相关论文: A cortical-inspired sub-Riemannian model for Pogge…

There has been great progress in understanding of anatomical and functional microcircuitry of the primate cortex. However, the fundamental principles of cortical computation - the principles that allow the visual cortex to bind retinal…

In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…

The heat kernel associated with an elliptic second-order partial differential operator of Laplace type acting on smooth sections of a vector bundle over a Riemannian manifold, is studied. A general manifestly covariant method for…

We study spectral properties of sub-Riemannian Laplacians, which are hypoelliptic operators. The main objective is to obtain quantum ergodicity results, what we have achieved in the 3D contact case. In the general case we study the…

We assess the use of variational quantum imaginary time evolution for solving partial differential equations. Our results demonstrate that real-amplitude ansaetze with full circular entangling layers lead to higher-fidelity solutions…

Coherent, continuous spatial representations are critical for synthesizing physical and perceptual phenomena into a single representational space. Radial basis kernels provide a path forward for this type of distributed representation. In…

Computationally weak systems and demanding graphical applications are still mostly dependent on linear blendshapes for facial animations. The accompanying artifacts such as self-intersections, loss of volume, or missing soft tissue…

This paper advocates Riemannian multi-manifold modeling in the context of network-wide non-stationary time-series analysis. Time-series data, collected sequentially over time and across a network, yield features which are viewed as points…

Graph kernels based on the $1$-dimensional Weisfeiler-Leman algorithm and corresponding neural architectures recently emerged as powerful tools for (supervised) learning with graphs. However, due to the purely local nature of the…

Geometrical illusions are a subclass of optical illusions in which the geometrical characteristics of patterns such as orientations and angles are distorted and misperceived as the result of low- to high-level retinal/cortical processing.…

Reconstructing visual stimulus (image) only from human brain activity measured with functional Magnetic Resonance Imaging (fMRI) is a significant and meaningful task in Human-AI collaboration. However, the inconsistent distribution and…

We propose a novel online learning paradigm for nonlinear-function estimation tasks based on the iterative projections in the L2 space with probability measure reflecting the stochastic property of input signals. The proposed learning…

Multimodal imaging has transformed neuroscience research. While it presents unprecedented opportunities, it also imposes serious challenges. Particularly, it is difficult to combine the merits of the interpretability attributed to a simple…

Quantum imaging has a potential of enhancing precision of the object reconstruction by using quantum correlations of the imaging field. This is especially important for imaging requiring low-intensity fields up to the level of few-photons.…

With the aim of creating virtual cloth deformations more similar to real world clothing, we propose a new computational framework that recasts three dimensional cloth deformation as an RGB image in a two dimensional pattern space. Then a…

The heat kernel for the Cauchy-Riemann subLaplacian on S(2n+1) is derived in a manner which is completely analogous to the classical derivation of elliptic heat kernels. This suggests that the classical hamiltonian construction of elliptic…

A variety of modeling techniques have been developed in the past decade to reduce the computational expense and improve the accuracy of modeling. In this study, a new framework of modeling is suggested. Compared with other popular methods,…

Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of…

The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…

Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…