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Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
Visual information is processed in hierarchically organized parallel pathways in the primate brain. In lower cortical areas, color information and shape information are processed in a parallel manner, while in higher cortical areas, various…
Understanding how the statistical and geometric properties of neural activity relate to performance is a key problem in theoretical neuroscience and deep learning. Here, we calculate how correlations between object representations affect…
Brain morphometry study plays a fundamental role in neuroimaging research. In this work, we propose a novel method for brain surface morphometry analysis based on surface foliation theory. Given brain cortical surfaces with automatically…
Modern artificial neural networks, including convolutional neural networks and vision transformers, have mastered several computer vision tasks, including object recognition. However, there are many significant differences between the…
Brain representations of curvature may be formed on the basis of either vision or touch. Experimental and theoretical work by the author and her colleagues has shown that the processing underlying such representations directly depends on…
This paper describes how realistic neuromorphic networks can have their connectivity properties fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…
We present a study on connection errors in networks of linear features and methods of error detection. We model networks with special connection specifications as networks with hierarchically connected features and define errors considering…
A method for extracting multiscale geometric features from a data cloud is proposed and analyzed. The basic idea is to map each pair of data points into a real-valued feature function defined on $[0,1]$. The construction of these feature…
Psychometrics and quantitative psychology rely strongly on statistical models to measure psychological processes. As a branch of mathematics, geometry is inherently connected to measurement and focuses on properties such as distance and…
This paper studies 3D dense shape correspondence, a key shape analysis application in computer vision and graphics. We introduce a novel hybrid geometric deep learning-based model that learns geometrically meaningful and…
The human cortical layer exhibits a convoluted morphology that is unique to each individual. Conventional volumetric fMRI processing schemes take for granted the rich information provided by the underlying anatomy. We present a method to…
Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities…
Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little…
Microscopic analysis of histological sections is considered the "gold standard" to verify structural parcellations in the human brain. Its high resolution allows the study of laminar and columnar patterns of cell distributions, which build…
Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…
For most animal species, quick and reliable identification of visual objects is critical for survival. This applies also to rodents, which, in recent years, have become increasingly popular models of visual functions. For this reason in…
Understanding the nature of the changes exhibited by evolving neuronal dynamics from high-dimensional activity data is essential for advancing neuroscience, particularly in the study of neuronal network development and the pathophysiology…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…