State Transition Density Research Articles

TRACKING ALGORITHM FOR MMW/IR MULTI-SENSORS FUSION

Millimeter wave(MMW)/infrared (IR) sensor is a key technology for composite guidance system of missiles. Aimming to solve the problems that there were linear errors in the algorithm of square-root unscented Kalman filter (SR-UKF) and it was difficult to obtain the importance density function for the algorithm of particle filter(PF), a square-root unscented Kalman particle filter (SR-UK-PF) algorithm with the sequential fusion was presented by combining SR-UKF with PF. The main idea of this algorithm was to calculate the state transition matrix and the error covariance matrix by SR-UKF, and to construct the importance density function by the sequential fusion of particle filter. Thus, the importance density function could integrate the latest observation into system state transition density, and the proposal distribution could be more in line with the distribution of real states. To demonstrate the effectiveness of this model, simulations were carried out based on tracking algorithm for the surface-to-air missile with MMW/IR sensor.The results show that this technique can overcome the flaw that it is hard to get the optimization importance density function in the particle filter, and it can significantly improve the accuracy of state estimation for the system with multi-sensors.

Interval diffracted particle filter

A new particle filter based on interval filter and particle diffraction is proposed for the on-line estimation of non-Gaussian and nonlinear system with uncertain dynamics modeling. This algorithm computes the more accurate importance density function, which integrates the latest observations into the system state transition density, so that the approximation to the system posterior density is improved. At the same time, the workload of calculation is reduced by treating particle diffraction like light diffraction. A simulation experiment on the SINS/CNS (strap-down inertial navigation system/celestial navigation system) attitude estimation shows the effectiveness and robustness of the improved algorithm.

Relativistic quasiparticle time blocking approximation. II. Pygmy dipole resonance in neutron-rich nuclei

Theoretical studies of low-lying dipole strength in even-even spherical nuclei within the relativistic quasiparticle time blocking approximation (RQTBA) are presented. The RQTBA developed recently as an extension of the self-consistent relativistic quasiparticle random-phase approximation (RQRPA) enables one to investigate the effects of the coupling of two-quasiparticle excitations to collective vibrations within a fully consistent calculation scheme based on covariant energy density functional theory. Dipole spectra of even-even $^{130}\mathrm{Sn}\text{\ensuremath{-}}^{140}\mathrm{Sn}$ and $^{68}\mathrm{Ni}\text{\ensuremath{-}}^{78}\mathrm{Ni}$ isotopes calculated within both RQRPA and RQTBA show two well-separated collective structures: the higher lying giant dipole resonance and the lower lying pygmy dipole resonance, which can be identified by the different behavior of the transition densities of states in these regions.

Efficient computation of the maximum a posteriori path and parameter estimation in integrate-and-fire and more general state-space models

A number of important data analysis problems in neuroscience can be solved using state-space models. In this article, we describe fast methods for computing the exact maximum a posteriori (MAP) path of the hidden state variable in these models, given spike train observations. If the state transition density is log-concave and the observation model satisfies certain standard assumptions, then the optimization problem is strictly concave and can be solved rapidly with Newton-Raphson methods, because the Hessian of the loglikelihood is block tridiagonal. We can further exploit this block-tridiagonal structure to develop efficient parameter estimation methods for these models. We describe applications of this approach to neural decoding problems, with a focus on the classic integrate-and-fire model as a key example.

Moment equations and Hermite expansion for nonlinear stochastic differential equations with application to stock price models

Exact moment equations for nonlinear Ito processes are derived. Taylor expansion of the drift and diffusion coefficients around the first conditional moment gives a hierarchy of coupled moment equations which can be closed by truncation or a Gaussian assumption. The state transition density is expanded into a Hermite orthogonal series with leading Gaussian term and the Fourier coefficients are expressed in terms of the moments. The resulting approximate likelihood is maximized by using a quasi Newton algorithm with BFGS secant updates. A simulation study for the CEV stock price model compares the several approximate likelihood estimators with the Euler approximation and the exact ML estimator (Feller, in Ann Math 54: 173---182, 1951).

Theoretical analysis of spin-dependent Mn K-edge x-ray absorption of MnP

Spin-dependent x-ray absorption near edge structure (XANES) spectra measured by selectively monitoring of the Mn K-beta emission while scanning the excitation energy through the Mn K absorption edge were analyzed. The method of calculation is based on a combination of self-consistent spin-polarized calculation of muffin-tin potential and a full multiple scattering theory for interpretation of x-ray absorption. This approach allows to separate influence of dipole transition matrix elements and density of empty electronic states on spin-dependent XANES. It is found that matrix elements affect the splitting between spin-up and spin-down spectra only near the absorption threshold, while differences in densities of states slightly shift spectra in the region 35–55 eV above the main edge. Effects of multielectron term dependent broadening of spin-dependent XANES spectra and different mean free paths of photoelectrons with spin-up and spin-down in ferromagnetic phase were taken into account. It is shown that these factors also contribute to the splitting of spectra with different spin directions near the absorption threshold.

Satellite propagation channel modelling using photogrammetry and hidden Markov model approach

In a typical satellite-earth propagation path, the field strength of the received signal level changes with respect to time and space according to the changing morphology of the environment. It has been shown that the switching between different attenuation levels can be represented as a Markov stochastic process using the assumption that the channel properties are quasi-stationary in small periods of time. A hidden Markov model is introduced to replace the often used channel fading models, such as Rice, Loo and Rayleigh distributions. Three sets of parameters are trained to simulate the state transition and observation conditional probability density function among three basic propagation states that are categorised according to the environmental images. The simulated data were compared to the real RF measurement of satellite signals in several propagation properties, such as the cumulative fading distribution, level cross rate and error probability performance, at typical user environments. With the help of observation sets and their conditional probability densities, the proposed propagation channel simulator can model the satellite propagation properties with better accuracy than three-state Markov transition models.

Monopole giant resonances and nuclear compressibility in relativistic mean field theory

Isoscalar and isovector monopole oscillations that correspond to giant resonances in spherical nuclei are described in the framework of time-dependent relativistic mean-field (RMF) theory. Excitation energies and the structure of eigenmodes are determined from a Fourier analysis of dynamical monopole moments and densities. The generator coordinate method, with generating functions that are solutions of constrained RMF calculations, is also used to calculate excitation energies and transition densities of giant monopole states. Calculations are performed with effective interactions which differ in their prediction of the nuclear matter compression modulus K nm, Both time-dependent and constrained RMF results indicate that empirical GMR energies are best reproduced by an effective force with K nm ≈ 250–270 MeV.

Semi-quantitative methods for studying disorder and hydrogenation in hydrogenated amorphous silicon using Auger lineshape analysis

Simple methods have been developed to enable the X-ray excited silicon L 2,3VV, and the experimentally more difficult L 1L 2,3V, Auger spectra to be treated routinely using numerical debroadening and deconvolution to obtain an indication of the valence band transition densities of states for the surface. A method based on the simplex algorithm has then been applied to enable both the Si L 2,3VV and Si L 1L 2,3V spectra to be decomposed (decoupled) into their component (pp-, sp- and ss-like) peaks. Changes in these components have been compared before and after disordering and hydrogenation of the surface to quantitatively probe the effect of these treatments on the surface valence band densities of states. It is shown that both the L 2,3VV and L 1L 2,3V lines give a simple semi-quantitative method for monitoring hydrogen incorporation in hydrogenated amorphous silicon. Examples of these methods applied to artificially and naturally hydrogenated amorphous silicon surfaces are presented to illustrate their usefulness for studying materials fabricated for use in solar cells.

13C-NMR study on β-(BEDT-TTF) 2I 3

The 13C-NMR and spin susceptibility measurements were performed to investigate the electronic state in β(BEDT-TTF) 2I 3 before and during annealing. Interrelation between incommensurate superlattice, low temperature electronic anomaly, superconducting transition temperature and density of states in this salt was found.

Effect of ground state correlations on the charge transition densities of vibrational states

An extension of a previous treatment of the ground state correlations beyond the random phase approximation, namely including their influence on the pairing, is presented. The effect of such correlations on the energies and transition densities of the vibrational states is studied. This effect results in a further suppression of the unphysical oscillations of the charge transition density in the interior part of the Zn isotopes, lending to good agreement with experimental data.

Ground state correlations and charge transition densities

The effect of the ground state correlations on the charge transition densities of the quadrupole vibration states in spherical nuclei is studied. The problem for the ground state correlations beyond the RPA leads to a non-linear system of equations, which is solved numerically. The calculations when the ground state correlations are taken into account give a 30% depletion of the charge transition density in the nuclear interior in comparison with the RPA calculation.

Theoretical stimulation and experimental determination of OH and OD stretching bands of isotopically diluted water-d molecules in aqueous electrolyte solutions

A combined theoretical and experimental study of the hydration of ions in aqueous electrolyte solutions is presented. Theoretical simulations of OH and OD stretching bands of isotopically diluted HDO molecules in a 0.44 m lithium formate solution have been performed. The positions of the atoms of the water molecules and the ions were taken from the trajectory file of a rigid-molecule room-temperature molecular dynamics simulation. V(r(OH)) potential energy functions were constructed as a sum of intra- and intermolecular energies and used in a variational calculation of the vibrational energy levels. Vibrational transition densities of states were calculated for HDO molecules in the first and second hydration shells of the ions. Infrared spectra of isotopically isolated HDO molecules in aqueous solutions of NaHCOO, LiClO4, NaClO4, Ca(ClO4)2, and Sr(ClO4)2 have been registered. The spectra were evaluated using an earlier developed double-difference method, where the number of ion-affected water molecules enters as a parameter in the analysis. In the present work, this number is obtained from the theoretical calculations, both for the Li+ and the HCOO- ion hydration. We find that OH/OD groups of water molecules in the second hydration shell of Li+, hydrogen-bonded to the first hydration shell, are affected by the ion. The earlier observed division of IR stretching frequencies for HDO molecules around cations into two distinct groups can now be explained by the presence or absence of such second-hydration-shell water molecules. For HDO molecules hydrogen-bonded to the HCOO- ions, the OH/OD frequency is lowered, compared to bulk water, for the OH/OD group involved in H-bonding to the ion, whereas the frequency is increased for the other OD/OH group, pointing away from the ion. The frequencies of HDO molecules surrounding the CH end of the formate ion are not influenced by the ion.

Corrections and additions to ‘a nonlinear equilibrium model of the term structure of interest rates’

Abstract Longstaff (1989) introduces a new process for the short rate of interest. He claims to derive the zero-coupon bond pricing formula and state transition density for his model. We demonstrate that Longstaff's pricing formula is not the solution to the pricing problem which he poses. The source of his error is a failure to properly account for a boundary condition. We introduce a new model economy and derive a new endogenous interest rate process, and find the Green's function and the price of a zero-coupon bond for our model economy.

Many-particle effects at core thresholds in simple metals.

We have analyzed inelastic electron-scattering (IES) data at the Na ${\mathit{L}}_{2,3}$ and K ${\mathit{M}}_{2,3}$ thresholds in terms of the Mahan-Nozi\`eres--De Dominicis (MND) model. We have also obtained the absorption coefficient \ensuremath{\mu} and imaginary dielectric function ${\mathrm{\ensuremath{\epsilon}}}_{2}$ from the IES data and analyzed them in the same manner as the raw data. For K the peaking parameter ${\mathrm{\ensuremath{\alpha}}}_{0}$ obtained from absorption depends upon whether IES data, \ensuremath{\mu}, or ${\mathrm{\ensuremath{\epsilon}}}_{2}$ is used. For Na, ${\mathrm{\ensuremath{\alpha}}}_{0}$ does not vary significantly among the three absorption spectral functions and has a value of 0.22\ifmmode\pm\else\textpm\fi{}0.03 if uncertainties in the transition density of states are included. Exchange mixing is found to be a small effect at the Na ${\mathit{L}}_{2,3}$ absorption edge. We have reanalyzed published p-core soft-x-ray emission data from Na and K and account for the effects of partial phonon relaxation on ${\mathrm{\ensuremath{\alpha}}}_{0}$. In both cases ${\mathrm{\ensuremath{\alpha}}}_{0}$ is significantly less than for the corresponding absorption spectra with values of about 0.15. We have also reanalyzed published Na core-level x-ray photoemission spectroscopy data including surface contributions and for the appropriate exponent obtain \ensuremath{\alpha}=0.22\ifmmode\pm\else\textpm\fi{}0.02. The results above taken in concert indicate a failure in the presently accepted MND model. We suggest that previously unconsidered dynamical effects must be included.

Effects of disorder on electronic structures of a-Si:H and a-SiO2.

Si ${L}_{23}$ x-ray emission spectra from c-Si, doped and intrinsic a-Si:H, quartz, and a-${\mathrm{SiO}}_{2}$ are presented. The first and second moments of the valence-band transition density of states of each of these samples were computed. The variance of the disorder potential that characterizes the amorphous network was found for the amorphous samples from their second moments. Lifetime broadening as a function of energy in the valence band of silicon samples was found to vary significantly between the crystalline and amorphous structures.

Transition density of states (TDOS) of the Si(100)2 × 1 surface derived from the L 2,3VV Auger lineshape compared with cluster calculations

The termination of a silicon crystal along the (100) orientation resulting in a 2 × 1 reconstructed surface induces relatively large variations in the local density of states (LDOS) of the different types of surface atoms, such as the up and down dimer atom and the backbond atom. Auger electron spectroscopy (AES) is able to probe the LDOS of the silicon atom in which the L 2,3 core hole has been created and is therefore a candidate to analyze the LDOS of the surface atoms. A detailed analysis of the SiL 2,3VV Auger electron spectrum allows us to determine a high quality transition density of state (TDOS) of the Si(100)2 × 1 reconstructed surface. The resolved peaks in the TDOS were compared with previous AES, UPS and EELS measurements reported by other investigators. Quantum chemical cluster calculations were used for the interpretation of the TDOS in the actual p-like and s-like partial local density of states for different types of silicon atoms. These quantum chemical cluster calculations of the partial LDOS localized at atoms of the Si(100)2 × 1 surface were found to be in agreement with other types of calculations. Comparing the experimental and the calculated DOS we were able to distinguish several new peaks in the TDOS obtained with AES and to discriminate features in the experimentally obtained TDOS into local electron distributions localized at different surface atoms.

Transition density of states (TDOS) of the Si(100)2 × 1 surface derived from the L 2,3VV auger lineshape compared with cluster calculations

Transition density of states (TDOS) of the Si(100)2 × 1 surface derived from the L 2,3VV auger lineshape compared with cluster calculations

Empirical application of Dyson's equation to the L2,3 soft-x-ray-emission transition densities of states of c-Si and a-Si:H.

We have measured the soft-x-ray--emission ${L}_{2}$,3 spectra of c-Si and a-Si:H and removed the shakeup and bremsstrahlung contributions using the method of Livins and Schnatterly [Phys. Rev. B 37, 6731 (1988); 37, 6742 (1988)]. We have obtained an estimate of the real part of the self-energy describing the effect of the random potential which characterizes a-Si:H on the c-Si transition density of states (TDOS), using an approach based on Dyson's equation. This approach also yields the TDOS of c-Si and a-Si:H outright. In addition, we resolve the spectra into ${L}_{2}$ and ${L}_{3}$ components using an iterative procedure and remove an estimate of the intrinsic broadening effects, and thereby obtain a second determination of the TDOS. These results and those obtained through the procedure based on Dyson's equation agree. The TDOS obtained for c-Si compares well with calculations.

Stoner transitions and spin-selective excitations in bcc cobalt.

Spin-selective excitations (Stoner excitations) have been unambiguously identified by comparisons between spin-polarized-electron energy-loss spectra and calculated transition density of states. Analysis of the specular beam for polarized electrons incident on thin films of bcc Co shows three sharp, highly polarized loss features (background corrected asymmetry near 100%). Comparison with the theoretical Stoner and spin-nonflip transition density of states shows excellent agreement, permitting identification of the associated loss mechanisms.