Fibration symmetries and cluster synchronization in the Caenorhabditis elegans connectome.

Capturing how the Caenorhabditis elegans connectome structure gives rise to its neuron functionality remains unclear. It is through fiber symmetries found in its neuronal connectivity that synchronization of a group of neurons can be determined. To understand these we investigate graph symmetries and search for such in the symmetrized versions of the forward and backward locomotive sub-networks of the Caenorhabditi elegans worm neuron network. The use of ordinarily differential equations simulations admissible to these graphs are used to validate the predictions of these fiber symmetries and are compared to the more restrictive orbit symmetries. Additionally fibration symmetries are used to decompose these graphs into their fundamental building blocks which reveal units formed by nested loops or multilayered fibers. It is found that fiber symmetries of the connectome can accurately predict neuronal synchronization even under not idealized connectivity as long as the dynamics are within stable regimes of simulations.

[WITHDRAWN] Predicting breast cancer with AI for individual risk-adjusted MRI screening and early detection.

This paper has been withdrawn by Lukas Hirsch. Major revisions and rewriting in progress.

Architecture of the brain's visual system enhances network stability and performance through layers, delays, and feedback.

In the visual system of primates, image information propagates across successive cortical areas, and there is also local feedback within an area and long-range feedback across areas. Recent findings suggest that the resulting temporal dynamics of neural activity are crucial in several vision tasks. In contrast, artificial neural network models of vision are typically feedforward and do not capitalize on the benefits of temporal dynamics, partly due to concerns about stability and computational costs. In this study, we focus on recurrent networks with feedback connections for visual tasks with static input corresponding to a single fixation. We demonstrate mathematically that a network's dynamics can be stabilized by four key features of biological networks: layer-ordered structure, temporal delays between layers, longer distance feedback across layers, and nonlinear neuronal responses. Conversely, when feedback has a fixed distance, one can omit delays in feedforward connections to achieve more efficient artificial implementations. We also evaluated the effect of feedback connections on object detection and classification performance using standard benchmarks, specifically the COCO and CIFAR10 datasets. Our findings indicate that feedback connections improved the detection of small objects, and classification performance became more robust to noise. We found that performance increased with the temporal dynamics, not unlike what is observed in core vision of primates. These results suggest that delays and layered organization are crucial features for stability and performance in both biological and artificial recurrent neural networks.

Fibration symmetry uncovers minimal regulatory networks for logical computation in bacteria.

Symmetry principles have proven important in physics, deep learning and geometry, allowing for the reduction of complicated systems to simpler, more comprehensible models that preserve the system's features of interest. Biological systems often show a high level of complexity and consist of a high number of interacting parts. Using symmetry fibrations, the relevant symmetries for biological 'message-passing' networks, we reduced the gene regulatory networks of E. coli and B. subtilis bacteria in a way that preserves information flow and highlights the computational capabilities of the network. Nodes that share isomorphic input trees are grouped into equivalence classes called fibers, whereby genes that receive signals with the same 'history' belong to one fiber and synchronize. We further reduce the networks to its computational core by removing "dangling ends" via k-core decomposition. The computational core of the network consists of a few strongly connected components in which signals can cycle while signals are transmitted between these "information vortices" in a linear feed-forward manner. These components are in charge of decision making in the bacterial cell by employing a series of genetic toggle-switch circuits that store memory, and oscillator circuits. These circuits act as the central computation machine of the network, whose output signals then spread to the rest of the network.

Fibration symmetries and cluster synchronization in the Caenorhabditis elegans connectome.

Capturing how the Caenorhabditis elegans connectome structure gives rise to its neuron functionality remains unclear. It is through fiber symmetries found in its neuronal connectivity that synchronization of a group of neurons can be determined. To understand these we investigate graph symmetries and search for such in the symmetrized versions of the forward and backward locomotive sub-networks of the Caenorhabditi elegans worm neuron network. The use of ordinarily differential equations simulations admissible to these graphs are used to validate the predictions of these fiber symmetries and are compared to the more restrictive orbit symmetries. Additionally fibration symmetries are used to decompose these graphs into their fundamental building blocks which reveal units formed by nested loops or multilayered fibers. It is found that fiber symmetries of the connectome can accurately predict neuronal synchronization even under not idealized connectivity as long as the dynamics are within stable regimes of simulations.

Machine learning approaches for the optimization of packing densities in granular matter.

The fundamental question of how densely granular matter can pack and how this density depends on the shape of the constituent particles has been a longstanding scientific problem. Previous work has mainly focused on empirical approaches based on simulations or mean-field theory to investigate the effect of shape variation on the resulting packing densities, focusing on a small set of pre-defined shapes like dimers, ellipsoids, and spherocylinders. Here we discuss how machine learning methods can support the search for optimally dense packing shapes in a high-dimensional shape space. We apply dimensional reduction and regression techniques based on random forests and neural networks to find novel dense packing shapes by numerical optimization. Moreover, an investigation of the regression function in the dimensionally reduced shape representation allows us to identify directions in the packing density landscape that lead to a strongly non-monotonic variation of the packing density. The predictions obtained by machine learning are compared with packing simulations. Our approach can be more widely applied to optimize the properties of granular matter by varying the shape of its constituent particles.

Political polarization of news media and influencers on Twitter in the 2016 and 2020 US presidential elections.

Social media has been transforming political communication dynamics for over a decade. Here using nearly a billion tweets, we analyse the change in Twitter's news media landscape between the 2016 and 2020 US presidential elections. Using political bias and fact-checking tools, we measure the volume of politically biased content and the number of users propagating such information. We then identify influencers-users with the greatest ability to spread news in the Twitter network. We observe that the fraction of fake and extremely biased content declined between 2016 and 2020. However, results show increasing echo chamber behaviours and latent ideological polarization across the two elections at the user and influencer levels.

Matryoshka and disjoint cluster synchronization of networks.

The main motivation for this paper is to characterize network synchronizability for the case of cluster synchronization (CS), in an analogous fashion to Barahona and Pecora [Phys. Rev. Lett. 89, 054101 (2002)] for the case of complete synchronization. We find this problem to be substantially more complex than the original one. We distinguish between the two cases of networks with intertwined clusters and no intertwined clusters and between the two cases that the master stability function is negative either in a bounded range or in an unbounded range of its argument. Our proposed definition of cluster synchronizability is based on the synchronizability of each individual cluster within a network. We then attempt to generalize this definition to the entire network. For CS, the synchronous solution for each cluster may be stable, independent of the stability of the other clusters, which results in possibly different ranges in which each cluster synchronizes (isolated CS). For each pair of clusters, we distinguish between three different cases: Matryoshka cluster synchronization (when the range of the stability of the synchronous solution for one cluster is included in that of the other cluster), partially disjoint cluster synchronization (when the ranges of stability of the synchronous solutions partially overlap), and complete disjoint cluster synchronization (when the ranges of stability of the synchronous solutions do not overlap).

Fast algorithm to identify minimal patterns of synchrony through fibration symmetries in large directed networks.

Recent studies have revealed the interplay between the structure of network circuits with fibration symmetries and the functionality of biological networks within which they have been identified. The presence of these symmetries in complex networks predicts the phenomenon of cluster synchronization, which produces patterns of a synchronized group of nodes. Here, we present a fast, and memory efficient, algorithm to identify fibration symmetries in networks. The algorithm is particularly suitable for large networks since it has a runtime of complexity O(Mlog⁡N) and requires O(M+N) of memory resources, where N and M are the number of nodes and edges in the network, respectively. The algorithm is a modification of the so-called refinement paradigm to identify circuits that are symmetrical to information flow (i.e., fibers) by finding the coarsest refinement partition over the network. Finally, we show that the algorithm provides an optimal procedure for identifying fibers, overcoming current approaches used in the literature.

Digital contact tracing and network theory to stop the spread of COVID-19 using big-data on human mobility geolocalization.

The spread of COVID-19 caused by the SARS-CoV-2 virus has become a worldwide problem with devastating consequences. Here, we implement a comprehensive contact tracing and network analysis to find an optimized quarantine protocol to dismantle the chain of transmission of coronavirus with minimal disruptions to society. We track billions of anonymized GPS human mobility datapoints to monitor the evolution of the contact network of disease transmission before and after mass quarantines. As a consequence of the lockdowns, people's mobility decreases by 53%, which results in a drastic disintegration of the transmission network by 90%. However, this disintegration did not halt the spreading of the disease. Our analysis indicates that superspreading k-core structures persist in the transmission network to prolong the pandemic. Once the k-cores are identified, an optimized strategy to break the chain of transmission is to quarantine a minimal number of 'weak links' with high betweenness centrality connecting the large k-cores.

Radiologist-Level Performance by Using Deep Learning for Segmentation of Breast Cancers on MRI Scans.

PURPOSE: To develop a deep network architecture that would achieve fully automated radiologist-level segmentation of cancers at breast MRI. MATERIALS AND METHODS: In this retrospective study, 38 229 examinations (composed of 64 063 individual breast scans from 14 475 patients) were performed in female patients (age range, 12-94 years; mean age, 52 years ± 10 [standard deviation]) who presented between 2002 and 2014 at a single clinical site. A total of 2555 breast cancers were selected that had been segmented on two-dimensional (2D) images by radiologists, as well as 60 108 benign breasts that served as examples of noncancerous tissue; all these were used for model training. For testing, an additional 250 breast cancers were segmented independently on 2D images by four radiologists. Authors selected among several three-dimensional (3D) deep convolutional neural network architectures, input modalities, and harmonization methods. The outcome measure was the Dice score for 2D segmentation, which was compared between the network and radiologists by using the Wilcoxon signed rank test and the two one-sided test procedure. RESULTS: The highest-performing network on the training set was a 3D U-Net with dynamic contrast-enhanced MRI as input and with intensity normalized for each examination. In the test set, the median Dice score of this network was 0.77 (interquartile range, 0.26). The performance of the network was equivalent to that of the radiologists (two one-sided test procedures with radiologist performance of 0.69-0.84 as equivalence bounds, P < .001 for both; n = 250). CONCLUSION: When trained on a sufficiently large dataset, the developed 3D U-Net performed as well as fellowship-trained radiologists in detailed 2D segmentation of breast cancers at routine clinical MRI.Keywords: MRI, Breast, Segmentation, Supervised Learning, Convolutional Neural Network (CNN), Deep Learning Algorithms, Machine Learning AlgorithmsPublished under a CC BY 4.0 license. Supplemental material is available for this article.

Eye-tracking as a proxy for coherence and complexity of texts.

Reading is a complex cognitive process that involves primary oculomotor function and high-level activities like attention focus and language processing. When we read, our eyes move by primary physiological functions while responding to language-processing demands. In fact, the eyes perform discontinuous twofold movements, namely, successive long jumps (saccades) interposed by small steps (fixations) in which the gaze "scans" confined locations. It is only through the fixations that information is effectively captured for brain processing. Since individuals can express similar as well as entirely different opinions about a given text, it is therefore expected that the form, content and style of a text could induce different eye-movement patterns among people. A question that naturally arises is whether these individuals' behaviours are correlated, so that eye-tracking while reading can be used as a proxy for text subjective properties. Here we perform a set of eye-tracking experiments with a group of individuals reading different types of texts, including children stories, random word generated texts and excerpts from literature work. In parallel, an extensive Internet survey was conducted for categorizing these texts in terms of their complexity and coherence, considering a large number of individuals selected according to different ages, gender and levels of education. The computational analysis of the fixation maps obtained from the gaze trajectories of the subjects for a given text reveals that the average "magnetization" of the fixation configurations correlates strongly with their complexity observed in the survey. Moreover, we perform a thermodynamic analysis using the Maximum-Entropy Model and find that coherent texts were closer to their corresponding "critical points" than non-coherent ones, as computed from the Pairwise Maximum-Entropy method, suggesting that different texts may induce distinct cohesive reading activities.

Predicting synchronized gene coexpression patterns from fibration symmetries in gene regulatory networks in bacteria.

BACKGROUND: Gene regulatory networks coordinate the expression of genes across physiological states and ensure a synchronized expression of genes in cellular subsystems, critical for the coherent functioning of cells. Here we address the question whether it is possible to predict gene synchronization from network structure alone. We have recently shown that synchronized gene expression can be predicted from symmetries in the gene regulatory networks described by the concept of symmetry fibrations. We showed that symmetry fibrations partition the genes into groups called fibers based on the symmetries of their 'input trees', the set of paths in the network through which signals can reach a gene. In idealized dynamic gene expression models, all genes in a fiber are perfectly synchronized, while less idealized models-with gene input functions differencing between genes-predict symmetry breaking and desynchronization. RESULTS: To study the functional role of gene fibers and to test whether some of the fiber-induced coexpression remains in reality, we analyze gene fibrations for the gene regulatory networks of E. coli and B. subtilis and confront them with expression data. We find approximate gene coexpression patterns consistent with symmetry fibrations with idealized gene expression dynamics. This shows that network structure alone provides useful information about gene synchronization, and suggest that gene input functions within fibers may be further streamlined by evolutionary pressures to realize a coexpression of genes. CONCLUSIONS: Thus, gene fibrations provide a sound conceptual tool to describe tunable coexpression induced by network topology and shaped by mechanistic details of gene expression.

Monolingual and bilingual language networks in healthy subjects using functional MRI and graph theory.

Bilingualism requires control of multiple language systems, and may lead to architectural differences in language networks obtained from clinical fMRI tasks. Emerging connectivity metrics such as k-core may capture these differences, highlighting crucial network components based on resiliency. We investigated the influence of bilingualism on clinical fMRI language tasks and characterized bilingual networks using connectivity metrics to provide a patient care benchmark. Sixteen right-handed subjects (mean age 42-years; nine males) without neurological history were included: eight native English-speaking monolinguals and eight native Spanish-speaking (L1) bilinguals with acquired English (L2). All subjects underwent fMRI with gold-standard clinical language tasks. Starting from active clusters on fMRI, we inferred the persistent functional network across subjects and ran centrality measures to characterize differences. Our results demonstrated a persistent network "core" consisting of Broca's area, the pre-supplementary motor area, and the premotor area. K-core analysis showed that Wernicke's area was engaged by the "core" with weaker connection in L2 than L1.

Predicting dengue outbreaks at neighbourhood level using human mobility in urban areas.

Dengue is a vector-borne disease transmitted by the Aedes genus mosquito. It causes financial burdens on public health systems and considerable morbidity and mortality. Tropical regions in the Americas and Asia are the areas most affected by the virus. Fortaleza is a city with approximately 2.6 million inhabitants in northeastern Brazil that, during the recent decades, has been suffering from endemic dengue transmission, interspersed with larger epidemics. The objective of this paper is to study the impact of human mobility in urban areas on the spread of the dengue virus, and to test whether human mobility data can be used to improve predictions of dengue virus transmission at the neighbourhood level. We present two distinct forecasting systems for dengue transmission in Fortaleza: the first using artificial neural network methods and the second developed using a mechanistic model of disease transmission. We then present enhanced versions of the two forecasting systems that incorporate bus transportation data cataloguing movement among 119 neighbourhoods in Fortaleza. Each forecasting system was used to perform retrospective forecasts for historical dengue outbreaks from 2007 to 2015. Results show that both artificial neural networks and mechanistic models can accurately forecast dengue cases, and that the inclusion of human mobility data substantially improves the performance of both forecasting systems. While the mechanistic models perform better in capturing seasons with large-scale outbreaks, the neural networks more accurately forecast outbreak peak timing, peak intensity and annual dengue time series. These results have two practical implications: they support the creation of public policies from the use of the models created here to combat the disease and help to understand the impact of urban mobility on the epidemic in large cities.

Influencer identification in dynamical complex systems.

The integrity and functionality of many real-world complex systems hinge on a small set of pivotal nodes, or influencers. In different contexts, these influencers are defined as either structurally important nodes that maintain the connectivity of networks, or dynamically crucial units that can disproportionately impact certain dynamical processes. In practice, identification of the optimal set of influencers in a given system has profound implications in a variety of disciplines. In this review, we survey recent advances in the study of influencer identification developed from different perspectives, and present state-of-the-art solutions designed for different objectives. In particular, we first discuss the problem of finding the minimal number of nodes whose removal would breakdown the network (i.e. the optimal percolation or network dismantle problem), and then survey methods to locate the essential nodes that are capable of shaping global dynamics with either continuous (e.g. independent cascading models) or discontinuous phase transitions (e.g. threshold models). We conclude the review with a summary and an outlook.

Circuits with broken fibration symmetries perform core logic computations in biological networks.

We show that logic computational circuits in gene regulatory networks arise from a fibration symmetry breaking in the network structure. From this idea we implement a constructive procedure that reveals a hierarchy of genetic circuits, ubiquitous across species, that are surprising analogues to the emblematic circuits of solid-state electronics: starting from the transistor and progressing to ring oscillators, current-mirror circuits to toggle switches and flip-flops. These canonical variants serve fundamental operations of synchronization and clocks (in their symmetric states) and memory storage (in their broken symmetry states). These conclusions introduce a theoretically principled strategy to search for computational building blocks in biological networks, and present a systematic route to design synthetic biological circuits.

Diversity increases the stability of ecosystems.

In 1972, Robert May showed that diversity is detrimental to an ecosystem since, as the number of species increases, the ecosystem is less stable. This is the so-called diversity-stability paradox, which has been derived by considering a mathematical model with linear interactions between the species. Despite being in contradiction with empirical evidence, the diversity-stability paradox has survived the test of time for over 40+ years. In this paper we first show that this paradox is a conclusion driven solely by the linearity of the model employed in its derivation which allows for the neglection of the fixed point solution in the stability analysis. The linear model leads to an ill-posed solution and along with it, its paradoxical stability predictions. We then consider a model ecosystem with nonlinear interactions between species, which leads to a stable ecosystem when the number of species is increased. The saturating non linear term in the species interaction is analogous to a Hill function appearing in systems like gene regulation, neurons, diffusion of information and ecosystems The exact fixed point solution of this model is based on k-core percolation and shows that the paradox disappears. This theoretical result, which is exact and non-perturbative, shows that diversity is beneficial to the ecosystem in agreement with analyzed experimental evidence.

Fibration symmetries uncover the building blocks of biological networks.

A major ambition of systems science is to uncover the building blocks of any biological network to decipher how cellular function emerges from their interactions. Here, we introduce a graph representation of the information flow in these networks as a set of input trees, one for each node, which contains all pathways along which information can be transmitted in the network. In this representation, we find remarkable symmetries in the input trees that deconstruct the network into functional building blocks called fibers. Nodes in a fiber have isomorphic input trees and thus process equivalent dynamics and synchronize their activity. Each fiber can then be collapsed into a single representative base node through an information-preserving transformation called "symmetry fibration," introduced by Grothendieck in the context of algebraic geometry. We exemplify the symmetry fibrations in gene regulatory networks and then show that they universally apply across species and domains from biology to social and infrastructure networks. The building blocks are classified into topological classes of input trees characterized by integer branching ratios and fractal golden ratios of Fibonacci sequences representing cycles of information. Thus, symmetry fibrations describe how complex networks are built from the bottom up to process information through the synchronization of their constitutive building blocks.

Core language brain network for fMRI language task used in clinical applications.

Functional magnetic resonance imaging (fMRI) is widely used in clinical applications to highlight brain areas involved in specific cognitive processes. Brain impairments, such as tumors, suppress the fMRI activation of the anatomical areas they invade and, thus, brain-damaged functional networks present missing links/areas of activation. The identification of the missing circuitry components is of crucial importance to estimate the damage extent. The study of functional networks associated with clinical tasks but performed by healthy individuals becomes, therefore, of paramount concern. These "healthy" networks can, indeed, be used as control networks for clinical studies. In this work we investigate the functional architecture of 20 healthy individuals performing a language task designed for clinical purposes. We unveil a common architecture persistent across all subjects under study, that we call "core" network, which involves Broca's area, Wernicke's area, the premotor area, and the pre-supplementary motor area. We study the connectivity of this circuitry by using the k-core centrality measure, and we find that three of these areas belong to the most robust structure of the functional language network for the specific task under study. Our results provide useful insights on primarily important functional connections.