Related papers: Automatic sorting of point pattern sets using Mink…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
We use machine learning algorithms to detect the crystalline phase in undercooled melts in molecular dynamics simulations. Our classification method is based on local conformation and environmental fingerprints of individual monomers. In…
This paper describes a process for combining patterns and features, to guide a search process and make predictions. It is based on the functionality that a human brain might have, which is a highly distributed network of simple neuronal…
We show that macro-molecular self-assembly can recognize and classify high-dimensional patterns in the concentrations of $N$ distinct molecular species. Similar to associative neural networks, the recognition here leverages dynamical…
We present an extension of sparse PCA, or sparse dictionary learning, where the sparsity patterns of all dictionary elements are structured and constrained to belong to a prespecified set of shapes. This \emph{structured sparse PCA} is…
Let N, N' and N'' be point processes such that N' is obtained from N by homogeneous independent thinning and N''= N- N'. We give a new elementary proof that N' and N'' are independent if and only if N is a Poisson point process. We present…
Due to the complexity of cancer, clustering algorithms have been used to disentangle the observed heterogeneity and identify cancer subtypes that can be treated specifically. While kernel based clustering approaches allow the use of more…
Automated identification of protein conformational states from simulation of an ensemble of structures is a hard problem because it requires teaching a computer to recognize shapes. We adapt the naive Bayes classifier from the machine…
We introduce the hierarchical compositional network (HCN), a directed generative model able to discover and disentangle, without supervision, the building blocks of a set of binary images. The building blocks are binary features defined…
Ou et al. (2022) introduce the problem of learning set functions from data generated by a so-called optimal subset oracle. Their approach approximates the underlying utility function with an energy-based model, whose parameters are…
Spatial pattern formation is a key feature of many natural systems in physics, chemistry and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…
We address the problem of comparing and aligning spatial point configurations in $\mathbb{R}^3$ arising from structured geometric patterns. Each pattern is decomposed into arms along which we define a normalized finite-difference operator…
The behaviour and functioning of a variety of complex physical and biological systems depend on the spatial organisation of their constituent units, and on the presence and formation of clusters of functionally similar or related…
I develop a feasible weighted projected principal component (FPPC) analysis for factor models in which observable characteristics partially explain the latent factors. This novel method provides more efficient and accurate estimators than…
Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…
In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…
Aleksandrov, and then Zeeman, showed that the causal relations among the set of points in a Minkowski space of dimension greater than 2 determine the Minkowski space structure of the set up to a global conformal factor. We show that in any…
Point Group (PG) symmetries play a fundamental role in many aspects of theoretical chemistry and computational materials science. With the objective to automatize the search of PG symmetry operations of generic atomic clusters, we present a…
It is crucial to learn the shared structures among functional predictors, as these structures characterize how predictor components exert common effects and, more generally, how predictors are homogeneously associated with the response.…