Related papers: Towards a Classification of Multi-Faced Independen…
We use the theory of fully matricial, or non-commutative, functions to investigate infinite divisibility and limit theorems in operator-valued non-commutative probability. Our main result is an operator-valued analogue of the Bercovici-Pata…
Precise representations of 3D faces are beneficial to various computer vision and graphics applications. Due to the data discretization and model linearity, however, it remains challenging to capture accurate identity and expression clues…
The datasets of face recognition contain an enormous number of identities and instances. However, conventional methods have difficulty in reflecting the entire distribution of the datasets because a mini-batch of small size contains only a…
Automatic face recognition is a research area with high popularity. Many different face recognition algorithms have been proposed in the last thirty years of intensive research in the field. With the popularity of deep learning and its…
We show that the level sets of automorphisms of free groups with respect to the Lipschitz metric are connected as subsets of Culler-Vogtmann space. In fact we prove our result in a more general setting of deformation spaces. As…
This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
This article is a fundamental study in computable analysis. In the framework of Type-2 effectivity, TTE, we investigate computability aspects on finite and infinite products of effective topological spaces. For obtaining uniform results we…
We continue to develop the theory of monads and multitensors. The central result of this paper - the lifting theorem for multitensors - enables us to see the Gray tensor product of 2-categories and the Crans tensor product of Gray…
In their usual form, representation independence metatheorems provide an external guarantee that two implementations of an abstract interface are interchangeable when they are related by an operation-preserving correspondence. If our…
Let $x$ be an $m$-dimensional umbilic-free hypersurface in an $(m+1)$-dimensional unit sphere $\mathbb{S}^{m+1}(m\geq3)$. One of important questions is to classify hypersurfaces with two distinct principal curvatures. In this paper, we…
This paper concerns the self-similarity of topological spaces, in the sense defined in math.DS/0411344. I show how to recognize self-similar spaces, or more precisely, universal solutions of self-similarity systems. Examples include the…
The Hardy space H^2(R) for the upper half plane together with a unimodular function group representation u(\lambda) = \exp(i(\lambda_1\psi_1 + ... + \lambda_n\psi_n)) for \lambda in R^n, gives rise to a manifold M of orthogonal projections…
We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…
Machine learning is typically framed from a perspective of i.i.d., and more importantly, isolated data. In parts, federated learning lifts this assumption, as it sets out to solve the real-world challenge of collaboratively learning a…
The purpose of this work is to close the local deformation problem of rank two Euclidean submanifolds in codimension two by describing their moduli space of deformations. In the process, we provide an explicit simple representation of these…
Recently, multi-view representation learning has become a rapidly growing direction in machine learning and data mining areas. This paper introduces two categories for multi-view representation learning: multi-view representation alignment…
Current face recognition systems typically operate via classification into known identities obtained from supervised identity annotations. There are two problems with this paradigm: (1) current systems are unable to benefit from often…
It is essential yet challenging for future home-assistant robots to understand and manipulate diverse 3D objects in daily human environments. Towards building scalable systems that can perform diverse manipulation tasks over various 3D…
We prove a boundedness criterion for a class of dyadic multilinear forms acting on two-dimensional functions. Their structure is more general than the one of classical multilinear Calder\'{o}n-Zygmund operators as several functions can now…