Related papers: Loewner functions for bilinear systems
We show that moment inequalities in a wide variety of economic applications have a particular linear conditional structure. We use this structure to construct uniformly valid confidence sets that remain computationally tractable even in…
Function fitting/approximation plays a fundamental role in computer graphics and other engineering applications. While recent advances have explored neural networks to address this task, these methods often rely on architectures with many…
We present a technique for learning control Lyapunov (potential) functions, which are used in turn to synthesize controllers for nonlinear dynamical systems. The learning framework uses a demonstrator that implements a black-box, untrusted…
This short note gives a new framework for dealing with nonlinear sampled-data systems. We introduce a new idea of lifting, which is well known for linear systems, but not successfully generalized to nonlinear systems. This paper introduces…
This work introduces Bilinear Classes, a new structural framework, which permit generalization in reinforcement learning in a wide variety of settings through the use of function approximation. The framework incorporates nearly all existing…
A new mathematical notation is proposed for the iteration of functions. It facilitates the application of the iteration of functions in mathematical and logical expressions, definitions of sets, and formulations of algorithms. Illustrations…
The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The…
Functional methods can be applied to the quantum effective action to efficiently determine counterterms and matching conditions for effective field theories. We extend the toolbox to two-loop order and beyond and show how to evaluate the…
Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…
Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…
This work characterizes the structure of third and forth order WENO weights by deducing data bounded condition on third order polynomial approximations. Using these conditions, non-linear weights are defined for third and fourth order data…
In this paper, we propose a new easily implementable method for solving a class of semi-infinite programs, where an approximate linear semidefinite program is constructed for the concerned semi-infinite program based on the duality theory…
Various methods have been proposed to approximate a solution to the truncated Hausdorff moment problem. In this paper, we establish a method of comparison for the performance of the approximations. Three ways of producing random moment…
In quantum mechanics, the Wigner function $\rho_W(\textbf{r},\textbf{p})$ serves as a phase-space representation, capturing information about both the position $\textbf{r}$ and momentum $\textbf{p}$ of a quantum system. The Wigner function…
In this paper we deal with the well-known nonlinear Lorenz system that describes the deterministic chaos phenomenon. We consider an interesting problem with time-varying phenomena in quantum optics. Then we establish from the motion…
Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention…
The Laguerre symmetric functions introduced in the note are indexed by arbitrary partitions and depend on two continuous parameters. The top degree homogeneous component of every Laguerre symmetric function coincides with the Schur function…
Motivated by recent results of Kapron and Steinberg (LICS 2018) we introduce new forms of iteration on length in the setting of applied lambda-calculi for higher-type poly-time computability. In particular, in a type-two setting, we…
The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an…
We prove one-to-one correspondences between certain decreasing Loewner chains in the upper half-plane, a special class of real-valued Markov processes, and quantum stochastic processes with monotonically independent additive increments.…