Multiple autoregressive models with random coefficients

This paper derives conditions for the stationarity of a class of multiple autoregressive models with random coefficients. The models considered include as special cases those previously discussed by Andel (Ann. Math. Statist.42 (1971), 755–759; Math. Operationsforsch. Statist.7 (1976), 735–741).     

The Role of Entanglement in Quantum Measurement and Information Processing

The significance of the quantum feature of entanglement between physical systems is investigated in the context of quantum measurements. It is shown that, while there are measurement couplings that leave the object and probe systems nonentangled, no information transfer from object to probe can take place unless there is at least some intermittent period where the two systems are entangled.     

Efficient evaluation of Casimir force in arbitrary three-dimensional geometries by integral equation methods

In this Letter, we generalized the surface integral equation method for the evaluation of Casimir force in arbitrary three-dimensional geometries. Similar to the two-dimensional case, the evaluation of the mean Maxwell stress tensor is cast into solving a series of three-dimensional scattering problems. The formulation and solution of the three-dimensional scattering problems are well-studied in classical computational electromagnetics. This Letter demonstrates that this quantum electrodynamic phenomenon can be studied using the knowledge and techniques of classical electrodynamics.     

Diffusional kurtosis imaging of cingulate fibers in Parkinson disease: Comparison with conventional diffusion tensor imaging

Objective

The pathological changes in Parkinson disease begin in the brainstem; reach the limbic system and ultimately spread to the cerebral cortex. In Parkinson disease (PD) patients, we evaluated the alteration of cingulate fibers, which comprise part of the limbic system, by using diffusional kurtosis imaging (DKI).

Methods

Seventeen patients with PD and 15 age-matched healthy controls underwent DKI with a 3-T MR imager. Diffusion tensor tractography images of the anterior and posterior cingulum were generated. The mean kurtosis (MK) and conventional diffusion tensor parameters measured along the images in the anterior and posterior cingulum were compared between the groups. Receiver operating characteristic (ROC) analysis was also performed to compare the diagnostic abilities of the MK and conventional diffusion tensor parameters.

Results

The MK and fractional anisotropy (FA) in the anterior cingulum were significantly lower in PD patients than in healthy controls. The area under the ROC curve was 0.912 for MK and 0.747 for FA in the anterior cingulum. MK in the anterior cingulum had the best diagnostic performance (mean cutoff, 0.967; sensitivity, 0.87; specificity, 0.94).

Conclusions

DKI can detect alterations of the anterior cingulum in PD patients more sensitively than can conventional diffusion tensor imaging. Use of DKI can be expected to improve the ability to diagnose PD.     

Eigen-spectra in the Dirac-attractive radial problem plus a tensor interaction under pseudospin and spin symmetry with the SUSY approach

We approximately solve the Dirac equation for attractive radial potential including a Coulomb-like tensor interaction under pseudospin and the spin symmetry limit for any arbitrary spin-orbit quantum number, by employing the supersymmetric （SUSY） quantum mechanics and supersymmetric shape invariance technique. We obtain the energy eigenvalue equation under the pseudospin and spin conditions. Some numerical results are compared with those obtained by the Nikiforove-Uvarov （NU） method.     

Monte Carlo studies of triangulated spherical surfaces in the two-dimensional space

We numerically study a triangulated surface model in R²${\mathbf{R}}^2$ by taking into account a viewpoint of string model. The models are defined by a mapping X from a two-dimensional surface M   to R²${\mathbf{R}}^2$, where the mapping X and the metric g of M are the dynamical variables. The sum over g in the partition function is simulated by the sum over bond lengths and deficit angles by using the Regge calculus technique, and the sum over g is defined to be performed independently of the sum over X. We find that the model undergoes a first-order transition of surface fluctuations, which accompanies a collapsing transition, and that the transitions are reflected in the internal geometry of surface. Fluid surface models are also studied on dynamically triangulated surfaces, and the transitions are found to be of second order. The order of the transition remains unchanged from that of the conventional model defined only by the variable X both in the fixed-connectivity and the fluid models.     

Reynolds stresses in a lattice gas

I use a previously proposed algorithm, based on Lévy walks, to calculate and discuss longitudinal and transverse velocity correlations in turbulent channel flow. The general approach is that of lattice gas hydrodynamics.     

Correlations between microstructural alterations and severity of cognitive deficiency in Alzheimer's disease and mild cognitive impairment: a diffusional kurtosis imaging study

Object

Diffusional kurtosis imaging (DKI), a natural extension of diffusion tensor imaging (DTI), can characterize non-Gaussian diffusion in the brain. We investigated the capability of DKI parameters for detecting microstructural changes in both gray matter (GM) and white matter (WM) in patients with mild cognitive impairment (MCI) and Alzheimer's disease (AD) and sought to determine whether these DKI parameters could serve as imaging biomarkers to indicate the severity of cognitive deficiency.

Materials and Methods

DKI was performed on 18 AD patients and 12 MCI patients. Fractional anisotropy, kurtosis and diffusivity parameters in the temporal, parietal, frontal and occipital lobes were compared between the two groups using Mann–Whitney U test. The correlations between regional DKI parameters and mini-mental state examination (MMSE) score were tested using Pearson's correlation.

Results

In ADs, significantly increased diffusivity and decreased kurtosis parameters were observed in both the GM and WM of the parietal and occipital lobes as compared to MCIs. Significantly decreased fractional anisotropy was also observed in the WM of these lobes in ADs. With the exception of fractional anisotropy and radial kurtosis, all the five other DKI parameters exhibited significant correlations with MMSE score in both GM and WM.

Conclusion

Bearing additional information, the DKI model can provide sensitive imaging biomarkers for assessing the severity of cognitive deficiency in reference to MMSE score and potentially improve early detection and progression monitoring of AD based on characterizing microstructures in both the WM and especially the GM.     

Ab initio ro-vibrational Hamiltonian in irreducible tensor formalism: a method for computing energy levels from potential energy surfaces for symmetric-top molecules

A theoretical approach to study ro-vibrational molecular states from a full nuclear Hamiltonian expressed in terms of normal-mode irreducible tensor operators is presented for the first time. Each term of the Hamiltonian expansion can thus be cast in the tensor form in a systematic way using the formalism of ladder operators. Pyramidal XY₃ molecules appear to be good candidates to validate this approach which allows taking advantage of the symmetry properties when doubly degenerate vibrational modes are considered. Examples of applications will be given for PH₃ where variational calculations have been carried out from our recent potential energy surface [Nikitin et al., J. Chem. Phys. 130, 244312 (2009)].     

Relativistic symmetry of position-dependent mass particles in a Coulomb field including tensor interaction

The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials,including a tensor interaction under the spin and pseudospin symmetric limits.Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ.Some numerical results are also given,and the effect of tensor interaction on the bound states is presented.It is shown that tensor interaction removes the degeneracy between two states in the spin doublets.We also investigate the effects of the spatially-dependent mass on the bound states under spin symmetric limit conditions in the absence of tensor interaction.