Embedding laws in diffusions by functions of time

We present a constructive probabilistic proof of the fact that if $B=(B_t)_{t\ge0}$ is standard Brownian motion started at $0$, and $\mu$ is a given probability measure on $\mathbb{R}$ such that $\mu(\{0\})=0$, then there exists a unique left-continuous increasing function $b:(0,\infty)\rightarrow\mathbb{R}\cup\{+\infty\}$ and a unique left-continuous decreasing function $c:(0,\infty)\rightarrow\mathbb{R}\cup\{-\infty\}$ such that $B$ stopped at $\tau_{b,c}=\inf\{t>0\vert B_t\ge b(t)$ or $B_t\le c(t)\}$ has the law $\mu$. The method of proof relies upon weak convergence arguments arising from Helly's selection theorem and makes use of the L\'{e}vy metric which appears to be novel in the context of embedding theorems. We show that $\tau_{b,c}$ is minimal in the sense of Monroe so that the stopped process $B^{\tau_{b,c}}=(B_{t\wedge\tau_{b,c}})_{t\ge0}$ satisfies natural uniform integrability conditions expressed in terms of $\mu$. We also show that $\tau_{b,c}$ has the smallest truncated expectation among all stopping times that embed $\mu$ into $B$. The main results extend from standard Brownian motion to all recurrent diffusion processes on the real line.Comment: Published at http://dx.doi.org/10.1214/14-AOP941 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

The blocks of the Brauer algebra in characteristic zero

We determine the blocks of the Brauer algebra in characteristic zero. We also give information on the submodule structure of standard modules for this algebra

An Optimal Skorokhod Embedding for Diffusions

Given a Brownian motion $B_t$ and a general target law $\mu$ (not necessarily centered or even integrable) we show how to construct an embedding of $\mu$ in $B$. This embedding is an extension of an embedding due to Perkins, and is optimal in the sense that it simultaneously minimises the distribution of the maximum and maximises the distribution of the minimum among all embeddings of $\mu$. The embedding is then applied to regular diffusions, and used to characterise the target laws for which a $H^p$-embedding may be found.Comment: 22 pages, 4 figure

Archaeological Studies for the San Antonio Channel Improvement Project, including Investigations at Guenther\u27s Upper Mill (41BX342)

Under Contract No. DACW63-81-C-0022 to the Department of the Army, Corps of Engineers, Fort Worth District, the Center for Archaeological Research, The University of Texas at San Antonio, in the spring of 1981, conducted historic research and survey in the areas to be affected by the San Antonio Channel Improvement Project. In the summer of 1981, extensive archaeological testing and excavation were done to determine the extent of the structural remains on the sites of Guenther\u27s Upper Mill and the Stribling House. In the spring and summer of 1982, the Center documented the removal and replacement of the mill\u27s west wall. As a result of the investigations, it can now be affirmed that most of the foundation of the east section of the mill is still present beneath the ground. The main foundation walls are made of cut limestone and measure two feet in thickness, except for the west wall which is three feet thick. Of the other buildings at various times related to the mill, only portions of a late (ca. 1910) stone and cement foundation for the Reigler Creamery still remain in the ground. The survey revealed no other cultural resources to be affected by the project

Differential Scattering Cross-Sections for the Different Product Vibrational States in the Ion-Molecule Reaction Ar+ + N2

The charge transfer reaction Ar+ + N2 --> Ar + N2+ has been investigated in a crossed beam experiment in combination with three-dimensional velocity map imaging. Angular differential state-to-state cross sections were determined as a function of the collision energy. We found that scattering into the first excited vibrational level dominates as expected, but only for scattering in the forward direction. Higher vibrational excitations up to v'=6 have been observed for larger scattering angles. For decreasing collision energy, scattering into higher scattering angles becomes increasingly important for all kinematically allowed quantum states. Our detailed measurements indicate that a quantitative agreement between experiment and theory for this basic ion-molecule reaction now comes within reach.Comment: accepted to Phys. Rev. Let

Ultrasound-induced emulsification of subcritical carbon dioxide/water with and without surfactant as a strategy for enhanced mass transport

Pulsed ultrasound was used to disperse a biphasic mixture of CO2/H2O in a 1 dm3 high-pressure reactor at 30 °C/80 bar. A view cell positioned in-line with the sonic vessel allowed observation of a turbid emulsion which lasted approximately 30 min after ceasing sonication. Within the ultrasound reactor, simultaneous CO2-continuous and H2O-continuous environments were identified. The hydrolysis of benzoyl chloride was employed to show that at similar power intensities, comparable initial rates (1.6 ± 0.3 × 10–3 s–1 at 95 W cm–2) were obtained with those reported for a 87 cm3 reactor (1.8 ± 0.2 × 10–3 s–1 at 105 W cm–2), demonstrating the conservation of the physical effects of ultrasound in high-pressure systems (emulsification induced by the action of acoustic forces near an interface). A comparison of benzoyl chloride hydrolysis rates and benzaldehyde mass transport relative to the non-sonicated, ‘silent’ cases confirmed that the application of ultrasound achieved reaction rates which were over 200 times faster, by reducing the mass transport resistance between CO2 and H2O. The versatility of the system was further demonstrated by ultrasound-induced hydrolysis in the presence of the polysorbate surfactant, Tween, which formed a more uniform CO2/H2O emulsion that significantly increased benzoyl chloride hydrolysis rates. Finally, pulse rate was employed as a means of slowing down the rate of hydrolysis, further illustrating how ultrasound can be used as a valuable tool for controlling reactions in CO2/H2O solvent mixtures

Anomalous aging phenomena caused by drift velocities

We demonstrate via several examples that a uniform drift velocity gives rise to anomalous aging, characterized by a specific form for the two-time correlation functions, in a variety of statistical-mechanical systems far from equilibrium. Our first example concerns the oscillatory phase observed recently in a model of competitive learning. Further examples, where the proposed theory is exact, include the voter model and the Ohta-Jasnow-Kawasaki theory for domain growth in any dimension, and a theory for the smoothing of sandpile surfaces.Comment: 7 pages, 3 figures. To appear in Europhysics Letter

Deep Proteomics of Mouse Skeletal Muscle Enables Quantitation of Protein Isoforms, Metabolic Pathways, and Transcription Factors

Skeletal muscle constitutes 40% of individual body mass and plays vital roles in locomotion and whole-body metabolism. Proteomics of skeletal muscle is challenging because of highly abundant contractile proteins that interfere with detection of regulatory proteins. Using a state-of-the art MS workflow and a strategy to map identifications from the C2C12 cell line model to tissues, we identified a total of 10,218 proteins, including skeletal muscle specific transcription factors like myod1 and myogenin and circadian clock proteins. We obtain absolute abundances for proteins expressed in a muscle cell line and skeletal muscle, which should serve as a valuable resource. Quantitation of protein isoforms of glucose uptake signaling pathways and in glucose and lipid metabolic pathways provides a detailed metabolic map of the cell line compared with tissue. This revealed unexpectedly complex regulation of AMP-activated protein kinase and insulin signaling in muscle tissue at the level of enzyme isoforms