Related papers: A Very Fast and Momentum-Conserving Tree Code
Suffix trees are a fundamental data structure in stringology, but their space usage, though linear, is an important problem for its applications. We design and implement a new compressed suffix tree targeted to highly repetitive texts, such…
We present the leading order non-linear density and velocity power spectra in the complete form; previous studies have omitted the vector- and tensor-type perturbations simultaneously excited by the scalar-type perturbation in nonlinear…
In this PhD thesis I make use of the "Effective Field Theory of Gravity for Extended Objects" by Goldberger and Rothstein in order to investigate theories of gravity and to take a different point of view on the physical information that can…
We propose a new cross-conv algorithm for approximate computation of convolution in different low-rank tensor formats (tensor train, Tucker, Hierarchical Tucker). It has better complexity with respect to the tensor rank than previous…
We have developed a parallel Particle-Particle, Particle-Mesh (P^3M) simulation code for the T3E well suited to studying the time evolution of systems of particles interacting via gravity and gas forces in cosmological contexts. The…
An exact solution has an axial symmetry is obtained in the teleparallel theory of gravitation. The associated metric has the structure function G(xi)=1-xi^2-2mA(xi)^3. The cubic nature of the structure function can make calculations…
A complexity-adaptive tree search algorithm is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding by using a successive decoding schedule. The average complexity is close to that of the successive…
Until now, it has been common to use Newton's gravity to study the non-linear clustering properties of the large-scale structures. Without confirmation from Einstein's theory, however, it has been unclear whether we can rely on the…
In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…
The cosmology of general fourth order corrections to Einstein gravity is considered, both for a homogeneous and isotropic background and for general tensor perturbations. It is explicitly shown how the standard cosmological history can be…
We introduce the spanning tree matching (STM) decoder for surface codes, which guarantees the error correction capability up to the code's designed distance by first employing an instance of the minimum spanning tree on a subset of ancilla…
We present a new method to compute higher-order corrections to physical cross-sections, at Next-to-Leading Order and beyond. This method, based on the Loop Tree Duality, leads to locally integrable expressions in four dimensions. By…
Based on a second-order approximation of nonlinear force-free magnetic field solutions in terms of uniformly twisted field lines derived in Paper I, we develop here a numeric code that is capable to forward-fit such analytical solutions to…
Trees are useful entities allowing to model data structures and hierarchical relationships in networked decision systems ubiquitously. An ordered tree is a rooted tree where the order of the subtrees (children) of a node is significant. In…
Based on a tentative interpretation of gravity as a pressure force, a scalar theory of gravity was previously investigated. It assumes gravitational contraction (dilation) of space (time) standards. In the static case, the same Newton law…
The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research focuses on designing an efficient algorithm to compute…
Natural language text corpora are often available as sets of syntactically parsed trees. A wide range of expressive tree queries are possible over such parsed trees that open a new avenue in searching over natural language text. They not…
At the heart of Newton based optimization methods is a sequence of symmetric linear systems. Each consecutive system in this sequence is similar to the next, so solving them separately is a waste of computational effort. Here we describe…
Establishing the correspondences between newly acquired points and historically accumulated data (i.e., map) through nearest neighbors search is crucial in numerous robotic applications. However, static tree data structures are inadequate…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…