Translating the Cantor set by a random

We determine the constructive dimension of points in random translates of the Cantor set. The Cantor set "cancels randomness" in the sense that some of its members, when added to Martin-Lof random reals, identify a point with lower constructive dimension than the random itself. In particular, we find the Hausdorff dimension of the set of points in a Cantor set translate with a given constructive dimension

The motif problem

Fix a choice and ordering of four pairwise non-adjacent vertices of a parallelepiped, and call a motif a sequence of four points in R^3 that coincide with these vertices for some, possibly degenerate, parallelepiped whose edges are parallel to the axes. We show that a set of r points can contain at most r^2 motifs. Generalizing the notion of motif to a sequence of L points in R^p, we show that the maximum number of motifs that can occur in a point set of a given size is related to a linear programming problem arising from hypergraph theory, and discuss some related questions.Comment: 17 pages, 1 figur

AnL 1 counting problem in ergodic theory

We give a negative solution to the following counting problem for measure preserving transformations. For ∈L 1+(μ), is it true that sup n (N n (f)(x)/n) 1/ n}? One of the consequences is the nonvalidity of J. Bourgain’s Return Time Theorem for pairs of (L 1,L 1) functions

Polya Trees and Random Distributions

1 online resource (PDF, 32 pages

Pacific Atmospheric Sulfur Experiment (PASE): dynamics and chemistry of the south Pacific tropical trade wind regime

The Pacific Atmospheric Sulfur Experiment (PASE) was a comprehensive airborne study of the chemistry and dynamics of the tropical trade wind regime (TWR) east of the island of Kiritibati (Christmas Island, 157º, 20′ W, 2º 52′ N). Christmas Island is located due south of Hawaii. Geographically it is in the northern hemisphere yet it is 6–12º south of the intertropical convergence zone (ITCZ) which places it in the southern hemisphere meteorologically. Christmas Island trade winds in August and September are from east south east at 3–15 ms−1. Clouds, if present, are fair weather cumulus located in the middle layer of the TWR which is frequently labeled the buffer layer (BuL). PASE provided clear support for the idea that small particles (80 nm) were subsiding into the tropical trade wind regime (TWR) where sulfur chemistry transformed them to larger particles. Sulfur chemistry promoted the growth of some of these particles until they were large enough to activate to cloud drops. This process, promoted by sulfur chemistry, can produce a cooling effect due to the increase in cloud droplet density and changes in cloud droplet size. These increases in particle size observed in PASE promote additional cooling due to direct scattering from the aerosol. These potential impacts on the radiation balance in the TWR are enhanced by the high solar irradiance and ocean albedo of the TWR. Finally because of the large area involved there is a large factional impact on earth’s radiation budget. The TWR region near Christmas Island appears to be similar to the TWR that persists in August and September, from southwest of the Galapagos to at least Christmas Island. Transport in the TWR between the Galapagos and Christmas involves very little precipitation which could have removed the aerosol thus explaining at least in part the high concentrations of CCN (≈300 at 0.5% supersaturation) observed in PASE. As expected the chemistry of sulfur in the trade winds was found to be initiated by the emission of DMS into the convective boundary layer (BL, the lowest of three layers). However, the efficiency with which this DMS is converted to SO2 has been brought into further question by this study. This unusual result has come about as result of our using two totally different approaches for addressing this long standing question. In the first approach, based on accepted kinetic rate constants and detailed steps for the oxidation of DMS reflecting detailed laboratory studies, a DMS to SO2 conversion efficiency of 60–73% was determined. This range of values lies well within the uncertainties of previous studies. However, using a completely different approach, involving a budget analysis, a conversion value of 100% was estimated. The latter value, to be consistent with all other sulfur studies, requires the existence of a completely independent sulfur source which would emit into the atmosphere at a source strength approximately half that measured for DMS under tropical Pacific conditions. At this time, however, there is no credible scientific observation that identifies what this source might be. Thus, the current study has opened for future scientific investigation the major question: is there yet another major tropical marine source of sulfur? Of equal importance, then, is the related question, is our global sulfur budget significantly in error due to the existence of an unknown marine source of sulfur? Pivotal to both questions may be gaining greater insight about the intermediate DMS oxidation species, DMSO, for which rather unusual measurements have been reported in previous marine sulfur studies. The 3 pptv bromine deficit observed in PASE must be lost over the lifetime of the aerosol which is a few days. This observation suggests that the primary BrO production rate is very small. However, considering the uncertainties in these observations and the possible importance of secondary production of bromine radicals through aerosol surface reactions, to completely rule out the importance of bromine chemistry under tropical conditions at this time cannot be justified. This point has been brought into focus from prior work that even at levels of 1 pptv, the effect of BrO oxidation on DMS can still be quite significant. Thus, as in the case of DMS conversion to SO2, future studies will be needed. In the latter case there will need to be a specific focus on halogen chemistry. Such studies clearly must involve specific measurements of radical species such as BrO

Coagulopathy, Bleeding Events, and Outcome According to Rotational Thromboelastometry in Patients With Acute Liver Injury/Failure

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/169284/1/hep31767_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/169284/2/hep31767-sup-0001-Supinfo.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/169284/3/hep31767.pd