Related papers: $\alpha$-Molecules
In this work we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the…
We consider $L^2$-approximation on weighted reproducing kernel Hilbert spaces of functions depending on infinitely many variables. We focus on unrestricted linear information, admitting evaluations of arbitrary continuous linear…
Multisite phosphorylation plays an important role in regulating switchlike protein activity and has been used widely in mathematical models. With the development of new experimental techniques and more molecular data, molecular…
Transformers have emerged as a preferred model for many tasks in natural langugage processing and vision. Recent efforts on training and deploying Transformers more efficiently have identified many strategies to approximate the…
The shearlets are a special case of the wavelets with composite dilation that, among other things, have a basis-like structure and multi resolution analysis properties. These relatively new representation systems have encountered wide range…
While world models learn compact representations of complex environments, they lack a physics-grounded metric to assess the structural fidelity of their latent spaces. We identify the wavelet scaling exponent $\alpha$ as a critical…
The parametrisation method for invariant manifolds is a powerful technique for deriving reduced-order models in the context of nonlinear vibrating systems, allowing accurate computations of nonlinear normal modes. Thanks to arbitrary order…
The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…
We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an $N$-particle…
Real-space refinement of atomic models in macromolecular crystallography or in cryo electron microscopy fits a model to a map obtained experimentally. This requires generating model maps of a limited resolution which moreover may vary from…
Generalizing wavelets by adding desired redundancy and flexibility,framelets are of interest and importance in many applications such as image processing and numerical algorithms. Several key properties of framelets are high vanishing…
We provide a characterization of wavelets on local fields of positive characteristic based on results on affine and quasi affine frames. This result generalizes the characterization of wavelets on Euclidean spaces by means of two basic…
Many popular learning algorithms (E.g. Regression, Fourier-Transform based algorithms, Kernel SVM and Kernel ridge regression) operate by reducing the problem to a convex optimization problem over a vector space of functions. These methods…
One of the most intriguing results of single molecule experiments on proteins and nucleic acids is the discovery of functional heterogeneity: the observation that complex cellular machines exhibit multiple, biologically active…
New explicit velocity- and position-Verlet-like algorithms of the second order are proposed to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an extended decomposition scheme at the…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size $n$ subject to a knapsack constraint, $\mathsf{DLA}$ and…
This work is devoted to the stability/resolution analysis of several imaging functionals in complex environments. We consider both linear functionals in the wavefield as well as quadratic functionals based on wavefield correlations. Using…
Faithfully representing chemical environments is essential for describing materials and molecules with machine learning approaches. Here, we present a systematic classification of these representations and then investigate: (i) the…