Fixed wages and bonuses in agency contracts: the case of a continuous state space

In this paper, we extend the state-contingent production approach to principal–agent problems to the case where the state space is an atomless continuum. The approach is modelled on the treatment of optimal tax problems. The central observation is that, under reasonable conditions, the optimal contract may involve a fixed wage with a bonus for above-normal performance. This is analogous to the phenomenon of "bunching" at the bottom in the optimal tax literature.

Constructing internationally comparable real income aggregates by combining sparse benchmark data with annual national accounts data: A state-space approach

The importance of availability of comparable real income aggregates and their components to applied economic research is highlighted by the popularity of the Penn World Tables. Any methodology designed to achieve such a task requires the combination of data from several sources. The first is purchasing power parities (PPP) data available from the International Comparisons Project roughly every five years since the 1970s. The second is national level data on a range of variables that explain the behaviour of the ratio of PPP to market exchange rates. The final source of data is the national accounts publications of different countries which include estimates of gross domestic product and various price deflators. In this paper we present a method to construct a consistent panel of comparable real incomes by specifying the problem in state-space form. We present our completed work as well as briefly indicate our work in progress.

Existence and uniqueness of Q-processes with a given finite μ-invariant measure

Let Q be a stable and conservative Q-matrix over a countable state space S consisting of an irreducible class C and a single absorbing state 0 that is accessible from C. Suppose that Q admits a finite mu-subinvariant measure in on C. We derive necessary and sufficient conditions for there to exist a Q-process for which m is mu-invariant on C, as well as a necessary condition for the uniqueness of such a process.

Estimating trends and seasonality in coronary heart disease

We present two methods of estimating the trend, seasonality and noise in time series of coronary heart disease events. In contrast to previous work we use a non-linear trend, allow multiple seasonal components, and carefully examine the residuals from the fitted model. We show the importance of estimating these three aspects of the observed data to aid insight of the underlying process, although our major focus is on the seasonal components. For one method we allow the seasonal effects to vary over time and show how this helps the understanding of the association between coronary heart disease and varying temperature patterns. Copyright (C) 2004 John Wiley Sons, Ltd.

Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

Output price subsidies in a stochastic world

This article studies the comparative statics of output subsidies for firms, with monotonic preferences over costs and returns, that face price and production uncertainty. The modeling of deficiency payments, support-price schemes, and stochastic supply shifts in a state-space framework is discussed. It is shown how these notions can be used, via a simple application of Shephard's lemma, to analyze input-demand shifts once comparative-static results for supply are available. A range of comparative-static results for supply are then developed and discussed.

A diffusion approach to approximating preservation probabilities for gene duplicates

Consider a haploid population and, within its genome, a gene whose presence is vital for the survival of any individual. Each copy of this gene is subject to mutations which destroy its function. Suppose one member of the population somehow acquires a duplicate copy of the gene, where the duplicate is fully linked to the original gene's locus. Preservation is said to occur if eventually the entire population consists of individuals descended from this one which initially carried the duplicate. The system is modelled by a finite state-space Markov process which in turn is approximated by a diffusion process, whence an explicit expression for the probability of preservation is derived. The event of preservation can be compared to the fixation of a selectively neutral gene variant initially present in a single individual, the probability of which is the reciprocal of the population size. For very weak mutation, this and the probability of preservation are equal, while as mutation becomes stronger, the preservation probability tends to double this reciprocal. This is in excellent agreement with simulation studies.

Distillability of Werner states using entanglement witnesses and robust semidefinite programs

We use robust semidefinite programs and entanglement witnesses to study the distillability of Werner states. We perform exact numerical calculations that show two-undistillability in a region of the state space, which was previously conjectured to be undistillable. We also introduce bases that yield interesting expressions for the distillability witnesses and for a tensor product of Werner states with an arbitrary number of copies.

Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems

We consider a problem of robust performance analysis of linear discrete time varying systems on a bounded time interval. The system is represented in the state-space form. It is driven by a random input disturbance with imprecisely known probability distribution; this distributional uncertainty is described in terms of entropy. The worst-case performance of the system is quantified by its a-anisotropic norm. Computing the anisotropic norm is reduced to solving a set of difference Riccati and Lyapunov equations and a special form equation.

A helicopter named Dolly: Behavioural cloning for autonomous helicopter control

This paper considers the pros and cons of using behavioural cloning for the development of low-level helicopter automation modules. Over the course of this project several Behavioural cloning approaches have been investigated. The results of the most effective Behavioural cloning approach are then compared to PID modules designed for the same aircraft. The comparison takes into consideration development time, reliability, and control performance. It has been found that Behavioural cloning techniques employing local approximators and a wide state-space coverage during training can produce stabilising control modules in less time than tuning PID controllers. However, performance and reliabity deficits have been found to exist with the Behavioural Cloning, attributable largely to the time variant nature of the dynamics due to the operating environment, and the pilot actions being poor for teaching. The final conclusion drawn here is that tuning PID modules remains superior to behavioural cloning for low-level helicopter automation.

Bitwise bell-inequality violations for an entangled state involving 2N ions

Following on from previous work [J.-A. Larsson, Phys. Rev. A 67, 022108 (2003)], Bell inequalities based on correlations between binary digits are considered for a particular entangled state involving 2N trapped ions. These inequalities involve applying displacement operations to half of the ions and then measuring correlations between pairs of corresponding bits in the binary representations of the number of center-of-mass phonons of N particular ions. It is shown that the state violates the inequalities and thus displays nonclassical correlations. It is also demonstrated that it violates a Bell inequality when the displacements are replaced by squeezing operations.

Tracking the states of a nonlinear and nonstationary system in the weight-space of artificial neural networks

We propose a novel interpretation and usage of Neural Network (NN) in modeling physiological signals, which are allowed to be nonlinear and/or nonstationary. The method consists of training a NN for the k-step prediction of a physiological signal, and then examining the connection-weight-space (CWS) of the NN to extract information about the signal generator mechanism. We de. ne a novel feature, Normalized Vector Separation (gamma(ij)), to measure the separation of two arbitrary states i and j in the CWS and use it to track the state changes of the generating system. The performance of the method is examined via synthetic signals and clinical EEG. Synthetic data indicates that gamma(ij) can track the system down to a SNR of 3.5 dB. Clinical data obtained from three patients undergoing carotid endarterectomy of the brain showed that EEG could be modeled (within a root-means-squared-error of 0.01) by the proposed method, and the blood perfusion state of the brain could be monitored via gamma(ij), with small NNs having no more than 21 connection weight altogether.