Related papers: A bounded partition approach to identifying one fa…
In this paper, we effectively solve the inverse source problem of the fractional Poisson equation using MC-fPINNs. We construct two neural networks $ u_{NN}(x;\theta )$ and $f_{NN}(x;\psi)$ to approximate the solution $u^{*}(x)$ and the…
We present a family of quantum money schemes with classical verification which display a number of benefits over previous proposals. Our schemes are based on hidden matching quantum retrieval games and they tolerate noise up to 23%, which…
A method is described to solve the Poisson problem for a three dimensional source distribution that is periodic into one direction. Perpendicular to the direction of periodicity a free space (or open) boundary is realized. In beam physics,…
In order to substantiate claims of quantum computational advantage, it is crucial to develop efficient methods for validating the experimental data. We propose a test of the correct functioning of a boson sampler with single-photon inputs…
Deepfake detection methods based on convolutional neural networks (CNN) have demonstrated high accuracy. \textcolor{black}{However, these methods often suffer from decreased performance when faced with unknown forgery methods and common…
A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of…
We present a numerical method for solving the Poisson equation on a nested grid. The nested grid consists of uniform grids having different grid spacing and is designed to cover the space closer to the center with a finer grid. Thus our…
The union-find decoder is a leading algorithmic approach to the correction of quantum errors on the surface code, achieving code thresholds comparable to minimum-weight perfect matching (MWPM) with amortised computational time scaling…
Partitioning a set of elements into an unknown number of mutually exclusive subsets is essential in many machine learning problems. However, assigning elements, such as samples in a dataset or neurons in a network layer, to an unknown and…
We discuss the Fermion sign problem and, by examining a very general Hubbard-Stratonovich (HS) transformation, argue that the sign problem cannot be solved with such methods. We propose a different kind of transformation which, while not…
We investigate mathematically a nonlinear approximation type approach recently introduced in [A. Ammar et al., J. Non-Newtonian Fluid Mech., 2006] to solve high dimensional partial differential equations. We show the link between the…
We present an explicit solver of the three-dimensional screened and unscreened Poisson's equation which combines accuracy, computational efficiency and versatility. The solver, based on a mixed plane-wave / interpolating scaling function…
Large-scale well-annotated datasets are of great importance for training an effective object detector. However, obtaining accurate bounding box annotations is laborious and demanding. Unfortunately, the resultant noisy bounding boxes could…
A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition…
In 1960 R\'enyi in his Michigan State University lectures asked for the number of random queries necessary to recover a hidden bijective labeling of $n$ distinct objects. In each query one selects a random subset of labels and asks, which…
We generalize the problem of coin flipping to more than two outcomes and parties. We term this problem dice rolling, and study both its weak and strong variants. We prove by construction that in quantum settings (i) weak N-sided dice…
Deepfake detection is formulated as a hypothesis testing problem to classify an image as genuine or GAN-generated. A robust statistics view of GANs is considered to bound the error probability for various GAN implementations in terms of…
In this note we compare two measures of the complexity of a class $\mathcal F$ of Boolean functions studied in (unconditional) pseudorandomness: $\mathcal F$'s ability to distinguish between biased and uniform coins (the coin problem), and…
Boson Sampling is a computational task strongly believed to be hard for classical computers, but efficiently solvable by orchestrated bosonic interference in a specialised quantum computer. Current experimental schemes, however, are still…
Given a sequence of $N$ positive real numbers $\{a_1,a_2,..., a_N \}$, the number partitioning problem consists of partitioning them into two sets such that the absolute value of the difference of the sums of $a_j$ over the two sets is…