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Parallel computing has turned out to be the enabling technology to solve complex physical systems. However, the transition from shared memory, vector computers to massively parallel, distributed memory systems and, recently, to hybrid…
An introduction to the density matrix renormalization group is contained here, including coding examples. The focus of this code is on basic operations involved in tensor network computations, and this forms the foundation of the DMRjulia…
We present a method for electronic structure calculations that retains all of the advantages of real space and addresses the inherent inefficiency of a regular grid, which has equal precision everywhere. The computations are carried out on…
Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users/items in the form of…
Following a review of metric, ultrametric and generalized ultrametric, we review their application in data analysis. We show how they allow us to explore both geometry and topology of information, starting with measured data. Some themes…
Following our previous work, we suggest here a large class of algebras of scalars in which simultaneous and correlated computations can be performed owing to the existence of surjective algebra homomorphisms. This may replace the currently…
Kernel methods are powerful tools in machine learning. They have to be computationally efficient. In this paper, we present a novel Geometric-based approach to compute efficiently the string subsequence kernel (SSK). Our main idea is that…
Geometrical modelling generally provides the geometrical description of a special structure and a set of services to "navigate" through its structure. HEP geometrical modellers are designed to handle high complexity detector geometries and…
We introduce the Stellar decomposition, a model for efficient topological data structures over a broad range of simplicial and cell complexes. A Stellar decomposition of a complex is a collection of regions indexing the complex's vertices…
We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces…
We present novel mixed-integer programming (MIP) formulations for optimization over nonconvex piecewise linear functions. We exploit recent advances in the systematic construction of MIP formulations to derive new formulations for…
Ordered nanoarrays, i.e. regular patterns of quantum structures at the nanometre scale, have recently been synthesized in a wide range of systems. Here I explore a possible route to technological exploitation: assuming a simple form of…
We report on the computer implementation for toric geometry in the computer algebra system $\texttt{OSCAR}$. The main architectural feature of $\texttt{OSCAR}$ is that its four fundamental tools $\texttt{Antic}$ (Hecke, Nemo),…
We consider parallel computation for Gaussian process calculations to overcome computational and memory constraints on the size of datasets that can be analyzed. Using a hybrid parallelization approach that uses both threading (shared…
High fidelity scientific simulations modeling physical phenomena typically require solving large linear systems of equations which result from discretization of a partial differential equation (PDE) by some numerical method. This step often…
In the nonlinear timeseries analysis literature, countless quantities have been presented as new ``entropy'' or ``complexity'' measures, often with similar roles. The ever-increasing pool of such measures makes creating a sustainable and…
We introduce a new algorithm computing the characteristic polynomials of hyperplane arrangements which exploits their underlying symmetry groups. Our algorithm counts the chambers of an arrangement as a byproduct of computing its…
The graph partitioning problem has many applications in scientific computing such as computer aided design, data mining, image compression and other applications with sparse-matrix vector multiplications as a kernel operation. In many cases…
The amount of remote sensing data available to applications is constantly growing due to the rise of very-high-resolution sensors and short repeat cycle satellites. Consequently, tackling computational complexity in Earth Observation…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…