Related papers: NMR implementations of Gauss sums
We study statistical properties of an NP-complete problem, the subset sum, using the methods and concepts of statistical mechanics. The problem is a generalization of the number partitioning problem, which is also an NP-complete problem and…
Computer experiments with both quantitative and qualitative (QQ) inputs are commonly used in science and engineering applications. Constructing desirable emulators for such computer experiments remains a challenging problem. In this…
Gauss quadrature integral approximation is extended to include integrals with a measure consisting of continuous as well as discrete components. That is, we give an approximation for the integral of a function plus its sum over a discrete…
Sum-of-norms clustering is a method for assigning $n$ points in $\mathbb{R}^d$ to $K$ clusters, $1\le K\le n$, using convex optimization. Recently, Panahi et al.\ proved that sum-of-norms clustering is guaranteed to recover a mixture of…
In this article, we present some specific aspects of symmetric Gamma process mixtures for use in regression models. We propose a new Gibbs sampler for simulating the posterior and we establish adaptive posterior rates of convergence related…
Normals with unknown parameters (NUP) can be used to convert nontrivial model-based estimation problems into iterations of linear least-squares or Gaussian estimation problems. In this paper, we extend this approach by augmenting factor…
The improved quantum scheduling algorithm proposed by Grover has been generalized using the generalized quantum search algorithm, in which a unitary operator replaces the Walsh-Hadamard transform, and $\pi/2$ phase rotations replace the…
Sum of powers 1^p+...+n^p, with n and p being natural numbers and n>=1, can be expressed as a polynomial function of n of degree p+1. Such representations are often called Faulhaber formulae. A simple recursive algorithm for computing…
Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in graph clustering where each element measures the…
The techniques for polynomial interpolation and Gaussian quadrature are generalized to matrix-valued functions. It is shown how the zeros and rootvectors of matrix orthonormal polynomials can be used to get a quadrature formula with the…
This paper covers some of the current techniques and issues involved in performing numerical simulations of the formation of singularities.
In this paper we use the equivariant version of factorization homology constructed using the parametrized higher category theory and show that it can be used to describe the results used in the series of papers.
We have taken significant steps towards the realization of a practical quantum computer: using nuclear spins and magnetic resonance techniques at room temperature, we provided proof of principle of quantum computing in a series of…
We recall the question of geometric integrators in the context of Poisson geometry, and explain their construction. These Poisson integrators are tested in some mechanical examples. Their properties are illustrated numerically and they are…
The theory of grey systems plays an important role in science,engineering and in the everyday life in general for handling approximate data. In the present paper grey numbers are used as a tool for assessing with linguistic expressions the…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. We apply it in random matrix…
In this paper we present experimental ways of evaluating Ramanujan`s quantities which as someone can see are related with algebraic numbers. The good thing with algebraic numbers is that can be found in a closed form, from there…
The problem of exactly summing n floating-point numbers is a fundamental problem that has many applications in large-scale simulations and computational geometry. Unfortunately, due to the round-off error in standard floating-point…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…