Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, sub-Riemannian, and Finslerian manifolds. These results generalize the results of [Nielsen, Dowling, Gu, and Doherty, Science 311, 1133 (2006)], which showed that the gate complexity can be related to distances on a Riemannian manifold.

Optimal preventive maintenance of leased equipment with corrective minimal repairs

For leased equipment, the lessor carries out the maintenance of the equipment. Usually, the contract of lease specifies the penalty for equipment failures and for repairs not being carried out within specified time limits. This implies that optimal preventive maintenance policies must take these penalty costs into account and properly traded against the cost of preventive maintenance actions. The costs associated with failures are high as unplanned corrective maintenance actions are costly and the resulting penalties due to lease contract terms being violated. The paper develops a model to determine the optimal parameters of a preventive maintenance policy that takes into account all these costs to minimize the total expected cost to the lessor for new item lease. The parameters of the policy are (i) the number of preventive maintenance actions to be carried out over the lease period, (ii) the time instants for such actions, and (iii) the level of action. (c) 2005 Elsevier B.V. All rights reserved.

Phosphoinositide regulation of neuroexocytosis: adding to the complexity

Exocytosis of neurotransmitter containing vesicles supports neuronal communication. The importance of molecular interactions involving specific lipids has become progressively more evident and the lipid composition of both the synaptic vesicle and the pre-synaptic plasma membrane at the active zone has significant functional consequences for neurotransmitter release. Several classes of lipids have been implicated in exocytosis including polyunsaturated fatty acids and phosphoinositides. This minireview will focus on recent developments regarding the role of phosphoinositides in neurosecretion.

Erratum: Two-Dimensional Failure Modeling with Minimal Repair which appeared in this journal of April 2004, Volume 51:3 on pages 345–362

In this Erratum, we point out the reason for an error in the derivation of a result in our earlier paper, “Two-Dimensional Failure Modeling with Minimal Repair” [1], which appeared in the April 2004 issue of this journal, 51:3, on pages 345–362, and give the correct derivation.

A flaw in the use of minimal defining sets for secret sharing schemes

It is shown that in some cases it is possible to reconstruct a block design D uniquely from incomplete knowledge of a minimal defining set for D. This surprising result has implications for the use of minimal defining sets in secret sharing schemes.

The complexity of p53 stabilization and activation

A number of proteins are activated by stress stimuli but none so spectacularly or with the degree of complexity as the tumour suppressor p53 (human p53 gene or protein). Once stabilized, p53 is responsible for the transcriptional activation of a series of proteins involved in cell cycle control, apoptosis and senescence. This protein is present at low levels in resting cells but after exposure to DNA-damaging agents and other stress stimuli it is stabilized and activated by a series of post-translational modifications that free it from MDM2 (mouse double minute 2 but used interchangeably to denote human also), a ubiquination ligase that ubiquitinates it prior to proteasome degradation. The stability of p53 is also influenced by a series of other interacting proteins. In this review, we discuss the post-translational modifications to p53 in response to different stresses and the consequences of these changes.

Minimal Homogeneous Latin Trades

A latin trade is a subset of a latin square which may be replaced with a disjoint mate to obtain a new latin square. A d-homogeneous latin trade is one which intersects each row, each column and each entry of the latin square either 0 or d times. In this paper we give a construction for minimal d-homogeneous latin trades of size dm, for every integer d >= 3, and m >= 1.75d(2) + 3. We also improve this bound for small values of d. Our proof relies on the construction of cyclic sequences whose adjacent sums are distinct. (c) 2006 Elsevier B.V. All rights reserved.

Boosting the tree augmented naive bayes classifier

The Tree Augmented Naïve Bayes (TAN) classifier relaxes the sweeping independence assumptions of the Naïve Bayes approach by taking account of conditional probabilities. It does this in a limited sense, by incorporating the conditional probability of each attribute given the class and (at most) one other attribute. The method of boosting has previously proven very effective in improving the performance of Naïve Bayes classifiers and in this paper, we investigate its effectiveness on application to the TAN classifier.

Quantifying the complexity of relative clause and cleft sentences

Explanations of the difficulty of relative-clause sentences implicate complexity but the measurement of complexity remains controversial. Four experiments investigated how far relational complexity (RC) theory, that has been found valid for cognitive development and human reasoning, accounts for the difficulty of 16 types of English, object- and subject-extracted relative-clause constructions. RC corresponds to the number of nouns assigned to thematic roles in the same decision. Complexity estimates based on RC and those based on maximal integration cost (MIC) were strongly correlated and accounted for similar variance in sentence difficulty (subjective ratings, comprehension accuracy, reading times). Consistent with RC theory, sentences that required more than 4 role assignments in the same decision were extremely difficult for many participants. Performance on nonlinguistic relational tasks predicted comprehension of object-extracted sentences, before and after controlling for subject-extractions. Working memory tasks predicted comprehension of object-extractions before controlling for subjectextractions. The studies extend the RC approach to a linguistic domain.

Trait physiology and crop modelling to link phenotypic complexity to underlying genetic systems

New tools derived from advances in molecular biology have not been widely adopted in plant breeding because of the inability to connect information at gene level to the phenotype in a manner that is useful for selection. We explore whether a crop growth and development modelling framework can link phenotype complexity to underlying genetic systems in a way that strengthens molecular breeding strategies. We use gene-to-phenotype simulation studies on sorghum to consider the value to marker-assisted selection of intrinsically stable QTLs that might be generated by physiological dissection of complex traits. The consequences on grain yield of genetic variation in four key adaptive traits – phenology, osmotic adjustment, transpiration efficiency, and staygreen – were simulated for a diverse set of environments by placing the known extent of genetic variation in the context of the physiological determinants framework of a crop growth and development model. It was assumed that the three to five genes associated with each trait, had two alleles per locus acting in an additive manner. The effects on average simulated yield, generated by differing combinations of positive alleles for the traits incorporated, varied with environment type. The full matrix of simulated phenotypes, which consisted of 547 location-season combinations and 4235 genotypic expression states, was analysed for genetic and environmental effects. The analysis was conducted in stages with gradually increased understanding of gene-to-phenotype relationships, which would arise from physiological dissection and modelling. It was found that environmental characterisation and physiological knowledge helped to explain and unravel gene and environment context dependencies. We simulated a marker-assisted selection (MAS) breeding strategy based on the analyses of gene effects. When marker scores were allocated based on the contribution of gene effects to yield in a single environment, there was a wide divergence in rate of yield gain over all environments with breeding cycle depending on the environment chosen for the QTL analysis. It was suggested that knowledge resulting from trait physiology and modelling would overcome this dependency by identifying stable QTLs. The improved predictive power would increase the utility of the QTLs in MAS. Developing and implementing this gene-to-phenotype capability in crop improvement requires enhanced attention to phenotyping, ecophysiological modelling, and validation studies to test the stability of candidate QTLs.