Symmetries and synchronization from whole-neural activity in C. elegans connectome: Integration of functional and structural networks.

Understanding the dynamical behavior of complex systems from their underlying network architectures is a long-standing question in complexity theory. Therefore, many metrics have been devised to extract network features like motifs, centrality, and modularity measures. It has previously been proposed that network symmetries are of particular importance since they are expected to underly the synchronization of a system's units, which is ubiquitously observed in nervous system activity patterns. However, perfectly symmetrical structures are difficult to assess in noisy measurements of biological systems, like neuronal connectomes. Here, we devise a principled method to infer network symmetries from combined connectome and neuronal activity data. Using nervous system-wide population activity recordings of the C.elegans backward locomotor system, we infer structures in the connectome called fibration symmetries, which can explain which group of neurons synchronize their activity. Our analysis suggests functional building blocks in the animal's motor periphery, providing new testable hypotheses on how descending interneuron circuits communicate with the motor periphery to control behavior. Our approach opens a new door to exploring the structure-function relations in other complex systems, like the nervous systems of larger animals.

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.

Dynamics and bifurcations in genetic circuits with fibration symmetries.

Circuit building blocks of gene regulatory networks (GRN) have been identified through the fibration symmetries of the underlying biological graph. Here, we analyse analytically six of these circuits that occur as functional and synchronous building blocks in these networks. Of these, the lock-on, toggle switch, Smolen oscillator, feed-forward fibre and Fibonacci fibre circuits occur in living organisms, notably Escherichia coli; the sixth, the repressilator, is a synthetic GRN. We consider synchronous steady states determined by a fibration symmetry (or balanced colouring) and determine analytic conditions for local bifurcation from such states, which can in principle be either steady-state or Hopf bifurcations. We identify conditions that characterize the first bifurcation, the only one that can be stable near the bifurcation point. We model the state of each gene in terms of two variables: mRNA and protein concentration. We consider all possible 'admissible' models-those compatible with the network structure-and then specialize these general results to simple models based on Hill functions and linear degradation. The results systematically classify using graph symmetries the complexity and dynamics of these circuits, which are relevant to understand the functionality of natural and synthetic cells.

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 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.

Neuroscience Needs Network Science.

The brain is a complex system comprising a myriad of interacting neurons, posing significant challenges in understanding its structure, function, and dynamics. Network science has emerged as a powerful tool for studying such interconnected systems, offering a framework for integrating multiscale data and complexity. To date, network methods have significantly advanced functional imaging studies of the human brain and have facilitated the development of control theory-based applications for directing brain activity. Here, we discuss emerging frontiers for network neuroscience in the brain atlas era, addressing the challenges and opportunities in integrating multiple data streams for understanding the neural transitions from development to healthy function to disease. We underscore the importance of fostering interdisciplinary opportunities through workshops, conferences, and funding initiatives, such as supporting students and postdoctoral fellows with interests in both disciplines. By bringing together the network science and neuroscience communities, we can develop novel network-based methods tailored to neural circuits, paving the way toward a deeper understanding of the brain and its functions, as well as offering new challenges for network science.

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.

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.

Association of Lack of Speech Arrest During Cortical Stimulation With Interhemispheric Reorganization of the Functional Language Network in Patients With Brain Tumors.

BACKGROUND. Brain tumors induce language reorganization, which may influence the extent of resection in surgical planning. Direct cortical stimulation (DCS) allows definitive language mapping during awake surgery by locating areas of speech arrest (SA) surrounding the tumor. Although functional MRI (fMRI) combined with graph theory analysis can illustrate whole-brain network reorganization, few studies have corroborated these findings with DCS intraoperative mapping and clinical language performance. OBJECTIVE. We evaluated whether patients with low-grade gliomas (LGGs) without SA during DCS show increased right-hemispheric connections and better speech performance compared with patients with SA. METHODS. We retrospectively recruited 44 consecutive patients with left perisylvian LGG, preoperative language task-based fMRI, speech performance evaluation, and awake surgery with DCS. We generated language networks from ROIs corresponding to known language areas (i.e., language core) on fMRI using optimal percolation. Language core connectivity in the left and right hemispheres was quantified as fMRI laterality index (LI) and connectivity LI on the basis of fMRI activation maps and connectivity matrices. We compared fMRI LI and connectivity LI between patients with SA and without SA and used multivariable logistic regression (p < .05) to assess associations between DCS and connectivity LI, fMRI LI, tumor location, Broca area and Wernicke area involvement, prior treatments, age, handedness, sex, tumor size, and speech deficit before surgery, within 1 week after surgery, and 3-6 months after surgery. RESULTS. Patients with SA showed left-dominant connectivity; patients without SA lateralized more to the right hemisphere (p < .001). Between patients with SA and those without, fMRI LI was not significantly different. Patients without SA showed right-greater-than-left connectivity of Broca area and premotor area compared with patients with SA. Regression analysis showed significant association between no SA and right-lateralized connectivity LI (p < .001) and fewer speech deficits before (p < .001) and 1 week after (p = .02) surgery. CONCLUSION. Patients without SA had increased right-hemispheric connections and right translocation of the language core, suggesting language reorganization. Lack of interoperative SA was associated with fewer speech deficits both before and immediately after surgery. CLINICAL IMPACT. These findings support tumor-induced language plasticity as a compensatory mechanism, which may lead to fewer postsurgical deficits and allow extended resection.

Neuroscience needs Network Science.

The brain is a complex system comprising a myriad of interacting elements, posing significant challenges in understanding its structure, function, and dynamics. Network science has emerged as a powerful tool for studying such intricate systems, offering a framework for integrating multiscale data and complexity. Here, we discuss the application of network science in the study of the brain, addressing topics such as network models and metrics, the connectome, and the role of dynamics in neural networks. We explore the challenges and opportunities in integrating multiple data streams for understanding the neural transitions from development to healthy function to disease, and discuss the potential for collaboration between network science and neuroscience communities. We underscore the importance of fostering interdisciplinary opportunities through funding initiatives, workshops, and conferences, as well as supporting students and postdoctoral fellows with interests in both disciplines. By uniting the network science and neuroscience communities, we can develop novel network-based methods tailored to neural circuits, paving the way towards a deeper understanding of the brain and its functions.

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.

Longitudinal Evaluation of Brain Plasticity in Low-Grade Gliomas: fMRI and Graph-Theory Provide Insights on Language Reorganization.

Language reorganization may represent an adaptive phenomenon to compensate tumor invasion of the dominant hemisphere. However, the functional changes over time underlying language plasticity remain unknown. We evaluated language function in patients with low-grade glioma (LGG), using task-based functional MRI (tb-fMRI), graph-theory and standardized language assessment. We hypothesized that functional networks obtained from tb-fMRI would show connectivity changes over time, with increased right-hemispheric participation. We recruited five right-handed patients (4M, mean age 47.6Y) with left-hemispheric LGG. Tb-fMRI and language assessment were conducted pre-operatively (pre-op), and post-operatively: post-op1 (4-8 months), post-op2 (10-14 months) and post-op3 (16-23 months). We computed the individual functional networks applying optimal percolation thresholding. Language dominance and hemispheric connectivity were quantified by laterality indices (LI) on fMRI maps and connectivity matrices. A fixed linear mixed model was used to assess the intra-patient correlation trend of LI values over time and their correlation with language performance. Individual networks showed increased inter-hemispheric and right-sided connectivity involving language areas homologues. Two patterns of language reorganization emerged: Three/five patients demonstrated a left-to-codominant shift from pre-op to post-op3 (type 1). Two/five patients started as atypical dominant at pre-op, and remained unchanged at post-op3 (type 2). LI obtained from tb-fMRI showed a significant left-to-right trend in all patients across timepoints. There were no significant changes in language performance over time. Type 1 language reorganization may be related to the treatment, while type 2 may be tumor-induced, since it was already present at pre-op. Increased inter-hemispheric and right-side connectivity may represent the initial step to develop functional plasticity.

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).

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.

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.

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.