Description of the Markov chain using the producing function

In article the way of creation of an assumed function of transformation with the help of a generating function and also a method of use of characteristic numbers and vectors for creation of a matrix which elements well describe conditions of process at any moment is described. This approach differs from preceding that, having used a concept of characteristic numbers and characteristic vectors of a matrix of the transitional probabilities, it is possible to simplify considerably calculation of the elements characterizing process. In article methods of stochastic model operation, ways of the description of a generating function, the solution of matrixes of the equations by means of characteristic numbers and vectors are used. Using properties of a generating function, made “dictionary” of z-transformations which helped to define an assumed function of transformation. The generating function of a vector was applied to a research of behavior of a vector of absolute probabilities which elements represent stationary probabilities. For definition of degree of a matrix of transition of probabilities used a concept of characteristic numbers and characteristic vectors of the transitional probabilities. Determined by such way an unlimited set of latent vectors of which made matrixes which describe a condition of a system at any moment. Reception of definition of latent vectors in more difficult examples which is that along with required coefficients of secular equations the system of auxiliary matrixes and an inverse matrix is under construction is also described.

Measuring (online) word segmentation in adults and children

Since Saffran, Aslin and Newport (1996) showed that infants were sensitive to transitional probabilities between syllables after being exposed to a few minutes of fluent speech, there has been ample research on statistical learning. Word segmentation studies usually test learning by making use of “offline methods” such as forced-choice tasks. However, cognitive factors besides statistical learning possibly influence performance on those tasks. The goal of the present study was to improve a method for measuring word segmentation online. Click sounds were added to the speech stream, both between words and within words. Stronger expectations for the next syllable within words as opposed to between words were expected to result in slower detection of clicks within words, revealing sensitivity to word boundaries. Unexpectedly, we did not find evidence for learning in multiple groups of adults and child participants. We discuss possible methodological factors that could have influenced our results.

Direct brain recordings reveal continuous encoding of structure in random stimuli

The brain excels at processing sensory input, even in rich or chaotic environments. Mounting evidence attributes this to the creation of sophisticated internal models of the environment that draw on statistical structures in the unfolding sensory input. Understanding how and where this modeling takes place is a core question in statistical learning. It is unknown how this modeling applies to random sensory signals. Here, we identify conditional relations, through transitional probabilities, as an implicit structure supporting the encoding of a random auditory stream. We evaluate this representation using intracranial electroencephalography recordings by applying information-theoretical principles to high-frequency activity (75-145 Hz). We demonstrate how the brain continuously encodes conditional relations between random stimuli in a network outside of the auditory system following a hierarchical organization including temporal, frontal and hippocampal regions. Our results highlight that hierarchically organized brain areas continuously attempt to order incoming information by maintaining a probabilistic representation of the sensory input, even under random stimuli presentation.

Online Statistical Learning in Developmental Language Disorder

Purpose: The vulnerability of statistical learning (SL) in developmental language disorder (DLD) has mainly been demonstrated with metacognitive offline measures which give little insight into the more specific nature and timing of learning. Our aims in this study were to test SL in children with and without DLD with both online and offline measures and to compare the efficiency of SL in the visual and acoustic modalities in DLD.Method: We explored SL in school-age children with and without DLD matched on age and sex (n = 36). SL was investigated with the use of acoustic verbal and visual nonverbal segmentation tasks relying on online (reaction times and accuracy) and offline (two-alternative forced choice, 2AFC and production) measures.Results: In online measures, learning was evident in both groups in both the visual and acoustic modalities, while offline measures showed difficulties in DLD. The visual production task showed a significant learning effect in both groups, while the visual two-alternative forced choice (2AFC) and the two acoustic offline tasks only showed evidence of learning in the control group. The comparison of learning indices revealed an SL impairment in DLD, which is present in both modalities.Conclusions: Our findings suggest that children with DLD are comparable to typically developing (TD) children in their ability to extract acoustic verbal and visual nonverbal patterns that are cued only by transitional probabilities in online tasks, but they show impairments on metacognitive measures of learning. The pattern of online and offline measures implies that online tests can be more sensitive and valid indices of SL than offline tasks, and the combined use of different measures provides a better picture of learning efficiency, especially in groups where metacognitive tasks are challenging.

Tracking transitional probabilities and segmenting auditory sequences are dissociable processes in adults and neonates

Since speech is a continuous stream with no systematic boundaries between words, how do pre-verbal infants manage to discover words? A proposed solution is that they might use the transitional probability between adjacent syllables, which drops at word boundaries. Here, we tested the limits of this mechanism by increasing the size of the word-unit to 4 syllables, and its automaticity by testing asleep neonates. Using markers of statistical learning in neonates' EEG, compared to adult' behavioral performances in the same task, we confirmed that statistical learning is automatic enough to be efficient even in sleeping neonates. But we also revealed that : 1) Successfully tracking transition probabilities in a sequence is not sufficient to segment it 2) Prosodic cues, as subtle as subliminal pauses, enable to recover segmenting capacities 3) Adults' and neonates' capacities are remarkably similar despite the difference of maturation and expertise. Finally, we observed that learning increased the similarity of neural responses across infants, providing a new neural marker to monitor learning. Thus, from birth, infants are equipped with adult-like tools, allowing to extract small coherent word-like units within auditory streams, based on the combination of statistical analyses and prosodic cues.

Age-Related Differences in Auditory Statistical Learning of Complex Speech Streams: Evidence From ERPs

Statistical learning (SL), the ability to pick up regularities in the sensory environment, is a fundamental skill that allows us to structure the world in a regular and predictable way. Although extensive evidence has been gathered from children and adults, the changes that SL might undergo throughout development remain contentious, particularly in the auditory modality (aSL) with linguistic materials. Here, we collected Event-Related Potentials (ERPs) while 5 years-old children and young adults (university students) were exposed to a complex speech stream in which eight three-syllable nonsense words - four with high (1.0) and four with low (.50) transitional probabilities were embedded to further examine how aSL works under less predictable conditions and to enhance age-related differences in the neural correlates of aSL. Moreover, to ascertain how previous knowledge of the to-be-learned regularities might also affect the results, participants performed the aSL task, firstly, under implicit and, subsequently, under explicit conditions. Although behavioral signs of aSL were observed only for adult participants, ERP data showed evidence of aSL in both groups, as indexed by modulations in the N100 and N400 components. A detailed analysis of the neural responses suggests, however, that adults and children rely on different mechanisms to assist aSL.

Dynamics of inhaled corticosteroid use are associated with asthma attacks

Inhaled corticosteroids (ICS) suppress eosinophilic airway inflammation in asthma, but patients may not adhere to prescribed use. Mean adherence—averaging total doses taken over prescribed—fails to capture many aspects of adherence. Patients with difficult-to-treat asthma underwent electronic monitoring of ICS, with data collected over 50 days. These were used to calculate entropy (H) a measure of irregular inhaler use over this period, defined in terms of transitional probabilities between different levels of adherence, further partitioned into increasing (Hinc) or decreasing (Hdec) adherence. Mean adherence, time between actuations (Gapmax), and cumulative time- and dose-based variability (area-under-the-curve) were measured. Associations between adherence metrics and 6-month asthma status and attacks were assessed. Only H and Hdec were associated with poor baseline status and 6-month outcomes: H and Hdec correlated negatively with baseline quality of life (H:Spearman rS = − 0·330, p = 0·019, Hdec:rS = − 0·385, p = 0·006) and symptom control (H:rS = − 0·288, p = 0·041, Hdec: rS = − 0·351, p = 0·012). H was associated with subsequent asthma attacks requiring hospitalisation (Wilcoxon Z-statistic = − 2.34, p = 0·019), and Hdec with subsequent asthma attacks of other severities. Significant associations were maintained in multivariable analyses, except when adjusted for blood eosinophils. Entropy analysis may provide insight into adherence behavior, and guide assessment and improvement of adherence in uncontrolled asthma.

IMPLICIT LANGUAGE APTITUDE: CONCEPTUALIZING THE CONSTRUCT, VALIDATING THE MEASURES, AND EXAMINING THE EVIDENCE

This article discusses the conceptualization, measurement, and validity of a recently emerged construct in the field of second language acquisition (SLA)—implicit language aptitude (alternatively “implicit aptitude”). Implicit aptitude is a set of cognitive abilities that enable learners to make unconscious computations of the distributional and transitional probabilities of linguistic input. Implicit aptitude is key to an accurate understanding of the cognitive foundation of language learning and contributes significantly to the advancement of SLA theory and pedagogy. The article starts by clarifying the concept and components of implicit aptitude, elaborating its role in SLA theories, identifying its attributes, and discussing its measurement. It then synthesizes the empirical evidence on its divergent, convergent, and predictive validity, which refers to whether it is distinct or separable from explicit aptitude, whether measures of implicit aptitude are correlated, and whether it is predictive of learning outcomes, respectively. Next, the article provides an overview of the seven empirical studies included in this special issue that examined implicit aptitude from various perspectives. The article concludes by identifying future directions.

The Influence of Different Prosodic Cues on Word Segmentation

A prerequisite for spoken language learning is segmenting continuous speech into words. Amongst many possible cues to identify word boundaries, listeners can use both transitional probabilities between syllables and various prosodic cues. However, the relative importance of these cues remains unclear, and previous experiments have not directly compared the effects of contrasting multiple prosodic cues. We used artificial language learning experiments, where native German speaking participants extracted meaningless trisyllabic “words” from a continuous speech stream, to evaluate these factors. We compared a baseline condition (statistical cues only) to five test conditions, in which word-final syllables were either (a) followed by a pause, (b) lengthened, (c) shortened, (d) changed to a lower pitch, or (e) changed to a higher pitch. To evaluate robustness and generality we used three tasks varying in difficulty. Overall, pauses and final lengthening were perceived as converging with the statistical cues and facilitated speech segmentation, with pauses helping most. Final-syllable shortening hindered baseline speech segmentation, indicating that when cues conflict, prosodic cues can override statistical cues. Surprisingly, pitch cues had little effect, suggesting that duration may be more relevant for speech segmentation than pitch in our study context. We discuss our findings with regard to the contribution to speech segmentation of language-universal boundary cues vs. language-specific stress patterns.

Statistical learning of unbalanced exclusive-or temporal sequences in humans

A pervasive issue in statistical learning has been to determine the parameters of regularity extraction. Our hypothesis was that the extraction of transitional probabilities can prevail over frequency if the task involves prediction. Participants were exposed to four repeated sequences of three stimuli (XYZ) with each stimulus corresponding to the position of a red dot on a touch screen that participants were required to touch sequentially. The temporal and spatial structure of the positions corresponded to a serial version of the exclusive-or (XOR) that allowed testing of the respective effect of frequency and first- and second-order transitional probabilities. The XOR allowed the first-order transitional probability to vary while being not completely related to frequency and to vary while the second-order transitional probability was fixed (p(Z|X, Y) = 1). The findings show that first-order transitional probability prevails over frequency to predict the second stimulus from the first and that it also influences the prediction of the third item despite the presence of second-order transitional probability that could have offered a certain prediction of the third item. These results are particularly informative in light of statistical learning models.