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Endothelial cell monolayers line the inner surfaces of blood and lymphatic vessels. They are continuously exposed to different mechanical loads, which may trigger mechanobiological signals and hence play a role in both physiological and pathological processes. Computer-based mechanical models of cells contribute to a better understanding of the relation between cell-scale loads and cues and the mechanical state of the hosting tissue. However, the confluency of the endothelial monolayer complicates these approaches since the intercellular cross-talk needs to be accounted for in addition to the cytoskeletal mechanics of the individual cells themselves. As a consequence, the computational approach must be able to efficiently model a large number of cells and their interaction. Here, we simulate cytoskeletal mechanics by means of molecular dynamics software, generally suitable to deal with large, locally interacting systems. Methods were developed to generate models of single cells and large monolayers with hundreds of cells. The single-cell model was considered for a comparison with experimental data. To this end, we simulated cell interactions with a continuous, deformable substrate, and computationally replicated multistep traction force microscopy experiments on endothelial cells. The results indicate that cell discrete network models are able to capture relevant features of the mechanical behaviour and are thus well-suited to investigate the mechanics of the large cytoskeletal network of individual cells and cell monolayers.

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Cholera remains a major public health problem that threatens human health worldwide and its severity is continuing. In this paper, an edge-based model for cholera transmission on random networks is proposed and investigated. The model assumes that two communities share a common water source and includes three transmission routes, namely intra- and inter-community human-to-human transmission as well as water-to-human transmission. Intra-community human-to-human contacts are modeled through a random contact network, while both inter-community and water-to-human transmission are modeled through external nodes that reach each individual in the network to the same extent. The basic reproduction number and the equations of the final epidemic size are obtained. In addition, our study considers the cholera situation in Banadir, which is one of the most severely infected regions in Somalia, during the period (2019-2021). According to the geographical location, two adjacent districts are selected and our model fits well with the real data on the monthly cumulative cholera cases of these two districts during the above-mentioned period. From the perspective of network topology, cutting off high-risk contacts by supervising, isolating, quarantining and closing places with high-degree cholera-infected individuals to reduce degree heterogeneity is an effective measure to control cholera transmission. Our findings might offer some useful insights on cholera control.

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We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size and link probability of smaller than one, the incoherent state is meta-stable for coupling strengths that are larger than the mean-field critical coupling. We observe chaotic transients with exponentially distributed escape times and study the scaling behavior of the mean time to synchronization.

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Pulmonary Fibrosis (PF) is a deadly disease that has limited treatment options and is caused by excessive deposition and cross-linking of collagen leading to stiffening of the lung parenchyma. The link between lung structure and function in PF remains poorly understood, although its spatially heterogeneous nature has important implications for alveolar ventilation. Computational models of lung parenchyma utilize uniform arrays of space-filling shapes to represent individual alveoli, but have inherent anisotropy, whereas actual lung tissue is isotropic on average. We developed a novel Voronoi-based 3D spring network model of the lung parenchyma, the Amorphous Network, that exhibits more 2D and 3D similarity to lung geometry than regular polyhedral networks. In contrast to regular networks that show anisotropic force transmission, the structural randomness in the Amorphous Network dissipates this anisotropy with important implications for mechanotransduction. We then added agents to the network that were allowed to carry out a random walk to mimic the migratory behavior of fibroblasts. To model progressive fibrosis, agents were moved around the network and increased the stiffness of springs along their path. Agents migrated at various path lengths until a certain percentage of the network was stiffened. Alveolar ventilation heterogeneity increased with both percent of the network stiffened, and walk length of the agents, until the percolation threshold was reached. The bulk modulus of the network also increased with both percent of network stiffened and path length. This model thus represents a step forward in the creation of physiologically accurate computational models of lung tissue disease.

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The SARS-CoV-2 epidemic has impacted children's education, with schools required to implement infection control measures that have led to periods of absence and classroom closures. We developed an agent-based epidemiological model of SARS-CoV-2 transmission in a school classroom that allows us to quantify projected infection patterns within primary school classrooms, and related uncertainties. Our approach is based on a contact model constructed using random networks, informed by structured expert judgement. The effectiveness of mitigation strategies in suppressing infection outbreaks and limiting pupil absence are considered. COVID-19 infections in primary schools in England in autumn 2020 were re-examined and the model was then used to estimate infection levels in autumn 2021, as the Delta variant was emerging and it was thought likely that school transmission would play a major role in an incipient new wave of the epidemic. Our results were in good agreement with available data. These findings indicate that testing-based surveillance is more effective than bubble quarantine, both for reducing transmission and avoiding pupil absence, even accounting for insensitivity of self-administered tests. Bubble quarantine entails large numbers of absences, with only modest impact on classroom infections. However, maintaining reduced contact rates within the classroom can have a major benefit for managing COVID-19 in school settings.

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This review paper is devoted to a brief overview of results and models concerning flows in networks and channels of networks. First of all, we conduct a survey of the literature in several areas of research connected to these flows. Then, we mention certain basic mathematical models of flows in networks that are based on differential equations. We give special attention to several models for flows of substances in channels of networks. For stationary cases of these flows, we present probability distributions connected to the substance in the nodes of the channel for two basic models: the model of a channel with many arms modeled by differential equations and the model of a simple channel with flows of substances modeled by difference equations. The probability distributions obtained contain as specific cases any probability distribution of a discrete random variable that takes values of 0,1,…. We also mention applications of the considered models, such as applications for modeling migration flows. Special attention is given to the connection of the theory of stationary flows in channels of networks and the theory of the growth of random networks.

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We perform a detailed computational study of the recently introduced Sombor indices on random networks. Specifically, we apply Sombor indices on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random networks and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the adjacency matrix.

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The inference of causal relations between observable phenomena is paramount across scientific disciplines; however, the means for such enterprise without experimental manipulation are limited. A commonly applied principle is that of the cause preceding and predicting the effect, taking into account other circumstances. Intuitively, when the temporal order of events is reverted, one would expect the cause and effect to apparently switch roles. This was previously demonstrated in bivariate linear systems and used in design of improved causal inference scores, while such behaviour in linear systems has been put in contrast with nonlinear chaotic systems where the inferred causal direction appears unchanged under time reversal. The presented work explores the conditions under which the causal reversal happens-either perfectly, approximately, or not at all-using theoretical analysis, low-dimensional examples, and network simulations, focusing on the simplified yet illustrative linear vector autoregressive process of order one. We start with a theoretical analysis that demonstrates that a perfect coupling reversal under time reversal occurs only under very specific conditions, followed up by constructing low-dimensional examples where indeed the dominant causal direction is even conserved rather than reversed. Finally, simulations of random as well as realistically motivated network coupling patterns from brain and climate show that level of coupling reversal and conservation can be well predicted by asymmetry and anormality indices introduced based on the theoretical analysis of the problem. The consequences for causal inference are discussed.

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In this paper, we focus on the emergence of diverse neuronal oscillations arising in a mixed population of neurons with different excitability properties. These properties produce mixed mode oscillations (MMOs) characterized by the combination of large amplitudes and alternate subthreshold or small amplitude oscillations. Considering the biophysically plausible, Izhikevich neuron model, we demonstrate that various MMOs, including MMBOs (mixed mode bursting oscillations) and synchronized tonic spiking appear in a randomly connected network of neurons, where a fraction of them is in a quiescent (silent) state and the rest in self-oscillatory (firing) states. We show that MMOs and other patterns of neural activity depend on the number of oscillatory neighbors of quiescent nodes and on electrical coupling strengths. Our results are verified by constructing a reduced-order network model and supported by systematic bifurcation diagrams as well as for a small-world network. Our results suggest that, for weak couplings, MMOs appear due to the de-synchronization of a large number of quiescent neurons in the networks. The quiescent neurons together with the firing neurons produce high frequency oscillations and bursting activity. The overarching goal is to uncover a favorable network architecture and suitable parameter spaces where Izhikevich model neurons generate diverse responses ranging from MMOs to tonic spiking.

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Network topologies can be highly non-trivial, due to the complex underlying behaviours that form them. While past research has shown that some processes on networks may be characterized by local statistics describing nodes and their neighbours, such as degree assortativity, these quantities fail to capture important sources of variation in network structure. We define a property called transsortativity that describes correlations among a node's neighbours. Transsortativity can be systematically varied, independently of the network's degree distribution and assortativity. Moreover, it can significantly impact the spread of contagions as well as the perceptions of neighbours, known as the majority illusion. Our work improves our ability to create and analyse more realistic models of complex networks.

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In this study, we revisited the Ziff-Gulari-Barshad (ZGB) model in order to study the behavior of its phase diagram when two well-known random networks play the role of the catalytic surfaces: the random geometric graph and the Erdös-Rényi network. The connectivity and, therefore, the average number of neighbors of the nodes of these networks can vary according to their control parameters, the neighborhood radius α, and the linking probability p, respectively. In addition, the catalytic reactions of the ZGB model are governed by the parameter y, the adsorption rate of carbon monoxide molecules on the catalytic surface. So, to study the phase diagrams of the model on both random networks, we carried out extensive steady-state Monte Carlo simulations in the space parameters (y, α) and (y, p) and showed that the continuous phase transition is greatly affected by the topological features of the networks while the discontinuous one remains present in the diagram throughout the interval of study.

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We present a series of SIR-network models, extended with a game-theoretic treatment of imitation dynamics which result from regular population mobility across residential and work areas and the ensuing interactions. Each considered SIR-network model captures a class of vaccination behaviours influenced by epidemic characteristics, interaction topology, and imitation dynamics. Our focus is the resultant vaccination coverage, produced under voluntary vaccination schemes, in response to these varying factors. Using the next generation matrix method, we analytically derive and compare expressions for the basic reproduction number R 0 for the proposed SIR-network models. Furthermore, we simulate the epidemic dynamics over time for the considered models, and show that if individuals are sufficiently responsive towards the changes in the disease prevalence, then the more expansive travelling patterns encourage convergence to the endemic, mixed equilibria. On the contrary, if individuals are insensitive to changes in the disease prevalence, we find that they tend to remain unvaccinated. Our results concur with earlier studies in showing that residents from highly connected residential areas are more likely to get vaccinated. We also show that the existence of the individuals committed to receiving vaccination reduces R 0 and delays the disease prevalence, and thus is essential to containing epidemics.

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Amorphous materials are being described by increasingly powerful computer simulations, but new approaches are still needed to fully understand their intricate atomic structures. Here, we show how machine-learning-based techniques can give new, quantitative chemical insight into the atomic-scale structure of amorphous silicon (a-Si). We combine a quantitative description of the nearest- and next-nearest-neighbor structure with a quantitative description of local stability. The analysis is applied to an ensemble of a-Si networks in which we tailor the degree of ordering by varying the quench rates down to 1010  K s-1 . Our approach associates coordination defects in a-Si with distinct stability regions and it has also been applied to liquid Si, where it traces a clear-cut transition in local energies during vitrification. The method is straightforward and inexpensive to apply, and therefore expected to have more general significance for developing a quantitative understanding of liquid and amorphous states of matter.

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Whether an idea, information, or infection diffuses throughout a society depends not only on the structure of the network of interactions, but also on the timing of those interactions. People are not always available to interact with others, and people differ in the timing of when they are active. Some people are active for long periods and then inactive for long periods, while others switch more frequently from being active to inactive and back. We show that maximizing diffusion in classic contagion processes requires heterogeneous activity patterns across agents. In particular, maximizing diffusion comes from mixing two extreme types of people: those who are stationary for long periods of time, changing from active to inactive or back only infrequently, and others who alternate frequently between being active and inactive.

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BACKGROUND: Estimation of functional connectivity in gene sets derived from genome-wide or other biological experiments is one of the essential tasks of bioinformatics. A promising approach for solving this problem is to compare gene networks built using experimental gene sets with random networks. One of the resources that make such an analysis possible is CrossTalkZ, which uses the FunCoup database. However, existing methods, including CrossTalkZ, do not take into account individual types of interactions, such as protein/protein interactions, expression regulation, transport regulation, catalytic reactions, etc., but rather work with generalized types characterizing the existence of any connection between network members. RESULTS: We developed the online tool FunGeneNet, which utilizes the ANDSystem and STRING to reconstruct gene networks using experimental gene sets and to estimate their difference from random networks. To compare the reconstructed networks with random ones, the node permutation algorithm implemented in CrossTalkZ was taken as a basis. To study the FunGeneNet applicability, the functional connectivity analysis of networks constructed for gene sets involved in the Gene Ontology biological processes was conducted. We showed that the method sensitivity exceeds 0.8 at a specificity of 0.95. We found that the significance level of the difference between gene networks of biological processes and random networks is determined by the type of connections considered between objects. At the same time, the highest reliability is achieved for the generalized form of connections that takes into account all the individual types of connections. By taking examples of the thyroid cancer networks and the apoptosis network, it is demonstrated that key participants in these processes are involved in the interactions of those types by which these networks differ from random ones. CONCLUSIONS: FunGeneNet is a web tool aimed at proving the functionality of networks in a wide range of sizes of experimental gene sets, both for different global networks and for different types of interactions. Using examples of thyroid cancer and apoptosis networks, we have shown that the links over-represented in the analyzed network in comparison with the random ones make possible a biological interpretation of the original gene/protein sets. The FunGeneNet web tool for assessment of the functional enrichment of networks is available at http://www-bionet.sscc.ru/fungenenet/ .

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In this paper we study first-passage percolation in the configuration model with empirical degree distribution that follows a power-law with exponent τ ∈ ( 2 , 3 ) . We assign independent and identically distributed (i.i.d.) weights to the edges of the graph. We investigate the weighted distance (the length of the shortest weighted path) between two uniformly chosen vertices, called typical distances. When the underlying age-dependent branching process approximating the local neighborhoods of vertices is found to produce infinitely many individuals in finite time-called explosive branching process-Baroni, Hofstad and the second author showed in Baroni et al. (J Appl Probab 54(1):146-164, 2017) that typical distances converge in distribution to a bounded random variable. The order of magnitude of typical distances remained open for the τ ∈ ( 2 , 3 ) case when the underlying branching process is not explosive. We close this gap by determining the first order of magnitude of typical distances in this regime for arbitrary, not necessary continuous edge-weight distributions that produce a non-explosive age-dependent branching process with infinite mean power-law offspring distributions. This sequence tends to infinity with the amount of vertices, and, by choosing an appropriate weight distribution, can be tuned to be any growing function that is O ( log log n ) , where n is the number of vertices in the graph. We show that the result remains valid for the the erased configuration model as well, where we delete loops and any second and further edges between two vertices.

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While organic semiconductors provide tantalizing possibilities for low-cost, light-weight, flexible electronic devices, their current use in transistors-the fundamental building block-is rather limited as their speed and reliability are not competitive with those of their inorganic counterparts and are simply too poor for many practical applications. Through self-assembly, highly ordered nanostructures can be prepared that have more competitive transport characteristics; however, no simple, scalable method has been discovered that can produce devices on the basis of such nanostructures. Here, we show how transistors of self-assembled molecular nanowires can be fabricated using a scalable, gradient sublimation technique, which have dramatically improved characteristics compared to those of their thin-film counterparts, both in terms of performance and stability. Nanowire devices based on copper phthalocyanine have been fabricated with threshold voltages as low as -2.1 V, high on/off ratios of 105, small subthreshold swings of 0.9 V/decade, and mobilities of 0.6 cm2/V s, and lower trap energies as deduced from temperature-dependent properties, in line with leading organic semiconductors involving more complex fabrication. High-performance transistors manufactured using our scalable deposition technique, compatible with flexible substrates, could enable integrated all-organic chips implementing conventional as well as neuromorphic computation and combining sensors, logic, data storage, drivers, and displays.

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Protein-protein interaction (PPI) networks are emerging as valuable prototypes to study important problems in molecular cellular biology and systems biomedicine. An analysis of the topological properties of a PPI network is very helpful for understanding the function and structure of networks. In this study, we analyzed the topological patterns in the BioPlex network containing interactions among 10,961 proteins; most interactions were previously undocumented. The BioPlex network is a comprehensive map of human protein interactions and represents the first phase of a long-term effort to profile the entire human ORFEOME collection. Similar to other biological networks, we observed that the BioPlex network has several topological properties. We also quantified correlations profiles for the BioPlex network and compared them to randomized versions of the same network. We found that for the BioPlex network, edges between proteins with intermediate degrees were strongly suppressed, whereas edges between low-connected proteins were favored. Finally, the degrees of essential genes were compared with the degrees of non-essential genes and randomly selected proteins. There were no significant differences between the groups.

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Biological networks are becoming a fundamental tool for the investigation of high-throughput data in several fields of biology and biotechnology. With the increasing amount of information, network-based models are gaining more and more interest and new techniques are required in order to mine the information and to validate the results. We have developed an app for the Cytoscape platform which allows the creation of randomized networks and the randomization of existing, real networks. Since there is a lack of tools for generating and randomizing networks, our app helps researchers to exploit different, well known random network models which could be used as a benchmark for validating real datasets. We also propose a novel methodology for creating random weighted networks starting from experimental data. Finally the app provides a statistical tool which compares real versus random attributes, in order to validate all the numerical findings. In summary, our app aims at creating a standardised methodology for the validation of the results in the context of the Cytoscape platform.

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Many experimental and theoretical studies have suggested that the reliable propagation of synchronous neural activity is crucial for neural information processing. The propagation of synchronous firing activity in so-called synfire chains has been studied extensively in feed-forward networks of spiking neurons. However, it remains unclear how such neural activity could emerge in recurrent neuronal networks through synaptic plasticity. In this study, we investigate whether local excitation, i.e., neurons that fire at a higher frequency than the other, spontaneously active neurons in the network, can shape a network to allow for synchronous activity propagation. We use two-dimensional, locally connected and heterogeneous neuronal networks with spike-timing dependent plasticity (STDP). We find that, in our model, local excitation drives profound network changes within seconds. In the emergent network, neural activity propagates synchronously through the network. This activity originates from the site of the local excitation and propagates through the network. The synchronous activity propagation persists, even when the local excitation is removed, since it derives from the synaptic weight matrix. Importantly, once this connectivity is established it remains stable even in the presence of spontaneous activity. Our results suggest that synfire-chain-like activity can emerge in a relatively simple way in realistic neural networks by locally exciting the desired origin of the neuronal sequence.