Daniel Coca

Identification of finite dimensional models of infinite dimensional dynamical systems

The identification of finite dimensional discrete-time models of deterministic linear and nonlinear infinite dimensional systems from pointwise observations is investigated. The input and output observations are used to construct finite dimensional approximations of the solution and the forcing function which are expanded in terms of a finite element basis. An algorithm to determine a minimal basis to approximate the data is introduced. Subsequently, the resulting coordinate vectors are used to identify a finite dimensional discrete-time model. Theoretical results concerning the existence, stability and convergence of the finite dimensional representation are established. Numerical results involving identification of finite dimensional models for both linear and nonlinear infinite dimensional systems are presented.

Stochastic, adaptive sampling of information by microvilli in fly photoreceptors.

Summary Background In fly photoreceptors, light is focused onto a photosensitive waveguide, the rhabdomere, consisting of tens of thousands of microvilli. Each microvillus is capable of generating elementary responses, quantum bumps, in response to single photons using a stochastically operating phototransduction cascade. Whereas much is known about the cascade reactions, less is known about how the concerted action of the microvilli population encodes light changes into neural information and how the ultrastructure and biochemical machinery of photoreceptors of flies and other insects evolved in relation to the information sampling and processing they perform. Results We generated biophysically realistic fly photoreceptor models, which accurately simulate the encoding of visual information. By comparing stochastic simulations with single cell recordings from Drosophila photoreceptors, we show how adaptive sampling by 30,000 microvilli captures the temporal structure of natural contrast changes. Following each bump, individual microvilli are rendered briefly (∼100–200 ms) refractory, thereby reducing quantum efficiency with increasing intensity. The refractory period opposes saturation, dynamically and stochastically adjusting availability of microvilli (bump production rate: sample rate), whereas intracellular calcium and voltage adapt bump amplitude and waveform (sample size). These adapting sampling principles result in robust encoding of natural light changes, which both approximates perceptual contrast constancy and enhances novel events under different light conditions, and predict information processing across a range of species with different visual ecologies. Conclusions These results clarify why fly photoreceptors are structured the way they are and function as they do, linking sensory information to sensory evolution and revealing benefits of stochasticity for neural information processing.

Identification of coupled map lattice models of complex spatio-temporal patterns

Abstract A method for the identification of nonlinear coupled map lattices (CML) equations from measured spatio-temporal data is introduced. The application of the algorithm is demonstrated using chaotic two-dimensional spatio-temporal patterns generated from interacting populations and the resulting models are validated by computing the attractors and the largest Lyapunov exponents.

DISCRETE WAVELET MODELS FOR IDENTIFICATION AND QUALITATIVE ANALYSIS OF CHAOTIC SYSTEMS

This paper develops an original approach for identifying models of chaotic systems directly from noise-corrupted data. The nonlinear functional describing the process is constructed using a new multiresolution model structure implemented with B-spline wavelet and scaling functions. Following an iterative strategy, a sequence of model sets of increasing complexity are postulated and tested until a suitable model is found. An orthogonal-forward-regression routine coupled with model validity tests is used to select parsimonious wavelet models and to measure the quality of the fit. The effectiveness of the identification procedure is demonstrated using both simulated and experimental data. It is shown that the proposed method can produce accurate models which exhibit qualitatively the same dynamical behavior as the observed system and are characterized by dynamical invariants which are very close to those of the original system.

Non-linear system identification using wavelet multiresolution models

A new methodology for identifying non-linear NARMAX models, from noise corrupted data, is introduced based on semi-orthogonal wavelet multiresolution approximations. An adaptive model sequencing strategy is introduced to infer model complexity from the data while reducing computational costs. This is used in conjunction with an iterative orthogonal-forward-regression routine coupled with model validity tests to identify sparse but accurate wavelet series representations of non-linear processes. Experimental data from two real systems, a liquid level system and from a civil engineering structure are used to illustrate the effectiveness of the new identification procedure.

Time-Lapse Analysis of Human Embryonic Stem Cells Reveals Multiple Bottlenecks Restricting Colony Formation and Their Relief upon Culture Adaptation

Summary Using time-lapse imaging, we have identified a series of bottlenecks that restrict growth of early-passage human embryonic stem cells (hESCs) and that are relieved by karyotypically abnormal variants that are selected by prolonged culture. Only a minority of karyotypically normal cells divided after plating, and these were mainly cells in the later stages of cell cycle at the time of plating. Furthermore, the daughter cells showed a continued pattern of cell death after division, so that few formed long-term proliferating colonies. These colony-forming cells showed distinct patterns of cell movement. Increasing cell density enhanced cell movement facilitating cell:cell contact, which resulted in increased proportion of dividing cells and improved survival postplating of normal hESCs. In contrast, most of the karyotypically abnormal cells reentered the cell cycle on plating and gave rise to healthy progeny, without the need for cell:cell contacts and independent of their motility patterns.

Direct parameter identification of distributed parameter systems

A new direct approach to identifying the parameters of distributed parameter systems from noise-corrupted data is introduced. The model of the system which takes the form of a set of linear or nonlinear partial differential equations is assumed known with the exception of a set of constant parameters. Using finite-difference approximations of the spatial derivatives the original equation is transformed into a set of ordinary differential equations. The identification approach involves smoothing the measured data and estimating the temporal derivatives using a fixed interval smoother. A least-squares method is then employed to estimate the unknown parameters. Three examples that illustrate the applicability of the proposed approach are presented and discussed.

Modeling the evolution of culture-adapted human embryonic stem cells

The long-term culture of human embryonic stem (ES) cells is inevitably subject to evolution, since any mutant that arises with a growth advantage will be selectively amplified. However, the evolutionary influences of population size, mutation rate, and selection pressure are frequently overlooked. We have constructed a Monte Carlo simulation model to predict how changes in these factors can influence the appearance and spread of mutant ES cells, and verified its applicability by comparison with in vitro data. This simulation provides an estimate for the expected rate of generation of culture-adapted ES cells under different assumptions for the key parameters. In particular, it highlights the effect of population size, suggesting that the maintenance of cells in small populations reduces the likelihood that abnormal cultures will develop.

A dynamic model of neurovascular coupling: Implications for blood vessel dilation and constriction

Neurovascular coupling in response to stimulation of the rat barrel cortex was investigated using concurrent multichannel electrophysiology and laser Doppler flowmetry. The data were used to build a linear dynamic model relating neural activity to blood flow. Local field potential time series were subject to current source density analysis, and the time series of a layer IV sink of the barrel cortex was used as the input to the model. The model output was the time series of the changes in regional cerebral blood flow (CBF). We show that this model can provide excellent fit of the CBF responses for stimulus durations of up to 16 s. The structure of the model consisted of two coupled components representing vascular dilation and constriction. The complex temporal characteristics of the CBF time series were reproduced by the relatively simple balance of these two components. We show that the impulse response obtained under the 16-s duration stimulation condition generalised to provide a good prediction to the data from the shorter duration stimulation conditions. Furthermore, by optimising three out of the total of nine model parameters, the variability in the data can be well accounted for over a wide range of stimulus conditions. By establishing linearity, classic system analysis methods can be used to generate and explore a range of equivalent model structures (e.g., feed-forward or feedback) to guide the experimental investigation of the control of vascular dilation and constriction following stimulation.

Identification of coupled map lattice models of deterministic distributed parameter systems

This paper introduces a novel approach to the identification of Coupled Map Lattice (CML) models of linear and nonlinear infinite-dimensional systems from discrete observations. The method exploits the regularity of the CML model so that only a finite number of spatial measurements are required. The measurement system associated with a CML is discussed and some necessary conditions for the input/output equations to form a CML are presented. Numerical simulations illustrate the applicability of the proposed method.