Related papers: Local invertibility and sensitivity of atomic stru…
The high-throughput screening of periodic inorganic solids using machine learning methods requires atomic positions to encode structural and compositional details into appropriate material descriptors. These atomic positions are not…
What are the symmetries of a dataset? Whereas the symmetries of an individual data element can be characterized by its invariance under various transformations, the symmetries of an ensemble of data elements are ambiguous due to Jacobian…
The most successful and popular machine learning models of atomic-scale properties derive their transferability from a locality ansatz. The properties of a large molecule or a bulk material are written as a sum over contributions that…
Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the…
We continue our investigation of the configuration space of general relativity begun in I (gr-qc/9411009). Here we examine the Hamiltonian constraint when the spatial geometry is momentarily static (MS). We show that MS configurations…
Physically-motivated and mathematically robust atom-centred representations of molecular structures are key to the success of modern atomistic machine learning (ML) methods. They lie at the foundation of a wide range of methods to predict…
Geometric properties of the fixed point set $Fix(f)$ of a self-mapping $f$ on a metric or a generalized metric space is an attractive issue. The set $Fix(f)$ can contain a geometric figure (a circle, an ellipse, etc.) or it can be a…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…
We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train…
We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be…
Machine-learning of atomic-scale properties amounts to extracting correlations between structure, composition and the quantity that one wants to predict. Representing the input structure in a way that best reflects such correlations makes…
The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The…
The permutation symmetry is a fundamental attribute of the collective wavefunction of indistinguishable particles. It makes a difference for the behavior of collective systems having different quantum statistics but existing in the same…
We expect the final theory of gravity to have more symmetries than we suspect and our research points in this direction. To start with, standard general coordinate invariance can be extended to complex holomorphic general coordinate…
Describing the evolution of quantum systems by means of non-Hermitian generators opens a new avenue to explore the dynamical properties naturally emerging in such a picture, e.g. operation at the so-called exceptional points, preservation…
Evaluating the (dis)similarity of crystalline, disordered and molecular compounds is a critical step in the development of algorithms to navigate automatically the configuration space of complex materials. For instance, a structural…
Theoretical prediction of antilocalization of light in ultracold atomic gas samples, in the weak localization regime, is reported. Calculations and Monte-Carlo simulations show that, for selected spectral ranges in the vicinity of atomic…
Extracting relevant information from atomistic simulations relies on a complete and accurate characterization of atomistic configurations. We present a framework for characterizing atomistic configurations in terms of a complete and…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…