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In this work, we present a new computational approach to characterize and classify molecular packing in the solid states. The key idea is to project each neighboring molecule (or short contact) from the centered molecule into a unit sphere…
In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of $L^2(\mathfrak{S})$ where $\mathfrak{S}$ is a second countable LCA group. The subspaces where the operators act are…
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…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
This paper introduces a coordinate descent version of the V\~u-Condat algorithm. By coordinate descent, we mean that only a subset of the coordinates of the primal and dual iterates is updated at each iteration, the other coordinates being…
This paper presents decentralized algorithms for formation control of multiple robots in three dimensions. Specifically, we leverage the mathematical properties of cyclic pursuit along with results from contraction and partial contraction…
Understanding how cortical activity represents natural whole-body behaviors in primates remains challenging. Limited by the diversity of movements and inaccessibility of large-scale neural representation of whole-body kinematics, previous…
We study the discretization of a Poincar\'e/Euclidean BF theory. Upon the addition of a boundary term, this theory is equivalent to the BFCG theory defined in terms of the Poincar\'e/Euclidean 2-group. At an intermediate step in the…
The skeleton is an essential shape characteristic providing a compact representation of the studied shape. Its computation on the image grid raises many issues. Due to the effects of discretization, the required properties of the skeleton -…
We propose mixed quantum-classical equations of motion that unify electronic coherence and phase evolution simultaneously within the exact factorization framework. Our derivation shows that incorporating the second-order electron-nuclear…
The aim of this paper is to perform a deeper geometric analysis of problems appearing in dynamics of affinely rigid bodies. First of all we present a geometric interpretation of the polar and two-polar decomposition of affine motion. Later…
In applied physics and in engineering intuitive understanding is a boost for creativity and almost a necessity for efficient product improvement. The existence of soliton solutions to the quantum equations in the presence of…
We develop a rigorous analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. By constructing a complex domain of holomorphy for the planetary Hamilto-nian, we estimate the size of the…
We study the dynamics of a two-mode Bose-Einstein condensate in the vicinity of a mean-field dynamical instability. Convergence to mean-field theory (MFT), with increasing total number of particles $N$, is shown to be logarithmically slow.…
Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This…
The morphological classification of galaxies is considered a relevant issue and can be approached from different points of view. The increasing growth in the size and accuracy of astronomical data sets brings with it the need for the use of…
This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
We revisit spatially flat, anisotropic cosmologies within the framework of mini-superspace. Putting special emphasis on the symmetries of the mini-superspace action and on the associated conservation laws, we unveil a new class of rotating…
In many robot control problems, factors such as stiffness and damping matrices and manipulability ellipsoids are naturally represented as symmetric positive definite (SPD) matrices, which capture the specific geometric characteristics of…