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Mobility is a crucial element in comprehending the possible expansion of the transmission chain in an epidemic. In the initial phases, strategies for containing cases can be directly linked to population mobility restrictions, especially when only non-pharmaceutical measures are available. During the pandemic of COVID-19 in Brazil, mobility limitation measures were strongly opposed by a large portion of the population. Hypothetically, if the population had supported such measures, the sharp rise in the number of cases could have been suppressed. In this context, computational modeling offers systematic methods for analyzing scenarios about the development of the epidemiological situation taking into account specific conditions. In this study, we examine the impacts of interstate mobility in Brazil. To do so, we develop a metapopulational model that considers both intra and intercompartmental dynamics, utilizing graph theory. We use a parameter estimation technique that allows us to infer the effective reproduction number in each state and estimate the time-varying transmission rate. This makes it possible to investigate scenarios related to mobility and quantify the effect of people moving between states and how certain measures to limit movement might reduce the impact of the pandemic. Our results demonstrate a clear association between the number of cases and mobility, which is heightened when states are closer to each other. This serves as a proof of concept and shows how reducing mobility in more heavily trafficked areas can be more effective.

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OBJECTIVE: To determine the association between neighborhood disadvantage (ND) and functional brain development of in utero fetuses. STUDY DESIGN: We conducted an observational study using Social Vulnerability Index (SVI) scores to assess the impact of ND on a prospectively recruited sample of healthy pregnant women from Washington, DC. Using 79 functional magnetic resonance imaging scans from 68 healthy pregnancies at a mean gestational age of 33.12 weeks, we characterized the overall functional brain network structure using a graph metric approach. We used linear mixed effects models to assess the relationship between SVI and gestational age on 5 graph metrics, adjusting for multiple scans. RESULTS: Exposure to greater ND was associated with less well integrated functional brain networks, as observed by longer characteristic path lengths and diminished global efficiency (GE), as well as diminished small world propensity (SWP). Across gestational ages, however, the association between SVI and network integration diminished to a negligible relationship in the third trimester. Conversely, SWP was significant across pregnancy, but the relationship changed such that there was a negative association with SWP earlier in the second trimester that inverted around the transition to the third trimester to a positive association. CONCLUSIONS: These data directly connect ND and altered functional brain maturation in fetuses. Our results suggest that, even before birth, proximity to environmental stressors in the wider neighborhood environment are associated with altered brain development.

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Analyzing transcription data requires intensive statistical analysis to obtain useful biological information and knowledge. A significant portion of this data is affected by random noise or even noise intrinsic to the modeling of the experiment. Without robust treatment, the data might not be explored thoroughly, and incorrect conclusions could be drawn. Examining the correlation between gene expression profiles is one way bioinformaticians extract information from transcriptomic experiments. However, the correlation measurements traditionally used have worrisome shortcomings that need to be addressed. This paper compares five already published and experimented-with correlation measurements to the newly developed coincidence index, a similarity measurement that combines Jaccard and interiority indexes and generalizes them to be applied to vectors containing real values. We used microarray and RNA-Seq data from the archaeonHalobacterium salinarumand the bacteriumEscherichia coli, respectively, to evaluate the capacity of each correlation/similarity measurement. The utilized method explores the co-expressed metabolic pathways by measuring the correlations between the expression levels of enzymes that share metabolites, represented in the form of a weighted graph. It then searches for local maxima in this graph using a simulated annealing algorithm. We demonstrate that the coincidence index extracts larger, more comprehensive, and more statistically significant pathways for microarray experiments. In RNA-Seq experiments, the results are more limited, but the coincidence index managed the largest percentage of significant components in the graph.

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OBJECTIVE: Apply Graph Theory to analyze and map knowledge about nursing diagnoses and interventions, based on records of consultations carried out by nurses, in women's health, in primary health care. METHODS: Secondary data from a cross-sectional study were used. Records of nursing consultations carried out during the month of October 2016, in 21 health units, in a Brazilian municipality were analyzed. Network analysis was carried out using Graphs from 61 nursing consultations. RESULTS: 175 diagnoses were recorded, an average of three per consultation; and 380 interventions, an average of six per consultation. In the analysis, four diagnostic and four intervention network groupings were identified. CONCLUSIONS: The mapping allowed reflection on phenomena of interest to Nursing and fostering critical thinking in decision making. The findings are useful for teaching and training nurses, as well as strengthening the use of standardized language systems.

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Selma Lagerlöf said that culture is what remains when one has forgotten everything we had learned. Without any warranty, through ongoing research tasks, that I will ever attain this high level of wisdom, I simply share here reminiscences that have played, during my life, an important role in my incursions in science, mainly in theoretical physics. I end by presenting some perspectives for future developments.

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A necessary condition for the probabilities of a set of events to exhibit Bell non-locality or Kochen-Specker contextuality is that the graph of exclusivity of the events contains induced odd cycles with five or more vertices, called odd holes, or their complements, called odd antiholes. From this perspective, events whose graph of exclusivity are odd holes or antiholes are the building blocks of contextuality. For any odd hole or antihole, any assignment of probabilities allowed by quantum theory can be achieved in specific contextuality scenarios. However, here we prove that, for any odd hole, the probabilities that attain the quantum maxima cannot be achieved in Bell scenarios. We also prove it for the simplest odd antiholes. This leads us to the conjecture that the quantum maxima for any of the building blocks cannot be achieved in Bell scenarios. This result sheds light on why the problem of whether a probability assignment is quantum is decidable, while whether a probability assignment within a given Bell scenario is quantum is, in general, undecidable. This also helps to understand why identifying principles for quantum correlations is simpler when we start by identifying principles for quantum sets of probabilities defined with no reference to specific scenarios. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.

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The connection between contextuality and graph theory has paved the way for numerous advancements in the field. One notable development is the realization that sets of probability distributions in many contextuality scenarios can be effectively described using well-established convex sets from graph theory. This geometric approach allows for a beautiful characterization of these sets. The application of geometry is not limited to the description of contextuality sets alone; it also plays a crucial role in defining contextuality quantifiers based on geometric distances. These quantifiers are particularly significant in the context of the resource theory of contextuality, which emerged following the recognition of contextuality as a valuable resource for quantum computation. In this paper, we provide a comprehensive review of the geometric aspects of contextuality. Additionally, we use this geometry to define several quantifiers, offering the advantage of applicability to other approaches to contextuality where previously defined quantifiers may not be suitable. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.

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Introduction: Stroke is the leading cause of functional disability worldwide. With the increase of the global population, motor rehabilitation of stroke survivors is of ever-increasing importance. In the last decade, virtual reality (VR) technologies for rehabilitation have been extensively studied, to be used instead of or together with conventional treatments such as physiotherapy or occupational therapy. The aim of this work was to evaluate the GestureCollection VR-based rehabilitation tool in terms of the brain changes and clinical outcomes of the patients. Methods: Two groups of chronic patients underwent a rehabilitation treatment with (experimental) or without (control) complementation with GestureCollection. Functional magnetic resonance imaging exams and clinical assessments were performed before and after the treatment. A functional connectivity graph-based analysis was used to assess differences between the connections and in the network parameters strength and clustering coefficient. Results: Patients in both groups showed improvement in clinical scales, but there were more increases in functional connectivity in the experimental group than in the control group. Discussion: The experimental group presented changes in the connections between the frontoparietal and the somatomotor networks, associative cerebellum and basal ganglia, which are regions associated with reward-based motor learning. On the other hand, the control group also had results in the somatomotor network, in its ipsilateral connections with the thalamus and with the motor cerebellum, which are regions more related to a purely mechanical activity. Thus, the use of the GestureCollection system was successfully shown to promote neuroplasticity in several motor-related areas.

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Filamentous fungi develop intricate hyphal networks that support mycelial foraging and transport of resources. These networks have been analyzed recently using graph theory, enabling the development of models that seek to predict functional traits. However, attention has focused mainly on mature colonies. Here, we report the extraction and analysis of the graph corresponding to Trichoderma atroviride mycelia only a few hours after conidia germination. To extract the graph for a given mycelium, a mosaic conformed of multiple bright-field, optical microscopy images is digitally processed using freely available software. The resulting graphs are characterized in terms of number of nodes and edges, average edge length, total mycelium length, hyphal growth unit, maximum edge length and mycelium diameter, for colonies between 8 h and 14 h after conidium germination. Our results show that the emerging hyphal network grows first by hyphal elongation and branching, and then it transitions to a stage where hyphal-hyphal interactions become significant. As a tangled hyphal network develops with decreasing hyphal mean length, the mycelium maintains long (∼2 mm) hyphae-a behavior that suggests a combination of aggregated and dispersed architectures to support foraging. Lastly, analysis of early network development in Podospora anserina reveals striking similarity with T. atroviride, suggesting common mechanisms during initial colony formation in filamentous fungi.

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In this work, we study the problem of designing control laws that achieve time-varying formation and flocking behaviors in robot networks where each agent or robot presents double integrator dynamics. To design the control laws, we adopt a hierarchical control approach. First, we introduce a virtual velocity, which is used as a virtual control input for the position subsystem (outer loop). The objective of the virtual velocity is to achieve collective behaviors. Then, we design a velocity tracking control law for the velocity subsystem (inner loop). An advantage of the proposed approach is that the robots do not require the velocity of their neighbors. Additionally, we address the case in which the second state of the system is not available for feedback. We include a set of simulation results to show the performance of the proposed control laws.

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Naturalistic paradigms are being increasingly applied to investigate human brain function. Compared with resting-state and task-based paradigms in neuroimaging, naturalistic stimuli and situations can be potentially more readily translated to daily-life applications. Among neuroimaging modalities, functional near-infrared spectroscopy (fNIRS) is particularly suitable for naturalistic investigations and applications. However, specific and tailored statistical analysis to interrogate brain function using naturalistic fNIRS is warranted. Here, we describe an exploratory graph-centrality-based approach to investigating participants' spatiotemporal similarities from the fNIRS signal. We illustrate the usefulness of our approach in a sample of typically developing children (10 males and 9 females; mean age of 5.2 years old; sd = 0.78) while they watch the Inscapes movie designed for neuroimaging acquisition. A node in the left dorsal prefrontal cortex presented similar responses across children, and those fNIRS responses were in line with scene transitions in the movie stimulus. Our results suggest the feasibility of applying centrality graph-based measures to investigate brain function in naturalistic fNIRS during development.

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Introduction: Clustering is usually the first exploratory analysis step in empirical data. When the data set comprises graphs, the most common approaches focus on clustering its vertices. In this work, we are interested in grouping networks with similar connectivity structures together instead of grouping vertices of the graph. We could apply this approach to functional brain networks (FBNs) for identifying subgroups of people presenting similar functional connectivity, such as studying a mental disorder. The main problem is that real-world networks present natural fluctuations, which we should consider. Methods: In this context, spectral density is an exciting feature because graphs generated by different models present distinct spectral densities, thus presenting different connectivity structures. We introduce two clustering methods: k-means for graphs of the same size and gCEM, a model-based approach for graphs of different sizes. We evaluated their performance in toy models. Finally, we applied them to FBNs of monkeys under anesthesia and a dataset of chemical compounds. Results: We show that our methods work well in both toy models and real-world data. They present good results for clustering graphs presenting different connectivity structures even when they present the same number of edges, vertices, and degree of centrality. Discussion: We recommend using k-means-based clustering for graphs when graphs present the same number of vertices and the gCEM method when graphs present a different number of vertices.

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The landscape configuration, the permeability of the matrix and the possibility of random dispersal movement of species are essential to robust modeling of the landscape connectivity. To represent this condition, we report a spatial model that integrates graph theory, circuit theory, metrics of habitat availability and includes a temporal aspect by looking into land use changes over time. We identify the possibilities of movement of species site-to-site over time in the landscape, taking into account not only the importance of sites of focal habitats, but also the potential relevance of the matrix for landscape connectivity. The modeling was applied to two rural landscapes, considering three functional groups of mammals with different resource-feeding and habitat requirements. The model indicated multiple and new dispersal non-linear potential routes to each group of mammals, considering its specific requirement to obtain resources and its movement pattern on the agricultural matrix.

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In the last decade, the exclusive role of the hippocampus in human declarative learning has been challenged. Recently, we have shown that gains in performance observed in motor sequence learning (MSL) during the quiet rest periods interleaved with practice are associated with increased hippocampal activity, suggesting a role of this structure in motor memory reactivation. Yet, skill also develops offline as memory stabilizes after training and overnight. To examine whether the hippocampus contributes to motor sequence memory consolidation, here we used a network neuroscience strategy to track its functional connectivity offline 30 min and 24 h post learning using resting-state functional magnetic resonance imaging. Using a graph-analytical approach we found that MSL transiently increased network modularity, reflected in an increment in local information processing at 30 min that returned to baseline at 24 h. Within the same time window, MSL decreased the connectivity of a hippocampal-sensorimotor network, and increased the connectivity of a striatal-premotor network in an antagonistic manner. Finally, a supervised classification identified a low-dimensional pattern of hippocampal connectivity that discriminated between control and MSL data with high accuracy. The fact that changes in hippocampal connectivity were detected shortly after training supports a relevant role of the hippocampus in early stages of motor memory consolidation.

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BACKGROUND: There have been significant challenges in understanding functional brain connectivity associated with adolescent depression, including the need for a more comprehensive approach to defining risk, the lack of representation of participants from low- and middle-income countries, and the need for network-based approaches to model connectivity. The current study aimed to address these challenges by examining resting-state functional connectivity of frontolimbic circuitry associated with the risk and presence of depression in adolescents in Brazil. METHODS: Adolescents in Brazil ages 14 to 16 years were classified into low-risk, high-risk, and depressed groups using a clinical assessment and composite risk score that integrates 11 sociodemographic risk variables. After excluding participants with excessive head movement, resting-state functional magnetic resonance imaging data of 126 adolescents were analyzed. We compared group differences in frontolimbic network connectivity using region of interest-to-region of interest, graph theory, and seed-based connectivity analyses. Associations between self-reported depressive symptoms and brain connectivity were also explored. RESULTS: Adolescents with depression showed greater dorsal anterior cingulate cortex (ACC) connectivity with the orbitofrontal cortex compared with the 2 risk groups and greater dorsal ACC global efficiency than the low-risk group. Adolescents with depression also showed reduced local efficiency and a lower clustering coefficient of the subgenual ACC compared with the 2 risk groups. The high-risk group also showed a lower subgenual ACC clustering coefficient relative to the low-risk group. CONCLUSIONS: These findings highlight altered connectivity and topology of the ACC within frontolimbic circuitry as potential neural correlates and risk factors of developing depression in adolescents in Brazil. This study broadens our understanding of the neural connectivity associated with adolescent depression in a global context.

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Hyperscanning is a promising tool for investigating the neurobiological underpinning of social interactions and affective bonds. Recently, graph theory measures, such as modularity, have been proposed for estimating the global synchronization between brains. This paper proposes the bootstrap modularity test as a way of determining whether a pair of brains is coactivated. This test is illustrated as a screening tool in an application to fNIRS data collected from the prefrontal cortex and temporoparietal junction of five dyads composed of a teacher and a preschooler while performing an interaction task. In this application, graph hub centrality measures identify that the dyad's synchronization is critically explained by the relation between teacher's language and number processing and the child's phonological processing. The analysis of these metrics may provide further insights into the neurobiological underpinnings of interaction, such as in educational contexts.

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A theoretical study of cell evolution is presented here. By using a toolbox containing an intracellular catalytic reaction network model and a mutation-selection process, four distinct phases of self-organization were unveiled. First, the nutrients prevail as the central substrate of the chemical reactions. Second, the cell becomes a small-world. Third, a highly connected core component emerges, concurrently with the nutrient carriers becoming the central product of reactions. Finally, the cell reaches a steady configuration where the concentrations of the core chemical species are described by Zipf's law.

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A pipeline is proposed here to describe different features to study brain microcircuits on a histological scale using multi-scale analyses, including the uniform manifold approximation and projection (UMAP) dimensional reduction technique and modularity algorithm to identify neuronal ensembles, Runs tests to show significant ensembles activation, graph theory to show trajectories between ensembles, and recurrence analyses to describe how regular or chaotic ensembles dynamics are. The data set includes ex-vivo NMDA-activated striatal tissue in control conditions as well as experimental models of disease states: decorticated, dopamine depleted, and L-DOPA-induced dyskinetic rodent samples. The goal was to separate neuronal ensembles that have correlated activity patterns. The pipeline allows for the demonstration of differences between disease states in a brain slice. First, the ensembles were projected in distinctive locations in the UMAP space. Second, graphs revealed functional connectivity between neurons comprising neuronal ensembles. Third, the Runs test detected significant peaks of coactivity within neuronal ensembles. Fourth, significant peaks of coactivity were used to show activity transitions between ensembles, revealing recurrent temporal sequences between them. Fifth, recurrence analysis shows how deterministic, chaotic, or recurrent these circuits are. We found that all revealed circuits had recurrent activity except for the decorticated circuits, which tended to be divergent and chaotic. The Parkinsonian circuits exhibit fewer transitions, becoming rigid and deterministic, exhibiting a predominant temporal sequence that disrupts transitions found in the controls, thus resembling the clinical signs of rigidity and paucity of movements. Dyskinetic circuits display a higher recurrence rate between neuronal ensembles transitions, paralleling clinical findings: enhancement in involuntary movements. These findings confirm that looking at neuronal circuits at the histological scale, recording dozens of neurons simultaneously, can show clear differences between control and diseased striatal states: "fingerprints" of the disease states. Therefore, the present analysis is coherent with previous ones of striatal disease states, showing that data obtained from the tissue are robust. At the same time, it adds heuristic ways to interpret circuitry activity in different states.

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- Objective: the use of motor imagery (MI) in motor rehabilitation protocols has been increasingly investigated as a potential technique for enhancing traditional treatments, yielding better clinical outcomes. However, since MI performance can be challenging, practice is usually required. This demands appropriate training, actively engaging the MI-related brain areas, consequently enabling the user to properly benefit from it. The role of feedback is central for MI practice. Yet, assessing which underlying neural changes are feedback-specific or purely due to MI practice is still a challenging effort, mainly due to the difficulty in isolating their contributions. In this work, we aimed to assess functional connectivity (FC) changes following MI practice that are either extrinsic or specific to feedback. APPROACH: to achieve this, we investigated FC, using graph theory, in electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data, during MI performance and at resting-state (rs), respectively. Thirty healthy subjects were divided into three groups, receiving no feedback (control), "false" feedback (sham) or actual neurofeedback (active). Participants underwent 12 to 13 hands-MI EEG sessions and pre- and post-MI training fMRI exams. MAIN RESULTS: following MI practice, control participants presented significant increases in degree and in eigenvector centrality for occipital nodes at rs-fMRI scans, whereas sham-feedback produced similar effects, but to a lesser extent. Therefore, MI practice, by itself, seems to stimulate visual information processing mechanisms that become apparent during basal brain activity. Additionally, only the active group displayed decreases in inter-subject FC patterns, both during MI performance and at rs-fMRI. SIGNIFICANCE: hence, actual neurofeedback impacted FC by disrupting common inter-subject patterns, suggesting that subject-specific neural plasticity mechanisms become important. Future studies should consider this when designing experimental NFBT protocols and analyses.

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BACKGROUND: Graph theory (GT) is a mathematical field that analyses complex networks that can be applied to neuroimaging to quantify brain's functional systems in Parkinson's disease (PD) and essential tremor (ET). OBJECTIVES: To evaluate the functional connectivity (FC) measured by the global efficiency (GE) of the motor network in PD and compare it to ET and healthy controls (HC), and correlate it to clinical parameters. METHODS: 103 subjects (54PD, 18ET, 31HC) were submitted to structural and functional MRI. A network was designed with regions of interest (ROIs) involved in motor function, and GT was applied to determine its GE. Clinical parameters were analyzed as covariates to estimate the impact of disease severity and medication on GE. RESULTS: GE of the motor circuit was reduced in PD in comparison with HC (p .042). Areas that most contributed to it were left supplementary motor area (SMA) and bilateral postcentral gyrus. Tremor scores correlated positively with GE of the motor network in PD subgroups. For ET, there was an increase in the connectivity of the anterior cerebellar network to the other ROIs of the motor circuit in comparison with PD. CONCLUSIONS: FC measured by the GE of the motor network is diminished in PD in comparison with HC, especially due to decreased connectivity of left SMA and bilateral postcentral gyrus. This finding supports the theory that there is a global impairment of the motor network in PD, and it does not affect just the basal ganglia, but also areas associated with movement modulation. The ET group presented an increased connectivity of the anterior cerebellar network to the other ROIs of the motor circuit when compared to PD, which reinforces what it is known about its role in this pathology.

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