Synchronization in Complex Networks Under Uncertainty

La sincronització en xarxes és la música dels sistemes complexes. Els ritmes col·lectius que emergeixen de molts oscil·ladors acoblats expliquen el batec constant del cor, els patrons recurrents d'activitat neuronal i la sincronia descentralitzada a les xarxes elèctriques. Els models matemàtics són sòlids i han avançat significativament, especialment en el problema del camp mitjà, on tots els oscil·ladors estan connectats mútuament. Tanmateix, les xarxes reals tenen interaccions complexes que dificulten el tractament analític. Falta un marc general i les soluciones existents en caixes negres numèriques i espectrals dificulten la interpretació. A més, la informació obtinguda en mesures empíriques sol ser incompleta. Motivats per aquestes limitacions, en aquesta tesi proposem un estudi teòric dels oscil·ladors acoblats en xarxes sota incertesa. Apliquem propagació d'errors per predir com una estructura complexa amplifica el soroll des dels pesos microscòpics fins al punt crític de sincronització, estudiem l'efecte d'equilibrar les interaccions de parelles i d'ordre superior en l'optimització de la sincronia i derivem esquemes d'ajust de pesos per mapejar el comportament de sincronització en xarxes diferents. A més, un desplegament geomètric rigorós de l'estat sincronitzat ens permet abordar escenaris descentralitzats i descobrir regles locals òptimes que indueixen transicions globals abruptes. Finalment, suggerim dreceres espectrals per predir punts crítics amb àlgebra lineal i representacions aproximades de xarxa. En general, proporcionem eines analítiques per tractar les xarxes d'oscil·ladors en condicions sorolloses i demostrem que darrere els supòsits predominants d'informació completa s'amaguen explicacions mecanicistes clares. Troballes rellevants inclouen xarxes particulars que maximitzen el ventall de comportaments i el desplegament exitós del binomi estructura-dinàmica des d'una perspectiva local. Aquesta tesi avança la recerca d'una teoria general de la sincronització en xarxes a partir de principis mecanicistes i geomètrics, una peça clau que manca en l'anàlisi, disseny i control de xarxes neuronals biològiques i artificials i sistemes d'enginyeria complexos.La sincronización en redes es la música de los sistemas complejos. Los ritmos colectivos que emergen de muchos osciladores acoplados explican el latido constante del corazón, los patrones recurrentes de actividad neuronal y la sincronía descentralizada de las redes eléctricas. Los modelos matemáticos son sólidos y han avanzado significativamente, especialmente en el problema del campo medio, donde todos los osciladores están conectados entre sí. Sin embargo, las redes reales tienen interacciones complejas que dificultan el tratamiento analítico. Falta un marco general y las soluciones en cajas negras numéricas y espectrales dificultan la interpretación. Además, las mediciones empíricas suelen ser incompletas. Motivados por estas limitaciones, en esta tesis proponemos un estudio teórico de osciladores acoplados en redes bajo incertidumbre. Aplicamos propagación de errores para predecir cómo una estructura compleja amplifica el ruido desde las conexiones microscópicas hasta puntos críticos macroscópicos, estudiamos el efecto de equilibrar interacciones por pares y de orden superior en la optimización de la sincronía y derivamos esquemas de ajuste de pesos para mapear el comportamiento en estructuras distintas. Una expansión geométrica del estado sincronizado nos permite abordar escenarios descentralizados y descubrir reglas locales que inducen transiciones abruptas globales. Por último, sugerimos atajos espectrales para predecir puntos críticos usando álgebra lineal y representaciones aproximadas de red. En general, proporcionamos herramientas analíticas para manejar redes de osciladores en condiciones ruidosas y demostramos que detrás de las suposiciones predominantes de información completa se ocultaban claras explicaciones mecanicistas. Hallazgos relevantes incluyen redes particulares que maximizan el rango de comportamientos y la explicación del binomio estructura-dinámica desde una perspectiva local. Esta tesis avanza en la búsqueda de una teoría general de sincronización en redes desde principios mecánicos y geométricos, una pieza clave que falta en el análisis, diseño y control de redes neuronales biológicas y artificiales y sistemas de ingeniería complejos.Synchronization in networks is the music of complex systems. Collective rhythms emerging from many interacting oscillators appear across all scales of nature, from the steady heartbeat and the recurrent patterns in neuronal activity to the decentralized synchrony in power-grids. The mathematics behind these processes are solid and have significantly advanced lately, especially in the mean-field problem, where oscillators are all mutually connected. However, real networks have complex interactions that difficult the analytical treatment. A general framework is missing and most existing results rely on numerical and spectral black-boxes that hinder interpretation. Also, the information obtained from measurements is usually incomplete. Motivated by these limitations, in this thesis we propose a theoretical study of network-coupled oscillators under uncertainty. We apply error propagation to predict how a complex structure amplifies noise from the link weights to the synchronization onset, study the effect of balancing pair-wise and higher-order interactions in synchrony optimization, and derive weight-tuning schemes to map the synchronization behavior of different structures. Also, we develop a rigorous geometric unfolding of the synchronized state to tackle decentralized scenarios and to discover optimal local rules that induce global abrupt transitions. Last, we suggest spectral shortcuts to predict critical points using linear algebra and network representations with limited information. Overall, we provide analytical tools to deal with oscillator networks under noisy conditions and prove that mechanistic explanations were hidden behind the prevalent assumptions of complete information. Relevant finding include particular networks that maximize the range of behaviors and the successful unfolding of the structure-dynamics interplay from a local perspective. This thesis advances the quest of a general theory of network synchronization built from mechanistic and geometric principles, a key missing piece in the analysis, design and control of biological and artificial neural networks and complex engineering systems

Synchronization invariance under network structural transformations

Synchronization processes are ubiquitous despite the many connectivity patterns that complex systems can show. Usually, the emergence of synchrony is a macroscopic observable; however, the microscopic details of the system, as, e.g., the underlying network of interactions, is many times partially or totally unknown. We already know that different interaction structures can give rise to a common functionality, understood as a common macroscopic observable. Building upon this fact, here we propose network transformations that keep the collective behavior of a large system of Kuramoto oscillators invariant. We derive a method based on information theory principles, that allows us to adjust the weights of the structural interactions to map random homogeneous in-degree networks into random heterogeneous networks and vice versa, keeping synchronization values invariant. The results of the proposed transformations reveal an interesting principle; heterogeneous networks can be mapped to homogeneous ones with local information, but the reverse process needs to exploit higher-order information. The formalism provides analytical insight to tackle real complex scenarios when dealing with uncertainty in the measurements of the underlying connectivity structure

Self-organized explosive synchronization in complex networks: Emergence of synchronization bombs

We introduce the concept of synchronization bombs as large networks of coupled heterogeneous oscillators that operate in a bistable regime and abruptly transit from incoherence to phase-locking (or vice-versa) by adding (or removing) one or a few links. Here we build a self-organized and stochastic version of these bombs, by optimizing global synchrony with decentralized information in a competitive link-percolation process driven by a local rule. We find explosive fingerprints on the emerging network structure, including frequency-degree correlations, disassortative patterns and a delayed percolation threshold. We show that these bomb-like transitions can be designed both in systems of Kuramoto -- periodic -- and R\"ossler -- chaotic -- oscillators and in a model of cardiac pacemaker cells. We analytically characterize the transitions in the Kuramoto case by combining a precise collective coordinates approach and the Ott-Antonsen ansatz. Furthermore, we study the robustness of the phenomena under changes in the main parameters and the unexpected effect of optimal noise in our model. Our results propose a minimal self-organized mechanism of network growth to understand and control explosive synchronization in adaptive biological systems like the brain and engineered ones like power-grids or electronic circuits. From a theoretical standpoint, the emergence of synchronization explosions and bistability induced by localized structural perturbations -- without any fine-tuning of global parameters -- joins explosive synchronization and percolation under the same mechanistic framework.Comment: 17 pages, 9 figure

Impact of a youth-led social marketing intervention run by adolescents to encourage healthy lifestyles among younger school peers (EYTO-Kids project): a parallel-cluster randomised controlled pilot study

Background: Encouraging healthy lifestyles in children is a challenge. This project aimed to improve lifestyles of younger peers by engaging adolescent creators (ACs) to design and implement peer-led and social marketing (SM) health-promoting activities. Methods: A 10-month parallel-cluster randomised controlled school-based pilot study was performed in disadvantaged neighbourhoods in Reus (Spain) spanning two academic years (2015-2016/2016-2017). Eight primary schools (n=375 children) and four high schools (n=94ACs) were randomly placed in the intervention group. The 94 ACs (12-14 years) designed and implemented four SM activities for their younger peers (9-11 years). Eight primary schools (n=327 children) and three high schools (n=98 adolescents) served as the control group and received no intervention. Primary (physical activity and fruit consumption) and secondary outcomes (screen time, vegetables, soft drinks, sweets and fast food consumptions) were assessed with validated questionnaires at baseline and at the end of the study. Results: After 10 months, fruit consumption and physical activity were maintained in the children who consumed ≥1 fruit/day and spent ≥6 hours/week physical activity. However, compared with the controls, the intervention significantly increased the physical activity of girls to 15.6 min/week, whereas the percentage of girls who consumed sweets, soft drinks and fast food decreased significantly by 8.4%, 14.5% and 5.9%, respectively. Additionally, the percentage of ≥2 hour/weekday of screen time by boys decreased significantly by 8.2%. Conclusion: The European Youth Tackling Obesity-Kids, SM and peer-led intervention, effectively increased physical activity hours/week in girls, but was not effective in improving the percentage of children who consumed the recommended fruit. Moreover, the percentages of girls who consumed sweets, soft drinks and fast food and boys screen time decreased

Potential Use of Mobile Phone Applications for Self-Monitoring and Increasing Daily Fruit and Vegetable Consumption: A Systematized Review

A wide range of chronic diseases could be prevented through healthy lifestyle choices, such as consuming five portions of fruits and vegetables daily, although the majority of the adult population does not meet this recommendation. The use of mobile phone applications for health purposes has greatly increased; these applications guide users in real time through various phases of behavioural change. This review aimed to assess the potential of self-monitoring mobile phone health (mHealth) applications to increase fruit and vegetable intake. PubMed and Web of Science were used to conduct this systematized review, and the inclusion criteria were: randomized controlled trials evaluating mobile phone applications focused on increasing fruit and/or vegetable intake as a primary or secondary outcome performed from 2008 to 2018. Eight studies were included in the final assessment. The interventions described in six of these studies were effective in increasing fruit and/or vegetable intake. Targeting stratified populations and using long-lasting interventions were identified as key aspects that could influence the effectiveness of these interventions. In conclusion, evidence shows the effectiveness of mHealth application interventions to increase fruit and vegetable consumption. Further research is needed to design effective interventions and to determine their efficacy over the long term

Molecular phenomics of a high-calorie diet-induced porcine model of prepubertal obesity

As obesity incidence is alarmingly rising among young individuals, we aimed to characterize an experimental model of this situation, considering the similarity between human and porcine physiology. For this reason, we fed prepubertal (63 days old) Duroc breed females (n=21) either with a standard growth diet (3800 kcal/day) or one with a high-calorie content (5200 kcal/day) during 70 days. Computerized tomography, mass-spectrometry-based metabolomics and lipidomics, as well as peripheral blood mononuclear cell transcriptomics, were applied to define traits linked to high-calorie intake. Samples from a human cohort confirmed potential lipidomic markers. Compared to those fed a standard growth diet, pigs fed a high-calorie diet showed an increased weight gain (13%), much higher adiposity (53%), hypertriacylglyceridemia and hypercholesterolemia in parallel to insulin resistance. This diet induced marked changes in the circulating lipidome, particularly in phosphatidylethanolamine-type molecules. Also, circulating specific diacylglycerol and monoacylglycerol contents correlated with visceral fat and intrahepatic triacylglycerol concentrations. Specific lipids associated with obesity in swine (mainly belonging to glycerophospholipid, triacylglyceride and sterol classes) were also linked with obesity traits in the human cohort, reinforcing the usefulness of the chosen approach. Interestingly, no overt inflammation in plasma or adipose tissue was evident in this model. The presented model is useful as a preclinical surrogate of prepubertal obesity in order to ascertain the pathophysiology interactions between energy intake and obesity development.Supported by Centro para el Desarrollo Tecnológico e Industrial, Spain, Project reference: IPT-20111008, and Generalitat de Catalunya grants 2017SGR1719 and 2017SGR696. MJ is a "Serra Hunter" program fellow. Supported by Instituto de Salud Carlos III, Spain, Project reference: 17-00134, co-financed by FEDER Funds A way to make Europe

Synchronization invariance under network structural transformations

Synchronization processes are ubiquitous despite the many connectivity patterns that complex systems can show. Usually, the emergence of synchrony is a macroscopic observable; however, the microscopic details of the system, as, e.g., the underlying network of interactions, is many times partially or totally unknown. We already know that different interaction structures can give rise to a common functionality, understood as a common macroscopic observable. Building upon this fact, here we propose network transformations that keep the collective behavior of a large system of Kuramoto oscillators invariant. We derive a method based on information theory principles, that allows us to adjust the weights of the structural interactions to map random homogeneous in-degree networks into random heterogeneous networks and vice versa, keeping synchronization values invariant. The results of the proposed transformations reveal an interesting principle; heterogeneous networks can be mapped to homogeneous ones with local information, but the reverse process needs to exploit higher-order information. The formalism provides analytical insight to tackle real complex scenarios when dealing with uncertainty in the measurements of the underlying connectivity structure

Higher-order interactions can better optimize network synchronization

Collective behavior plays a key role in the function of a wide range of physical, biological, and neurological systems where empirical evidence has recently uncovered the prevalence of higher-order interactions, i.e., structures that represent interactions between more than just two individual units, in complex network structures. Here, we study the optimization of collective behavior in networks with higher-order interactions encoded in clique complexes. Our approach involves adapting the synchrony alignment function framework to a composite Laplacian matrix that encodes multiorder interactions including, e.g., both dyadic and triadic couplings. We show that as higher-order coupling interactions are equitably strengthened, so that overall coupling is conserved, the optimal collective behavior improves. We find that this phenomenon stems from the broadening of a composite Laplacian\u27s eigenvalue spectrum, which improves the optimal collective behavior and widens the range of possible behaviors. Moreover, we find in constrained optimization scenarios that a nontrivial, ideal balance between the relative strengths of pairwise and higher-order interactions leads to the strongest collective behavior supported by a network. This work provides insight into how systems balance interactions of different types to optimize or broaden their dynamical range of behavior, especially for self-regulating systems like the brain

Effects of a post-weaning cafeteria diet in young rats: metabolic syndrome, reduced activity and low anxiety-like behaviour.

Among adolescents, overweight, obesity and metabolic syndrome are rapidly increasing in recent years as a consequence of unhealthy palatable diets. Animal models of diet-induced obesity have been developed, but little is known about the behavioural patterns produced by the consumption of such diets. The aim of the present study was to determine the behavioural and biochemical effects of a cafeteria diet fed to juvenile male and female rats, as well as to evaluate the possible recovery from these effects by administering standard feeding during the last week of the study. Two groups of male and female rats were fed with either a standard chow diet (ST) or a cafeteria (CAF) diet from weaning and for 8 weeks. A third group of males (CAF withdrawal) was fed with the CAF diet for 7 weeks and the ST in the 8th week. Both males and females developed metabolic syndrome as a consequence of the CAF feeding, showing overweight, higher adiposity and liver weight, increased plasma levels of glucose, insulin and triglycerides, as well as insulin resistance, in comparison with their respective controls. The CAF diet reduced motor activity in all behavioural tests, enhanced exploration, reduced anxiety-like behaviour and increased social interaction; this last effect was more pronounced in females than in males. When compared to animals only fed with a CAF diet, CAF withdrawal increased anxiety in the open field, slightly decreased body weight, and completely recovered the liver weight, insulin sensitivity and the standard levels of glucose, insulin and triglycerides in plasma. In conclusion, a CAF diet fed to young animals for 8 weeks induced obesity and metabolic syndrome, and produced robust behavioural changes in young adult rats, whereas CAF withdrawal in the last week modestly increased anxiety, reversed the metabolic alterations and partially reduced overweight