相关论文: SymPlex Plots for Visualizing Properties in High-D…
Two-dimensional embeddings remain the dominant approach to visualize high dimensional data. The choice of embeddings ranges from highly non-linear ones, which can capture complex relationships but are difficult to interpret quantitatively,…
Dissipation can be represented in Hamiltonian mechanics in an extended phase space as a symplectic process. The method uses an auxiliary variable which represents the excitation of unresolved dynamics and a Hamiltonian for the interaction…
Partial differential equations can be solved on general polygonal and polyhedral meshes, through Polytopal Element Methods (PEMs). Unfortunately, the relation between geometry and analysis is still unknown and subject to ongoing research in…
Self-assembly processes provide the means to achieve scalable and versatile metamaterials by "bottom-up" fabrication. Despite their enormous potential, especially as a platform for energy materials, self-assembled metamaterials are often…
In recent years, machine learning (ML) has gained significant popularity in the field of chemical informatics and electronic structure theory. These techniques often require researchers to engineer abstract "features" that encode chemical…
This work develops a new open source API and software package called \textit{SymPhas} for simulations of phase-field, phase-field crystal and reaction-diffusion models, supporting up to three dimensions and an arbitrary number of fields.…
Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological,is constructed…
Boxplots and related visualization methods are widely used exploratory tools for taking a first look at collections of univariate variables. In this note an extension is provided that is specifically designed to detect and display…
We introduce a practical approach to extract the symplectic transfer maps for arbitrary magnetic beam-line elements. Beam motion in particle accelerators depends on linear and nonlinear magnetic fields of the beam-line elements. These…
The finite-element analysis of three-dimensional magnetostatic problems in terms of magnetic vector potential has proven to be one of the most efficient tools capable of providing the excellent quality results but becoming computationally…
Researchers attributed the orderly arranged nanoscale phases observed in many multi-principal element alloys (MPEAs) to spinodal/spinodal-mediated phase transformation pathways. However, spinodal decomposition is not well understood in…
We derive a framework to apply topological quantum chemistry in systems subject to magnetic flux. We start by deriving the action of spatial symmetry operators in a uniform magnetic field, which extends Zak's magnetic translation groups to…
This paper proposes an automatic procedure, based on ROOT data Analysis Framework, for the analysis of Silicon Photomultipliers (SiPM) characteristics. In particular, it can be used to analyze experimental waveforms, from oscilloscope,…
We report an implementation of a program for visualizing complex-valued molecular orbitals. The orbital phase information is encoded on each of the vertices of triangle meshes using the standard color wheel. Using this program, we…
Variable importance, interaction measures, and partial dependence plots are important summaries in the interpretation of statistical and machine learning models. In this paper we describe new visualization techniques for exploring these…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…
Mechanical meta-materials are solids whose geometric structure results in exotic nonlinear behaviors that are not typically achievable via homogeneous materials. We show how to drastically expand the design space of a class of mechanical…
Parametric Embedding (PE) has recently been proposed as a general-purpose algorithm for class visualisation. It takes class posteriors produced by a mixture-based clustering algorithm and projects them in 2D for visualisation. However,…
In this paper I propose a new model for representing the formation energies of multicomponent crystalline alloys as a function of atom types. In the cases when displacements of atoms from their equilibrium positions are not large, the…