Some new examples for nonuniqueness of the evolution problem of harmonic maps

We find some new examples to show nonuniquence for the heat flow of harmonic maps where weak solutions satisfy the same monotonicity property.

The evolution and star formation of dwarf galaxies in the Fornax Cluster

We present the results of a spectroscopic survey of 675 bright (16.5 < b(J) < 18) galaxies in a 6 degrees field centred on the Fornax cluster with the FLAIR-II spectrograph on the UK Schmidt Telescope. Three galaxy samples were observed: compact galaxies to search for new blue compact dwarfs, candidate M 32-like compact dwarf ellipticals, and a subset of the brightest known cluster members in order to study the cluster dynamics. We measured redshifts for 516 galaxies, of which 108 were members of the Fornax Cluster. Defining dwarf galaxies to be those with b(J) greater than or equal to 15 (M-B greater than or equal to - 16.5), there are a total of 62 dwarf cluster galaxies in our sample. Nine of these are new cluster members previously misidentified as background galaxies. The cluster dynamics show that the dwarf galaxies are still falling into the cluster whereas the giants are virialized. We classified the observed galaxies as late-type if we detected H alpha emission at an equivalent width greater than 1 Angstrom. The spectra were obtained through fixed apertures, so they reflect activity in the galaxy cores, but this does not significantly bias the classifications of the compact dwarfs in our sample. The new classifications reveal a higher rate of star formation among the dwarf galaxies than suggested by morphological classification: 35 per cent have significant H alpha emission indicative of star formations but only 19 per cent were morphologically classified as late-types. The star-forming dwarf galaxies span the full range of physical sizes and we find no evidence in our data for a distinct class of star-forming blue compact dwarf (BCD) galaxy. The distribution of scale sizes is consistent with evolutionary processes which transform late-type dwarfs to early-type dwarfs. The fraction of dwarfs with active star formation drops rapidly towards the cluster centre: this is the usual density-morphology relation confirmed here for dwarf galaxies. The star-forming dwarfs are concentrated in the outer regions of the cluster, the most extreme in an infalling subcluster. We estimate gas depletion time-scales for five dwarfs with detected Hi emission: these are long (of order 10(10) yr), indicating that an active gas removal process must be involved if they are transformed into gas-poor dwarfs as they fall further into the cluster. Finally, in agreement with our previous results, we find no compact dwarf elliptical (M 32-like) galaxies in the Fornax Cluster.

Radiation of the Australian flora: What can comparisons of molecular phylogenies across multiple taxa tell us about the evolution of diversity in present-day communities?

The Australian fossil record shows that from ca. 25 Myr ago, the aseasonal-wet biome (rainforest and wet heath) gave way to the unique Australian sclerophyll biomes dominated by eucalypts, acacias and casuarinas. This transition coincided with tectonic isolation of Australia, leading to cooler, drier, more seasonal climates. From 3 Myr ago, aridification caused rapid opening of the central Australian and zone. Molecular phylogenies with dated nodes have provided new perspectives on how these events could have affected the evolution of the Australian flora. During the Mid-Cenozoic (25-10 Myr ago) period of climatic change, there were rapid radiations in sclerophyll taxa, such as Banksia, eucalypts, pea-flowered legumes and Allocasuarina. At the same time, taxa restricted to the aseasonal-wet biome (Nothofagus, Podocarpaceae and Araucariaceae) did not radiate or were depleted by extinction. During the Pliocene aridification, two Eremean biome taxa (Lepidium and Chenopodiaceae) radiated rapidly after dispersing into Australia from overseas. It is clear that the biomes have different histories. Lineages in the aseasonal-wet biome are species poor, with sister taxa that are species rich, either outside Australia or in the sclerophyll biomes. In conjunction with the fossil record, this indicates depletion of the Australian aseasonal-wet biome from the Mid-Cenozoic. In the sclerophyll biomes, there have been multiple exchanges between the southwest and southeast, rather than single large endemic radiations after a vicariance event. There is need for rigorous molecular phylogenetic studies so that additional questions can be addressed, such as how interactions between biomes may have driven the speciation process during radiations. New studies should include the hither-to neglected monsoonal tropics.

Time-dependent master equation simulation of complex elementary reactions in combustion: Application to the reaction of (CH2)-C-1 with C2H2 from 300-2000 K

Computational simulations of the title reaction are presented, covering a temperature range from 300 to 2000 K. At lower temperatures we find that initial formation of the cyclopropene complex by addition of methylene to acetylene is irreversible, as is the stabilisation process via collisional energy transfer. Product branching between propargyl and the stable isomers is predicted at 300 K as a function of pressure for the first time. At intermediate temperatures (1200 K), complex temporal evolution involving multiple steady states begins to emerge. At high temperatures (2000 K) the timescale for subsequent unimolecular decay of thermalized intermediates begins to impinge on the timescale for reaction of methylene, such that the rate of formation of propargyl product does not admit a simple analysis in terms of a single time-independent rate constant until the methylene supply becomes depleted. Likewise, at the elevated temperatures the thermalized intermediates cannot be regarded as irreversible product channels. Our solution algorithm involves spectral propagation of a symmetrised version of the discretized master equation matrix, and is implemented in a high precision environment which makes hitherto unachievable low-temperature modelling a reality.

Subspace wavepacket evolution with Newton polynomials

Time-dependent wavepacket evolution techniques demand the action of the propagator, exp(-iHt/(h)over-bar), on a suitable initial wavepacket. When a complex absorbing potential is added to the Hamiltonian for combating unwanted reflection effects, polynomial expansions of the propagator are selected on their ability to cope with non-Hermiticity. An efficient subspace implementation of the Newton polynomial expansion scheme that requires fewer dense matrix-vector multiplications than its grid-based counterpart has been devised. Performance improvements are illustrated with some benchmark one and two-dimensional examples. (C) 2001 Elsevier Science B.V. All rights reserved.

MRI based diffusion and perfusion predictive model to estimate stroke evolution

In this study we present a novel automated strategy for predicting infarct evolution, based on MR diffusion and perfusion images acquired in the acute stage of stroke. The validity of this methodology was tested on novel patient data including data acquired from an independent stroke clinic. Regions-of-interest (ROIs) defining the initial diffusion lesion and tissue with abnormal hemodynamic function as defined by the mean transit time (MTT) abnormality were automatically extracted from DWI/PI maps. Quantitative measures of cerebral blood flow (CBF) and volume (CBV) along with ratio measures defined relative to the contralateral hemisphere (r(a)CBF and r(a)CBV) were calculated for the MTT ROIs. A parametric normal classifier algorithm incorporating these measures was used to predict infarct growth. The mean r(a)CBF and r(a)CBV values for eventually infarcted MTT tissue were 0.70 +/-0.19 and 1.20 +/-0.36. For recovered tissue the mean values were 0.99 +/-0.25 and 1.87 +/-0.71, respectively. There was a significant difference between these two regions for both measures (P

Molecular clocks in reptiles: Life history influences rate of molecular evolution

Life history has been implicated as a determinant of variation in rate of molecular evolution amongst vertebrate species because of a negative correlation between bode size and substitution rate for many Molecular data sets. Both the generality and the cause of the negative bode size trend have been debated, and the validity of key studies has been questioned (particularly concerning the failure to account for phylogenetic bias). In this study, a comparative method has been used to test for an association between a range of life-history variables-such as body size age at maturity, and clutch size-and DNA substitution rate for three genes (NADH4, cytochrome b, and c-mos). A negative relationship between body size and rate of molecular evolution was found for phylogenetically independent pairs of reptile species spanning turtles. lizards. snakes, crocodile, and tuatara. Although this Study was limited by the number of comparisons for which both sequence and lite-history data were available, the results, suggest that a negative bode size trend in rate of molecular evloution may be a general feature of reptile molecular evolution. consistent with similar studies of mammals and birds. This observation has important implications for uncovering the mechanisms of molecular evolution and warns against assuming that related lineages will share the same substitution rate (a local molecular clock) in order to date evolutionary divergences from DNA sequences.

Stress correlation function evolution in lattice solid elasto-dynamic models of shear and fracture zones and earthquake prediction

It has been argued that power-law time-to-failure fits for cumulative Benioff strain and an evolution in size-frequency statistics in the lead-up to large earthquakes are evidence that the crust behaves as a Critical Point (CP) system. If so, intermediate-term earthquake prediction is possible. However, this hypothesis has not been proven. If the crust does behave as a CP system, stress correlation lengths should grow in the lead-up to large events through the action of small to moderate ruptures and drop sharply once a large event occurs. However this evolution in stress correlation lengths cannot be observed directly. Here we show, using the lattice solid model to describe discontinuous elasto-dynamic systems subjected to shear and compression, that it is for possible correlation lengths to exhibit CP-type evolution. In the case of a granular system subjected to shear, this evolution occurs in the lead-up to the largest event and is accompanied by an increasing rate of moderate-sized events and power-law acceleration of Benioff strain release. In the case of an intact sample system subjected to compression, the evolution occurs only after a mature fracture system has developed. The results support the existence of a physical mechanism for intermediate-term earthquake forecasting and suggest this mechanism is fault-system dependent. This offers an explanation of why accelerating Benioff strain release is not observed prior to all large earthquakes. The results prove the existence of an underlying evolution in discontinuous elasto-dynamic, systems which is capable of providing a basis for forecasting catastrophic failure and earthquakes.

Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.

Testing the link between the latitudinal gradient in species richness and rates of molecular evolution

Numerous hypotheses have been proposed to explain latitudinal gradients in species richness, but all are subject to ongoing debate. Here we examine Rohde's (1978, 1992) hypothesis, which proposes that climatic conditions at low latitudes lead to elevated rates of speciation. This hypothesis predicts that rates of molecular evolution should increase towards lower latitudes, but this prediction has never been tested. We discuss potential links between rates of molecular evolution and latitudinal diversity gradients, and present the first test of latitudinal variation in rates of molecular evolution. Using 45 phylogenetically independent, latitudinally separated pairs of bird species and higher taxa, we compare rates of evolution of two mitochondrial genes and DNA-DNA hybridization distances. We find no support for an effect of latitude on rate of molecular evolution. This result casts doubt on the generality of a key component of Rohde's hypothesis linking climate and speciation.

The variety of variables in automated real-time refinement

The refinement calculus is a well-established theory for deriving program code from specifications. Recent research has extended the theory to handle timing requirements, as well as functional ones, and we have developed an interactive programming tool based on these extensions. Through a number of case studies completed using the tool, this paper explains how the tool helps the programmer by supporting the many forms of variables needed in the theory. These include simple state variables as in the untimed calculus, trace variables that model the evolution of properties over time, auxiliary variables that exist only to support formal reasoning, subroutine parameters, and variables shared between parallel processes.

Mental time travel in animals?

Are humans alone in their ability to reminisce about the past and imagine the future? Recent evidence suggests that food-storing birds (scrub jays) have access to information about what they have stored where and when. This has raised the possibility of mental time travel (MTT) in animals and sparked similar research with other species. Here we caution that such data do not provide convincing evidence for MTT. Examination of characteristics of human MTT (e.g. non-verbal declaration, generativity, developmental prerequisites) points to other avenues as to how a case for animal MTT could be made. In light of the current lack of evidence, however, we maintain that MTT is a uniquely human characteristic.

Practicality of time-optimal two-qubit Hamiltonian simulation

What is the time-optimal way of using a set of control Hamiltonians to obtain a desired interaction? Vidal, Hammerer, and Cirac [Phys. Rev. Lett. 88, 237902 (2002)] have obtained a set of powerful results characterizing the time-optimal simulation of a two-qubit quantum gate using a fixed interaction Hamiltonian and fast local control over the individual qubits. How practically useful are these results? We prove that there are two-qubit Hamiltonians such that time-optimal simulation requires infinitely many steps of evolution, each infinitesimally small, and thus is physically impractical. A procedure is given to determine which two-qubit Hamiltonians have this property, and we show that almost all Hamiltonians do. Finally, we determine some bounds on the penalty that must be paid in the simulation time if the number of steps is fixed at a finite number, and show that the cost in simulation time is not too great.

Changes in organic matter production and accumulation as a mechanism for isotopic evolution in the Mesoproterozoic ocean

Mesoproterozoic marine successions worldwide record a shift in average delta(13)C values from 0 to +3.5parts per thousand, with the latter value evident in successions younger than 1250 Ma. New carbon isotope data from the similar to 1300 to 1270 Ma Dismal Lakes Group, Arctic Canada, provide further insight into this fundamental transition. Data reveal that the shift to higher VC values was gradual and marked by occasional excursions to values less than 0 parts per thousand. When compared to records from older and younger marine successions, it is evident that the difference between isotopic minima and maxima increased with time, indicating that the marine system evolved to become isotopically more variable. We interpret these patterns to record an increase in the crustal inventory of organic carbon, reflecting eukaryotic diversification and a change in the locus of organic carbon burial to include anoxic deep marine sites where preservation potential was high. We speculate that the release of O-2 to Earth's surface environments associated with increased organic carbon storage induced irreversible changes in the Mesoproterozoic biosphere, presaging the more extreme environmental and evolutionary developments of the Neoproterozoic.