ASU Scholarship Showcase

Extreme events, a type of collective behavior in complex networked dynamical systems, often can have catastrophic consequences. To develop effective strategies to control extreme events is of fundamental importance and practical interest. Utilizing transportation dynamics on complex networks as a prototypical setting, we find that making the network “mobile” can effectively suppress extreme events. A striking, resonance-like phenomenon is uncovered, where an optimal degree of mobility exists for which the probability of extreme events is minimized. We derive an analytic theory to understand the mechanism of control at a detailed and quantitative level, and validate the theory numerically. Implications of our finding to current areas such as cybersecurity are discussed.

The relation between flux and fluctuation is fundamental to complex physical systems that support and transport flows. A recently obtained law predicts monotonous enhancement of fluctuation as the average flux is increased, which in principle is valid but only for large systems. For realistic complex systems of small sizes, this law breaks down when both the average flux and fluctuation become large. Here we demonstrate the failure of this law in small systems using real data and model complex networked systems, derive analytically a modified flux-fluctuation law, and validate it through computations of a large number of complex networked systems. Our law is more general in that its predictions agree with numerics and it reduces naturally to the previous law in the limit of large system size, leading to new insights into the flow dynamics in small-size complex systems with significant implications for the statistical and scaling behaviors of small systems, a topic of great recent interest.

Evolutionary dynamical models for cyclic competitions of three species (e.g., rock, paper, and scissors, or RPS) provide a paradigm, at the microscopic level of individual interactions, to address many issues in coexistence and biodiversity. Real ecosystems often involve competitions among more than three species. By extending the RPS game model to five (rock-paper-scissors-lizard-Spock, or RPSLS) mobile species, we uncover a fundamental type of mesoscopic interactions among subgroups of species. In particular, competitions at the microscopic level lead to the emergence of various local groups in different regions of the space, each involving three species. It is the interactions among the groups that fundamentally determine how many species can coexist. In fact, as the mobility is increased from zero, two transitions can occur: one from a five- to a three-species coexistence state and another from the latter to a uniform, single-species state. We develop a mean-field theory to show that, in order to understand the first transition, group interactions at the mesoscopic scale must be taken into account. Our findings suggest, more broadly, the importance of mesoscopic interactions in coexistence of great many species.

Dynamical systems based on the minority game (MG) have been a paradigm for gaining significant insights into a variety of social and biological behaviors. Recently, a grouping phenomenon has been unveiled in MG systems of multiple resources (strategies) in which the strategies spontaneously break into an even number of groups, each exhibiting an identical oscillation pattern in the attendance of game players. Here we report our finding of spontaneous breakup of resources into three groups, each exhibiting period-three oscillations. An analysis is developed to understand the emergence of the striking phenomenon of triple grouping and period-three oscillations. In the presence of random disturbances, the triple-group/period-three state becomes transient, and we obtain explicit formula for the average transient lifetime using two methods of approximation. Our finding indicates that, period-three oscillation, regarded as one of the most fundamental behaviors in smooth nonlinear dynamical systems, can also occur in much more complex, evolutionary-game dynamical systems. Our result also provides a plausible insight for the occurrence of triple grouping observed, for example, in the U.S. housing market.

Understanding the dynamics of human movements is key to issues of significant current interest such as behavioral prediction, recommendation, and control of epidemic spreading. We collect and analyze big data sets of human movements in both cyberspace (through browsing of websites) and physical space (through mobile towers) and find a superlinear scaling relation between the mean frequency of visit〈f〉and its fluctuation σ : σ ∼〈f⟩^β with β ≈ 1.2. The probability distribution of the visiting frequency is found to be a stretched exponential function. We develop a model incorporating two essential ingredients, preferential return and exploration, and show that these are necessary for generating the scaling relation extracted from real data. A striking finding is that human movements in cyberspace and physical space are strongly correlated, indicating a distinctive behavioral identifying characteristic and implying that the behaviors in one space can be used to predict those in the other.

Vertebrates cannot synthesize carotenoid pigments de novo, so to produce carotenoid-based coloration they must ingest carotenoids. Most songbirds that deposit red carotenoids in feathers, bills, eyes, or skin ingest only yellow or orange dietary pigments, which they oxidize to red pigments via a ketolation reaction. It has been hypothesized that carotenoid ketolation occurs in the liver of vertebrates, but this hypothesis remains to be confirmed. To better understand the role of hepatocytes in the production of ketolated carotenoids in songbirds, we measured the carotenoid content of subcellular components of hepatocytes from wild male house finches (Haemorhous mexicanus) that were molting red, ketocarotenoid-containing feathers (e.g., 3-hydroxy-echinenone). We homogenized freshly collected livers of house finches and isolated subcellular fractions, including mitochondria. We found the highest concentration of ketocarotenoids in the mitochondrial fraction. These observations are consistent with the hypothesis that carotenoid pigments are oxidized on or within hepatic mitochondria, esterified, and then transported to the Golgi apparatus for secretory processing.

Background: The coevolution of male traits and female mate preferences has led to the elaboration and diversification of sexually selected traits; however the mechanisms that mediate trait-preference coevolution are largely unknown. Carotenoid acquisition and accumulation are key determinants of the expression of male sexually selected carotenoid-based coloration and a primary mechanism maintaining the honest information content of these signals. Carotenoids also influence female health and reproduction in ways that may alter the costs and benefits of mate choice behaviors and thus provide a potential biochemical link between the expression of male traits and female preferences. To test this hypothesis, we manipulated the dietary carotenoid levels of captive female house finches (Carpodacus mexicanus) and assessed their mate choice behavior in response to color-manipulated male finches.

Results: Females preferred to associate with red males, but carotenoid supplementation did not influence the direction or strength of this preference. Females receiving a low-carotenoid diet were less responsive to males in general, and discrimination among the colorful males was positively linked to female plasma carotenoid levels at the beginning of the study when the diet of all birds was carotenoid-limited.

Conclusions: Although female preference for red males was not influenced by carotenoid intake, changes in mating responsiveness and discrimination linked to female carotenoid status may alter how this preference is translated into choice. The reddest males, with the most carotenoid rich plumage, tend to pair early in the breeding season. If carotenoid-related variations in female choice behavior shift the timing of pairing, then they have the potential to promote assortative mating by carotenoid status and drive the evolution of carotenoid-based male plumage coloration.

Resource allocation takes place in various types of real-world complex systems such as urban traffic, social services institutions, economical and ecosystems. Mathematically, the dynamical process of resource allocation can be modeled as minority games. Spontaneous evolution of the resource allocation dynamics, however, often leads to a harmful herding behavior accompanied by strong fluctuations in which a large majority of agents crowd temporarily for a few resources, leaving many others unused. Developing effective control methods to suppress and eliminate herding is an important but open problem. Here we develop a pinning control method, that the fluctuations of the system consist of intrinsic and systematic components allows us to design a control scheme with separated control variables. A striking finding is the universal existence of an optimal pinning fraction to minimize the variance of the system, regardless of the pinning patterns and the network topology. We carry out a generally applicable theory to explain the emergence of optimal pinning and to predict the dependence of the optimal pinning fraction on the network topology. Our work represents a general framework to deal with the broader problem of controlling collective dynamics in complex systems with potential applications in social, economical and political systems.

Background: Diet-derived carotenoid pigments are concentrated in the retinas of birds and serve a variety of functions, including photoprotection. In domesticated bird species (e.g., chickens and quail), retinal carotenoid pigmentation has been shown to respond to large manipulations in light exposure and provide protection against photodamage. However, it is not known if or how wild birds respond to ecologically relevant variation in sun exposure.

Methods: We manipulated the duration of natural sunlight exposure and dietary carotenoid levels in wild-caught captive House Finches (Haemorhous mexicanus), then measured carotenoid accumulation and oxidative stress in the retina.

Results: We found no significant effects of sun exposure on retinal levels of carotenoids or lipid peroxidation, in replicate experiments, in winter (Jan–Mar) and spring/summer (May–June). Dietary carotenoid supplementation in the spring/summer experiment led to significantly higher retinal carotenoid levels, but did not affect lipid peroxidation. Carotenoid levels differed significantly between the winter and spring/summer experiments, with higher retinal and lower plasma carotenoid levels in birds from the later experiment.

Conclusion: Our results suggest that variation in the duration of exposure to direct sunlight have limited influence on intraspecific variation in retinal carotenoid accumulation, but that accumulation may track other seasonal–environmental cues and physiological processes.

Introduction: Nutrient availability, assimilation, and allocation can have important and lasting effects on the immune system development of growing animals. Though carotenoid pigments have immunostimulatory properties in many animals, relatively little is known regarding how they influence the immune system during development. Moreover, studies linking carotenoids to health at any life stage have largely been restricted to birds and mammals. We investigated the effects of carotenoid supplementation on multiple aspects of immunity in juvenile veiled chameleons (Chamaeleo calyptratus). We supplemented half of the chameleons with lutein (a xanthophyll carotenoid) for 14 weeks during development and serially measured multiple aspects of immune function, including: agglutination and lysis performance of plasma, wound healing, and plasma nitric oxide concentrations before and after wounding.

Results: Though lutein supplementation effectively elevated circulating carotenoid concentrations throughout the developmental period, we found no evidence that carotenoid repletion enhanced immune function at any point. However, agglutination and lysis scores increased, while baseline nitric oxide levels decreased, as chameleons aged.

Conclusions: Taken together, our results indicate that body mass and age, but not carotenoid access, may play an important role in immune performance of growing chameleons. Hence, studying well-understood physiological processes in novel taxa can provide new perspectives on alternative physiological processes and nutrient function.