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The growth of several biological tissues is known to be controlled in part by local geometrical features, such as the curvature of the tissue interface. This control leads to changes in tissue shape that in turn can affect the tissue's…

Cross-sections of cell shapes in a tissue monolayer typically resemble a tiling of convex polygons. Yet, examples exist where the polygons are not convex with curved cell-cell interfaces, as seen in the adaxial epidermis. To date,…

The neural manifold hypothesis postulates that the activity of a neural population forms a low-dimensional manifold whose structure reflects that of the encoded task variables. In this work, we combine topological deep generative models and…

The emergence of explainability methods has enabled a better comprehension of how deep neural networks operate through concepts that are easily understood and implemented by the end user. While most explainability methods have been designed…

Understanding the relation between cortical neuronal network structure and neuronal activity is a fundamental unresolved question in neuroscience, with implications to our understanding of the mechanism by which neuronal networks evolve…

Tomographic imaging reveals internal structures of 3D objects and is crucial for medical diagnoses. Visualizing the morphology and appearance of non-planar sparse anatomical structures that extend over multiple 2D slices in tomographic…

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…

The field of computational modeling of the brain is advancing so rapidly that now it is possible to model large scale networks representing different brain regions with a high level of biological detail in terms of numbers and synapses. For…

Deep convolutional neural networks (CNNs) trained on objects and scenes have shown intriguing ability to predict some response properties of visual cortical neurons. However, the factors and computations that give rise to such ability, and…

Cell monolayers are a central model system to tissue biophysics. In vivo, epithelial tissues are curved on the scale of microns, and curvature's role in the onset of spontaneous tissue flows is still not well-understood. Here, we present a…

As the cover of embryos and adult organisms, epithelial tissues are subjected to substantial mechanical forces in tissue morphogenesis. However, the finite deformation behaviors of epithelial tissues remain largely unexplored. This study…

Identifying cerebral cortex layers is crucial for comparative studies of the cytoarchitecture aiming at providing insights into the relations between brain structure and function across species. The absence of extensive annotated datasets…

We consider the problem of finding an accurate representation of neuron shapes, extracting sub-cellular features, and classifying neurons based on neuron shapes. In neuroscience research, the skeleton representation is often used as a…

Exploiting the specific structure of neuron conductance-based models, the paper investigates the mathematical modeling of neuronal bursting modulation. The proposed approach combines singularity theory and geometric singular perturbations…

We propose a framework for jointly modeling the geometry and functionality in high dimensional functional surfaces. The proposed mixed effects model characterizes effects of subject-specific covariates and exogenous stimuli on functional…

Neurons in the visual cortex are correlated in their variability. The presence of correlation impacts cortical processing because noise cannot be averaged out over many neurons. In an effort to understand the functional purpose of…

Understanding body part geometry is crucial for precise medical diagnostics. Curves effectively describe anatomical structures and are widely used in medical imaging applications related to cardiovascular, respiratory, and skeletal…

We model the elasticity of the cerebral cortex as a layered material with bending energy along the layers and elastic energy between them in both planar and polar geometries. The cortex is also subjected to axons pulling from the underlying…

We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive…

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…