Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Birth weight and age at menopause in Australian female twin pairs: exploration of the fetal origin hypothesis

In a twin sample where duration of gestation can be controlled, a specific example of the fetal origins hypothesis concerning association between low birth weight and early age at menopause is explored. The hypothesis is based on the physiologically plausible path from intrauterine growth retardation and reduced numbers of primary follicles to an earlier menopause. The sample comprised 323 Australian female twin pairs where both co-twins had reached menopause naturally and reported on their weight at birth. Regression analysis showed no linear association between the two variables (P = 0.371, r(2) = 0.0009). Intra-pair differences in age at menopause were investigated in the context of relative birth weight of co-twins. In 265 pairs an intra-pair birth a eight difference was reported. In monozygotic (MZ) pairs (n = 168) this allowed for control of genetic effects as well as gestation duration. No significant differences dependent on birth weight relative to co-twin were found for age at natural menopause in either MZ or dizygotic (DZ) twin pairs, even in pairs whose birth weights differed markedly. There was some indication that twins with premature ovarian failure were heavier at birth than twins with normal or later menopausal age. We conclude that the hypothesis that lower birth weight is associated with earlier menopause is not supported by our data.

A scheme for efficient quantum computation wtih linear optics

Quantum computers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology.

Acquisition of the English article system in SLA and the Missing Surface Inflection Hypothesis

This paper examines the article system in interlanguage grammar focusing on Japanese learners of English, whose native language lacks articles. It will be demonstrated that for the acquisition of the English article system, count/mass distinctions and definiteness are the crucial factors. Although Japanese does not employ the article system to encode these aspects, it will be argued that they are nevertheless syntactically encoded through its classifier system. Hence, the problem for these learners must be to map these features onto the appropriate surface forms as the Missing Surface Inflection Hypothesis predicts (Prévost & White 2000). This suggestion will further be supported empirically by a fill-in-the article task. It will be concluded that these Japanese learners understand the English article system fairly well, possibly due to their native language, yet have problems with realizing the relevant features (i.e. count/mass distinctions and definiteness) in the target language.

Dependence of public support for survival of wildlife species on their likeability

We surveyed a sample of 204 individuals selected from the public in Brisbane, Australia, to ascertain the extent to which they like or dislike 24 species of wildlife present in tropical Australia. The species belong to three classes: mammals, birds and reptiles. We calculated likeability indices for each of these species. We also asked respondents if they favoured the survival of each of these species and so the percentage of respondents favouring survival of each of these species could be calculated. Thus, using linear regression analysis, the percentage of respondents favouring survival of each of the species was related to their indices of likeability. In addition, the data enables the average likeability of species in the three classes (mammals, birds and reptiles) to be compared with the average support for survival of species in each of these three classes. As a result, we are able to assess how important stated likeability seems to be for preferences for survival of species, and to reconsider the hypothesis in the literature that there is likely to be more public support for the survival of mammals than for birds than for reptiles.

Regulation of photosynthetic pigments in micro-algae by multiple environmental factors: a dynamic balance hypothesis

Environmental effects on the concentration of photosynthetic pigments in micro-algae can be explained by dynamics of photosystem synthesis and deactivation. A model that couples photosystem losses to the relative cellular rates of energy harvesting (light absorption) and assimilation predicts optimal concentrations of light-harvesting pigments and balanced energy flow under environmental conditions that affect light availability and metabolic rates. Effects of light intensity, nutrient supply and temperature on growth rate and pigment levels were similar to general patterns observed across diverse micro-algal taxa. Results imply that dynamic behaviour associated with photophysical stress, and independent of gene regulation, might constitute one mechanism for photo-acclimation of photosynthesis.

Molecular cocrystals of carboxylic acids. XXVII - An investigation into the use of triphenylphosphine oxide cocrystals for non-linear optics: the crystal structure of the adduct of triphenylphosphine oxide with N-methylpyrrole-2-carboxylic acid

Four adducts of triphenylphosphine oxide with aromatic carboxylic acids have been synthesized and tested for second-order non-linear optical properties. These were with N-methylpyrrole-2-carboxylic acid (I), indole-2-carboxylic acid (2), 3-dimethylaminobenzoic acid (3), and thiophen-2-carboxylic acid (4). Compound (1) produced clear, colourless crystals (space group P2(1)2(1)2(1) With a 9.892(1), b 14.033(1), c 15.305(1) Angstrom, Z 4) which allowed the structure to be determined by X-ray diffraction.

Temperature and sowing date affect the linear increase of sunflower harvest index

The linearity of daily linear harvest index (HI) increase can provide a simple means to predict grain growth and yield in field crops. However, the stability of the rate of increase across genotypes and environments is uncertain. Data from three field experiments were collated to investigate the phase of linear HI increase of sunflower (Helianthus annuus L,) across environments by changing genotypes, sowing time, N level, and solar irradiation level. Linear increase in HI was similar among different genotypes, N levels, and radiation treatments (mean 0.0125 d(-1)). but significant differences occurred between sowings, The linear increase in HI was not stable at very low temperatures (down to 9 degrees C) during grain filling, due to possible limitations to biomass accumulation and translocation (mean 0.0091 d(-1)). Using the linear increase in HI to predict grain yield requires predictions of the duration from anthesis to the onset of linear HI increase (lag phase) and the cessation of linear RT increase. These studies showed that the lag phase differed, and the linear HI increase ceased when 91% of the anthesis to physiological maturity period had been completed.

Cannabis use and psychosis

This paper reviews evidence on two hypotheses about the relationship between cannabis use and psychosis. The first hypothesis is that heavy cannabis use may cause a cannabis psychosis-a psychosis that would not occur in the absence of cannabis use, the symptoms of which are preceded by heavy cannabis use and remit after abstinence. The second hypothesis is that cannabis use may precipitate schizophrenia, or exacerbate its symptoms. Evaluation of these hypotheses requires evidence of an association between cannabis use and psychosis, that is unlikely to be due to chance, in which cannabis use precedes psychosis, and in which we can exclude the hypothesis that the relationship is due to other factors, such as other drug use, or a personal vulnerability to psychosis. There is some clinical support for the first hypothesis. If these disorders exist they seem to be rare, because they require very high doses of THC, the prolonged use of highly potent forms of cannabis, or a pre-existing (but as yet unspecified) vulnerability. There is more support for the second hypothesis, in that a large prospective study has shown a linear relationship between the frequency with which cannabis has been used by age 18 and the risks over the subsequent 15 years of a diagnosis of schizophrenia. It is still unclear whether this means that cannabis use precipitates schizophrenia, whether it is a form of self-medication, or whether the association is due to the use of other drugs, such as amphetamines, which heavy cannabis users are more Likely to use. There is stronger evidence that cannabis use can exacerbate the symptoms of schizophrenia. Mental health services should identify patients with schizophrenia who use alcohol, cannabis and other drugs and advise them to abstain or to greatly reduce their drug use.

Patient matching in treatment for alcohol dependence: is the null hypothesis still alive and well?

In the light of Project MATCH, is it reasonable to accept the null hypothesis that there are no clinically signi® cant matching effects between patient characteristics and cognitive± behaviour therapy (CBT), motivational enhancement therapy (MET) and Twelve-Step facilitation therapy (TSF)? The Project MATCH investigators considered the null hypothesis but preferred the alternative hypothesis that further analysis may reveal combinations of patient and therapist characteristics that show more substantial matching effects than any of the variables that they have examined to date.1

The Heisenberg antiferromagnet on an anisotropic triangular lattice: linear spin-wave theory

We consider the effect of quantum spin fluctuations on the ground-state properties of the Heisenberg antiferromagnet on an anisotropic triangular lattice using linear spin-wave (LSW) theory. This model should describe the magnetic properties of the insulating phase of the kappa-(BEDT-TTF)(2)X family of superconducting molecular crystals. The ground-state energy, the staggered magnetization, magnon excitation spectra, and spin-wave velocities are computed as functions of the ratio of the antiferromagnetic exchange between the second and first neighbours, J(2)/J(1). We find that near J(2)/J(1) = 0.5, i.e., in the region where the classical spin configuration changes from a Neel-ordered phase to a spiral phase, the staggered magnetization vanishes, suggesting the possibility of a quantum disordered state. in this region, the quantum correction to the magnetization is large but finite. This is in contrast to the case for the frustrated Heisenberg model on a square lattice, for which the quantum correction diverges logarithmically at the transition from the Neel to the collinear phase. For large J(2)/J(1), the model becomes a set of chains with frustrated interchain coupling. For J(2) > 4J(1), the quantum correction to the magnetization, within LSW theory, becomes comparable to the classical magnetization, suggesting the possibility of a quantum disordered state. We show that, in this regime, the quantum fluctuations are much larger than for a set of weakly coupled chains with non-frustrated interchain coupling.