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This paper examines the extent to which large language models (LLMs) have developed higher-order theory of mind (ToM); the human ability to reason about multiple mental and emotional states in a recursive manner (e.g. I think that you believe that she knows). This paper builds on prior work by introducing a handwritten test suite -- Multi-Order Theory of Mind Q&A -- and using it to compare the performance of five LLMs to a newly gathered adult human benchmark. We find that GPT-4 and Flan-PaLM reach adult-level and near adult-level performance on ToM tasks overall, and that GPT-4 exceeds adult performance on 6th order inferences. Our results suggest that there is an interplay between model size and finetuning for the realisation of ToM abilities, and that the best-performing LLMs have developed a generalised capacity for ToM. Given the role that higher-order ToM plays in a wide range of cooperative and competitive human behaviours, these findings have significant implications for user-facing LLM applications.

The personal network of relationships is structured in circles of friendships, that go from the most intense relationships to the least intense ones. While this is a well established result, little is known about the stability of those circles and their evolution in time. To shed light on this issue, we study the temporal evolution of friendships among teenagers during two consecutive academic years by means of a survey administered on five occasions. We show that the first two circles, best friends and friends, can be clearly observed in the survey but also that being in one or the other leads to more or less stable relationships. We find that being in the same class is one of the key drivers of friendship evolution. We also observe an almost constant degree of reciprocity in the relationships, around 60%, a percentage influenced both by being in the same class and by gender homophily. Not only do our results confirm the mounting evidence supporting the circle structure of human social networks, but they also show that these structures persist in time despite the turnover of individual relationships -- a fact that may prove particularly useful for understanding the social environment in middle schools., Comment: 10 pages, 7 figures, requires wlscirep.cls, jabbrv.sty, jabbrv-ltwa-all.ldf, and jabbrv-ltwa-en.ldf (included)

In recent years it has become evident the need of understanding how failure of coordination imposes constraints on the size of stable groups that highly social mammals can live in. We examine here the forces that keep animals together as a herd and others that drive them apart. Different phenotypes (e.g. genders) have different rates of gut fill, causing them to spend different amounts of time performing activities. By modeling a group as a set of semi-coupled oscillators on a disc, we show that the members of the group may become less and less coupled until the group dissolves and breaks apart. We show that when social bonding creates a stickiness, or gravitational pull, between pairs of individuals, fragmentation is reduced., Comment: Dedicated to Prof. Fidel A. Schaposnik on the occasion of his 75th birthday

Humans are social animals and the interpersonal bonds formed between them are crucial for their development and well being in a society. These relationships are usually structured into several layers (Dunbar's layers of friendship) depending on their significance in an individual's life with closest friends and family being the most important ones taking major part of their time and communication effort. However, we have little idea how the initiation and termination of these relationships occurs across the lifespan. To explore this, we analyse a national cellphone database to determine how and when changes in close relationships occur in the two genders. In general, membership of this inner circle of intimate relationships is extremely stable, at least over a three-year period. However, around 1-4% of alters change every year, with the rate of change being higher among 17-21 year olds than older adults. Young adult females terminate more of their opposite-gender relationships, while older males are more persistent in trying to maintain relationships in decline. These results emphasise the variability in relationship dynamics across age and gender, and remind us that individual differences play an important role in the structure of social networks. Overall, our study provides a holistic understanding of the dynamic nature of relationships during the life-course of humans., Comment: 11 pages, 6 figures

Timings of human activities are marked by circadian clocks which in turn are entrained to different environmental signals. In an urban environment the presence of artificial lighting and various social cues tend to disrupt the natural entrainment with the sunlight. However, it is not completely understood to what extent this is the case. Here we exploit the large-scale data analysis techniques to study the mobile phone calling activity of people in large cities to infer the dynamics of urban daily rhythms. From the calling patterns of about 1,000,000 users spread over different cities but lying inside the same time-zone, we show that the onset and termination of the calling activity synchronizes with the east-west progression of the sun. We also find that the onset and termination of the calling activity of users follows a yearly dynamics, varying across seasons, and that its timings are entrained to solar midnight. Furthermore, we show that the average mid-sleep time of people living in urban areas depends on the age and gender of each cohort as a result of biological and social factors., Comment: This manuscript includes and extends content from our old manuscript "Seasonal and geographical influence on sleeping patterns inferred from mobile phone data", which was split into two parts due to its length and new investigations added

In human relations individuals' gender and age play a key role in the structures and dynamics of their social arrangements. In order to analyze the gender preferences of individuals in interaction with others at different stages of their lives we study a large mobile phone dataset. To do this we consider four fundamental gender-related caller and callee combinations of human interactions, namely male to male, male to female, female to male, and female to female, which together with age, kinship, and different levels of friendship give rise to a wide scope of human sociality. Here we analyse the relative strength of these four types of interaction using a large dataset of mobile phone communication records. Our analysis suggests strong age dependence for an ego of one gender choosing to call an individual of either gender. We observe a strong opposite sex bonding across most of their reproductive age. However, older women show a strong tendency to connect to another female that is one generation younger in a way that is suggestive of the \emph{grandmothering effect}. We also find that the relative strength among the four possible interactions depends on phone call duration. For calls of medium and long duration, opposite gender interactions are significantly more probable than same gender interactions during the reproductive years, suggesting potential emotional exchange between spouses. By measuring the fraction of calls to other generations we find that mothers tend to make calls more to their daughters than to their sons, whereas fathers make calls more to their sons than to their daughters. For younger people, most of their calls go to same generation alters, while older people call the younger people more frequently, which supports the suggestion that \emph{affection flows downward}., Comment: 12 pages, 8 figures

We study the influence of seasonally and geographically related daily dynamics of daylight and ambient temperature on human resting or sleeping patterns using mobile phone data of a large number of individuals. We observe two daily inactivity periods in the people's aggregated mobile phone calling patterns and infer these to represent the resting times of the population. We find that the nocturnal resting period is strongly influenced by the length of daylight, and that its seasonal variation depends on the latitude, such that for people living in two different cities separated by eight latitudinal degrees, the difference in the resting period of people between the summer and winter in southern cities is almost twice that in the northern cities. We also observe that the duration of the afternoon resting period is influenced by the temperature, and that there is a threshold from which this influence sets in. Finally, we observe that the yearly dynamics of the afternoon and nocturnal resting periods appear to be counterbalancing each other. This also lends support to the notion that the total daily resting time of people is more or less conserved across the year., Comment: This version substitutes the previous manuscript (with old title "Seasonal and geographical influence on sleeping patterns inferred from mobile phone data"), which now is split into two manuscripts due to its length and new investigations added. The current version includes the part related to seasonal variations of the resting periods

Age and gender are two important factors that play crucial roles in the way organisms allocate their social effort. In this study, we analyse a large mobile phone dataset to explore the way lifehistory influences human sociality and the way social networks are structured. Our results indicate that these aspects of human behaviour are strongly related to the age and gender such that younger individuals have more contacts and, among them, males more than females. However, the rate of decrease in the number of contacts with age differs between males and females, such that there is a reversal in the number of contacts around the late 30s. We suggest that this pattern can be attributed to the difference in reproductive investments that are made by the two sexes. We analyse the inequality in social investment patterns and suggest that the age and gender-related differences that we find reflect the constraints imposed by reproduction in a context where time (a form of social capital) is limited., Comment: 11 pages, 6 figures

Humans follow circadian rhythms, visible in their activity levels as well as physiological and psychological factors. Such rhythms are also visible in electronic communication records, where the aggregated activity levels of e.g. mobile telephone calls or Wikipedia edits are known to follow their own daily patterns. Here, we study the daily communication patterns of 24 individuals over 18 months, and show that each individual has a different, persistent communication pattern. These patterns may differ for calls and text messages, which points towards calls and texts serving a different role in communication. For both calls and texts, evenings play a special role. There are also differences in the daily patterns of males and females both for calls and texts, both in how they communicate with individuals of the same gender vs. opposite gender, and also in how communication is allocated at social ties of different nature (kin ties vs. non-kin ties). Taken together, our results show that there is an unexpected richness to the daily communication patterns, from different types of ties being activated at different times of day to different roles of communication channels and gender differences.

Circadian rhythms are known to be important drivers of human activity and the recent availability of electronic records of human behaviour has provided fine-grained data of temporal patterns of activity on a large scale. Further, questionnaire studies have identified important individual differences in circadian rhythms, with people broadly categorised into morning-like or evening-like individuals. However, little is known about the social aspects of these circadian rhythms, or how they vary across individuals. In this study we use a unique 18-month dataset that combines mobile phone calls and questionnaire data to examine individual differences in the daily rhythms of mobile phone activity. We demonstrate clear individual differences in daily patterns of phone calls, and show that these individual differences are persistent despite a high degree of turnover in the individuals' social networks. Further, women's calls were longer than men's calls, especially during the evening and at night, and these calls were typically focused on a small number of emotionally intense relationships. These results demonstrate that individual differences in circadian rhythms are not just related to broad patterns of morningness and eveningness, but have a strong social component, in directing phone calls to specific individuals at specific times of day.

The dynamics of close relationships is important for understanding the migration patterns of individual life-courses. The bottom-up approach to this subject by social scientists has been limited by sample size, while the more recent top-down approach using large-scale datasets suffers from a lack of detail about the human individuals. We incorporate the geographic and demographic information of millions of mobile phone users with their communication patterns to study the dynamics of close relationships and its effect in their life-course migration. We demonstrate how the close age- and sex-biased dyadic relationships are correlated with the geographic proximity of the pair of individuals, e.g., young couples tend to live further from each other than old couples. In addition, we find that emotionally closer pairs are living geographically closer to each other. These findings imply that the life-course framework is crucial for understanding the complex dynamics of close relationships and their effect on the migration patterns of human individuals., Comment: 9 pages, 7 figures

We used a large database of 9 billion calls from 20 million mobile users to examine the relationships between aggregated time spent on the phone, personal network size, tie strength and the way in which users distributed their limited time across their network (disparity). Compared to those with smaller networks, those with large networks did not devote proportionally more time to communication and had on average weaker ties (as measured by time spent communicating). Further, there were not substantially different levels of disparity between individuals, in that mobile users tend to distribute their time very unevenly across their network, with a large proportion of calls going to a small number of individuals. Together, these results suggest that there are time constraints which limit tie strength in large personal networks, and that even high levels of mobile communication do not fundamentally alter the disparity of time allocation across networks., Comment: 10 pages, 3 figures. Accepted for publication in Social Networks

Mobile phone communication as digital service generates ever-increasing datasets of human communication actions, which in turn allow us to investigate the structure and evolution of social interactions and their networks. These datasets can be used to study the structuring of such egocentric networks with respect to the strength of the relationships by assuming direct dependence of the communication intensity on the strength of the social tie. Recently we have discovered that there are significant differences between the first and further "best friends" from the point of view of age and gender preferences. Here we introduce a control parameter $p_{\rm max}$ based on the statistics of communication with the first and second "best friend" and use it to filter the data. We find that when $p_{\rm max}$ is decreased the identification of the "best friend" becomes less ambiguous and the earlier observed effects get stronger, thus corroborating them., Comment: 11 pages, 7 figures

Social networks have turned out to be of fundamental importance both for our understanding human sociality and for the design of digital communication technology. However, social networks are themselves based on dyadic relationships and we have little understanding of the dynamics of close relationships and how these change over time. Evolutionary theory suggests that, even in monogamous mating systems, the pattern of investment in close relationships should vary across the lifespan when post-weaning investment plays an important role in maximising fitness. Mobile phone data sets provide us with a unique window into the structure of relationships and the way these change across the lifespan. We here use data from a large national mobile phone dataset to demonstrate striking sex differences in the pattern in the gender-bias of preferred relationships that reflect the way the reproductive investment strategies of the two sexes change across the lifespan: these differences mainly reflect women's shifting patterns of investment in reproduction and parental care. These results suggest that human social strategies may have more complex dynamics than we have tended to assume and a life-history perspective may be crucial for understanding them., Comment: 5 pages, 3 figures, contains electronic supplementary material