Related papers: Increasing precision of uniform pseudorandom numbe…
We provide a preliminary study on utilizing GPU (Graphics Processing Unit) to accelerate computation for three simulation optimization tasks with either first-order or second-order algorithms. Compared to the implementation using only CPU…
A software product line models the variability of highly configurable systems. Complete exploration of all valid configurations (the configuration space) is infeasible as it grows exponentially with the number of features in the worst case.…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
Debugging accumulation of floating-point errors is hard; ideally, computer should track it automatically. Here we consider twofold approximation of an exact real with value + error pair of floating-point numbers. Normally, value + error sum…
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…
In recent years graphical processing units (GPUs) have become a powerful tool in scientific computing. Their potential to speed up highly parallel applications brings the power of high performance computing to a wider range of users.…
The graphics processing unit (GPU) has emerged as a powerful and cost effective processor for general performance computing. GPUs are capable of an order of magnitude more floating-point operations per second as compared to modern central…
This article presents a new class of Pseudorandom Number Generators. The generators are based on traversing a n-cube where a Balanced Hamiltonian Cycle has been removed. The construction of such generators is automatic for small number of…
The spectral test of random number generators (R.R. Coveyou and R.D. McPherson, 1967) is generalized. The sequence of random numbers is analyzed explicitly, not just via their n-tupel distributions. We find that the mixed multiplicative…
Given a matrix $A\in \mathrm{GL}_d(\mathbb{Z})$. We study the pseudorandomness of vectors $\mathbf{u}_n$ generated by a linear recurrent relation of the form $$ \mathbf{u}_{n+1} \equiv A \mathbf{u}_n \pmod {p^t}, \qquad n = 0, 1, \ldots, $$…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…
For single-photon quantum key generation between two users, it is shown that the use of a shared secret key extended via a pseudo-random number generator may simultaneously enhance the security and efficiency of the cryptosystem. This…
This paper considers the problem of simultaneously estimating rare-event probabilities for a class of Gaussian random fields. A conventional rare-event simulation method is usually tailored to a specific rare event and consequently would…
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…
We give an overview of the worldline numerics technique, and discuss the parallel CUDA implementation of a worldline numerics algorithm. In the worldline numerics technique, we wish to generate an ensemble of representative closed-loop…
Random numbers are widely used for information security, cryptography, stochastic modeling, and quantum simulations. Key technical challenges for physical random number generation are speed and scalability. We demonstrate a method for…
A compiler approach for generating low-level computer code from high-level input for discontinuous Galerkin finite element forms is presented. The input language mirrors conventional mathematical notation, and the compiler generates…
Strong gravitational lensing is a powerful probe of cosmology and the dark matter distribution. Efficient lensing software is already a necessity to fully use its potential and the performance demands will only increase with the upcoming…
We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…