相关论文: On Brain as a Mathematical Manifold: Neural Manifo…

A Sheaf Neural Network (SNN) is a type of Graph Neural Network (GNN) that operates on a sheaf, an object that equips a graph with vector spaces over its nodes and edges and linear maps between these spaces. SNNs have been shown to have…

In neuroscience, functional brain connectivity describes the connectivity between brain regions that share functional properties. Neuroscientists often characterize it by a time series of covariance matrices between functional measurements…

The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…

We introduce a sheaf-theoretic characterization of task solvability in general distributed computing models, unifying distinct approaches to message-passing models. We establish cellular sheaves as a natural mathematical framework for…

The human brain is a complex inter-wired system that emerges spontaneous functional fluctuations. In spite of tremendous success in the experimental neuroscience field, a system-level understanding of how brain anatomy supports various…

Human brain activity is often measured using the blood-oxygen-level dependent (BOLD) signals obtained through functional magnetic resonance imaging (fMRI). The strength of connectivity between brain regions is then measured as a Pearson…

In Functional Data Analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional…

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by…

Conceptual and mathematical models of neurons have lagged behind empirical understanding for decades. Here we extend previous work in modeling biological systems with fully scale-independent quantum information-theoretic tools to develop a…

Functional connections in the brain are frequently represented by weighted networks, with nodes representing locations in the brain, and edges representing the strength of connectivity between these locations. One challenge in analyzing…

This paper introduces function alignment, a novel theory of mind and intelligence that is both intuitively compelling and structurally grounded. It explicitly models how meaning, interpretation, and analogy emerge from interactions among…

Membrane particles such as proteins and lipids organize into zones that perform unique functions. Here, I introduce a topological and category-theoretic framework to represent particle and zone intra-scale interactions and inter-scale…

The brain is a paradigmatic example of a complex system as its functionality emerges as a global property of local mesoscopic and microscopic interactions. Complex network theory allows to elicit the functional architecture of the brain in…

Language is contextual and sheaf theory provides a high level mathematical framework to model contextuality. We show how sheaf theory can model the contextual nature of natural language and how gluing can be used to provide a global…

We present a statistical framework that jointly models brain shape and functional connectivity, which are two complex aspects of the brain that have been classically studied independently. We adopt a Riemannian modeling approach to account…

For the study of functional aspects of the brain network. This paper is a study on the hypergraph representation, based on the functional regions of the brain network. A new parameter that can measure how many multifunctioning regions each…

As data grows in size and complexity, finding frameworks which aid in interpretation and analysis has become critical. This is particularly true when data comes from complex systems where extensive structure is available, but must be drawn…

This paper introduces the concept of supermanifolds, viewed as the super-analogues of classical manifolds. Instead of treating supermanifolds as sets of points, we adopt an algebraic-geometric perspective, emphasizing the algebra of…

Functional connectivity plays an essential role in modern neuroscience. The modality sheds light on the brain's functional and structural aspects, including mechanisms behind multiple pathologies. One such pathology is schizophrenia which…

Recent developments in experimental neuroscience make it possible to simultaneously record the activity of thousands of neurons. However, the development of analysis approaches for such large-scale neural recordings have been slower than…