Distinguishing the noise and attractor strength of coordinated limb movements using recurrence analysis

The variability of coupled rhythmic limb movements is assumed to be a consequence of the strength of a movement’s attractor dynamic and a constant stochastic noise process that continuously perturbs the movement system away from this dynamic. Recently, it has been suggested that the nonlinear technique of recurrence analysis can be used to index the effects of noise and attractor strength on movement variability. To test this, three experiments were conducted in which the attractor strength of bimanual wrist-pendulum movements (using coordination mode, movement frequency and detuning), as well as the magnitude of stochastic perturbations affecting the variability of these movements (using a temporally fluctuating visual metronome) was manipulated. The results of these experiments demonstrate that recurrence analysis can index parametric changes in the attractor strength of coupled rhythmic limb movements and the magnitude of metronome induced stochastic perturbations independently. The results of Experiments 1 and 2 also support the claim that differences between the variability of inphase and antiphase coordination, and between slow and fast movement frequencies are due to differences in attractor strength. In contrast to the standard assumption that the noise that characterizes interlimb coordination remains constant for different magnitudes of detuning (Δ ω) the results of Experiment 3 suggest that the magnitude of noise increases with increases in |Δ ω|.     

Third-order reverse correlation analysis of muscle spindle primary afferent fiber responses to random muscle stretch

 The response of primary muscle spindle afferent fibers to muscle stretch is nonlinear. Now spindle responses (trains of action potentials) to band-limited Gaussian white noise length perturbations of the gastrocnemius muscles (input signal) are described in cats. The input noise upper cutoff frequency was clearly above the frequency range of physiological length changes in cat hindleg muscles. The input–output relation was analyzed by means of peri-spike averages (PSAs), which could be shown to correspond to the kernels of Wiener’s white noise approach to systems identification. The present approach (the reverse correlation analysis) was applied up to the third order. An experiment consisted of two recordings: one (the source recording) to determine PSAs and the other (the test recording) to provide an input signal for predicting responses. The predictions of different orders were compared with the actual neuronal response (the observation) of the test recording. Four different approximation procedures were developed to adapt prediction and observation and to determine weighting factors for the predictions of different orders. The approximations also yielded the value of the power density P of the input noise signal: at a variety of stimulus parameters, P from approximations had the same magnitude as P determined directly from the input signal amplitude spectrum. The prediction of a sequence of action potentials improved the higher the order of components. 37 of 42 action potentials of a test recording (the observation) could be confidently predicted from PSAs or kernels. Compared with the size of the linear first-order prediction curve, the relative sizes of the second and third-order prediction curves were: 1.0 : 0.47 : 0.26. Received: 15 November 1994/Accepted in revised form: 23 May 1995     

Neuronal precision and the limits for acoustic signal recognition in a small neuronal network

Recognition of acoustic signals may be impeded by two factors: extrinsic noise, which degrades sounds before they arrive at the receiver’s ears, and intrinsic neuronal noise, which reveals itself in the trial-to-trial variability of the responses to identical sounds. Here we analyzed how these two noise sources affect the recognition of acoustic signals from potential mates in grasshoppers. By progressively corrupting the envelope of a female song, we determined the critical degradation level at which males failed to recognize a courtship call in behavioral experiments. Using the same stimuli, we recorded intracellularly from auditory neurons at three different processing levels, and quantified the corresponding changes in spike train patterns by a spike train metric, which assigns a distance between spike trains. Unexpectedly, for most neurons, intrinsic variability accounted for the main part of the metric distance between spike trains, even at the strongest degradation levels. At consecutive levels of processing, intrinsic variability increased, while the sensitivity to external noise decreased. We followed two approaches to determine critical degradation levels from spike train dissimilarities, and compared the results with the limits of signal recognition measured in behaving animals.     

Computational model for perception of objects and motions

Perception of objects and motions in the visual scene is one of the basic problems in the visual system. There exist ‘What’ and ‘Where’ pathways in the superior visual cortex, starting from the simple cells in the primary visual cortex. The former is able to perceive objects such as forms, color, and texture, and the latter perceives ‘where’, for example, velocity and direction of spatial movement of objects. This paper explores brain-like computational architectures of visual information processing. We propose a visual perceptual model and computational mechanism for training the perceptual model. The computational model is a three-layer network. The first layer is the input layer which is used to receive the stimuli from natural environments. The second layer is designed for representing the internal neural information. The connections between the first layer and the second layer, called the receptive fields of neurons, are self-adaptively learned based on principle of sparse neural representation. To this end, we introduce Kullback-Leibler divergence as the measure of independence between neural responses and derive the learning algorithm based on minimizing the cost function. The proposed algorithm is applied to train the basis functions, namely receptive fields, which are localized, oriented, and bandpassed. The resultant receptive fields of neurons in the second layer have the characteristics resembling that of simple cells in the primary visual cortex. Based on these basis functions, we further construct the third layer for perception of what and where in the superior visual cortex. The proposed model is able to perceive objects and their motions with a high accuracy and strong robustness against additive noise. Computer simulation results in the final section show the feasibility of the proposed perceptual model and high efficiency of the learning algorithm.     

Ontogenetic divergence of growth among rainbow smelt morphotypes

Multiple, sympatric morphotypes of rainbow smelt (Osmerus mordax) are known in Lake Utopia, New Brunswick. The largest, ‘giant’ form is predominantly a piscivore, the smaller, ‘dwarf’ form are predominantly planktivores, and there is an intermediate body-sized form. The forms exhibit some genetic variability, but it is body size that best defines morphotypes, trophic status, and spawning behaviour. We compared egg size, spawning date, incubation time, size at hatching, and daily and annual growth to determine when divergence in body size occurs among morphotypes. Giant form larvae hatched earlier and grew faster during their first year. Dwarf and intermediate form larvae displayed inter-annual variability in degree of overlap and divergence in growth which occurred in their first growing season or at age 1+ or 2+. We conclude that earlier hatching, early growth trajectories, and later niche shifting are linked to the persistence of morphotypes, i.e., the process is controlled by the environment and sustained to some degree by spawning segregation.     

Spatially distributed stochasticity and the constancy of ecosystems

Ifconstancy is a measure of an ecosystem's (in) variability through time andstability is a measure of the system's ability to damp and recover from environmental perturbations, then constancy depends not only on stability but also on the frequency and amplitude of perturbations—theenvironmental “noise level”. The stability of an ecosystem reflects its texture, extent, and viscosity (fine-scale structure); the noise level experienced by the system (“effective” noise level) reflects the level at any point (“ambient” noise level), the spectrum of stochastic scale (regional distribution of stochasticity), and the system's spatial extent (size, or number of patches included). The coefficient of variation of a limiting stochastic variate is a measure of the effective noise level. Ifp is the total number of patches in the system (its extent) andn is the number of contiguous patches with noise signals correlated through time (its stochastic scale), then the coefficient of variation is directly proportional to whenevern<p. Thus ecosystems of small stochastic scalen or large sizep damp out environmental noise by “spreading the risk” in space, thereby reducing their variability in time.     

Comments on ‘Is Partial Coherence a Viable Technique for Identifying Generators of Neural Oscillations?’

To aid prospective neural connectivity inference analysts and hoping to preclude misconception spread, we exploit the didatic value of some of the issues raised by Albo et al. (Biol Cybern 90: 318–326, 2004) who claim that signal-to-noise ratio (SNR) values can lead to mistakes in structural inference when using partial coherence in connection to Gersch’s 1970 method for spotting signal sources (Gersch in Math Biosci 14: 177– 196, 1972). We show theoretically that Gersch’s method is able only to spot which measurement of some common underlying factor has the least amount of additive noise and that this has nothing to do with any reasonable notion of ‘causality’ as suggested by Albo et al. (Biol Cybern 90: 318–326, 2004). We also show that despite the inherent structural ambiguity of the model used by Albo et al. (Biol Cybern 90: 318–326, 2004) to back their claim, its data can nonetheless furnish the correct time precedence hierarchy between the activities in its measured structures, both when simple (correlation) and more sophisticated methods are used (partial directed coherence) (Baccala and Sameshima in Biol Cybern 84:463–474, 2001a) in a true depiction of time series causality.     

Latitudinal clines in<Emphasis Type="Italic">Drosophila melanogaster</Emphasis>: Body size,allozyme frequencies,inversion frequencies,and the insulin-signalling pathway

Many latitudinal clines exist inDrosophila melanogaster: in adult body size, in allele frequency at allozyme loci, and in frequencies of common cosmopolitan inversions. The question is raised whether these latitudinal clines are causally related. This review aims to connect data from two very different fields of study, evolutionary biology and cell biology, in explaining such natural genetic variation inD. melanogaster body size and development time. It is argued that adult body size clines, inversion frequency clines, and clines in allele frequency at loci involved in glycolysis and glycogen storage are part of the same adaptive strategy. Selection pressure is expected to differ at opposite ends of the clines. At high latitudes, selection onD. melanogaster would favour high larval growth rate at low temperatures, and resource storage in adults to survive winter. At low latitudes selection would favour lower larval critical size to survive crowding, and increased male activity leading to high male reproductive success. Studies of the insulin-signalling pathway inD. melanogaster point to the involvement of this pathway in metabolism and adult body size. The genes involved in the insulin-signalling pathway are associated with common cosmopolitan inversions that show latitudinal clines. Each chromosome region connected with a large common cosmopolitan inversion possesses a gene of the insulin transmembrane complex, a gene of the intermediate pathway and a gene of the TOR branch. The hypothesis is presented that temperateD. melanogaster populations have a higher frequency of a ’thrifty’ genotype corresponding to high insulin level or high signal level, while tropical populations possess a more ’spendthrift’ genotype corresponding to low insulin or low signal level.     

Non-visual environmental imaging and object detection through active electrolocation in weakly electric fish

Weakly electric fish orient at night by employing active electrolocation. South American and African species emit electric signals and perceive the consequences of these emissions with epidermal electroreceptors. Objects are detected by analyzing the electric images which they project onto the animal’s electroreceptive skin surface. Electric images depend on size, distance, shape, and material of objects and on the morphology of the electric organ and the fish’s body. It is proposed that the mormyrid Gnathonemus petersii possesses two electroreceptive “foveae” at its Schnauzenorgan and its nasal region, both of which resemble the visual fovea in the retina of many animals in design, function, and behavioral use. Behavioral experiments have shown that G. petersii can determine the resistive and capacitive components of an object’s complex impedance in order to identify prey items during foraging. In addition, fish can measure the distance and three-dimensional shape of objects. In order to determine object properties during active electrolocation, the fish have to determine at least four parameters of the local signal within an object’s electric image: peak amplitude, maximal slope, image width, and waveform distortions. A crucial parameter is the object distance, which is essential for unambiguous evaluation of object properties.     

Mathematical modeling and parameter estimation of axonal cargo transport

This paper is about how cortical recurrent interactions in primary visual cortex (V1) together with feedback from extrastriate cortex can account for spectral peaks in the V1 local field potential (LFP). Recent studies showed that visual stimulation enhances the γ-band (25–90 Hz) of the LFP power spectrum in macaque V1. The height and location of the γ-band peak in the LFP spectrum were correlated with visual stimulus size. Extensive spatial summation, possibly mediated by feedback connections from extrastriate cortex and long-range horizontal connections in V1, must play a crucial role in the size dependence of the LFP. To analyze stimulus-effects on the LFP of V1 cortex, we propose a network model for the visual cortex that includes two populations of V1 neurons, excitatory and inhibitory, and also includes feedback to V1 from extrastriate cortex. The neural network model for V1 was a resonant system. The model’s resonance frequency (ResF) was in the γ-band and varied up or down in frequency depending on cortical feedback. The model’s ResF shifted downward with stimulus size, as in the real cortex, because increased size recruited more activity in extrastriate cortex and V1 thereby causing stronger feedback. The model needed to have strong local recurrent inhibition within V1 to obtain ResFs that agree with cortical data. Network resonance as a consequence of recurrent excitation and inhibition appears to be a likely explanation for γ-band peaks in the LFP power spectrum of the primary visual cortex.     

Spatial coherence and stationarity of local field potentials in an isolated whole hippocampal preparation <Emphasis Type="Italic">in vitro</Emphasis>

Local field potential (LFP) multielectrode recordings of spontaneous rhythms in an isolated whole hippocampal preparation are characterized with respect to their spatial variability within the hippocampus, and their frequency properties. Using simulated data, we categorize potential relationships between frequency variation over time in LFP recordings and spatial variability between electrodes. We then use data recorded from the intact preparation to distinguish between our theoretical categories. We find that the LFP recordings have a close to spatially invariant frequency distribution (not phase) across the hippocampus, and differ in frequency only in a component that may be seen as physiological noise. From these facts, we conclude that the isolated hippocampal LFP recordings represent a single signal and may be regarded as a unitary circuitry. We additionally examine phase differences across our recording sites. We use our characterization of the hippocampal isolate’s properties to predict its spatial coherence in response to high frequency stimulation. We find that there is a finely tuned inverse relationship between temporal variability in the hippocampal isolate’s LFP recordings and their spatial coherence.     

Relative spike time coding and STDP-based orientation selectivity in the early visual system in natural continuous and saccadic vision: a computational model

We have built a phenomenological spiking model of the cat early visual system comprising the retina, the Lateral Geniculate Nucleus (LGN) and V1’s layer 4, and established four main results (1) When exposed to videos that reproduce with high fidelity what a cat experiences under natural conditions, adjacent Retinal Ganglion Cells (RGCs) have spike-time correlations at a short timescale (~30 ms), despite neuronal noise and possible jitter accumulation. (2) In accordance with recent experimental findings, the LGN filters out some noise. It thus increases the spike reliability and temporal precision, the sparsity, and, importantly, further decreases down to ~15 ms adjacent cells’ correlation timescale. (3) Downstream simple cells in V1’s layer 4, if equipped with Spike Timing-Dependent Plasticity (STDP), may detect these fine-scale cross-correlations, and thus connect principally to ON- and OFF-centre cells with Receptive Fields (RF) aligned in the visual space, and thereby become orientation selective, in accordance with Hubel and Wiesel (Journal of Physiology 160:106–154, 1962) classic model. Up to this point we dealt with continuous vision, and there was no absolute time reference such as a stimulus onset, yet information was encoded and decoded in the relative spike times. (4) We then simulated saccades to a static image and benchmarked relative spike time coding and time-to-first spike coding w.r.t. to saccade landing in the context of orientation representation. In both the retina and the LGN, relative spike times are more precise, less affected by pre-landing history and global contrast than absolute ones, and lead to robust contrast invariant orientation representations in V1.     

Binocular fusion in Panum’s limiting case of stereopsis obeys the uniqueness constraint

In the information processing procedure of stereo vision, the uniqueness constraint has been used as one of the constraints to solve the “correspondence problem”. While the uniqueness constraint is valid in most cases, whether it is still valid in some particular stimulus configuration (such as Panum’s limiting case) has been a problem of widespread debate for a long time. To investigate the problem, we adopted the Panum’s limiting case as its basic stimulus configuration, and delved into the phenomenon of binocular fusion from two distinct aspects: visual direction and orientation disparity. The results show that in Panum’s limiting case binocular fusion does not comply with the rules governing regular binocular fusion as far as visual direction and orientation disparity are concerned. This indicates that double fusion does not happen in Panum’s limiting case and that the uniqueness constraint is still valid.     

Binding and segmentation of multiple objects through neural oscillators inhibited by contour information

 Temporal correlation of neuronal activity has been suggested as a criterion for multiple object recognition. In this work, a two-dimensional network of simplified Wilson-Cowan oscillators is used to manage the binding and segmentation problem of a visual scene according to the connectedness Gestalt criterion. Binding is achieved via original coupling terms that link excitatory units to both excitatory and inhibitory units of adjacent neurons. These local coupling terms are time independent, i.e., they do not require Hebbian learning during the simulations. Segmentation is realized by a two-layer processing of the visual image. The first layer extracts all object contours from the image by means of “retinal cells” with an “on-center” receptive field. Information on contour is used to selectively inhibit Wilson-Cowan oscillators in the second layer, thus realizing a strong separation among neurons in different objects. Accidental synchronism between oscillations in different objects is prevented with the use of a global inhibitor, i.e., a global neuron that computes the overall activity in the Wilson-Cowan network and sends back an inhibitory signal. Simulations performed in a 50×50 neural grid with 21 different visual scenes (containing up to eight objects + background) with random initial conditions demonstrate that the network can correctly segment objects in almost 100% of cases using a single set of parameters, i.e., without the need to adjust parameters from one visual scene to the next. The network is robust with reference to dynamical noise superimposed on oscillatory neurons. Moreover, the network can segment both black objects on white background and vice versa and is able to deal with the problem of “fragmentation.” The main limitation of the network is its sensitivity to static noise superimposed on the objects. Overcoming this problem requires implementation of more robust mechanisms for contour enhancement in the first layer in agreement with mechanisms actually realized in the visual cortex. Received: 25 October 2001 / Accepted: 26 February 2003 / Published online: 20 May 2003 Correspondence to: Mauro Ursino (e-mail: mursino@deis.unibo.it, Tel.: +39-051-2093008, Fax: +39-051-2093073)     

On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics

During an adaptive immune response, lymphocytes proliferate for five to twenty-five cell divisions, then stop and die over a period of weeks. Based on extensive flow cytometry data, Hawkins et al. (Proc Natl Acad Sci USA 104:5032–5037, 2007) introduced a cell-level stochastic model of lymphocyte population dynamics, called the Cyton Model, that accurately captures mean lymphocyte population size as a function of time. In Subramanian et al. (J Math Biol 56(6):861–892, 2008), we performed a branching process analysis of the Cyton Model and deduced from parameterizations for in vitro and in vivo data that the immune response is predictable despite each cell’s fate being highly variable. One drawback of flow cytometry data is that individual cells cannot be tracked, so that it is not possible to investigate dependencies in the fate of cells within family trees. In the absence of this information, while the Cyton Model abandons one of the usual assumptions of branching processes (the independence of lifetime and progeny number), it adopts another of the standard branching processes hypotheses: that the fates of progeny are stochastically independent. However, new experimental observations of lymphocytes show that the fates of cells in the same family tree are not stochastically independent. Hawkins et al. (2008, submitted) report on ciné lapse photography experiments where every founding cell’s family tree is recorded for a system of proliferating lymphocytes responding to a mitogenic stimulus. Data from these experiments demonstrate that the death-or-division fates of collaterally consanguineous cells (those in the same generation within a founding cell’s family tree) are strongly correlated, while there is little correlation between cells of distinct generations and between cells in distinct family trees. As this finding contrasts with one of the assumptions of the Cyton Model, in this paper we introduce three variants of the Cyton Model with increasing levels of collaterally consanguineous correlation structure to incorporate these new found dependencies. We investigate their impact on the predicted expected variability of cell population size. Mathematically we conclude that while the introduction of correlation structure leaves the mean population size unchanged from the Cyton Model, the variance of the population size distribution is typically larger. Biologically, through comparison of model predictions for Cyton Model parameterizations determined by in vitro and in vivo experiments, we deduce that if collaterally consanguineous correlation extends beyond cousins, then the immune response is less predictable than would be concluded from the original Cyton Model. That is, some of the variability seen in data that we previously attributed to experimental error could be due to intrinsic variability in the cell population size dynamics.      

Wide-field, motion-sensitive neurons and matched filters for optic flow fields

 The receptive field organization of a class of visual interneurons in the fly brain (vertical system, or VS neurons) shows a striking similarity to certain self-motion-induced optic flow fields. The present study compares the measured motion sensitivities of the VS neurons (Krapp et al. 1998) to a matched filter model for optic flow fields generated by rotation or translation. The model minimizes the variance of the filter output caused by noise and distance variability between different scenes. To that end, prior knowledge about distance and self-motion statistics is incorporated in the form of a “world model”. We show that a special case of the matched filter model is able to predict the local motion sensitivities observed in some VS neurons. This suggests that their receptive field organization enables the VS neurons to maintain a consistent output when the same type of self-motion occurs in different situations. Received: 14 June 1999 / Accepted in revised form: 20 March 2000     

Evaluation of Analytical Techniques to Predict Viability after Cryopreservation

Preservation of plant germplasm is important to safeguard biodiversity and to store elite plants. Cryopreservation is one of the possible preservation techniques. Research for a cryopreservation protocol is often inefficient because of slow or poor regrowth of plant material. Therefore, at least one technique, that allows a quick and accurate prognosis of viability after cryopreservation, is required. We evaluated five techniques: electrolyte leakage, triphe-nyltetrazoliumchloride (TTC) staining (visual and spectrophotometrical analysis), malondialdehyde concentrations in plant tissue and a mathematical model that relates ‘water content’ to the weight of encapsulated plant material. Electrolyte leakage and TTC-staining (if visually analysed) are efficient to predict viability. Our mathematical model allows us to save time and plant material in order to develop an efficient encapsulation—dehydration protocol. All other techniques were rejected because of the high variability of the results. This is due to the variability of biochemical activity in plant tissue and the small amount of tissue used in the experiments.     

Effects of Music on the Recovery of Autonomic and Electrocortical Activity After Stress Induced by Aversive Visual Stimuli

The purpose of this study was to compare the effects of music and white noise on the recovery of physiological measures after stressful visual stimulation. Twenty-nine participants took part in the experiment. Visual stimulation with slides eliciting disgust was followed by subjectively pleasant music, sad music, and white noise in three consecutive sessions. The spectral power of the frontal and temporal EEG, skin conductance, heart rate, heart period variability, facial capillary blood flow, and respiration rate were recorded and analyzed. Aversive visual stimulation evoked heart rate deceleration, increased high frequency component of heart period variability, increased skin conductance level and skin conductance response frequency, decreased facial blood flow and velocity, decreased temporal slow alpha and increased frontal fast beta power in all three sessions. Both subjectively pleasant and sad music led to the restoration of baseline levels on most parameters; while white noise did not enhance the recovery process. The effects of pleasant music on post-stress recovery, when compared to white noise, were significantly different on heart rate, respiration rate, and peripheral blood flow. Both positive and negative music exerted positive modulatory effects on cardiovascular and respiratory activity, namely increased heart rate, balanced heart period variability, increased vascular blood flow and respiration rate during the post-stress recovery. Data only partially supported the “undoing” hypothesis, which states that positive emotions may facilitate the process of physiological recovery following negative emotions.     

The use of self-pollinated progenies as ’in-groups’ for the genetic characterization of cocoa germplasm

Theobroma cacao ) genotypes. Six primers were sufficient to distinguish all but three pairs of the 62 accessions examined. A UPGMA dendrogram was used to provide a measure of the genetic variability between genotypes. The scale was supplied by the inclusion of Theobroma grandiflora as an ’out group’ and also by the use of two contrasting progenies as ’in groups’. The ’in groups’ were obtained from the self-pollination of one plant (SPEC 54.1) known to be highly homozygous and also of a second, highly heterozygous, clone (P 19B). These reference points allowed several documentation errors to be resolved and provided a basis for identifying unwanted or low-priority material. Implications of the work for the routine maintenance of large germplasm collections are briefly discussed. Received: 20 January 1999 / Accepted: 25 May 1999     

Temporal coding in vision: coding by the spike arrival times leads to oscillations in the case of moving targets

The ‘oscillations’ which have been observed in the visual cortex of cats and monkeys in the case of moving targets are discussed in relation to a temporal coding based on the arrival times of spikes or bursts. A decoding process for this temporal coding is proposed in which neurons work in a correlator mode. In the case of motion analysis, periodic resetting is needed to avoid information jamming. This resetting is proposed to be responsible for the ‘oscillations’. Good initial synchronization is required for the decoding process to be performed efficiently. A diffusive process based on interdendritic ionic currents is proposed and shown to operate efficiently, without any loss of spatial and temporal resolving powers. Received: 2 June 1994 / Accepted in revised form: 23 January 1996