AS we were teaching a multivariate statistics course for doctoral students, one of the students in the class asked,"What are degrees of freedom? I know it is not good to lose degrees of freedom, but what are they?" Other students in the class waited for a clear-cut response. As we tried to give a textbook answer, we were not satisfied and we did not get the sense that our students understood. W...

We experimentally study the optical- and terahertz-induced rotational dynamics of asymmetric molecules in the gas phase. Terahertz and optical fields are identified as two distinct control handles over asymmetric molecules, as they couple to the rotational degrees of freedom via the molecular dipole and polarizability selectively. The distinction between those two rotational handles is highligh...

Modular robots offer the possibility to quickly design robots with a high diversity of shapes and functionalities. This nice feature also brings an important challenge: namely how to design efficient locomotion gaits for arbitrary robot structures with many degrees of freedom. In this paper, we present a framework that allows one to explore and identify highly different gaits for a given arbitr...

We discuss the relevance of chaotic scattering in heavy–ion reactions at energies around the Coulomb barrier. A model in two and three dimensions which takes into account rotational degrees of freedom is discussed both classically and quantum-mechanically. The typical chaotic features found in this description of heavy-ion collisions are connected with the anomalous behaviour of several experim...

We report primitive semiclassical rotation-vibrational energy levels for a triatomic molecule, H20, with inclusion of all three vibrational degrees of freedom. Both the Lai-Hagstrom and Hoy-Bunker potential surfaces are used. Vibrational and rotational actions are calculated usinn the fast Fourier transform Sorbie-Handy method. Overall, encouraging agreement with the quantum variational results...

We discuss the relevance of chaotic scattering in heavy-ion reactions at energies around the Coulomb barrier. A model in two and three dimensions which takes into account rotational degrees of freedom is discussed both classically and quantum mechanically. The typical chaotic features found in this description of heavy-ion collisions are connected with the anomalous behavior of several experime...

We demonstrate that single photons from a rotating q-plate exhibit an entanglement in three degrees of freedom of spin, orbital angular momentum, and the rotational Doppler shift (RDS) due to the nonconservation of total spin and orbital angular momenta. We find that the rotational Doppler shift deltaomega = Omega((delta)s + deltal) , where s, l and Omega are quantum numbers of spin, orbital an...

A computationally efficient method is presented - 'fast rotational matching' or FRM - that significantly accelerates the search of the three rotational degrees of freedom (DOF) in biomolecular matching problems. This method uses a suitable parametrization of the three-dimensional rotation group along with spherical harmonics, which allows efficient computation of the Fourier Transform of the ro...

PURPOSE Image guided radiotherapy (IGRT) using cone beam computed tomography (CBCT) images greatly reduces interfractional patient positional uncertainties. An understanding of uncertainties in the IGRT process itself is essential to ensure appropriate use of this technology. The purpose of this study was to develop a phantom capable of assessing the accuracy of IGRT hardware and software inclu...