In this letter, we propose control theoretic smoothing splines with L1optimality for reducing the number of parameters that describes the fitted curve as well as removing outlier data. A control theoretic spline is a smoothing spline that is generated as an output of a given linear dynamical system. Conventional design requires exactly the same number of base functions as given data, and the result is not robust against outliers. To solve these problems, we propose to use L1optimality, that is, we use the L1norm for the regularization term and/or the empirical risk term. The optimization is described by a convex optimization, which can be efficiently solved via a numerical optimization software. A numerical example shows the effectiveness of the proposed method.

In a dynamical system the input is to be recovered from finitely many measurements, blurred by random error, of the output of the system. As usual, the differential equation describing the system is reduced to multiplication with a polynomial after applying the Laplace transform. It appears that there exists a natural, unbiased, estimator for the Laplace transform of the output, from which an estimator of the input can be obtained by multiplication with the polynomial and subsequent application of a regularized inverse of the Laplace transform. It is possible, moreover, to balance the effect of this inverse so that ill-posedness remains restricted to its actual source: differentiation. The rate of convergence of the integrated mean-square error is a positive power of the number of data. The order of the differential equation has an adverse effect on the rate which, on the other hand, increases with the smoothness of the input as usual.

Examines the effects of geometry and material properties on criteria that could be used in establishing a notion of optimal form in bone or prosthetic devices. This is accomplished by determining extreme values of functionals that are measures of strain energy and compliance. The governing differential equation includes the effects of collageneous tissue acting on the bone and in the case of the prosthetic model, interfacial interactions between the device and the bone. Augmented Lagrange techniques and non-linear conjugate gradient methods are used to determine the optimal solution.>

A muscular control model is examined in order to determine possible fatigue effects on the monosynaptic reflex. The muscle dynamics and neural spindle receptors are represented in standard fashion as 4-element viscoelastic models. A theoretical derivation of the afferent spindle output is given. This afferent information from the muscle-spindle and delay effects are incorporated into the feedback loop. Fatigue effects upon system performance and stability are illustrated by means of numerical simulations.>

Certain applications require pseudo-random sequences which are unpredictable in the sense that recovering more of the sequence from a short segment must be computationally infeasible. It is shown that linear complexity is useful in determining such sequences. A generalized linear complexity that has application to the security of stream ciphers is proposed, and an efficient algorithm is given for the case in which the sequence is binary with period 2/sup n/. This algorithm generalizes an algorithm presented by R.A. Games and A.H. Chan (1983).>

Given that the autocorrelations for any repeating number sequence are known, this paper gives an algorithm for determining the autocorrelation structure of a new sequence obtained from the original sequence by proper decimation. Therefore, for certain random number generators, it is possible to choose a proper decimation which results in a long interval in which the autocorrelations are small for all shifts.