Selected Essays on the Conflict of Laws. By Brainerd Currie.

Most subspace identication algorithms are not applicable to closed-loop identication because they require future input to be uncorrelated with pastinnovation. In this paper, we propose a new subspace identication method that remove this requirement by using a parsimonious model formulation with innovation estimation. A simulation example is included to show the effectiveness of the proposed method

Public Law by Private Bargain: Title VII Consent Decrees and the Fairness of Negotiated Institutional Reform

Large-scale Title VII remedies are typical of public law litigation, which differs in kind from the conventional compensatory lawsuit. Title VII remedies are commonly adopted by way of consent decrees. By approving these consent decrees, federal courts take responsibility for extensive institutional reforms while acting independently of the adversary process. Courts have frequently approved consent decrees without fair hearings for those whose interests are at stake. Professor Schwarzschild suggests a systematic procedure for approving Title VII consent decrees. This procedure would not discourage settlements, but would ensure that courts act on the basis of fair hearings, consistently with the quasi-legislative character of public law remedies

An Interacting model of Dark Energy in Brans-Dicke theory

In this paper it is shown that in non-minimally coupled Brans-Dicke theory containing a self-interacting potential, a suitable conformal transformation can automatically give rise to an interaction between the normal matter and the Brans-Dicke scalar field. Considering the scalar field in the Einstein frame as the quintessence matter, it has been shown that such a non-minimal coupling between the matter and the scalar field can give rise to a late time accelerated expansion for the universe preceded by a decelerated expansion for very high values of the Brans-Dicke parameter $\omega$. We have also studied the observational constraints on the model parameters considering the Hubble and Supernova data.Comment: 12 pages, 15 figures. Accepted for publication in Astrophysics and Space Scienc

Foreword

In this paper, we show that the consistency of closed-loop subspace identification methods (SIMs) can be achieved through innovation estimation. Based on this analysis, a sufficient condition for the consistency of a new proposed closed-loop SIM is given, A consistent estimate of the Kalman gain under closed-loop conditions is also provided based on the algorithm. A multi-input-multi-output simulation shows that itis consistent under closed-loop conditions, when traditional SIMs fail to provide consistent estimates

Optimal Pooling in Claims Resolution Facilities

A class of nonlinear stochastic processes satysfying a "Lipschitz-type strip condition" and supplied by a linear output equation, is considered. Robust asymptotic (high-gain) state estimation for nonlinear stochastic processes via differential neural networks is discussed. A new type learning law for the weight dynamics is suggested. By a stochastic Lyapunov-like analysis (with Ito formula implementation), the stability conditions for the state estimation error as well as for the neural network weights are established. The upper bound for this error is derived. The numerical example, dealing with "module"-type nonlinearities, illustrates the effectiveness of the suggested approach

Competing Interactions among Supramolecular Structures on Surfaces

A simple model was constructed to describe the polar ordering of non-centrosymmetric supramolecular aggregates formed by self assembling triblock rodcoil polymers. The aggregates are modeled as dipoles in a lattice with an Ising-like penalty associated with reversing the orientation of nearest neighbor dipoles. The choice of the potentials is based on experimental results and structural features of the supramolecular objects. For films of finite thickness, we find a periodic structure along an arbitrary direction perpendicular to the substrate normal, where the repeat unit is composed of two equal width domains with dipole up and dipole down configuration. When a short range interaction between the surface and the dipoles is included the balance between the up and down dipole domains is broken. Our results suggest that due to surface effects, films of finite thickness have a none zero macroscopic polarization, and that the polarization per unit volume appears to be a function of film thickness.Comment: 3 pages, 3 eps figure

Improved model identification for non-linear systems using a random subsampling and multifold modelling (RSMM) approach

In non-linear system identification, the available observed data are conventionally partitioned into two parts: the training data that are used for model identification and the test data that are used for model performance testing. This sort of 'hold-out' or 'split-sample' data partitioning method is convenient and the associated model identification procedure is in general easy to implement. The resultant model obtained from such a once-partitioned single training dataset, however, may occasionally lack robustness and generalisation to represent future unseen data, because the performance of the identified model may be highly dependent on how the data partition is made. To overcome the drawback of the hold-out data partitioning method, this study presents a new random subsampling and multifold modelling (RSMM) approach to produce less biased or preferably unbiased models. The basic idea and the associated procedure are as follows. First, generate K training datasets (and also K validation datasets), using a K-fold random subsampling method. Secondly, detect significant model terms and identify a common model structure that fits all the K datasets using a new proposed common model selection approach, called the multiple orthogonal search algorithm. Finally, estimate and refine the model parameters for the identified common-structured model using a multifold parameter estimation method. The proposed method can produce robust models with better generalisation performance

Spectral Line Removal in the LIGO Data Analysis System (LDAS)

High power in narrow frequency bands, spectral lines, are a feature of an interferometric gravitational wave detector's output. Some lines are coherent between interferometers, in particular, the 2 km and 4 km LIGO Hanford instruments. This is of concern to data analysis techniques, such as the stochastic background search, that use correlations between instruments to detect gravitational radiation. Several techniques of `line removal' have been proposed. Where a line is attributable to a measurable environmental disturbance, a simple linear model may be fitted to predict, and subsequently subtract away, that line. This technique has been implemented (as the command oelslr) in the LIGO Data Analysis System (LDAS). We demonstrate its application to LIGO S1 data.Comment: 11 pages, 5 figures, to be published in CQG GWDAW02 proceeding