Abstract: We study the problem of determining all possible asymptotic dynamics of Boolean Networks (BNs) such as Discrete Hopfield Nets, Sequential and Synchronous Dynamical Systems, and (finite) Cellular Automata. Viewing BNs as an abstraction for a broad variety of decentralized cyber-physical, biological, social and socio-technical systems, we discuss similarities and differences between open vs. closed such decentralized systems, in an admittedly simplified but rigorous mathematical setting. We revisit the problem of enumerating all possible dynamical evolutions of a large-scale decentralized complex system abstracted as a BN. We show that, in general, the problem of enumerating possible dynamics is provably computationally hard for both "open" and "closed" variants of BNs, even when all of the following restrictions simultaneously hold: i) the local behaviors (that is, node update rules) are very simple, monotone Boolean-valued functions; ii) the network topology is sparse; and iii) either there is no external environment impact on the system modeled as a BN (this case captures "closed systems"), or the model of the environment and how it influences individual nodes in the BN, is of a rather simple, deterministic nature. Our results should be viewed as lower bounds on the complexity of possible behaviors of "the real" large-scale cyber-physical, biological, social and other decentralized systems, with some far-reaching implications insofar as (un)predictability of possible dynamics of such systems.

Abstract: Networks are the skeleton that support dynamical processes in complex systems. Links in many real-world networks activate and deactivate in correspondence to the sporadic interactions between the elements of the system. Activation patterns may be irregular or bursty and play an important role on the dynamics of processes taking place in the network. Most of recent results point towards a delay of these processes due to the interplay between topology and link activation. Social networks and information or disease spreading processes are paradigmatic examples of this situation. Besides the burstiness, several correlations may appear in the process of link activation: Memory effects imply temporal correlations and the existence of communities in the network may mediate the activation patterns of internal an external links. Here, we study how these different types of correlations influence dynamical systems on the networks. As paradigmatic examples, we consider the SI spreading and the voter model on networks. As noted in the literature, the relation between topology and activation leads to a delay in the dynamics. However, we find that memory effects can notably accelerate the models' arrival at the absorbing states. A theoretical explanation about how this phenomenon occurs is provided. Furthermore, we show that when both types of correlations are present, the final dynamics crucially depends on the mix. The characteristic times of the dynamics suffers a divergence for some particular correlation combinations. Some mixes between topology and memory notably speed up the dynamics, while others strongly slow it down. Mixed correlations, topological and memory effects, are commonly present in any real system, so understanding their non-trivial competition is of great importance. In this sense, the SI and voter models are simple benchmark dynamics, but we expect our results to be generalizable to more elaborated dynamical processes. The complete work is available in https://arxiv.org/abs/1604.04155

Abstract: We introduce a new type of evolution equation for 1-dimensional complex systems where the order of differentiation is itself one of the variables. We show that such ultra-fast growing systems with evolution determined by the variable order of differentiation can be mapped into a fractional differential equation and further into a Volterra integral equation. We elaborate on the existence and stability of the evolution solutions for various initial conditions and we present several case studies. The core of this approach is related to the observational connection between the evolution of the degree of complexity, and the rate of accelerated change on one hand, and the degree of time non-locality (history dependent) of the model equation, on the other hand. Since the latter quantity is connected to the number of neighbors or steps taken into account in discretized models, it results the need for a new type of equation whose order of differentiation changes in a dynamical way. We present applications of this approach in: nonlinear evolution equations for long-term memory systems, [1], fast growing computer/internet systems (e.g. Kryder’s or Nielsen's laws), [2], and accelerating change systems like populations (e.g. Reed’s and Carlson’s laws, Ribeiro model). We also present some novel applications developed from this model on cell growing, phase transitions, and avalanches. References [1] Spectral decomposition of nonlinear systems with memory A. Svenkeson, B. Glaz, S. Stanton, and B. J. West, Phys. Rev. E 93 (2016) 022211. [2] A. Ludu, Boundaries of a Complex World (Springer-Verlag, Heidelberg 2016).

Abstract: In academia, nepotism has been blamed for poor graduate career support, gender inequality, and emigration of the intelligentsia. To support this idea Allesina reported an unnatural scarcity of distinct surnames among tenured faculties in Italy while Ferlazzo and Sdoia repeated the same analysis in the UK, finding a more objective expression of social capital. Albeit with very careful consideration of surnames’ distributions across regions and time, surname clustering can be used to reflect family ties or kinship, and interpreted in relation to measures of social capital (including corruption, income inequality, scientific output). Here, we examine co-authorship patterns in the health science literature over five decades, by country using over 21 million papers indexed by the MEDLINE®/PubMed® database. Our analysis shows that kinship in the health literature has increased over the past fifty years with substantial differences between nations. I.e. Italy and Poland exhibited a dramatic increase in kinship starting from very low values and crossing the overall trend in the early eighties. We also observed low kinship among countries with low perceived corruption, and an association with income inequality. Investigating the co-authorship network from top publishing countries, we found that authors who are part of a kin tend to have a larger degree and occupy central positions in network. We could interpret this as increased information flows and allied activities such as grant applications, emanating from influential individuals who are more commonly kin co-authors. Our results also highlight that the local structure of collaborations of a kin co-author is usually very centralized, while authors who are not part of a kin tend to create ‘democratic’ structures. Finally, the analysis of mixing patterns strongly supports the idea that important kin authors form robust collaborations among their peers while do not collaborate with scientists who are not part of a kin.