How a "Hit" is Born: The Emergence of Popularity from the Dynamics of Collective Choice

In recent times there has been a surge of interest in seeking out patterns in the aggregate behavior of socio-economic systems. One such domain is the emergence of statistical regularities in the evolution of collective choice from individual behavior. This is manifested in the sudden emergence of popularity or "success" of certain ideas or products, compared to their numerous, often very similar, competitors. In this paper, we present an empirical study of a wide range of popularity distributions, spanning from scientific paper citations to movie gross income. Our results show that in the majority of cases, the distribution follows a log-normal form, suggesting that multiplicative stochastic processes are the basis for emergence of popular entities. This suggests the existence of some general principles of complex organization leading to the emergence of popularity. We discuss the theoretical principles needed to explain this socio-economic phenomenon, and present a model for collective behavior that exhibits bimodality, which has been observed in certain empirical popularity distributions.Comment: 17 pages, 14 figures, A version of the work is published in Econophysics and Sociophysics: Trends and Perspectives, (eds.) Bikas K. Chakrabarti, Anirban Chakraborti, Arnab Chatterjee; Wiley-VCH, Berlin (2006); Chapter-15, pages: 417-44

Effects of temporal correlations on cascades: Threshold models on temporal networks

A person's decision to adopt an idea or product is often driven by the decisions of peers, mediated through a network of social ties. A common way of modeling adoption dynamics is to use threshold models, where a node may become an adopter given a high enough rate of contacts with adopted neighbors. We study the dynamics of threshold models that take both the network topology and the timings of contacts into account, using empirical contact sequences as substrates. The models are designed such that adoption is driven by the number of contacts with different adopted neighbors within a chosen time. We find that while some networks support cascades leading to network-level adoption, some do not: the propagation of adoption depends on several factors from the frequency of contacts to burstiness and timing correlations of contact sequences. More specifically, burstiness is seen to suppress cascades sizes when compared to randomised contact timings, while timing correlations between contacts on adjacent links facilitate cascades.Comment: 9 pages, 7 figures, Published versio

The strength of strong ties in scientific collaboration networks

Network topology and its relationship to tie strengths may hinder or enhance the spreading of information in social networks. We study the correlations between tie strengths and topology in networks of scientific collaboration, and show that these are very different from ordinary social networks. For the latter, it has earlier been shown that strong ties are associated with dense network neighborhoods, while weaker ties act as bridges between these. Because of this, weak links act as bottlenecks for the diffusion of information. We show that on the contrary, in co-authorship networks dense local neighborhoods mainly consist of weak links, whereas strong links are more important for overall connectivity. The important role of strong links is further highlighted in simulations of information spreading, where their topological position is seen to dramatically speed up spreading dynamics. Thus, in contrast to ordinary social networks, weight-topology correlations enhance the flow of information across scientific collaboration networks.Comment: 6 Pages, 6 Figures, Published version, Minor changes, Results also verified using new weight-schem

Cosmology in a Time-Crystal Background

We investigate the effects of a Time Crystal-like Condensate on cosmological dynamics. It is well known that quadratic gravity reduces to Einstein gravity along with a decoupled higher derivative dynamical scalar \cite{Alvarez-Gaume:2015rwa}. According to \cite{Chakraborty:2020ktp}, the above scalar sector can sustain a Time Crystal-like minimum energy state, with non-trivial time dependence. In the present work we treat the Time Crystal-like state as the background (that replaces the classical Minkowski vacuum) and study cosmic evolution on this ``dynamic'' ground state. In the first part we re-derive \cite{Chakraborty:2020ktp}, in a covariant and more systematic way, the frequencies that characterize the oscillator like Time crystalline condensate and interpret it as a background energy-momentum tensor simulating a matter-like effect. Importantly, no external matter is introduced here and the condensate, consists of a combination of the metric field $g_{\mu\nu}$ and is generated due to the $R^2$-term ($R$ is the Ricci scalar) in quadratic gravity \cite{Alvarez-Gaume:2015rwa}. In a way the spurious degrees of freedom of $R^2$-gravity turns into a useful component. The second part comprises of new effects where the cosmology in Friedmann-Lem\^{i}atre-Robertson-Walker (FLRW) universe is studied in presence of the energy-momentum tensor characterizing the Time Crystal Condensate. Under certain approximations, the scale factor of the FLRW universe is analytically obtained for any spatial geometry. We also find that the Time Crystal Condensate contributes as a new matter candidate having radiation-like behavior in the universe. Additionally, irrespective of the spatial geometry of the universe, the Time Crystal condensate generates a decelerating phase before the early acceleration starts. This is an indication of a contracting phase of the universe before its accelerated expansion.Comment: 11 pages, 4 compound figures. Comments are welcom

Time-Varying Priority Queuing Models for Human Dynamics

Queuing models provide insight into the temporal inhomogeneity of human dynamics, characterized by the broad distribution of waiting times of individuals performing tasks. We study the queuing model of an agent trying to execute a task of interest, the priority of which may vary with time due to the agent's "state of mind." However, its execution is disrupted by other tasks of random priorities. By considering the priority of the task of interest either decreasing or increasing algebraically in time, we analytically obtain and numerically confirm the bimodal and unimodal waiting time distributions with power-law decaying tails, respectively. These results are also compared to the updating time distribution of papers in the arXiv.org and the processing time distribution of papers in Physical Review journals. Our analysis helps to understand human task execution in a more realistic scenario.Comment: 8 pages, 6 figure

Contextual analysis framework for bursty dynamics

To understand the origin of bursty dynamics in natural and social processes we provide a general analysis framework, in which the temporal process is decomposed into sub-processes and then the bursts in sub-processes, called contextual bursts, are combined to collective bursts in the original process. For the combination of sub-processes, it is required to consider the distribution of different contexts over the original process. Based on minimal assumptions for inter-event time statistics, we present a theoretical analysis for the relationship between contextual and collective inter-event time distributions. Our analysis framework helps to exploit contextual information available in decomposable bursty dynamics.Comment: 5 pages, 3 figure

Collective behavior of stock price movements in an emerging market

To investigate the universality of the structure of interactions in different markets, we analyze the cross-correlation matrix C of stock price fluctuations in the National Stock Exchange (NSE) of India. We find that this emerging market exhibits strong correlations in the movement of stock prices compared to developed markets, such as the New York Stock Exchange (NYSE). This is shown to be due to the dominant influence of a common market mode on the stock prices. By comparison, interactions between related stocks, e.g., those belonging to the same business sector, are much weaker. This lack of distinct sector identity in emerging markets is explicitly shown by reconstructing the network of mutually interacting stocks. Spectral analysis of C for NSE reveals that, the few largest eigenvalues deviate from the bulk of the spectrum predicted by random matrix theory, but they are far fewer in number compared to, e.g., NYSE. We show this to be due to the relative weakness of intra-sector interactions between stocks, compared to the market mode, by modeling stock price dynamics with a two-factor model. Our results suggest that the emergence of an internal structure comprising multiple groups of strongly coupled components is a signature of market development.Comment: 10 pages, 10 figure