Deep Convolutional Neural Networks Based on Semi-Discrete Frames

Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called scattering networks based on identical semi-discrete wavelet frames in each network layer, and proved translation-invariance as well as deformation stability of the resulting feature extractor. The purpose of this paper is to develop Mallat's theory further by allowing for different and, most importantly, general semi-discrete frames (such as, e.g., Gabor frames, wavelets, curvelets, shearlets, ridgelets) in distinct network layers. This allows to extract wider classes of features than point singularities resolved by the wavelet transform. Our generalized feature extractor is proven to be translation-invariant, and we develop deformation stability results for a larger class of deformations than those considered by Mallat. For Mallat's wavelet-based feature extractor, we get rid of a number of technical conditions. The mathematical engine behind our results is continuous frame theory, which allows us to completely detach the invariance and deformation stability proofs from the particular algebraic structure of the underlying frames.Comment: Proc. of IEEE International Symposium on Information Theory (ISIT), Hong Kong, China, June 2015, to appea

An atom-photon pair laser

We study the quantum dynamics of an ultracold atomic gas in a deep optical lattice within an optical high-$Q$ resonator. The atoms are coherently illuminated with the cavity resonance tuned to a blue vibrational sideband, so that photon scattering to the resonator mode is accompanied by vibrational cooling of the atoms. This system exhibits a threshold above which pairwise stimulated generation of a cavity photon and an atom in the lowest vibrational band dominates spontaneous scattering and we find a combination of optical lasing with a buildup of a macroscopic population in the lowest lattice band. Including output coupling of ground-state atoms and replenishing of hot atoms into the cavity volume leads to a coherent, quantum correlated atom-photon pair source very analogous to twin light beam generation in a nondegenerate optical parametric oscillator.Comment: 10 pages, 4 figure

O Brother, Where Art Thou?: The Effects of Having a Sibling on Geographic Mobility and Labor Market Outcomes

In most industrialized countries, more people than ever are having to cope with the burden of caring for elderly parents. This paper formulates a model to explain how parental care responsibilities and family structure interact in affecting children's mobility characteristics. A key insight we obtain is that the mobility of young adults crucially depends on the presence of a sibling. Our explanation is mainly, but not ex-clusively, based on a sibling power effect. Siblings compete in location and employment decisions so as to direct parental care decisions at later stages towards their preferred outcome. Only children are not exposed to this kind of competition. This causes an equilibrium in which siblings not only exhibit higher mobility than only children, but also have better labor market outcomes. Using data from the German Socio-Economic Panel Study (SOEP) and from the American National Survey of Families and House- holds (NSFH), we find strong evidence that confirms these patterns. The implications of our results are then discussed in the context of current population trends in Europe and the United States.Geographic Mobility, Intergenerational Relationships, Care of the Elderly, Family Bargaining.

Does Democracy Foster Trust?

The level of trust inherent in a society is important for a wide range of microeconomic and macroeconomic outcomes. This paper investigates how individuals' attitudes toward social and institutional trust are shaped by the political regime in which they live. The German reunification is a unique natural experiment that allows us to conduct such a study. Using data from the German General Social Survey (ALLBUS) and from the German Socio-Economic Panel Study (SOEP), we obtain two sets of results. On one side, we find that, shortly after reunification, East Germans displayed a significantly less trusting attitude than West Germans. This suggests a negative effect of communism in East Germany versus democracy in West Germany on social and institutional trust. However, the experience of democracy by East Germans since reunification did not serve to increase levels of social trust significantly. In fact, we cannot reject the hypothesis that East Germans, after more than a decade of democracy, have the same levels of social distrust as shortly after the collapse of communism. In trying to understand the underlying causes, we show that the persistence of social distrust in the East can be explained by negative economic outcomes that many East Germans experienced in the post-reunification period. Our main conclusion is that democracy can foster trust in post-communist societies only when citizens' economic outcomes are right.Social Trust, Institutional Trust, Political Regimes.

Family Location and Caregiving Patterns from an International Perspective

This paper conducts a cross-national econometric analysis of intra-family location and caregiving patterns. First, we assess, from an international perspective, the relationship between family structure and the geographic proximity between adult children and their parents. We then examine whether differences in family structure affect the amount of informal care adult children provide to their elderly parents. Lastly, we look for cross-country differences in family location and caregiving patterns, and interpret observed differences in terms of heterogenous institutional solutions to the long-term care problem. Our results not only provide a new empirical perspective on the geography of the family, but also give interesting insights into how family-related and institutional factors shape patterns of time transfers from adult children to elderly parents.geography of the family, child-to-parent time transfers

Does Democracy Foster Trust? Evidence from the German Reunification

The level of trust inherent in a society is important for a wide range of microeconomic and macroeconomic outcomes. This paper investigates how individuals' attitudes toward social and institutional trust are shaped by the political regime in which they live. The German reunification is a unique natural experiment that allows us to conduct such a study. Using data from the German General Social Survey (ALLBUS) and from the German Socio-Economic Panel Study (SOEP), we obtain two sets of results. On one side, we find that, shortly after reunification, East Germans displayed a significantly less trusting attitude than West Germans. This suggests a negative effect of communism in East Germany versus democracy in West Germany on social and institutional trust. However, the experience of democracy by East Germans since reunification did not serve to increase levels of social trust significantly. In fact, we cannot reject the hypothesis that East Germans, after more than a decade of democracy, have the same levels of social distrust as shortly after the collapse of communism. In trying to understand the underlying causes, we show that the persistence of social distrust in the East can be explained by negative economic outcomes that many East Germans experienced in the post-reunification period. Our main conclusion is that democracy can foster trust in post-communist societies only when citizens' economic outcomes are right.

Family Location and Caregiving Patterns from an International Perspective

This paper conducts a cross-national econometric analysis of intra-family location and caregiving patterns. First, we assess, from an international perspective, the relationship between family structure and the geographic proximity between adult children and their parents. We then examine whether differences in family structure affect the amount of informal care adult children provide to their elderly parents. Lastly, we look for cross-country differences in family location and caregiving patterns, and interpret observed differences in terms of heterogenous institutional solutions to the long-term care problem. Our results not only provide a new empirical perspective on the geography of the family, but also give interesting insights into how family-related and institutional factors shape patterns of time transfers from adult children to elderly parents.geography of the family, child-to-parent time transfers

O Brother, Where Art Thou? The Effects of Having a Sibling on Geographic Mobility and Labor Market Outcomes

In most industrialized countries, more people than ever are having to cope with the burden of caring for elderly parents. This paper formulates a model to explain how parental care responsibilities and family structure interact in affecting children's mobility characteristics. A key insight we obtain is that the mobility of young adults crucially depends on the presence of a sibling. Our explanation is mainly, but not exclusively, based on a sibling power effect. Siblings compete in location and employment decisions so as to direct parental care decisions at later stages towards their preferred outcome. Only children are not exposed to this kind of competition. This causes an equilibrium in which siblings not only exhibit higher mobility than only children, but also have better labor market outcomes. Using data from the German Socio-Economic Panel Study (SOEP) and from the American National Survey of Families and Households (NSFH), we find strong evidence that confirms these patterns. The implications of our results are then discussed in the context of current population trends in Europe and the United States.