Cognition & Foundations  (CF) Session 2

Abstract: How similar are two examples of music or text from different authors or disciplines? How fast is the vocabulary of a language changing over time? How can one distinguish between coding and noncoding regions in DNA? Quantifying the similarity between symbolic sequences is a traditional problem in information theory which requires comparing the frequencies of symbols in different sequences. We will address this problem for the important case in which the frequencies of symbols show heavy-tailed distributions (e.g. the famous Zipf's law for word-frequencies), which hinder an accurate finite-size estimation of entropies, and for a family of similarity measures based on the generalized entropy of order α. We will show analytically how the systematic (bias) and statistical (fluctuations) errors in these estimations depend on the sample size N, on the exponent γ of the heavy-tailed distribution and the order alpha of the similarity measure. Our primary finding is that, for heavy-tailed distributions, (i) the error decay is often much slower than 1/N, illustrating the difficulty in obtaining accurate estimates even for large sample sizes, and (ii) there is a critical value of the order of the entropy α∗=1+1/γ≤2 for which the normal 1/N dependence is recovered. We emphasize the importance of these findings in the example of quantifying how fast the English vocabulary has changed within the last 200 years, showing that these finite-size effects have to be taken into account even for very large databases (N≳1,000,000,000 words). Associated reference: DOI:http://dx.doi.org/10.1103/PhysRevX.6.021009 Close

Abstract: Understanding the formation of subjective human traits, such as preference and opinions, is an important, but poorly explored problem. It is essential that traits collectively evolve under the repeated action of social influence, which is the focus of many studies of cultural dynamics. In this paradigm, other mechanisms potentially relevant for trait formation are reduced to specifying the initial cultural state for the social influence models, state which usually is generated in a uniformly random way. However, recent work has shown that the outcome of social influence dynamics strongly depends on the nature of the initial state: a higher level of cultural diversity is found after long-term dynamics, for the same level of propensity towards collective behaviour in the short term, if the initial cultural state is sampled from empirical data instead of being generated in a uniformly random way. First, this study shows that this effect is remarkably robust across data sets. In a certain sense, the analysis suggests that systems from which such data is extracted function close to criticality. Second, this study presents a stochastic model for generating cultural states that retain the universal properties. One ingredient of the model, already used in previous work, assumes that every individual's set of traits is partly dictated by one of several ``cultural prototypes'', which are abstract entities informally postulated by several social science theories. A second, new ingredient, taken from the same theories, assumes that apart from a dominant prototype, each individual also has a certain exposure to the other prototypes. The fact that this combination of ingredients is compatible with regularities of empirical data suggests that cultural traits in the real world form under the combined influence of several cultural prototypes, thus providing indirect evidence for the class of social science theories compatible with this description. Close

Abstract: The analysis of school-age children engaged in engineering projects has proceeded by examining the conversations that take place among those children. The analysis of classroom discourse often considers a conversational turn to be the unit of analysis. In this study, small-group conversations among students engaged in a robotics project are analyzed by forming a dynamic network with the students as nodes and the utterances of each turn as edges. The data collected for this project contained more than 1000 turns for each group, with each group consisting of 4 students (and the occasional inclusion of a teacher or other interloper). The conversational turns were coded according to their content to form edges that vary qualitatively, with the content codes taken from prior literature on small group discourse during engineering design projects, resulting in approximately 10 possible codes for each edge. Analyzed as a time sequence of networks, clusters across turns were created that allow for a larger unit of analysis than is usually used. These larger units of analysis are more fruitfully connected to the stages of engineering design. Furthermore, the patterns uncovered allow for hypotheses to be made about the dynamics of transition between these stages, and also allow for these hypotheses to be compared to expert consideration of the group’s stage at various times. Although limited by noise and inter-group variation, the larger units allowed for greater insight into group processes during the engineering design cycle. Close

Abstract: In directed networks, edges often represent a transfer of power, social influence, or confidence. In some cases, this is explicit, as in the case of directed acts of dominance inflicted by one animal upon another. In other cases, the relationship is more implicit: when one university hires another's graduate, the hiring department is expressing confidence in the quality of the graduate's department's training. Given such a network, it is possible to rank individual vertices using a variety of methods, such as minimum violations or PageRank. However, in many real-world systems, groups of individuals are ranked, and expressions of influence or dominance by individuals, captured by network edges, simply reflect group affiliations--a type of large-scale network structure that has not been previously described. In this work, we introduce a definition of ranked communities in directed networks and propose an algorithm to efficiently identify them. The mathematical framework of our method is placed in the context of the related problem of classic modularity maximization and we introduce an important distinction between strict (dominance) and inclusive (endorsement) hierarchies. We confirm our method's ability to extract planted ranked community structure in synthetic networks before applying it to learn about real-world networks. In particular, this method allows us to quantitatively study a question posed over half a century ago regarding the relationship between social network structure and the Indian caste system. We show that our recently collected data of a social support network in two South Indian villages is structured according to a mixture of ranked caste-based communities and community-transcending individual relationships. In this system, organization by ranked community is related to known social structure, but we also apply our method to learn about other social and ecological networks in which the organizing mechanisms have yet to be identified. Close

Abstract: One important aspect of studying the behavior of dynamical systems is the analysis of processes of stability and change over time. This requires an estimation of auto-correlative and cyclical patterns in sets of frequently repeated measurements of the behavior of such systems. Traditional mean and (co)variance computations typically used for cross-sectional data are not adequate to characterize these distributions, and may actually be misleading (Beran, 1994). Daily school attendance is presented as a case in point. Since 2004 and to this day, the New York City Department of Education has published daily attendance rates on its website for all of its schools. These data exhibit the degree of resolution needed to detect underlying systems dynamics that are hidden in the conventionally reported weekly, monthly or yearly average rates. Daily attendance rates in six small high schools were analyzed over a ten-year period (2005 – 2014). The analysis proceeded as follows: 1. intervention models were fitted to handle the most extreme values in the series (usually low attendance) for each school, 2. Conventional time series analyses were used to estimate short-term dependencies and cyclical patterns, 3. The goodness of fit of those models was compared with that of models including long-range estimates (fractional differencing parameter, Hurst exponent). Preliminary analyses suggest significant long-range dependencies in two of these six schools, suggesting self-organized criticality (tension-release, unpredictable cycles), and strong weekly cycles in the four others. The presentation will illustrate how the initial appearance of the data in the various diagnostic plots suggests long-range dependencies, and the parameters of the best fitting models are interpreted. Implications of the findings for the field are discussed, and a note is included about the available software options for conducting these types of analyses. References: Beran, J. (1994). Statistics for long-memory processes. Boca Raton, FL: Chapman & Hall/CRC. Close

Abstract: Organisational decision making, where many individuals interact to share information, formulate decisions and perform actions, is at heart a social system oriented towards outcomes - success in a military mission or business venture. In recent years I have proposed the Kuramoto model of synchronising oscillators to represent such a system that may be developed towards predictive modelling against specific scenarios. Essentially here, the oscillator limit cycle represents what is known in cognitive psychology as a Perception-Action cycle, or in military parlance an Observe-Orient-Decide-Action loop; the network of interactions may represent the range of formal, information and technology based exchanges of information; finally, a native frequency represents the individual speed of decision-making for an agent left to themselves. To such a system may be added stochastic influences, or “noise”, to represent the human properties of intuition, indecision or degrading of communication under stress or mood shifts. In this paper, I propose the model in application to a military organisation as may be located in a deployed headquarters. I use data based on a recent study of such an organisation where participants responded to surveys and interviews probing their pattern of interactions and level of cognition (in the sense of the Perception-Action cycle) for two scenarios: routine business and an emergency response. For noise I use a combination of stable Lévy noise both in spatial and temporal dimensions, where the underlying probability distributions for this exhibit power-law heavy tails. I summarise an initial validation of the model, invoking another approach in organisation theory known as Contingency Theory. The model thus integrates ideas from quantitative and qualitative complexity theory. To illustrate the utility of the model, I study a number of interventions in the model: local network modifications and/or training in order to tighten frequency distributions. I conclude with prospects for future work. Close