Comparison of Amersham and Agilent microarray technologies through quantitative noise analysis

We carried out a series of replicate experiments on DNA microarrays using two cell lines and two technologies--the Agilent Human 1A Microarray and the GE Amersham Codelink Uniset Human 20K I Bioarray. We demonstrated that quantifying the noise level as a function of signal strength allows identification of the absolute and differential mRNA expression levels at which biological variability can be resolved above measurement noise. This represents a new formulation of a sensitivity threshold that can be used to compare platforms. It was found that the correlation in expression level between platforms is considerably worse than the correlation between replicate measurements taken using the same platform. In addition, we carried out replicate measurements at different stages of sample processing. This novel approach enables us to quantify the noise introduced into the measurements at each step of the experimental protocol. We demonstrated how this information can be used to determine the most efficient means of using replicates to reduce experimental uncertainty.     

Registration of pedobarographic image data in the frequency domain

Image registration has been used to support pixel-level data analysis on pedobarographic image data sets. Some registration methods have focused on robustness and sacrificed speed, but a recent approach based on external contours offered both high computational processing speed and high accuracy. However, since contours can be influenced by local perturbations, we sought more global methods. Thus, we propose two new registration methods based on the Fourier transform, cross-correlation and phase correlation which offer high computational speed. We found out that both proposed methods revealed high accuracy for the similarity measures considered, using control geometric transformations. Additionally, both methods revealed high computational processing speed which, combined with their accuracy and robustness, allows their implementation in near-real-time applications. Furthermore, we found that the current methods were robust to moderate levels of noise, and consequently, do not require noise removal procedure like the contours method does.     

Relating priming and repetition suppression

We present a prototype of a recently proposed two stage model of the entorhinal-hippocampal loop. Our aim is to form a general computational model of the sensory neocortex. The model--grounded on pure information theoretic principles--accounts for the most characteristic features of long-term memory (LTM), performs bottom-up novelty detection, and supports noise filtering. Noise filtering can also serve to correct the temporal ordering of information processing. Surprisingly, as we examine the temporal characteristics of the model, the emergent dynamics can be interpreted as perceptual priming, a fundamental type of implicit memory. In the model's framework, computational results support the hypothesis of a strong correlation between perceptual priming and repetition suppression and this correlation is a direct consequence of the temporal ordering in forming the LTM. We also argue that our prototype offers a relatively simple and coherent explanation of priming and its relation to a general model of information processing by the brain.     

Reducing noise in computed correlation functions using techniques from signal processing

Time correlation functions invariably suffer from random noise, especially at longer time intervals for which fewer data pairs are available. This noise is particularly of concern when calculating correlations that cannot be averaged over per-molecule contributions, such as stress in molecular simulations. In this work, a set of methods based in signal processing has been developed to reduce the inherent noise that is present in time- and frequency-domain representations of correlation functions. The stress time autocorrelation function, which leads to stress relaxation modulus and complex modulus, is used as an example. The difference between initial and final values of a time correlation function over a finite time domain is found to create so-called ‘leakage’ of noise from disallowed into harmonic frequencies during fast Fourier transformation. Decreasing this leakage effect through reflection to negative time and through applying a window function reduces noise levels significantly. Removing frequency components of insignificant magnitudes also provides significant noise reduction. Applying moving averages in the frequency and time domains also contributes to noise reduction. Specific results obtained by applying these methods to a model asphalt system enable more clear physical interpretations of the underlying relaxations after dramatic noise level reductions were attained.     

Statistical analysis of fluorescence correlation spectroscopy: the standard deviation and bias

We present a detailed statistical analysis of fluorescence correlation spectroscopy for a wide range of timescales. The derivation is completely analytical and can provide an excellent tool for planning and analysis of FCS experiments. The dependence of the signal-to-noise ratio on different measurement conditions is extensively studied. We find that in addition to the shot noise and the noise associated with correlated molecular dynamics there is another source of noise that appears at very large lag times. We call this the "particle noise," as its behavior is governed by the number of particles that have entered and left the laser beam sample volume during large dwell times. The standard deviations of all the points on the correlation function are calculated analytically and shown to be in good agreement with experiments. We have also investigated the bias associated with experimental correlation function measurements. A "phase diagram" for FCS experiments is constructed that demonstrates the significance of the bias for any given experiment. We demonstrate that the value of the bias can be calculated and added back as a first-order correction to the experimental correlation function.     

A correlational analysis of electroencephalograms based on the modeling of biopotentials of the cerebral cortex

Our previous study on the quantitative nonlinear analysis of integral equations of the averaged membrane potentials in excitatory (the EEG analogue) and inhibitory neurons of the neocortex has shown that the characteristic equation has a set of oscillating solutions with negative decrements in the stability region. We have shown that an electroencephalogram can be represented as a convolution of harmonic functions with negative decrements and discrete (uniformly discontinuous) white Gaussian noise. We have suggested methods of decrement calculation in encephalograms using correlation functions and tested them on both modeled processes with preset parameters and actual encephalograms of rats and mice. Investigation of decrements and amplitude-frequency parameters potentially increases the capacity of spectral correlation analysis of electroencephalograms and expands the results of mathematical processing of brain signals.     

Aperiodic stochastic resonance in neural information processing with Gaussian colored noise

The aim of this paper is to explore the phenomenon of aperiodic stochastic resonance in neural systems with colored noise. For nonlinear dynamical systems driven by Gaussian colored noise, we prove that the stochastic sample trajectory can converge to the corresponding deterministic trajectory as noise intensity tends to zero in mean square, under global and local Lipschitz conditions, respectively. Then, following forbidden interval theorem we predict the phenomenon of aperiodic stochastic resonance in bistable and excitable neural systems. Two neuron models are further used to verify the theoretical prediction. Moreover, we disclose the phenomenon of aperiodic stochastic resonance induced by correlation time and this finding suggests that adjusting noise correlation might be a biologically more plausible mechanism in neural signal processing.     

Noise Reduction in Electron Tomographic Reconstructions Using Nonlinear Anisotropic Diffusion

Electron tomography is a powerful technique capable of giving unique insights into the three-dimensional structural organization of pleomorphic biological objects. However, visualization and interpretation of the resulting volumetric data are hampered by an extremely low signal-to-noise ratio, especially when ice-embedded biological specimens are investigated. Usually, isosurface representation or volume rendering of such data is hindered without any further signal enhancement. We propose a novel technique for noise reduction based on nonlinear anisotropic diffusion. The approach combines efficient noise reduction with excellent signal preservation and is clearly superior to conventional methods (e.g., low-pass and median filtering) and invariant wavelet transform filtering. The gain in the signal-to-noise ratio is verified and demonstrated by means of Fourier shell correlation. Improved visualization performance after processing the 3D images is demonstrated with two examples, tomographic reconstructions of chromatin and of a mitochondrion. Parameter settings and discretization stencils are presented in detail.     

Noise and correlations in parallel perceptual decision making

Perceptual decisions involve the accumulation of sensory evidence over time, a process that is corrupted by noise [1]. Here, we extend the decision-making framework to crossmodal research [2, 3] and the parallel processing of two distinct signals presented to different sensory modalities like vision and audition. Contrary to the widespread view that multisensory signals are integrated prior to a single decision [4-10], we show that evidence is accumulated for each signal separately and that consequent decisions are flexibly coupled by logical operations. We find that the strong correlation of response latencies from trial to trial is critical to explain the short latencies of multisensory decisions. Most critically, we show that increased noise in multisensory decisions is needed to explain the mean and the variability of response latencies. Precise knowledge of these key factors is fundamental for the study and understanding of parallel decision processes with multisensory signals.     

Efficient temporal processing of naturalistic sounds

In this study, we investigate the ability of the mammalian auditory pathway to adapt its strategy for temporal processing under natural stimulus conditions. We derive temporal receptive fields from the responses of neurons in the inferior colliculus to vocalization stimuli with and without additional ambient noise. We find that the onset of ambient noise evokes a change in receptive field dynamics that corresponds to a change from bandpass to lowpass temporal filtering. We show that these changes occur within a few hundred milliseconds of the onset of the noise and are evident across a range of overall stimulus intensities. Using a simple model, we illustrate how these changes in temporal processing exploit differences in the statistical properties of vocalizations and ambient noises to increase the information in the neural response in a manner consistent with the principles of efficient coding.     

Noise in the nervous system

Noise--random disturbances of signals--poses a fundamental problem for information processing and affects all aspects of nervous-system function. However, the nature, amount and impact of noise in the nervous system have only recently been addressed in a quantitative manner. Experimental and computational methods have shown that multiple noise sources contribute to cellular and behavioural trial-to-trial variability. We review the sources of noise in the nervous system, from the molecular to the behavioural level, and show how noise contributes to trial-to-trial variability. We highlight how noise affects neuronal networks and the principles the nervous system applies to counter detrimental effects of noise, and briefly discuss noise's potential benefits.     

Investigation of a two-point maximum entropy regularization method for signal enhancement applied to magnetoencephalography data

A two-point maximum entropy method (TPMEM) was investigated for post-acquisition signal recovery in magnetoencephalography (MEG) data, as a potential replacement of a low-pass (LP) filtering technique currently in use. We first applied TPMEM and the LP filter for signal recovery of synthetically noise corrupted MEG “phantom” data sets in which the true underlying signal was known. Results were quantified with the use of visual plots, percent error histograms, and the statistical parameters root mean squared error and Pearson’s correlation coefficient. Synthetically noise corrupted data from a simulated magnetic dipole was used to quantify the improvements gained in using TPMEM over LP filters in reconstructing known dipole parameters such as position, orientation, and magnitude. Finally, we applied TPMEM and LP filters to a sample MEG patient data set. Our results show that TPMEM has improved noise-reduction and signal recovery capabilities than those of the LP filter, and furthermore data processed with TPMEM shows less error in the reconstructed dipole parameters. We propose that TPMEM can be used for MEG signal processing, resulting in improved MEG source characterization.     

Do neocortical pyramidal neurons display stochastic resonance?

Neocortical pyramidal neurons in vivo are subject to an intense synaptic background activity that has a significant impact on various electrophysiological properties and dendritic integration. Using detailed biophysical models of a morphologically reconstructed neocortical pyramidal neuron, in which synaptic background activity was simulated according to recent measurements in cat parietal cortex in vivo, we show that the responsiveness of the cell to additional periodic subthreshold stimuli can be significantly enhanced through mechanisms similar to stochastic resonance. We compare several paradigms leading to stochastic resonance-like behavior, such as varying the strength or the correlation in the background activity. A new type of resonance-like behavior was obtained when the correlation was varied, in which case the responsiveness is sensitive to the statistics rather than the strength of the noise. We suggest that this type of resonance may be relevant to information processing in the cerebral cortex.     

Noise affects the shape of female preference functions for acoustic signals

The shape of female mate preference functions influences the speed and direction of sexual signal evolution. However, the expression of female preferences is modulated by interactions between environmental conditions and the female's sensory processing system. Noise is an especially relevant environmental condition because it interferes directly with the neural processing of signals. Although noise is therefore likely a significant force in the evolution of communication systems, little is known about its effects on preference function shape. In the grasshopper Chorthippus biguttulus, female preferences for male calling song characteristics are likely to be affected by noise because its auditory system is sensitive to fine temporal details of songs. We measured female preference functions for variation in male song characteristics in several levels of masking noise and found strong effects of noise on preference function shape. The overall responsiveness to signals in noise generally decreased. Preference strength increased for some signal characteristics and decreased for others, largely corresponding to expectations based on neurophysiological studies of acoustic signal processing. These results suggest that different signal characteristics will be favored under different noise conditions, and thus that signal evolution may proceed differently depending on the extent and temporal patterning of environmental noise.     

Single particle 3D reconstruction for 2D crystal images of membrane proteins

In cases where ultra-flat cryo-preparations of well-ordered two-dimensional (2D) crystals are available, electron crystallography is a powerful method for the determination of the high-resolution structures of membrane and soluble proteins. However, crystal unbending and Fourier-filtering methods in electron crystallography three-dimensional (3D) image processing are generally limited in their performance for 2D crystals that are badly ordered or non-flat. Here we present a single particle image processing approach, which is implemented as an extension of the 2D crystallographic pipeline realized in the 2dx software package, for the determination of high-resolution 3D structures of membrane proteins. The algorithm presented, addresses the low single-to-noise ratio (SNR) of 2D crystal images by exploiting neighborhood correlation between adjacent proteins in the 2D crystal. Compared with conventional single particle processing for randomly oriented particles, the computational costs are greatly reduced due to the crystal-induced limited search space, which allows a much finer search space compared to classical single particle processing. To reduce the considerable computational costs, our software features a hybrid parallelization scheme for multi-CPU clusters and computer with high-end graphic processing units (GPUs). We successfully apply the new refinement method to the structure of the potassium channel MloK1. The calculated 3D reconstruction shows more structural details and contains less noise than the map obtained by conventional Fourier-filtering based processing of the same 2D crystal images.     

Parallel processing by a homogeneous group of coupled model neurons can enhance, reduce and generate signal correlations

 Correlated activities have been proposed as correlates of flexible association and assembly coding. We addressed the basic question of how signal correlations on parallel pathways are enhanced, reduced and generated by homogeneous groups of coupled neurons, and how this depends on the input activities and their interactions with internal coupling processes. For this we simulated a fully connected group of identical impulse-coded neurons with dynamic input and threshold processes and additive or multiplicative lateral coupling. Input signals were Gaussian white noise (GWN), completely independent or partially correlated on a subgroup of the parallel inputs. We show that in states of high average spike rates input-output correlations were weak while the network could generate correlated activities of stochastic, oscillatory and rhythmic bursting types depending exclusively on lateral coupling strength. In states of low average spike rates input-output correlations were high and the network could effectively enhance or reduce differences in spatial correlation applied to its parallel inputs. The correlation differences were more pronounced with multiplicative lateral coupling than with the additive interactions commonly used. As the different modes of correlation processing emerged already by global changes in the average spike rate and lateral coupling strength, we assume that in real cortical circuits changes in correlational processing may also be induced by unspecific modulations of activation and lateral coupling. Received: 11 December 1995 / Accepted in revised form: 29 November 1996     

Interspike interval correlations in neuron models with adaptation and correlated noise

The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel’s time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.     

Predictive coding: a fresh view of inhibition in the retina

Interneurons exhibiting centre--surround antagonism within their receptive fields are commonly found in peripheral visual pathways. We propose that this organization enables the visual system to encode spatial detail in a manner that minimizes the deleterious effects of intrinsic noise, by exploiting the spatial correlation that exists within natural scenes. The antagonistic surround takes a weighted mean of the signals in neighbouring receptors to generate a statistical prediction of the signal at the centre. The predicted value is subtracted from the actual centre signal, thus minimizing the range of outputs transmitted by the centre. In this way the entire dynamic range of the interneuron can be devoted to encoding a small range of intensities, thus rendering fine detail detectable against intrinsic noise injected at later stages in processing. This predictive encoding scheme also reduces spatial redundancy, thereby enabling the array of interneurons to transmit a larger number of distinguishable images, taking into account the expected structure of the visual world. The profile of the required inhibitory field is derived from statistical estimation theory. This profile depends strongly upon the signal: noise ratio and weakly upon the extent of lateral spatial correlation. The receptive fields that are quantitatively predicted by the theory resemble those of X-type retinal ganglion cells and show that the inhibitory surround should become weaker and more diffuse at low intensities. The latter property is unequivocally demonstrated in the first-order interneurons of the fly's compound eye. The theory is extended to the time domain to account for the phasic responses of fly interneurons. These comparisons suggest that, in the early stages of processing, the visual system is concerned primarily with coding the visual image to protect against subsequent intrinsic noise, rather than with reconstructing the scene or extracting specific features from it. The treatment emphasizes that a neuron's dynamic range should be matched to both its receptive field and the statistical properties of the visual pattern expected within this field. Finally, the analysis is synthetic because it is an extension of the background suppression hypothesis (Barlow & Levick 1976), satisfies the redundancy reduction hypothesis (Barlow 1961 a, b) and is equivalent to deblurring under certain conditions (Ratliff 1965).     

Noise Suppression and Surplus Synchrony by Coincidence Detection

The functional significance of correlations between action potentials of neurons is still a matter of vivid debate. In particular, it is presently unclear how much synchrony is caused by afferent synchronized events and how much is intrinsic due to the connectivity structure of cortex. The available analytical approaches based on the diffusion approximation do not allow to model spike synchrony, preventing a thorough analysis. Here we theoretically investigate to what extent common synaptic afferents and synchronized inputs each contribute to correlated spiking on a fine temporal scale between pairs of neurons. We employ direct simulation and extend earlier analytical methods based on the diffusion approximation to pulse-coupling, allowing us to introduce precisely timed correlations in the spiking activity of the synaptic afferents. We investigate the transmission of correlated synaptic input currents by pairs of integrate-and-fire model neurons, so that the same input covariance can be realized by common inputs or by spiking synchrony. We identify two distinct regimes: In the limit of low correlation linear perturbation theory accurately determines the correlation transmission coefficient, which is typically smaller than unity, but increases sensitively even for weakly synchronous inputs. In the limit of high input correlation, in the presence of synchrony, a qualitatively new picture arises. As the non-linear neuronal response becomes dominant, the output correlation becomes higher than the total correlation in the input. This transmission coefficient larger unity is a direct consequence of non-linear neural processing in the presence of noise, elucidating how synchrony-coded signals benefit from these generic properties present in cortical networks.