Optimization in complex networks

Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous distributions of links, providing an extraordinary source of robustness against perturbations. Although most theories concerning the origin of these topologies use growing graphs, here we show that a simple optimization process can also account for the observed regularities displayed by most complex nets. Using an evolutionary algorithm involving minimization of link density and average distance, four major types of networks are encountered: (a) sparse exponential-like networks, (b) sparse scale-free networks, (c) star networks and (d) highly dense networks, apparently defining three major phases. These constraints provide a new explanation for scaling of exponent about -3. The evolutionary consequences of these results are outlined.Peer ReviewedPostprint (author's final draft

Patterns in syntactic dependency networks

Many languages are spoken on Earth. Despite their diversity, many robust language universals are known to exist. All languages share syntax, i.e., the ability of combining words for forming sentences. The origin of such traits is an issue of open debate. By using recent developments from the statistical physics of complex networks, we show that different syntactic dependency networks (from Czech, German, and Romanian) share many nontrivial statistical patterns such as the small world phenomenon, scaling in the distribution of degrees, and disassortative mixing. Such previously unreported features of syntax organization are not a trivial consequence of the structure of sentences, but an emergent trait at the global scale.Peer ReviewedPostprint (published version

Selection, tinkering and emergence in complex networks: crossing the land of tinkering

Complex biological networks have very different origins than technologic ones. The latter involve extensive design and, as engineered structures, include a high level of optimization. The former involve (in principle) contingency and structural constraints, with new structures being incorporated through tinkering with previously evolved modules or units. However, the observation of the topological features of different biological nets suggests that nature can have a limited repertoire of ”attractors” that essentially optimize communication under some basic constraints of cost and architecture or that allow the biological nets to reach a high degree of homeostasis. Conversely, the topological features exhibited by some technology graphs indicate that tinkering and internal constraints play a key role, in spite of the ”designed” nature of these structures. Previous scenarios suggested to explain the overall trends of evolution are re-analyzed in light of topological patterns.Peer ReviewedPostprint (author's final draft

The evolution of the ventilatory ratio is a prognostic factor in mechanically ventilated COVID-19 ARDS patients

Background: Mortality due to COVID-19 is high, especially in patients requiring mechanical ventilation. The purpose of the study is to investigate associations between mortality and variables measured during the first three days of mechanical ventilation in patients with COVID-19 intubated at ICU admission. Methods: Multicenter, observational, cohort study includes consecutive patients with COVID-19 admitted to 44 Spanish ICUs between February 25 and July 31, 2020, who required intubation at ICU admission and mechanical ventilation for more than three days. We collected demographic and clinical data prior to admission; information about clinical evolution at days 1 and 3 of mechanical ventilation; and outcomes. Results: Of the 2,095 patients with COVID-19 admitted to the ICU, 1,118 (53.3%) were intubated at day 1 and remained under mechanical ventilation at day three. From days 1 to 3, PaO2/FiO2 increased from 115.6 [80.0-171.2] to 180.0 [135.4-227.9] mmHg and the ventilatory ratio from 1.73 [1.33-2.25] to 1.96 [1.61-2.40]. In-hospital mortality was 38.7%. A higher increase between ICU admission and day 3 in the ventilatory ratio (OR 1.04 [CI 1.01-1.07], p = 0.030) and creatinine levels (OR 1.05 [CI 1.01-1.09], p = 0.005) and a lower increase in platelet counts (OR 0.96 [CI 0.93-1.00], p = 0.037) were independently associated with a higher risk of death. No association between mortality and the PaO2/FiO2 variation was observed (OR 0.99 [CI 0.95 to 1.02], p = 0.47). Conclusions: Higher ventilatory ratio and its increase at day 3 is associated with mortality in patients with COVID-19 receiving mechanical ventilation at ICU admission. No association was found in the PaO2/FiO2 variation

Nonequilibrium entropic bounds for darwinian replicators

Life evolved on our planet by means of a combination of Darwinian selection and innovations leading to higher levels of complexity. The emergence and selection of replicating entities is a central problem in prebiotic evolution. Theoretical models have shown how populations of different types of replicating entities exclude or coexist with other classes of replicators. Models are typically kinetic, based on standard replicator equations. On the other hand, the presence of thermodynamical constraints for these systems remain an open question. This is largely due to the lack of a general theory of statistical methods for systems far from equilibrium. Nonetheless, a first approach to this problem has been put forward in a series of novel developements falling under the rubric of the extended second law of thermodynamics. The work presented here is twofold: firstly, we review this theoretical framework and provide a brief description of the three fundamental replicator types in prebiotic evolution: parabolic, malthusian and hyperbolic. Secondly, we employ these previously mentioned techinques to explore how replicators are constrained by thermodynamics. Finally, we comment and discuss where further research should be focused on.This work was supported by the Botín Foundation by Banco Santander through its Santander Universities Global Division, the Spanish Ministry of Economy and Competitiveness, grant FIS2015-67616-P and the Santa Fe Institute

Zipf's law and random texts

Random-text models have been proposed as an explanation for the power law relationship between word frequency and rank, the so-called Zipf's law. They are generally regarded as null hypotheses rather than models in the strict sense. In this context, recent theories of language emergence and evolution assume this law as a priori information with no need of explanation. Here, random texts and real texts are compared through (a) the so-called lexical spectrum and (b) the distribution of words having the same length. It is shown that real texts fill the lexical spectrum much more efficiently and regardless of the word length, suggesting that the meaningfulness of Zipf's law is high.Peer Reviewe

Two regimes in the frequency of words and the origin of complex lexicons: Zipf's law revisited

Zipf's law states that the frequency of a word is a power function of its rank. The exponent of the power is usually accepted to be close to (-)1. Great deviations between the predicted and real number of different words of a text, disagreements between the predicted and real exponent of the probability density function and statistics on a big corpus, make evident that word frequency as a function of the rank follows two different exponents, ~(-)1 for the first regime and ~(-)2 for the second. The implications of the change in exponents for the metrics of texts and for the origins of complex lexicons are analyzed.Peer ReviewedPostprint (author's final draft

Ecological complexity and the biosphere: the next 30 years

Global warming, habitat loss and overexploitation of limited resources are leading to alarming biodiversity declines. Ecosystems are complex adaptive systems that display multiple alternative states and can shift from one to another in abrupt ways. Some of these tipping points have been identified and predicted by mathematical and computational models. Moreover, multiple scales are involved and potential mitigation or intervention scenarios are tied to particular levels of complexity, from cells to human-environment coupled systems. In dealing with a biosphere where humans are part of a complex, endangered ecological network, novel theoretical and engineering approaches need to be considered. At the centre of most research efforts is biodiversity, which is essential to maintain community resilience and ecosystem services. What can be done to mitigate, counterbalance or prevent tipping points? Using a 30-year window, we explore recent approaches to sense, preserve and restore ecosystem resilience as well as a number of proposed interventions (from afforestation to bioengineering) directed to mitigate or reverse ecosystem collapse. The year 2050 is taken as a representative future horizon that combines a time scale where deep ecological changes will occur and proposed solutions might be effective. This article is part of the theme issue 'Ecological complexity and the biosphere: the next 30 years'

A cultural diffusion model for the rise and fall of programming languages

Our interaction with complex computing machines is mediated by programming languages (PLs), which constitute one of the major innovations in the evolution of technology. PLs allow flexible, scalable, and fast use of hardware and are largely responsible for shaping the history of information technology since the rise of computers in the 1950s. The rapid growth and impact of computers were followed closely by the development of PLs. As occurs with natural, human languages, PLs have emerged and gone extinct. There has been always a diversity of coexisting PLs that compete somewhat while occupying special niches. Here we show that the statistical patterns of language adoption, rise, and fall can be accounted for by a simple model in which a set of programmers can use several PLs, decide to use existing PLs used by other programmers, or decide not to use them. Our results highlight the influence of strong communities of practice in the diffusion of PL innovationsThis work has been supported by Fundación Botín, the Spanish Ministry of Economy and Competitiveness (Grants FIS2013-44674-P to S.V.) and FEDER and by the Santa Fe Institute

Before the endless forms: embodied model of transition from single cells to aggregates to ecosystem engineering

The emergence of complex multicellular systems and their associated developmental programs is one of the major problems of evolutionary biology. The advantages of cooperation over individuality seem well known but it is not clear yet how such increase of complexity emerged from unicellular life forms. Current multicellular systems display a complex cell-cell communication machinery, often tied to large-scale controls of body size or tissue homeostasis. Some unicellular life forms are simpler and involve groups of cells cooperating in a tissue-like fashion, as it occurs with biofilms. However, before true gene regulatory interactions were widespread and allowed for controlled changes in cell phenotypes, simple cellular colonies displaying adhesion and interacting with their environments were in place. In this context, models often ignore the physical embedding of evolving cells, thus leaving aside a key component. The potential for evolving pre-developmental patterns is a relevant issue: how far a colony of evolving cells can go? Here we study these pre-conditions for morphogenesis by using CHIMERA, a physically embodied computational model of evolving virtual organisms in a pre-Mendelian world. Starting from a population of identical, independent cells moving in a fluid, the system undergoes a series of changes, from spatial segregation, increased adhesion and the development of generalism. Eventually, a major transition occurs where a change in the flow of nutrients is triggered by a sub-population. This ecosystem engineering phenomenon leads to a subsequent separation of the ecological network into two well defined compartments. The relevance of these results for evodevo and its potential ecological triggers is discussedThis work has been supported by grants of the James McDonnell Foundation (RVS, SV), Fundación Marcelino Botín (RVS, SV), FIS2004-05422 (RVS) and by the Santa Fe Institut