8,562 research outputs found
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 . 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 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 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
Overcoming system-size limitations in spin glasses
In order to overcome the limitations of small system sizes in spin-glass
simulations, we investigate the one-dimensional Ising spin chain with power-law
interactions. The model has the advantage over traditional higher-dimensional
Hamiltonians in that a large range of system sizes can be studied. In addition,
the universality class of the model can be changed by tuning the power law
exponent, thus allowing us to scan from the mean-field to long-range and
short-range universality classes. We illustrate the advantages of this model by
studying the nature of the spin glass state where our results hint towards a
replica symmetry breaking scenario. We also compute ground-state energy
distributions and show that mean-field and non-mean-field models are
intrinsically different.Comment: 5 pages, 2x2 figures, proceedings of the 2004 SPDSA Conference in
Hayama, Japan, July 12 - 15, 200
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