Dynamic recursive

The sum in Eq. (43) can be obtained by a recursion algorithm used commonly in dynamic programming [62]. 

From this first example, it is obvious that, apart from a CA-like pai allel updating of an ever-increasing number of sites and the set of recursive symbol-strings to which such a dynamics inevitably leads, there is no real internal geometry, as such. Each string at time t remains essentially a static collection of abstract symbols. 

Historically, treatment of measurement noise has been addressed through two distinct avenues. For steady-state data and processes, Kuehn and Davidson (1961) presented the seminal paper describing the data reconciliation problem based on least squares optimization. For dynamic data and processes, Kalman filtering (Gelb, 1974) has been successfully used to recursively smooth measurement data and estimate parameters. Both techniques were developed for linear systems and weighted least squares objective functions. 

As was previously shown, Kalman filtering techniques can be, and have been, successfully used on dynamic process data, to smooth measurement data recursively and... 

In this chapter different aspects of data processing and reconciliation in a dynamic environment were briefly discussed. Application of the least square formulation in a recursive way was shown to lead to the classical Kalman filter formulation. A simpler situation, assuming quasi-steady-state behavior of the process, allows application of these ideas to practical problems, without the need of a complete dynamic model of the process. 

Recursive Solutions to Large Eigenproblems in Molecular Spectroscopy and Reaction Dynamics... 

For time-dependent Hamiltonians, one can reformulate the problem with the (t, l ) scheme,227 in which the time is treated as an extra degree of freedom. Thus, the techniques developed for stationary problems can be applied in a straightforward manner. Applications of recursive methods to laser-driven dynamics have been reported by several authors.99,228-230... 

The aforementioned applications of recursive methods in reaction dynamics do not involve diagonalization explicitly. In some quantum mechanical formulations of reactive scattering problems, however, diagonalization of sub-Hamiltonian matrices is needed. Recursive diagonalizers for Hermitian and real-symmetric matrices described earlier in this chapter have been used by several authors.73,81... 

Quantum Dynamics The Recursive-Residue-Generation Method. 

Willoughby, Eds., North Holland, Amsterdam, 1986, pp. 67-79. Quantum Dynamics with the Recursive Residue Generation Method Improved Algorithm for Chain Propagation. 

Moore [Moore, 1977b] studied the effect of oscillator implementation using lookup tables and found that linear interpolation produces the least distortion and that truncation produces the worst. This result was confirmed by Hartmann [Hartmann, 1987], Another possibility is to use a recursive (HR) filter with poles located on the unit circle. This coupled form [Tierney et al., 1971] offers a alternate method that avoids using memoiy space. Frequency resolution requirements were calculated by Snell in a superpipeline oscillator design for dynamic Fourier synthesis [Snell, 1977]. 

After ruling out slow modulation as a possible approach to complexity, we are left with the search for a more satisfactory approach to complexity that accounts for the renewal BQD properties. Is it possible to propose a more exhaustive approach to complexity, which explains both non-Poisson statistics and renewal at the same time We attempt at realizing this ambitious task in Section XVII. In Section XVII.A we show that a non-Ohmic bath can regarded as a source of memory and cooperation. It can be used for a dynamic approach to Fractional Brownian Motion, which, is, however, a theory without critical events. In Section XVIII.B we show, however, that the recursion process is renewal and fits the requests emerging from the statistical analysis of real data afforded by the researchers in the BQD held. In Section XVII.C we explain why this model might afford an exhaustive approach to complexity. 

---