Highly optimized tolerance: a mechanism for power laws in designed systems

Parrondo's paradox reveals counterintuitive wins in biology and decision making in society

Parrondo's paradox refers to the paradoxical phenomenon of combining two losing strategies in a certain manner to obtain a winning outcome. It has been applied to uncover unexpected outcomes across various disciplines, particularly at different spatiotemporal scales within ecosystems. In this article, we provide a comprehensive review of recent developments in Parrondo's paradox within the interdisciplinary realm of the physics of life, focusing on its significant applications across biology and the broader life sciences. Specifically, we examine its relevance from genetic pathways and phenotypic regulation, to intercellular interaction within multicellular organisms, and finally to the competition between populations and species in ecosystems. This phenomenon, spanning multiple biological domains and scales, enhances our understanding of the unified characteristics of life and reveals that adaptability in a drastically changing environment, rather than the inherent excellence of a trait, underpins survival in the process of evolution. We conclude by summarizing our findings and discussing future research directions that hold promise for advancing the field.

Emergent scale-free networks

Many complex systems-from the Internet to social, biological, and communication networks-are thought to exhibit scale-free structure. However, prevailing explanations require that networks grow over time, an assumption that fails in some real-world settings. Here, we explain how scale-free structure can emerge without growth through network self-organization. Beginning with an arbitrary network, we allow connections to detach from random nodes and then reconnect under a mixture of preferential and random attachment. While the numbers of nodes and edges remain fixed, the degree distribution evolves toward a power-law with an exponent γ = 1 + 1 p that depends only on the proportion p of preferential (rather than random) attachment. Applying our model to several real networks, we infer p directly from data and predict the relationship between network size and degree heterogeneity. Together, these results establish how scale-free structure can arise in networks of constant size and density, with broad implications for the structure and function of complex systems.

Birth-death-suppression Markov process and wildfires

Birth and death Markov processes can model stochastic physical systems from percolation to disease spread and, in particular, wildfires. We introduce and analyze a birth-death-suppression Markov process as a model of controlled culling of an abstract, dynamic population. Using analytic techniques, we characterize the probabilities and timescales of outcomes like absorption at zero (extinguishment) and the probability of the cumulative population (burned area) reaching a given size. The latter requires control over the embedded Markov chain: this discrete process is solved using the Pollazcek orthogonal polynomials, a deformation of the Gegenbauer/ultraspherical polynomials. This allows analysis of processes with bounded cumulative population, corresponding to finite burnable substrate in the wildfire interpretation, with probabilities represented as spectral integrals. This technology is developed to lay the foundations for a dynamic decision support framework. We devise real-time risk metrics and suggest future directions for determining optimal suppression strategies, including multievent resource allocation problems and potential applications for reinforcement learning.

A master equation for power laws

We propose a new mechanism for generating power laws. Starting from a random walk, we first outline a simple derivation of the Fokker-Planck equation. By analogy, starting from a certain Markov chain, we derive a master equation for power laws that describes how the number of cascades changes over time (cascades are consecutive transitions that end when the initial state is reached). The partial differential equation has a closed form solution which gives an explicit dependence of the number of cascades on their size and on time. Furthermore, the power law solution has a natural cut-off, a feature often seen in empirical data. This is due to the finite size a cascade can have in a finite time horizon. The derivation of the equation provides a justification for an exponent equal to 2, which agrees well with several empirical distributions, including Richardson's Law on the size and frequency of deadly conflicts. Nevertheless, the equation can be solved for any exponent value. In addition, we propose an urn model where the number of consecutive ball extractions follows a power law. In all cases, the power law is manifest over the entire range of cascade sizes, as shown through log-log plots in the frequency and rank distributions.

Friend of a friend models of network growth

One of the best-known models in network science is preferential attachment. In this model, the probability of attaching to a node depends on the degree of all nodes in the population, and thus depends on global information. In many biological, physical and social systems, however, interactions between individuals depend only on local information. Here, we investigate a truly local model of network formation-based on the idea of a friend of a friend-with the following rule: individuals choose one node at random and link to it with probability p, then they choose a neighbour of that node and link with probability q. Our model produces power-laws with empirical exponents ranging from 1.5 upwards and clustering coefficients ranging from 0 up to 0.5 (consistent with many real networks). For small p and q = 1, the model produces super-hub networks, and we prove that for p = 0 and q = 1, the proportion of non-hubs tends to 1 as the network grows. We show that power-law degree distributions, small world clustering and super-hub networks are all outcomes of this, more general, yet conceptually simple model.

Extending the Lifespan of Multicellular Organisms via Periodic and Stochastic Intercellular Competition

Resolution of the intrinsic conflict between the reproduction of single cells and the homeostasis of a multicellular organism is central to animal biology and has direct impact on aging and cancer. Intercellular competition is indispensable in multicellular organisms because it weeds out senescent cells, thereby increasing the organism's fitness and delaying aging. In this Letter, we describe the growth dynamics of multicellular organisms in the presence of intercellular competition and show that the lifespan of organisms can be extended and the onset of cancer can be delayed if cells alternate between competition (a fair strategy) and noncompetitive growth, or cooperation (a losing strategy). This effect recapitulates the weak form of the game-theoretic Parrondo's paradox, whereby strategies that are individually fair or losing achieve a winning outcome when alternated. We show in a population model that periodic and stochastic switching between competitive and cooperative cellular strategies substantially extends the organism lifespan and reduces cancer incidence, which cannot be achieved simply by optimizing the competitive ability of the cells. These results indicate that cells could have evolved to optimally mix competitive and cooperative strategies, and that periodic intercellular competition could potentially be exploited and tuned to delay aging.

The Fractal Tapestry of Life: III Multifractals Entail the Fractional Calculus

This is the third essay advocating the use the (non-integer) fractional calculus (FC) to capture the dynamics of complex networks in the twilight of the Newtonian era. Herein, the focus is on drawing a distinction between networks described by monfractal time series extensively discussed in the prequels and how they differ in function from multifractal time series, using physiological phenomena as exemplars. In prequel II, the network effect was introduced to explain how the collective dynamics of a complex network can transform a many-body non-linear dynamical system modeled using the integer calculus (IC) into a single-body fractional stochastic rate equation. Note that these essays are about biomedical phenomena that have historically been improperly modeled using the IC and how fractional calculus (FC) models better explain experimental results. This essay presents the biomedical entailment of the FC, but it is not a mathematical discussion in the sense that we are not concerned with the formal infrastucture, which is cited, but we are concerned with what that infrastructure entails. For example, the health of a physiologic network is characterized by the width of the multifractal spectrum associated with its time series, and which becomes narrower with the onset of certain pathologies. Physiologic time series that have explicitly related pathology to a narrowing of multifractal time series include but are not limited to heart rate variability (HRV), stride rate variability (SRV) and breath rate variability (BRV). The efficiency of the transfer of information due to the interaction between two such complex networks is determined by their relative spectral width, with information being transferred from the network with the broader to that with the narrower width. A fractional-order differential equation, whose order is random, is shown to generate a multifractal time series, thereby providing a FC model of the information exchange between complex networks. This equivalence between random fractional derivatives and multifractality has not received the recognition in the bioapplications literature we believe it warrants.

Fast GPU-Based Generation of Large Graph Networks From Degree Distributions

Synthetically generated, large graph networks serve as useful proxies to real-world networks for many graph-based applications. The ability to generate such networks helps overcome several limitations of real-world networks regarding their number, availability, and access. Here, we present the design, implementation, and performance study of a novel network generator that can produce very large graph networks conforming to any desired degree distribution. The generator is designed and implemented for efficient execution on modern graphics processing units (GPUs). Given an array of desired vertex degrees and number of vertices for each desired degree, our algorithm generates the edges of a random graph that satisfies the input degree distribution. Multiple runtime variants are implemented and tested: 1) a uniform static work assignment using a fixed thread launch scheme, 2) a load-balanced static work assignment also with fixed thread launch but with cost-aware task-to-thread mapping, and 3) a dynamic scheme with multiple GPU kernels asynchronously launched from the CPU. The generation is tested on a range of popular networks such as Twitter and Facebook, representing different scales and skews in degree distributions. Results show that, using our algorithm on a single modern GPU (NVIDIA Volta V100), it is possible to generate large-scale graph networks at rates exceeding 50 billion edges per second for a 69 billion-edge network. GPU profiling confirms high utilization and low branching divergence of our implementation from small to large network sizes. For networks with scattered distributions, we provide a coarsening method that further increases the GPU-based generation speed by up to a factor of 4 on tested input networks with over 45 billion edges.

Critical Indices and Self-Similar Power Transform

“Odd” factor approximants of the special form suggested by Gluzman and Yukalov (J. Math. Chem. 2006, 39, 47) are amenable to optimization by power transformation and can be successfully applied to critical phenomena. The approach is based on the idea that the critical index by itself should be optimized through the parameters of power transform to be calculated from the minimal sensitivity (derivative) optimization condition. The critical index is a product of the algebraic self-similar renormalization which contributes to the expressions the set of control parameters typical to the algebraic self-similar renormalization, and of the power transform which corrects them even further. The parameter of power transformation is, in a nutshell, the multiplier connecting the critical exponent and the correction-to-scaling exponent. We mostly study the minimal model of critical phenomena based on expansions with only two coefficients and critical points. The optimization appears to bring quite accurate, uniquely defined results given by simple formulas. Many important cases of critical phenomena are covered by the simple formula. For the longer series, the optimization condition possesses multiple solutions, and additional constraints should be applied. In particular, we constrain the sought solution by requiring it to be the best in prediction of the coefficients not employed in its construction. In principle, the error/measure of such prediction can be optimized by itself, with respect to the parameter of power transform. Methods of calculation based on optimized power-transformed factors are applied and results presented for critical indices of several key models of conductivity and viscosity of random media, swelling of polymers, permeability in two-dimensional channels. Several quantum mechanical problems are discussed as well.

Optimized Factor Approximants and Critical Index

Based on expansions with only two coefficients and known critical points, we consider a minimal model of critical phenomena. The method of analysis is both based on and inspired with the symmetry properties of functional self-similarity relation between the consecutive functional approximations. Factor approximants are applied together with various natural optimization conditions of non-perturbative nature. The role of control parameter is played by the critical index by itself. The minimal derivative condition imposed on critical amplitude appears to bring the most reasonable, uniquely defined results. The minimal difference condition also imposed on amplitudes produces upper and lower bound on the critical index. While one of the bounds is close to the result from the minimal difference condition, the second bound is determined by the non-optimized factor approximant. One would expect that for the minimal derivative condition to work well, the bounds determined by the minimal difference condition should be not too wide. In this sense the technique of optimization presented above is self-consistent, since it automatically supplies the solution and the bounds. In the case of effective viscosity of passive suspensions the bounds could be found that are too wide to make any sense from either of the solutions. Other optimization conditions imposed on the factor approximants, lead to better estimates for the critical index for the effective viscosity. The optimization is based on equating two explicit expressions following from two different definitions of the critical index, while optimization parameter is introduced as the trial third-order coefficient in the expansion.

Phase transitions and assortativity in models of gene regulatory networks evolved under different selection processes

We study a simplified model of gene regulatory network evolution in which links (regulatory interactions) are added via various selection rules that are based on the structural and dynamical features of the network nodes (genes). Similar to well-studied models of 'explosive' percolation, in our approach, links are selectively added so as to delay the transition to large-scale damage propagation, i.e. to make the network robust to small perturbations of gene states. We find that when selection depends only on structure, evolved networks are resistant to widespread damage propagation, even without knowledge of individual gene propensities for becoming 'damaged'. We also observe that networks evolved to avoid damage propagation tend towards disassortativity (i.e. directed links preferentially connect high degree 'source' genes to low degree 'target' genes and vice versa). We compare our simulations to reconstructed gene regulatory networks for several different species, with genes and links added over evolutionary time, and we find a similar bias towards disassortativity in the reconstructed networks.

Scarcity of scale-free topology is universal across biochemical networks

Biochemical reactions underlie the functioning of all life. Like many examples of biology or technology, the complex set of interactions among molecules within cells and ecosystems poses a challenge for quantification within simple mathematical objects. A large body of research has indicated many real-world biological and technological systems, including biochemistry, can be described by power-law relationships between the numbers of nodes and edges, often described as "scale-free". Recently, new statistical analyses have revealed true scale-free networks are rare. We provide a first application of these methods to data sampled from across two distinct levels of biological organization: individuals and ecosystems. We analyze a large ensemble of biochemical networks including networks generated from data of 785 metagenomes and 1082 genomes (sampled from the three domains of life). The results confirm no more than a few biochemical networks are any more than super-weakly scale-free. Additionally, we test the distinguishability of individual and ecosystem-level biochemical networks and show there is no sharp transition in the structure of biochemical networks across these levels of organization moving from individuals to ecosystems. This result holds across different network projections. Our results indicate that while biochemical networks are not scale-free, they nonetheless exhibit common structure across different levels of organization, independent of the projection chosen, suggestive of shared organizing principles across all biochemical networks.

Lipid Hydroperoxidation Effect on the Dynamical Evolution of the Conductance Process in Bilayer Lipid Membranes: A Condition Toward Criticality

Cell membranes are one of the main targets of oxidative processes mediated by reactive oxygen species (ROS). These chemical species interact with unsaturated fatty acids of membrane lipids, triggering an autocatalytic chain reaction, producing lipid hydroperoxides (LOOHs) as the first relatively stable product of the ROS-mediated lipid peroxidation (LPO) process. Numerous biophysical and computational studies have been carried out to elucidate the LPO impact on the structure and organization of lipid membranes. However, although LOOHs are the major primary product of LPO of polyunsaturated fatty acids (PUFAs), to the best of our knowledge, there is no experimental evidence on the effects of the accumulation of these LPO byproducts on the electrical properties and the underlying dynamics of lipid membranes. In this work, bilayer lipid membranes (BLMs) containing 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocoline (POPC) with increasing hydroperoxidized POPC (POPC-OOH) molar proportions (BLM_PC/PC-OOH) are used as model membranes to investigate the effect of LOOH-mediated LPO propagation on the electrical behavior of lipid bilayers. Voltage-induced ion current signals are analyzed by applying the fractal method of power spectrum density (PSD) analysis. We experimentally prove that, when certain LOOH concentration and energy threshold are overcome, oxidized membranes evolve toward a critical state characterized by the emergence of non-linear electrical behavior dynamics and the pore-type metastable structures formation. PSD analysis shows that temporal dynamics exhibiting "white" noise (non-time correlations) reflects a linear relationship between the input and output signals, while long-term correlations (β > 0.5) begin to be observed closely to the transition (critical point) from linear (Ohmic) to nonlinear (non-Ohmic) behavior. The generation of lipid pores appears to arise as an optimized energy dissipation mechanism based on the system's ability to self-organize and generate ordered structures capable of dissipating energy gradients more efficiently under stressful oxidative conditions.

Power-law distribution of degree-degree distance: A better representation of the scale-free property of complex networks

Whether real-world complex networks are scale free or not has long been controversial. Recently, in Broido and Clauset [A. D. Broido, A. Clauset, Nat. Commun. 10, 1017 (2019)], it was claimed that the degree distributions of real-world networks are rarely power law under statistical tests. Here, we attempt to address this issue by defining a fundamental property possessed by each link, the degree-degree distance, the distribution of which also shows signs of being power law by our empirical study. Surprisingly, although full-range statistical tests show that degree distributions are not often power law in real-world networks, we find that in more than half of the cases the degree-degree distance distributions can still be described by power laws. To explain these findings, we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted, two-way selection process. The model does not always produce solid power-law distributions but predicts that the degree-degree distance distribution exhibits stronger power-law behavior than the degree distribution of a finite-size network, especially when the network is dense. We test the strength of our model and its predictive power by examining how real-world networks evolve into an overly dense stage and how the corresponding distributions change. We propose that being scale free is a property of a complex network that should be determined by its underlying mechanism (e.g., preferential attachment) rather than by apparent distribution statistics of finite size. We thus conclude that the degree-degree distance distribution better represents the scale-free property of a complex network.

Core transcriptional regulatory circuits in prion diseases

Complex diseases involve dynamic perturbations of pathophysiological processes during disease progression. Transcriptional programs underlying such perturbations are unknown in many diseases. Here, we present core transcriptional regulatory circuits underlying early and late perturbations in prion disease. We first identified cellular processes perturbed early and late using time-course gene expression data from three prion-infected mouse strains. We then built a transcriptional regulatory network (TRN) describing regulation of early and late processes. We found over-represented feed-forward loops (FFLs) comprising transcription factor (TF) pairs and target genes in the TRN. Using gene expression data of brain cell types, we further selected active FFLs where TF pairs and target genes were expressed in the same cell type and showed correlated temporal expression changes in the brain. We finally determined core transcriptional regulatory circuits by combining these active FFLs. These circuits provide insights into transcriptional programs for early and late pathophysiological processes in prion disease.

Load-Dependent Changes in Left Ventricular Structure and Function in a Pathophysiologically Relevant Murine Model of Reversible Heart Failure

BACKGROUND

To better understand reverse left ventricular (LV) remodeling, we developed a murine model wherein mice develop LV remodeling after transverse aortic constriction (TAC) and a small apical myocardial infarct (MI) and undergo reverse LV remodeling after removal of the aortic band.

METHODS AND RESULTS

Mice studied were subjected to sham (n=6) surgery or TAC+MI (n=12). Two weeks post-TAC+MI, 1 group underwent debanding (referred to as heart failure debanding [HF-DB] mice; n=6), whereas the aortic band remained in a second group (heart failure [HF] group; n=6). LV remodeling was evaluated by 2D echocardiography at 1 day, 2 weeks and 6 weeks post-TAC+MI. The hearts were analyzed by transcriptional profiling at 4 and 6 weeks and histologically at 6 weeks. Debanding normalized LV volumes, LV mass, and cardiac myocyte hypertrophy at 6 weeks in HF-DB mice, with no difference in myofibrillar collagen in the HF and HF-DB mice. LV ejection fraction and radial strain improved after debanding; however, both remained decreased in the HF-DB mice relative to sham and were not different from HF mice at 6 weeks. Hemodynamic unloading in the HF-DB mice was accompanied by a 35% normalization of the HF genes at 2 weeks and 80% of the HF genes at 4 weeks.

CONCLUSIONS

Hemodynamic unloading of a pathophysiologically relevant mouse model of HF results in normalization of LV structure, incomplete recovery of LV function, and incomplete reversal of the HF transcriptional program. The HF-DB mouse model may provide novel insights into mechanisms of reverse LV remodeling.

Scale-free networks are rare

Real-world networks are often claimed to be scale free, meaning that the fraction of nodes with degree k follows a power law k-α, a pattern with broad implications for the structure and dynamics of complex systems. However, the universality of scale-free networks remains controversial. Here, we organize different definitions of scale-free networks and construct a severe test of their empirical prevalence using state-of-the-art statistical tools applied to nearly 1000 social, biological, technological, transportation, and information networks. Across these networks, we find robust evidence that strongly scale-free structure is empirically rare, while for most networks, log-normal distributions fit the data as well or better than power laws. Furthermore, social networks are at best weakly scale free, while a handful of technological and biological networks appear strongly scale free. These findings highlight the structural diversity of real-world networks and the need for new theoretical explanations of these non-scale-free patterns.

Self-organization of dragon king failures

The mechanisms underlying cascading failures are often modeled via the paradigm of self-organized criticality. Here we introduce a simple network model where nodes self-organize to be either weakly or strongly protected against failure in a manner that captures the trade-off between degradation and reinforcement of nodes inherent in many network systems. If strong nodes cannot fail, any failure is contained to a single, isolated cluster of weak nodes and the model produces power-law distributions of failure sizes. We classify the large, rare events that involve the failure of only a single cluster as "black swans." In contrast, if strong nodes fail once a sufficient fraction of their neighbors fail, then failure can cascade across multiple clusters of weak nodes. If over 99.9% of the nodes fail due to this cluster hopping mechanism, we classify this as a "dragon king," which are massive failures caused by mechanisms distinct from smaller failures. The dragon kings observed are self-organized, existing over a wide range of reinforcement rates and system sizes. We find that once an initial cluster of failing weak nodes is above a critical size, the dragon king mechanism kicks in, leading to piggybacking system-wide failures. We demonstrate that the size of the initial failed weak cluster predicts the likelihood of a dragon king event with high accuracy and we develop a simple control strategy that can dramatically reduce dragon kings and other large failures.

Physical foundations of biological complexity

Biological systems reach hierarchical complexity that has no counterpart outside the realm of biology. Undoubtedly, biological entities obey the fundamental physical laws. Can today's physics provide an explanatory framework for understanding the evolution of biological complexity? We argue that the physical foundation for understanding the origin and evolution of complexity can be gleaned at the interface between the theory of frustrated states resulting in pattern formation in glass-like media and the theory of self-organized criticality (SOC). On the one hand, SOC has been shown to emerge in spin-glass systems of high dimensionality. On the other hand, SOC is often viewed as the most appropriate physical description of evolutionary transitions in biology. We unify these two faces of SOC by showing that emergence of complex features in biological evolution typically, if not always, is triggered by frustration that is caused by competing interactions at different organizational levels. Such competing interactions lead to SOC, which represents the optimal conditions for the emergence of complexity. Competing interactions and frustrated states permeate biology at all organizational levels and are tightly linked to the ubiquitous competition for limiting resources. This perspective extends from the comparatively simple phenomena occurring in glasses to large-scale events of biological evolution, such as major evolutionary transitions. Frustration caused by competing interactions in multidimensional systems could be the general driving force behind the emergence of complexity, within and beyond the domain of biology.

Network Dynamics of Attention During a Naturalistic Behavioral Paradigm

This study investigates the dynamics of attention during continuous, naturalistic interactions in a video game. Specifically, the effect of repeated distraction on a continuous primary task is related to a functional model of network connectivity. We introduce the Non-linear Attentional Saturation Hypothesis (NASH), which predicts that effective connectivity within attentional networks increases non-linearly with decreasing distraction over time, and exhibits dampening at critical parameter values. Functional magnetic resonance imaging (fMRI) data collected using a naturalistic behavioral paradigm coupled with an interactive video game is used to test the hypothesis. As predicted, connectivity in pre-defined regions corresponding to attentional networks increases as distraction decreases. Moreover, the functional relationship between connectivity and distraction is convex, that is, network connectivity somewhat increases as distraction decreases during the continuous primary task, however, connectivity increases considerably as distraction falls below critical levels. This result characterizes the non-linear pattern of connectivity within attentional networks, particularly with respect to their dynamics during behavior. These results are also summarized in the form of a network structure analysis, which underscores the role of various nodes in regulating the global network state. In conclusion, we situate the implications of this research in the context of cognitive complexity and an emerging theory of flow during media exposure.

Not Normal: the uncertainties of scientific measurements

Judging the significance and reproducibility of quantitative research requires a good understanding of relevant uncertainties, but it is often unclear how well these have been evaluated and what they imply. Reported scientific uncertainties were studied by analysing 41 000 measurements of 3200 quantities from medicine, nuclear and particle physics, and interlaboratory comparisons ranging from chemistry to toxicology. Outliers are common, with 5σ disagreements up to five orders of magnitude more frequent than naively expected. Uncertainty-normalized differences between multiple measurements of the same quantity are consistent with heavy-tailed Student's t-distributions that are often almost Cauchy, far from a Gaussian Normal bell curve. Medical research uncertainties are generally as well evaluated as those in physics, but physics uncertainty improves more rapidly, making feasible simple significance criteria such as the 5σ discovery convention in particle physics. Contributions to measurement uncertainty from mistakes and unknown problems are not completely unpredictable. Such errors appear to have power-law distributions consistent with how designed complex systems fail, and how unknown systematic errors are constrained by researchers. This better understanding may help improve analysis and meta-analysis of data, and help scientists and the public have more realistic expectations of what scientific results imply.

On a Possible Unified Scaling Law for Volcanic Eruption Durations

Volcanoes constitute dissipative systems with many degrees of freedom. Their eruptions are the result of complex processes that involve interacting chemical-physical systems. At present, due to the complexity of involved phenomena and to the lack of precise measurements, both analytical and numerical models are unable to simultaneously include the main processes involved in eruptions thus making forecasts of volcanic dynamics rather unreliable. On the other hand, accurate forecasts of some eruption parameters, such as the duration, could be a key factor in natural hazard estimation and mitigation. Analyzing a large database with most of all the known volcanic eruptions, we have determined that the duration of eruptions seems to be described by a universal distribution which characterizes eruption duration dynamics. In particular, this paper presents a plausible global power-law distribution of durations of volcanic eruptions that holds worldwide for different volcanic environments. We also introduce a new, simple and realistic pipe model that can follow the same found empirical distribution. Since the proposed model belongs to the family of the self-organized systems it may support the hypothesis that simple mechanisms can lead naturally to the emergent complexity in volcanic behaviour.

Heterogeneous dynamics, robustness/fragility trade-offs, and the eradication of the macroparasitic disease, lymphatic filariasis

BACKGROUND

The current WHO-led initiative to eradicate the macroparasitic disease, lymphatic filariasis (LF), based on single-dose annual mass drug administration (MDA) represents one of the largest health programs devised to reduce the burden of tropical diseases. However, despite the advances made in instituting large-scale MDA programs in affected countries, a challenge to meeting the goal of global eradication is the heterogeneous transmission of LF across endemic regions, and the impact that such complexity may have on the effort required to interrupt transmission in all socioecological settings.

METHODS

Here, we apply a Bayesian computer simulation procedure to fit transmission models of LF to field data assembled from 18 sites across the major LF endemic regions of Africa, Asia and Papua New Guinea, reflecting different ecological and vector characteristics, to investigate the impacts and implications of transmission heterogeneity and complexity on filarial infection dynamics, system robustness and control.

RESULTS

We find firstly that LF elimination thresholds varied significantly between the 18 study communities owing to site variations in transmission and initial ecological parameters. We highlight how this variation in thresholds lead to the need for applying variable durations of interventions across endemic communities for achieving LF elimination; however, a major new result is the finding that filarial population responses to interventions ultimately reflect outcomes of interplays between dynamics and the biological architectures and processes that generate robustness/fragility trade-offs in parasite transmission. Intervention simulations carried out in this study further show how understanding these factors is also key to the design of options that would effectively eliminate LF from all settings. In this regard, we find how including vector control into MDA programs may not only offer a countermeasure that will reliably increase system fragility globally across all settings and hence provide a control option robust to differential locality-specific transmission dynamics, but by simultaneously reducing transmission regime variability also permit more reliable macroscopic predictions of intervention effects.

CONCLUSIONS

Our results imply that a new approach, combining adaptive modelling of parasite transmission with the use of biological robustness as a design principle, is required if we are to both enhance understanding of complex parasitic infections and delineate options to facilitate their elimination effectively.

Integrating Ecological and Engineering Concepts of Resilience in Microbial Communities

Many definitions of resilience have been proffered for natural and engineered ecosystems, but a conceptual consensus on resilience in microbial communities is still lacking. We argue that the disconnect largely results from the wide variance in microbial community complexity, which range from compositionally simple synthetic consortia to complex natural communities, and divergence between the typical practical outcomes emphasized by ecologists and engineers. Viewing microbial communities as elasto-plastic systems that undergo both recoverable and unrecoverable transitions, we argue that this gap between the engineering and ecological definitions of resilience stems from their respective emphases on elastic and plastic deformation, respectively. We propose that the two concepts may be fundamentally united around the resilience of function rather than state in microbial communities and the regularity in the relationship between environmental variation and a community's functional response. Furthermore, we posit that functional resilience is an intrinsic property of microbial communities and suggest that state changes in response to environmental variation may be a key mechanism driving functional resilience in microbial communities.

Dynamical analysis and visualization of tornadoes time series

In this paper we analyze the behavior of tornado time-series in the U.S. from the perspective of dynamical systems. A tornado is a violently rotating column of air extending from a cumulonimbus cloud down to the ground. Such phenomena reveal features that are well described by power law functions and unveil characteristics found in systems with long range memory effects. Tornado time series are viewed as the output of a complex system and are interpreted as a manifestation of its dynamics. Tornadoes are modeled as sequences of Dirac impulses with amplitude proportional to the events size. First, a collection of time series involving 64 years is analyzed in the frequency domain by means of the Fourier transform. The amplitude spectra are approximated by power law functions and their parameters are read as an underlying signature of the system dynamics. Second, it is adopted the concept of circular time and the collective behavior of tornadoes analyzed. Clustering techniques are then adopted to identify and visualize the emerging patterns.

Synthetic biology for the directed evolution of protein biocatalysts: navigating sequence space intelligently

The amino acid sequence of a protein affects both its structure and its function. Thus, the ability to modify the sequence, and hence the structure and activity, of individual proteins in a systematic way, opens up many opportunities, both scientifically and (as we focus on here) for exploitation in biocatalysis. Modern methods of synthetic biology, whereby increasingly large sequences of DNA can be synthesised de novo, allow an unprecedented ability to engineer proteins with novel functions. However, the number of possible proteins is far too large to test individually, so we need means for navigating the 'search space' of possible protein sequences efficiently and reliably in order to find desirable activities and other properties. Enzymologists distinguish binding (Kd) and catalytic (kcat) steps. In a similar way, judicious strategies have blended design (for binding, specificity and active site modelling) with the more empirical methods of classical directed evolution (DE) for improving kcat (where natural evolution rarely seeks the highest values), especially with regard to residues distant from the active site and where the functional linkages underpinning enzyme dynamics are both unknown and hard to predict. Epistasis (where the 'best' amino acid at one site depends on that or those at others) is a notable feature of directed evolution. The aim of this review is to highlight some of the approaches that are being developed to allow us to use directed evolution to improve enzyme properties, often dramatically. We note that directed evolution differs in a number of ways from natural evolution, including in particular the available mechanisms and the likely selection pressures. Thus, we stress the opportunities afforded by techniques that enable one to map sequence to (structure and) activity in silico, as an effective means of modelling and exploring protein landscapes. Because known landscapes may be assessed and reasoned about as a whole, simultaneously, this offers opportunities for protein improvement not readily available to natural evolution on rapid timescales. Intelligent landscape navigation, informed by sequence-activity relationships and coupled to the emerging methods of synthetic biology, offers scope for the development of novel biocatalysts that are both highly active and robust.

The smarter, the stronger: intelligence level correlates with brain resilience to systematic insults

Neuroimaging evidences posit human intelligence as tightly coupled with several structural and functional brain properties, also suggesting its potential protective role against aging and neurodegenerative conditions. However, whether higher order cognition might in fact lead to a more resilient brain has not been quantitatively demonstrated yet. Here we document a relationship between individual intelligence quotient (IQ) and brain resilience to targeted and random attacks, as measured through resting-state fMRI graph-theoretical analysis in 102 healthy individuals. In this modeling context, enhanced brain robustness to targeted attacks (TA) in individuals with higher IQ is supported by an increased distributed processing capacity despite the systematic loss of the most important node(s) of the system. Moreover, brain resilience in individuals with higher IQ is supported by a set of neocortical regions mainly belonging to language and memory processing network(s), whereas regions related to emotional processing are mostly responsible for lower IQ individuals. Results suggest intelligence level among the predictors of post-lesional or neurodegenerative recovery, also promoting the evolutionary role of higher order cognition, and simultaneously suggesting a new framework for brain stimulation interventions aimed at counteract brain deterioration over time.

Toy models for macroevolutionary patterns and trends

Many models have been used to simplify and operationalize the subtle but complex mechanisms of biological evolution. Toy models are gross simplifications that nevertheless attempt to retain major essential features of evolution, bridging the gap between empirical reality and formal theoretical understanding. In this paper, we examine thirteen models which describe evolution that also qualify as such toy models, including the tree of life, branching processes, adaptive ratchets, fitness landscapes, and the role of nonlinear avalanches in evolutionary dynamics. Such toy models are intended to capture features such as evolutionary trends, coupled evolutionary dynamics of phenotype and genotype, adaptive change, branching, and evolutionary transience. The models discussed herein are applied to specific evolutionary contexts in various ways that simplify the complexity inherent in evolving populations. While toy models are overly simplistic, they also provide sufficient dynamics for capturing the fundamental mechanism(s) of evolution. Toy models might also be used to aid in high-throughput data analysis and the understanding of cultural evolutionary trends. This paper should serve as an introductory guide to the toy modeling of evolutionary complexity.

The Matthew effect in empirical data

The Matthew effect describes the phenomenon that in societies, the rich tend to get richer and the potent even more powerful. It is closely related to the concept of preferential attachment in network science, where the more connected nodes are destined to acquire many more links in the future than the auxiliary nodes. Cumulative advantage and success-breads-success also both describe the fact that advantage tends to beget further advantage. The concept is behind the many power laws and scaling behaviour in empirical data, and it is at the heart of self-organization across social and natural sciences. Here, we review the methodology for measuring preferential attachment in empirical data, as well as the observations of the Matthew effect in patterns of scientific collaboration, socio-technical and biological networks, the propagation of citations, the emergence of scientific progress and impact, career longevity, the evolution of common English words and phrases, as well as in education and brain development. We also discuss whether the Matthew effect is due to chance or optimization, for example related to homophily in social systems or efficacy in technological systems, and we outline possible directions for future research.

Self-organization processes in field-invasion team sports : implications for leadership

In nature, the interactions between agents in a complex system (fish schools; colonies of ants) are governed by information that is locally created. Each agent self-organizes (adjusts) its behaviour, not through a central command centre, but based on variables that emerge from the interactions with other system agents in the neighbourhood. Self-organization has been proposed as a mechanism to explain the tendencies for individual performers to interact with each other in field-invasion sports teams, displaying functional co-adaptive behaviours, without the need for central control. The relevance of self-organization as a mechanism that explains pattern-forming dynamics within attacker-defender interactions in field-invasion sports has been sustained in the literature. Nonetheless, other levels of interpersonal coordination, such as intra-team interactions, still raise important questions, particularly with reference to the role of leadership or match strategies that have been prescribed in advance by a coach. The existence of key properties of complex systems, such as system degeneracy, nonlinearity or contextual dependency, suggests that self-organization is a functional mechanism to explain the emergence of interpersonal coordination tendencies within intra-team interactions. In this opinion article we propose how leadership may act as a key constraint on the emergent, self-organizational tendencies of performers in field-invasion sports.

AKT as locus of cancer multidrug resistance and fragility

Complexity and robustness of cancer hypoxic microenvironment are supported by the robust signaling networks of autocrine and paracrine elements creating powerful interactome for multidrug resistance. These elements generate a positive feedback loops responsible for the extreme robustness and multidrug resistance in solid cancer, leukemia, myeloma, and lymphoma. Phosphorylated AKT is a cancer multidrug resistance locus. Targeting that locus by oxidant/antioxidant balance modulation, positive feedback loops are converted into negative feedback loops, leading to disappearance of multidrug resistance. This is a new principle for targeting cancer multidrug resistance by the locus chemotherapy inducing a phenomenon of loops conversion.

The role of the circadian system in fractal neurophysiological control

Many neurophysiological variables such as heart rate, motor activity, and neural activity are known to exhibit intrinsic fractal fluctuations - similar temporal fluctuation patterns at different time scales. These fractal patterns contain information about health, as many pathological conditions are accompanied by their alteration or absence. In physical systems, such fluctuations are characteristic of critical states on the border between randomness and order, frequently arising from nonlinear feedback interactions between mechanisms operating on multiple scales. Thus, the existence of fractal fluctuations in physiology challenges traditional conceptions of health and disease, suggesting that high levels of integrity and adaptability are marked by complex variability, not constancy, and are properties of a neurophysiological network, not individual components. Despite the subject's theoretical and clinical interest, the neurophysiological mechanisms underlying fractal regulation remain largely unknown. The recent discovery that the circadian pacemaker (suprachiasmatic nucleus) plays a crucial role in generating fractal patterns in motor activity and heart rate sheds an entirely new light on both fractal control networks and the function of this master circadian clock, and builds a bridge between the fields of circadian biology and fractal physiology. In this review, we sketch the emerging picture of the developing interdisciplinary field of fractal neurophysiology by examining the circadian system's role in fractal regulation.

Robustness and aging--a systems-level perspective

The theory of robustness describes a system level property of evolutionary systems, which predicts tradeoffs of great interest for the systems biology of aging, such as accumulation of non-heritable damage, occurrence of fragilities and limitations in performance, optimized allocation of restricted resources and confined redundancies. According to the robustness paradigm cells and organisms evolved into a state of highly optimized tolerance (HOT), which provides robustness to common perturbations, but causes tradeoffs generally characterized as "robust yet fragile". This raises the question whether the ultimate cause of aging is more than a lack of adaptation, but an inherent fragility of complex evolutionary systems. Since robustness connects to evolutionary designs, consideration of this theory provides a deeper connection between evolutionary aspects of aging, mathematical models and experimental data. In this review several mechanisms influential for aging are re-evaluated in support of robustness tradeoffs. This includes asymmetric cell division improving performance and specialization with limited capacities to prevent and repair age-related damage, as well as feedback control mechanisms optimized to respond to acute stressors, but unable to halt nor revert aging. Improvement in robustness by increasing efficiencies through cellular redundancies in larger organisms alleviates some of the damaging effects of cellular specialization, which can be expressed in allometric relationships. The introduction of the robustness paradigm offers unique insights for aging research and provides novel opportunities for systems biology endeavors.

AKT as locus of cancer positive feedback loops and extreme robustness

A positive feedback loops induce extreme robustness in metastatic cancer, relapsed leukemia, myeloma or lymphoma. The loops are generated by the signaling interactome networks of autocrine and paracrine elements from cancer hypoxic microenvironment. The elements of the networks are signaling proteins synthesized in hypoxic microenvironment such as the vascular endothelial growth factor, HIF-1α, hepatocyte growth factor, and molecules nitric oxide and H(2)O(2). The signals from upstream or rebound downstream pathways are amplified by the short or wide positive feedback loops, hyperstimulating AKT-inducing cancer extreme robustness. Targeting the phosphorylated AKT locus by an oxidant/antioxidant modulation induces collapse of positive feedback loops and establishment of negative feedback loops leading to stability of the system and disappearance of cancer extreme robustness. This is a new principle for the conversion of cancer positive loops into negative feedback loops by the locus chemotherapy.

AKT as locus of cancer angiogenic robustness and fragility

Angiogenesis get full robustness in metastatic cancer, relapsed leukemia or lymphoma when complex positive feedback loop signaling systems become integrative. A cancer hypoxic microenvironment generates positive loops inducing formation of the vascular functional shunts. AKT is an upstream angiogenic locus of integrative robustness and fragility activated by the positive loops. AKT controls two downstream nodes the mTOR and NOS in nodal organization of the signaling genes. AKT phosphorylation is regulated by a balance of an oxidant/antioxidant. Targeting AKT locus represents new principle to control integrative angiogenic robustness by the locus chemotherapy.

Trade-off of dynamic fragility but not of robustness in metabolic pathways in silico

Selective robustness is a key feature of biochemical networks. It confers a fitness benefit to organisms living in dynamic environments. The (in-)sensitivity of a network to external perturbations results from the interplay between network dynamics, structure and enzyme kinetics. In this work, we focus on the subtle interplay between robustness and control (fragility). We describe a quantitative method for defining the fragility and robustness of system fluxes to perturbations. We find that for many mathematical models of metabolic pathways, the robustness of fluxes vis-à-vis perturbations of all the enzyme activities is captured by a broad distribution of the robustness coefficients. We find that in cases where a metabolic pathway flux is made less robust with respect to the perturbation of a particular network step, the average robustness may still be increased. We then show that fragility is conserved upon a perturbation of network processes and equate fragility with control as defined in metabolic control analysis. This highlights the non-intuitive nature of the interplay between fragility and robustness and the need for a dynamic network understanding.

Dynamic resource allocation in disaster response: tradeoffs in wildfire suppression

Challenges associated with the allocation of limited resources to mitigate the impact of natural disasters inspire fundamentally new theoretical questions for dynamic decision making in coupled human and natural systems. Wildfires are one of several types of disaster phenomena, including oil spills and disease epidemics, where (1) the disaster evolves on the same timescale as the response effort, and (2) delays in response can lead to increased disaster severity and thus greater demand for resources. We introduce a minimal stochastic process to represent wildfire progression that nonetheless accurately captures the heavy tailed statistical distribution of fire sizes observed in nature. We then couple this model for fire spread to a series of response models that isolate fundamental tradeoffs both in the strength and timing of response and also in division of limited resources across multiple competing suppression efforts. Using this framework, we compute optimal strategies for decision making scenarios that arise in fire response policy.

Evolutionary Systems Theory: A Unifying Meta-Theory of Psychological Science

Psychology is a theoretically heterogeneous discipline seeking a single, cohesive framework to unite the subdisciplines. To address this issue, I propose a hierarchical metatheory of psychological science that synthesizes neo-Darwinian selectionist thinking and dynamic systems theory by organizing evolutionary psychology, evolutionary developmental biology, developmental psychobiology, and the subdisciplines of psychology around four specific, interrelated levels of analysis: functional explanations for evolved, species-typical characteristics; explanations for between-groups differences arising from phylogenetic mechanisms; explanations for individual differences resulting from ontogenetic processes; and mechanistic explanations for real-time phenomena, respectively. Informational exchange between these levels advances their integration and facilitates important innovations, and the nonsubstantive metatheories of general selection and self-organization interpenetrate all four levels to promote consilience. I conclude by discussing the implications of this model for theory and research.

Topological biosignatures: large-scale structure of chemical networks from biology and astrochemistry

The chemical basis of life involves more than simply the presence of biological molecules; biochemical systems embody a complex network of reactions with characteristic topological features. At the same time, chemical complexity is also present in nonbiological contexts, inviting us to clarify the relationship between chemistry and life through comparative studies. This study examines chemical networks from biology (the metabolism of E. coli) and astronomy (gas-phase reactions in dark molecular clouds) to establish common topological features that may be generic for any complex chemical system, as well as clear differences that may be topological signatures of life. The biological and astrochemical networks exhibit different scaling behaviors, and the network motifs found in the two systems show similarities as well as significant differences. The PageRank algorithm was used to quantify the degree to which individual species act primarily as products or reactants; in the metabolic network, these two roles are nearly identical for most species, whereas the astrochemical network shows a clearer partitioning into reactants and products.

Overview of metrics and their correlation patterns for multiple-metric topology analysis on heterogeneous graph ensembles

This study is an overview of network topology metrics and a computational approach to analyzing graph topology via multiple-metric analysis on graph ensembles. The paper cautions against studying single metrics or combining disparate graph ensembles from different domains to extract global patterns. This is because there often exists considerable diversity among graphs that share any given topology metric, patterns vary depending on the underlying graph construction model, and many real data sets are not actual statistical ensembles. As real data examples, we present five airline ensembles, comprising temporal snapshots of networks of similar topology. Wikipedia language networks are shown as an example of a nontemporal ensemble. General patterns in metric correlations, as well as exceptions, are discussed by representing the data sets via hierarchically clustered correlation heat maps. Most topology metrics are not independent and their correlation patterns vary across ensembles. In general, density-related metrics and graph distance-based metrics cluster and the two groups are orthogonal to each other. Metrics based on degree-degree correlations have the highest variance across ensembles and cluster the different data sets on par with principal component analysis. Namely, the degree correlation, the s metric, their elasticities, and the rich club moments appear to be most useful in distinguishing topologies.