We show for the first time that Delta(9)-THCV acts as a functional CB1 receptor antagonist in the CNS to modulate inhibitory neurotransmission at IN-PC synapses and spontaneous PC output. Delta(9)-THCV- and AM251-induced increases in mIPSC frequency beyond basal levels were consistent with basal CB1 receptor activity. WIN55-induced increases in PC spike firing rate were consistent with synaptic disinhibition; whilst Delta(9)-THCV-and AM251-induced decreases in spike firing suggest a mechanism of PC inhibition.

Model predictive control using dynamic integrated system optimisation and parameter estimation (DISOPE)

DISOPE is a technique for solving optimal control problems where there are differences in structure and parameter values between reality and the model employed in the computations. The model reality differences can also allow for deliberate simplification of model characteristics and performance indices in order to facilitate the solution of the optimal control problem. The technique was developed originally in continuous time and later extended to discrete time. The main property of the procedure is that by iterating on appropriately modified model based problems the correct optimal solution is achieved in spite of the model-reality differences. Algorithms have been developed in both continuous and discrete time for a general nonlinear optimal control problem with terminal weighting, bounded controls and terminal constraints. The aim of this paper is to show how the DISOPE technique can aid receding horizon optimal control computation in nonlinear model predictive control.

Microcontroller-based peak current mode control using digital slope compensation

Microcontroller-based peak current mode control of a buck converter is investigated. The new solution uses a discrete time controller with digital slope compensation. This is implemented using only a single-chip microcontroller to achieve desirable cycle-by-cycle peak current limiting. The digital controller is implemented as a two-pole, two-zero linear difference equation designed using a continuous time model of the buck converter and a discrete time transform. Subharmonic oscillations are removed with digital slope compensation using a discrete staircase ramp. A 16 W hardware implementation directly compares analog and digital control. Frequency response measurements are taken and it is shown that the crossover frequency and expected phase margin of the digital control system match that of its analog counterpart.

Smart-phone based electrocardiogram wavelet decomposition and neural network classification

This paper discusses ECG classification after parametrizing the ECG waveforms in the wavelet domain. The aim of the work is to develop an accurate classification algorithm that can be used to diagnose cardiac beat abnormalities detected using a mobile platform such as smart-phones. Continuous time recurrent neural network classifiers are considered for this task. Records from the European ST-T Database are decomposed in the wavelet domain using discrete wavelet transform (DWT) filter banks and the resulting DWT coefficients are filtered and used as inputs for training the neural network classifier. Advantages of the proposed methodology are the reduced memory requirement for the signals which is of relevance to mobile applications as well as an improvement in the ability of the neural network in its generalization ability due to the more parsimonious representation of the signal to its inputs.

Prefrontal cortical-ventral striatal interactions involved in affective modulation of attentional performance: implications for corticostriatal circuit function

Anatomically segregated systems linking the frontal cortex and the striatum are involved in various aspects of cognitive, affective, and motor processing. In this study, we examined the effects of combined unilateral lesions of the medial prefrontal cortex (mPFC) and the core subregion of the nucleus accumbens (AcbC) in opposite hemispheres (disconnection) on a continuous performance, visual attention test [five-choice serial reaction-time task (5CSRTT)]. The disconnection lesion produced a set of specific changes in performance of the 5CSRTT, resembling changes that followed bilateral AcbC lesions while, in addition, comprising a subset of the behavioral changes after bilateral mPFC lesions previously reported using the same task. Specifically, both mPFC/AcbC disconnection and bilateral AcbC lesions markedly affected aspects of response control related to affective feedback, as indexed by perseverative responding in the 5CSRTT. These effects were comparable, although not identical, to those in animals with either bilateral AcbC or mPFC/AcbC disconnection lesions. The mPFC/AcbC disconnection resulted in a behavioral profile largely distinct from that produced by disconnection of a similar circuit described previously, between the mPFC and the dorsomedial striatum, which were shown to form a functional network underlying aspects of visual attention and attention to action. This distinction provides an insight into the functional specialization of corticostriatal circuits in similar behavioral contexts.

Time course of oculomotor inhibition revealed by saccade trajectory modulation

Selecting a stimulus as the target for a goal-directed movement involves inhibiting other competing possible responses. Both target and distractor stimuli activate populations of neurons in topographic oculomotor maps such as the superior colliculus. Local inhibitory interconnections between these populations ensure only one saccade target is selected. Suppressing saccades to distractors may additionally involve inhibiting corresponding map regions to bias the local competition. Behavioral evidence of these inhibitory processes comes from the effects of distractors on oculomotor and manual trajectories. Individual saccades may initially deviate either toward or away from a distractor, but the source of this variability has not been investigated. Here we investigate the relation between distractor-related deviation of trajectory and saccade latency. Targets were presented with, or without, distractors, and the deviation of saccade trajectories arising from the presence of distractors was measured. A fixation gap paradigm was used to manipulate latency independently of the influence of competing distractors. Shorter- latency saccades deviated toward distractors and longer-latency saccades deviated away from distractors. The transition between deviation toward or away from distractors occurred at a saccade latency of around 200 ms. This shows that the time course of the inhibitory process involved in distractor related suppression is relatively slow.