Uniqueness of signature for simple curves

We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p-variation, 1≤p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLEκ null set, where 0<κ≤4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.

Statistical characterisation of the growth and spatial scales of the substorm onset arc

We present the first multi-event study of the spatial and temporal structuring of the aurora to provide statistical evidence of the near-Earth plasma instability which causes the substorm onset arc. Using data from ground-based auroral imagers, we study repeatable signatures of along-arc auroral beads, which are thought to represent the ionospheric projection of magnetospheric instability in the near-Earth plasma sheet. We show that the growth and spatial scales of these wave-like fluctuations are similar across multiple events, indicating that each sudden auroral brightening has a common explanation. We find statistically that growth rates for auroral beads peak at low wavenumber with the most unstable spatial scales mapping to an azimuthal wavelength λ≈1700 − 2500 km in the equatorial magnetosphere at around 9-12 RE. We compare growth rates and spatial scales with a range of theoretical predictions of magnetotail instabilities, including the cross-field current instability and the shear-flow ballooning instability. We conclude that, although the cross-field current instability can generate similar magnitude of growth rates, the range of unstable wavenumbers indicates that the shear-flow ballooning instability is the most likely explanation for our observations.

Climatology, storm morphologies, and environments of tornadoes in the British Isles: 1980–2012

A climatology is developed for tornadoes during 1980–2012 in the British Isles, defined in this article as England, Scotland, Wales, Northern Ireland, Republic of Ireland, Channel Islands, and the Isle of Man. The climatology includes parent storm type, interannual variability, annual and diurnal cycles, intensities, oc- currence of outbreaks (defined as three or more tornadoes in the same day), geographic distribution, and environmental conditions derived from proximity soundings of tornadoes. Tornado reports are from the Tornado and Storm Research Organization (TORRO). Over the 33 years, there were a mean of 34.3 tor- nadoes and 19.5 tornado days (number of days in which at least one tornado occurred) annually. Tornadoes and tornado outbreaks were most commonly produced from linear storms, defined as radar signatures at least 75 km long and approximately 3 times as long as wide. Most (78%) tornadoes occurred in England. The probability of a tornado within 10 km of a point was highest in the south, southeast, and west of England. On average, there were 2.5 tornado outbreaks every year. Where intensity was known, 95% of tornadoes were classified as F0 or F1 with the remainder classified as F2. There were no tornadoes rated F3 or greater during this time period. Tornadoes occurred throughout the year with a maximum from May through October. Finally, tornadoes tended to occur in low-CAPE, high-shear environments. Tornadoes in the British Isles were difficult to predict using only sounding-derived parameters because there were no clear thresholds between null, tornadic, outbreak, and significant tornado cases.

Climatology and variability of trace gases in extratropical double-tropopause regions from MLS, HIRDLS, and ACE-FTS measurements

Upper tropospheric and lower stratospheric measurements from the Aura Microwave Limb Sounder (MLS), the Aura High Resolution Dynamics Limb Sounder (HIRDLS), and the Atmospheric Chemistry Experiment-Fourier transform spectrometer (ACE-FTS) are used to present the first global climatological comparison of extratropical, nonpolar trace gas distributions in double-tropopause (DT) and single-tropopause (ST) regions. Stratospheric tracers, O3, HNO3, and HCl, have lower mixing ratios ∼2–8 km above the primary (lowermost) tropopause in DT than in ST regions in all seasons, with maximum Northern Hemisphere (NH) differences near 50% in winter and 30% in summer. Southern Hemisphere winter differences are somewhat smaller, but summer differences are similar in the two hemispheres. H2O in DT regions of both hemispheres shows strong negative anomalies in November through February and positive anomalies in July through October, reflecting the strong seasonal cycle in H2O near the tropical tropopause. CO and other tropospheric tracers examined have higher DT than ST values 2–7 km above the primary tropopause, with the largest differences in winter. Large DT-ST differences extend to high NH latitudes in fall and winter, with longitudinal maxima in regions associated with enhanced wave activity and subtropical jet variations. Results for O3 and HNO3 agree closely between MLS and HIRDLS, and differences from ACE-FTS are consistent with its sparse and irregular midlatitude sampling. Consistent signatures in climatological trace gas fields provide strong evidence that transport from the tropical upper troposphere into the layer between double tropopauses is an important pathway for stratosphere-troposphere exchange.

Late Quaternary environmental change in the interior South American tropics: new insight from leaf wax stable isotopes

Stable isotope analysis of leaf waxes in a sediment core from Laguna La Gaiba, a shallow lake located at the Bolivian margin of the Pantanal wetlands, provides new perspective on vegetation and climate change in the lowland interior tropics of South America over the past 40,000 years. The carbon isotopic compositions (δ13C) of long-chain n-alkanes reveal large shifts between C3-and C4-dominated vegetation communities since the last glacial period, consistent with landscape reconstructions generated with pollen data from the same sediment core. Leaf wax δ13C values during the last glacial period reflect an open landscape composed of C4grasses and C3herbs from 41–20ka. A peak in C4abundance during the Last Glacial Maximum (LGM, ∼21ka) suggests drier or more seasonal conditions relative to the earlier glacial period, while the development of a C3-dominated forest community after 20 ka points to increased humidity during the last deglaciation. Within the Holocene, large changes in the abundance of C4 vegetation indicate a transition from drier or more seasonal conditions during the early/mid-Holocene to wetter conditions in the late Holocene coincident with increasing austral summer insolation. Strong negative correlations between leaf wax δ13C and δD values over the entire record indicate that the majority of variability in leaf wax δD at this site can be explained by variability in the magnitude of biosynthetic fractionation by different vegetation types rather than changes in meteoric water δD signatures. However, positive δD deviations from the observed δ13C–δD trends are consistent with more enriched source water and drier or more seasonal conditions during the early/mid-Holocene and LGM. Overall, our record adds to evidence of varying influence of glacial boundary conditions and orbital forcing on South American Summer Monsoon precipitation in different regions of the South American tropics. Moreover, the relationships between leaf wax stable isotopes and pollen data observed at this site underscore the complementary nature of pollen and leaf wax δ13C data for reconstructing past vegetation changes and the potentially large effects of such changes on leaf wax δD signatures.

Do the legs of magnetic clouds contain twisted flux-rope magnetic fields?

Magnetic clouds (MCs) are a subset of interplanetary coronal mass ejections (ICMEs) characterised primarily by a smooth rotation in the magnetic field direction indicative of the presence of a magnetic flux rope. Energetic particle signatures suggest MC flux ropes remain magnetically connected to the Sun at both ends, leading to widely used model of global MC structure as an extended flux rope, with a loop-like axis stretching out from the Sun into the heliosphere and back to the Sun. The time of flight of energetic particles, however, suggests shorter magnetic field line lengths than such a continuous twisted flux rope would produce. In this study, two simple models are compared with observed flux rope axis orientations of 196 MCs to show that the flux rope structure is confined to the MC leading edge. The magnetic cloud “legs,” which magnetically connect the flux rope to the Sun, are not recognisable as MCs and thus are unlikely to contain twisted flux rope fields. Spacecraft encounters with these non-flux rope legs may provide an explanation for the frequent observation of non-magnetic cloud ICMEs.

The signature of a rough path: uniqueness

In the context of controlled differential equations, the signature is the exponential function on paths. B. Hambly and T. Lyons proved that the signature of a bounded variation path is trivial if and only if the path is tree-like. We extend Hambly–Lyons' result and their notion of tree-like paths to the setting of weakly geometric rough paths in a Banach space. At the heart of our approach is a new definition for reduced path and a lemma identifying the reduced path group with the space of signatures.

GALAXY EVOLUTION IN A COMPLEX ENVIRONMENT: A MULTI-WAVELENGTH STUDY OF HCG 7

The environment where galaxies are found heavily influences their evolution. Close groupings, like the ones in the cores of galaxy clusters or compact groups, evolve in ways far more dramatic than their isolated counterparts. We have conducted a multi-wavelength study of Hickson Compact Group 7 (HCG 7), consisting of four giant galaxies: three spirals and one lenticular. We use Hubble Space Telescope (HST) imaging to identify and characterize the young and old star cluster populations. We find young massive clusters (YMCs) mostly in the three spirals, while the lenticular features a large, unimodal population of globular clusters (GCs) but no detectable clusters with ages less than a few Gyr. The spatial and approximate age distributions of the similar to 300 YMCs and similar to 150 GCs thus hint at a regular star formation history in the group over a Hubble time. While at first glance the HST data show the galaxies as undisturbed, our deep ground-based, wide-field imaging that extends the HST coverage reveals faint signatures of stellar material in the intragroup medium (IGM). We do not, however, detect the IGM in H I or Chandra X-ray observations, signatures that would be expected to arise from major mergers. Despite this fact, we find that the H I gas content of the individual galaxies and the group as a whole are a third of the expected abundance. The appearance of quiescence is challenged by spectroscopy that reveals an intense ionization continuum in one galaxy nucleus, and post-burst characteristics in another. Our spectroscopic survey of dwarf galaxy members yields a single dwarf elliptical galaxy in an apparent stellar tidal feature. Based on all this information, we suggest an evolutionary scenario for HCG 7, whereby the galaxies convert most of their available gas into stars without the influence of major mergers and ultimately result in a dry merger. As the conditions governing compact groups are reminiscent of galaxies at intermediate redshift, we propose that HCGs are appropriate for studying galaxy evolution at z similar to 1-2.

Palaeomagnetism, rock magnetism and AMS of the Cabo Magmatic Province, NE Brazil, and the opening of South Atlantic

P>Reconstruction of the South Atlantic opening has long been a matter of debate and several models have been proposed. One problem in tracing properly the Atlantic history arises from the existence of a long interval without geomagnetic reversals, the Cretaceous Normal Superchron, for which ages are difficult to assign. Palaeomagnetism may help in addressing this issue if high-quality palaeomagnetic poles are available for the two drifting continental blocks, and if precise absolute ages are available. In this work we have investigated the Cabo Magmatic Province, northeastern Brazil, recently dated at 102 +/- 1 Ma (zircon fission tracks, Ar39/Ar40). All volcanic and plutonic rocks showed stable thermal and AF demagnetization patterns, and exhibit primary magnetic signatures. AMS data also support a primary origin for the magnetic fabric and is interpreted to be contemporaneous of the rock formation. The obtained pole is located at 335.9 degrees E/87.9 degrees S (N = 24; A(95) = 2.5; K = 138) and satisfies modern quality criteria, resulting in a reference pole for South America at similar to 100 Ma. This new pole also gives an insight to test and discuss the kinematic models currently proposed for the South Atlantic opening during mid-Cretaceous.

Paleoamerican Morphology in the Context of European and East Asian Late Pleistocene Variation: Implications for Human Dispersion Into the New World

Early American crania show a different morphological pattern from the one shared by late Native Americans. Although the origin of the diachronic morphological diversity seen on the continents is still debated, the distinct morphology of early Americans is well documented and widely dispersed. This morphology has been described extensively for South America, where larger samples are available. Here we test the hypotheses that the morphology of Early Americans results from retention of the morphological pattern of Late Pleistocene modern humans and that the occupation of the New World precedes the morphological differentiation that gave rise to recent Eurasian and American morphology. We compare Early American samples with European Upper Paleolithic skulls, the East Asian Zhoukoudian Upper Cave specimens and a series of 20 modern human reference crania. Canonical Analysis and Minimum Spanning Tree were used to assess the morphological affinities among the series, while Mantel and Dow-Cheverud tests based on Mahalanobis Squared Distances were used to test different evolutionary scenarios. Our results show strong morphological affinities among the early series irrespective of geographical origin, which together with the matrix analyses results favor the scenario of a late morphological differentiation of modern humans. We conclude that the geographic differentiation of modern human morphology is a late phenomenon that occurred after the initial settlement of the Americas. Am J Phys Anthropol 144:442-453, 2011. (c) 2010 Wiley-Liss, Inc.

Balanced polymorphism in bottlenecked populations: The case of the CCR5 5 ` cis-regulatory region in Amazonian Amerindians

The 5` cis-regulatory region of the CCR5 gene exhibits a strong signature of balancing selection in several human populations. Here we analyze the polymorphism of this region in Amerindians from Amazonia, who have a complex demographic history, including recent bottlenecks that are known to reduce genetic variability. Amerindians show high nucleotide diversity (pi = 0.27%) and significantly positive Tajima`s D, and carry haplotypes associated with weak and strong gene expression. To evaluate whether these signatures of balancing selection could be explained by demography, we perform neutrality tests based on empiric and simulated data. The observed Tajima`s D was higher than that of other world populations: higher than that found for 18 noncoding regions of South Amerindians, and higher than 99.6% of simulated genealogies, which assume nonequilibrium conditions. Moreover, comparing Amerindians and Asians, the Fst for CCR5 cis-regulatory region was unusually low, in relation to neutral markers. These findings indicate that, despite their complex demographic history, South Amerindians carry a detectable signature of selection on the CCR5 cis-regulatory region. (C) 2010 American Society for Histocompatibility and Immunogenetics. Published by Elsevier Inc. All rights reserved.

Human Stem Cell Cultures from Cleft Lip/Palate Patients Show Enrichment of Transcripts Involved in Extracellular Matrix Modeling By Comparison to Controls

Nonsyndromic cleft lip and palate (NSCL/P) is a complex disease resulting from failure of fusion of facial primordia, a complex developmental process that includes the epithelial-mesenchymal transition (EMT). Detection of differential gene transcription between NSCL/P patients and control individuals offers an interesting alternative for investigating pathways involved in disease manifestation. Here we compared the transcriptome of 6 dental pulp stem cell (DPSC) cultures from NSCL/P patients and 6 controls. Eighty-seven differentially expressed genes (DEGs) were identified. The most significant putative gene network comprised 13 out of 87 DEGs of which 8 encode extracellular proteins: ACAN, COL4A1, COL4A2, GDF15, IGF2, MMP1, MMP3 and PDGFa. Through clustering analyses we also observed that MMP3, ACAN, COL4A1 and COL4A2 exhibit co-regulated expression. Interestingly, it is known that MMP3 cleavages a wide range of extracellular proteins, including the collagens IV, V, IX, X, proteoglycans, fibronectin and laminin. It is also capable of activating other MMPs. Moreover, MMP3 had previously been associated with NSCL/P. The same general pattern was observed in a further sample, confirming involvement of synchronized gene expression patterns which differed between NSCL/P patients and controls. These results show the robustness of our methodology for the detection of differentially expressed genes using the RankProd method. In conclusion, DPSCs from NSCL/P patients exhibit gene expression signatures involving genes associated with mechanisms of extracellular matrix modeling and palate EMT processes which differ from those observed in controls. This comparative approach should lead to a more rapid identification of gene networks predisposing to this complex malformation syndrome than conventional gene mapping technologies.

Craniometric Similarities Within and Between Human Populations in Comparison with Neutral Genetic Data

The statement that pairs of individuals from different populations are often more genetically similar than pairs from the same population is a widespread idea inside and outside the scientific community. Witherspoon et al. [""Genetic similarities within and between human populations,"" Genetics 176:351-359 (2007)] proposed an index called the dissimilarity fraction (omega) to access in a quantitative way the validity of this statement for genetic systems. Witherspoon demonstrated that, as the number of loci increases, omega decreases to a point where, when enough sampling is available, the statement is false. In this study, we applied the dissimilarity fraction to Howells`s craniometric database to establish whether or not similar results are obtained for cranial morphological traits. Although in genetic studies thousands of loci are available, Howells`s database provides no more than 55 metric traits, making the contribution of each variable important. To cope with this limitation, we developed a routine that takes this effect into consideration when calculating. omega Contrary to what was observed for the genetic data, our results show that cranial morphology asymptotically approaches a mean omega of 0.3 and therefore supports the initial statement-that is, that individuals from the same geographic region do not form clear and discrete clusters-further questioning the idea of the existence of discrete biological clusters in the human species. Finally, by assuming that cranial morphology is under an additive polygenetic model, we can say that the population history signal of human craniometric traits presents the same resolution as a neutral genetic system dependent on no more than 20 loci.

Partitions selection strategy for set of clustering solutions

Clustering is a difficult task: there is no single cluster definition and the data can have more than one underlying structure. Pareto-based multi-objective genetic algorithms (e.g., MOCK Multi-Objective Clustering with automatic K-determination and MOCLE-Multi-Objective Clustering Ensemble) were proposed to tackle these problems. However, the output of such algorithms can often contains a high number of partitions, becoming difficult for an expert to manually analyze all of them. In order to deal with this problem, we present two selection strategies, which are based on the corrected Rand, to choose a subset of solutions. To test them, they are applied to the set of solutions produced by MOCK and MOCLE in the context of several datasets. The study was also extended to select a reduced set of partitions from the initial population of MOCLE. These analysis show that both versions of selection strategy proposed are very effective. They can significantly reduce the number of solutions and, at the same time, keep the quality and the diversity of the partitions in the original set of solutions. (C) 2010 Elsevier B.V. All rights reserved.

Multi-objective clustering ensemble for gene expression data analysis

In this paper, we present an algorithm for cluster analysis that integrates aspects from cluster ensemble and multi-objective clustering. The algorithm is based on a Pareto-based multi-objective genetic algorithm, with a special crossover operator, which uses clustering validation measures as objective functions. The algorithm proposed can deal with data sets presenting different types of clusters, without the need of expertise in cluster analysis. its result is a concise set of partitions representing alternative trade-offs among the objective functions. We compare the results obtained with our algorithm, in the context of gene expression data sets, to those achieved with multi-objective Clustering with automatic K-determination (MOCK). the algorithm most closely related to ours. (C) 2009 Elsevier B.V. All rights reserved.