Optimal price regulation in a growth model with monopolistic suppliers of intermediate goods

In this paper we investigate the trade-off faced by regulators who must set a price for an intermediate good somewhere between the marginal cost and the monopoly price. We utilize a growth model with monopolistic suppliers of intermediate goods. Investment in innovation is required to produce a new intermediate good. Marginal cost pricing deters innovation, while monopoly pricing maximizes innovation and economic growth at the cost of some static inefficiency. We demonstrate the existence of a second-best price above the marginal cost but below the monopoly price, which maximizes consumer welfare. Simulation results suggest that substantial reductions in consumption, production, growth, and welfare occur where regulators focus on static efficiency issues by setting prices at or near marginal cost.

Generalized optimal lattice covering of finite-dimensional Euclidean space

A generalization of the classical problem of optimal lattice covering of R-n is considered. Solutions to this generalized problem are found in two specific classes of lattices. The global optimal solution of the generalization is found for R-2. (C) 1998 Elsevier Science Inc. All rights reserved.

The co-segregation of psychosis and selected physical disorders within families of patients with psychosis versus well controls

While it has been reported that individuals with psychosis are at increased or decreased risk of various physical disorders such as cancer and rheumatoid arthritis, there has been less research on the co-segregation of physical disorders within the first-degree relatives of those with psychosis compared to relatives of well controls. The aim of this study was to examine these issues in an epidemiologically informed catchment-area based case-control study. Patients with psychosis were drawn from a prevalence study undertaken as part of the Australian National Mental Health Survey. In addition, we recruited well controls who resided in the same catchment area. For each subject, we drew pedigrees and used a structured checklist to assess the presence of selected psychiatric disorders, and selected disorders such as multiple sclerosis, epilepsy, spina bifida, thyroid disorders, diabetes, asthma and eczema. Data based on pedigrees from 293 individuals with psychosis and 292 well controls was available. As expected, the odds of havingschizophrenia and affective disorders were significantly increased in the families of cases versus controls. The odds of havingeczema were significantly reduced in the relatives of those with psychosis. All other disorders occurred with equal frequency in cases versus control pedigrees. Current theories of eczema suggest that an absence of early life exposure to antigens and infectious agents may fail to prime the na¨ıve immune system, and leave the person at increased risk of eczema. The results of this study suggest that genetic andror environmental factors that facilitate psychosis may protect against eczema. The Stanley Foundation supported this project.

Lateralized deficit of response inhibition in early-onset schizophrenia

Background. The ability to inhibit inappropriate or unwanted actions is a key element of executive control. The existence OF executive function deficits in schizophrenia is consistent with frontal lobe theories of the disorder. Relatively few Studies have examined response inhibition in schizophrenia, and none in adolescent patients with early-onset schizophrenia (EOS). Methods. Twenty-one adolescents with (lie onset of clinically impairing psychosis before 19 years of age and 16 matched controls performed a stop-signal task to assess response inhibition. The patients with EOS were categorized Lis paranoid (n= 10) and Undifferentiated subtypes (n= 11). The undifferentiated group had higher levels of negative symptomatology. Stop-signal reaction time (SSRT) and go-signal reaction time (Go-RT) were analysed with respect to hand of response. Results. The Undifferentiated early-onset patients had significantly longer SSRTs, indicative of poor response inhibition, for the left hand compared to the paranoid early-onset patients and control participants. No differences existed for inhibitory control with the right hand. The three groups did not differ in Go-RT. Conclusions. Our results indicate a specific lateralized impairment of response inhibition in patients With Undifferentiated, but not paranoid, EOS. These findings are consistent with reports of immature frontostriatal networks in EOS and implicate areas such as the pre-motor cortex and Supplementary motor area (SMA) that are thought to play a role in both voluntary initiation and inhibition of movement.

Optimal estimation of one-parameter quantum channels

We explore the task of optimal quantum channel identification and in particular, the estimation of a general one-parameter quantum process. We derive new characterizations of optimality and apply the results to several examples including the qubit depolarizing channel and the harmonic oscillator damping channel. We also discuss the geometry of the problem and illustrate the usefulness of using entanglement in process estimation.

Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves

Denote the set of 21 non-isomorphic cubic graphs of order 10 by L. We first determine precisely which L is an element of L occur as the leave of a partial Steiner triple system, thus settling the existence problem for partial Steiner triple systems of order 10 with cubic leaves. Then we settle the embedding problem for partial Steiner triple systems with leaves L is an element of L. This second result is obtained as a corollary of a more general result which gives, for each integer v greater than or equal to 10 and each L is an element of L, necessary and sufficient conditions for the existence of a partial Steiner triple system of order v with leave consisting of the complement of L and v - 10 isolated vertices. (C) 2004 Elsevier B.V. All rights reserved.

Optimal control and operation of drum granulation processes

Process optimisation and optimal control of batch and continuous drum granulation processes are studied in this paper. The main focus of the current research has been: (i) construction of optimisation and control relevant, population balance models through the incorporation of moisture content, drum rotation rate and bed depth into the coalescence kernels; (ii) investigation of optimal operational conditions using constrained optimisation techniques; (iii) development of optimal control algorithms based on discretized population balance equations; and (iv) comprehensive simulation studies on optimal control of both batch and continuous granulation processes. The objective of steady state optimisation is to minimise the recycle rate with minimum cost for continuous processes. It has been identified that the drum rotation-rate, bed depth (material charge), and moisture content of solids are practical decision (design) parameters for system optimisation. The objective for the optimal control of batch granulation processes is to maximize the mass of product-sized particles with minimum time and binder consumption. The objective for the optimal control of the continuous process is to drive the process from one steady state to another in a minimum time with minimum binder consumption, which is also known as the state-driving problem. It has been known for some time that the binder spray-rate is the most effective control (manipulative) variable. Although other possible manipulative variables, such as feed flow-rate and additional powder flow-rate have been investigated in the complete research project, only the single input problem with the binder spray rate as the manipulative variable is addressed in the paper to demonstrate the methodology. It can be shown from simulation results that the proposed models are suitable for control and optimisation studies, and the optimisation algorithms connected with either steady state or dynamic models are successful for the determination of optimal operational conditions and dynamic trajectories with good convergence properties. (c) 2005 Elsevier Ltd. All rights reserved.

On the distributed compression of quantum information

The problem of distributed compression for correlated quantum sources is considered. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the local sources created by the presence of correlations. Here it is shown that, in general, this is not the case for quantum sources, by proving a lower bound on the rate sum for irreducible sources of product states which is stronger than the one given by a naive application of Slepian-Wolf. Nonetheless, strategies taking advantage of correlation do exist for some special classes of quantum sources. For example, Devetak and Winter demonstrated the existence of such a strategy when one of the sources is classical. Optimal nontrivial strategies for a different extreme, sources of Bell states, are presented here. In addition, it is explained how distributed compression is connected to other problems in quantum information theory, including information-disturbance questions, entanglement distillation and quantum error correction.

Water Flow Through the Gills of Port Jackson Sharks

Evidence is presented for the existence of a countercurrent flow between water and blood at the respiratory surfaces of the Port Jackson shark gill.

Decomposition of complete tripartite graphs into gregarious 4-cycles

A 4-cycle in a tripartite graph with vertex partition {V-1, V-2, V-3} is said to be gregarious if it has at least one vertex in each V-i, 1 less than or equal to i less than or equal to 3. In this paper, necessary and sufficient conditions are given for the existence of an edge-disjoint decomposition of any complete tripartite graph into gregarious 4-cycles.

Least energy solutions of a critical Neumann problem with a weight

We investigate the effect of the coefficient of the critical nonlinearity for the Neumann problem on the existence of least energy solutions. As a by-product we establish a Sobolev inequality with interior norm.