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Vital to primary visual processing, retinal circuitry shows many similar structures across a very broad array of species, both vertebrate and non-vertebrate, especially functional components such as lateral inhibition. This surprisingly…
We generalize the SiZer of Chaudhuri and Marron (J. Amer. Statist. Assoc. 94 (1999) 807-823, Ann. Statist. 28 (2000) 408-428) for the detection of shape parameters of densities on the real line to the case of circular data. It turns out…
A classic theorem in the theory of connections on principal fiber bundles states that the evaluation of all holonomy functions gives enough information to characterize the bundle structure (among those sharing the same structure group and…
Neural systems can be modeled as networks of functionally connected neural elements. The resulting network can be analyzed using mathematical tools from network science and graph theory to quantify the system's topological organization and…
Left-right axis specification establishes embryonic laterality through asymmetric signaling cascades originating at the cellular scale. We previously reported the presence of a directionality bias in confined pairs of endothelial (and…
Convolutional networks (ConvNets) have achieved promising accuracy for various anatomical segmentation tasks. Despite the success, these methods can be sensitive to data appearance variations. Considering the large variability of scans…
The classical sparse coding model represents visual stimuli as a linear combination of a handful of learned basis functions that are Gabor-like when trained on natural image data. However, the Gabor-like filters learned by classical sparse…
Drawing parallels with hyperplane arrangements, we develop the theory of arrangements of submanifolds. Given a smooth, finite dimensional, real manifold $X$ we consider a finite collection $\mathcal{A}$ of locally flat, codimension-1…
We investigate the Coherence--Curvature Model (CCM), a dynamical ensemble of connected graphs governed by a Hamiltonian that couples algebraic connectivity, Ollivier-Ricci curvature, and an edge-density penalty. Using connected simulated…
Natural metric structures on tangent bundles and tangent sphere bundles enclose many important problems, from the topology of the base to the determination of their holonomy. We make here a brief study of the topic. We find the…
Deep convolutional neural networks (CNNs) have demonstrated impressive performance on many visual tasks. Recently, they became useful models for the visual system in neuroscience. However, it is still not clear what are learned by CNNs in…
Understanding how receptive fields emerge and organize within brain networks and how neural dynamics couple with stimuli space is fundamental to neuroscience. Models often rely on fine-tuning connectivity to match empirical data, which may…
Most machine learning-based coronary artery segmentation methods represent the vascular lumen surface in an implicit way by the centerline and the associated lumen radii, which makes the subsequent modeling process to generate a whole piece…
We show that model molecules with particular rotational symmetries can self-assemble into network structures equivalent to rhombus tilings. This assembly happens in an emergent way, in the sense that molecules spontaneously select irregular…
Rigidity transitions in simple models of confluent cells have been a powerful organizing principle in understanding the dynamics and mechanics of dense biological tissue. In this work we explore the interplay between geometry and rigidity…
In this paper we study categories of tilting modules. Our starting point is the tilting modules for a reductive algebraic group G in positive characteristic. Here we extend the main result in [8] by proving that these tilting modules form a…
In an ideal perfectly straight multimode fiber with a circular-core, the symmetry ensures that rotating the input wavefront leads to a corresponding rotation of the output wavefront. This invariant property, known as the rotational memory…
The affine Gaussian derivative model can in several respects be regarded as a canonical model for receptive fields over a spatial image domain: (i) it can be derived by necessity from scale-space axioms that reflect structural properties of…
Hair cells, the sensory receptors of the internal ear, subserve different functions in various receptor organs: they detect oscillatory stimuli in the auditory system, but transduce constant and step stimuli in the vestibular and…
Developing an idea of Kapranov and Voevodsky, we introduce a model of weak omega-categories based on directed complexes, combinatorial presentations of pasting diagrams. We propose this as a convenient framework for higher-dimensional…