Targeting the dynamics of complex networks

We report on a generic procedure to steer (target) a network's dynamics towards a given, desired evolution. The problem is here tackled through a Master Stability Function approach, assessing the stability of the aimed dynamics, and through a selection of nodes to be targeted. We show that the degree of a node is a crucial element in this selection process, and that the targeting mechanism is most effective in heterogeneous scale-free architectures. This makes the proposed approach applicable to the large majority of natural and man-made networked systems

Fractal Dimension Analysis of Transient Visual Evoked Potentials: Optimisation and Applications

Purpose The visual evoked potential (VEP) provides a time series signal response to an external visual stimulus at the location of the visual cortex. The major VEP signal components, peak latency and amplitude, may be affected by disease processes. Additionally, the VEP contains fine detailed and non-periodic structure, of presently unclear relevance to normal function, which may be quantified using the fractal dimension. The purpose of this study is to provide a systematic investigation of the key parameters in the measurement of the fractal dimension of VEPs, to develop an optimal analysis protocol for application. Methods VEP time series were mathematically transformed using delay time, τ, and embedding dimension, m, parameters. The fractal dimension of the transformed data was obtained from a scaling analysis based on straight line fits to the numbers of pairs of points with separation less than r versus log(r) in the transformed space. Optimal τ, m, and scaling analysis were obtained by comparing the consistency of results using different sampling frequencies. The optimised method was then piloted on samples of normal and abnormal VEPs. Results Consistent fractal dimension estimates were obtained using τ = 4 ms, designating the fractal dimension = D2 of the time series based on embedding dimension m = 7 (for 3606 Hz and 5000 Hz), m = 6 (for 1803 Hz) and m = 5 (for 1000Hz), and estimating D2 for each embedding dimension as the steepest slope of the linear scaling region in the plot of log(C(r)) vs log(r) provided the scaling region occurred within the middle third of the plot. Piloting revealed that fractal dimensions were higher from the sampled abnormal than normal achromatic VEPs in adults (p = 0.02). Variances of fractal dimension were higher from the abnormal than normal chromatic VEPs in children (p = 0.01). Conclusions A useful analysis protocol to assess the fractal dimension of transformed VEPs has been developed

Reconstruction of Underlying Nonlinear Deterministic Dynamics Embedded in Noisy Spike Trains

An experimentally recorded time series formed by the exact times of occurrence of the neuronal spikes (spike train) is likely to be affected by observational noise that provokes events mistakenly confused with neuronal discharges, as well as missed detection of genuine neuronal discharges. The points of the spike train may also suffer a slight jitter in time due to stochastic processes in synaptic transmission and to delays in the detecting devices. This study presents a procedure aimed at filtering the embedded noise (denoising the spike trains) the spike trains based on the hypothesis that recurrent temporal patterns of spikes are likely to represent the robust expression of a dynamic process associated with the information carried by the spike train. The rationale of this approach is tested on simulated spike trains generated by several nonlinear deterministic dynamical systems with embedded observational noise. The application of the pattern grouping algorithm (PGA) to the noisy time series allows us to extract a set of points that form the reconstructed time series. Three new indices are defined for assessment of the performance of the denoising procedure. The results show that this procedure may indeed retrieve the most relevant temporal features of the original dynamics. Moreover, we observe that additional spurious events affect the performance to a larger extent than the missing of original points. Thus, a strict criterion for the detection of spikes under experimental conditions, thus reducing the number of spurious spikes, may raise the possibility to apply PGA to detect endogenous deterministic dynamics in the spike train otherwise masked by the observational noise

Observing and predicting chaotic signals: Is 2% noise too much?

: We discuss the influence of noise on the analysis of complex time series data. How harmful it is depends on the nature of the noise, the complexity of the signal and on the application in mind. We will give generally valid upper bounds on the feasible noise level for dimension, entropy and Lyapunov estimates and lower bounds for the optimal achievable prediction error. We illustrate in a number of examples why it is hard to reach these bounds in practice. We briefly sketch methods to detect, analyze and reduce measurement noise. Contents 1 Introduction 2 2 Measurement error and dynamical noise 2 3 Noise and prediction 3 3.1 Examples with known dynamics : : : : : : : : : : : : : : : : : : : : : : : : : : 4 3.2 Dynamics from a time series : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 4 Noise and scaling 8 4.1 Dimensions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 4.2 Entropies : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :..

Mathematical Analysis of Glioma Growth in a Murine Model

Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of the tumor. After 25 days, the final tumor volumes of the mice varied from 12 mm(3) to 62 mm(3), even though mice were inoculated from the same tumor cell line under carefully controlled conditions. We generated hypotheses to explore large variances in final tumor size and tested them with our simple reaction-diffusion model in both a 3-dimensional (3D) finite difference method and a 2-dimensional (2D) level set method. The parameters obtained from a best-fit procedure, designed to yield simulated tumors as close as possible to the observed ones, vary by an order of magnitude between the three mice analyzed in detail. These differences may reflect morphological and biological variability in tumor growth, as well as errors in the mathematical model, perhaps from an oversimplification of the tumor dynamics or nonidentifiability of parameters. Our results generate parameters that match other experimental in vitro and in vivo measurements. Additionally, we calculate wave speed, which matches with other rat and human measurements.Graduate Assistance of Areas in National Need (GAANN) [P200A120120]; NSF [DMS-1148771]; National Science Foundation [DGE-1311230, 1512553, DMS-1518529, DMS-1615879]; Barrow Neurological Foundation and Arizona State University; Newsome United Kingdom Chair in Neurosurgery ResearchThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]