Optimal Transport and Skorokhod Embedding

The Skorokhod embedding problem is to represent a given probability as the distribution of Brownian motion at a chosen stopping time. Over the last 50 years this has become one of the important classical problems in probability theory and a number of authors have constructed solutions with particular optimality properties. These constructions employ a variety of techniques ranging from excursion theory to potential and PDE theory and have been used in many different branches of pure and applied probability. We develop a new approach to Skorokhod embedding based on ideas and concepts from optimal mass transport. In analogy to the celebrated article of Gangbo and McCann on the geometry of optimal transport, we establish a geometric characterization of Skorokhod embeddings with desired optimality properties. This leads to a systematic method to construct optimal embeddings. It allows us, for the first time, to derive all known optimal Skorokhod embeddings as special cases of one unified construction and leads to a variety of new embeddings. While previous constructions typically used particular properties of Brownian motion, our approach applies to all sufficiently regular Markov processes.Comment: Substantial revision to improve the readability of the pape

The Purpose of Remittances – Evidence from Germany

This paper examines the purpose of remittances using individual data of migrants in Germany. Particular attention is paid to migrants’ savings and transfers to family members in the home country. Our findings indicate that migrants who intend to stay in Germany only temporarily have a higher propensity to save and save larger amounts in their home country than permanent migrants. A similar picture emerges when considering migrants’ payments to family members abroad. The results of a decomposition analysis indicate that temporary and permanent migrants seem to have different preferences towards sending transfers abroad, while economic characteristics and the composition of households in home and host countries are less relevant.International migration, savings, remittances

Unraveling radial dependency effects in fiber thermal drawing

Fiber-based devices with advanced functionalities are emerging as promising solutions for various applications in flexible electronics and bioengineering. Multimaterial thermal drawing, in particular, has attracted strong interest for its ability to generate fibers with complex architectures. Thus far, however, the understanding of its fluid dynamics has only been applied to single material preforms for which higher order effects, such as the radial dependency of the axial velocity, could be neglected. With complex multimaterial preforms, such effects must be taken into account, as they can affect the architecture and the functional properties of the resulting fiber device. Here, we propose a versatile model of the thermal drawing of fibers, which takes into account a radially varying axial velocity. Unlike the commonly used cross section averaged approach, our model is capable of predicting radial variations of functional properties caused by the deformation during drawing. This is demonstrated for two effects observed, namely, by unraveling the deformation of initially straight, transversal lines in the preform and the dependence on the draw ratio and radial position of the in-fiber electrical conductivity of polymer nanocomposites, an important class of materials for emerging fiber devices. This work sets a thus far missing theoretical and practical understanding of multimaterial fiber processing to better engineer advanced fibers and textiles for sensing, health care, robotics, or bioengineering applications

A universal scaling law for the evolution of granular gases

Dry, freely evolving granular materials in a dilute gaseous state coalesce into dense clusters only due to dissipative interactions. This clustering transition is important for a number of problems ranging from geophysics to cosmology. Here we show that the evolution of a dilute, freely cooling granular gas is determined in a universal way by the ratio of inertial flow and thermal velocities, that is, the Mach number. Theoretical calculations and direct numerical simulations of the granular Navier--Stokes equations show that irrespective of the coefficient of restitution, density or initial velocity distribution, the density fluctuations follow a universal quadratic dependence on the system's Mach number. We find that the clustering exhibits a scale-free dynamics but the clustered state becomes observable when the Mach number is approximately of $\mathcal{O}(1)$. Our results provide a method to determine the age of a granular gas and predict the macroscopic appearance of clusters

The Reverse Cuthill-McKee Algorithm in Distributed-Memory

Ordering vertices of a graph is key to minimize fill-in and data structure size in sparse direct solvers, maximize locality in iterative solvers, and improve performance in graph algorithms. Except for naturally parallelizable ordering methods such as nested dissection, many important ordering methods have not been efficiently mapped to distributed-memory architectures. In this paper, we present the first-ever distributed-memory implementation of the reverse Cuthill-McKee (RCM) algorithm for reducing the profile of a sparse matrix. Our parallelization uses a two-dimensional sparse matrix decomposition. We achieve high performance by decomposing the problem into a small number of primitives and utilizing optimized implementations of these primitives. Our implementation shows strong scaling up to 1024 cores for smaller matrices and up to 4096 cores for larger matrices

Identifying Earth matter effects on supernova neutrinos at a single detector

The neutrino oscillations in Earth matter introduce modulations in the supernova neutrino spectra. These modulations can be exploited to identify the presence of Earth effects on the spectra, which would enable us to put a limit on the value of the neutrino mixing angle $\theta_{13}$ and to identify whether the mass hierarchy is normal or inverted. We demonstrate how the Earth effects can be identified at a single detector without prior assumptions about the flavor-dependent source spectra, using the Fourier transform of the ``inverse-energy'' spectrum of the signal. We explore the factors affecting the efficiency of this method, and find that the energy resolution of the detector is the most crucial one. In particular, whereas water Cherenkov detectors may need a few ten thousand events to identify the Earth effects, a few thousand may be enough at scintillation detectors, which generically have a much better energy resolution. A successful identification of the Earth effects through this method can also provide $\Delta m^2_\odot$ to a good accuracy. The relative strength of the detected Earth effects as a function of time provides a test for supernova models.Comment: 18 pages, 10 figures, JCAP format. Final version to be published in JCAP. References and some minor clarifications added to the original versio

Neighborhood Diversity and the Appreciation of Native- and Immigrant-Owned Homes

This paper examines the effect of neighborhood diversity on the nativity gap in homevalue appreciation in Australia. Specifically, immigrant homeowners experienced a 41.7 percent increase in median home values between 2001 and 2006, while the median value of housing owned by the native-born increased by 59.4 percent over the same period. We use a semi-parametric decomposition approach to assess the relative importance of the various determinants of home values in producing this gap. We find that the differential returns to housing wealth are not related to changes in the nature of the houses or the neighborhoods in which immigrants and native-born homeowners live. Rather, the gap stems from the fact that over time there were differential changes across groups in the hedonic prices (i.e., returns) associated with the underlying determinants of home values.International migration, home-ownership, decomposition analysis

Locus of control and savings

Abstract: This paper analyzes the relationship between individuals’ locus of control and their savings behavior, i.e. wealth accumulation, savings rates, and portfolio choices. Locus of control is a psychological concept that captures individuals’ beliefs about the controllability of life events and is a key component of self-control. We find that households with an internal reference person save more both in terms of levels and as a percentage of their permanent incomes. Although the locus-of-control gap in savings rates is largest among rich households, the gap in wealth accumulation is particularly large for poor households. Finally, households with an internal reference person and average net worth hold significantly less financial wealth, but significantly more pension wealth, than otherwise similar households with an external reference person

Neighborhood Diversity and the Appreciation of Native- and Immigrant-Owned Homes

This paper examines the effect of neighborhood diversity on the nativity gap in homevalue appreciation in Australia. Specifically, immigrant homeowners experienced a 41.7 percent increase in median home values between 2001 and 2006, while the median value of housing owned by the native-born increased by 59.4 percent over the same period. We use a semi-parametric decomposition approach to assess the relative importance of the various determinants of home values in producing this gap. We find that the differential returns to housing wealth are not related to changes in the nature of the houses or the neighborhoods in which immigrants and native-born homeowners live. Rather, the gap stems from the fact that over time there were differential changes across groups in the hedonic prices (i.e., returns) associated with the underlying determinants of home values.international migration, home-ownership, decomposition analysis