Stochastic cascade processes as a model of multi-stage concurrent information processing

McClelland's (Psychol. Rev. 86 (1979) 287) influential cascade model of reaction time (RT) is often seen as an important explicitly formulated alternative to strictly serial models because some of its basic notions fit in with known characteristics of neural activation processes. A disadvantage is that it is an essentially deterministic model to which noise is added by across-trials parameter variability that is unrelated to the concept of cascaded activation propagation per se. We propose and analyze a general stochastic cascade model based on neural counting processes; within this framework we present a new process-oriented interpretation of McClelland's cascade activation equation. We then theoretically explain and numerically explore conditions under which the stochastic cascade model predicts additive vs. interactive mean RT effects, and compare them to known properties of McClelland's model. Some of these properties remain valid even within a stochastic neural counting formulation, while others reflect assumptions which are essentially unrelated to the concept of cascaded activation.     

Spike coding from the perspective of a neurone

In this paper, we compare existing methods for quantifying the coding capacity of a spike train, and review recent developments in the application of information theory to neural coding. We present novel methods for characterising single-unit activity based on the perspective of a downstream neurone and propose a simple yet universally applicable framework to characterise the order of complexity of neural coding by single units. We establish four orders of complexity in the capacity for neural coding. First-order coding, quantified by firing rates, is conveyed by frequencies and is thus entirely described by first moment processes. Second-order coding, represented by the variability of interspike intervals, is quantified by the log interval entropy. Third-order coding is the result of spike motifs that associate adjacent inter-spike intervals beyond chance levels; it is described by the joint interval histogram, and is measured by the mutual information between adjacent log intervals. Finally, nonstationarities in activity represent coding of the fourth-order that arise from the effects of a known or unknown stimulus.     

Use of speech-modulated noise adds strong “bottom-up” cues for phonemic restoration

When deleted segments of speech are replaced by extraneous sounds rather than silence, the missing speech fragments may be perceptually restored and intelligibility improved. This phonemic restoration (PhR) effect has been used to measure various aspects of speech processing, with deleted portions of speech typically being replaced by stochastic noise. However, several recent studies of PhR have used speech-modulated noise, which may provide amplitude-envelope cues concerning the replaced speech. The present study compared the effects upon intelligibility of replacing regularly spaced portions of speech with stochastic (white) noise versus speech-modulated noise. In Experiment 1, filling periodic gaps in sentences with noise modulated by the amplitude envelope of the deleted speech fragments produced twice the intelligibility increase obtained with interpolated stochastic noise. Moreover, when lists of isolated monosyllables were interrupted in Experiment 2, interpolation of speech-modulated noise increased intelligibility whereas stochastic noise reduced intelligibility. The augmentation of PhR produced by modulated noise appeared without practice, suggesting that speech processing normally involves not only a narrowband analysis of spectral information but also a wideband integration of amplitude levels across critical bands. This is of considerable theoretical interest, but it also suggests that since PhRs produced by speech-modulated noise utilize potent bottom-up cues provided by the noise, they differ from the PhRs produced by extraneous sounds, such as coughs and stochastic noise.     

Some deterministic models of concept identification

It is shown that deterministic models can compete effectively with stochastic models in summarizing concept identification behavior. Three groups of deterministic models are examined. Examination of individual learners' trial by trial behavior in a concept experiment shows: (1) One person exhibited behavior consistent with a Hypothesis Permutation (HP) model despite being a nonlearner who showed no evidence of improvement over a period of 24 trials. However, when all 50 persons studied in each of two treatment groups were examined, only 22 members of one group and 10 of the other showed no inconsistencies with deterministic local consistency assumptions. (2) Certain deterministic computer programs could find at least one satisfactory order for predicting all responses by 18 of the 22 consistent solvers and 6 of the 10 consistent solvers, respectively, in the two groups just mentioned. For these 24 persons, then, a less restrictive deterministic model is adequate than for the others. (3) Those 38 original members of the first treatment group who met a stringent learning criterion were compared with respect to predictions generated by stochastic and mathematized deterministic models. One deterministic model (RSS-U 9-state) is in some respects the best of the models examined, but this success is a partial reflection of estimating eight parameters from the data.     

The role of the central nervous system in sudden cardiac death: Heartbeat dynamics in conscious pigs during coronary occlusion,psychologic stress and intracerebral propranolol

Electrocardiograms were recorded in conscious pigs during psychological stress (touching), left anterior descending coronary artery occlusion, intracerebral levo-propranolol (0.05 mg/kg), and their respective controls. The R-R intervals were evaluated with both a deterministic measure (point correlation dimension) and a stochastic one (mean). Only the deterministic measure was sensitive to between-subject responses (P<.01), whereas both measures were sensitive to within-subject changes. The results are explained by a deterministic model of heartbeat generation. Supported by the National Institute of Health Grant NS 27745.     

The impact of broadband noise on serial memory: changes in band-pass frequency increase disruption

Irrelevant sound consisting of bursts of broadband noise, in which centre frequency changes with each burst, markedly impaired short-term memory for order. In contrast, a sequence of irrelevant sound in which the same band-pass noise burst was repeated did not produce significant disruption. Serial recall for both visual-verbal (Experiment 1) and visual-spatial items (Experiment 2) was sensitive to the increased disruption produced by changing irrelevant noise. The results provide evidence that sounds that are largely aperiodic can produce marked disruption of serial recall in a similar manner to periodic sounds (e.g., speech, musical streams, and tones), and thus show a changing-state effect.     

Noise methods in pattern perception

This experiment investigated 4 methods of inducing visual noise at 7 levels of noise. Fortysix Ss were presented 4800 sets of 3 pattems, with the task of judging which of 2 noisy patterns was more similar to the prototype pattern. The noisy patterns were generated by adding, moving, deleting or both adding and deleting elements of the prototype. All possible comparisons of each noise method were made at each noise level and the results plotted. The results show that the various methods of introducing noise do not produce identical results, and that the similarity assessment is dependent on noise koel. Explanations are offered to account for the results.     

Information encoding in short firing rate epochs by single neurons in the primate temporal visual cortex

Abstract

The information available about face identity from the firing rate and from temporal encoding in the spike train of single neurons recorded in the temporal lobe visual cortical areas of rhesus macaques was analysed using principal component and information theory analyses of smoothed spike trains. The neurons analysed had responses selective for faces. The stimulus set consisted of 20 different faces. The first principal component provided by a considerable extent the most information (57%) available in principal components 1–5, with the second adding 18%, the third 16%, and the fourth and fifth adding 9%. For each image, the weighting on the first principal component was highly correlated with the mean firing rate of the neuron to that image. The information available from the firing rate of the neuron was very close to that available in the first principal component. Information theory analysis showed that in short epochs (e.g. 50 msec) the information available from the firing rate can be as high, on average, as 65% of that available from the firing rate calculated over 400 msec, and 38% of that available from principal components 1–3 in the 400-msec period. It was also found that 30% of the information calculated from the first three principal components is available in the firing rates calculated over epochs as short as 20 msec. More information was available near the start of the neuronal response, and the information available from short epochs became less later in the neuronal response. Taken together, these analyses provide evidence that a short period of firing taken close to the start of the neuronal response provides a reasonable proportion of the total information that would be available if a long period of neuronal firing (e.g. 400 msec) were utilized to extract it, even if temporal encoding were used. The implications of these and related findings are that at least for rapid object recognition, each cortical stage provides information to the next in a short period of 20–50 msec, does not rely on temporal encoding, and completes sufficient computation to provide an output to the next stage in this same 20- to 50-msec period.     

Temporal specificity of fear conditioning: effects of different conditioned stimulus-unconditioned stimulus intervals on the fear-potentiated startle effect

Separate groups of rats were given 30 pairings of a light (conditioned stimulus, CS) and 500-ms shock (unconditioned stimulus, US) at CS-US intervals of 0, 25, 50, 100, 200, 800, 3,200, 12,800, or 51,200 ms. Other groups had lights and shocks inconsistently paired. The startle reflex was elicited 2-4 days later with a noise burst alone or 25-51,200 ms after light onset. After CS-US pairings over a wide range of intervals (25-51,200 ms), startle was potentiated in testing, sometimes as rapidly as 50 ms after light onset. Magnitude of potentiation and resistance to extinction were generally greater with longer CS-US intervals. In several groups, potentiation was maximal at a test interval that matched the CS-US interval used in training. This temporal specificity sharpened with increasing numbers of training trials but even occurred with a single training trial in which a 51,200-ms CS-US interval was used. The data indicate that even during simple fear conditioning, animals rapidly learn a temporal CS-US relationship. This has important implications for understanding the neural mechanisms of fear conditioning.     

Modification of the rat's acoustic startle response by antecedent visual stimulation.

Male hooded and albino rats were exposed to a light flash followed at various temporal intervals by a startle-eliciting 117 db. (re 20 muN/m2) burst of white noise. The visual stimulus engendered startle response inhibition (maximally when the lead time was 64-250 msec) as well as startle response latency reduction (maximally when the lead time was 2-8 msec). The temporal functions for the effects of visual stimuli paralleled those previously reported for startle modification by acoustic events. Further study revealed that, given optimal lead times, inhibition is produced reliably by weaker visual stimuli (3 X 10-6 cd-sec/cm2) than latency reduction (3 X 10-4 cd-sec/cm2). This differential sensitivity to visual stimuli is also analogous to previously reported findings for events in the acoustic environment. It reveals that the neural mechanisms that mediate latency reduction and inhibition can be engaged by either acoustic or visual stimulation.     

The Advantages of Predictive Interval Forecasts for Non‐Expert Users and the Impact of Visualizations

Three experiments demonstrated advantages over conventional deterministic forecasts for participants making temperature estimates and precautionary decisions with predictive interval weather forecasts showing the upper and lower boundaries within which the observed value is expected with a specified probability. Participants using predictive intervals were better able to identify unreliable forecasts, expected a narrower range of outcomes, and were more decisive than were participants using deterministic forecasts. Predictive interval format was also manipulated to determine whether adding visualizations enhanced understanding. Some participants using visualizations misinterpreted predictive intervals as expressions of diurnal fluctuations (deterministic forecasts). Almost no misinterpretations occurred when the predictive interval was expressed in text alone. Moreover, no advantages were found for visualizations over text‐only formats, demonstrating that visualizations, especially those investigated in these studies, may not be suitable for expressing this concept. Thus, predictive intervals are both understandable and advantageous to non‐expert decision makers, as long as they are carefully expressed. Copyright © 2013 John Wiley & Sons, Ltd.     

How the brain encodes the order of letters in a printed word: the SERIOL model and selective literature review

This paper describes a novel theoretical framework of how the position of a letter within a string is encoded, the SERIOL model (sequential encoding regulated by inputs to oscillations within letter units). Letter order is represented by a temporal activation pattern across letter units, as is consistent with current theories of information coding based on the precise timing of neural spikes. The framework specifies how this pattern is invoked via an activation gradient that interacts with subthreshold oscillations and how it is decoded via contextual units that activate word units. Using mathematical modeling, this theoretical framework is shown to account for the experimental data from a wide variety of string-processing studies, including hemispheric asymmetries, the optimal viewing position, and positional priming effects.     

Is consciousness a gradual phenomenon? Evidence for an all-or-none bifurcation during the attentional blink

Several theories of the neural correlates of consciousness assume that there is a continuum of perception, associated with a gradual change in the intensity of brain activation. But some models, considering reverberation of neural activity as necessary for conscious perception, predict a sharp nonlinear transition between unconscious and conscious processing. We asked participants to evaluate the visibility of target words on a continuous scale during the attentional blink, which is known to impede explicit reports. Participants used this continuous scale in an all-or-none fashion: Targets presented during the blink were either identified as well as targets presented outside the blink period or not detected at all. We suggest that a stochastic nonlinear bifurcation in neural activity underlies the all-or-none perception observed during the attentional blink.     

Temporal ventriloquism in a purely temporal context

This study examines how audiovisual signals are combined in time for a temporal analogue of the ventriloquist effect in a purely temporal context, that is, no spatial grounding of signals or other spatial facilitation. Observers were presented with two successive intervals, each defined by a 1250-ms tone, and indicated in which interval a brief audiovisual stimulus (visual flash + noise burst) occurred later. In "test" intervals, the audiovisual stimulus was presented with a small asynchrony, while in "probe" intervals it was synchronous and presented at various times guided by an adaptive staircase to find the perceived temporal location of the asynchronous stimulus. As in spatial ventriloquism, and consistent with maximum likelihood estimation (MLE), the asynchronous audiovisual signal was shifted toward the more reliably localized component (audition, for all observers). Moreover, these temporal shifts could be forward or backward in time, depending on the asynchrony order, suggesting perceived timing is not entirely determined by physical timing. However, the critical signature of MLE combination--better bimodal than unimodal precision--was not found. Regardless of the underlying model, these results demonstrate temporal ventriloquism in a paradigm that is defined in a purely temporal context.     

Vibro-tactile and visual asynchronies: sensitivity and consistency

We investigated the consistency between tactually and visually designated empty time intervals. In a forced-choice discrimination task, participants judged whether the second of two intervals was shorter or longer than the first interval. Two pulses defined the intervals. The pulse was either a vibro-tactile burst presented to the fingertip, or a foveally presented white square. The comparisons were made for uni-modal and cross-modal intervals. We used four levels of standard interval durations in the range of 100- 800 ms. The results showed that tactile empty intervals must be 8.5% shorter to be perceived as long as visual intervals. This cross-modal bias is larger for small intervals and decreases with increasing standard intervals. The Weber fractions (the threshold divided by the standard interval) are 20% and are constant over the standard intervals. This indicates that the Weber law holds for the range of interval lengths tested. Furthermore, the Weber fractions are consistent over uni-modal and cross-modal comparisons, which indicates that there is no additional noise involved in the cross-modal comparisons.     

Age-related changes in auditory temporal processing

Two tone bursts separated by a silent interval and imbedded in a background white noise were presented to elderly subjects (M age = 71.3 years) and young subjects (M age = 22.2 years). Subjects were required to judge when the two tone bursts fused perceptually by adjusting the duration of tone-one. The bursts were separated by six discrete interstimulus intervals of 4, 8, 16, 24, 32, or 40 ms. The tone-two burst was held constant at 100 ms. Fusion point was defined as that critical tone-one duration at which the two tones fused (were perceived as one). Elderly subjects reached fusion point at longer critical tone-one durations than young subjects at each interval tested. The function relating tone-one duration and interval conformed to an exponential curve and is discussed with respect to an exponential decay model of the inhibitory interactions of neural systems responding to onsets and offsets of sensory events.     

Neural synchrony in stochastic resonance, attention, and consciousness.

We describe briefly three of our lab's ongoing projects studying the role of neural synchrony in human perception and cognition. These projects arise from two main interests: the role of noise both in human perception and in neural synchrony, and neural synchrony as a basis for integration of functional modules in the brain. Our experimental work on these topics began with a study of the possibility that noise-influenced neural synchrony might be responsible for the fact that small amounts of noise added to weak signals can enhance their detectability (stochastic resonance). We are also studying the role of neural synchrony in attention and consciousness in several paradigms. On the basis of our own and related work by others, we conclude that (1) neural synchrony plays an important role in the integration of functional modules in the brain and (2) neural synchrony is profoundly affected and possibly regulated, in part, by the "noisiness" of the brain.     

Developing an Output‐Oriented Super Slacks‐Based Measure Model with an Application to Third‐Party Reverse Logistics Providers

Outsourcing is an increasingly significant topic pursued via corporations seeking enhanced efficiency. Third‐party reverse logistics involves the employ of external firms to carry out some or all of the firm's logistics activities. Output‐oriented super slacks‐based measure (SBM) model is one of the models in data envelopment analysis (DEA). In many real‐world applications, data are often stochastic. A successful approach to address uncertainty in data is to replace deterministic data via random variables, leading to chance‐constrained DEA. In this paper, a chance‐constrained output‐oriented super SBM model is developed and also its deterministic equivalent, which is a nonlinear program, is derived. Furthermore, it is shown that the deterministic equivalent of the stochastic output‐oriented super SBM model can be converted into a quadratic program. In addition, sensitivity analysis of the stochastic output‐oriented super SBM model is discussed with respect to changes on parameters. Finally, a numerical example demonstrates the application of the proposed model. Copyright © 2011 John Wiley & Sons, Ltd.     

The temporal organization of behavior on periodic food schedules.

Various theories of temporal control and schedule induction imply that periodic schedules temporally modulate an organism's motivational states within interreinforcement intervals. This speculation has been fueled by frequently observed multimodal activity distributions created by averaging across interreinforcement intervals. We tested this hypothesis by manipulating the cost associated with schedule-induced activities and the availability of other activities to determine the degree to which (a) the temporal distributions of activities within the interreinforcement interval are fixed or can be temporally displaced, (b) rats can reallocate activities across different interreinforcement intervals, and (c) noninduced activities can substitute for schedule-induced activities. Obtained multimodal activity distributions created by averaging across interreinforcement intervals were not representative of the transitions occurring within individual intervals, so the averaged multimodal distributions should not be assumed to represent changes in the subject's motivational states within the interval. Rather, the multimodal distributions often result from averaging across interreinforcement intervals in which only a single activity occurs. A direct influence of the periodic schedule on the motivational states implies that drinking and running should occur at different periods within the interval, but in three experiments the starting times of drinking and running within interreinforcement intervals were equal. Thus, the sequential pattern of drinking and running on periodic schedules does not result from temporal modulation of motivational states within interreinforcement intervals.     

Spectral restoration of speech: Intelligibility is increased by inserting noise in spectral gaps

In order to function effectively as a means of communication, speech must be intelligible under the noisy conditions encountered in everyday life. Two types of perceptual synthesis have been reported that can reduce or cancel the effects of masking by extraneous sounds: Phonemic restoration can enhance intelligibility when segments are replaced or masked by noise, and contralateral induction can prevent mislateralization by effectively restoring speech masked at one ear when it is heard in the other. The present study reports a third type of perceptual synthesis induced by noise: enhancement of intelligibility produced by adding noise to spectral gaps. In most of the experiments, the speech stimuli consisted of two widely separated narrow bands of speech (center frequencies of 370 and 6000 Hz, each band having high-pass and low-pass slopes of 115 dB/octave meeting at the center frequency). These very narrow bands effectively reduced the available information to frequency-limited patterns of amplitude fluctuation lacking information concerning formant structure and frequency transitions. When stochastic noise was introduced into the gap separating the two speech bands, intelligibility increased for “everyday” sentences, for sentences that varied in the transitional probability of keywords, and for monosyllabic word lists. Effects produced by systematically varying noise amplitude and noise bandwidth are reported, and the implications of some of the novel effects observed are discussed.