Related papers: A general method for rotational averages
The recent growing interest in nonlinear optical spectroscopy in optically active medium demands the three-dimensional rotational average of high-rank tensors. In the present paper, we present a new method for finding the rotational average…
A generalized covariant method of analysis applicable to frames for which time is not orthogonal to space, such as spacetime around a star possessing angular momentum or on a rotating disk, is presented. Important aspects of such an…
Torque is ubiquitous in many molecular systems, including collisions, chemical reactions, vibrations, electronic excitations and especially rotor molecules. We present a straightforward theoretical method based on forces acting on atoms and…
Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In…
A solid object's geometry, density, and elastic moduli completely determine its spectrum of normal modes. Solving the inverse problem - determining a material's elastic moduli given a set of resonance frequencies and sample geometry -…
The development of energy selective, photon counting X-ray detectors allows for a wide range of new possibilities in the area of computed tomographic image formation. Under the assumption of perfect energy resolution, here we propose a…
Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and…
We describe a convergence acceleration technique for unconstrained optimization problems. Our scheme computes estimates of the optimum from a nonlinear average of the iterates produced by any optimization method. The weights in this average…
The rich information content of measurements in the molecular frame rather than the laboratory frame has motivated the development of several methods for aligning gas phase molecules in space. Even so, for asymmetric tops the problem of…
We consider the theory of the non-linear spectroscopy for a single molecule undergoing stochastic dynamics and interacting with a sequence of two laser pulses. General expressions for photon counting statistics are obtained, and an exact…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In spite of being an integral part of bundle adjustment and…
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…
A non-perturbative approach to the time-averaging of nonlinear, autonomous ODE systems is developed based on invariant manifold methodology. The method is implemented computationally and applied to model problems arising in the mechanics of…
A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…
In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear…
We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…
In this paper we demonstrate how asymmetric molecular rotational spectra may be introduced to students both "pictorially" and with simple formulae. It is shown that the interpretation of such spectra relies heavily upon pattern recognition.…
The basic principles of classical and semi-classical theories of molecular optical activity are discussed. These theories are valid for dilute solutions of optically active organic molecules. It is shown that all phenomena known in the…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…