LMMSE Estimation and Interpolation of Continuous-Time Signals from Discrete-Time Samples Using Factor Graphs

The factor graph approach to discrete-time linear Gaussian state space models is well developed. The paper extends this approach to continuous-time linear systems/filters that are driven by white Gaussian noise. By Gaussian message passing, we then obtain MAP/MMSE/LMMSE estimates of the input signal, or of the state, or of the output signal from noisy observations of the output signal. These estimates may be obtained with arbitrary temporal resolution. The proposed input signal estimation does not seem to have appeared in the prior Kalman filtering literature

Evolution of Bulk Scale Factor in Warped Space-time

In this work the role of extra dimensions in the accelerated universe through the scenario of higher-dimensional Friedmann-Robertson-Walker (FRW) cosmology has been studied. For this purpose, we first consider warped space-time in the standard flat brane scenario as the modified form of Robertson-Walker (RW) metric in five-dimension (5D) space-time and then the variation of the bulk scale factor (warp factor), with respect to both space-like and time-like extra dimensions is obtained. Finally, it is shown that both of two types of extra dimensions are important in this scenario and also the bulk scale factor plays two different roles.Comment: This paper has been withdrawn by the author due to text overlap with arXiv:0710.3790 by other author

Time-domain scars: resolving the spectral form factor in phase space

We study the relationship of the spectral form factor with quantum as well as classical probabilities to return. Defining a quantum return probability in phase space as a trace over the propagator of the Wigner function allows us to identify and resolve manifolds in phase space that contribute to the form factor. They can be associated to classical invariant manifolds such as periodic orbits, but also to non-classical structures like sets of midpoints between periodic points. By contrast to scars in wavefunctions, these features are not subject to the uncertainty relation and therefore need not show any smearing. They constitute important exceptions from a continuous convergence in the classical limit of the Wigner towards the Liouville propagator. We support our theory with numerical results for the quantum cat map and the harmonically driven quartic oscillator.Comment: 10 pages, 4 figure

Periodic interference structures in the time-like proton form factor

An intriguing and elusive feature of the timelike hadron form factor is the possible presence of an imaginary part associated to rescattering processes. We find evidence of that in the recent and precise data on the proton timelike form factor measured by the BABAR collaboration. By plotting these data as a function of the 3-momentum of the relative motion of the final proton and antiproton, a systematic sinusoidal modulation is highlighted in the near-threshold region. Our analysis attributes this pattern to rescattering processes at a relative distance of 0.7-1.5 fm between the centers of the forming hadrons. This distance implies a large fraction of inelastic processes in $\bar{p}p$ interactions, and a large imaginary part in the related $e^+e^- \rightarrow \bar{p}p$ reaction because of unitarity.Comment: 5 pages 3 figures - Discussion modified. To appear in Phys Rev Letter

Fitting dynamic factor models to non-stationary time series

Factor modelling of a large time series panel has widely proven useful to reduce its cross-sectional dimensionality. This is done by explaining common co-movements in the panel through the existence of a small number of common components, up to some idiosyncratic behaviour of each individual series. To capture serial correlation in the common components, a dynamic structure is used as in traditional (uni- or multivariate) time series analysis of second order structure, i.e. allowing for infinite-length filtering of the factors via dynamic loadings. In this paper, motivated from economic data observed over long time periods which show smooth transitions over time in their covariance structure, we allow the dynamic structure of the factor model to be non-stationary over time, by proposing a deterministic time variation of its loadings. In this respect we generalise existing recent work on static factor models with time-varying loadings as well as the classical, i.e. stationary, dynamic approximate factor model. Motivated from the stationary case, we estimate the common components of our dynamic factor model by the eigenvectors of a consistent estimator of the now time-varying spectral density matrix of the underlying data-generating process. This can be seen as time-varying principal components approach in the frequency domain. We derive consistency of this estimator in a "double-asymptotic" framework of both cross-section and time dimension tending to infinity. A simulation study illustrates the performance of our estimators.econometrics;

Capital investments in the context of time factor

The market economy creates various variants that an investor or another should know very well, should analyze them and choose the variant of investment which is the closes to its purposes. Such a variant of investments is the one that may materialize in certain manufacturing capacities, case in which the gain of the investor turns into profit; on this plan, we may assert that gaining much profit is the final purpose pursued by any investor in such a variant of capital placement. On the other side, we also must emphasize that profit is earned in time, and the time factor, on its turn, should be known, analyzed, localized and, certainly, quantified, so that the investment decision should not be empirical, but substantiated. This paper proposes to focus on few of the most important aspects of the impact of time factor on the capital investments, generally, and on their economic efficiency, particularly.profit, final profit, efficient period, functioning period, recovery period