Graph theory

Maria Chudnovsky introduces graph theory through relationships represented as vertices and edges. She discusses the perfect graph problem, practical uses of abstract structure and her path into mathematics, including an application to wedding seating, in conversation with Janna Levin.

…a geometric approach, combining Graph Theory and Riemannian Geometry to build "a graph of graphs" a

Richard Montgomery explores graph theory as the mathematics underlying networks, from infrastructure to biological connections. He discusses his contribution to the proof of Ringel’s conjecture and why extremal questions about graphs are mathematically productive. The interview follows recognition of his work with an EMS Prize.

…magneto- and electroencephalography (

…how brain areas communicate and graph theory analyses can characterise this at a network level. We modeled typical developmental trajectories of the functional connectome using graph theory to explore network-level development during childhood and adolescence. Using resting state functional MRI, we measured functional connectivity between 106 ROIs (Harvard-Oxford atlas), in a cross-sectional

This study explores the impact of past experiences on resting state brain networks in animals, particularly focusing on the difference between naive mice and those subjected to contextual fear conditioning. We analyzed the resting activity of 41 brain regions, observing significant changes in brain activity 24 hours post-learning. Mice with associative learning experience showed a notable increase in c-Fos-positive cells in specific brain areas known for their role in fear memory formation, such as the prelimbic, retrosplenial, and temporal associative cortex, alongside various amygdala nuclei

…Four graph theory metrics were computed to characterize structural networks. Structural and cognitive phenotypes were identified using an unsupervised learning algorithm, and the association between them evaluated. Three cognitive clusters were identifie

Several studies highlight motivation's crucial role in motor decision-making for maximizing potential rewards. However, how explicit rewards impact the neural dynamics of decision-making processes and their effects on neural organization at the network level, is still unexplored. To address this gap, we analyzed neuronal activity recorded from the premotor cortex (PMd) of three monkeys while performing a modified version of the stop signal task. In this task, the motivation to either act or inhibit action was manipulated using Cues that informed about different reward contexts. We conducted an

Understanding communication and information processing in nervous systems is a central goal of neuroscience. Over the past two decades, advances in connectomics and network neuroscience have opened new avenues for investigating polysynaptic communication in complex brain networks. Recent work has brought into question the mainstay assumption that connectome signalling occurs exclusively via shortest paths, resulting in a sprawling constellation of alternative network communication models. This Review surveys the latest developments in models of brain network communication. We begin by drawing

…are often represented in the form of a graph – a visual representation of connections between the elements of the system, which form a network. However, this does not mean that an ANN was designed based on graph theory or with consideration of the special properties of complex networks. These representations ar

INTRODUCTION Graph theory is a state of the art approach to assess functional connectivity (FC) disruption in neurological disorders. However, this methodology does not allow distinction between positive and negative FC correlations; negative correlations, or anticorrelations, are usually either discardes or taken as positive values, and therefore its influence is rarely studied. RESEARCH QUESTION In the present study, we used magnetoencephalography (MEG) to construct cross-frequency networks, and studied the positive and negative correlations independently and jointly, to evaluate the contri

The human brain is a complex organ characterized by heterogeneous patterns of interconnections. Non-invasive imaging techniques now allow for these patterns to be carefully and comprehensively mapped in individual humans, paving the way for a better understanding of how wiring supports cognitive processes. While a large body of work now focuses on descriptive statistics to characterize these wiring patterns, a critical open question lies in how the organization of these networks constrains the potential repertoire of brain dynamics. In this talk, I will describe an approach for understanding