Stochastic versus deterministic variability in simple neuronal circuits: II. Hippocampal slice.

Long time series of Schaffer collateral to CA1 pyramidal cell presynaptic volleys (stratum radiatum) and population spikes (stratum pyramidale) were evoked (driven) in rat hippocampal slices. From the driven CA1 region in normal [K+] perfusate, both population spike amplitude and an input-output function consisting of population spike amplitude divided by the presynaptic volley amplitude were analyzed. Raising [K+] in the perfusion medium to 8.5 mM, slices were induced to spontaneously burst fire in CA3 and long time series of inter-burst intervals were recorded. Three tests for determinism were applied to these series: a discrete adaptation of a local flow approach, a local dispersion approach, and nonlinear prediction. Surrogate data were generated to serve as mathematical and statistical controls. All of the population spike (6/6) and input-output (6/6) time series from the normal [K+] driven circuitry were stochastic by all three methods. Although most of the time series (5/6) from the autonomously bursting high [K+] state failed to demonstrate evidence of determinism, one (1/6) of these time series did demonstrate significant determinism. This single instance of predictability could not be accounted for by the linear correlation in these data.     

Predictability of EEG interictal spikes.

To determine whether EEG spikes are predictable, time series of EEG spike intervals were generated from subdural and depth electrode recordings from four patients. The intervals between EEG spikes were hand edited to ensure high accuracy and eliminate false positive and negative spikes. Spike rates (per minute) were generated from longer time series, but for these data hand editing was usually not feasible. Linear and nonlinear models were fit to both types of data. One patient had no linear or nonlinear predictability, two had predictability that could be well accounted for with a linear stochastic model, and one had a degree of nonlinear predictability for both interval and rate data that no linear model could adequately account for.     

P3b Reflects Periodicity in Linguistic Sequences

Temporal predictability is thought to affect stimulus processing by facilitating the allocation of attentional resources. Recent studies have shown that periodicity of a tonal sequence results in a decreased peak latency and a larger amplitude of the P3b compared with temporally random, i.e., aperiodic sequences. We investigated whether this applies also to sequences of linguistic stimuli (syllables), although speech is usually aperiodic. We compared aperiodic syllable sequences with two temporally regular conditions. In one condition, the interval between syllable onset was fixed, whereas in a second condition the interval between the syllables’ perceptual center (p-center) was kept constant. Event-related potentials were assessed in 30 adults who were instructed to detect irregularities in the stimulus sequences. We found larger P3b amplitudes for both temporally predictable conditions as compared to the aperiodic condition and a shorter P3b latency in the p-center condition than in both other conditions. These findings demonstrate that even in acoustically more complex sequences such as syllable streams, temporal predictability facilitates the processing of deviant stimuli. Furthermore, we provide first electrophysiological evidence for the relevance of the p-center concept in linguistic stimulus processing.     

The interstitial nucleus of Cajal of the cat. II. Effects of kainic acid lesion on vertical optokinetic nystagmus and after-nystagmus

The effects of bilateral lesions of the interstitial nucleus of Cajal (INC) by ka?nic acid on vertical optokinetic nystagmus (OKN) and after-nystagmus (OKAN) were studied in four cats: in three cats, in the acute stage from 1 to 60 days after the lesions; in the fourth cat, they were studied 3 years after the lesions were made. Histological control of lesions showed that the whole INC was bilaterally destroyed in two cats of the acute group and only the upper part of INC in the third cat. In the chronic cat, the density of cell bodies in both INC was lower than normal. In the acute group, the cats exhibited a spontaneous downward eye drift in light and in darkness. During an upward optokinetic stimulation, the effect of INC lesions was dramatic: upward slow phases and downward quick phases of OKN were abolished. Sixty days post lesions, small upward slow eye movements were again observed. During a downward optokinetic stimulation, the defect was much less; in particular, after a slight impairment of downward slow phases, during the first days post lesions, they recovered quickly. The secondary optokinetic after nystagmus (OKAN II) ensuing a downward OKN was cancelled and did not reappear 60 days post lesions. In the chronic stage, three years after the lesions, during an upward optokinetic stimulation, the cat showed upward slow phases with velocities close to normal. However, upward slow phases were curved: the velocity at the end of the slow phases was lower than at the beginning. After an upward OKN (the direction of slow phases gives the direction of the OKN and OKAN), the ensuing OKAN was present but abnormal.     

Effects of amplitude and predictability of perturbations to the arm on anticipatory and reactionary muscle responses to maintain balance

Disturbances to balance arising from forces applied to the upper limb have received relatively little attention compared to disturbances arising from support surface perturbations. In this study we applied fast ramp perturbations to the hand in anterior, posterior, medial and lateral directions. The effects of perturbation predictability and amplitude on the postural response of upper limb, trunk and lower limb muscles were investigated. Perturbations were applied either in blocks of constant amplitude and direction (predictable) or with direction and amplitude varying randomly (random) from trial to trial. The spatial-temporal patterns of anticipatory muscle activation under the predictable condition and the reactionary responses following the perturbation under both conditions were similarly organized. The size of the response increased systematically with the perturbation magnitude for both anticipatory and reactionary changes in muscle activation. However, the slope of the relation between perturbation amplitude and the magnitude of the change in muscle activation was greater when perturbations were predictable than when they were randomly selected. The timing of both the anticipatory and reactionary increases in muscle activation was invariant across perturbation amplitudes. The characteristics of the reactionary responses have a similar organization to the long latency muscle responses to support surface perturbations.     

On the correlation dimension of optokinetic nystagmus eye movements: computational parameters, filtering, nonstationarity, and surrogate data

 We discuss the estimation of the correlation dimension of optokinetic nystagmus (OKN), a type of reflexive eye movement. Parameters of the time-delay reconstruction of the attractor are investigated, including the number of data points, the time delay, the window duration, and the duration of the signal being analyzed. Adequate values are recommended. Digital low-pass filtering causes the dimension to increase as the filter cutoff frequency decreases, in accord with a previously published prediction. The stationarity of the correlation dimension is examined; the dimension appears to decrease over the course of 120 s of continuous stimulation. Implications for the reliable estimation of the dimension are considered. Several surrogate data sets are constructed, based on both early (0–30 s) and late (100–130 s) OKN segments. Most of the surrogate data sets randomize some aspect of the original OKN, while maintaining other aspects. Dimensions are found for all surrogates and for the original OKN. Evidence is found that is consistent with some amount of deterministic and nonlinear dynamics in OKN. When this structure is randomized in the surrogate, the dimension changes or the dimension algorithm ceases to converge to a finite value. Implications for further analysis and modeling of OKN are discussed. Received: 30 August 1996/Accepted in revised form: 13 November 1996     

Simulation of observed types of dynamics of plants and plant communities

Abstract. Observations of different plant communities over several decades reveal five types of dynamics: constant, fluctuating, growing, decaying, intermittent. With a modelling approach based on interacting particle systems (cellular automata), these distinct types of dynamics can be simulated. In addition, the proposed model shows a strong tendency towards the formation of patches when started with random initial conditions. Further, it gives evidence for dominance resulting from the interplay of plant characteristics and patterns rather than being attributable to certain plant types alone, so making questionable the existence of key species and the usefulness of a constant mapping key over extended periods. The presented model unifies the fundamental dichotomy in vegetation dynamics between determinism (predictability) and disorder (chance effects) by showing the outcome of both classical theories as special cases.     

Driver Gaze Behavior Is Different in Normal Curve Driving and when Looking at the Tangent Point

Several steering models in the visual science literature attempt to capture the visual strategies in curve driving. Some of them are based on steering points on the future path (FP), others on tangent points (TP). It is, however, challenging to differentiate between the models’ predictions in real–world contexts. Analysis of optokinetic nystagmus (OKN) parameters is one useful measure, as the different strategies predict measurably different OKN patterns. Here, we directly test this prediction by asking drivers to either a) “drive as they normally would” or b) to “look at the TP”. The design of the experiment is similar to a previous study by Kandil et al., but uses more sophisticated methods of eye–movement analysis. We find that the eye-movement patterns in the “normal” condition are indeed markedly different from the “tp” condition, and consistent with drivers looking at waypoints on the future path. This is the case for both overall fixation distribution, as well as the more informative fixation–by–fixation analysis of OKN. We find that the horizontal gaze speed during OKN corresponds well to the quantitative prediction of the future path models. The results also definitively rule out the alternative explanation that the OKN is produced by an involuntary reflex even while the driver is “trying” to look at the TP. The results are discussed in terms of the sequential organization of curve driving.     

Fixed vs. Random Temporal Predictability of Predation Risk: An Extension of the Risk Allocation Hypothesis

Predation is a strong selective force acting on prey animals. Predation is by nature highly variable in time; however, this aspect of predation risk has traditionally been overlooked by behavioural ecologists. Lima and Bednekoff proposed the predation risk allocation hypothesis (RAH), predicting how temporal variation in predation risk drives prey antipredator behaviours. This model is based on the concept that prey adaptively allocate their foraging and antipredator efforts across high‐ and low‐risk situations, depending on the duration of high‐ vs. low‐risk situations and the relative risk associated with each of them. An unstudied extension of the RAH is the effect of predictability of predation risk. A predictable risk should lead to prey displaying minimal vigilance behaviours during predictable low‐risk periods and the strongest antipredator behaviours during risky periods. Conversely, an unpredictable predation risk should result in prey displaying constant vigilance behaviour, with suboptimal foraging rates during periods of safety but antipredator behaviours of lower intensity during periods of risk. We tested this extension of the RAH using convict cichlids exposed to high‐risk alarm cues at two frequencies of risk (1× vs. 3×) per day, on either a fixed or random schedule for 5 d. We then tested the fish for a response to high‐risk cues (alarm cues) and to low‐risk cues (disturbance resulting from the introduction of distilled water). Our study supports previous results on the effects of risk frequency and cue intensity on cichlid behaviour. We failed to show an effect of risk predictability on the behavioural responses of cichlids to high‐risk alarm cues, but predictability did influence responses to low‐risk cues. We encourage further studies to test the effect of predictability in other systems.     

Cross-validation analysis for genetic evaluation models for ranking in endurance horses

Ranking trait was used as a selection criterion for competition horses to estimate racing performance. In the literature the most common approaches to estimate breeding values are the linear or threshold statistical models. However, recent studies have shown that a Thurstonian approach was able to fix the race effect (competitive level of the horses that participate in the same race), thus suggesting a better prediction accuracy of breeding values for ranking trait. The aim of this study was to compare the predictability of linear, threshold and Thurstonian approaches for genetic evaluation of ranking in endurance horses. For this purpose, eight genetic models were used for each approach with different combinations of random effects: rider, rider–horse interaction and environmental permanent effect. All genetic models included gender, age and race as systematic effects. The database that was used contained 4065 ranking records from 966 horses and that for the pedigree contained 8733 animals (47% Arabian horses), with an estimated heritability around 0.10 for the ranking trait. The prediction ability of the models for racing performance was evaluated using a cross-validation approach. The average correlation between real and predicted performances across genetic models was around 0.25 for threshold, 0.58 for linear and 0.60 for Thurstonian approaches. Although no significant differences were found between models within approaches, the best genetic model included: the rider and rider–horse random effects for threshold, only rider and environmental permanent effects for linear approach and all random effects for Thurstonian approach. The absolute correlations of predicted breeding values among models were higher between threshold and Thurstonian: 0.90, 0.91 and 0.88 for all animals, top 20% and top 5% best animals. For rank correlations these figures were 0.85, 0.84 and 0.86. The lower values were those between linear and threshold approaches (0.65, 0.62 and 0.51). In conclusion, the Thurstonian approach is recommended for the routine genetic evaluations for ranking in endurance horses.     

Effects of food abundance and predictability on body condition and health parameters: experimental tests with the Hooded Crow

It has been shown that small passerines can counteract variability of food resources by actively regulating their body reserves through an increase of mass. However, the effects of food predictability on body mass regulation and other body parameters, such as immune functions, in larger species have been little studied. To analyse the response of the Hooded Crow Corvus corone to food abundance and predictability, we performed three experiments with controlled food provisioning under laboratory conditions. Body mass, TOBEC (total body electrical conductivity) lean mass index, blood parameters and immune organ masses were measured at the beginning and end of a 15‐day period. In the first experiment, the food release was predictable (same amount each day) but the quantity of food delivered to five groups of birds varied (37, 75, 100, 150 or 300 g/day). Low food levels induced a greater decrease in mass accompanied by an increase in erythrocyte sedimentation rate. In the second experiment, the same average quantity of food (100 g) was supplied according to either predictable or unpredictable (random) schedules. In this case, the crows lost more mass, and their erythrocyte sedimentation rate increased when food was unpredictable. In the third experiment, the same average quantity of food (150 g) was supplied according to either a predictable schedule or two schedules with different levels of variability. The group with a low level of variability did not differ from the control, while the group with a highly variable feeding schedule lost more mass. In this group, the higher mass loss was associated with greater variation of the erythrocyte sedimentation rate and a reduced Phytohaemagglutinin index of immunocompetence and haematocrit value. The results of experiments 2 and 3 contrast with findings in other passerines, which increase their mass when food availability is unpredictable. It appears that a body mass decrease in the Hooded Crow can be induced by a reduction of either food abundance (exp. 1) or food predictability (exp. 2, 3), and it is accompanied by a worsening of health state.     

The Effects of Incidentally Learned Temporal and Spatial Predictability on Response Times and Visual Fixations during Target Detection and Discrimination

Responses are quicker to predictable stimuli than if the time and place of appearance is uncertain. Studies that manipulate target predictability often involve overt cues to speed up response times. However, less is known about whether individuals will exhibit faster response times when target predictability is embedded within the inter-trial relationships. The current research examined the combined effects of spatial and temporal target predictability on reaction time (RT) and allocation of overt attention in a sustained attention task. Participants responded as quickly as possible to stimuli while their RT and eye movements were measured. Target temporal and spatial predictability were manipulated by altering the number of: 1) different time intervals between a response and the next target; and 2) possible spatial locations of the target. The effects of target predictability on target detection (Experiment 1) and target discrimination (Experiment 2) were tested. For both experiments, shorter RTs as target predictability increased across both space and time were found. In addition, the influences of spatial and temporal target predictability on RT and the overt allocation of attention were task dependent; suggesting that effective orienting of attention relies on both spatial and temporal predictability. These results indicate that stimulus predictability can be increased without overt cues and detected purely through inter-trial relationships over the course of repeated stimulus presentations.     

Evaluating empirical scaling relations of pattern metrics with simulated landscapes

Landscape patterns demonstrate scale-dependent properties that have been parsimoniously described by empirical scaling functions. These functions, derived from multiple-scale analysis of real landscapes, are evaluated here for their generality and robustness via a series of simulated landscapes with known landscape patterns. A factorial design was used to generate these landscapes, varying the number of classes, class abundance distribution, and patch dispersion. The results confirm that the three types of scaling relations were both general and robust. Type I metrics were predictable with simple scaling functions (e.g. power laws or linear functions); Type II metrics showed stair-case like response patterns and were essentially not predictable; Type III metrics exhibited erratic response patterns that were unpredictable in most cases. However, significant differences were found between real and simulated landscapes when landscape extent was increased. Systematic changes in grain size show that the predictability of scaling relations increases with the number of classes, the evenness of class abundance distribution, and the aggregation of patch dispersion. However, random patch dispersion seemed to enhance the predictability of scaling relations when changing spatial extent.     

Circadian Time Structure of Cardiovascular Characteristics in Human Pregnancy

Conventional time-unspecified single measurements of blood pressure and heart rate may be misleading because they may be influenced, among other factors, by the patient's emotional state, position, diet, and external stimuli. All of these effects depend on the stages of a (mathematical) spectrum of rhythms and trends with age. The evaluation of predictable variability in blood pressure and heart rate by (a) the use of fully ambulatory devices, and (b) chronobiologic data processing, assesses early cardiovascular disease risk, e.g., in pregnancy. We have used this approach to quantify changes in 24-h synchronized (circadian) characteristics of cardiovascular variables in two consecutive pregnancies of a clinically healthy woman. Blood pressure and heart rate were automatically monitored, with few interruptions, at I-h intervals, each time for at least 48 consecutive h, and for a total of 76 days of monitoring in each pregnancy. Circadian parameters of those circulatory variables were computed for each single day of measurement by the least-squares fit of a 24-h cosine curve. Regression analysis of parameters thus obtained revealed patterns of variation of circadian-rhythm-adjusted means and amplitudes with gestational age. In both pregnancies, the predictable variability of the circadian-rhythm-adjusted mean of blood pressure can be approximated by a second-order polynomial model on gestational age: a steady linear decrease in systolic, diastolic, and mean arterial blood pressure up to the 22nd week of pregnancy is followed by an increase in blood pressure up to the day of delivery. This longitudinal study confirms and extends to ambulatory everyday life conditions the predictable pregnancy-associated variability in blood pressure and heart rate and also allows the establishment of prediction and confidence limits for cardiovascular parameters in a healthy pregnancy.     

Estimating the distribution of a renewal process from times at which events from an independent process are detected

The analysis of length-biased data has been mostly limited to the interarrival interval of a renewal process covering a specific time point. Motivated by a surveillance problem, we consider a more general situation where this time point is random and related to a specific event, for example, status change or onset of a disease. We also consider the problem when additional information is available on whether the event intervals (interarrival intervals covering the random event) end within or after a random time period (which we call a window period) following the random event. Under the assumptions that the occurrence rate of the random event is low and the renewal process is independent of the random event, we provide formulae for the estimation of the distribution of interarrival times based on the observed event intervals. Procedures for testing the required assumptions are also furnished. We apply our results to human immunodeficiency virus (HIV) test data from public test sites in Seattle, Washington, where the random event is HIV infection and the window period is from the onset of HIV infection to the time at which a less sensitive HIV test becomes positive. Results show that the estimator of the intertest interval length distribution from event intervals ending within the window period is less biased than the estimator from all event intervals; the latter estimator is affected by right truncation. Finally, we discuss possible applications to estimating HIV incidence and analyzing length-biased samples with right or left truncated data.     

Timing Rhythms: Perceived Duration Increases with a Predictable Temporal Structure of Short Interval Fillers

Variations in the temporal structure of an interval can lead to remarkable differences in perceived duration. For example, it has previously been shown that isochronous intervals, that is, intervals filled with temporally regular stimuli, are perceived to last longer than intervals left empty or filled with randomly timed stimuli. Characterizing the extent of such distortions is crucial to understanding how duration perception works. One account to explain effects of temporal structure is a non-linear accumulator-counter mechanism reset at the beginning of every subinterval. An alternative explanation based on entrainment to regular stimulation posits that the neural response to each filler stimulus in an isochronous sequence is amplified and a higher neural response may lead to an overestimation of duration. If entrainment is the key that generates response amplification and the distortions in perceived duration, then any form of predictability in the temporal structure of interval fillers should lead to the perception of an interval that lasts longer than a randomly filled one. The present experiments confirm that intervals filled with fully predictable rhythmically grouped stimuli lead to longer perceived duration than anisochronous intervals. No general over- or underestimation is registered for rhythmically grouped compared to isochronous intervals. However, we find that the number of stimuli in each group composing the rhythm also influences perceived duration. Implications of these findings for a non-linear clock model as well as a neural response magnitude account of perceived duration are discussed.     

Scaling structure factor amplitudes in electron cryomicroscopy using X-Ray solution scattering

The structure factors derived from electron cryomicroscopic images are modified by the contrast transfer function of the microscope's objective lens and other influences. The phases of the structure factors can be corrected in a straightforward way when the positions of the contrast transfer function rings are determined. However, corrected amplitudes are also essential to yield an accurate distribution of mass in the reconstruction. The correct scale factors for the amplitudes are difficult to evaluate for data that are merged from many different micrographs. We opt to use X-ray solution scattering intensity from a concentrated suspension of the specimen to correct the amplitudes of the spherically averaged structure factors. When this approach is applied to the three-dimensional image data of ice-embedded acrosomal bundles, the core of a filament in a three-dimensional reconstruction of the acrosomal bundle becomes denser and matches more closely the outer density ascribed to scruin.     

Rhythmic Manipulation of Objects with Complex Dynamics: Predictability over Chaos

The study of object manipulation has been largely confined to discrete tasks, where accuracy, mechanical effort, or smoothness were examined to explain subjects'' preferred movements. This study investigated a rhythmic manipulation task, which involved continuous interaction with a nonlinear object that led to unpredictable object behavior. Using a simplified virtual version of the task of carrying a cup of coffee, we studied how this unpredictable object behavior affected the selected strategies. The experiment was conducted in a virtual set-up, where subjects moved a cup with a ball inside, modeled by cart-and-pendulum dynamics. Inverse dynamics calculations of the system showed that performing the task with different amplitudes and relative phases required different force profiles and rendered the object''s dynamics with different degrees of predictability (quantified by Mutual Information between the applied force and the cup kinematics and its sensitivity). Subjects (n = 8) oscillated the virtual cup between two targets via a robotic manipulandum, paced by a metronome at 1 Hz for 50 trials, each lasting 45 s. They were free to choose their movement amplitude and relative phase between the ball and cup. Experimental results showed that subjects increased their movement amplitudes, which rendered the interactions with the object more predictable and with lower sensitivity to the execution variables. These solutions were associated with higher average exerted force and lower object smoothness, contradicting common expectations from studies on discrete object manipulation and unrestrained movements. Instead, the findings showed that humans selected strategies with higher predictability of interaction dynamics. This finding expressed that humans seek movement strategies where force and kinematics synchronize to repeatable patterns that may require less sensorimotor information processing.     

Filter-paper blood samples for ELISA detection of Brucella antibodies in caribou

We evaluated blood collected on Nobuto filter-paper (FP) strips for use in detecting Brucella spp. antibodies in caribou. Whole blood (for serum) and blood-saturated FP strips were obtained from 185 killed arctic caribou (Rangifer tarandus groenlandicus). Sample pairs (serum and FP eluates) were simultaneously tested in duplicate using competitive enzyme-linked immunosorbent assay (c-ELISA) and indirect ELISA (i-ELISA) for Brucella spp. Prior work based on isolation of Brucella spp. revealed sensitivity (SE) and specificity (SP) of 100% and 99%, respectively, for both these serum assays in caribou. Infection status of the animals in the current study was unknown but recent sampling had revealed clinical brucellosis and >40% Brucella antibody prevalence in the herd. To assess the performance of FP relative to serum in these assays, serum was used as the putative gold standard. On both assays, the findings for duplicate runs (A and B) were similar. For c-ELISA run A, the FP Brucella prevalence (47%) was lower than serum prevalence (52%), with SE 89% (95% confidence interval [CI]: 82-95%) and SP 99% (97-100%). For i-ELISA run A, serum and FP Brucella prevalence rates were identical (43%), and the SE and SP of FP testing were 100% and 99% (97-100%), respectively. The findings suggest better FP test performance with i-ELISA than with c-ELISA; however, i-ELISA does not distinguish cross-reacting antibodies induced by Brucella vaccination or exposure to certain other Gram-negative pathogens. Results for duplicate FP eluates (prepared using separate FP strips from each animal) were strongly correlated for both protocols (r=0.996 and 0.999 for c-ELISA and i-ELISA, respectively), indicating minimal variability among FPs from any individual caribou. Dried caribou FP blood samples stored for 2 mo at room temperature are comparable with serum for use in Brucella spp. c-ELISA and i-ELISA. Hunter-based FP sampling can facilitate detection of disease exposure in remote regions and under adverse conditions, and can expand wildlife disease surveillance across temporospatial scales.