Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

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Collective dynamics of small-world networks

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. 
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. 
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. 
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

/pdf/statistical-mechanics-of-complex-networks-1zfjpvxipu.pdf

Statistical mechanics of complex networks

Imagined communities: Reflections on the origin and spread of nationalism

https://www.thelancet.com/pdfs/journals/lancet/PIIS0140-6736(12)61766-8.pdf

A comparative risk assessment of burden of disease and injury attributable to 67 risk factors and risk factor clusters in 21 regions, 1990-2010: a systematic analysis for the Global Burden of Disease Study 2010

And the Noise Played on: Stochastic Gene Expression and HIV-1 Infection

BACKGROUND The United States is currently experiencing the largest hepatitis A virus (HAV) outbreak since the introduction of a vaccine in 1996. More than 31,000 cases have been reported since 2016. Although HAV had largely been considered a foodborne pathogen in recent years, this outbreak has been spread primarily through person-to-person transmission in urban settings and has been associated with homelessness and substance use. Michigan was one of the first states to report an outbreak, with 910 reported cases between August 2016 and December 2018. METHODS We analyzed surveillance and vaccination data from Michigan using a disease transmission model to investigate how vaccine timing and coverage influenced the spatiotemporal patterns of the outbreak, distinguishing between Southeast Michigan, where the outbreak began, and the rest of the state. RESULTS We estimated that vaccination had little impact in Southeast Michigan (3% cases averted [95% confidence interval (CI) = 1%, 8%]) but had a substantial impact in the rest of the state, preventing a larger outbreak (91% cases averted [95% CI = 85%, 97%]) lasting several more years. CONCLUSIONS Our results emphasize the value of targeting populations where local transmission is not yet sustained rather than populations where transmission is already waning. Simulation modeling can aid in proactive rather than reactive decision-making and may help direct the response to outbreaks emerging in other states. See video abstract: http://links.lww.com/EDE/B704.

The Impact of Vaccination Efforts on the Spatiotemporal Patterns of the Hepatitis A Outbreak in Michigan, 2016-2018.

Provided herein are compositions and methods to improve treatment of chronic infections, and reduce, delay, or inhibit formation of biofilms, using specific combinations of aminoglycoside antibiotics and high, localized concentrations of one or more PMF stimulating compounds. These novel methods are easily adapted to clinical settings as toxicity and efficacy of the antibiotics and metabolites used have already been studied in vivo, and as dosing for both the antibiotics and metabolites are known. These approaches and therapeutic methods are also useful with non-metabolic chemicals that induce proton-motive force in bacteria.

Proton-motive force stimulation to potentiate aminoglycoside antibiotics against persistent bacteria

Classifying migrants in the field of health: sociolinguistic scale and neoliberal statecraft

Described herein are novel biological converter switches that utilize modular components, such as genetic toggle switches and single invertase memory modules (SIMMs), for converting analog inputs to digital outputs, and digital inputs to analog outputs, in cells and cellular systems. Flexibility in these biological converter switches is provided by combining individual modular components, i.e. , SIMMs and genetic toggle switches, together. These biological converter switches can be combined in a variety of network topologies to create circuits that act, for example, as switchboards, and regulate the production of an output product(s) based on the combination and nature of input signals received.

James J. Collins

Papers

And the Noise Played on: Stochastic Gene Expression and HIV-1 Infection

The Impact of Vaccination Efforts on the Spatiotemporal Patterns of the Hepatitis A Outbreak in Michigan, 2016-2018.

Proton-motive force stimulation to potentiate aminoglycoside antibiotics against persistent bacteria

Classifying migrants in the field of health: sociolinguistic scale and neoliberal statecraft

Biological analog-to-digital and digital-to-analog converter switches