Related papers: An Optimal-Dimensionality Sampling for Spin-$s$ Fu…
Spherical $t$-designs on $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$ provide $N$ nodes for an equal weight numerical integration rule which is exact for all spherical polynomials of degree at most $t$. This paper considers the generation of…
In this manuscript, we present a novel approach for sampling from a continuous multivariate probability distribution, which may either be explicitly known (up to a normalization factor) or represented via empirical samples. Our method…
We explore the degrees of freedom required to jointly fit projected and redshift-space clustering of galaxies selected in three bins of stellar mass from the Sloan Digital Sky Survey Main Galaxy Sample (SDSS MGS) using a subhalo abundance…
We present a theoretical framework for analyzing spatial sampling of fields in three-dimensional space. The framework bridges Shannon's sampling and information theory to Bayesian probabilistic inference and experimental design. Based on…
A utility-function approach to optimal spatial sampling design is a powerful way to quantify what "optimality" means. The emphasis then should be to capture all possible contributions to utility, including scientific impact and the cost of…
A new method is presented that allows for efficient evaluation of spin-orbit coupling (SOC) in density-functional theory calculations. In the so-called second-variational scheme, where Kohn-Sham functions obtained in a scalar-relativistic…
We investigate the sampling-based optimal path planning problem for robotics in complex and dynamic environments. Most existing sampling-based algorithms neglect environmental information or the information from previous samples. Yet, these…
In this paper, we investigate in detail the structures of the variational characterization $A_{N,t}$ of the spherical $t$-design, its gradient $\nabla A_{N,t}$, and its Hessian $\mathcal{H}(A_{N,t})$ in terms of fast spherical harmonic…
The quantum geometric tensor (QGT) embodies the geometry of the eigenstates of a system's Hamiltonian, and its full characterization across diverse quantum systems is essential. However, it is challenging to characterize the QGT of…
We study the large $N$-dimensional limit of the Hessian spectrum at the global minimum of some subclasses of the spherical mixed $p$-spin models. Specifically, we show that its empirical spectral measure converges in probability to a…
We determine optimal designs for some regression models which are frequently used for describing three-dimensional shapes. These models are based on a Fourier expansion of a function defined on the unit sphere in terms of spherical harmonic…
Spin squeezing provides crucial quantum resource for quantum metrology and quantum information science. Here we propose that one axis-twisted (OAT) spin squeezing can be generated from free evolution under a general coupled-spin model with…
We study the problem of sampling a random signal with sparse support in frequency domain. Shannon famously considered a scheme that instantaneously samples the signal at equispaced times. He proved that the signal can be reconstructed as…
We revisit the classical problem of finding an approximately stationary point of the average of $n$ smooth and possibly nonconvex functions. The optimal complexity of stochastic first-order methods in terms of the number of gradient…
The evolution of the scanning modules for scanning transmission electron microscopes (STEM) has realized the possibility to generate arbitrary scan pathways, an approach currently explored to improve acquisition speed and to reduce electron…
Logconcave functions represent the current frontier of efficient algorithms for sampling, optimization and integration in R^n. Efficient sampling algorithms to sample according to a probability density (to which the other two problems can…
We propose a trajectory-based method for simulating nonadiabatic dynamics in molecular systems with two coupled electronic states. Employing a quantum-mechanically exact mapping of the two-level problem to a spin-1/2 coherent state, we…
This paper investigates aliasing effects emerging from the reconstruction from discrete samples of spin spherical random fields defined on the two-dimensional sphere. We determine the location in the frequency domain and the intensity of…
We study the random sampling of band-limited functions of several variables. If a bandlimited function with bandwidth one has its essential support on a cube of volume $R^d$, then $\cO (R^d \log R^d)$ random samples suffice to approximate…
This paper is concerned with the problem of frequency estimation from multiple-snapshot data. It is well-known that ESPRIT (and spatial-smoothing ESPRIT in presence of coherent sources or given limited snapshots) can locate the true…