Spikes and rhythms organize control and communication in the animal world, in contrast to the bits and clocks of digital technology. As continuous-time signals that can be counted, spikes have a mixed nature. This article reviews ongoing efforts to develop a control theory of spiking systems. The central thesis is that the mixed nature of spiking results from a mixed feedback principle, and a control theory of mixed feedback can be grounded in the operator theoretic concept of maximal monotonicity. As a nonlinear generalization of passivity, maximal monotonicity acknowledges at once the physics of electrical circuits, the algorithmic tractability of convex optimization, and the feedback control theory of incremental passivity. We discuss the relevance of a theory of spiking control systems in the emerging age of event-based technology.

This article proposes a methodology to extract a low-dimensional integrate-and-fire model from an arbitrarily detailed single-compartment biophysical model. The method aims at relating the modulation of maximal conductance parameters in the biophysical model to the modulation of parameters in the proposed integrate-and-fire model. The approach is illustrated on two well-documented examples of cellular neuromodulation: the transition between type I and type II excitability and the transition between spiking and bursting.

We show how the geodesic distance on S++n, the cone of n × n real symmetric or complex Hermitian positive definite matrices regarded as a Riemannian manifold, may be used to naturally define a distance between two such matrices of different dimensions. Given that S++nalso parameterizes n-dimensional ellipsoids, inner products on ℝn, and n × n covariances of nondegenerate probability distributions, this gives us a natural way to define a geometric distance between a pair of such objects of different dimensions.

By controlling the state of neuronal populations, neuromodulators ultimately affect behavior. A key neuromodulation mechanism is the alteration of neuronal excitability via the modulation of ion channel expression. This type of neuromodulation is normally studied with conductance-based models, but those models are computationally challenging for large-scale network simulations needed in population studies. This article studies the modulation properties of the multiquadratic integrate-and-fire model, a generalization of the classical quadratic integrate-and-fire model. The model is shown to combine the computational economy of integrate-and-fire modeling and the physiological interpretability of conductance-based modeling. It is therefore a good candidate for affordable computational studies of neuromodulation in large networks.

Neuronal information processing is regulated by fast and localized fluctuations of brain states. Brain states reliably switch between distinct spatiotemporal signatures at a network scale even though they are composed of heterogeneous and variable rhythms at a cellular scale. We investigated the mechanisms of this network control in a conductance-based population model that reliably switches between active and oscillatory mean-fields. Robust control of the mean-field properties relies critically on a switchable negative intrinsic conductance at the cellular level. This conductance endows circuits with a shared cellular positive feedback that can switch population rhythms on and off at a cellular resolution. The switch is largely independent from other intrinsic neuronal properties, network size and synaptic connectivity. It is therefore compatible with the temporal variability and spatial heterogeneity induced by slower regulatory functions such as neuromodulation, synaptic plasticity and homeostasis. Strikingly, the required cellular mechanism is available in all cell types that possess T-type calcium channels but unavailable in computational models that neglect the slow kinetics of their activation.

We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that provide a negative feedback at resting potential (restorative channels) and those that provide a positive feedback at resting potential (regenerative channels). Geometrically, the condition imposes a transcritical bifurcation that rules the switch of excitability through the variation of a single physiological parameter. Our analysis of six different published conductance based models always finds the transcritical bifurcation and the associated switch in excitability, which suggests that the mathematical predictions have a physiological relevance and that a same regulatory mechanism is potentially involved in the excitability and signaling of many neurons.

Midbrain dopaminergic neurons are endowed with endogenous slow pacemaking properties. In recent years, many different groups have studied the basis for this phenomenon, often with conflicting conclusions. In particular, the role of a slowly-inactivating L-type calcium channel in the depolarizing phase between spikes is controversial, and the analysis of slow oscillatory potential (SOP) recordings during the blockade of sodium channels has led to conflicting conclusions. Based on a minimal model of a dopaminergic neuron, our analysis suggests that the same experimental protocol may lead to drastically different observations in almost identical neurons. For example, complete L-type calcium channel blockade eliminates spontaneous firing or has almost no effect in two neurons differing by less than 1% in their maximal sodium conductance. The same prediction can be reproduced in a state of the art detailed model of a dopaminergic neuron. Some of these predictions are confirmed experimentally using single-cell recordings in brain slices. Our minimal model exhibits SOPs when sodium channels are blocked, these SOPs being uncorrelated with the spiking activity, as has been shown experimentally. We also show that block of a specific conductance (in this case, the SK conductance) can have a different effect on these two oscillatory behaviors (pacemaking and SOPs), despite the fact that they have the same initiating mechanism. These results highlight the fact that computational approaches, besides their well known confirmatory and predictive interests in neurophysiology, may also be useful to resolve apparent discrepancies between experimental results.

DNA microarrays provide a huge amount of data and require therefore dimensionality reduction methods to extract meaningful biological information. Independent component analysis (ICA) was proposed by several authors as an interesting means. Unfortunately, experimental data are usually of poor quality because of noise, outliers and lack of samples. Robustness to these hurdles will thus be a key feature for an ICA algorithm. This paper identifies a robust contrast function and proposes a new ICA algorithm.

This paper addresses the design of mobile sensor networks for optimal data collection. The development is strongly motivated by the application to adaptive ocean sampling for an autonomous ocean observing and prediction system. A performance metric, used to derive optimal paths for the network of mobile sensors, defines the optimal data set as one which minimizes error in a model estimate of the sampled field. Feedback control laws are presented that stably coordinate sensors on structured tracks that have been optimized over a minimal set of parameters. Optimal, closed-loop solutions are computed in a number of low-dimensional cases to illustrate the methodology. Robustness of the performance to the influence of a steady flow field on relatively slow-moving mobile sensors is also explored

The quantity of mRNA transcripts in a cell is determined by a complex interplay of cooperative and counteracting biological processes. Independent Component Analysis (ICA) is one of a few number of unsupervised algorithms that have been applied to microarray gene expression data in an attempt to understand phenotype differences in terms of changes in the activation/inhibition patterns of biological pathways. While the ICA model has been shown to outperform other linear representations of the data such as Principal Components Analysis (PCA), a validation using explicit pathway and regulatory element information has not yet been performed. We apply a range of popular ICA algorithms to six of the largest microarray cancer datasets and use pathway-knowledge and regulatory-element databases for validation. We show that ICA outperforms PCA and clustering-based methods in that ICA components map closer to known cancer-related pathways, regulatory modules, and cancer phenotypes. Furthermore, we identify cancer signalling and oncogenic pathways and regulatory modules that play a prominent role in breast cancer and relate the differential activation patterns of these to breast cancer phenotypes. Importantly, we find novel associations linking immune response and epithelial-mesenchymal transition pathways with estrogen receptor status and histological grade, respectively. In addition, we find associations linking the activity levels of biological pathways and transcription factors (NF1 and NFAT) with clinical outcome in breast cancer. ICA provides a framework for a more biologically relevant interpretation of genomewide transcriptomic data. Adopting ICA as the analysis tool of choice will help understand the phenotype-pathway relationship and thus help elucidate the molecular taxonomy of heterogeneous cancers and of other complex genetic diseases.

The paper considers the feedback stabilization of periodic orbits in a planar juggler. The juggler is “blind,” i.e, he has no other sensing capabilities than the detection of impact times. The robustness analysis of the proposed control suggests that the arms acceleration at impact is a crucial design parameter even though it plays no role in the stability analysis. Analytical results and convergence proofs are provided for a simplified model of the juggler. The control law is then adapted to a more accurate model and validated in an experimental setup.

The paper studies the properties of a sinusoidally vibrating wedge billiard as a model for 2-D bounce juggling. It is shown that some periodic orbits that are unstable in the elastic fixed wedge become exponentially stable in the nonelastic vibrating wedge. These orbits are linked with certain classical juggling patterns, providing an interesting benchmark for the study of the frequency-locking properties in human rhythmic tasks. Experimental results on sensorless stabilization of juggling patterns are described.

Pencil Beam Scanning is a dynamic beam delivery system developed at IBA s.a. for proton therapy. The radiation field necessary to reach in a fast and robust way a prescribed 3D dose distribution is obtained by accurately controlling both the extraction of the beam from a 235 MeV accelerator and the motion of the beam spot thanks to scanning magnets. Compared to existing beam delivery systems, the hardware of the PBS system is considerably simplified while offering the possibility of accurate delivery and short treatment time. The simplification in hardware is compensated for by advanced actuation, which is the topic of the present paper.