Pontryagin invariants and integral formulas for Milnor's triple linking number

To each three-component link in the 3-sphere, we associate a geometrically natural characteristic map from the 3-torus to the 2-sphere, and show that the pairwise linking numbers and Milnor triple linking number that classify the link up to link homotopy correspond to the Pontryagin invariants that classify its characteristic map up to homotopy. This can be viewed as a natural extension of the familiar fact that the linking number of a two-component link in 3-space is the degree of its associated Gauss map from the 2-torus to the 2-sphere. When the pairwise linking numbers are all zero, we give an integral formula for the triple linking number analogous to the Gauss integral for the pairwise linking numbers. The integrand in this formula is geometrically natural in the sense that it is invariant under orientation-preserving rigid motions of the 3-sphere, while the integral itself can be viewed as the helicity of a related vector field on the 3-torus.Comment: 60 pages, 37 figure

Differential Income Taxation and Household Asset Allocation

This paper empirically investigates the effects of differential income taxation on households' portfolio choice and asset allocation applying a two-stage budgeting model of asset demand to German survey data. The model is structured into the discrete asset choice and the continuous asset choice, and the marginal income tax rate is simulated in a module of income taxation. Households that face relatively higher tax rates are found to have relatively greater demand for tax-privileged assets than households in the lower tax brackets. The higher the marginal tax rate the greater demand is for non-owner-occupied housing, for mortgage repayments, for building society deposits, for stocks, for insurances, and for consumer credits, whereas demand is lower for owner-occupied housing, bank deposits, and bonds

Estimating a Consumer Demand System of Energy, Mobility and Leisure: A Microdata Approach for Germany

This paper investigates empirically the consumer demand of environmentally relevant goods for Germany, as well as their relationship to the demand for leisure. Higher prices for energy goods like gas, electricity or fuel oil due to higher indirect taxation amongst others may have serious welfare and distributional effects for households. Also, there is very little evidence of the labor market implications of environmental taxation, as there is e.g. no quantification of labor supply effects, respectively leisure demand effects for Germany. Using a demand system to estimate the price, cross-price and income effects of the goods mobility, electricity, heating and leisure from microdata, there will also be accounted for the extensive demand for leisure, which is the not negligible labor market participation. Additionally, the extensive and intensive leisure demand is combined to total leisure demand elasticities, which can then be used for welfare and behavior analyses

A hierarchical kinetic theory of birth, death, and fission in age-structured interacting populations

We study mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we develop a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies

Cross-sectional study of drivers of animal-source food consumption in low-income urban areas of Nairobi, Kenya

Background Malnutrition, including undernutrition and micronutrient deficiencies is a chronic problem in most developing countries. Animal-source foods (ASFs) provide essential sources of proteins and micronutrients, yet little is known about ASF consumption patterns or household preferences towards animal-source products among low-income populations. This is particularly critical for malnourished children for whom even small increases in consumption could help improve nutrition and health outcomes. This study analysed both the demand as well as the drivers and barriers for ASF consumption among households in two low-income areas in Nairobi, Kenya. Methods Data on ASF expenditures and quantities purchased in the previous week, and reasons for consuming or not consuming ASFs were collected in a cross-sectional study from 205 randomly selected households in Korogocho and Dagoretti settlements. Self-reported reasons for consuming or not-consuming ASFs were described. Demand for ASFs was estimated using the Almost Ideal Demand System to provide measures of demand elasticity for changes in food prices and expenditures. Results On average households purchased 48 grams of ASFs, including fresh milk, per week per household member. Expenditure on ASFs counted for 38% (520 Kenyan Schillings) of the overall food expenditure of which, on average, 48% was spent on fresh milk. Price was the most commonly self-reported barrier for consumption, while taste was reported as the main driver for consumption. The perceived nutritional value was an important driver for consuming more commonly purchased ASFs (beef, eggs, fish and milk). For less commonly purchased ASFs (pork, sausages, sheep and goat meat, offal) taste, access and tradition were given as main reasons for not consuming. Estimated demand elasticities indicated that increases in total food expenditure would lead to greatest increase in the demand for beef meat. Price reductions would increase the demand relatively more for fish, other meats and dairy. Conclusions For most ASFs better affordability would be a clear driver to increase the consumption. However, to increase the variety and quantity of ASFs eaten, other policies targeting improvements in physical access, food safety and consumer education on nutritional values and cooking methods should be considered

Protection Motivation Theory and Contingent Valuation: Perceived Realism, Threat and WTP Estimates for Biodiversity Protection

We report on a discrete-choice CV study conducted in Germany to value the WTP for biodiversity protection in less developed countries. To systematically investigate survey realism and subjective threat assessment from the loss of biodiversity described in the scenario the study includes questions to uncover the constructs of Protection Motivation Theory, which is introduced to the CV literature. The patterns of responses to such questions are analysed using an Expectation-Maximization algorithm to derive class membership probabilities. These are found to match the predictions of Protection Motivation Theory and systematically improve the logistic analysis of the WTP responses