Balian-Low Theorems in Several Variables

Recently, Nitzan and Olsen showed that Balian-Low theorems (BLTs) hold for discrete Gabor systems defined on $\mathbb{Z}_d$. Here we extend these results to a multivariable setting. Additionally, we show a variety of applications of the Quantitative BLT, proving in particular nonsymmetric BLTs in both the discrete and continuous setting for functions with more than one argument. Finally, in direct analogy of the continuous setting, we show the Quantitative Finite BLT implies the Finite BLT.Comment: To appear in Approximation Theory 16 conference proceedings volum

Lessons Learned from Two Years of On-Orbit Global Positioning System Experience on International Space Station

The Global Positioning System Subsystem (GPS) for International Space Station (ISS) was activated April 12,2002 following the installation of the SO truss segment that included the GPS antennas on Shuttle mission STS-110. The ISS GPS receiver became the primary source for position, velocity, and attitude information for ISS two days after activation. The GPS receiver also provides a time reference for manual control of ISS time, and will be used for automatic time updates after problems are resolved with the output from the receiver. After two years of on-orbit experience, the GPS continues to be used as the primary navigation source for ISS; however, enough problems have surfaced that the firmware in the GPS attitude code has had to be totally rewritten and new algorithms developed, the firmware that processed the time output from the GPS receiver had to be rewritten, while the GPS navigation code has had minor revisions. The factors contributing to the delivery of a GPS receiver for use on ISS that requires extensive operator intervention to function are discussed. Observations from two years worth of GPS solutions will also be discussed. The technical solutions to the anomalous GPS receiver behavior will be discussed

EFFECTS OF LAND COVER, WATER REDISTRIBUTION, AND TEMPERATURE ON ECOSYSTEM PROCESSES IN THE SOUTH PLATTE BASIN

Over one‐third of the land area in the South Platte Basin of Colorado, Nebraska, and Wyoming, has been converted to croplands. Irrigated cropland now comprises 8% of the basin, while dry croplands make up 31%. We used the RHESSys model to compare the changes in plant productivity and vegetation‐related hydrological processes that occurred as a result of either land cover alteration or directional temperature changes (−2°C, +4°C). Land cover change exerted more control over annual plant productivity and water fluxes for converted grasslands, while the effect of temperature changes on productivity and water fluxes was stronger in the mountain vegetation. Throughout the basin, land cover change increased the annual loss of water to the atmosphere by 114 mm via evaporation and transpiration, an increase of 37%. Both irrigated and nonirrigated grains became active earlier in the year than shortgrass steppe, leading to a seasonal shift in water losses to the atmosphere. Basin‐wide photosynthesis increased by 80% due to grain production. In contrast, a 4°C warming scenario caused annual transpiration to increase by only 3% and annual evaporation to increase by 28%, for a total increase of 71 mm. Warming decreased basin‐wide photosynthesis by 16%. There is a large elevational range from east to west in the South Platte Basin, which encompasses the western edge of the Great Plains and the eastern front of the Rocky Mountains. This elevational gain is accompanied by great changes in topographic complexity, vegetation type, and climate. Shortgrass steppe and crops found at elevations between 850 and 1800 m give way to coniferous forests and tundra between 1800 and 4000 m. Climate is increasingly dominated by winter snow precipitation with increasing elevation, and the timing of snowmelt influences tundra and forest ecosystem productivity, soil moisture, and downstream discharge. Mean annual precipitation of \u3c500 mm on the plains below 1800 m is far less than potential evapotranspiration of 1000–1500 mm and is insufficient for optimum plant productivity. The changes in water flux and photosynthesis from conversion of steppe to cropland are the result of redistribution of snowmelt water from the mountains and groundwater pumping through irrigation projects

Sticky Flavors

The Fr\'echet mean, a generalization to a metric space of the expectation of a random variable in a vector space, can exhibit unexpected behavior for a wide class of random variables. For instance, it can stick to a point (more generally to a closed set) under resampling: sample stickiness. It can stick to a point for topologically nearby distributions: topological stickiness, such as total variation or Wasserstein stickiness. It can stick to a point for slight but arbitrary perturbations: perturbation stickiness. Here, we explore these and various other flavors of stickiness and their relationship in varying scenarios, for instance on CAT($\kappa$) spaces, $\kappa\in \mathbb{R}$. Interestingly, modulation stickiness (faster asymptotic rate than $\sqrt{n}$) and directional stickiness (a generalization of moment stickiness from the literature) allow for the development of new statistical methods building on an asymptotic fluctuation, where, due to stickiness, the mean itself features no asymptotic fluctuation. Also, we rule out sticky flavors on manifolds in scenarios with curvature bounds

Compensatory embryonic response to allele-specific inactivation of the murine X-linked gene Hcfc1.

Early in female mammalian embryonic development, cells randomly inactivate one of the two X chromosomes to achieve overall equal inactivation of parental X-linked alleles. Hcfc1 is a highly conserved X-linked mouse gene that encodes HCF-1 - a transcriptional co-regulator implicated in cell proliferation in tissue culture cells. By generating a Cre-recombinase inducible Hcfc1 knock-out (Hcfc1(lox)) allele in mice, we have probed the role of HCF-1 in actively proliferating embryonic cells and in cell-cycle re-entry of resting differentiated adult cells using a liver regeneration model. HCF-1 function is required for both extraembryonic and embryonic development. In heterozygous Hcfc1(lox/+) female embryos, however, embryonic epiblast-specific Cre-induced Hcfc1 deletion (creating an Hcfc1(epiKO) allele) around E5.5 is well tolerated; it leads to a mixture of HCF-1-positive and -negative epiblast cells owing to random X-chromosome inactivation of the wild-type or Hcfc1(epiKO) mutant allele. At E6.5 and E7.5, both HCF-1-positive and -negative epiblast cells proliferate, but gradually by E8.5, HCF-1-negative cells disappear owing to cell-cycle exit and apoptosis. Although generating a temporary developmental retardation, the loss of HCF-1-negative cells is tolerated, leading to viable heterozygous offspring with 100% skewed inactivation of the X-linked Hcfc1(epiKO) allele. In resting adult liver cells, the requirement for HCF-1 in cell proliferation was more evident as hepatocytes lacking HCF-1 fail to re-enter the cell cycle and thus to proliferate during liver regeneration. The survival of the heterozygous Hcfc1(epiKO/+) female embryos, even with half the cells genetically compromised, illustrates the developmental plasticity of the post-implantation mouse embryo - in this instance, permitting survival of females heterozygous for an X-linked embryonic lethal allele

Азовська операція Революційної Повстанської Армії України (махновців)

В історії України знайдеться не так вже й багато явищ та подій, які б значимістю та силою переросли рамки регіональної та національної історії і ставали повноправними надбаннями історії всесвітньої. Ще менше подібних подій та явищ існувало на рівні південноукраїнського регіону. І було б логічно, якби такі явища посилено досліджувались істориками, а результати досліджень ставали надбанням якомога ширшого загалу, що перетворювало б ці явища на бренд, який швидко вгадувався і запам’ятовувся будь-де. Проте в умовах сучасної України ми цього не спостерігаємо

Gaia Data Processing Architecture

Gaia is ESA's ambitious space astrometry mission the main objective of which is to astrometrically and spectro-photometrically map 1000 Million celestial objects (mostly in our galaxy) with unprecedented accuracy. The announcement of opportunity for the data processing will be issued by ESA late in 2006. The Gaia Data Processing and Analysis Consortium (DPAC) has been formed recently and is preparing an answer. The satellite will downlink close to 100 TB of raw telemetry data over 5 years. To achieve its required accuracy of a few 10s of Microarcsecond astrometry, a highly involved processing of this data is required. In addition to the main astrometric instrument Gaia will host a Radial Velocity instrument, two low-resolution dispersers for multi-color photometry and two Star Mappers. Gaia is a flying Giga Pixel camera. The various instruments each require relatively complex processing while at the same time being interdependent. We describe the overall composition of the DPAC and the envisaged overall architecture of the Gaia data processing system. We shall delve further into the core processing - one of the nine, so-called, coordination units comprising the Gaia processing system.Comment: 10 Pages, 2 figures. To appear in ADASS XVI Proceeding

Snowmass 2001: Jet Energy Flow Project

Conventional cone jet algorithms arose from heuristic considerations of LO hard scattering coupled to independent showering. These algorithms implicitly assume that the final states of individual events can be mapped onto a unique set of jets that are in turn associated with a unique set of underlying hard scattering partons. Thus each final state hadron is assigned to a unique underlying parton. The Jet Energy Flow (JEF) analysis described here does not make such assumptions. The final states of individual events are instead described in terms of flow distributions of hadronic energy. Quantities of physical interest are constructed from the energy flow distribution summed over all events. The resulting analysis is less sensitive to higher order perturbative corrections and the impact of showering and hadronization than the standard cone algorithms.Comment: REVTeX4, 13 pages, 6 figures; Contribution to the P5 Working Group on QCD and Strong Interactions at Snowmass 200

Types of Stickiness in BHV Phylogenetic Tree Spaces and Their Degree

It has been observed that the sample mean of certain probability distributions in Billera-Holmes-Vogtmann (BHV) phylogenetic spaces is confined to a lower-dimensional subspace for large enough sample size. This non-standard behavior has been called stickiness and poses difficulties in statistical applications when comparing samples of sticky distributions. We extend previous results on stickiness to show the equivalence of this sampling behavior to topological conditions in the special case of BHV spaces. Furthermore, we propose to alleviate statistical comparision of sticky distributions by including the directional derivatives of the Fr\'echet function: the degree of stickiness.Comment: 8 Pages, 1 Figure, conference submission to GSI 202