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Multimodal MRI offers complementary multi-scale information to characterize the brain structure. However, it remains challenging to effectively integrate multimodal MRI while achieving neuroscience interpretability. Here we propose to use…
Conformal fields are a recently discovered class of representations of the algebra of vector fields in $N$ dimensions. Invariant first-order differential operators (exterior derivatives) for conformal fields are constructed.
We use two ingredients to prove the hyperbolicity of generic hypersurfaces of sufficiently high degree and of their complements in the complex projective space. One is the pullbacks of appropriate low pole order meromorphic jet…
Let K be the Lie superalgebra of contact vector fields on the supersymmetric line. We compute the action of K on the modules of differential and pseudodifferential operators between spaces of tensor densities, in terms of their conformal…
We develop a human-centred, cognitive model of visuospatial complexity in everyday, naturalistic driving conditions. With a focus on visual perception, the model incorporates quantitative, structural, and dynamic attributes identifiable in…
We investigate, in some details, symplectic equivalence between several conformal classes of Lorentz metrics on the hyperboloid of one sheet $H^{1,1} \cong T \times T - \Delta$ and affine coadjoint orbits of the group $Diff_+(\Delta)$ of…
We derive correspondences of correlation functions among dual conformal field theories in two dimensions by developing a "first order formulation" of coset models. We examine several examples, and the most fundamental one may be a…
Tree-like structures such as retinal images are widely studied in computer-aided diagnosis systems for large-scale screening programs. Despite several segmentation and tracking methods proposed in the literature, there still exist several…
The architecture of iso-orientation domains in the primary visual cortex of placental carnivores and primates apparently follows species invariant quantitative laws. Dynamical optimization models assuming that neurons coordinate their…
Using conformal field theory, we derive several new crossing formulas at the two-dimensional percolation point. High-precision simulation confirms these results. Integrating them gives a unified derivation of Cardy's formula for the…
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…
Accurate cortical surface reconstruction from magnetic resonance imaging (MRI) data is crucial for reliable neuroanatomical analyses. Current methods have to contend with complex cortical geometries, strict topological requirements, and…
We present and analyze a framework for designing symplectic neural networks (SympNets) based on geometric integrators for Hamiltonian differential equations. The SympNets are universal approximators in the space of Hamiltonian…
Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where…
Geometrical optical illusions have been object of many studies due to the possibility they offer to understand the behaviour of low-level visual processing. They consist in situations in which the perceived geometrical properties of an…
In this paper, we will study the following pattern recognition problem: Every pattern is a 3-dimensional graph, its surface can be split up into some regions, every region is composed of the pixels with the approximately same colour value…
Understanding how neural activity gives rise to perception is a central challenge in neuroscience. We address the problem of decoding visual information from high-density intracortical recordings in primates, using the THINGS Ventral Stream…
This Dissertation is comprised of two main projects, addressing questions in neuroscience through applications of generative modeling. Project #1 (Chapter 4) explores how neurons encode features of the external world. I combine Helmholtz's…
Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the…
We introduce decorated piecewise hyperbolic and spherical surfaces and discuss their discrete conformal equivalence. A decoration is a choice of circle about each vertex of the surface. Our decorated surfaces are closely related to…