Related papers: Truncated Moment Problem for Dirac Mixture Densiti…
Resonance plays critical roles in the formation of many physical phenomena, and many techniques have been developed for the exploration of resonance. In a recent letter [Phys. Rev. Lett. 117, 062502 (2016)], we proposed a new method for…
Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical post-processing resources growing exponentially…
We present an alternating least squares type numerical optimization scheme to estimate conditionally-independent mixture models in $\mathbb{R}^n$, without parameterizing the distributions. Following the method of moments, we tackle an…
Understanding posterior contraction behavior in Bayesian hierarchical models is of fundamental importance, but progress in this question is relatively sparse in comparison to the theory of density estimation. In this paper, we study two…
Linear stationary reaction-convection-diffusion equations with Dirichlet boundary conditions are approximated using a simple finite difference method corresponding to central differences and the addition of a high-order stabilization term…
Estimating the p-th frequency moment of data stream is a very heavily studied problem. The problem is actually trivial when p = 1, assuming the strict Turnstile model. The sample complexity of our proposed algorithm is essentially O(1) near…
We investigate when a linear functional $L$ defined on a linear subspace $B$ of a unital commutative real algebra $A$ admits an integral representation w.r.t. a positive Radon measure supported on a closed subset $K$ of the character space…
Progress on modern scientific questions regularly depends on using large-scale datasets to understand complex dynamical systems. An especially challenging case that has grown to prominence with advances in single-cell sequencing…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
The Collatz Conjecture's connection to dynamical systems opens it to a variety of techniques aimed at recurrence and density results. First, we turn to density results and strengthen the result of Terras through finding a strict rate of…
We study mixed-moment models (full zeroth moment, half higher moments) for a Fokker-Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcome the zero net-flux problem of full-moment minimum entropy…
The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The problem is singular and the perturbation series is asymptotic, so that the methods for…
Estimating truncated density models is difficult, as these models have intractable normalising constants and hard to satisfy boundary conditions. Score matching can be adapted to solve the truncated density estimation problem, but requires…
This paper studies distributionally robust optimization (DRO) when the ambiguity set is given by moments for the distributions. The objective and constraints are given by polynomials in decision variables. We reformulate the DRO with…
We study the problem of learning a distribution from samples, when the underlying distribution is a mixture of product distributions over discrete domains. This problem is motivated by several practical applications such as crowd-sourcing,…
We study the truncated multidimensional moment problem with a general type of truncations. The operator approach to the moment problem is presented. A way to construct atomic solutions of the moment problem is indicated.
In the linear random effects model, when distributional assumptions such as normality of the error variables cannot be justified, moments may serve as alternatives to describe relevant distributions in neighborhoods of their means.…
A moment body is a linear projection of the spectraplex, the convex set of trace-one positive semidefinite matrices. Determining whether a given point lies within a given moment body is a problem with numerous applications in quantum state…
Eigenvalues are defined for any element of an algebra of observables and do not require a representation in terms of wave functions or density matrices. A systematic algebraic derivation based on moments is presented here for the harmonic…
In the phase retrieval problem, an unknown vector is to be recovered given quadratic measurements. This problem has received considerable attention in recent times. In this paper, we present an algorithm to solve a nonconvex formulation of…