Related papers: Towards a representer theorem for identification o…

In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued…

In quantum process tomography, it is possible to express the experimenter's prior information as a sequence of quantum operations, i.e., trace-preserving completely positive maps. In analogy to de Finetti's concept of exchangeability for…

In this paper, a bipartite output regulation problem is solved for a class of nonlinear multi-agent systems subject to static signed communication networks. A nonlinear distributed observer is proposed for a nonlinear exosystem with…

This paper is concerned with the question of reconstructing a vector in a finite-dimensional real or complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new…

It has been known that the Wigner representation theory for positive energy orbits permits a useful localization concept in terms of certain lattices of real subspaces of the complex Hilbert -space. This ''modular localization'' is not only…

This manuscript presents a novel approach to nonlinear system identification leveraging densely defined Liouville operators and a new "kernel" function that represents an integration functional over a reproducing kernel Hilbert space (RKHS)…

Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep…

To develop a unitary quantum theory with probabilistic description for pseudo- Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different…

A set of reproducing kernel Hilbert spaces are obtained on Hilbert spaces over quaternion slices with the aid of coherent states. It is proved that the so obtained set forms a measurable field of Hilbert spaces and their direct integral…

In this work, we show that neural networks can be represented via the mathematical theory of quiver representations. More specifically, we prove that a neural network is a quiver representation with activation functions, a mathematical…

A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and…

This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…

For a parameter-unknown linear descriptor system, this paper proposes data-driven methods to testify the system's type and controllability and then to stabilize it. First, a data-based condition is developed to identify whether this unknown…

A causal input-output system may be described by a function space for inputs, a function space for outputs, and a causal operator mapping the input space into the output space. A particular representation of the state of such a system at…

We consider a general class of regularization methods which learn a vector of parameters on the basis of linear measurements. It is well known that if the regularizer is a nondecreasing function of the inner product then the learned vector…

In this article, the operator approach to modeling numeral systems is introduced. This approach can be useful for coding information and providing computer protection. Certain examples of such numeral systems are considered. In addition,…

The paper deals with the data-based design of state-feedback controllers that solve the output regulation problem for a class of nonlinear systems. Inspired by recent developments in model-based output regulation design techniques and in…

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…

A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum…

We present a representation learning algorithm that learns a low-dimensional latent dynamical system from high-dimensional \textit{sequential} raw data, e.g., video. The framework builds upon recent advances in amortized inference methods…