Estimating persistent Betti numbers for discrete shape analysis

Persistent Topology is an innovative way of matching topology and geometry, and it proves to be an effective mathematical tool in shape analysis. In order to express its full potential for applications, it has to interface with the typical environment of Computer Science: It must be possible to deal with a finite sampling of the object of interest, and with combinatorial representations of it. Following that idea, the main result claims that it is possible to construct a relation between the persistent Betti numbers (PBNs; also called rank invariant) of a compact, Riemannian submanifold X of R^m and the ones of an approximation U of X itself, where U is generated by a ball covering centered in the points of the sampling. Moreover we can state a further result in which, this time, we relate X with a finite simplicial complex S generated, thanks to a particular construction, by the sampling points. To be more precise, strict inequalities hold only in "blind strips'', i.e narrow areas around the discontinuity sets of the PBNs of U (or S). Out of the blind strips, the values of the PBNs of the original object, of the ball covering of it, and of the simplicial complex coincide, respectively.

GEOSTATISTICAL INFERENCE UNDER PREFERENTIAL SAMPLING

Geostatistics involves the fitting of spatially continuous models to spatially discrete data (Chil`es and Delfiner, 1999). Preferential sampling arises when the process that determines the data-locations and the process being modelled are stochastically dependent. Conventional geostatistical methods assume, if only implicitly, that sampling is non-preferential. However, these methods are often used in situations where sampling is likely to be preferential. For example, in mineral exploration samples may be concentrated in areas thought likely to yield high-grade ore. We give a general expression for the likelihood function of preferentially sampled geostatistical data and describe how this can be evaluated approximately using Monte Carlo methods. We present a model for preferential sampling, and demonstrate through simulated examples that ignoring preferential sampling can lead to seriously misleading inferences. We describe an application of the model to a set of bio-monitoring data from Galicia, northern Spain, in which making allowance for preferential sampling materially changes the inferences.

Hermitian curve interpolation for CT-data re-sampling

Purpose: Development of an interpolation algorithm for re‐sampling spatially distributed CT‐data with the following features: global and local integral conservation, avoidance of negative interpolation values for positively defined datasets and the ability to control re‐sampling artifacts. Method and Materials: The interpolation can be separated into two steps: first, the discrete CT‐data has to be continuously distributed by an analytic function considering the boundary conditions. Generally, this function is determined by piecewise interpolation. Instead of using linear or high order polynomialinterpolations, which do not fulfill all the above mentioned features, a special form of Hermitian curve interpolation is used to solve the interpolation problem with respect to the required boundary conditions. A single parameter is determined, by which the behavior of the interpolation function is controlled. Second, the interpolated data have to be re‐distributed with respect to the requested grid. Results: The new algorithm was compared with commonly used interpolation functions based on linear and second order polynomial. It is demonstrated that these interpolation functions may over‐ or underestimate the source data by about 10%–20% while the parameter of the new algorithm can be adjusted in order to significantly reduce these interpolation errors. Finally, the performance and accuracy of the algorithm was tested by re‐gridding a series of X‐ray CT‐images. Conclusion: Inaccurate sampling values may occur due to the lack of integral conservation. Re‐sampling algorithms using high order polynomialinterpolation functions may result in significant artifacts of the re‐sampled data. Such artifacts can be avoided by using the new algorithm based on Hermitian curve interpolation

Ambulacral length with number of pore pairs/tubercles for both species of sea urchins and for six sampling sites to quantify fluctuating asymmetry

The surroundings of the Cortiou sewage are among the most polluted environments of the French Mediterranean Sea (Marseilles, France). So far, no studies have precisely quantified the impact of pollution on the development of organisms in this area.Methods: We used a fluctuating asymmetry (FA) measure of developmental instability (DI) to assess environmental stress in two species of radially symmetric sea urchins (Arbacia lixula and Paracentrotus lividus). For six sampling sites (Cortiou, Riou, Maire, East Maire, Mejean, and Niolon), levels of FA were calculated from continuous and discrete skeletal measures of ambulacral length, number of pore pairs and primary tubercles.Results: For both species, the most polluted sampling site, Cortiou, displayed the highest level of FA, while the Maire and East Maire sampling sites displayed the lowest levels. A. lixula revealed systematic differences in FA among sampling sites for all characters and P. lividus showed differences in FA for the number of primary tubercles.Conclusions: Statistical analyses of FA show a concordance between the spatial patterns of FA among sampling sites and the spatial distribution of sewage discharge pollutants in the Cortiou area. High developmental stress in these sampling sites is associated with exposure to high concentrations of heavy metals and many harmful organic substances contained in wastewater. FA estimated from structures with complex symmetry appears to be a fast and reliable tool to detect subtle differences in FA. Its use in biomonitoring programs for inferring anthropogenic and natural environmental stress is suggested.

Properties of seawater (pH total scale) from a Satlantic SeaFET instrument mounted on the continuous surface water sampling system during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) sampled the world oceans on board a 36 m long schooner, collecting environmental data and organisms from viruses to planktonic metazoans for later analyses using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set provides continuous pH measurements made during 2013 expedition with a Satlantic SeaFET instrument that was connected to the flowthrough system. Data calibration was performed according to Bresnahan et al. (2014) (using spectrophotometric pH measurements on discrete samples (Clayton and Byrne 1993). pH_internal values were taken to calibrate the data (rather than pH_external) because of the better calibration coefficient (there was no trend associated with it). The equations of Clayton and Byrne (1993) was used to compute pH from the measured absorbance values at the temperature of measurement. The data was converted to in situ temperature using the "CO2-sys" program which can be downloaded from http://cdiac.ornl.gov/ftp/co2sys/.

Properties of seawater (partial pressure of carbon dioxide (pCO2)) from a ProOceanus CO2-Pro sensor mounted on the continuous surface water sampling system during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) sampled the world oceans on board a 36 m long schooner, collecting environmental data and organisms from viruses to planktonic metazoans for later analyses using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set provides continuous measurements of partial pressure of carbon dioxide (pCO2), using a ProOceanus CO2-Pro instrument mounted on the flowthrough system. This automatic sensor is fitted with an equilibrator made of gas permeable silicone membrane and an internal detection loop with a non-dispersive infrared detector of PPSystems SBA-4 CO2 analyzer. A zero-CO2 baseline is provided for the subsequent measurements circulating the internal gas through a CO2 absorption chamber containing soda lime or Ascarite. The frequency of this automatic zero point calibration was set to be 24 hours. All data recorded during zeroing processes were discarded with the 15-minute data after each calibration. The output of CO2-Pro is the mole fraction of CO2 in the measured water and the pCO2 is obtained using the measured total pressure of the internal wet gas. The fugacity of CO2 (fCO2) in the surface seawater, whose difference with the atmospheric CO2 fugacity is proportional to the air-sea CO2 fluxes, is obtained by correcting the pCO2 for non-ideal CO2 gas concentration according to Weiss (1974). The fCO2 computed using CO2-Pro measurements was corrected to the sea surface condition by considering the temperature effect on fCO2 (Takahashi et al., 1993). The surface seawater observations that were initially estimated with a 15 seconds frequency were averaged every 5-min cycle. The performance of CO2-Pro was adjusted by comparing the sensor outputs against the thermodynamic carbonate calculation of pCO2 using the carbonic system constants of Millero et al. (2006) from the determinations of total inorganic carbon (CT ) and total alkalinity (AT ) in discrete samples collected at sea surface. AT was determined using an automated open cell potentiometric titration (Haraldsson et al. 1997). CT was determined with an automated coulometric titration (Johnson et al. 1985; 1987), using the MIDSOMMA system (Mintrop, 2005). fCO2 data are flagged according to the WOCE guidelines following Pierrot et al. (2009) identifying recommended values and questionable measurements giving additional information about the reasons of the questionability.

Efficient sampling of band-limited signals from sine wave crossings

This correspondence presents an efficient method for reconstructing a band-limited signal in the discrete domain from its crossings with a sine wave. The method makes it possible to design A/D converters that only deliver the crossing timings, which are then used to interpolate the input signal at arbitrary instants. Potentially, it may allow for reductions in power consumption and complexity in these converters. The reconstruction in the discrete domain is based on a recently-proposed modification of the Lagrange interpolator, which is readily implementable with linear complexity and efficiently, given that it re-uses known schemes for variable fractional-delay (VFD) filters. As a spin-off, the method allows one to perform spectral analysis from sine wave crossings with the complexity of the FFT. Finally, the results in the correspondence are validated in several numerical examples.

Shift, scaling and derivative properties for the discrete cosine transform

A set of DCT domain properties for shifting and scaling by real amounts, and taking linear operations such as differentiation is described. The DCT coefficients of a sampled signal are subjected to a linear transform, which returns the DCT coefficients of the shifted, scaled and/or differentiated signal. The properties are derived by considering the inverse discrete transform as a cosine series expansion of the original continuous signal, assuming sampling in accordance with the Nyquist criterion. This approach can be applied in the signal domain, to give, for example, DCT based interpolation or derivatives. The same approach can be taken in decoding from the DCT to give, for example, derivatives in the signal domain. The techniques may prove useful in compressed domain processing applications, and are interesting because they allow operations from the continuous domain such as differentiation to be implemented in the discrete domain. An image matching algorithm illustrates the use of the properties, with improvements in computation time and matching quality.

Quantifying the pathology of neurodegenerative disorders:Quantitative measurements, sampling strategies and data analysis

The use of quantitative methods has become increasingly important in the study of neurodegenerative disease. Disorders such as Alzheimer's disease (AD) are characterized by the formation of discrete, microscopic, pathological lesions which play an important role in pathological diagnosis. This article reviews the advantages and limitations of the different methods of quantifying the abundance of pathological lesions in histological sections, including estimates of density, frequency, coverage, and the use of semiquantitative scores. The major sampling methods by which these quantitative measures can be obtained from histological sections, including plot or quadrat sampling, transect sampling, and point-quarter sampling, are also described. In addition, the data analysis methods commonly used to analyse quantitative data in neuropathology, including analyses of variance (ANOVA) and principal components analysis (PCA), are discussed. These methods are illustrated with reference to particular problems in the pathological diagnosis of AD and dementia with Lewy bodies (DLB).

Hybrid sampling on mutual information entropy-based clustering ensembles for optimizations

In this paper, we focus on the design of bivariate EDAs for discrete optimization problems and propose a new approach named HSMIEC. While the current EDAs require much time in the statistical learning process as the relationships among the variables are too complicated, we employ the Selfish gene theory (SG) in this approach, as well as a Mutual Information and Entropy based Cluster (MIEC) model is also set to optimize the probability distribution of the virtual population. This model uses a hybrid sampling method by considering both the clustering accuracy and clustering diversity and an incremental learning and resample scheme is also set to optimize the parameters of the correlations of the variables. Compared with several benchmark problems, our experimental results demonstrate that HSMIEC often performs better than some other EDAs, such as BMDA, COMIT, MIMIC and ECGA. © 2009 Elsevier B.V. All rights reserved.

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_209 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_131 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_132 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_139 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles at station TARA_124 during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) was a global survey of ocean ecosystems aboard the Sailing Vessel Tara. It carried out extensive measurements of evironmental conditions and collected plankton (viruses, bacteria, protists and metazoans) for later analysis using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set includes properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically. More than 200 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).