Time consistency and risk averse dynamic decision models: Definition,interpretation and practical consequences

This paper aims at resolving a major obstacle to practical usage of time-consistent risk-averse decision models. The recursive objective function, generally used to ensure time consistency, is complex and has no clear/direct interpretation. Practitioners rather choose a simpler and more intuitive formulation, even though it may lead to a time inconsistent policy. Based on rigorous mathematical foundations, we impel practical usage of time consistent models as we provide practitioners with an intuitive economic interpretation for the referred recursive objective function. We also discourage time-inconsistent models by arguing that the associated policies are sub-optimal. We developed a new methodology to compute the sub-optimality gap associated with a time-inconsistent policy, providing practitioners with an objective method to quantify practical consequences of time inconsistency. Our results hold for a quite general class of problems and we choose, without loss of generality, a CVaR-based portfolio selection application to illustrate the developed concepts.     

Idempotent splittings,colimit completion,and weak aspects of the theory of monads

We show that some recent constructions in the literature, named ‘weak’ generalizations, can be systematically treated by passing from 2-categories to categories enriched in the Cartesian monoidal category of Cauchy complete categories.     

Spectroscopic analysis of the tribological behavior of a model boundary layer lubricant

Highly ordered alkanethiol self-assembled monolayers (SAMs) on gold substrates are suitable models of boundary layer lubricants and may be used in actual nanoscale device applications. Here, such monolayers were studied by spectroscopic methods as a function of tribological wear (rubbing) using a pin-on-disk microtribometer. The coefficient of friction (COF) (ratio of the frictional force to the load) was measured with the tribometer, and reflectance infrared spectra and X-ray photoelectron spectra were obtained as the monolayer film failed and the COF changed. The results show that it is possible to correlate disorder in the monolayer film with tribological failure of the film, and that continued rubbing produces a chemical change in the monolayer film. Disorder in the monolayer is distinct from the influence of wear in the underlying gold substrate. Aged SAMs, having sulfonate rather than thiol headgroups and initially less well ordered, behave differently to the well-ordered freshly prepared SAMs. Interestingly, they show a lower COF over many more cycles of exposure to the rubbing pin. The impact of the mechanism of film failure in boundary layer lubrication is discussed.     

Photoconductivity of amorphous semiconductors

An analysis of photoconductivity is presented for a material with a carrier mobility which decreases as a power law with time. We calculate the steady state and transient response, and show that the model applies to hydrogenated amorphous silicon and other amorphous semiconductors. In a-Si:H the effective mobility is obtained from 10^?6 to 1 sec. The recombination is of bimolecular type and the carrier density is almost independent of excitation intensity.     

Higher categories,strings, cubes and simplex equations

This survey of categorical structures, occurring naturally in mathematics, physics and computer science, deals with monoidal categories; various structures in monoidal categories; free monoidal structures; Penrose string notation; 2-dimensional categorical structures; the simplex equations of field theory and statistical mechanics; higher-order categories and computads; the (v,d)-cube equations; the simplex equations as cubical cocycle equations; and, cubes, braids and higher braids.     

A coupled multigrid-domain-splitting technique for simulating incompressible flows in geometrically complex domains

This paper describes a domain decomposition numerical procedure for solving the Navier-Stokes equations in regions with complex geometries. The numerical method includes a modified version of QUICK (quadratic upstream interpolation convective kinematics) for the formulation of convective terms and a central difference scheme for the diffusion terms. A second-order-accurate predictor-corrector scheme is employed for the explicit time stepping. Although the momentum equations are solved independently on each subdomain, the pressure field is computed simultaneously on the entire flow field. A multigrid technique coupled with a Schwarz-like iteration method is devised to solve the pressure equation over the composite domains. The success of this strategy depends crucially on appropriate methods for specifying intergrid pressure boundary conditions on subdomains. A proper method for exchanging information among subdomains during the Schwarz sweep is equally important to the success of the multigrid solution for the overall pressure field. These methods are described and subsequently applied to two forced convection flow problems involving complex geometries to demonstrate the power and versatility of the technique. The resulting pressure and velocity fields exhibit excellent global consistency. The ability to simulate complex flow fields with this method provides a powerful tool for analysis and prediction of mixing and transport phenomenon.     

Doubling and Tripling Constructions for Defining Sets in Steiner Triple Systems

 A minimal defining set of a Steiner triple system on v points (STS(v)) is a partial Steiner triple system contained in only this STS(v), and such that any of its proper subsets is contained in at least two distinct STS(v)s. We consider the standard doubling and tripling constructions for STS(2v+1) and STS(3v) from STS(v) and show how minimal defining sets of an STS(v) gives rise to minimal defining sets in the larger systems. We use this to construct some new families of defining sets. For example, for Steiner triple systems on 3 ⁿ points, we construct minimal defining sets of volumes varying by as much as 7 ⁿ⁻² . Received: September 16, 2000 Final version received: September 13, 2001 RID="*" ID="*" Research supported by the Australian Research Council A49937047, A49802044