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.

The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.

Modelling spectral reflectance of open cork oak woodland: a simulation analysis of the effects of vegetation structure and background

This study analyses the influence of vegetation structure (i.e. leaf area index and canopy cover) and seasonal background changes on moderate-resolution imaging spectrometer (MODIS)-simulated reflectance data in open woodland. Approximately monthly spectral reflectance and transmittance field measurements (May 2011 to October 2013) of cork oak tree leaves (Quercus suber) and of the herbaceous understorey were recorded in the region of Ribatejo, Portugal. The geometric-optical and radiative transfer (GORT) model was used to simulate MODIS response (red, near-infrared) and to calculate vegetation indices, investigating their response to changes in the structure of the overstorey vegetation and to seasonal changes in the understorey using scenarios corresponding to contrasting phenological status (dry season vs. wet season). The performance of normalized difference vegetation index (NDVI), soil-adjusted vegetation index (SAVI), and enhanced vegetation index (EVI) is discussed. Results showed that SAVI and EVI were very sensitive to the emergence of background vegetation in the wet season compared to NDVI and that shading effects lead to an opposing trend in the vegetation indices. The information provided by this research can be useful to improve our understanding of the temporal dynamic of vegetation, monitored by vegetation indices.

A potential vorticity signature for the cold sector of winter extratropical cyclones

The cold sector of a midlatitude storm is characterized by distinctive features such as strong surface heat fluxes, shallow convection, convective precipitation and synoptic subsidence. In order to evaluate the contribution of processes occurring in the cold sector to the mean climate, an appropriate indicator is needed. This study describes the systematic presence of negative potential vorticity (PV) behind the cold front of extratropical storms in winter. The origin of this negative PV is analyzed using ERA-Interim data, and PV tendencies averaged over the depth of the boundary layer are evaluated. It is found that negative PV is generated by diabatic processes in the cold sector and by Ekman pumping at the low centre, whereas positive PV is generated by Ekman advection of potential temperature in the warm sector. We suggest here that negative PV at low levels can be used to identify the cold sector. A PV-based indicator is applied to estimate the respective contributions of the cold sector and the remainder of the storm to upward motion and large-scale and convective precipitation. We compare the PV-based indicator with other distinctive features that could be used as markers of the cold sector and find that potential vorticity is the best criterion when taken alone and the best when combined with any other.

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.

Possible signature of hypernova nucleosynthesis in a beryllium-rich halo dwarf

As part of a large survey of halo and thick disc stars, we found one halo star, HD106038, exceptionally overabundant in beryllium. In spite of its low metallicity, [Fe/H] = -1.26, the star has log(Be/H) = -10.60, which is similar to the solar meteoritic abundance, log(Be/H)=-10.58. This abundance is more than 10 times higher the abundance of stars with similar metallicity and cannot be explained by models of chemical evolution of the Galaxy that include the standard theory of cosmic ray spallation. No other halo star exhibiting such a beryllium overabundance is known. In addition, overabundances of Li, Si, Ni, Y and Ba are also observed. We suggest that all these chemical peculiarities, excepting the Ba abundance, can be simultaneously explained if the star was formed in the vicinity of a hypernova.

Evolutionary placement of Xanthomonadales based on conserved protein signature sequences

Xanthomonadales comprises one of the largest phytopathogenic bacterial groups, and is currently classified within the gamma-proteobacteria. However, the phylogenetic placement of this group is not clearly resolved, and the results of different studies contradict one another. In this work, the evolutionary position of Xanthomonadales was determined by analyzing the presence of shared insertions and deletions (INDELs) in highly conserved proteins. Several distinctive insertions found in most of the members of the gamma-proteobacteria are absent in Xanthomonadales and groups such as Legionelalles, Chromatiales, Methylococcales, Thiotrichales and Cardiobacteriales. These INDELs were most likely introduced after the branching of Xanthomonadales from most of the gamma-proteobacteria and provide evidence for the phylogenetic placement of the early gamma-proteobacteria. Moreover, other proteins contain insertions exclusive to the Xanthomonadales order, confirming that this is a monophyletic group and provide important specific genetic markers. Thus, the data presented clearly support the Xanthomonadales group as an independent subdivision, and constitute one of the deepest branching lineage within the gamma-proteobacteria clade. (C) 2009 Elsevier Inc. All rights reserved.

MODIS aerosol optical depth Retrievals with high spatial resolution over an urban area using the critical reflectance

[1] The retrieval of aerosol optical depth (Ta) over land by satellite remote sensing is still a challenge when a high spatial resolution is required. This study presents a tool that uses satellite measurements to dynamically identify the aerosol optical model that best represents the optical properties of the aerosol present in the atmosphere. We use aerosol critical reflectance to identify the single scattering albedo of the aerosol layer. Two case studies show that the Sao Paulo region can have different aerosol properties and demonstrates how the dynamic methodology works to identify those differences to obtain a better T a retrieval. The methodology assigned the high single scattering albedo aerosol model (pi o( lambda = 0.55) = 0.90) to the case where the aerosol source was dominated by biomass burning and the lower pi(o) model (pi(o) (lambda = 0.55) = 0.85) to the case where the local urban aerosol had the dominant influence on the region, as expected. The dynamic methodology was applied using cloud-free data from 2002 to 2005 in order to retrieve Ta with Moderate Resolution Imaging Spectroradiometer ( MODIS). These results were compared with collocated data measured by AERONET in Sao Paulo. The comparison shows better results when the dynamic methodology using two aerosol optical models is applied (slope 1.06 +/- 0.08 offset 0.01 +/- 0.02 r(2) 0.6) than when a single and fixed aerosol model is used (slope 1.48 +/- 0.11 and offset - 0.03 +/- 0.03 r(2) 0.6). In conclusion the dynamical methodology is shown to work well with two aerosol models. Further studies are necessary to evaluate the methodology in other regions and under different conditions.

The signature of dark energy perturbations in galaxy cluster surveys

Models of dynamical dark energy unavoidably possess fluctuations in the energy density and pressure of that new component. In this paper we estimate the impact of dark energy fluctuations on the number of galaxy clusters in the Universe using a generalization of the spherical collapse model and the Press-Schechter formalism. The observations we consider are several hypothetical Sunyaev-Zel`dovich and weak lensing (shear maps) cluster surveys, with limiting masses similar to ongoing (SPT, DES) as well as future (LSST, Euclid) surveys. Our statistical analysis is performed in a 7-dimensional cosmological parameter space using the Fisher matrix method. We find that, in some scenarios, the impact of these fluctuations is large enough that their effect could already be detected by existing instruments such as the South Pole Telescope, when priors from other standard cosmological probes are included. We also show how dark energy fluctuations can be a nuisance for constraining cosmological parameters with cluster counts, and point to a degeneracy between the parameter that describes dark energy pressure on small scales (the effective sound speed) and the parameters describing its equation of state.

Signature of the interaction between dark energy and dark matter in galaxy clusters

We investigate the influence of ail interaction between dark energy and dark matter upon the dynamics of galaxy clusters. We obtain file general Layser-Irvine equation in the presence of interactions, and find how, in that case. the virial theorem stands corrected. Using optical, X-ray and weak lensing data from 33 relaxed galaxy clusters, we put constraints on the strength of the coupling between the dark sectors. Available data Suggests that this coupling is small but positive, indicating that dark energy might be decaying into dark matter. Systematic effects between the several mass estimates, however, should be better known, before definitive conclusions oil the magnitude and significance of this coupling could be established. (C) 2009 Published by Elsevier B.V.

Theoretical Analysis of Aggregation in Block-Copolymer Films: The Optical Signature

We focus this work on the theoretical investigation of the block-copolymer poly [oxyoctyleneoxy-(2,6-dimethoxy-1,4phenylene-1,2-ethinylene-phenanthrene-2,4diyl) named as LaPPS19, recently proposed for optoelectronic applications. We used for that a variety of methods, from molecular mechanics to quantum semiempirical techniques (AMI, ZINDO/S-CIS). Our results show that as expected isolated LaPPS19 chains present relevant electron localization over the phenanthrene group. We found, however, that LaPPS19 could assemble in a pi-stacked form, leading to impressive interchain interaction; the stacking induces electronic delocalization between neighbor chains and introduces new states below the phenanthrene-related absorption; these results allowed us to associate the red-shift of the absorption edge, seen in the experimental results, to spontaneous pi-stack aggregation of the chains. (C) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 110: 885-892, 2010

Optimisation of solid-phase microextraction combined with gas chromatography–mass spectrometry based methodology to establish the global volatile signature in pulp and skin of Vitis vinifera L. grape varieties

The volatiles (VOCs) and semi-volatile organic compounds (SVOCs) responsible for aroma are mainly present in skin of grape varieties. Thus, the present investigation is directed towards the optimisation of a solvent free methodology based on headspace-solid-phase microextraction (HS-SPME) combined with gas chromatography–quadrupole mass spectrometry (GC–qMS) in order to establish the global volatile composition in pulp and skin of Bual and Bastardo Vitis vinifera L. varieties. A deep study on the extraction-influencing parameters was performed, and the best results, expressed as GC peak area, number of identified compounds and reproducibility, were obtained using 4 g of sample homogenised in 5 mL of ultra-pure Milli-Q water in a 20 mL glass vial with addition of 2 g of sodium chloride (NaCl). A divinylbenzene/carboxen/polydimethylsiloxane fibre was selected for extraction at 60 °C for 45 min under continuous stirring at 800 rpm. More than 100 VOCs and SVOCs, including 27 monoterpenoids, 27 sesquiterpenoids, 21 carbonyl compounds, 17 alcohols (from which 2 aromatics), 10 C13 norisoprenoids and 5 acids were identified. The results showed that, for both grape varieties, the levels and number of volatiles in skin were considerably higher than those observed in pulp. According to the data obtained by principal component analysis (PCA), the establishment of the global volatile signature of grape and the relationship between different part of grapes—pulp and skin, may be an useful tool to winemaker decision to define the vinification procedures that improves the organoleptic characteristics of the corresponding wines and consequently contributed to an economic valorization and consumer acceptance.

Nitrogen content identification in crop plants using spectral reflectance and artificial neural networks

The accurate identification of the nitrogen content in crop plants is extremely important since it involves economic aspects and environmental impacts. Several experimental tests have been carried out to obtain characteristics and parameters associated with the health of plants and its growing. The nitrogen content identification involves a lot of nonlinear parametes and complexes mathematical models. This paper describes a novel approach for identification of nitrogen content thought spectral reflectance of plant leaves using artificial neural networks. The network acts as identifier of relationships among pH of soil, fertilizer treatment, spectral reflectance and nitrogen content in the plants. So, nitrogen content can be estimated and generalized from an input parameter set. This approach can be form the basis for development of an accurate real time nitrogen applicator.

Exploring Elko typical signature

We study the prospects of observing the presence of a relatively light Elko particle as a possible dark matter candidate, by pointing out a typical signature for the process encompassing the Elko non-locality, exploring some consequences of the unusual Elko propagator behavior when analyzed outside the Elko axis of propagation. We also consider the production of a light Elko associated to missing energy and isolated leptons at the LHC, with center of mass energy of 7 and 14 TeV and total luminosity from 1 fb(-1) to 10 fb(-1). Basically, the Elko non-locality engenders a peculiar signal in the missing energy turning it sensible to the angle of detection. (C) 2011 Elsevier B.V. All rights reserved.