Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completelyabsent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and byMartín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involvedparts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method isintroduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that thetheoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approachhas reasonable properties from a compositional point of view. In particular, it is “natural” in the sense thatit recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in thesame paper a substitution method for missing values on compositional data sets is introduced

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel densityestimation techniques in the context of compositional data analysis. Indeed, they gavetwo options for the choice of the kernel to be used in the kernel estimator. One ofthese kernels is based on the use the alr transformation on the simplex SD jointly withthe normal distribution on RD-1. However, these authors themselves recognized thatthis method has some deficiencies. A method for overcoming these dificulties based onrecent developments for compositional data analysis and multivariate kernel estimationtheory, combining the ilr transformation with the use of the normal density with a fullbandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu-Figueras (2006). Here we present an extensive simulation study that compares bothmethods in practice, thus exploring the finite-sample behaviour of both estimators

CODAMAT: a modern analogue techinque for compositional data

The quantitative estimation of Sea Surface Temperatures from fossils assemblages is afundamental issue in palaeoclimatic and paleooceanographic investigations. TheModern Analogue Technique, a widely adopted method based on direct comparison offossil assemblages with modern coretop samples, was revised with the aim ofconforming it to compositional data analysis. The new CODAMAT method wasdeveloped by adopting the Aitchison metric as distance measure. Modern coretopdatasets are characterised by a large amount of zeros. The zero replacement was carriedout by adopting a Bayesian approach to the zero replacement, based on a posteriorestimation of the parameter of the multinomial distribution. The number of modernanalogues from which reconstructing the SST was determined by means of a multipleapproach by considering the Proxies correlation matrix, Standardized Residual Sum ofSquares and Mean Squared Distance. This new CODAMAT method was applied to theplanktonic foraminiferal assemblages of a core recovered in the Tyrrhenian Sea.Kew words: Modern analogues, Aitchison distance, Proxies correlation matrix,Standardized Residual Sum of Squares

Elemental analysis of New Zealand Nephrite Jade (pounamu) for forensic purposes

Pounamu (NZ jade), or nephrite, is a protected mineral in its natural form following thetransfer of ownership back to Ngai Tahu under the Ngai Tahu (Pounamu Vesting) Act 1997.Any theft of nephrite is prosecutable under the Crimes Act 1961. Scientific evidence isessential in cases where origin is disputed. A robust method for discrimination of thismaterial through the use of elemental analysis and compositional data analysis is required.Initial studies have characterised the variability within a given nephrite source. This hasincluded investigation of both in situ outcrops and alluvial material. Methods for thediscrimination of two geographically close nephrite sources are being developed.Key Words: forensic, jade, nephrite, laser ablation, inductively coupled plasma massspectrometry, multivariate analysis, elemental analysis, compositional data analysis

A Factor analysis of hidrochemical composition of Llobregat river basin

Hydrogeological research usually includes some statistical studies devised to elucidate mean background state, characterise relationships among different hydrochemical parameters, and show the influence of human activities. These goals are achieved either by means of a statistical approach or by mixing modelsbetween end-members. Compositional data analysis has proved to be effective with the first approach, but there is no commonly accepted solution to the end-member problem in a compositional framework.We present here a possible solution based on factor analysis of compositions illustrated with a case study.We find two factors on the compositional bi-plot fitting two non-centered orthogonal axes to the most representative variables. Each one of these axes defines a subcomposition, grouping those variables thatlay nearest to it. With each subcomposition a log-contrast is computed and rewritten as an equilibrium equation. These two factors can be interpreted as the isometric log-ratio coordinates (ilr) of three hiddencomponents, that can be plotted in a ternary diagram. These hidden components might be interpreted as end-members.We have analysed 14 molarities in 31 sampling stations all along the Llobregat River and its tributaries, with a monthly measure during two years. We have obtained a bi-plot with a 57% of explained totalvariance, from which we have extracted two factors: factor G, reflecting geological background enhanced by potash mining; and factor A, essentially controlled by urban and/or farming wastewater. Graphicalrepresentation of these two factors allows us to identify three extreme samples, corresponding to pristine waters, potash mining influence and urban sewage influence. To confirm this, we have available analysisof diffused and widespread point sources identified in the area: springs, potash mining lixiviates, sewage, and fertilisers. Each one of these sources shows a clear link with one of the extreme samples, exceptfertilisers due to the heterogeneity of their composition.This approach is a useful tool to distinguish end-members, and characterise them, an issue generally difficult to solve. It is worth note that the end-member composition cannot be fully estimated but only characterised through log-ratio relationships among components. Moreover, the influence of each endmember in a given sample must be evaluated in relative terms of the other samples. These limitations areintrinsic to the relative nature of compositional data

Knowledge management for systems biology a general and visually driven framework applied to translational medicine

Background: To enhance our understanding of complex biological systems like diseases we need to put all of the available data into context and use this to detect relations, pattern and rules which allow predictive hypotheses to be defined. Life science has become a data rich science with information about the behaviour of millions of entities like genes, chemical compounds, diseases, cell types and organs, which are organised in many different databases and/or spread throughout the literature. Existing knowledge such as genotype - phenotype relations or signal transduction pathways must be semantically integrated and dynamically organised into structured networks that are connected with clinical and experimental data. Different approaches to this challenge exist but so far none has proven entirely satisfactory. Results: To address this challenge we previously developed a generic knowledge management framework, BioXM™, which allows the dynamic, graphic generation of domain specific knowledge representation models based on specific objects and their relations supporting annotations and ontologies. Here we demonstrate the utility of BioXM for knowledge management in systems biology as part of the EU FP6 BioBridge project on translational approaches to chronic diseases. From clinical and experimental data, text-mining results and public databases we generate a chronic obstructive pulmonary disease (COPD) knowledge base and demonstrate its use by mining specific molecular networks together with integrated clinical and experimental data. Conclusions: We generate the first semantically integrated COPD specific public knowledge base and find that for the integration of clinical and experimental data with pre-existing knowledge the configuration based set-up enabled by BioXM reduced implementation time and effort for the knowledge base compared to similar systems implemented as classical software development projects. The knowledgebase enables the retrieval of sub-networks including protein-protein interaction, pathway, gene - disease and gene - compound data which are used for subsequent data analysis, modelling and simulation. Pre-structured queries and reports enhance usability; establishing their use in everyday clinical settings requires further simplification with a browser based interface which is currently under development.

Quantifying urban attractiveness from the distribution and density of digital footprints

In the past, sensors networks in cities have been limited to fixed sensors, embedded in particular locations, under centralised control. Today, new applications can leverage wireless devices and use them as sensors to create aggregated information. In this paper, we show that the emerging patterns unveiled through the analysis of large sets of aggregated digital footprints can provide novel insights into how people experience the city and into some of the drivers behind these emerging patterns. We particularly explore the capacity to quantify the evolution of the attractiveness of urban space with a case study of in the area of the New York City Waterfalls, a public art project of four man-made waterfalls rising from the New York Harbor. Methods to study the impact of an event of this nature are traditionally based on the collection of static information such as surveys and ticket-based people counts, which allow to generate estimates about visitors’ presence in specific areas over time. In contrast, our contribution makes use of the dynamic data that visitors generate, such as the density and distribution of aggregate phone calls and photos taken in different areas of interest and over time. Our analysis provides novel ways to quantify the impact of a public event on the distribution of visitors and on the evolution of the attractiveness of the points of interest in proximity. This information has potential uses for local authorities, researchers, as well as service providers such as mobile network operators.

Rules of origin : from analysis to reform

General Introduction This thesis can be divided into two main parts :the first one, corresponding to the first three chapters, studies Rules of Origin (RoOs) in Preferential Trade Agreements (PTAs); the second part -the fourth chapter- is concerned with Anti-Dumping (AD) measures. Despite wide-ranging preferential access granted to developing countries by industrial ones under North-South Trade Agreements -whether reciprocal, like the Europe Agreements (EAs) or NAFTA, or not, such as the GSP, AGOA, or EBA-, it has been claimed that the benefits from improved market access keep falling short of the full potential benefits. RoOs are largely regarded as a primary cause of the under-utilization of improved market access of PTAs. RoOs are the rules that determine the eligibility of goods to preferential treatment. Their economic justification is to prevent trade deflection, i.e. to prevent non-preferred exporters from using the tariff preferences. However, they are complex, cost raising and cumbersome, and can be manipulated by organised special interest groups. As a result, RoOs can restrain trade beyond what it is needed to prevent trade deflection and hence restrict market access in a statistically significant and quantitatively large proportion. Part l In order to further our understanding of the effects of RoOs in PTAs, the first chapter, written with Pr. Olivier Cadot, Celine Carrère and Pr. Jaime de Melo, describes and evaluates the RoOs governing EU and US PTAs. It draws on utilization-rate data for Mexican exports to the US in 2001 and on similar data for ACP exports to the EU in 2002. The paper makes two contributions. First, we construct an R-index of restrictiveness of RoOs along the lines first proposed by Estevadeordal (2000) for NAFTA, modifying it and extending it for the EU's single-list (SL). This synthetic R-index is then used to compare Roos under NAFTA and PANEURO. The two main findings of the chapter are as follows. First, it shows, in the case of PANEURO, that the R-index is useful to summarize how countries are differently affected by the same set of RoOs because of their different export baskets to the EU. Second, it is shown that the Rindex is a relatively reliable statistic in the sense that, subject to caveats, after controlling for the extent of tariff preference at the tariff-line level, it accounts for differences in utilization rates at the tariff line level. Finally, together with utilization rates, the index can be used to estimate total compliance costs of RoOs. The second chapter proposes a reform of preferential Roos with the aim of making them more transparent and less discriminatory. Such a reform would make preferential blocs more "cross-compatible" and would therefore facilitate cumulation. It would also contribute to move regionalism toward more openness and hence to make it more compatible with the multilateral trading system. It focuses on NAFTA, one of the most restrictive FTAs (see Estevadeordal and Suominen 2006), and proposes a way forward that is close in spirit to what the EU Commission is considering for the PANEURO system. In a nutshell, the idea is to replace the current array of RoOs by a single instrument- Maximum Foreign Content (MFC). An MFC is a conceptually clear and transparent instrument, like a tariff. Therefore changing all instruments into an MFC would bring improved transparency pretty much like the "tariffication" of NTBs. The methodology for this exercise is as follows: In step 1, I estimate the relationship between utilization rates, tariff preferences and RoOs. In step 2, I retrieve the estimates and invert the relationship to get a simulated MFC that gives, line by line, the same utilization rate as the old array of Roos. In step 3, I calculate the trade-weighted average of the simulated MFC across all lines to get an overall equivalent of the current system and explore the possibility of setting this unique instrument at a uniform rate across lines. This would have two advantages. First, like a uniform tariff, a uniform MFC would make it difficult for lobbies to manipulate the instrument at the margin. This argument is standard in the political-economy literature and has been used time and again in support of reductions in the variance of tariffs (together with standard welfare considerations). Second, uniformity across lines is the only way to eliminate the indirect source of discrimination alluded to earlier. Only if two countries face uniform RoOs and tariff preference will they face uniform incentives irrespective of their initial export structure. The result of this exercise is striking: the average simulated MFC is 25% of good value, a very low (i.e. restrictive) level, confirming Estevadeordal and Suominen's critical assessment of NAFTA's RoOs. Adopting a uniform MFC would imply a relaxation from the benchmark level for sectors like chemicals or textiles & apparel, and a stiffening for wood products, papers and base metals. Overall, however, the changes are not drastic, suggesting perhaps only moderate resistance to change from special interests. The third chapter of the thesis considers whether Europe Agreements of the EU, with the current sets of RoOs, could be the potential model for future EU-centered PTAs. First, I have studied and coded at the six-digit level of the Harmonised System (HS) .both the old RoOs -used before 1997- and the "Single list" Roos -used since 1997. Second, using a Constant Elasticity Transformation function where CEEC exporters smoothly mix sales between the EU and the rest of the world by comparing producer prices on each market, I have estimated the trade effects of the EU RoOs. The estimates suggest that much of the market access conferred by the EAs -outside sensitive sectors- was undone by the cost-raising effects of RoOs. The chapter also contains an analysis of the evolution of the CEECs' trade with the EU from post-communism to accession. Part II The last chapter of the thesis is concerned with anti-dumping, another trade-policy instrument having the effect of reducing market access. In 1995, the Uruguay Round introduced in the Anti-Dumping Agreement (ADA) a mandatory "sunset-review" clause (Article 11.3 ADA) under which anti-dumping measures should be reviewed no later than five years from their imposition and terminated unless there was a serious risk of resumption of injurious dumping. The last chapter, written with Pr. Olivier Cadot and Pr. Jaime de Melo, uses a new database on Anti-Dumping (AD) measures worldwide to assess whether the sunset-review agreement had any effect. The question we address is whether the WTO Agreement succeeded in imposing the discipline of a five-year cycle on AD measures and, ultimately, in curbing their length. Two methods are used; count data analysis and survival analysis. First, using Poisson and Negative Binomial regressions, the count of AD measures' revocations is regressed on (inter alia) the count of "initiations" lagged five years. The analysis yields a coefficient on measures' initiations lagged five years that is larger and more precisely estimated after the agreement than before, suggesting some effect. However the coefficient estimate is nowhere near the value that would give a one-for-one relationship between initiations and revocations after five years. We also find that (i) if the agreement affected EU AD practices, the effect went the wrong way, the five-year cycle being quantitatively weaker after the agreement than before; (ii) the agreement had no visible effect on the United States except for aone-time peak in 2000, suggesting a mopping-up of old cases. Second, the survival analysis of AD measures around the world suggests a shortening of their expected lifetime after the agreement, and this shortening effect (a downward shift in the survival function postagreement) was larger and more significant for measures targeted at WTO members than for those targeted at non-members (for which WTO disciplines do not bind), suggesting that compliance was de jure. A difference-in-differences Cox regression confirms this diagnosis: controlling for the countries imposing the measures, for the investigated countries and for the products' sector, we find a larger increase in the hazard rate of AD measures covered by the Agreement than for other measures.

A importância do sector microcrédito e o perfil do microempresário: Ilha de Santo Antão Cabo Verde

As microempresas desempenham um papel fundamental na promoção do emprego, na inovação, na criação de rendimentos e no desenvolvimento económico e social. Para os países em vias de desenvolvimento, crê-se que a dinamização das microempresas pode ser um instrumento privilegiado de promoção e combate à pobreza, na medida em que esta poderá ser a via para incentivar as camadas mais pobres das populações rurais e urbanas a criarem os seus próprios negócios e a providenciarem os seus próprios rendimentos. A criação e o crescimento das microempresas estão, todavia, condicionados por vários constrangimentos. A inexistência de capital inicial (Start-Up Capital) é apontada na literatura financeira como uma das mais relevantes. O recurso ao capital externo, como fonte de financiamento, dependerá, por sua vez, de vários factores. O presente estudo foi realizado em Santo Antão, a ilha mais a norte e a mais montanhosa do Arquipélago de Cabo Verde. O sector micro crédito chama atenção pelo facto de ser um instrumento de importância primordial para Cabo Verde e, particularmente, para a ilha de Santo Antão que possui uma estrutura económica e social muito vulnerável o que nos leva a compreender melhor, o funcionamento das microempresas, instaladas nos três municípios da Ilha (Paul, Ribeira Grande e Porto Novo). Ao longo do estudo definimos o perfil sócio económico do micro empresário Santantonense, com o objectivo de compreender e quantificar o contributo do sector para o desenvolvimento empresarial da ilha, sem esquecer os constrangimentos e dificuldades que se colocam aos micros empresários na procura de financiamento. O processo de recolha de informação foi efectuado com recurso a pesquisas de campo, a partir da elaboração e aplicação de entrevistas de uma forma semi-estruturada, no sentido de identificar as principais características/perfil do empresário. Os dados recolhidos pelas entrevistas têm por base uma apreciação crítica da gestão para melhor compreender e comparar as fragilidades existentes e analisar a capacidade de sucesso dos micros empresários. A configuração da actividade económica foi feita com base na análise quantitativa e qualitativa, dos dados obtidos na aplicação dos questionários. De igual modo, analisamos e comparamos os casos de sucesso e insucesso nas microempresas em estudo, casos de sucesso no que diz respeito aos benefícios de micro créditos para a redução da pobreza e do desemprego, de criação do auto-emprego, e da formação/informação aos micros empresários santantonenses. Nos casos de insucesso analisamos as causas que estiveram na sua origem assim como as consequências daí advenientes. Uma das constatações do estudo, como se verá pela análise dos dados, é que o micro empresário Santantonense, possui um baixo nível de escolaridade e que na sua maioria são mulheres. Um outro resultado evidenciado pelo estudo, é que há uma necessidade da política pública de desenvolvimento no sentido de definição de incentivos à criação e à promoção de micro negócios, atendendo às características demográficas e às necessidades específicas dos beneficiários. Micro enterprises perform a fundamental component in promoting employment, innovation, and earnings-generation and in socio-economic development. For countries en route to development, the belief is that the dynamic engine of the micro enterprises could be a privileged instrument to promote in the battle against poverty, in the hope that this could be the venue to incentivize the poorest of the rural and urban populations to create their own businesses and forecast their own earnings. The creation and the growth of micro enterprises is, however, conditional upon various constraints. The inexistence of initial capital is cited in financial literature as one of the more important. To resort to external capital as a financing source, is itself dependent on various factors. The current study was conducted in Santo Antão, the most northern and mountainous island in the Archipelago of Cape Verde. The micro credit´s sector calls attention to the fact that it is an essential instrument in Cape Verde, particularly in the island of Santo Antão which has an economic and social structure extremely vulnerable, leading us to a better understanding of how micro enterprises operate in the three municipalities of the Island (Paul, Ribeira Grande and Porto Novo). During the course of the study we defined the socio-economic character of the micro entrepreneur Santantonense, with the goal of understanding and quantifying the sector´s contribution to the Island´s entrepreneurial development, keeping in mind the contraints and difficulties that confront the entrepreneurs when seeking financing. The process for gathering the information was performed through field research, beginning with elaboration and application of interviews, designed to identify the entrepreneur´s major characteristics and the importance of micro credit for the island of Santo Antão. The data gathered through the interviews have un underlying basic and critic appreciation of management for a better understanding and comparing the existing fragilities and for analyzing the micro entrepreneurs´ capacity to succeed. The configuration of economic activities was designed based on quantitative and qualitative analysis from data obtained from the questionnaires. Likewise, we analyzed and compared the success and non-success cases of the micro enterprises in the study, success cases with respect to the benefits of micro credit in reducing poverty and unemployment, creation of self-employment, and the education/information for the micro entrepreneurs of Santo Antão. In the non-success cases we analyzed the original causes as well as the impending consequences. One of the study´s contentions, as the data analysis shows, is that micro entrepreneur of Santo Antão has a low level of education with the majority of them being women. In addition the study shows that there is a need for a public discourse in terms of defining and developing incentives for creating and promoting micro businesses given the demographic characteristics and the specific necessities of the beneficiaries.

Compositional Data in Biomedical Research

Modern methods of compositional data analysis are not well known in biomedical research.Moreover, there appear to be few mathematical and statistical researchersworking on compositional biomedical problems. Like the earth and environmental sciences,biomedicine has many problems in which the relevant scienti c information isencoded in the relative abundance of key species or categories. I introduce three problemsin cancer research in which analysis of compositions plays an important role. Theproblems involve 1) the classi cation of serum proteomic pro les for early detection oflung cancer, 2) inference of the relative amounts of di erent tissue types in a diagnostictumor biopsy, and 3) the subcellular localization of the BRCA1 protein, and it'srole in breast cancer patient prognosis. For each of these problems I outline a partialsolution. However, none of these problems is \solved". I attempt to identify areas inwhich additional statistical development is needed with the hope of encouraging morecompositional data analysts to become involved in biomedical research

Compositions in life science data

The aim of this talk is to convince the reader that there are a lot of interesting statisticalproblems in presentday life science data analysis which seem ultimately connected withcompositional statistics.Key words: SAGE, cDNA microarrays, (1D-)NMR, virus quasispecies

Mapping of Environmental Data Using Kernel-Based Methods

Recently, kernel-based Machine Learning methods have gained great popularity in many data analysis and data mining fields: pattern recognition, biocomputing, speech and vision, engineering, remote sensing etc. The paper describes the use of kernel methods to approach the processing of large datasets from environmental monitoring networks. Several typical problems of the environmental sciences and their solutions provided by kernel-based methods are considered: classification of categorical data (soil type classification), mapping of environmental and pollution continuous information (pollution of soil by radionuclides), mapping with auxiliary information (climatic data from Aral Sea region). The promising developments, such as automatic emergency hot spot detection and monitoring network optimization are discussed as well.

Psychological pressure in competitive environments: Evidence from a randomized natural experiment

Much like cognitive abilities, emotional skills can have major effects on performance and economic outcomes. This paper studies the behavior of professionalsubjects involved in a dynamic competition in their own natural environment. Thesetting is a penalty shoot-out in soccer where two teams compete in a tournamentframework taking turns in a sequence of five penalty kicks each. As the kicking order is determined by the random outcome of a coin flip, the treatment and control groups are determined via explicit randomization. Therefore, absent any psychological effects, both teams should have the same probability of winning regardless of the kicking order. Yet, we find a systematic first-kicker advantage. Using data on 2,731 penalty kicks from 262 shoot-outs for a three decade period, we find that teams kicking first win the penalty shoot-out 60.5% of the time. A dynamic panel data analysis shows that the psychological mechanism underlying this result arises from the asymmetry in the partial score. As most kicks are scored, kicking first typically means having the opportunity to lead in the partial score, whereas kicking second typically means lagging in the score and having the opportunity to, at most, get even. Having a worse prospect than the opponent hinders subjects' performance.Further, we also find that professionals are self-aware of their own psychological effects. When a recent change in regulations gives winners of the coin toss the chance to choose the kicking order, they rationally react to it by systematically choosing to kick first. A survey of professional players reveals that when asked to explain why they prefer to kick first, they precisely identify the psychological mechanism for which we find empirical support in the data: they want to lead in the score inorder to put pressure on the opponent.

Sampling strategies for tropical forest nutrient cycling studies: a case study in São Paulo, Brazil

The precise sampling of soil, biological or micro climatic attributes in tropical forests, which are characterized by a high diversity of species and complex spatial variability, is a difficult task. We found few basic studies to guide sampling procedures. The objective of this study was to define a sampling strategy and data analysis for some parameters frequently used in nutrient cycling studies, i. e., litter amount, total nutrient amounts in litter and its composition (Ca, Mg, Κ, Ν and P), and soil attributes at three depths (organic matter, Ρ content, cation exchange capacity and base saturation). A natural remnant forest in the West of São Paulo State (Brazil) was selected as study area and samples were collected in July, 1989. The total amount of litter and its total nutrient amounts had a high spatial independent variance. Conversely, the variance of litter composition was lower and the spatial dependency was peculiar to each nutrient. The sampling strategy for the estimation of litter amounts and the amount of nutrient in litter should be different than the sampling strategy for nutrient composition. For the estimation of litter amounts and the amount of nutrients in litter (related to quantity) a large number of randomly distributed determinations are needed. Otherwise, for the estimation of litter nutrient composition (related to quality) a smaller amount of spatially located samples should be analyzed. The determination of sampling for soil attributes differed according to the depth. Overall, surface samples (0-5 cm) showed high short distance spatial dependent variance, whereas, subsurface samples exhibited spatial dependency in longer distances. Short transects with sampling interval of 5-10 m are recommended for surface sampling. Subsurface samples must also be spatially located, but with transects or grids with longer distances between sampling points over the entire area. Composite soil samples would not provide a complete understanding of the relation between soil properties and surface dynamic processes or landscape aspects. Precise distribution of Ρ was difficult to estimate.

Post-detection analysis for grating-based ultra-small angle X-ray scattering.

Until recently, the hard X-ray, phase-sensitive imaging technique called grating interferometry was thought to provide information only in real space. However, by utilizing an alternative approach to data analysis we demonstrated that the angular resolved ultra-small angle X-ray scattering distribution can be retrieved from experimental data. Thus, reciprocal space information is accessible by grating interferometry in addition to real space. Naturally, the quality of the retrieved data strongly depends on the performance of the employed analysis procedure, which involves deconvolution of periodic and noisy data in this context. The aim of this article is to compare several deconvolution algorithms to retrieve the ultra-small angle X-ray scattering distribution in grating interferometry. We quantitatively compare the performance of three deconvolution procedures (i.e., Wiener, iterative Wiener and Lucy-Richardson) in case of realistically modeled, noisy and periodic input data. The simulations showed that the algorithm of Lucy-Richardson is the more reliable and more efficient as a function of the characteristics of the signals in the given context. The availability of a reliable data analysis procedure is essential for future developments in grating interferometry.