Algorithmic complexity for psychology: a user-friendly implementation of the coding theorem method

Kolmogorov-Chaitin complexity has long been believed to be impossible to approximate when it comes to short sequences (e.g. of length 5-50). However, with the newly developed coding theorem method the complexity of strings of length 2-11 can now be numerically estimated. We present the theoretical basis of algorithmic complexity for short strings (ACSS) and describe an R-package providing functions based on ACSS that will cover psychologists’ needs and improve upon previous methods in three ways: (1) ACSS is now available not only for binary strings, but for strings based on up to 9 different symbols, (2) ACSS no longer requires time-consuming computing, and (3) a new approach based on ACSS gives access to an estimation of the complexity of strings of any length. Finally, three illustrative examples show how these tools can be applied to psychology.     

Information‐Theoretic Measures Predict the Human Judgment of Rhythm Complexity

To formalize the human judgment of rhythm complexity, we used five measures from information theory and algorithmic complexity to measure the complexity of 48 artificially generated rhythmic sequences. We compared these measurements to human prediction accuracy and easiness judgments obtained from a listening experiment, in which 32 participants guessed the last beat of each sequence. We also investigated the modulating effects of musical expertise and general pattern identification ability. Entropy rate and Kolmogorov complexity were correlated with prediction accuracy, and highly correlated with easiness judgments. A logistic regression showed main effects of musical training, entropy rate, and Kolmogorov complexity, and an interaction between musical training and both entropy rate and Kolmogorov complexity. These results indicate that information‐theoretic concepts capture some salient features of the human judgment of rhythm complexity, and they confirm the influence of musical expertise on complexity judgments.     

A fast numerical algorithm for the estimation of diffusion model parameters

In this paper, we describe a new algorithmic approach for parameter estimation in Ratcliff's [(1978). A theory of memory retrieval. Psychological Review, 85 (2), 59-108] diffusion model. This problem, especially if inter-trial variabilities of parameters are included in the model, is computationally very expensive; the parameter estimation procedure often takes a long time even with today's high-speed computers. The algorithm described here makes the calculation of the cumulative distribution functions for predicted process durations computationally much less expensive. This improvement is achieved by solving the Kolmogorov backward equation numerically instead of employing the previously used closed form solution. Additionally, the algorithm can determine the optimum fit for one of the model parameters (the starting point z) directly, thereby reducing the dimension of the parameter search space by one. The resulting method is shown to be notably faster than the standard (closed-form solution) method for parameter estimation.     

AN ALGORITHMIC INFORMATION THEORY CHALLENGE TO INTELLIGENT DESIGN

William Dembski claims to have established a decision process to determine when highly unlikely events observed in the natural world are due to Intelligent Design. This article argues that, as no implementable randomness test is superior to a universal Martin‐Löf test, this test should be used to replace Dembski's decision process. Furthermore, Dembski's decision process is flawed, as natural explanations are eliminated before chance. Dembski also introduces a fourth law of thermodynamics, his “law of conservation of information,” to argue that information cannot increase by natural processes. However, this article, using algorithmic information theory, shows that this law is no more than the second law of thermodynamics. The article concludes that any discussions on the possibilities of design interventions in nature should be articulated in terms of the algorithmic information theory approach to randomness and its robust decision process.     

Hypnotic assessment based on the Recurrence Quantification Analysis of EEG recorded in the ordinary state of consciousness

The cerebral cortical correlates of the susceptibility to hypnosis in the ordinary states of consciousness have not been clarified. Aim of the study was to characterize the EEG dynamics of subjects with high (highs) and low hypnotisability (lows) through the non-linear method of Recurrence Quantification Analysis (RQA). The EEG of 16 males – 8 highs and 8 lows – was monitored for 1 min without instructions other than keeping the eyes closed, being silent and avoiding movements (short resting), and during 15 min of simple relaxation, that is with the instruction to relax at their best. Highs and lows were compared on the RQA measures of Determinism (DET) and Entropy (ENT), which are related to the signal determinism and complexity. In the short resting condition discriminant analysis could classify highs and lows on the basis of DET and ENT values at temporo-parietal sites. Many differences in DET and all differences in ENT disappeared during simple relaxation, although DET still separated the two groups in the earliest 6 min of relaxation at temporo-parietal sites. Our RQA based approach allows to develop computer-based methods of hypnotic assessment using short-lasting, single channel EEG recordings analyzed through standard mathematical methods.     

The Soundness of Internalized Polarity Marking

This paper provides a foundation for the polarity marking technique introduced by David Dowty [3] in connection with monotonicity reasoning in natural language and in linguistic analyses of negative polarity items based on categorial grammar. Dowty??s work is an alternative to the better-known algorithmic approach first proposed by Johan van Benthem [11], and elaborated by Víctor Sánchez Valencia [10]. Dowty??s system internalized the monotonicity/polarity markings by generating strings using a categorial grammar whose categories already contain the markings that the earlier system would obtain by separate steps working on an already-derived string. Despite the linguistic advantages of the internalized system, no soundness proof has yet been given for it. This paper offers an account. The leading mathematical idea is to interpret categorial types as preorders (in order to talk about monotonicity in the first place), and then to add a primitive operation to the type hierarchy of taking the opposite of a preorder (in order to capture monotone decreasing functions). At the same time, the use of internalized categories also raises issues. Although these will not be addressed in full, the paper points out possible approaches to them.     

Similarity, kernels, and the triangle inequality

Similarity is used as an explanatory construct throughout psychology and multidimensional scaling (MDS) is the most popular way to assess similarity. In MDS, similarity is intimately connected to the idea of a geometric representation of stimuli in a perceptual space. Whilst connecting similarity and closeness of stimuli in a geometric representation may be intuitively plausible, Tversky and Gati [Tversky, A., & Gati, I. (1982). Similarity, separability, and the triangle inequality. Psychological Review, 89(2), 123-154] have reported data which are inconsistent with the usual geometric representations that are based on segmental additivity. We show that similarity measures based on Shepard’s universal law of generalization [Shepard, R. N. (1987). Toward a universal law of generalization for psychologica science. Science, 237(4820), 1317-1323] lead to an inner product representation in a reproducing kernel Hilbert space. In such a space stimuli are represented by their similarity to all other stimuli. This representation, based on Shepard’s law, has a natural metric that does not have additive segments whilst still retaining the intuitive notion of connecting similarity and distance between stimuli. Furthermore, this representation has the psychologically appealing property that the distance between stimuli is bounded.     

Yes, we still need Universal Grammar

In a recent paper [Lidz, J., Gleitman, H., & Gleitman, L. (2003). Understanding how input matters: Verb learning and the footprint of universal grammar. Cognition, 87, 151-178], we provided cross-linguistic evidence in favor of the following linked assertions: (i) Verb argument structure is a correlate of verb meaning; (ii) However, argument structure is not directly available to learners as a cue for reconstructing verb meaning, owing to the complexity of form-meaning mappings within and across languages; (iii) A major correlate of argument-structure, namely, noun phrase number, is statistically available on the surface in all languages, and serves as a quasi-universal derivative cue to the meanings of verbs; (iv) this cue is privileged, in the sense that it is used early and selectively by learners, despite within- and cross-language differences in its availability. Goldberg [Goldberg, A. (2004). But do we need Universal Grammar? Comment on Lidz, Gleitman and Gleitman 2003. Cognition] suggests that this cue is not linguistic, that it is too sicklied o'er with exceptions and provisos to be useful to learners, and that conversational conspiracies can in any case serve as the alternative theoretical framework for a theory of predicate learning, and language acquisition more generally. In the present reply, we review and further explicate our original position, to wit: A large part of any generative grammar is a formal statement of the complex alignments between predicate-argument structures and the surface forms (linear strings of words) of sentences. Because the several rules for alignment interact, the surface outcomes reveal individual systematicities only abstractly. Therefore, learning would be impossible if infants could not analyze probabilistically available patterns to recover their principled linguistic sources. This statistics-based discovery procedure is in certain relevant regards specific to language learning. Finally, we argue that while pragmatics and theory of mind properties in learner and tutor necessarily frame language acquisition, that these have not been shown—and probably cannot be shown—to be sufficient to this computational problem.     

Masked transposition effects for simple versus complex nonalphanumeric objects

When two letters/digits/symbols are switched in a string (e.g., jugde–judge; 1492–1942; *?When two letters/digits/symbols are switched in a string (e.g., jugde-judge; 1492-1942; *?$&-*$?&), the resulting strings are perceptually similar to each other and produce a sizable masked transposition priming effect with the masked priming same-different matching task. However, a parallel effect does not occur for strings of pseudoletters (e.g., [letters in the text]); García-Orza, Perea, & Mu?oz, Quarterly Journal of Experimental Psychology, 63, 1603-1618, 2010). In the present study, we examined whether masked transposition priming is specific to alphanumeric stimuli or whether it also occurs with strings composed of other "objects"-namely, line drawings of common objects (Experiment 1) and geometrical shapes (Experiment 2). Results showed a significant masked transposition priming effect for geometrical shapes (e.g., [geometrical shapes in the text]), but not for line drawings of common objects (e.g., [symbols in the text]). These findings suggest that the mechanism involved in the coding of position in masked priming works only with perceptually simple, familiar "objects" (i.e., letters, numbers, symbols, or geometrical shapes), once their identities have been well ascertained.     

Structuring temporal sequences: Comparison of models and factors of complexity

Two stages for structuring tone sequences have been distinguished by Povel and Essens (1985). In the first, a mental clock segments a sequence into equal time units (clock model); in the second, intervals are specified in terms of subdivisions of these units. The present findings support the clock model in that it predicts human performance better than three other algorithmic models. Two further experiments in which clock and subdivision characteristics were varied did not support the hypothesized effect of the nature of the subdivisions on complexity. A model focusing on the variations in the beat-anchored envelopes of the tone clusters was proposed. Errors in reproduction suggest a dual-code representation comprising temporaland figural characteristics. The temporal part of the representation is based on the clock model but specifies, in addition, the metric of the level below the clock. The beat-tone-cluster envelope concept was proposed to specify the figural part.     

Retinal painting and visual information storage

As a measure of visual information storage (VIS), Haber and Nathanson (1968) have used a retinal painting task involving passing a narrow slit across a drawing which the S has to see as a single percept. Two experiments were conducted to evaluate this task as a measure of VIS. In experiment 1 it was shown that contrary to other measures of VIS, adults have longer values than children. In experiment 2 dyslexic and control children performed at equivalent levels on this task. It is suggested that retinal painting involves a different persistence effect to that normally used as a measure of VIS.     

Individual behavior in learning of an artificial grammar

Artificial grammar learning (AGL) is a widely used experimental paradigm that investigates how syntactic structures are processed. After a familiarization phase, participants have to distinguish strings consistent with a set of grammatical rules from strings that violate these rules. Many experiments report performance solely at a group level and as the total number of correct judgments. This report describes a systematic approach for investigating individual performance and a range of different behaviors. Participants were exposed to strings of the nonfinite grammar A ⁿ B ⁿ . To distinguish grammatical from ungrammatical strings, participants had to pay attention to local dependencies while comparing the number of stimuli from each class. Individual participants showed substantially different behavioral patterns despite exposure to the same stimuli. The results were replicated across auditory and visual sensory modalities. It is suggested that an analysis that looks at individual differences grants new insights into the processes involved in AGL. It also provides a solid basis from which to investigate sequence-processing abilities in special populations, such as patients with neurological lesions.     

Phonological complexity in school-aged children who stutter and exhibit a language disorder

PurposeThe Index of Phonological Complexity and the Word Complexity Measure are two measures of the phonological complexity of a word. Other phonological measures such as phonological neighborhood density have been used to compare stuttered versus fluent words. It appears that in preschoolers who stutter, the length and complexity of the utterance is more influential than the phonetic features of the stuttered word. The present hypothesis was that in school-age children who stutter, stuttered words would be more phonologically complex than fluent words, when the length and complexity of the utterance containing them is comparable. School-age speakers who stutter were hypothesized to differ from those with a concomitant language disorder.MethodsSixteen speakers, six females and ten males (M age = 12;3; Range = 7;7 to 19;5) available from an online database, were divided into eight who had a concomitant language disorder (S + LD) and eight age- and sex-matched speakers who did not (S-Only).ResultsWhen all stuttered content words were identified, S + LD speakers produced more repetitions, and S-Only speakers produced more inaudible sound prolongations. When stuttered content words were matched to fluent content words and when talker groups were combined, stuttered words were significantly (p ≤ 0.01) higher in both the Index of Phonological Complexity and the Word Complexity Measure and lower in density (“sparser”) than fluent words.ConclusionsResults corroborate those of previous researchers. Future research directions are suggested, such as cross-sectional designs to evaluate developmental patterns of phonological complexity and stuttering plus language disordered connections.Educational objectives: The reader will be able to: (a) Define and describe phonological complexity; (b) Define phonological neighborhood density and summarize the literature on the topic; (c) Describe the Index of Phonological Complexity (IPC) for a given word; (d) Describe the Word Complexity Measure (WCM) for a given word; (e) Summarize two findings from the current study and describe how each relates to studies of phonological complexity and fluency disorders.     

Isolating visual units in the perception of words and nonwords

In three experiments, reaction times for same-different judgments were obtained for pairs of words, pronounceable nonwords (pseudowords), and unpronounceable nonwords. The stimulus strings were printed either in a single letter case or in one of several mixtures of upper- and lowercase letters. In Experiment 1, the stimuli were common one- and two-syllable words; in Experiment 2, the stimuli included both words and pseudowords; and in Experiment 3, words, pseudowords, and nonwords were used. The functional visual units for each string type were inferred from the effects that the number and placement of letter case transitions had onsame reaction time judgments. The evidence indicated a preference to encode strings in terms of multiletter perceptual units if they are present in the string. The data .also suggested that whole words can be used as functional visual units, although the extent of their use depends on contextual parameters such as knowledge that a word will be presented.     

Simple visual reaction time,personality and strength of the nervous system: A signal-detection theory approach

Eysenck (1967) has reviewed evidence which suggests that introverts have a higher level of arousal than extraverts. Moreover, Gray (1967) has proposed that introverts have weak nervous systems, in the Russian terminology. Studies of simple reaction time such as that of Mangan and Farmer (1967) have posed problems for these views, but it is suggested that this may have been due to criterion differences between introverts and extraverts. In the present study a simple visual reaction-time task and a signal-detection task were conducted side by side. No significant differences between introverts and extraverts were found in measures of strength derived from the former, or measures of criterion derived from the latter. However, high N Ss were found to have a significantly lower value for Nebylitsyn's index of the slope of the reaction time/stimulus intensity function, thus supporting the view that high N Ss have relatively weak nervous systems.     

Measuring the validity and psychometric properties of a short form of the Hypomanic Personality Scale

The Hypomanic Personality Scale (HPS) is used to investigate hypomanic traits and risk for bipolar spectrum disorders; however, the length of the HPS (48 items) may be prohibitive for clinical research and screening purposes. Meads and Bentall (2008) developed a promising 20-item version of the HPS; however, the psychometric properties and validity of the short form have not been thoroughly examined. The present study investigated the construct validity and psychometric properties of the short HPS. A sample of 2713 non-clinically ascertained young adults was used to assess psychometric properties of the short form relative to the original scale. Two non-overlapping subsamples (n = 522; n = 145) were used to investigate the validity of the short HPS using personality and temperament questionnaires and clinical interviews of bipolar psychopathology and diagnoses. The short and original HPS generally had comparable correlations with measures of temperament, personality, impulsivity, borderline personality, grandiosity, psychosocial functioning, and alcohol use, and comparably predicted DSM bipolar and bipolar spectrum diagnoses. Overall, the short HPS was found to be both reliable and valid. However, the short HPS tended to be more strongly correlated with pathological components of hypomanic personality and less strongly correlated with exuberant and potentially adaptive aspects of the construct.     

BodiMojo: Effective Internet-based promotion of positive body image in adolescent girls

This study tested the efficacy of an Internet-based health promotion program, BodiMojo, designed to promote positive body image in adolescents. Participants were 178 students (mean age 15.2 years, 67.6% ethnic minority) in three public high schools. Intervention groups used BodiMojo for four weekly health class periods, while controls participated in their usual health curriculum. Body image measures were given at baseline, post-intervention, and 3 months. Girls reported decreased body dissatisfaction (p < .05), decreased physical appearance comparison (p < .05), and increased appearance satisfaction (p < .05), relative to controls. Effects were not maintained at 3-month follow-up. No significant differences were found between the intervention and control groups with boys. Moderation analyses suggested positive effects for diverse adolescents as well as those who were overweight or indicated baseline high body dissatisfaction. BodiMojo appears to be modestly effective in decreasing body image concerns among adolescent girls in the short term.     

Identifying and explaining apparent universal sex differences in cognition and behavior

With growing recognition that there are universal sex differences in cognition and behavior, four theories have been proposed to account for these differences: the founder effect theory, the social structuralist theory, the evolutionary theory, and the evolutionary neuroandrogenic (ENA) theory. The latter of these theories is described in considerable detail as offering an explanation for most of 65 recently identified apparent universal sex differences (AUSDs) in cognition and behavior. Regarding “ultimate causes” (why), ENA theory asserts that (a) evolutionary-genetic factors incline females to bias their mate choices toward males who are loyal and competent provisioners of resources and (b) males are merely a genetic variant on the female sex selected for responding to female mating biases. In terms of “proximate causes” (how), the theory maintains that high exposure to androgens has evolved to alter the male brain functioning in two specific ways relative to most female brains: (a) suboptimal arousal and (b) a rightward shift in neocortical functioning. These two functional patterns are described and hypothesized to incline males and females to learn differently in many respects. The most fundamental differences involve males learning ways of either complying with or circumventing female mate preferences. Numerous universal sex differences in cognition and behavior are hypothesized to result from these evolved neurohormonal factors, including most of the 65 AUSDs herein summarized in seven categorical tables.     

Selective auditory grouping by zebra finches: testing the iambic–trochaic law

Humans have a strong tendency to spontaneously group visual or auditory stimuli together in larger patterns. One of these perceptual grouping biases is formulated as the iambic/trochaic law, where humans group successive tones alternating in pitch and intensity as trochees (high–low and loud–soft) and alternating in duration as iambs (short–long). The grouping of alternations in pitch and intensity into trochees is a human universal and is also present in one non-human animal species, rats. The perceptual grouping of sounds alternating in duration seems to be affected by native language in humans and has so far not been found among animals. In the current study, we explore to which extent these perceptual biases are present in a songbird, the zebra finch. Zebra finches were trained to discriminate between short strings of pure tones organized as iambs and as trochees. One group received tones that alternated in pitch, a second group heard tones alternating in duration, and for a third group, tones alternated in intensity. Those zebra finches that showed sustained correct discrimination were next tested with longer, ambiguous strings of alternating sounds. The zebra finches in the pitch condition categorized ambiguous strings of alternating tones as trochees, similar to humans. However, most of the zebra finches in the duration and intensity condition did not learn to discriminate between training stimuli organized as iambs and trochees. This study shows that the perceptual bias to group tones alternating in pitch as trochees is not specific to humans and rats, but may be more widespread among animals.