Spreading of Infections on Network Models: Percolation Clusters and Random Trees

We discuss network models as a general and suitable framework for describing the spreading of an infectious disease within a population. We discuss two types of finite random structures as building blocks of the network, one based on percolation concepts and the second one on random tree structures. We study, as is done for the SIR model, the time evolution of the number of susceptible (S), infected (I) and recovered (R) individuals, in the presence of a spreading infectious disease, by incorporating a healing mechanism for infecteds. In addition, we discuss in detail the implementation of lockdowns and how to simulate them. For percolation clusters, we present numerical results based on site percolation on a square lattice, while for random trees we derive new analytical results, which are illustrated in detail with a few examples. It is argued that such hierarchical networks can complement the well-known SIR model in most circumstances. We illustrate these ideas by revisiting USA COVID-19 data.

Percolation of temporal hierarchical mobility networks during COVID-19

Percolation theory is essential for understanding disease transmission patterns on the temporal mobility networks. However, the traditional approach of the percolation process can be inefficient when analysing a large-scale, dynamic network for an extended period. Not only is it time-consuming but it is also hard to identify the connected components. Recent studies demonstrate that spatial containers restrict mobility behaviour, described by a hierarchical topology of mobility networks. Here, we leverage crowd-sourced, large-scale human mobility data to construct temporal hierarchical networks composed of over 175 000 block groups in the USA. Each daily network contains mobility between block groups within a Metropolitan Statistical Area (MSA), and long-distance travels across the MSAs. We examine percolation on both levels and demonstrate the changes of network metrics and the connected components under the influence of COVID-19. The research reveals the presence of functional subunits even with high thresholds of mobility. Finally, we locate a set of recurrent critical links that divide components resulting in the separation of core MSAs. Our findings provide novel insights into understanding the dynamical community structure of mobility networks during disruptions and could contribute to more effective infectious disease control at multiple scales. This article is part of the theme issue ‘Data science approaches to infectious disease surveillance’.

Optimizing weighted gene co-expression network analysis with a multi-threaded calculation of the topological overlap matrix

Biomolecular networks are often assumed to be scale-free hierarchical networks. The weighted gene co-expression network analysis (WGCNA) treats gene co-expression networks as undirected scale-free hierarchical weighted networks. The WGCNA R software package uses an Adjacency Matrix to store a network, next calculates the topological overlap matrix (TOM), and then identifies the modules (sub-networks), where each module is assumed to be associated with a certain biological function. The most time-consuming step of WGCNA is to calculate TOM from the Adjacency Matrix in a single thread. In this paper, the single-threaded algorithm of the TOM has been changed into a multi-threaded algorithm (the parameters are the default values of WGCNA). In the multi-threaded algorithm, Rcpp was used to make R call a C++ function, and then C++ used OpenMP to start multiple threads to calculate TOM from the Adjacency Matrix. On shared-memory MultiProcessor systems, the calculation time decreases as the number of CPU cores increases. The algorithm of this paper can promote the application of WGCNA on large data sets, and help other research fields to identify sub-networks in undirected scale-free hierarchical weighted networks. The source codes and usage are available at https://github.com/do-somethings-haha/multi-threaded_calculate_unsigned_TOM_from_unsigned_or_signed_Adjacency_Matrix_of_WGCNA.

Molecular convolutional neural networks with DNA regulatory circuits

Complex biomolecular circuits enable cells with intelligent behavior for survival before neural brains evolved. Synthesized DNA circuits in liquid phase developed as computational hardware can perform neural-network-like computation that harness the collective properties of complex biochemical systems, however the scaling up in complexity remains challenging to support more powerful computation. we present a systematic molecular implementation of the convolutional neural network (ConvNet) algorithm with synthetic DNA regulatory circuits based on a simple DNA switching gate architecture. We experimentally demonstrated that a DNA-based ConvNet based on shared-weight architecture of a 3×6 sized kernel can simultaneously implement parallel multiply-accumulate (MAC) operations for 144 bits inputs and recognize patterns up to 8 categories autonomously. Furthermore, it can connect with another DNA circuits to construct hierarchical networks, which can recognize patterns up to 32 categories with a two-step classification approach of performing coarse classification on language (Arabic numerals, Chinese oracles, English alphabets and Greek alphabets) and then classifying them into specific handwritten symbols. With a simple cyclic freeze/thaw approach, we can decrease computation time from hours to minutes. Our approach shows great promise in the realization of high computing power molecular computer with ability to classify complex and noisy information.

Power from Below in Premodern Societies

This volume challenges previous views of social organization focused on elites by offering innovative perspectives on 'power from below.' Using a variety of archaeological, anthropological, and historical data to question traditional narratives of complexity as inextricably linked to top-down power structures, it exemplifies how commoners have developed strategies to sustain non-hierarchical networks and contest the rise of inequalities. Through case studies from around the world – ranging from Europe to New Guinea, and from Mesoamerica to China – an international team of contributors explore the diverse and dynamic nature of power relations in premodern societies. The theoretical models discussed throughout the volume include a reassessment of key concepts such as heterarchy, collective action, and resistance. Thus, the book adds considerable nuance to our understanding of power in the past, and also opens new avenues of reflection that can help inform discussions about our collective present and future.

Hierarchy of homeostasis mechanisms of human-machine complexes: problems of their analysis and Implementation

Developing control systems for regional socio-economic and large technical systems is inevitably associated with the concept of human-machine complexes (HMC). They are considered as a set of a large number of hierarchically dependent complex subsystems, including staffs and machines, possessing a certain degree of organization and autonomy, interconnected by mechanisms and means of organization (i.e. material and informational links) to ensure the purposeful functioning of the entire system as a single whole in conditions of tense internal resource close to the limiting ones. The article discusses the hierarchy of interrelated homeostasis mechanisms of the HMC, ensuring both its parameter constancy and the performance of systemic functions at all hierarchy levels. In particular, the following types of homeostasis are considered: a parametric type (the internal circuit of homeostasis), designed to maintain the parameter constancy of HMC active elements and a functional type (the external circuit of homeostasis), ensuring the constancy of its functioning. At the same time, the functional integrity of the system is ensured by the work of the interrelated static-dynamic and entropy-organizational homeostasis mechanisms, which, in turn, in practical activity are implemented through coordination-motivational (CMR), organizational-motivational (OMP) and functional (FMR) mechanisms of regulation. The need for an integrated application of all entropy-organizational regulation mechanisms (CMR, OMR, FMR) in the operators’ activities determines the necessity to use multivariate methods to determine their composition and application. To solve this problem, the article examines the supersystem elements of the activity regulation, which are formed as a result of the operators’ psychological interaction in the process of their activity, as a kind of an abstract system of a higher order, which has its own supersystem properties, its own autonomous metric and conservation laws, and most importantly, its situation reflection which is different from the system one. In this case, homeostatic hierarchical networks, the elements of which are homeostatic mechanisms of HMC operators at various levels, become the basis of HMC structural-hierarchical homeostasis. Thus, being complex systems, HMC synergistically change (adapt) their internal characteristics, thereby ensure the integrity of the entire system functioning, which allows speaking, on the one hand, of their homeostaticity as the HMC most important characteristic, and on the other hand, determining the need to search for new approaches to their methodological description, and, consequently, to organizing their management and design.

Defining hierarchical protein interaction networks from spectral analysis of bacterial proteomes

Cellular phenotypes emerge from a hierarchy of molecular interactions: proteins interact to form complexes, pathways, and phenotypes. We show that hierarchical networks of protein interactions can be extracted from the statistical pattern of proteome variation as measured across thousands of bacteria and that these hierarchies reflect the emergence of complex bacterial phenotypes. We describe the mathematics underlying our statistical approach and validate our results through gene-set enrichment analysis and comparison to existing experimentally-derived hierarchical databases. We demonstrate the biological utility of our unbiased hierarchical models by creating a model of motility in Pseudomonas aeruginosa and using it to discover a previously unappreciated genetic effector of twitch-based motility. Overall, our approach, SCALES (Spectral Correlation Analysis of Layered Evolutionary Signals), predicts hierarchies of protein interaction networks describing emergent biological function using only the statistical pattern of bacterial proteome variation.

The structure and behaviour of hierarchical infrastructure networks

Critical services depend on infrastructure networks for their operation and any disruption to these networks can have significant impacts on society, the economy, and quality of life. Such networks can be characterised as graphs which can be used to understand their structural properties, and the effect on their behaviour and robustness to hazards. Using a suite of graphs and critical infrastructure networks, this study aims to show that networks which exhibit a hierarchical structure are more likely to be less robust comparatively to non-hierarchical networks when exposed to failures, including those which supply critical services. This study investigates the properties of a hierarchical structure through identifying a set of key characteristics from an ensemble of graph models which are then used in a comparative analysis against a suite of spatial critical infrastructure networks. A failure model is implemented and applied to understand the implications of hierarchical structures in real world networks for their robustness to perturbations. The study concludes that a set of three graph metrics, cycle basis, maximum betweenness centrality and assortativity coefficient, can be used to identify the extent of a hierarchy in graphs, where a lack of robustness is linked to the hierarchical structure, a feature exhibited in both graph models and infrastructure networks.

Multiscale criticality measures as general-purpose gauges of proper brain function

The brain is universally regarded as a system for processing information. If so, any behavioral or cognitive dysfunction should lend itself to depiction in terms of information processing deficiencies. Information is characterized by recursive, hierarchical complexity. The brain accommodates this complexity by a hierarchy of large/slow and small/fast spatiotemporal loops of activity. Thus, successful information processing hinges upon tightly regulating the spatiotemporal makeup of activity, to optimally match the underlying multiscale delay structure of such hierarchical networks. Reduced capacity for information processing will then be expressed as deviance from this requisite multiscale character of spatiotemporal activity. This deviance is captured by a general family of multiscale criticality measures (MsCr). MsCr measures reflect the behavior of conventional criticality measures (such as the branching parameter) across temporal scale. We applied MsCr to MEG and EEG data in several telling degraded information processing scenarios. Consistently with our previous modeling work, MsCr measures systematically varied with information processing capacity: MsCr fingerprints showed deviance in the four states of compromised information processing examined in this study, disorders of consciousness, mild cognitive impairment, schizophrenia and even during pre-ictal activity. MsCr measures might thus be able to serve as general gauges of information processing capacity and, therefore, as normative measures of brain health.