Search results for "Hess"
showing 10 items of 97 documents
Analytic evaluation of the dipole Hessian matrix in coupled-cluster theory
2013
The general theory required for the calculation of analytic third energy derivatives at the coupled-cluster level of theory is presented and connected to preceding special formulations for hyperpolarizabilities and polarizability gradients. Based on our theory, we have implemented a scheme for calculating the dipole Hessian matrix in a fully analytical manner within the coupled-cluster singles and doubles approximation. The dipole Hessian matrix is the second geometrical derivative of the dipole moment and thus a third derivative of the energy. It plays a crucial role in IR spectroscopy when taking into account anharmonic effects and is also essential for computing vibrational corrections t…
Computer-aided detection of cerebral microbleeds in susceptibility-weighted imaging.
2014
Susceptibility-weighted imaging (SWI) is recognized as the preferred MRI technique for visualizing cerebral vasculature and related pathologies such as cerebral microbleeds (CMBs). Manual identification of CMBs is time-consuming, has limited reliability and reproducibility, and is prone to misinterpretation. In this paper, a novel computer-aided microbleed detection technique based on machine learning is presented: First, spherical-like objects (potential CMB candidates) with their corresponding bounding boxes were detected using a novel multi-scale Laplacian of Gaussian technique. A set of robust 3-dimensional Radon- and Hessian-based shape descriptors within each bounding box were then ex…
Second-Order CASSCF Algorithm with the Cholesky Decomposition of the Two-Electron Integrals
2021
In this contribution, we present the implementation of a second-order complete active space–self-consistent field (CASSCF) algorithm in conjunction with the Cholesky decomposition of the two-electron repulsion integrals. The algorithm, called norm-extended optimization, guarantees convergence of the optimization, but it involves the full Hessian and is therefore computationally expensive. Coupling the second-order procedure with the Cholesky decomposition leads to a significant reduction in the computational cost, reduced memory requirements, and an improved parallel performance. As a result, CASSCF calculations of larger molecular systems become possible as a routine task. The performance …
Stability of radial symmetry for a Monge-Ampère overdetermined problem
2008
Recently the symmetry of solutions to overdetermined problems has been established for the class of Hessian operators, including the Monge-Ampère operator. In this paper we prove that the radial symmetry of the domain and of the solution to an overdetermined Dirichlet problem for the Monge-Ampère equation is stable under suitable perturbations of the data. © 2008 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.
AMYR 2: A new version of a computer program for pair potential calculation of molecular associations
1998
AMYR is a computer program for the calculation of molecular associations using Fraga's pairwise atom-atom potential. The interaction energy is evaluated through a 1R expansion. The electrostatic energy is calculated through either the one-centre-per atom or the three-centres-per atom model by Hunter and Sanders. A pairwise dispersion energy term is included in the potential and corrected by a damping function. The program carries out energy minimizations through variable metric methods. The new version allows for the stationary point analysis of the intermolecular potential by means of the Hessian eigenvalues. Although using low-gradient thresholds optimization procedures to avoid many stat…
Electron-density critical points analysis and catastrophe theory to forecast structure instability in periodic solids
2018
The critical points analysis of electron density,i.e. ρ(x), fromab initiocalculations is used in combination with the catastrophe theory to show a correlation between ρ(x) topology and the appearance of instability that may lead to transformations of crystal structures, as a function of pressure/temperature. In particular, this study focuses on the evolution of coalescing non-degenerate critical points,i.e. such that ∇ρ(xc) = 0 and λ1, λ2, λ3≠ 0 [λ being the eigenvalues of the Hessian of ρ(x) atxc], towards degenerate critical points,i.e. ∇ρ(xc) = 0 and at least one λ equal to zero. The catastrophe theory formalism provides a mathematical tool to model ρ(x) in the neighbourhood ofxcand allo…
Interactive simulation of one-dimensional flexible parts
2006
Computer simulations play an ever growing role for the development of automotive products. Assembly simulation, as well as many other processes, are used systematically even before the first physical prototype of a vehicle is built in order to check whether particular components can be assembled easily or whether another part is in the way. Usually, this kind of simulation is limited to rigid bodies. However, a vehicle contains a multitude of flexible parts of various types: cables, hoses, carpets, seat surfaces, insulations, weatherstrips... Since most of the problems using these simulations concern one-dimensional components and since an intuitive tool for cable routing is still needed, w…
On the Symmetry of Solutions to a k-Hessian Type Equation
2013
Abstract In this note we prove that if u is a negative solution to a nonlinear elliptic equation involving a Hessian operator, and u is zero on the boundary of a ball, then u is radially symmetric and increasing along the radii.
AUTOMATIC DETECTION OF SMALL SPHERICAL LESIONS USING MULTISCALE APPROACH IN 3D MEDICAL IMAGES
2013
International audience; Automated detection of small, low level shapes such as circular/spherical objects in images is a challenging computer vision problem. For many applications, especially microbleed detection in Alzheimer's disease, an automatic pre-screening scheme is required to identify potential seeds with high sensitivity and reasonable specificity. A new method is proposed to detect spherical objects in 3D medical images within the multi-scale Laplacian of Gaussian framework. The major contributions are (1) breaking down 3D sphere detection into 1D line profile detection along each coordinate dimension, (2) identifying center of structures by normalizing the line response profile …
Comparison results for Hessian equations via symmetrization
2007
where the λ’s are the eigenvalues of the Hessian matrix D2u of u and Sk is the kth elementary symmetric function. For example, for k = 1, S1(Du) = 1u, while, for k = n, Sn(D 2u) = detD2u. Equations involving these operators, and some more general equations of the form F(λ1, . . . , λn) = f in , (1.2) have been widely studied by many authors, who restrict their considerations to convenient cones of solutions with respect to which the operator in (1.2) is elliptic. Following [25] we define the cone 0k of ellipticity for (1.1) to be the connected component containing the positive cone 0 = {λ ∈ R : λi > 0 ∀i = 1, . . . , n} of the set where Sk is positive. Thus 0k is an open, convex, symmetric…