True scale-free networks hidden by finite size effects.

We analyze about 200 naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned on the basis of statistical testing of the validity of power law distributions of network degrees. Specifically, we analyze by finite size scaling analysis the datasets of real networks to check whether the purported departures from power law behavior are due to the finiteness of sample size. We find that a large number of the networks follows a finite size scaling hypothesis without any self-tuning. This is the case of biological protein interaction networks, technological computer and hyperlink networks, and informational networks in general. Marked deviations appear in other cases, especially involving infrastructure and transportation but also in social networks. We conclude that underlying scale invariance properties of many naturally occurring networks are extant features often clouded by finite size effects due to the nature of the sample data.

A community detection analysis of malocclusion classes from orthodontics and upper airway data.

OBJECTIVE: The interaction between skeletal class and upper airway has been extensively studied. Nevertheless, this relationship has not been clearly elucidated, with the heterogeneity of results suggesting the existence of different patterns for patients' classification, which has been elusive so far, probably due to oversimplified approaches. Hence, a network analysis was applied to test whether different patterns in patients' grouping exist. SETTINGS AND SAMPLE POPULATION: Ninety young adult patients with no obvious signs of respiratory diseases and no previous adeno-tonsillectomy procedures, with thirty patients characterized as Class I (0 < ANB < 4); 30 Class II (ANB > 4); and 30 as Class III (ANB < 0). MATERIALS AND METHODS: A community detection approach was applied on a graph obtained from a previously analysed sample: thirty-two measurements (nineteen cephalometric and thirteen upper airways data) were considered. RESULTS: An airway-orthodontic complex network has been obtained by cross-correlating patients. Before entering the correlation, data were controlled for age and gender using linear regression and standardized. By including or not the upper airway measurements as independent variables, two different community structures were obtained. Each contained five modules, though with different patients' assignments. CONCLUSION: The community detection algorithm found the existence of more than the three classical skeletal classifications. These results support the development of alternative tools to classify subjects according to their craniofacial morphology. This approach could offer a powerful tool for implementing novel strategies for clinical and research in orthodontics.

Complexity and data mining in dental research: A network medicine perspective on interceptive orthodontics.

Procedures and models of computerized data analysis are becoming researchers' and practitioners' thinking partners by transforming the reasoning underlying biomedicine. Complexity theory, Network analysis and Artificial Intelligence are already approaching this discipline, intending to provide support for patient's diagnosis, prognosis and treatments. At the same time, due to the sparsity, noisiness and time-dependency of medical data, such procedures are raising many unprecedented problems related to the mismatch between the human mind's reasoning and the outputs of computational models. Thanks to these computational, non-anthropocentric models, a patient's clinical situation can be elucidated in the orthodontic discipline, and the growth outcome can be approximated. However, to have confidence in these procedures, orthodontists should be warned of the related benefits and risks. Here we want to present how these innovative approaches can derive better patients' characterization, also offering a different point of view about patient's classification, prognosis and treatment.

River landscapes and optimal channel networks.

We study tree structures termed optimal channel networks (OCNs) that minimize the total gravitational energy loss in the system, an exact property of steady-state landscape configurations that prove dynamically accessible and strikingly similar to natural forms. Here, we show that every OCN is a so-called natural river tree, in the sense that there exists a height function such that the flow directions are always directed along steepest descent. We also study the natural river trees in an arbitrary graph in terms of forbidden substructures, which we call k-path obstacles, and OCNs on a d-dimensional lattice, improving earlier results by determining the minimum energy up to a constant factor for every [Formula: see text] Results extend our capabilities in environmental statistical mechanics.

Anatomy of news consumption on Facebook.

The advent of social media and microblogging platforms has radically changed the way we consume information and form opinions. In this paper, we explore the anatomy of the information space on Facebook by characterizing on a global scale the news consumption patterns of 376 million users over a time span of 6 y (January 2010 to December 2015). We find that users tend to focus on a limited set of pages, producing a sharp community structure among news outlets. We also find that the preferences of users and news providers differ. By tracking how Facebook pages "like" each other and examining their geolocation, we find that news providers are more geographically confined than users. We devise a simple model of selective exposure that reproduces the observed connectivity patterns.

Network Analysis of Gut Microbiome and Metabolome to Discover Microbiota-Linked Biomarkers in Patients Affected by Non-Small Cell Lung Cancer.

Several studies in recent times have linked gut microbiome (GM) diversity to the pathogenesis of cancer and its role in disease progression through immune response, inflammation and metabolism modulation. This study focused on the use of network analysis and weighted gene co-expression network analysis (WGCNA) to identify the biological interaction between the gut ecosystem and its metabolites that could impact the immunotherapy response in non-small cell lung cancer (NSCLC) patients undergoing second-line treatment with anti-PD1. Metabolomic data were merged with operational taxonomic units (OTUs) from 16S RNA-targeted metagenomics and classified by chemometric models. The traits considered for the analyses were: (i) condition: disease or control (CTRLs), and (ii) treatment: responder (R) or non-responder (NR). Network analysis indicated that indole and its derivatives, aldehydes and alcohols could play a signaling role in GM functionality. WGCNA generated, instead, strong correlations between short-chain fatty acids (SCFAs) and a healthy GM. Furthermore, commensal bacteria such as Akkermansia muciniphila, Rikenellaceae, Bacteroides, Peptostreptococcaceae, Mogibacteriaceae and Clostridiaceae were found to be more abundant in CTRLs than in NSCLC patients. Our preliminary study demonstrates that the discovery of microbiota-linked biomarkers could provide an indication on the road towards personalized management of NSCLC patients.

The price of complexity in financial networks.

Financial institutions form multilayer networks by engaging in contracts with each other and by holding exposures to common assets. As a result, the default probability of one institution depends on the default probability of all of the other institutions in the network. Here, we show how small errors on the knowledge of the network of contracts can lead to large errors in the probability of systemic defaults. From the point of view of financial regulators, our findings show that the complexity of financial networks may decrease the ability to mitigate systemic risk, and thus it may increase the social cost of financial crises.

The spreading of misinformation online.

The wide availability of user-provided content in online social media facilitates the aggregation of people around common interests, worldviews, and narratives. However, the World Wide Web (WWW) also allows for the rapid dissemination of unsubstantiated rumors and conspiracy theories that often elicit rapid, large, but naive social responses such as the recent case of Jade Helm 15--where a simple military exercise turned out to be perceived as the beginning of a new civil war in the United States. In this work, we address the determinants governing misinformation spreading through a thorough quantitative analysis. In particular, we focus on how Facebook users consume information related to two distinct narratives: scientific and conspiracy news. We find that, although consumers of scientific and conspiracy stories present similar consumption patterns with respect to content, cascade dynamics differ. Selective exposure to content is the primary driver of content diffusion and generates the formation of homogeneous clusters, i.e., "echo chambers." Indeed, homogeneity appears to be the primary driver for the diffusion of contents and each echo chamber has its own cascade dynamics. Finally, we introduce a data-driven percolation model mimicking rumor spreading and we show that homogeneity and polarization are the main determinants for predicting cascades' size.

Understanding interactions among cephalometrics variables during growth in untreated Class III subjects.

OBJECTIVE: The aim of the present study was to apply a computational method commonly used in data mining discipline, classification trees (CTs), to evaluate the growth features in untreated Class III subjects. MATERIALS AND METHODS: CT was applied to data from 91 untreated Class III subjects (48 females and 43 males) and compared with the results of discriminant analysis (DA). For all subjects, lateral cephalograms were available at T1 (mean age 10.4 ± 2.0 years) and at T2 (mean age 15.4 ± 1.9 years). A cephalometric analysis comprising 11 variables was performed. The subjects were divided into two subgroups, unfavourable ('Bad') and favourable ('Good') growers, according to the quality of the skeletal growth rate in comparison with the normal craniofacial growth. RESULTS: CTs showed that the most informative attribute for the prediction of favourable/unfavourable skeletal growth was the SNA angle. Subjects with SNA values lower than 79.1 degrees showed a risk of 94 per cent of growing unfavourably. DA was able to select palatal plane to mandibular plane angle as predictors. DA, however, showed a statistically significant higher rate of misclassification when compared with CTs (40.7 per cent versus 12.1 per cent, binomial exact test: odds ratio = 6.20; P < 0.0001). CONCLUSIONS: CTs provided a valid measure of elucidating the effective contribution of craniofacial characteristics in predicting favourable/unfavourable growth in untreated Class III subjects.

Evidence of scale-free clusters of vegetation in tropical rainforests.

Tropical rainforests exhibit a rich repertoire of spatial patterns emerging from the intricate relationship between the microscopic interaction between species. In particular, the distribution of vegetation clusters can shed much light on the underlying process that regulates the ecosystem. Analyzing the distribution of vegetation clusters at different resolution scales, we show the first robust evidence of scale-invariant clusters of vegetation, suggesting the coexistence of multiple intertwined scales in the collective dynamics of tropical rainforests. We use field data and computational simulations to confirm our hypothesis, proposing a predictor that could be particularly interesting to monitor the ecological resilience of the world's "green lungs."

Fluctuations and extreme events in the public attention on Italian legislative elections.

The share of social media attention to political candidates was shown to be a good predictor of election outcomes in several studies. This attention to individual candidates fluctuates due to incoming daily news and sometimes reflects long-term trends. By analyzing Twitter data in the 2013 and 2022 election campaign we observe that, on short timescales, the dynamics can be effectively characterized by a mean-reverting diffusion process on a logarithmic scale. This implies that the response to news and the exchange of opinions on Twitter lead to attention fluctuations spanning orders of magnitudes. However, these fluctuations remain centered around certain average levels of popularity, which change slowly in contrast to the rapid daily and hourly variations driven by Twitter trends and news. In particular, on our 2013 data we are able to estimate the dominant timescale of fluctuations at around three hours. Finally, by considering the extreme data points in the tail of the attention variation distribution, we could identify critical events in the electoral campaign period and extract useful information from the flow of data.

Multi-scale analysis of the community structure of the Twitter discourse around the Italian general elections of September 2022.

We perform a multi-scale analysis of the geometric structure of the network of X (Twitter at the time of data collection) interactions surrounding the Italian snap general elections of September 25th 2022. We identify within it the communities related to the major Italian political parties and after it we analyse both the large-scale structure of interactions between different parties, showing that it resembles the coalitions formed in the run-up to the elections and the internal structure of each community. We observe that some parties have a very centralised communication with the major leaders clearly occupying the central role, while others have a more horizontal communication strategy, with many accounts playing an important role. We observe that this can be characterized by checking whether the network in the community has a strongly connected giant component or not.

Network topology mapping of chemical compounds space.

We define bipartite and monopartite relational networks of chemical elements and compounds using two different datasets of inorganic chemical and material compounds, as well as study their topology. We discover that the connectivity between elements and compounds is distributed exponentially for materials, and with a fat tail for chemicals. Compounds networks show similar distribution of degrees, and feature a highly-connected club due to oxygen . Chemical compounds networks appear more modular than material ones, while the communities detected reveal different dominant elements specific to the topology. We successfully reproduce the connectivity of the empirical chemicals and materials networks by using a family of fitness models, where the fitness values are derived from the abundances of the elements in the aggregate compound data. Our results pave the way towards a relational network-based understanding of the inherent complexity of the vast chemical knowledge atlas, and our methodology can be applied to other systems with the ingredient-composite structure.

Fibration symmetry-breaking supports functional transitions in a brain network engaged in language.

In his book 'A Beautiful Question' 1, physicist Frank Wilczek argues that symmetry is 'nature's deep design,' governing the behavior of the universe, from the smallest particles to the largest structures 1-4. While symmetry is a cornerstone of physics, it has not yet been found widespread applicability to describe biological systems 5, particularly the human brain. In this context, we study the human brain network engaged in language and explore the relationship between the structural connectivity (connectome or structural network) and the emergent synchronization of the mesoscopic regions of interest (functional network). We explain this relationship through a different kind of symmetry than physical symmetry, derived from the categorical notion of Grothendieck fibrations 6. This introduces a new understanding of the human brain by proposing a local symmetry theory of the connectome, which accounts for how the structure of the brain's network determines its coherent activity. Among the allowed patterns of structural connectivity, synchronization elicits different symmetry subsets according to the functional engagement of the brain. We show that the resting state is a particular realization of the cerebral synchronization pattern characterized by a fibration symmetry that is broken 7 in the transition from rest to language. Our findings suggest that the brain's network symmetry at the local level determines its coherent function, and we can understand this relationship from theoretical principles.

Fibration symmetry-breaking supports functional transitions in a brain network engaged in language.

In his book 'A Beautiful Question', physicist Frank Wilczek argues that symmetry is 'nature's deep design,' governing the behavior of the universe, from the smallest particles to the largest structures. While symmetry is a cornerstone of physics, it has not yet been found widespread applicability to describe biological systems, particularly the human brain. In this context, we study the human brain network engaged in language and explore the relationship between the structural connectivity (connectome or structural network) and the emergent synchronization of the mesoscopic regions of interest (functional network). We explain this relationship through a different kind of symmetry than physical symmetry, derived from the categorical notion of Grothendieck fibrations. This introduces a new understanding of the human brain by proposing a local symmetry theory of the connectome, which accounts for how the structure of the brain's network determines its coherent activity. Among the allowed patterns of structural connectivity, synchronization elicits different symmetry subsets according to the functional engagement of the brain. We show that the resting state is a particular realization of the cerebral synchronization pattern characterized by a fibration symmetry that is broken in the transition from rest to language. Our findings suggest that the brain's network symmetry at the local level determines its coherent function, and we can understand this relationship from theoretical principles.

Inflammatory bowel disease biomarkers revealed by the human gut microbiome network.

Inflammatory bowel diseases (IBDs) are complex medical conditions in which the gut microbiota is attacked by the immune system of genetically predisposed subjects when exposed to yet unclear environmental factors. The complexity of this class of diseases makes them suitable to be represented and studied with network science. In this paper, the metagenomic data of control, Crohn's disease, and ulcerative colitis subjects' gut microbiota were investigated by representing this data as correlation networks and co-expression networks. We obtained correlation networks by calculating Pearson's correlation between gene expression across subjects. A percolation-based procedure was used to threshold and binarize the adjacency matrices. In contrast, co-expression networks involved the construction of the bipartite subjects-genes networks and the monopartite genes-genes projection after binarization of the biadjacency matrix. Centrality measures and community detection were used on the so-built networks to mine data complexity and highlight possible biomarkers of the diseases. The main results were about the modules of Bacteroides, which were connected in the control subjects' correlation network, Faecalibacterium prausnitzii, where co-enzyme A became central in IBD correlation networks and Escherichia coli, whose module has different patterns of integration within the whole network in the different diagnoses.

Systemic risk measured by the resiliency of the system to initial shocks.

The analysis of systemic risk often revolves around examining various measures utilized by practitioners and policymakers. These measures typically focus on assessing the extent to which external events can impact a financial system, without delving into the nature of the initial shock. In contrast, our approach takes a symmetrical standpoint and introduces a set of measures centered on the quantity of external shock that the system can absorb before experiencing deterioration. To achieve this, we employ a linearized version of DebtRank, which facilitates a clear depiction of the onset of financial distress, thereby enabling accurate estimation of systemic risk. Through the utilization of spectral graph theory, we explicitly compute localized and uniform exogenous shocks, elucidating their behavior. Additionally, we expand the analysis to encompass heterogeneous shocks, necessitating computation via Monte Carlo simulations. We firmly believe that our approach is both comprehensive and intuitive, enabling a standardized assessment of failure risk in financial systems.

Bow-tie structures of twitter discursive communities.

Bow-tie structures were introduced to describe the World Wide Web (WWW): in the direct network in which the nodes are the websites and the edges are the hyperlinks connecting them, the greatest number of nodes takes part to a bow-tie, i.e. a Weakly Connected Component (WCC) composed of 3 main sectors: IN, OUT and SCC. SCC is the main Strongly Connected Component of WCC, i.e. the greatest subgraph in which each node is reachable by any other one. The IN and OUT sectors are the set of nodes not included in SCC that, respectively, can access and are accessible to nodes in SCC. In the WWW, the greatest part of the websites can be found in the SCC, while the search engines belong to IN and the authorities, as Wikipedia, are in OUT. In the analysis of Twitter debate, the recent literature focused on discursive communities, i.e. clusters of accounts interacting among themselves via retweets. In the present work, we studied discursive communities in 8 different thematic Twitter datasets in various languages. Surprisingly, we observed that almost all discursive communities therein display a bow-tie structure during political or societal debates. Instead, they are absent when the argument of the discussion is different as sport events, as in the case of Euro2020 Turkish and Italian datasets. We furthermore analysed the quality of the content created in the various sectors of the different discursive communities, using the domain annotation from the fact-checking website Newsguard: we observe that, when the discursive community is affected by m/disinformation, the content with the lowest quality is the one produced and shared in SCC and, in particular, a strong incidence of low- or non-reputable messages is present in the flow of retweets between the SCC and the OUT sectors. In this sense, in discursive communities affected by m/disinformation, the greatest part of the accounts has access to a great variety of contents, but whose quality is, in general, quite low; such a situation perfectly describes the phenomenon of infodemic, i.e. the access to "an excessive amount of information about a problem, which makes it difficult to identify a solution", according to WHO.

The Validity of Machine Learning Procedures in Orthodontics: What Is Still Missing?

Artificial intelligence (AI) models and procedures hold remarkable predictive efficiency in the medical domain through their ability to discover hidden, non-obvious clinical patterns in data. However, due to the sparsity, noise, and time-dependency of medical data, AI procedures are raising unprecedented issues related to the mismatch between doctors' mentalreasoning and the statistical answers provided by algorithms. Electronic systems can reproduce or even amplify noise hidden in the data, especially when the diagnosis of the subjects in the training data set is inaccurate or incomplete. In this paper we describe the conditions that need to be met for AI instruments to be truly useful in the orthodontic domain. We report some examples of computational procedures that are capable of extracting orthodontic knowledge through ever deeper patient representation. To have confidence in these procedures, orthodontic practitioners should recognize the benefits, shortcomings, and unintended consequences of AI models, as algorithms that learn from human decisions likewise learn mistakes and biases.

Automatic classification of signal regions in 1H Nuclear Magnetic Resonance spectra.

The identification and characterization of signal regions in Nuclear Magnetic Resonance (NMR) spectra is a challenging but crucial phase in the analysis and determination of complex chemical compounds. Here, we present a novel supervised deep learning approach to perform automatic detection and classification of multiplets in 1H NMR spectra. Our deep neural network was trained on a large number of synthetic spectra, with complete control over the features represented in the samples. We show that our model can detect signal regions effectively and minimize classification errors between different types of resonance patterns. We demonstrate that the network generalizes remarkably well on real experimental 1H NMR spectra.