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Graphene moir\'e systems are ideal environments for investigating complex phase diagrams and gaining fundamental insights into the mechanisms underlying exotic states of matter, as they permit controlled manipulation of electronic…
We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions.…
Machine learning (ML) methods are extraordinarily successful at denoising photographic images. The application of such denoising methods to scientific images is, however, often complicated by the difficulty in experimentally obtaining a…
At partial fillings of its flat electronic bands, magic-angle twisted bilayer graphene (MATBG) hosts a rich variety of competing correlated phases that show sample to sample variations. Divergent phase diagrams in MATBG are often attributed…
The discovery of different phases as a result of correlations, especially in low-dimensional materials, has been always an exciting and fundamental subject of research. Recent experiments on twisted bilayer graphene have revealed reentrant…
By combining related objects, unsupervised machine learning techniques aim to reveal the underlying patterns in a data set. Non-negative Matrix Factorization (NMF) is a data mining technique that splits data matrices by imposing…
In this work we performed density functional theory calculations for a twisted bilayer graphene (BLG). Several conmensurable rotation angles were analyzed and for each one a constant height mode STM image was obtained. These STM images,…
Determining the optimal number and identity of structural clusters from an ensemble of molecular configurations continues to be a challenge. Recent structural clustering methods have focused on the use of internal coordinates due to the…
Microbiome research has immense potential for unlocking insights into human health and disease. A common goal in human microbiome research is identifying subgroups of individuals with similar microbial composition that may be linked to…
Recently, symmetry-broken ground states, such as correlated insulating states, magnetic order and superconductivity, have been discovered in twisted bilayer graphene (tBLG) and twisted trilayer graphene (tTLG) near the so-called…
Moir\'e superlattices created by the twisted stacking of two-dimensional crystalline monolayers can host electronic bands with flat energy dispersion in which interaction among electrons is strongly enhanced. These superlattices can also…
Graphene moir\'e superlattices display electronic flat bands. At integer fillings of these flat bands, energy gaps due to strong electron-electron interactions are generally observed. However, the presence of other correlation-driven phases…
Network models provide a powerful framework for analysing single-cell count data, facilitating the characterisation of cellular identities, disease mechanisms, and developmental trajectories. However, uncertainty modeling in unsupervised…
A computational approach via implementation of the Principle Component Analysis (PCA) and Gaussian Mixture (GM) clustering methods from Machine Learning (ML) algorithms to identify domain structures of supercooled liquids is developed. Raw…
We develop here a semiparametric Gaussian mixture model (SGMM) for unsupervised learning with valuable spatial information taken into consideration. Specifically, we assume for each instance a random location. Then, conditional on this…
This study presents a novel integration of unsupervised learning and decision-making strategies for the advanced analysis of 4D-STEM datasets, with a focus on non-negative matrix factorization (NMF) as the primary clustering method. Our…
Unsupervised machine learning offers significant opportunities for extracting knowledge from unlabeled data sets and for achieving maximum machine learning performance. This paper demonstrates how to construct, use, and evaluate a high…
Financial studies require volatility based models which provides useful insights on risks related to investments. Stochastic volatility models are one of the most popular approaches to model volatility in such studies. The asset returns…
Two-dimensional multi-layer materials with an induced moir\'e pattern, either due to strain or relative twist between layers, provide a versatile platform for exploring strongly correlated and topological electronic phenomena. While these…
Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. However, for cluster analysis, using a traditional finite mixture model framework,…