Related papers: Tensor-Lifted Multivariate Functional Calculus Bey…
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking…
Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing…
Modern ConvNets continue to achieve state-of-the-art results over a vast array of vision and image classification tasks, but at the cost of increasing parameters. One strategy for compactifying a network without sacrificing much expressive…
A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…
Spectral theory and functional calculus for unbounded self-adjoint operators on a Hilbert space are usually treated through von Neumann's Cayley transform. Based on ideas of Woronowicz, we redevelop this theory from the point of view of…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
This paper refines the main results from our previous study on sparse bounds of generalized commutators of multilinear fractional singular integral operators in \cite{CenSong2412}. The key improvements are: 1. We replace pointwise…
In this paper we introduce Hausdorff locally convex algebra topologies on subalgebras of the whole algebra of nonlinear generalized functions. These topologies are strong duals of Fr\'echet-Schwartz space topologies and even strong duals of…
We consider a functional calculus for compact operators, acting on the singular values rather than the spectrum, which appears frequently in applied mathematics. Necessary and sufficient conditions for this singular value functional…
Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…
The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest,…
In this paper, we develop new continuous and discrete relaxations for nonlinear expressions in an MINLP. In contrast to factorable programming, our techniques utilize the inner-function structure by encapsulating it in a polyhedral set,…
We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional 2D and 3D elliptic operators with variable coefficients. We solve the governing equation for the control function which…
We set up a parametrised monadic translation for a class of call-by-value functional languages, and prove a corresponding soundness theorem. We then present a series of concrete instantiations of our translation, demonstrating that a number…
Though there has been substantial progress in developing quantum algorithms to study classical datasets, the cost of simply \textit{loading} classical data is an obstacle to quantum advantage. When the amplitude encoding is used, loading an…
We describe classical top-like integrable systems arising from the quantum exchange relations and corresponding Sklyanin algebras. The Lax operator is expressed in terms of the quantum non-dynamical $R$-matrix even at the classical level,…
Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…
Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…
We introduce the new notion of a conjugate weight function and provide a detailed study of this operation and its properties. Then we apply this knowledge to study classes of ultradifferentiable functions defined in terms of fast growing…
Unravelings provide a probabilistic representation of solutions of master equations and a method of computation of the density operator dynamics. The trajectories generated by unravelings may also be treated as real -- as in the stochastic…