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We propose a method for characterizing the local structure of weighted multivariate time series networks. We draw intensity and coherence of network motifs, i.e. statistically recurrent subgraphs, to characterize the system behavior via higher-order structures derived upon effective transfer entropy networks. The latter consists of a model-free methodology enabling to correct for small sample biases affecting Shannon transfer entropy, other than conducting inference on the estimated directional time series information flows. We demonstrate the usefulness of our proposed method with an application to a set of global commodity prices. Our main result shows that, despite simple triadic structures are the most intense, coherent and statistically recurrent over time, their intensity suddenly decreases after the Global Financial Crisis, in favor of most complex triadic structures, while all types of subgraphs tend to become more coherent thereafter. [ABSTRACT FROM AUTHOR]

Network motifs are recurrent, small-scale patterns of interactions observed frequently in a system. They shed light on the interplay between the topology and the dynamics of complex networks across various domains. In this work, we focus on the problem of counting occurrences of small sub-hypergraph patterns in very large hypergraphs, where higher-order interactions connect arbitrary numbers of system units. We show how directly exploiting higher-order structures speeds up the counting process compared to traditional data mining techniques for exact motif discovery. Moreover, with hyperedge sampling, performance is further improved at the cost of small errors in the estimation of motif frequency. We evaluate our method on several real-world datasets describing face-to-face interactions, co-authorship and human communication. We show that our approximated algorithm allows us to extract higher-order motifs faster and on a larger scale, beyond the computational limits of an exact approach. [ABSTRACT FROM AUTHOR]

Bots in online social networks can be used for good or bad but their presence is unavoidable and will increase in the future. To investigate how the interaction networks of bots and humans evolve, we created six social bots on Twitter with AI language models and let them carry out standard user operations. Three different strategies were implemented for the bots: a trend-targeting strategy (TTS), a keywords-targeting strategy (KTS) and a user-targeting strategy (UTS). We examined the interaction patterns such as targeting users, spreading messages, propagating relationships, and engagement. We focused on the emergent local structures or motifs and found that the strategies of the social bots had a significant impact on them. Motifs resulting from interactions with bots following TTS or KTS are simple and show significant overlap, while those resulting from interactions with UTS-governed bots lead to more complex motifs. These findings provide insights into human-bot interaction patterns in online social networks, and can be used to develop more effective bots for beneficial tasks and to combat malicious actors. [ABSTRACT FROM AUTHOR]

Cities are widely considered as the lifeblood of a nations' economy housing the bulk of industries, commercial and trade activities, and employment opportunities. Within this economic context, multinational corporations play an important role in this economic development of cities in particular, and subsequently the countries and regions they belong to, in general. As multinational companies are spread throughout the world by virtue of ownership–subsidiary relationship, these ties create complex inter-dependent networks of cities that shape and define socio-economic status, as well as macro-regional influences impacting the world economy. In this paper, we study these networks of cities formed as a result of ties between multinational firms. We analyze these networks using intra-regional, inter-regional, and hybrid ties (conglomerate integration) as spatial motifs defined by geographic delineation of world's economic regions. We attempt to understand how global cities position themselves in spatial and economic geographies and how their ties promote regional integration along with global expansion for sustainable growth and economic development. We study these networks over four time periods from 2010 to 2019 and discover interesting trends and patterns. The most significant result is the domination of inter-regional motifs representing cross-regional ties among cities rather than national and regional integration. [ABSTRACT FROM AUTHOR]

Abstract The cell stress‐responsive transcription factor p53 influences the expression of its target genes and subsequent cellular responses based in part on its dynamics (changes in level over time). The mechanisms decoding p53 dynamics into subsequent target mRNA and protein dynamics remain unclear. We systematically quantified p53 target mRNA and protein expression over time under two p53 dynamical regimes, oscillatory and rising, using RNA‐sequencing and TMT mass spectrometry. Oscillatory dynamics allowed for a greater variety of dynamical patterns for both mRNAs and proteins. Mathematical modeling of empirical data revealed three distinct mechanisms that decode p53 dynamics. Specific combinations of these mechanisms at the transcriptional and post‐transcriptional levels enabled exclusive induction of proteins under particular dynamics. In addition, rising induction of p53 led to higher induction of proteins regardless of their functional class, including proteins promoting arrest of proliferation, the primary cellular outcome under rising p53. Our results highlight the diverse mechanisms cells employ to distinguish complex transcription factor dynamics to regulate gene expression.

The behaviour of individual users in an online social network is a major contributing factor in determining the outcome of multiple network phenomenon. Group formation, growth of the network, information propagation, and rumour blocking are some of the many network behavioural traits that are influenced by the interaction patterns of the users in the network. Network motifs capture one such interaction pattern between users in online social networks (OSNs). For this work, four second-order (two-edged) network motifs have been considered, namely, message receiving pattern, message broadcasting pattern, message passing pattern, and reciprocal message pattern, to analyse user behaviour in online social networks. This work provides and utilizes a node interaction pattern-finding algorithm to identify the frequency of aforementioned second-order network motifs in six real-life online social networks (Facebook, GPlus, GNU, Twitter, Enron Email, and Wiki-vote). The frequency of network motifs participated in by a node is considered for the relative ranking of all nodes in the online social networks. The highest-rated nodes are considered seeds for information propagation. The performance of using network motifs for ranking nodes as seeds for information propagation is validated using statistical metrics Z-score, concentration, and significance profile and compared with baseline ranking methods in-degree centrality, out-degree centrality, closeness centrality, and PageRank. The comparative study shows the performance of centrality measures to be similar or better than second-order network motifs as seed nodes in information diffusion. The experimental results on finding frequencies and importance of different interaction patterns provide insights on the significance and representation of each such interaction pattern and how it varies from network to network. [ABSTRACT FROM AUTHOR]

Chaotic resonance (CR) is the response of a nonlinear system to weak signals enhanced by internal or external chaotic activity (such as the signal derived from Lorenz system). The triple-neuron feed-forward loop (FFL) Izhikevich neural network motifs with eight types are constructed as the nonlinear systems in this paper, and the effects of EMI on CR phenomenon in FFL neuronal network motifs are studied. It is found that both the single Izhikevich neural model under electromagnetic induction (EMI) and its network motifs exhibit CR phenomenon depending on the chaotic current intensity. There exists an optimal chaotic current intensity ensuring the best detection of weak signal in single Izhikevich neuron or its network motifs via CR. The EMI can enhance the ability of neuron to detect weak signals. For T1-FFL and T2-FFL motifs, the adjustment of EMI parameters makes T2-FFL show a more obvious CR phenomenon than that for T1-FFL motifs, which is different from the impact of system parameters (e.g., the weak signal frequency, the coupling strength, and the time delay) on CR. Another interesting phenomenon is that the variation of CR with time delay exhibits quasi-periodic characteristics. Our results showed that CR effect is a robust phenomenon which is observed in both single Izhikevich neuron and network motifs, which might help one understand how to improve the ability of weak signal detection and propagation in neuronal system. [ABSTRACT FROM AUTHOR]

Temporal graphs are structures which model relational data between entities that change over time. Due to the complex structure of data, mining statistically significant temporal subgraphs, also known as temporal motifs, is a challenging task. In this work, we present an efficient technique for extracting temporal motifs in temporal networks. Our method is based on the novel notion of egocentric temporal neighborhoods, namely multi-layer structures centered on an ego node. Each temporal layer of the structure consists of the first-order neighborhood of the ego node, and corresponding nodes in sequential layers are connected by an edge. The strength of this approach lies in the possibility of encoding these structures into a unique bit vector, thus bypassing the problem of graph isomorphism in searching for temporal motifs. This allows our algorithm to mine substantially larger motifs with respect to alternative approaches. Furthermore, by bringing the focus on the temporal dynamics of the interactions of a specific node, our model allows to mine temporal motifs which are visibly interpretable. Experiments on a number of complex networks of social interactions confirm the advantage of the proposed approach over alternative non-egocentric solutions. The egocentric procedure is indeed more efficient in revealing similarities and discrepancies among different social environments, independently of the different technologies used to collect data, which instead affect standard non-egocentric measures. [ABSTRACT FROM AUTHOR]

GTPases are molecular switches that regulate a wide range of cellular processes, such as organelle biogenesis, position, shape, function, vesicular transport between organelles, and signal transduction. These hydrolase enzymes operate by toggling between an active (“ON”) guanosine triphosphate (GTP)-bound state and an inactive (“OFF”) guanosine diphosphate (GDP)-bound state; such a toggle is regulated by GEFs (guanine nucleotide exchange factors) and GAPs (GTPase activating proteins). Here we propose a model for a network motif between monomeric (m) and trimeric (t) GTPases assembled exclusively in eukaryotic cells of multicellular organisms. We develop a system of ordinary differential equations in which these two classes of GTPases are interlinked conditional to their ON/OFF states within a motif through coupling and feedback loops. We provide explicit formulae for the steady states of the system and perform classical local stability analysis to systematically investigate the role of the different connections between the GTPase switches. Interestingly, a coupling of the active mGTPase to the GEF of the tGTPase was sufficient to provide two locally stable states: one where both active/inactive forms of the mGTPase can be interpreted as having low concentrations and the other where both m- and tGTPase have high concentrations. Moreover, when a feedback loop from the GEF of the tGTPase to the GAP of the mGTPase was added to the coupled system, two other locally stable states emerged. In both states the tGTPase is inactivated and active tGTPase concentrations are low. Finally, the addition of a second feedback loop, from the active tGTPase to the GAP of the mGTPase, gives rise to a family of steady states that can be parametrized by a range of inactive tGTPase concentrations. Our findings reveal that the coupling of these two different GTPase motifs can dramatically change their steady-state behaviors and shed light on how such coupling may impact signaling mechanisms in eukaryotic cells. [ABSTRACT FROM AUTHOR]

We critique the organizational account of biological functions by showing how its basis in the closure of constraints fails to be objective. While the account treats constraints as objective features of physical systems, the number and relationship of potential constraints are subject to potentially arbitrary redescription by investigators. For example, we show that self-maintaining systems such as candle flames can realize closure on a more thorough analysis of the case, contradicting the claim that these "simple" systems lack functional organization. This also raises problems for Moreno and Mossio's associated theory of biological autonomy, which asserts that living beings are distinguished by their possession of a closed system of constraints that channel and regulate their metabolic processes. [ABSTRACT FROM AUTHOR]

In this paper, we propose a network analysis-based approach to help experts in their analyses of subjects with mild cognitive impairment (hereafter, MCI) and Alzheimer's disease (hereafter, AD) and to investigate the evolution of these subjects over time. The inputs of our approach are the electroencephalograms (hereafter, EEGs) of the patients to analyze, performed at a certain time and, again, 3 months later. Given an EEG of a subject, our approach constructs a network with nodes that represent the electrodes and edges that denote connections between electrodes. Then, it applies several network-based techniques allowing the investigation of subjects with MCI and AD and the analysis of their evolution over time. (i) A connection coefficient, supporting experts to distinguish patients with MCI from patients with AD; (ii) A conversion coefficient, supporting experts to verify if a subject with MCI is converting to AD; (iii) Some network motifs, i.e., network patterns very frequent in one kind of patient and absent, or very rare, in the other. Patients with AD, just by the very nature of their condition, cannot be forced to stay motionless while undergoing examinations for a long time. EEG is a non-invasive examination that can be easily done on them. Since AD and MCI, if prodromal to AD, are associated with a loss of cortical connections, the adoption of network analysis appears suitable to investigate the effects of the progression of the disease on EEG. This paper confirms the suitability of this idea Graphical Abstract Ability of our proposed model to distinguish a control subject from a patient with MCI and a patient with AD. Blue edges represent strong connections among the corresponding brain areas; red edges denote middle connections, whereas green edges indicate weak connections. In the control subject (at the top), most connections are blue. In the patient with MCI (at the middle), most connections are red and green. In the patient with AD (at the bottom), most connections are either absent or green. . [ABSTRACT FROM AUTHOR]

Abstract Organisms use circadian clocks to generate 24‐h rhythms in gene expression. However, the clock can interact with other pathways to generate shorter period oscillations. It remains unclear how these different frequencies are generated. Here, we examine this problem by studying the coupling of the clock to the alternative sigma factor sigC in the cyanobacterium Synechococcus elongatus. Using single‐cell microscopy, we find that psbAI, a key photosynthesis gene regulated by both sigC and the clock, is activated with two peaks of gene expression every circadian cycle under constant low light. This two‐peak oscillation is dependent on sigC, without which psbAI rhythms revert to one oscillatory peak per day. We also observe two circadian peaks of elongation rate, which are dependent on sigC, suggesting a role for the frequency doubling in modulating growth. We propose that the two‐peak rhythm in psbAI expression is generated by an incoherent feedforward loop between the clock, sigC and psbAI. Modelling and experiments suggest that this could be a general network motif to allow frequency doubling of outputs.

Abstract Cells react to nutritional cues in changing environments via the integrated action of signaling, transcriptional, and metabolic networks. Mechanistic insight into signaling processes is often complicated because ubiquitous feedback loops obscure causal relationships. Consequently, the endogenous inputs of many nutrient signaling pathways remain unknown. Recent advances for system‐wide experimental data generation have facilitated the quantification of signaling systems, but the integration of multi‐level dynamic data remains challenging. Here, we co‐designed dynamic experiments and a probabilistic, model‐based method to infer causal relationships between metabolism, signaling, and gene regulation. We analyzed the dynamic regulation of nitrogen metabolism by the target of rapamycin complex 1 (TORC1) pathway in budding yeast. Dynamic transcriptomic, proteomic, and metabolomic measurements along shifts in nitrogen quality yielded a consistent dataset that demonstrated extensive re‐wiring of cellular networks during adaptation. Our inference method identified putative downstream targets of TORC1 and putative metabolic inputs of TORC1, including the hypothesized glutamine signal. The work provides a basis for further mechanistic studies of nitrogen metabolism and a general computational framework to study cellular processes.

Abstract The importance of post‐transcriptional regulation by small non‐coding RNAs has recently been recognized in both pro‐ and eukaryotes. Small RNAs (sRNAs) regulate gene expression post‐transcriptionally by base pairing with the mRNA. Here we use dynamical simulations to characterize this regulation mode in comparison to transcriptional regulation mediated by protein–DNA interaction and to post‐translational regulation achieved by protein–protein interaction. We show quantitatively that regulation by sRNA is advantageous when fast responses to external signals are needed, consistent with experimental data about its involvement in stress responses. Our analysis indicates that the half‐life of the sRNA–mRNA complex and the ratio of their production rates determine the steady‐state level of the target protein, suggesting that regulation by sRNA may provide fine‐tuning of gene expression. We also describe the network of regulation by sRNA in Escherichia coli, and integrate it with the transcription regulation network, uncovering mixed regulatory circuits, such as mixed feed‐forward loops. The integration of sRNAs in feed‐forward loops provides tight repression, guaranteed by the combination of transcriptional and post‐transcriptional regulations.

This paper offers a novel view of unity in neuroscience. I set out by discussing problems with the classical account of unity-by-reduction, due to Oppenheim and Putnam. That view relies on a strong notion of levels, which has substantial problems. A more recent alternative, the mechanistic 'mosaic' view due to Craver, does not have such problems. But I argue that the mosaic ideal of unity is too minimal, and we should, if possible, aspire for more. Relying on a number of recent works in theoretical neuroscience-network motifs, canonical neural computations (CNCs) and design-principles-I then present my alternative: a 'flat' view of unity, i.e. one that is not based on levels. Instead, it treats unity as attained via the identification of recurrent explanatory patterns, under which a range of neuroscientific phenomena are subsumed. I develop this view by recourse to a causal conception of explanation, and distinguish it from Kitcher's view of explanatory unification and related ideas. Such a view of unity is suitably ambitious, I suggest, and has empirical plausibility. It is fit to serve as an appropriate working hypothesis for 21st century neuroscience. [ABSTRACT FROM AUTHOR]

Division of labor is an emergent and dynamic process that intimately mingles social dynamics and individual behavior. Individuals engage in work, and social interactions between workers couple an individual's behavior to that of its nestmates, thereby creating flexible and robust division of labor. Because social networks mirror the dual nature of division of labor by representing the individual in the connected web of the society, they are ideally suited to investigate the mechanistic underpinnings that organize social life and drive division of labor. Network analyses provide a panoply of tools that help shed light on the functional role of network structure, and that, if carefully used and combined with well-designed experiments, can revolutionize our comprehension of the distributed regulation of work in social insects. Here, I summarize the emergent nature of division of labor, lay out caveats of social network analysis and then discuss how a selection of network measures can dissect individual level and colony level connectivity to enhance our understanding of division of labor, and provide a more integrated view of how insect societies function. [ABSTRACT FROM AUTHOR]

Twentieth-century theoretical efforts towards the articulation of general system properties came short of having the significant impact on biological practice that their proponents envisioned. Although the latter did arrive at preliminary mathematical formulations of such properties, they had little success in showing how these could be productively incorporated into the research agenda of biologists. Consequently, the gap that kept system-theoretic principles cut-off from biological experimentation persisted. More recently, however, simple theoretical tools have proved readily applicable within the context of systems biology. In particular, examples reviewed in this paper suggest that rigorous mathematical expressions of design principles, imported primarily from engineering, could produce experimentally confirmable predictions of the regulatory properties of small biological networks. But this is not enough for contemporary systems biologists who adopt the holistic aspirations of early systemologists, seeking high-level organizing principles that could provide insights into problems of biological complexity at the whole-system level. While the presented evidence is not conclusive about whether this strategy could lead to the realization of the lofty goal of a comprehensive explanatory integration, it suggests that the ongoing quest for organizing principles is pragmatically advantageous for systems biologists. The formalisms postulated in the course of this process can serve as bridges between system-theoretic concepts and the results of molecular experimentation: they constitute theoretical tools for generalizing molecular data, thus producing increasingly accurate explanations of system-wide phenomena. [ABSTRACT FROM AUTHOR]

Determining the frequency of small subgraphs is an important graph mining primitive. One major class of algorithms for this task is based upon the enumeration of all sets of $$k$$ connected nodes. These are known as network-centric algorithms. FAst Subgraph Enumeration (FaSE) is a exact algorithm for subgraph counting that contrasted with its past approaches by performing the isomorphism tests while doing the enumeration, encapsulating the topological information in a g-trie and thus largely reducing the number of required isomorphism tests. Our goal with this paper is to expand this approach by providing an approximate algorithm, which we called Rand-FaSE. It uses an unbiased sampling estimator for the number of subgraphs of each type, allowing an user to trade some accuracy for even faster execution times. We tested our algorithm on a set of representative complex networks, comparing it with the exact alternative, FaSE. We also do an extensive analysis by studying its accuracy and speed gains against previous sampling approaches. With all of this, we believe FaSE and Rand-FaSE pave the way for faster network-centric census algorithms. [ABSTRACT FROM AUTHOR]

Oscillatory responses are ubiquitous in regulatory networks of living organisms, a fact that has led to extensive efforts to study and replicate the circuits involved. However, to date, design principles that underlie the robustness of natural oscillators are not completely known. Here we study a three-component enzymatic network model in order to determine the topological requirements for robust oscillation. First, by simulating every possible topological arrangement and varying their parameter values, we demonstrate that robust oscillators can be obtained by augmenting the number of both negative feedback loops and positive autoregulations while maintaining an appropriate balance of positive and negative interactions. We then identify network motifs, whose presence in more complex topologies is a necessary condition for obtaining oscillatory responses. Finally, we pinpoint a series of simple architectural patterns that progressively render more robust oscillators. Together, these findings can help in the design of more reliable synthetic biomolecular networks and may also have implications in the understanding of other oscillatory systems. [ABSTRACT FROM AUTHOR]

The ability to find and count subgraphs of a given network is an important non trivial task with multidisciplinary applicability. Discovering network motifs or computing graphlet signatures are two examples of methodologies that at their core rely precisely on the subgraph counting problem. Here we present the g-trie, a data-structure specifically designed for discovering subgraph frequencies. We produce a tree that encapsulates the structure of the entire graph set, taking advantage of common topologies in the same way a prefix tree takes advantage of common prefixes. This avoids redundancy in the representation of the graphs, thus allowing for both memory and computation time savings. We introduce a specialized canonical labeling designed to highlight common substructures and annotate the g-trie with a set of conditional rules that break symmetries, avoiding repetitions in the computation. We introduce a novel algorithm that takes as input a set of small graphs and is able to efficiently find and count them as induced subgraphs of a larger network. We perform an extensive empirical evaluation of our algorithms, focusing on efficiency and scalability on a set of diversified complex networks. Results show that g-tries are able to clearly outperform previously existing algorithms by at least one order of magnitude. [ABSTRACT FROM AUTHOR]

The analysis of brain network topological features has served to better understand these networks and reveal particular characteristics of their functional behavior. The distribution of brain network motifs is particularly useful for detecting and describing differences between brain networks and random and computationally optimized artificial networks. In this paper we use a multi-objective evolutionary optimization approach to generate optimized artificial networks that have a number of topological features resembling brain networks. The Pareto set approximation of the optimized networks is used to extract network descriptors that are compared to brain and random network descriptors. To analyze the networks, the clustering coefficient, the average path length, the modularity and the betweenness centrality are computed. We argue that the topological complexity of a brain network can be estimated using the number of evaluations needed by an optimization algorithm to output artificial networks of similar complexity. For the analyzed network examples, our results indicate that while original brain networks have a reduced structural motif number and a high functional motif number, they are not optimal with respect to these two topological features. We also investigate the correlation between the structural and functional motif numbers, the average path length and the clustering coefficient in random, optimized and brain networks. [ABSTRACT FROM AUTHOR]

Despite several algorithms for searching subgraphs in motif detection presented in the literature, no effort has been done for characterizing their performance till now. This paper presents a methodology to evaluate the performance of three algorithms: edge sampling algorithm (ESA), enumerate subgraphs (ESU) and randomly enumerate subgraphs (RAND-ESU). A series of experiments are performed to test sampling speed and sampling quality. The results show that RAND-ESU is more efficient and has less computational cost than other algorithms for large-size motif detection, and ESU has its own advantage in small-size motif detection. [ABSTRACT FROM AUTHOR]

High-dimensional switches have been proposed as a way to model cellular differentiation, particularly in the context of basic Helix-Loop-Helix (bHLH) competitive heterodimerization networks. A previous study derived a simple rule showing how many elements can be co-expressed, depending on the rate of competition within the network. A limitation to that rule, however, is that many biochemical parameters were considered to be identical. Here, we derive a generalized rule. This in turns allows one to study more ways in which these networks could be regulated, linking intrinsic cellular differentiation determinants to extracellular cues. [ABSTRACT FROM AUTHOR]

Network motifs are patterns of over-represented node interactions in a network which have been previously used as building blocks to understand various aspects of the social networks. In this paper, we use motif patterns to characterize the information diffusion process in social networks. We study the lifecycle of information cascades to understand what leads to saturation of growth in terms of cascade reshares, thereby resulting in expiration, an event we call "diffusion inhibition". In an attempt to understand what causes inhibition, we use motifs to dissect the network obtained from information cascades coupled with traces of historical diffusion or social network links. Our main results follow from experiments on a dataset of cascades from the Weibo platform and the Flixster movie ratings. We observe the temporal counts of 5-node undirected motifs from the cascade temporal networks leading to the inhibition stage. Empirical evidences from the analysis lead us to conclude the following about stages preceding inhibition: (1) individuals tend to adopt information more from users they have known in the past through social networks or previous interactions thereby creating patterns containing triads more frequently than acyclic patterns with linear chains and (2) users need multiple exposures or rounds of social reinforcement for them to adopt an information and as a result information starts spreading slowly thereby leading to the death of the cascade. Following these observations, we use motif-based features to predict the edge cardinality of the network exhibited at the time of inhibition. We test features of motif patterns using regression models for both individual patterns and their combination and we find that motifs as features are better predictors of the future network organization than individual node centralities. [ABSTRACT FROM AUTHOR]