Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

Random numbers from astronomical imaging

This article describes a method to turn astronomical imaging into a random number generator by using the positions of incident cosmic rays and hot pixels to generate bit streams. We subject the resultant bit streams to a battery of standard benchmark statistical tests for randomness and show that these bit streams are statistically the same as a perfect random bit stream. Strategies for improving and building upon this method are outlined.

Maternal transmission efficiency of Wolbachia superinfections in Aedes albopictus populations in Thailand

We examined the transmission efficiency of 2 strains of Wolbachia bacteria that cause cytoplasmic incompatibility in field populations of Aedes albopictus by polymerase chain reaction assay. We found mainland and island populations throughout Thailand to be superinfected with group A and B bacteria. Of 320 Wolbachia-positive adult mosquitoes, 97.5% were infected with both groups. Single infected individuals of each Wolbachia group were encountered in nearly equal numbers. We screened 550 offspring from 80 field-collected mothers and found the transmission efficiency of group A Wolbachia to be 96.7% and that of group B Wolbachia to be 99.6%. Mothers that did not transmit both Wolbachia infections to all of their offspring were significantly larger in size than those with perfect transmission fidelity. We discuss our findings in relation to the prospects of the use of Wolbachia as a gene-driving mechanism.

Theory manual to OctVCE – a cartesian cell CFD code with special application to blast wave problems, Department of Mechanical Engineering Report 2007/12

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries, in particular, from explosions. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel for its simplicity and sufficiency for practical engineering design problems. The code uses a finite-volume formulation of the unsteady Euler equations with a second order explicit Runge-Kutta Godonov (MUSCL) scheme. Gradients are calculated using a least-squares method with a minmod limiter. Flux solvers used are AUSM, AUSMDV and EFM. No fluid-structure coupling or chemical reactions are allowed, but gas models can be perfect gas and JWL or JWLB for the explosive products. This report also describes the code’s ‘octree’ mesh adaptive capability and point-inclusion query procedures for the VCE geometry engine. Finally, some space will also be devoted to describing code parallelization using the shared-memory OpenMP paradigm. The user manual to the code is to be found in the companion report 2007/13.

Modelling dispersal behaviour on a fractal landscape

We use a spatially explicit population model to explore the population consequences of different habitat selection mechanisms on landscapes with fractal variation in habitat quality. We consider dispersal strategies ranging from random walks to perfect habitat selectors for two species of arboreal marsupial, the greater glider (Petauroides volans) and the mountain brushtail possum (Trichosurus caninus). In this model increasing habitat selection means individuals obtain higher quality territories, but experience increased mortality during dispersal. The net effect is that population sizes are smaller when individuals actively select habitat. We find positive relationships between habitat quality and population size can occur when individuals do not use information about the entire landscape when habitat quality is spatially autocorrelated. We also find that individual behaviour can mitigate the negative effects of spatial variation on population average survival and fecundity. (C) 1998 Elsevier Science Ltd. All rights reserved.

Swapping space for time and unfair tests of ecological models

Testing ecological models for management is an increasingly important part of the maturation of ecology as an applied science. Consequently, we need to work at applying fair tests of models with adequate data. We demonstrate that a recent test of a discrete time, stochastic model was biased towards falsifying the predictions. If the model was a perfect description of reality, the test falsified the predictions 84% of the time. We introduce an alternative testing procedure for stochastic models, and show that it falsifies the predictions only 5% of the time when the model is a perfect description of reality. The example is used as a point of departure to discuss some of the philosophical aspects of model testing.

General properties of cosmological models with an isotropic singularity

Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a gamma-law equation of state. There are, however, some general properties of cosmological models which admit an Isotropic Singularity, irrespective of the matter source. In particular, we show that the Isotropic Singularity is a point-like singularity and that vacuum space-times cannot admit an Isotropic Singularity. The relationships between the Isotropic Singularity, and the energy conditions, and the Hubble parameter is explored. A review of work by the authors, regarding the Isotropic Singularity, is presented.

A model of seller holdout

We model a buyer who wishes to combine objects owned by two separate sellers in order to realize higher value. Sellers are able to avoid entering into negotiations with the buyer, so that the order in which they negotiate is endogenous. Holdout occurs if at least one of the sellers is not present in the first round of negotiations. We demonstrate that complementarity of the buyer's technology is a necessary condition for equilibrium holdout. Moreover, a rise in complementarity leads to an increased likelihood of holdout, and an increased efficiency loss. Applications include patents, the land assembly problem, and mergers.

Forward-looking versus recursive-dynamic modeling in climate policy analysis: A comparison

This paper develops a multi-regional general equilibrium model for climate policy analysis based on the latest version of the MIT Emissions Prediction and Policy Analysis (EPPA) model. We develop two versions so that we can solve the model either as a fully inter-temporal optimization problem (forward-looking, perfect foresight) or recursively. The standard EPPA model on which these models are based is solved recursively, and it is necessary to simplify some aspects of it to make inter-temporal solution possible. The forward-looking capability allows one to better address economic and policy issues such as borrowing and banking of GHG allowances, efficiency implications of environmental tax recycling, endogenous depletion of fossil resources, international capital flows, and optimal emissions abatement paths among others. To evaluate the solution approaches, we benchmark each version to the same macroeconomic path, and then compare the behavior of the two versions under a climate policy that restricts greenhouse gas emissions. We find that the energy sector and CO(2) price behavior are similar in both versions (in the recursive version of the model we force the inter-temporal theoretical efficiency result that abatement through time should be allocated such that the CO(2) price rises at the interest rate.) The main difference that arises is that the macroeconomic costs are substantially lower in the forward-looking version of the model, since it allows consumption shifting as an additional avenue of adjustment to the policy. On the other hand, the simplifications required for solving the model as an optimization problem, such as dropping the full vintaging of the capital stock and fewer explicit technological options, likely have effects on the results. Moreover, inter-temporal optimization with perfect foresight poorly represents the real economy where agents face high levels of uncertainty that likely lead to higher costs than if they knew the future with certainty. We conclude that while the forward-looking model has value for some problems, the recursive model produces similar behavior in the energy sector and provides greater flexibility in the details of the system that can be represented. (C) 2009 Elsevier B.V. All rights reserved.

Reproductive biology of Echinodorus longipetalus (Alismataceae): Sexual morphs, breeding system and pollinators

The floral biology, pollinators and breeding system of Echinodorus longipetalus Micheli were studied in a marshy area of the district of Taquaritinga (State of Sao Paulo), southeastern Brazil. E. longipetalus is gynodioecious and as far as is known, this is the first record of unisexual flowers, besides perfect flowers, in Echinodorus. Proportion of female individuals in the studied population is 50% and produces 31% more flowers than hermaphrodites. Perfect and pistillate flowers of E. longipetalus are similar in appearance and are pollinated by several species of Hymenoptera (mainly by Xylocopa (Neoxylocopa) suspecta Moure & Camargo). Perfect flowers offer pollen as a reward. Pistillate flowers attract floral visitors by deceit with their staminodes that resemble the stamens of the perfect flowers. Visits to pistillate flowers are quick (1-2 s), while visits to perfect flowers last up to 120 s. The perfect flowers are self-compatible and produce fruits through spontaneous self-pollination (control flowers), whereas the pistillate ones only set fruits through cross-pollinations. Perfect and pistillate flowers set more fruits under natural conditions than in manual treatments, respectively. Although the pistillate and perfect flowers bear a strong similarity, the selective pollinator behavior seems to be responsible for the increase of fruit set in perfect flowers. (C) 2008 Elsevier B.V. All rights reserved.

Activation of visual areas during the attentional blink

When two targets are presented in rapid succession, identification of the first target is nearly perfect while identification of the second is severely impaired at shorter inter-target lags, and then gradually improves as lag increases. This second-target deficit is known as the attentional blink (AB). Numerous studies have implicated competition for access to higher-order processing mechanisms as the primary cause of the AB. However, relatively few studies have directly examined how the AB modulates activity in specific brain areas. To this end, we used fMRI to measure activation in the occipital and parietal cortices (including V1, V2, and area MT) during an AB task. Participants were presented with an initial target of oriented line segments embedded in a central stream of letter distractors. This central target was followed 100 - 700 ms later by a peripheral ‘X’ presented at one of four locations along with three ‘+’ distractors. All peripheral items were presented in the centre of a small field of moving dots. Participants made non-speeded judgments about line-segment orientation and the location of the second target at the end of a trial and to ignore all other stimuli. The results showed a robust AB characterised by a linear improvement in second-target accuracy as lag increased. This pattern of behavioural results was mirrored by changes in activation patterns across a number of visual areas indicating robust modulation of brain activity by the AB.

Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach

We prove that, once an algorithm of perfect simulation for a stationary and ergodic random field F taking values in S(Zd), S a bounded subset of R(n), is provided, the speed of convergence in the mean ergodic theorem occurs exponentially fast for F. Applications from (non-equilibrium) statistical mechanics and interacting particle systems are presented.

Cognitive deficits, length of illness and symptom severity in schizophrenia

Background Research using neuropsychological testing has demonstrated that patients with schizophrenia show deficits in multiple neurocognitive domains. The aim of this study is to identify cognitive deficits that correlate with length of illness and symptom severity. Method Twenty clinically stable outpatients with chronic schizophrenia (18M : 2F) and 14 healthy controls (13M : 1F), matched on age, gender and parental education, were administered a neuropsychological battery consisting of the Hayling Sentence Completion Test (HSCT), WMS-III Verbal Paired Associates & Letter Number Sequencing, Modified Card Sort Test (MCST), Pyramids & Palm Trees Test, National Adult Reading Test (NART), Controlled Oral Word Association Test (COWAT), and WAIS-III. Severity of symptoms was rated with the Structured Clinical Interview – Positive and Negative Syndromes Scale (SCI-PANSS). Results In comparison to controls, patients showed significant deficits on all of the neuropsychological tasks except for the COWAT. MCST total categories, NART, Verbal IQ and arithmetic, similarities & digit symbol of the WAIS-III had the largest effect size between the groups. The longer the illness duration, the poorer the performance on WAISIII block design and the lower the performance IQ score. The poorer the performance on WMS-III letter number sequencing, the greater the positive symptoms, negative symptoms and general psychopathology. Conclusion Compared to controls, patients showed large effect sizes on measures of executive functioning, intelligence, working memory, verbal comprehension and speed of processing. The findings suggest that impairment in executive functioning and performance IQ is associated with length of illness, while impairment in working memory is associated with heightened symptom severity.

Differential expression of mitochondrial NADH dehydrogenase in ethanol-treated rat brain: Revealed by differential display

The technique of polymerase chain reaction (PCR) differential display was used to detect alterations in gene expression after chronic alcohol administration. Male Wistar rats were treated with ethanol vapor for 14 days. The cDNA generated from mRNA isolated from the hippocampi of ethanol-treated and control animals was compared by PCR differential display. A differentially expressed cDNA fragment was used to screen mRNA samples by Northern analysis. The level of a mRNA was significantly elevated (x 2.5) in the hippocampus, but not the cortex of alcohol-treated rats up to 48 hr after withdrawal. Sequence analysis of the cDNA fragment revealed an almost perfect homology to rat mitochondrial NADH dehydrogenase subunit 4 mRNA. The selective induction of this mRNA in alcohol-treated rat brain areas suggests altered metabolic processes and possible dysfunction of the mitochondria. The technique of PCR differential display may prove useful in further analysis of gene expression during alcohol dependence and withdrawal.

Sphenoid sinus symmetry and differences between sexes

Objectives: To evaluate the anatomic variations of neurovascular structures adjacent to the sphenoid sinus and their agreement between right and left sides as well as differences between sexes. Methods: Forty-five cadavers were dissected (24 men, and differences between sexes and agreement of anatomic variations of the sphenoid sinus between sides were analyzed. Results: The mean distance from the sphenoid sinus ostium to the anterior nasal spine was greater in males than in females by an average of 3.0 mm (p = 0.001) while the mean difference of distances between the right and left side was -1.1 +/- 3.1 mm. Female cadavers had a greater frequency of optic-carotid recess (p = 0.04) and dehiscence over the maxillary nerve (p = 0.02), as well as greater relative risk of optic nerve protrusion (p < 0.001), and dehiscence over the internal carotid artery (ICA) (p = 0.002). In male cadavers the intersinus septum was inserted on the course of the ICA 3.5 times more often than in female (p = 0.02). Agreement of anatomic variations between sides ranged from moderate to almost perfect depending on the structures evaluated. Conclusions: There are anatomic differences of the sphenoid sinus between sexes and between right and left sides, and these differences should be taken into consideration during surgery.