Related papers: Separable Dual Space Gaussian Pseudo-potentials
We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble…
Accurate ab initio modelling of surfaces and interfaces, especially under an applied external potential bias, is important for describing and characterizing various phenomena that occur in electronic, catalytic, and energy storage devices.…
We show how certain non-perturbative superpotentials W, which are the two-dimensional analogs of the Seiberg-Witten prepotential in 4d, can be computed via geometric engineering from 4-folds. We analyze an explicit example for which the…
We show a power 2.5 separation between bounded-error randomized and quantum query complexity for a total Boolean function, refuting the widely believed conjecture that the best such separation could only be quadratic (from Grover's…
With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of…
Since in periodic systems, a given element may be present in different spatial arrangements displaying vastly different physical and chemical properties, an elemental basis set that is independent of physical properties of materials may…
The sparse pseudo-input Gaussian process (SPGP) is a new approximation method for speeding up GP regression in the case of a large number of data points N. The approximation is controlled by the gradient optimization of a small set of M…
We discuss the requirements of good statistics for quantifying non-Gaussianity in the Cosmic Microwave Background. The importance of rotational invariance and statistical independence is stressed, but we show that these are sometimes…
Many real world problems exhibit patterns that have periodic behavior. For example, in astrophysics, periodic variable stars play a pivotal role in understanding our universe. An important step when analyzing data from such processes is the…
New solutions for second-order intertwining relations in two-dimensional SUSY QM are found via the repeated use of the first order supersymmetrical transformations with intermediate constant unitary rotation. Potentials obtained by this…
We give a factorization procedure for a strictly hyperbolic partial differential operator of second order with logarithmic slow scale coefficients. From this we can microlocally diagonalize the full wave operator which results in a coupled…
A magnetic separation algorithm originally introduced by Gauss has been revisited in recent years with application to magnetically-confined fusion experiments. The main result offered by Gauss' Separation Algorithm~(GSA) is a magnetic field…
We develop an automated procedure to select the local potential of a separable pseudopotential that minimizes transferability errors for the isolated atom, and we show that this optimization leads to significant improvements in the accuracy…
We conduct a theoretical study to understand the periodic superradiance observed in an Er:YSO crystal. First, we construct a model based on the Maxwell-Bloch equations for a reduced level system, a pair of superradiance states and a…
In paper approach of double complex SUSY-transformations with not coincident complex energies of transformation is developed, allowing to deform given real potential $V_{1}$ with obtaining exact solutions. The explicit solutions of the…
We study a generalization of the Gaussian effective potential for self-interacting scalar fields in one and two spatial dimensions. We compute the two-loop corrections and discuss the renormalization of the generalized Gaussian effective…
Sharing the spectrum with in-band full-duplex (FD) primary users (PU) is a challenging and interesting problem in the underlay cognitive radio (CR) systems. The self-interference introduced at the primary network may dramatically impede the…
The sum-rate capacity of the parallel Gaussian interference channel is shown to be achieved by independent transmission across sub-channels and treating interference as noise in each sub-channel if the channel coefficients and power…
We propose an algorithm for Bayesian functional optimisation - that is, finding the function to optimise a process - guided by experimenter beliefs and intuitions regarding the expected characteristics (length-scale, smoothness, cyclicity…
Using the Nikiforov-Uvarov (NU) method, the energy levels and the wave functions of an electron confined in a two-dimensional (2D) pseudoharmonic quantum dot are calculated under the influence of temperature and an external magnetic field…