相关论文: Implementation of standard testbeds for numerical …

Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…

Generating confidence calibrated outputs is of utmost importance for the applications of deep neural networks in safety-critical decision-making systems. The output of a neural network is a probability distribution where the scores are…

Many beautiful experiments have been addressed to test standard quantum mechanics against local realistic models. Even if a strong evidence favouring standard quantum mechanics is emerged, a conclusive experiment is still lacking, because…

The paper estimates the Chernoff rate for the efficiency of quantum hypothesis testing. For both joint and separable measurements, approximate bounds for the rate are given if both states are mixed and exact expressions are derived if at…

This work provides an additional step in the theoretical understanding of neural networks. We consider neural networks with one hidden layer and show that when learning symmetric functions, one can choose initial conditions so that standard…

In this paper, we propose a new primality test, and then we employ this test to find a formula for {\pi} that computes the number of primes within any interval. We finally propose a new formula that computes the nth prime number as well as…

Quantifying the robustness of neural networks or verifying their safety properties against input uncertainties or adversarial attacks have become an important research area in learning-enabled systems. Most results concentrate around the…

Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…

In this article, we try to explain and unify standard divisibility tests found in various books. We then look at recurring decimals, and list a few of their properties. We show how to compute the number of digits in the recurring part of…

Recently, network error correction coding (NEC) has been studied extensively. Several bounds in classical coding theory have been extended to network error correction coding, especially the Singleton bound. In this paper, following the…

In this paper we show error bounds for randomly subsampled rank-1 lattices. We pay particular attention to the ratio of the size of the subset to the size of the initial lattice, which is decisive for the computational complexity. In the…

Local robustness verification can verify that a neural network is robust wrt. any perturbation to a specific input within a certain distance. We call this distance Robustness Radius. We observe that the robustness radii of correctly…

Theoretical considerations of Bell-inequality experiments usually assume identically prepared and independent pairs of particles. Here we consider pairs that exhibit both intra- and inter-pair entanglement. The pairs are taken from a large…

What is called "numerical reproducibility" is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing…

Experimental methods are being developed to enable quantum communication systems research in testbeds. We describe testbed architectures for emerging quantum technologies and how they can integrate with existing fibre optical testbeds,…

Localization of a set of nodes is an important and a thoroughly researched problem in robotics and sensor networks. This paper is concerned with the theory of localization from inner-angle measurements. We focus on the challenging case…

We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities…

Neural network potentials (NNPs) combine the computational efficiency of classical interatomic potentials with the high accuracy and flexibility of the ab initio methods used to create the training set, but can also result in unphysical…

We initiate the complexity theoretic study of the problem of computing the bits of (real) algebraic numbers. This extends the work of Yap on computing the bits of transcendental numbers like \pi, in Logspace. Our main result is that…

Integer data sets frequently appear in many applications in sciences and technology. To analyze these, integer low rank approximation has received much attention due to its capacity of representing the results in integers preserving the…