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The two pillars of Algebraic topology - Homology and homotopy theory rely on the availability of basic building blocks called cells. Cells take the form of simplexes, and have properties such as faces, sub-cells, convexity and…
This paper presents results of combining (i) theoretical analysis regarding connections between the orientation selectivity and the elongation of receptive fields for the affine Gaussian derivative model with (ii) biological measurements of…
The cell cortex, a thin film of active material assembled below the cell membrane, plays a key role in cellular symmetry breaking processes such as cell polarity establishment and cell division. Here, we present a minimal model of the…
Continuous attractor networks (CANs) are widely used to model how the brain temporarily retains continuous behavioural variables via persistent recurrent activity, such as an animal's position in an environment. However, this memory…
The human visual system has a hierarchical structure consisting of layers of processing, such as the retina, V1, V2, etc. Understanding the functional roles of these visual processing layers would help to integrate the psychophysiological…
Protrusions at the leading-edge of a cell play an important role in sensing the extracellular cues, during cellular spreading and motility. Recent studies provided indications that these protrusions wrap (coil) around the extra-cellular…
Neuronal circuits of the cerebral cortex are the structural basis of mammalian cognition. The same qualitative components and connectivity motifs are repeated across functionally specialized cortical areas and mammalian species, suggesting…
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,…
Symmetry is closely intertwined with the function, genetics, and chemical properties of multiprotein complexes. Here, we explore the relation between structural symmetry and the ability of membrane proteins to sense and induce membrane…
We introduce a deep recurrent neural network architecture that approximates visual cortical circuits. We show that this architecture, which we refer to as the gamma-net, learns to solve contour detection tasks with better sample efficiency…
This paper gives an in-depth theoretical analysis of the direction and speed selectivity properties of idealized models of the spatio-temporal receptive fields of simple cells and complex cells, based on the generalized Gaussian derivative…
A contact twisted cubic structure (M,C,S) is a 5-dimensional manifold M together with a contact distribution C and a bundle S of twisted cubics that is compatible with the conformal symplectic form on C. In Engel's classical work, the Lie…
Interpreting computations in the visual cortex as learning and inference in a generative model of the environment has received wide support both in neuroscience and cognitive science. However, hierarchical computations, a hallmark of visual…
The operational characteristics of a linear neural network image processing system based on the brain's vision system are investigated. The final stage of the network consists of edge detectors of various orienations arranged in a feature…
Cell shape changes are largely controlled by the actin cytoskeleton, a dynamic filament network beneath the plasma membrane. Several cell types can form extended free-standing protrusions not supported by an extracellular substrate or…
A Cartan-geometric, jet bundle formulation of curvature-aware variance bounds in parametric statistical estimation is developed. Building on our earlier extrinsic Hilbert space approach to the Cram\'er-Rao and Bhattacharyya-type…
We develop a model for representing visual texture in a low-dimensional feature space, along with a novel self-supervised learning objective that is used to train it on an unlabeled database of texture images. Inspired by the architecture…
We propose and theoretically study a new hollow-core fiber-based curvature sensor with the capability of detecting both bending magnitude and angle (direction). The new sensor relies on a tubular-lattice fiber that encompasses, in its…
Self-organization of orientation-wheels observed in the visual cortex is discussed from the view point of topology. We argue in a generalized model of Kohonen's feature mappings that the existence of the orientation-wheels is a consequence…
In this note we consider a few interesting properties of discrete connections on principal bundles when the structure group of the bundle is an abelian Lie group. In particular, we show that the discrete connection form and its curvature…