Neuron dynamics in the presence of 1/f noise

Interest in understanding the interplay between noise and the response of a non-linear device cuts across disciplinary boundaries. It is as relevant for unmasking the dynamics of neurons in noisy environments as it is for designing reliable nanoscale logic circuit elements and sensors. Most studies of noise in non-linear devices are limited to either time-correlated noise with a Lorentzian spectrum (of which the white noise is a limiting case) or just white noise. We use analytical theory and numerical simulations to study the impact of the more ubiquitous "natural" noise with a 1/f frequency spectrum. Specifically, we study the impact of the 1/f noise on a leaky integrate and fire model of a neuron. The impact of noise is considered on two quantities of interest to neuron function: The spike count Fano factor and the speed of neuron response to a small step-like stimulus. For the perfect (non-leaky) integrate and fire model, we show that the Fano factor can be expressed as an integral over noise spectrum weighted by a (low pass) filter function. This result elucidates the connection between low frequency noise and disorder in neuron dynamics. We compare our results to experimental data of single neurons in vivo, and show how the 1/f noise model provides much better agreement than the usual approximations based on Lorentzian noise. The low frequency noise, however, complicates the case for information coding scheme based on interspike intervals by introducing variability in the neuron response time. On a positive note, the neuron response time to a step stimulus is, remarkably, nearly optimal in the presence of 1/f noise. An explanation of this effect elucidates how the brain can take advantage of noise to prime a subset of the neurons to respond almost instantly to sudden stimuli.Comment: Phys. Rev. E in pres

Artifacts with uneven sampling of red noise

The vast majority of sampling systems operate in a standard way: at each tick of a fixed-frequency master clock a digitizer reads out a voltage that corresponds to the value of some physical quantity and translates it into a bit pattern that is either transmitted, stored, or processed right away. Thus signal sampling at evenly spaced time intervals is the rule: however this is not always the case, and uneven sampling is sometimes unavoidable. While periodic or quasi-periodic uneven sampling of a deterministic signal can reasonably be expected to produce artifacts, it is much less obvious that the same happens with noise: here I show that this is indeed the case only for long-memory noise processes, i.e., power-law noises $1/f^\alpha$ with $\alpha > 2$. The resulting artifacts are usually a nuisance although they can be eliminated with a proper processing of the signal samples, but they could also be turned to advantage and used to encode information.Comment: 5 figure

Better Nonlinear Models from Noisy Data: Attractors with Maximum Likelihood

A new approach to nonlinear modelling is presented which, by incorporating the global behaviour of the model, lifts shortcomings of both least squares and total least squares parameter estimates. Although ubiquitous in practice, a least squares approach is fundamentally flawed in that it assumes independent, normally distributed (IND) forecast errors: nonlinear models will not yield IND errors even if the noise is IND. A new cost function is obtained via the maximum likelihood principle; superior results are illustrated both for small data sets and infinitely long data streams.Comment: RevTex, 11 pages, 4 figure

A new in vitro assay for quantitation of chemotherapy-induced mucositis.

Patients receiving high-dose chemotherapy (HD-CT) are at risk of severe mucositis. Most prevention studies evaluate the degree of mucositis on clinical, and therefore subjective, measurements. The aim of this study was to develop an objective in vitro assay of chemotherapy-induced mucositis. Twelve patients with locally advanced breast carcinoma received HD-CT followed by peripheral stem cell reinfusion. Before and twice weekly after HD-CT, the mucosa was evaluated by an oral washing, a buccal smear and the World Health Organization (WHO) toxicity grading; furthermore, blood leucocyte levels were determined. For the oral washings, the percentage of viable epithelial cells was determined by trypan blue dye exclusion and leucocytes were counted by fluorescence microscopy after incubation with acridine orange. Maturity of buccal cells was assessed by staining buccal smears for morphology according to Papanicolaou (Whitacker D and Williams V, 1994). Eight healthy volunteers served as controls. The mean percentage (+/- s.e.m.) of viable oral epithelial cells was stable in controls (44 +/- 2%). In patients, they increased after HD-CT, which was significant after day 7 compared with pretreatment (P < or = 0.05). In addition, a shift from mature to immature epithelial cells in buccal smears was observed. Oral leucocyte levels were closely correlated with the blood leucocyte counts. The WHO score followed the results of these other evaluations with some delay. The viability of buccal cells obtained by oral washings increases after HD-CT. This is possibly because of desquamation of the upper oral mucosa layer, with a shift from mature to more immature cells. These data can be quantitated, and this assay may therefore be useful in studies aimed at prevention of mucositis

Point process model of 1/f noise versus a sum of Lorentzians

We present a simple point process model of $1/f^{\beta}$ noise, covering different values of the exponent $\beta$. The signal of the model consists of pulses or events. The interpulse, interevent, interarrival, recurrence or waiting times of the signal are described by the general Langevin equation with the multiplicative noise and stochastically diffuse in some interval resulting in the power-law distribution. Our model is free from the requirement of a wide distribution of relaxation times and from the power-law forms of the pulses. It contains only one relaxation rate and yields $1/f^ {\beta}$ spectra in a wide range of frequency. We obtain explicit expressions for the power spectra and present numerical illustrations of the model. Further we analyze the relation of the point process model of $1/f$ noise with the Bernamont-Surdin-McWhorter model, representing the signals as a sum of the uncorrelated components. We show that the point process model is complementary to the model based on the sum of signals with a wide-range distribution of the relaxation times. In contrast to the Gaussian distribution of the signal intensity of the sum of the uncorrelated components, the point process exhibits asymptotically a power-law distribution of the signal intensity. The developed multiplicative point process model of $1/f^{\beta}$ noise may be used for modeling and analysis of stochastic processes in different systems with the power-law distribution of the intensity of pulsing signals.Comment: 23 pages, 10 figures, to be published in Phys. Rev.

Parameter estimation in spatially extended systems: The Karhunen-Loeve and Galerkin multiple shooting approach

Parameter estimation for spatiotemporal dynamics for coupled map lattices and continuous time domain systems is shown using a combination of multiple shooting, Karhunen-Loeve decomposition and Galerkin's projection methodologies. The resulting advantages in estimating parameters have been studied and discussed for chaotic and turbulent dynamics using small amounts of data from subsystems, availability of only scalar and noisy time series data, effects of space-time parameter variations, and in the presence of multiple time-scales.Comment: 11 pages, 5 figures, 4 Tables Corresponding Author - V. Ravi Kumar, e-mail address: [email protected]

Quantitative analysis by renormalized entropy of invasive electroencephalograph recordings in focal epilepsy

Invasive electroencephalograph (EEG) recordings of ten patients suffering from focal epilepsy were analyzed using the method of renormalized entropy. Introduced as a complexity measure for the different regimes of a dynamical system, the feature was tested here for its spatio-temporal behavior in epileptic seizures. In all patients a decrease of renormalized entropy within the ictal phase of seizure was found. Furthermore, the strength of this decrease is monotonically related to the distance of the recording location to the focus. The results suggest that the method of renormalized entropy is a useful procedure for clinical applications like seizure detection and localization of epileptic foci.Comment: 10 pages, 5 figure

The nature of the intranight variability of radio-quiet quasars

We select a sample of 10 radio-quiet quasars with confirmed intranight optical variability and with available X-ray data. We compare the variability properties and the broad band spectral constraints to the predictions of intranight variability by three models: (i) irradiation of an accretion disk by a variable X-ray flux (ii) an accretion disk instability (iii) the presence of a weak blazar component. We concluded that the third model, e.g. the blazar component model, is the most promising if we adopt a cannonball model for the jet variable emission. In this case, the probability of detecting the intranight variability is within 20-80%, depending on the ratio of the disk to the jet optical luminosity. Variable X-ray irradiation mechanism is also possible but only under additional requirement: either the source should have a very narrow Hbeta line or occasional extremely strong flares should appear at very large disk radii.Comment: MNRAS (in press