A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New findings show fundamental group is not audible in spherical space forms.
The first isospectral pairs of metrics are constructed on balls and spheres. This long standing problem, concerning the existence of such pairs, has been solved by a new method called "Anticommutator Technique." Among the wide range of such pairs, the most striking examples are provided on (4k-1)-dimensional spheres, w…
Paper proves non-compact inaudibility of symmetry and commutativity.
Paper proves naturally reductive property is inaudible for certain manifolds.
Mapping states to actions in deep reinforcement learning is mainly based on visual information. The commonly used approach for dealing with visual information is to extract pixels from images and use them as state representation for reinforcement learning agent. But, any vision only agent is handicapped by not being ab…
Deep generative models such as Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs) have recently been applied to style and domain transfer for images, and in the case of VAEs, music. GAN-based models employing several generators and some form of cycle consistency loss have been among the most suc…
We study the length, weak length and complex length spectrum of closed geodesics of a compact flat Riemannian manifold, comparing length-isospectrality with isospectrality of the Laplacian acting on p-forms. Using integral roots of the Krawtchouk polynomials, we give many pairs of p-isospectral flat manifolds having di…
The wave trace of certain convex domains can be smooth near some points in the length spectrum.
We introduce coroICA, confounding-robust independent component analysis, a novel ICA algorithm which decomposes linearly mixed multivariate observations into independent components that are corrupted (and rendered dependent) by hidden group-wise stationary confounding. It extends the ordinary ICA model in a theoretical…
Inspired by the role geometric structures play in our understanding of surfaces and three-manifolds, and Berger's observation that a surface of constant sectional curvature is determined up to local isometry by its Laplace spectrum, we explore the extent to which compact locally homogeneous three-manifolds are characte…
A musical instrument based on moduli spaces lets users hear geometric concepts.
Blockchain aims to improve trust in AI systems, but lacks systematic studies.