Complex System

Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks.

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. Here we review the state of the art by focusing on a wide list of topics ranging from opinion, cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, social spreading. We highlight the connections between these problems and other, more traditional, topics of statistical physics. We also emphasize the comparison of model results with empirical data from social systems. * Electronic address: [email protected] † Electronic address: [email protected] ‡ Electronic address: [email protected]

We present a new symbolic execution tool, KLEE, capable of automatically generating tests that achieve high coverage on a diverse set of complex and environmentally-intensive programs. We used KLEE to thoroughly check all 89 stand-alone programs in the GNU COREUTILS utility suite, which form the core user-level environment installed on millions of Unix systems, and arguably are the single most heavily tested set of open-source programs in existence. KLEE-generated tests achieve high line coverage -on average over 90% per tool (median: over 94%) -and significantly beat the coverage of the developers' own hand-written test suite. When we did the same for 75 equivalent tools in the BUSYBOX embedded system suite, results were even better, including 100% coverage on 31 of them.

Community detection and analysis is an important methodology for understanding the organization of various real-world networks and has applications in problems as diverse as consensus formation in social communities or the identification of functional modules in biochemical networks. Currently used algorithms that identify the community structures in large-scale real-world networks require a priori information such as the number and sizes of communities or are computationally expensive. In this paper we investigate a simple label propagation algorithm that uses the network structure alone as its guide and requires neither optimization of a pre-defined objective function nor prior information about the communities. In our algorithm every node is initialized with a unique label and at every step each node adopts the label that most of its neighbors currently have. In this iterative process densely connected groups of nodes form a consensus on a unique label to form communities. We validate the algorithm by applying it to networks whose community structures are known. We also demonstrate that the algorithm takes an almost linear time and hence it is computationally less expensive than what was possible so far.

This paper is an attempt to integrate in a general model the major findings reported earlier in this series on: lability and history dependence of circadian period, τ (Pittendrigh and Daan, 1976 a); dependence of τ and α on light intensity as described in Aschoff's Rule (Daan and Pittendrigh, 1976b); the interrelationships between τ and phase response curves (Daan and Pittendrigh, 1976a); and those inconsistencies between experimental facts on entrainment and theoretical predictions based on a single oscillator with fixed parameters τ and PRC, which pointed to a more complex system (Pittendrigh and Daan, 1976b). The qualitative model developed consists of two oscillators. The evidence that two separate oscillators are involved in circadian activity rhythms rests largely on the “splitting” phenomenon, known to occur in several species of mammals and birds. The empirical regularities of “splitting” in hamsters exposed to constant illumination (LL) are described: Splitting, i.e. the dissociation of a single activity band into two components which become stably coupled in circa 180° antiphase, occurs in about 50% of the animals in 100–200 lux, and has not been observed in lower light intensities. Splitting never occurred before 40 days after the transition to LL, unless the pretreatment had been LL of low intensity. In some animals the unsplit condition returned spontaneously. The attainment of antiphase is usually accompanied by a decrease in τ, and refusion of the two components by an increase in τ. These data show that both the split and the unsplit condition are metastable states, characterized by different phase relationships (ψ EM ) of two constituent oscillators. ψEM is history-dependent and determines τ of the coupled system. Observations in Peromyscus leucopus transferred from LL to DD to LD 12∶12 show that the two components of the bimodal activity peak (in LD) can for some time run at different frequencies (in DD), suggesting that bimodality of activity peaks and splitting are based on the same two-oscillator system. The model developed assumes the existence of two oscillators or principal groups of oscillators E and M, with opposite dependence of spontaneous frequency on light intensity. The dependence of the phase relationship (ψ EM ) between the two on light intensity and the dependence of τ onψ EM account for all the history-dependent characteristics of circadian pacemakers, and for the interdependence of τ, PRC, and τ-lability. The model qualitatively accommodates the interdependence of τ and α summarized in Aschoffs Rule. It is noted that the major intuitive elements in the model have been found to characterize an explicit version of it in computer simulations. The relevance of the model to seasonal change in photoperiod is discussed. A pacemaker comprising two oscillators mutually interacting but coupled separately to sunrise and sunset enhances its competence to accommodate to seasonal change in the daily pattern of external conditions; and it could well be involved in the pacemaker's known ability to discriminate between daylengths in the phenomena of photoperiodic induction.

In the so-called “microscopic” models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a “particle”; the nature of the “interactions” among these particles is determined by the way the vehicles influence each others’ movement. Therefore, vehicular traffic, modeled as a system of interacting “particles” driven far from equilibrium, offers the possibility to study various fundamental aspects of truly nonequilibrium systems which are of current interest in statistical physics. Analytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Some of these phenomena, observed in vehicular traffic under different circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. In this critical review, written from the perspective of statistical physics, we explain the guiding principles behind all the main theoretical approaches. But we present detailed discussions on the results obtained mainly from the so-called “particle-hopping” models, particularly emphasizing those which have been formulated in recent years using the language of cellular automata.

Though word-of-mouth (w-o-m) communications is a pervasive and intriguing phenomenon, little is known on its underlying process of personal communications. Moreover as marketers are getting more interested in harnessing the power of w-o-m, for e-business and other net related activities, the effects of the different communications types on macro level marketing is becoming critical. In particular we are interested in the breakdown of the personal communication between closer and stronger communications that are within an individual's own personal group (strong ties) and weaker and less personal communications that an individual makes with a wide set of other acquaintances and colleagues (weak ties).

Uncovering the community structure exhibited by real networks is a crucial step towards an understanding of complex systems that goes beyond the local organization of their constituents. Many algorithms have been proposed so far, but none of them has been subjected to strict tests to evaluate their performance. Most of the sporadic tests performed so far involved small networks with known community structure and/or artificial graphs with a simplified structure, which is very uncommon in real systems. Here we test several methods against a recently introduced class of benchmark graphs, with heterogeneous distributions of degree and community size. The methods are also tested against the benchmark by Girvan and Newman and on random graphs. As a result of our analysis, three recent algorithms introduced by Rosvall and Bergstrom, Blondel et al. and Ronhovde and Nussinov, respectively, have an excellent performance, with the additional advantage of low computational complexity, which enables one to analyze large systems.

We present an overview of the current status of transition-state theory and its generalizations. We emphasize (i) recent improvements in available methodology for calculations on complex systems, including the interface with electronic structure theory, (ii) progress in the theory and application of transition-state theory to condensedphase reactions, and (iii) insight into the relation of transition-state theory to accurate quantum dynamics and tests of its accuracy via comparisons with both experimental and other theoretical dynamical approximations.

Graphics have been used since ancient times to portray things that are inherently spatiovisual, like maps and building plans. More recently, graphics have been used to portray things that are metaphorically spatiovisual, like graphs and organizational charts. The assumption is that graphics can facilitate comprehension, learning, memory, communication and inference. Assumptions aside, research on static graphics has shown that only carefully designed and appropriate graphics prove to be beneficial for conveying complex systems. Effective graphics conform to the Congruence Principle according to which the content and format of the graphic should correspond to the content and format of the concepts to be conveyed. From this, it follows that animated graphics should be effective in portraying change over time. Yet the research on the efficacy of animated over static graphics is not encouraging. In cases where animated graphics seem superior to static ones, scrutiny reveals lack of equivalence between animated and static graphics in content or procedures; the animated graphics convey more information or involve interactivity. Animations of events may be ineffective because animations violate the second principle of good graphics, the Apprehension Principle, according to which graphics should be accurately perceived and appropriately conceived. Animations are often too complex or too fast to be accurately perceived. Moreover, many continuous events are conceived of as sequences of discrete steps. Judicious use of interactivity may overcome both these disadvantages. Animations may be more effective than comparable static graphics in situations other than conveying complex systems, for example, for real time reorientations in time and space. #

The epidermal growth factor receptor (EGFR) belongs to the ErbB family of receptor tyrosine kinases (RTK). These trans-membrane proteins are activated following binding with peptide growth factors of the EGF-family of proteins. Evidence suggests that the EGFR is involved in the pathogenesis and progression of different carcinoma types. The EGFR and EGF-like peptides are often over-expressed in human carcinomas, and in vivo and in vitro studies have shown that these proteins are able to induce cell transformation. Amplification of the EGFR gene and mutations of the EGFR tyrosine kinase domain have been recently demonstrated to occur in carcinoma patients. Interestingly, both these genetic alterations of the EGFR are correlated with high probability to respond to anti-EGFR agents. However, ErbB proteins and their ligands form a complex system in which the interactions occurring between receptors and ligands affect the type and the duration of the intracellular signals that derive from receptor activation. In fact, proteins of the ErbB family form either homo-or hetero-dimers following ligand binding, each dimer showing different affinity for ligands and different signaling properties. In this regard, evidence suggests that cooperation of multiple ErbB receptors and cognate ligands is necessary to induce cell transformation. In particular, the growth and the survival of carcinoma cells appear to be sustained by a network of receptors/ligands of the ErbB family. This phenomenon is also important for therapeutic approaches, since the response to anti-EGFR agents might depend on the total level of expression of ErbB receptors and ligands in tumor cells. Published by Elsevier B.V.

This article reviews the concepts and methods of transition path sampling. These methods allow computational studies of rare events without requiring prior knowledge of mechanisms, reaction coordinates, and transition states. Based upon a statistical mechanics of trajectory space, they provide a perspective with which time dependent phenomena, even for systems driven far from equilibrium, can be examined with the same types of importance sampling tools that in the past have been applied so successfully to static equilibrium properties.

We present a line-search algorithm for large-scale continuous optimization. The algorithm is matrix-free in that it does not require the factorization of derivative matrices. Instead, it uses iterative linear system solvers. Inexact step computations are supported in order to save computational expense during each iteration. The algorithm is an interior-point approach derived from an inexact Newton method for equality constrained optimization proposed by Curtis, Nocedal, and Wächter [SIAM J. Optim., 20 (2009), pp. 1224-1249, with additional functionality for handling inequality constraints. The algorithm is shown to be globally convergent under loose assumptions. Numerical results are presented for nonlinear optimization test set collections and a pair of PDEconstrained model problems.

In this paper we study the effect of false data injection attacks on state estimation carried over a sensor network monitoring a discrete-time linear time-invariant Gaussian system. The steady state Kalman filter is used to perform state estimation while a failure detector is employed to detect anomalies in the system. An attacker wishes to compromise the integrity of the state estimator by hijacking a subset of sensors and sending altered readings. In order to inject fake sensor measurements without being detected the attacker will need to carefully design his actions to fool the estimator as abnormal sensor measurements would result in an alarm. It is important for a designer to determine the set of all the estimation biases that an attacker can inject into the system without being detected, providing a quantitative measure of the resilience of the system to such attacks. To this end, we will provide an ellipsoidal algorithm to compute its inner and outer approximations of such set. A numerical example is presented to further illustrate the effect of false data injection attack on state estimation.

With advanced computer technology, systems are getting larger to fulfill more complicated tasks, however, they are also becoming less reliable. Consequently, testing is an indispensable part of system design and implementation; yet it has proved to be a formidable task for complex systems. This motivates the study of testing finite state machines to ensure the correct functioning of systems and to discover aspects of their behavior.

Many communication and social networks have power-law link distributions, containing a few nodes that have a very high degree and many with low degree. The high connectivity nodes play the important role of hubs in communication and networking, a fact that can be exploited when designing efficient search algorithms. We introduce a number of local search strategies that utilize high degree nodes in power-law graphs and that have costs scaling sublinearly with the size of the graph. We also demonstrate the utility of these strategies on the GNUTELLA peer-to-peer network.

The magnitude of the August 2003 blackout affecting the United States has put the challenges of energy transmission and distribution into limelight. Despite all the interest and concerted effort, the complexity and interconnectivity of the electric infrastructure have so far precluded us from understanding why certain events happened. In this paper we study the power grid from a network perspective and determine its ability to transfer power between generators and consumers when certain nodes are disrupted. We find that the power grid is robust to most perturbations, yet disturbances affecting key transmision substations greatly reduce its ability to function. We emphasize that the global properties of the underlying network must be understood as they greatly affect local behavior.

Solid-state disks (SSDs) have the potential to revolutionize the storage system landscape. However, there is little published work about their internal organization or the design choices that SSD manufacturers face in pursuit of optimal performance. This paper presents a taxonomy of such design choices and analyzes the likely performance of various configurations using a trace-driven simulator and workload traces extracted from real systems. We find that SSD performance and lifetime is highly workload-sensitive, and that complex systems problems that normally appear higher in the storage stack, or even in distributed systems, are relevant to device firmware.

Resource managers and scientists from disparate disciplines are rising to the challenge of understanding and moderating human impacts on marine ecosystems. Traditional barriers to communication between marine ecologists, fisheries biologists, social scientists and economists are beginning to break down, and the distinction between applied and basic research is fading. These ongoing trends arise, in part, from an increasing awareness of the profound influence of people on the functioning of all marine ecosystems, an increased focus on spatial and temporal scale, and a renewed assessment of the role of biodiversity in the sustainability of ecosystem goods and services upon which human societies depend. Here, we highlight the emergence of a complex systems approach for sustaining and repairing marine ecosystems, linking ecological resilience to governance structures, economics and society.

Introduced in its contemporary form in 1946 (ref. 1), but with roots that go back to the eighteenth century, the gravity law is the prevailing framework with which to predict population movement, cargo shipping volume and inter-city phone calls, as well as bilateral trade flows between nations. Despite its widespread use, it relies on adjustable parameters that vary from region to region and suffers from known analytic inconsistencies. Here we introduce a stochastic process capturing local mobility decisions that helps us analytically derive commuting and mobility fluxes that require as input only information on the population distribution. The resulting radiation model predicts mobility patterns in good agreement with mobility and transport patterns observed in a wide range of phenomena, from long-term migration patterns to communication volume between different regions. Given its parameter-free nature, the model can be applied in areas where we lack previous mobility measurements,...

We present a detailed analytical and numerical study for the spreading of infections in complex population networks with acquired immunity. We show that the large connectivity fluctuations usually found in these networks strengthen considerably the incidence of epidemic outbreaks. Scale-free networks, which are characterized by diverging connectivity fluctuations, exhibit the lack of an epidemic threshold and always show a finite fraction of infected individuals. This particular weakness, observed also in models without immunity, defines a new epidemiological framework characterized by a highly heterogeneous response of the system to the introduction of infected individuals with different connectivity. The understanding of epidemics in complex networks might deliver new insights in the spread of information and diseases in biological and technological networks that often appear to be characterized by complex heterogeneous architectures.

Brain graphs provide a relatively simple and increasingly popular way of modeling the human brain connectome, using graph theory to abstractly define a nervous system as a set of nodes (denoting anatomical regions or recording electrodes) and interconnecting edges (denoting structural or functional connections). Topological and geometrical properties of these graphs can be measured and compared to random graphs and to graphs derived from other neuroscience data or other (nonneural) complex systems. Both structural and functional human brain graphs have consistently demonstrated key topological properties such as small-worldness, modularity, and heterogeneous degree distributions. Brain graphs are also physically embedded so as to nearly minimize wiring cost, a key geometric property. Here we offer a conceptual review and methodological guide to graphical analysis of human neuroimaging data, with an emphasis on some of the key assumptions, issues, and trade-offs facing the investigator.

We have developed a method to study transition pathways for rare events in complex systems. The method can be used to determine rate constants for transitions between stable states by turning the calculation of reactive flux correlation functions into the computation of an isomorphic reversible work. In contrast to previous dynamical approaches, the method relies neither on prior knowledge nor on explicit specification of transition states. Rather, it provides an importance sampling from which transition states can be characterized statistically. A simple model is analyzed to illustrate the methodology.

The defense of the host from foreign pathogens is the commonly accepted function of the vertebrate immune system. A complex system consisting of many differing cells and structures communicating by both soluble and cell bound ligands, serves to protect the host from infection, and plays a role in preventing the development of certain types of tumours. Numerous signalling pathways are involved in the coordination of the immune system, serving both to activate and attenuate its responses to attack. The ability of the immune system, specifically those cells involved in acute inflammatory responses, to mediate the directed (and sometimes indirect) killing of cells and pathogens, make it a potential threat to host survival. Furthermore, the production and release of various survival factors such as the pleiotropic cytokine IL-6, a major mediator of inflammation and activator of signal transducer and activator of transcription 3, serves to block apoptosis in cells during the inflammatory process, keeping them alive in very toxic environments. Unfortunately, these same pathways serve also to maintain cells progressing towards neoplastic growth, protecting them from cellular apoptotic deletion and chemotherapeutic drugs. Here, we discuss the relationships between cancer and inflammation, and some of the molecular mechanisms involved in mediating the unintended consequences of host defense and tumour survival.

In this review we will focus on a topic of fundamental importance for both plasma physics and astrophysics, namely the occurrence of large-amplitude low-frequency fluctuations of the fields that describe the plasma state. This subject will be treated within the context of the expanding solar wind and the most meaningful advances in this research field will be reported emphasizing the results obtained in the past decade or so. As a matter of fact, Ulysses' high latitude observations and new numerical approaches to the problem, based on the dynamics of complex systems, brought new important insights which helped to better understand how turbulent fluctuations behave in the solar wind. In particular, numerical simulations within the realm of magnetohydrodynamic (MHD) turbulence theory unraveled what kind of physical mechanisms are at the basis of turbulence generation and energy transfer across the spectral domain of the fluctuations. In other words, the advances reached in these past years in the investigation of solar wind turbulence now offer a rather complete picture of the phenomenological aspect of the problem to be tentatively presented in a rather organic way.

The cortex is a complex system, characterized by its dynamics and architecture, which underlie many functions such as action, perception, learning, language, and cognition. Its structural architecture has been studied for more than a hundred years; however, its dynamics have been addressed much less thoroughly. In this paper, we review and integrate, in a unifying framework, a variety of computational approaches that have been used to characterize the dynamics of the cortex, as evidenced at different levels of measurement. Computational models at different space-time scales help us understand the fundamental mechanisms that underpin neural processes and relate these processes to neuroscience data. Modeling at the single neuron level is necessary because this is the level at which information is exchanged between the computing elements of the brain; the neurons. Mesoscopic models tell us how neural elements interact to yield emergent behavior at the level of microcolumns and cortical columns. Macroscopic models can inform us about whole brain dynamics and interactions between large-scale neural systems such as cortical regions, the thalamus, and brain stem. Each level of description relates uniquely to neuroscience data, from single-unit recordings, through local field potentials to functional magnetic resonance imaging (fMRI), electroencephalogram (EEG), and magnetoencephalogram (MEG). Models of the cortex can establish which types of large-scale neuronal networks can perform computations and characterize their emergent properties. Mean-field and related formulations of dynamics also play an essential and complementary role as forward models that can be inverted given empirical data. This makes dynamic models critical in integrating theory and experiments. We argue that elaborating principled and informed models is a prerequisite for grounding empirical neuroscience in a cogent theoretical framework, commensurate with the achievements in the physical sciences. Citation: Deco G, Jirsa VK, Robinson PA, Breakspear M, Friston K (2008) The Dynamic Brain: From Spiking Neurons to Neural Masses and Cortical Fields. PLoS Comput Biol 4(8): e1000092.

Haematopoiesis involves the complex regulation of proliferation and differentiation of many cell types -from the parent stem cell to the functional components of the bone marrow and peripheral blood, including the erythroid, myeloid, lymphoid and platelet lineages . Despite the many genetic checks and balances that are in place to regulate haematopoesis, mutations of crucial regulatory genes can occur that disrupt normal haematopoiesis and promote leukemogenesis.

The mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection. We show that finding the modularity of a network is analogous to finding the ground-state energy of a spin system. Moreover, we demonstrate that, due to fluctuations, stochastic network models give rise to modular networks. Specifically, we show both numerically and analytically that random graphs and scale-free networks have modularity. We argue that this fact must be taken into consideration to define statistically-significant modularity in complex networks.

The NAD-dependent deacetylase Sir2 was initially identified as a mediator of replicative lifespan in budding yeast and was subsequently shown to modulate longevity in worms and flies 1,2 . Its mammalian homologue, SIRT1, appears to have evolved complex systemic roles in cardiac function, DNA repair, and genomic stability. Recent studies suggest a functional relevance of SIRT1 in normal brain physiology and neurological disorders. However, it is unknown if SIRT1 plays a role in higher-order brain functions. We report that SIRT1 modulates synaptic plasticity and memory formation via a microRNA-mediated mechanism. Activation of SIRT1 enhances, while its loss-of-function impairs, synaptic plasticity. Surprisingly, these effects were mediated via post-transcriptional regulation of CREB expression by a brain-specific microRNA, miR-134. SIRT1 normally functions to limit expression of miR-134 via a repressor complex containing the transcription factor YY1, and unchecked miR-134 expression following SIRT1 deficiency results in the down-regulated expression of CREB and BDNF, thereby impairing synaptic plasticity. These findings demonstrate a novel role for SIRT1 in cognition and a previously unknown microRNA-based mechanism by which SIRT1 regulates these processes. Furthermore, these results describe a separate branch of SIRT1 signaling, in which SIRT1 has a direct role in regulating normal brain function in a manner that is disparate from its cell survival functions, demonstrating its value as a potential therapeutic target for the treatment of CNS disorders.