Mathematical aspects of Feynman integrals

In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals.rnrnThe integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph.rnrnStarting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative step to an abstract combinatorial problem, known as Hironaka's polyhedra game. We present a publicly available implementation of the improved algorithm. Furthermore we explain the relationship of the sector decomposition method with the resolution of singularities of a variety, given by a sequence of blow-ups, in algebraic geometry.rnrnMotivated by the connection between Feynman integrals and topics of algebraic geometry we consider the set of periods as defined by Kontsevich and Zagier. This special set of numbers contains the set of multiple zeta values and certain values of polylogarithms, which in turn are known to be present in results for Laurent coefficients of certain dimensionally regularized Feynman integrals. By use of the extended sector decomposition algorithm we prove a theorem which implies, that the Laurent coefficients of an arbitrary Feynman integral are periods if the masses and kinematical invariants take values in the Euclidean momentum region. The statement is formulated for an even more general class of integrals, allowing for an arbitrary number of polynomials in the integrand.

Productivity growth in Australian manufacturing sector: some new evidence

This article examines the productivity performance of Australia's manufacturing sector by decomposing its output growth into input growth, technological progress and gains in technical efficiency. This three-way decomposition is done with an improved version of the stochastic frontier model using eight, two-digit industry level data from 1968/9 to 1994/5. Empirical evidence shows that input growth fueled output growth from 1968/9 to 1973/4, but since then, total factor productivity (TFP) growth has been the main contributor of output growth. While the trend of TFP growth was found to be promising for most industries with positive and increasing technological progress, the negative gains from technical efficiency over time is however cause for concern.

An analysis of strategic paths through the decomposition of total factor productivity: the case of Spanish savings banks

The Spanish savings banks attracted quite a considerable amount of interest within the scientific arena, especially subsequent to the disappearance of the regulatory constraints during the second decade of the 1980s. Nonetheless, a lack of research identified with respect to mainstream paths given by strategic groups, and the analysis of the total factor productivity. Therefore, on the basis of the resource-based view of the firm and cluster analysis, we make use of changes in structure and performance ratios in order to identify the strategic groups extant in the sector. We attain a threeways division, which we link with different input-output specifications defining strategic paths. Consequently, on the basis of these three dissimilar approaches we compute and decompose a Hicks-Moorsteen total factor productivity index. Obtained results put forward an interesting interpretation under a multi-strategic approach, together with the setbacks of employing cluster analysis within a complex strategic environment. Moreover, we also propose an ex-post method of analysing the outcomes of the decomposed total factor productivity index that could be merged with non-traditional techniques of forming strategic groups, such as cognitive approaches.

Structural decomposition analysis and input-output subsystems: An application to Spanish CO2 emissions

Analysis of gas emissions by the input-output subsystem approach provides detailed insight into pollution generation in an economy. Structural decomposition analysis, on the other hand, identifies the factors behind the changes in key variables over time. Extending the input-output subsystem model to account for the changes in these variables reveals the channels by which environmental burdens are caused and transmitted throughout the production system. In this paper we propose a decomposition of the changes in the components of CO2 emissions captured by an input-output subsystems representation. The empirical application is for the Spanish service sector, and the economic and environmental data are for years 1990 and 2000. Our results show that services increased their CO2 emissions mainly because of a rise in emissions generated by non-services to cover the final demand for services. In all service activities, the decomposed effects show an increase in CO2 emissions due to a decrease in emission coefficients (i.e., emissions per unit of output) compensated by an increase in emissions caused both by the input-output coefficients and the rise in demand for services. Finally, large asymmetries exist not only in the quantitative changes in the CO2 emissions of the various services but also in the decomposed effects of these changes. Keywords: structural decomposition analysis, input-output subsystems, CO2 emissions, service sector.

Disentangling water usage in the European Union: A decomposition analysis

The Water Framework Directive (WFD) defines common objectives for water resources throughout the European Union (EU). Given this general approach to water preservation and water policy, the objective of this paper is to analyse whether common patterns of water consumption exist within Europe. In particular, our study uses two methods to reveal the reasons behind sectoral water use in all EU countries. The first method is based on an accounting indicator that calculates the water intensity of an economy as the sum of sectoral water intensities. The second method is a subsystem input‐output model that divides total water use into different income channels within the production system. The application uses data for the years 2005 and 2009 on water consumption in the production system of the 27 countries of the EU. From our analysis it emerges that EU countries are characterized by very different patterns of water consumption. In particular water consumption by the agriculture sector is extremely high in Central/Eastern Europe, relative to the rest of Europe. In most countries, the water used by the fuel, power and water sector is consumed to satisfy domestic final demand. However, our analysis shows that for some countries exports from this sector are an important driver of water consumption. Focusing on the agricultural sector, the decomposition analysis suggests that water usage in Mediterranean countries is mainly driven by final demand for, and exports of, agricultural products. In Central/Eastern Europe domestic final demand is the main driver of water consumption, but in this region the proportion of water use driven by demand for exports is increasing over time. Given these heterogeneous water consumption patterns, our analysis suggests that Mediterranean and Central/Eastern European countries should adopt specific water policies in order to achieve efficient levels of water consumption in the European Union. JEL codes: N5; C67 Keywords: Water use, Subsystem input–output model; Water intensity, European Union.

Environmental Structural Decomposition Analysis of Italian Emissions, 1995-2005

[spa] El estudio analiza la evolución de los gases de efecto invernadero (GEI) y las emisiones de acidificación para Italia durante el periodo 1995-2005. Los datos muestran que mientras las emisiones que contribuyen a la acidificación han disminuido constantemente, las emisiones de GEI han aumentado debido al aumento de dióxido de carbono. El objetivo de este estudio es poner de relieve cómo diferentes factores económicos, en particular el crecimiento económico, el desarrollo de una tecnología menos contaminante y la estructura del consumo, han impulsado la evolución de las emisiones. La metodología propuesta es un análisis de descomposición estructural (ADE), método que permite descomponer los cambios de la variable de interés entre las diferentes fuerzas y revelar la importancia de cada factor. Por otra parte, este estudio considera la importancia del comercio internacional e intenta incluir el “problema de la responsabilidad”. Es decir, a través de las relaciones comerciales internacionales, un país podría estar exportando procesos de producción contaminantes sin una reducción real de la contaminación implícita en su patrón de consumo. Con este fin, siguiendo primero un enfoque basado en la “responsabilidad del productor”, el ADE se aplica a las emisiones causadas por la producción nacional. Sucesivamente, el análisis se mueve hacia un enfoque basado en la “responsabilidad del consumidor" y la descomposición se aplica a las emisiones relacionadas con la producción nacional o la producción extranjera que satisface la demanda interna. De esta manera, el ejercicio permite una primera comprobación de la importancia del comercio internacional y pone de relieve algunos resultados a nivel global y a nivel sectorial.

Environmental Structural Decomposition Analysis of Italian Emissions, 1995-2005

[spa] El estudio analiza la evolución de los gases de efecto invernadero (GEI) y las emisiones de acidificación para Italia durante el periodo 1995-2005. Los datos muestran que mientras las emisiones que contribuyen a la acidificación han disminuido constantemente, las emisiones de GEI han aumentado debido al aumento de dióxido de carbono. El objetivo de este estudio es poner de relieve cómo diferentes factores económicos, en particular el crecimiento económico, el desarrollo de una tecnología menos contaminante y la estructura del consumo, han impulsado la evolución de las emisiones. La metodología propuesta es un análisis de descomposición estructural (ADE), método que permite descomponer los cambios de la variable de interés entre las diferentes fuerzas y revelar la importancia de cada factor. Por otra parte, este estudio considera la importancia del comercio internacional e intenta incluir el “problema de la responsabilidad”. Es decir, a través de las relaciones comerciales internacionales, un país podría estar exportando procesos de producción contaminantes sin una reducción real de la contaminación implícita en su patrón de consumo. Con este fin, siguiendo primero un enfoque basado en la “responsabilidad del productor”, el ADE se aplica a las emisiones causadas por la producción nacional. Sucesivamente, el análisis se mueve hacia un enfoque basado en la “responsabilidad del consumidor" y la descomposición se aplica a las emisiones relacionadas con la producción nacional o la producción extranjera que satisface la demanda interna. De esta manera, el ejercicio permite una primera comprobación de la importancia del comercio internacional y pone de relieve algunos resultados a nivel global y a nivel sectorial.

Public-private sector wage differentials by type of contract: evidence from Spain

The article examines public-private sector wage differentials in Spain using microdata from the Structure of Earnings Survey (Encuesta de Estructura Salarial). When applying various decomposition techniques, we find that it is important to distinguish by gender and type of contract. Our results also highlight the presence of a positive wage premium for public sector workers that can be partially explained by their better endowment of characteristics, in particular by the characteristics of the establishment where they work. The wage premium is greater for female and fixed-term employees and falls across the wage distribution, being negative for more highly skilled workers.

Public-private sector wage differentials by type of contract: evidence from Spain

The article examines public-private sector wage differentials in Spain using microdata from the Structure of Earnings Survey (Encuesta de Estructura Salarial). When applying various decomposition techniques, we find that it is important to distinguish by gender and type of contract. Our results also highlight the presence of a positive wage premium for public sector workers that can be partially explained by their better endowment of characteristics, in particular by the characteristics of the establishment where they work. The wage premium is greater for female and fixed-term employees and falls across the wage distribution, being negative for more highly skilled workers.

EVALUATION OF TECHNOLOGICAL INTENSITY OF EXPORTS IN THE FORESTRY SECTOR

ABSTRACT One of the fastest growing sectors in the domestic industry is the forestry, which has contributed significantly to economic development, job creation, income taxes, putting Brazil in a prominent position in the world market. This paper analyzes the evolution of the technological intensity of 12 main products exported by the sector, from 2000 to 2011. For that, utilizes an indicator called PRODY, which allows classifying different products according to their technological intensity or income content and considers the GDP per capita of exporting countries of each product, weighted by its revealed comparative advantage. It can be seen by the results, a continuous growth in all products' technology indicators and their decomposition into income effects, comparative advantage and joint effects, allowed to verify the main causes of this growth. Products with lower PRODY values are those that presented a higher evolution during the period studied. Products of higher processing, and those from pulp and paper industry, had greater technological advances, thanks to a joint effect, while the ones of lower processing, had a technological improvement due to the increase in GDP per capita in exporting countries. Sawn wood was the standout product, being the only one who proved to be dependent of comparative advantage effect, confirming that this industry has been reinventing itself and incorporating, in fact, more technology. This study revealed the importance of technological intensification to generate comparative advantage and be able to stand against international competition.

Administración en la cadena de suministro y su relación con el desempeño de las PYME del sector agroindustrial

En la actualidad las organizaciones están en búsqueda de una mejora continua, esto lleva a que las empresas hagan una revisión de estrategias que permitan alcanzar una posición de líderes en los diferentes sectores en los que se desempeñan. Una de las estrategias para lograr un alto posicionamiento en las nuevas empresas es la adecuada gestión que hacen de la cadena de suministro. El sector agroindustrial tiene un amplia cadena de suministro desde la obtención de materias primas hasta la llegada al cliente final, por su gran magnitud requiere de una adecuada administración de procesos que permitan ser eficaces y eficientes para alcanzar logros propuestos, aprovechar los recursos limitados con los que cuentan para su cumplimiento y, por último, la capacidad propia para la transformación de sus recursos. Para lograr que las empresas obtengan ventajas competitivas, es necesario que los distintos eslabones de la cadena de suministros cuenten con una capacidad de interacción que les permita, tanto agilizar como asegurar el éxito durante la incorporación de los nuevos productos en el mercado. Por medio de esta investigación se busca esclarecer y analizar la importancia de la administración en la cadena de suministro y la relación con el desempeño, basándose en las Pymes del sector agroindustrial. La intención es evaluar la información de diversos autores quienes han hablado de la relación que existe entre la cadena de suministro y su desempeño, teniendo en cuenta variables como el sector agroindustrial y las Pymes.

Lipids and polycyclic aromatic hydrocarbons in bottom sediments from the Atlantic sector of the Southern Ocean

Distribution and composition of lipids and contents of alkanes and polycyclic aromatic hydrocarbons(PAHs) in bottom sediments of the Scotia and Weddell seas are discussed. Comparatively low concentrations of organic carbon (average 0.35%) and lipids (average 0.024%) result from rapid decomposition of organic matter in upper layers of the water column. Composition of alkanes indicates that lipids are of autochthonous origin, and stable concentrations of PAHs (average 25.8 ppb, sigma 15.3 ppb) indicate that they represent the background level for bottom sediments. Higher concentrations of PAHs in sediments near the King George Island (252.1 ppb) and different distributions of individual polyarenes are produced there by the heating systems of the Polish Antarctic Station.

Application of factor decomposition techniques to vertical specialisation measurements

The increasing importance of vertical specialisation (VS) trade has been a notable feature of rapid economic globalisation and regional integration. In an attempt to understand countries’ depth of participation in global production chains, many Input-Output based VS indicators have been developed. However, most of them focus on showing the overall magnitude of a country’s VS trade, rather than explaining the roles that specific sectors or products play in VS trade and what factors make the VS change over time. Changes in vertical specialisation indicators are, in fact, determined by mixed and complex factors such as import substitution ratios, types of exported goods and domestic production networks. In this paper, decomposition techniques are applied to VS measurement based on the OECD Input-Output database. The decomposition results not only help us understand the structure of VS at detailed sector and product levels, but also show us the contributions of trade dependency, industrial structures of foreign trade and domestic production system to a country’s vertical specialisation trade.

Allocation efficiency in China : an extension of the dynamic Olley-Pakes productivity decomposition

This paper develops a quantitative measure of allocation efficiency, which is an extension of the dynamic Olley-Pakes productivity decomposition proposed by Melitz and Polanec (2015). The extended measure enables the simultaneous capture of the degree of misallocation within a group and between groups and parallel to capturing the contribution of entering and exiting firms to aggregate productivity growth. This measure empirically assesses the degree of misallocation in China using manufacturing firm-level data from 2004 to 2007. Misallocation among industrial sectors has been found to increase over time, and allocation efficiency within an industry has been found to worsen in industries that use more capital and have firms with relatively higher state-owned market shares. Allocation efficiency among three ownership sectors (state-owned, domestic private, and foreign sectors) tends to improve in industries wherein the market share moves from a less-productive state-owned sector to a more productive private sector.

Is a little sunshine all we need? On the impact of sunshine regulation on profits, productivity and prices in the Dutch drinking water sector

This paper analyzes the performance of Dutch drinking water utilities before and after the introduction of sunshine regulation, which involves publication of the performance of utilities but no formal price regulation. By decomposing profit change into its economic drivers, our results suggest that, in the Dutch political and institutional context, sunshine regulation was effective in improving the productivity of publicly organised services. Nevertheless, while sunshine regulation did bring about a moderate reduction in water prices, sustained and substantial economic profits suggest that it may not have the potential to fully align output prices with economic costs in the long run. In methodological terms, the DEA based profit decomposition is extended to robust and conditional non-parametric efficiency measures, so as to account better for both uncertainty and differences in operating environment between utilities.