Spectral peculiarity and criticality of a human connectome

Free-energy density functional for Strauss's model of transitive networks

Ensemble models of graphs are one of the most important theoretical tools to study complex networks. Among them, exponential random graphs (ERGs) have proven to be very useful in the analysis of social networks. In this paper we develop a technique, borrowed from the statistical mechanics of lattice gases, to solve Strauss's model of transitive networks. This model was introduced long ago as an ERG ensemble for networks with high clustering and exhibits a first-order phase transition above a critical value of the triangle interaction parameter where two different kinds of networks with different densities of links (or, alternatively, different clustering) coexist. Compared to previous mean-field approaches, our method describes accurately even small networks and can be extended beyond Strauss's classical model-e.g., to networks with different types of nodes. This allows us to tackle, for instance, models with node homophily. We provide results for the latter and show that they accurately reproduce the outcome of Monte Carlo simulations.

DotMotif: an open-source tool for connectome subgraph isomorphism search and graph queries

Recent advances in neuroscience have enabled the exploration of brain structure at the level of individual synaptic connections. These connectomics datasets continue to grow in size and complexity; methods to search for and identify interesting graph patterns offer a promising approach to quickly reduce data dimensionality and enable discovery. These graphs are often too large to be analyzed manually, presenting significant barriers to searching for structure and testing hypotheses. We combine graph database and analysis libraries with an easy-to-use neuroscience grammar suitable for rapidly constructing queries and searching for subgraphs and patterns of interest. Our approach abstracts many of the computer science and graph theory challenges associated with nanoscale brain network analysis and allows scientists to quickly conduct research at scale. We demonstrate the utility of these tools by searching for motifs on simulated data and real public connectomics datasets, and we share simple and complex structures relevant to the neuroscience community. We contextualize our findings and provide case studies and software to motivate future neuroscience exploration.

Introduction to the special issue on physics of mind

In recent years, both fields of physics and psychology have made important scientific advances. The emergence of new instruments gave rise to a data-driven neuroscience allowing us to learn about the state of the brain supporting known mental functions and conversely. In parallel, the appearance of new mathematics allowed the development of computational models describing fundamental brain functions and implementing them in technological applications. While emphasizing the methodology of physics, the special issue aims to bring together these trends in both the experimental and theoretical sciences in order to explain some of the most basic mental processes such as perception, cognition, emotion, consciousness, and learning. In this editorial, we define unsolved problems for brain and psychological sciences, discuss possible means toward their respective solutions, and outline some collaborative initiatives aiming toward these goals. The following problems are defined in gradual order of difficulty: what are the universal properties of human behavior across conditions and cultures? What have each culture learned over historical times and why should specific elements of knowledge be accumulated over cultural evolution? Can computational psychiatry help predict, understand, and cure mental disorders? What is the function of art and cultural artifacts such as music, fiction, or poetry for the cognitive system? How to explain the relation between first-person subjective experience and third-person objective physiological data? What neural mechanisms operate on which mental content at the highest levels of organization of the hierarchical brain? How do abstract ideas emerge from sensory-motor contingencies and what are the conditions for the birth of a new concept? Could symmetry play a role in psychogenesis and support the emergence of new hierarchical layers in cognition? How can we start addressing the question of meaning scientifically, and what does it entail for the physical sciences?