Related papers: A Very Fast and Momentum-Conserving Tree Code
A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two…
Traditional tree search algorithms supply a blueprint for modeling problem solving behaviour. A diverse spectrum of problems can be formulated in terms of tree search. Quantum computation, in particular Grover's algorithm, has aroused a…
According to a recent paper by Robinson and Wilczek, the leading gravitational corrections to the running of gauge couplings tend to reduce the values of the couplings at energies below the gravitational scale, defined to be the energy…
Non-perturbative studies of quantum gravity have recently suggested the possibility that the strength of gravitational interactions might slowly increase with distance. Here a set of generally covariant effective field equations are…
Graham and Sloane proposed in 1980 a conjecture stating that every tree has a harmonious labelling, a graph labelling closely related to additive base. Very limited results on this conjecture are known. In this paper, we proposed a…
Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…
Following the ideas of effective field theories, we derive classically effective field equations of recently developed Lorentz gauge theory of gravity. It is shown that Newton's gravitational constant emerges as an effective coupling…
In this paper, we develop a highly efficient molecular dynamics code fully implemented on graphics processing units for thermal conductivity calculations using the Green-Kubo formula. We compare two different schemes for force evaluation, a…
We describe the two-dimensional TreePM method in this paper. The 2d TreePM code is an accurate and efficient technique to carry out large two-dimensional N-body simulations in cosmology. This hybrid code combines the 2d Barnes and Hut Tree…
Starting from the multiplicative torsion approach of gravity and assuming a Killing vector to be proportional to the axial-vector matter current, here we derive Newton's law of gravity where the logarithm of the proportionality factor has…
The problem of realizing finite metric spaces in terms of weighted graphs has many applications. For example, the mathematical and computational properties of metrics that can be realized by trees have been well-studied and such research…
We study some essential arithmetic properties of a new tree-based number representation, {\em hereditarily binary numbers}, defined by applying recursively run-length encoding of bijective base-2 digits. Our representation expresses giant…
We present four novel approximation algorithms for finding triangulation of minimum treewidth. Two of the algorithms improve on the running times of algorithms by Robertson and Seymour, and Becker and Geiger that approximate the optimum by…
We consider maintaining the contour tree $\mathbb{T}$ of a piecewise-linear triangulation $\mathbb{M}$ that is the graph of a time varying height function $h: \mathbb{R}^2 \rightarrow \mathbb{R}$. We carefully describe the combinatorial…
In this paper, a novel sixth order energy-conserved method is proposed for solving the three-dimensional time-domain Maxwell's equations. The new scheme preserves five discrete energy conservation laws, three momentum conservation laws,…
Efficient index structures for fast approximate nearest neighbor queries are required in many applications such as recommendation systems. In high-dimensional spaces, many conventional methods suffer from excessive usage of memory and slow…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
Research into the classification of time series has made enormous progress in the last decade. The UCR time series archive has played a significant role in challenging and guiding the development of new learners for time series…
In this paper we show the usability of the Gray code with constant weight words for computing linear combinations of codewords. This can lead to a big improvement of the computation time for finding the minimum distance of a code. We have…
We describe a parallel, cosmological N-body code based on a hybrid scheme using the particle-mesh (PM) and Barnes-Hut (BH) oct-tree algorithm. We call the algorithm GOTPM for Grid-of-Oct-Trees-Particle-Mesh. The code is parallelized using…