WIENER AMALGAM SPACES IN GENERALIZED HARMONIC ANALYSIS AND WAVELET THEORY

This thesis is divided into four parts. Part I, Introduction and Notation, describes the results contained in the thesis and their background. Part II, Wiener Amalgam Spaces, is an expository introduction to Feichtinger's general amalgam space theory, which is used in the remainder of the thesis to formulate and prove results. Part III, Generalized Harmonic Analysis, presents new results in that area. Part IV, Wavelet Theory, contains exposition and miscellaneous results on Gabor ( also known as Weyl-Heisenberg) wavelets. Amalgam, or mixed-norm, spaces are Banach spaces of functions determined by a norm which distinguishes between local and global properties of functions. Specific cases were introduced by Wiener. Feichtinger has developed a far-reaching generalization of amalgam spaces, which allows general function spaces norms as local or global components. We use Feichtinger's amalgam theory, on d-dimensional Euclidean space under componentwise multiplication, to prove that the Wiener transform (introduced by Wiener to analyze the spectra of infinite-energy signals) is an invertible mapping of the amalgam space with local L2 and global Lq. components onto an appropriate space defined in terms of the variation of functions, for each q between one and infinity. As corollaries, we obtain results of Beurling on the Fourier transform and results of Lau and Chen on the Wiener transform. Moreover, our results are carried out in higher dimensions. In addition, we prove that the higher-dimensional variation spaces are complete by using Masani's helices; this generalizes a one-dimensional result of Lau and Chen. In wavelet theory, we present a survey of frames in Hilbert and Banach spaces and the use of the Zak transform in analyzing Gabor wavelets. Frames are an alternative to unconditional bases in these spaces; like bases, they Provide representations of each element of the space in terms of the frame elements, and do so in a way in which the scalars in the representation are explicitly known. However, unlike bases, the representations need not be unique. We then discuss the specific case of Gabor frames in the space of square-integrable functions, concentrating on the role of the Zak transform in the analysis of such frames

Aptamer-based multiplexed proteomic technology for biomarker discovery

Interrogation of the human proteome in a highly multiplexed and efficient manner remains a coveted and challenging goal in biology. We present a new aptamer-based proteomic technology for biomarker discovery capable of simultaneously measuring thousands of proteins from small sample volumes (15 [mu]L of serum or plasma). Our current assay allows us to measure ~800 proteins with very low limits of detection (1 pM average), 7 logs of overall dynamic range, and 5% average coefficient of variation. This technology is enabled by a new generation of aptamers that contain chemically modified nucleotides, which greatly expand the physicochemical diversity of the large randomized nucleic acid libraries from which the aptamers are selected. Proteins in complex matrices such as plasma are measured with a process that transforms a signature of protein concentrations into a corresponding DNA aptamer concentration signature, which is then quantified with a DNA microarray. In essence, our assay takes advantage of the dual nature of aptamers as both folded binding entities with defined shapes and unique sequences recognizable by specific hybridization probes. To demonstrate the utility of our proteomics biomarker discovery technology, we applied it to a clinical study of chronic kidney disease (CKD). We identified two well known CKD biomarkers as well as an additional 58 potential CKD biomarkers. These results demonstrate the potential utility of our technology to discover unique protein signatures characteristic of various disease states. More generally, we describe a versatile and powerful tool that allows large-scale comparison of proteome profiles among discrete populations. This unbiased and highly multiplexed search engine will enable the discovery of novel biomarkers in a manner that is unencumbered by our incomplete knowledge of biology, thereby helping to advance the next generation of evidence-based medicine

The state of the Martian climate

60°N was +2.0°C, relative to the 1981–2010 average value (Fig. 5.1). This marks a new high for the record. The average annual surface air temperature (SAT) anomaly for 2016 for land stations north of starting in 1900, and is a significant increase over the previous highest value of +1.2°C, which was observed in 2007, 2011, and 2015. Average global annual temperatures also showed record values in 2015 and 2016. Currently, the Arctic is warming at more than twice the rate of lower latitudes

Policy statement from the Society for Healthcare Epidemiology of America (SHEA): Only medical contraindications should be accepted as a reason for not receiving all routine immunizations as recommended by the Centers for Disease Control and Prevention

SHEA endorses adhering to the recommendations by the CDC and ACIP for immunizations of all children and adults. All persons providing clinical care should be familiar with these recommendations and should routinely assess immunization compliance of their patients and strongly recommend all routine immunizations to patients. All healthcare personnel (HCP) should be immunized against vaccine-preventable diseases as recommended by the CDC/ACIP (unless immunity is demonstrated by another recommended method). SHEA endorses the policy that immunization should be a condition of employment or functioning (students, contract workers, volunteers, etc) at a healthcare facility. Only recognized medical contraindications should be accepted for not receiving recommended immunizations

State of the climate in 2010

Several large-scale climate patterns influenced climate conditions and weather patterns across the globe during 2010. The transition from a warm El Nino phase at the beginning of the year to a cool La Nina phase by July contributed to many notable events, ranging from record wetness across much of Australia to historically low Eastern Pacific basin and near-record high North Atlantic basin hurricane activity. The remaining five main hurricane basins experienced below-to well-below-normal tropical cyclone activity. The negative phase of the Arctic Oscillation was a major driver of Northern Hemisphere temperature patterns during 2009/10 winter and again in late 2010. It contributed to record snowfall and unusually low temperatures over much of northern Eurasia and parts of the United States, while bringing above-normal temperatures to the high northern latitudes. The February Arctic Oscillation Index value was the most negative since records began in 1950. The 2010 average global land and ocean surface temperature was among the two warmest years on record. The Arctic continued to warm at about twice the rate of lower latitudes. The eastern and tropical Pacific Ocean cooled about 1 C from 2009 to 2010, reflecting the transition from the 2009/10 El Nino to the 2010/11 La Nina. Ocean heat fluxes contributed to warm sea surface temperature anomalies in the North Atlantic and the tropical Indian and western Pacific Oceans. Global integrals of upper ocean heat content for the past several years have reached values consistently higher than for all prior times in the record, demonstrating the dominant role of the ocean in the Earth's energy budget. Deep and abyssal waters of Antarctic origin have also trended warmer on average since the early 1990s. Lower tropospheric temperatures typically lag ENSO surface fluctuations by two to four months, thus the 2010 temperature was dominated by the warm phase El Nino conditions that occurred during the latter half of 2009 and early 2010 and was second warmest on record. The stratosphere continued to be anomalously cool. Annual global precipitation over land areas was about five percent above normal. Precipitation over the ocean was drier than normal after a wet year in 2009. Overall, saltier (higher evaporation) regions of the ocean surface continue to be anomalously salty, and fresher (higher precipitation) regions continue to be anomalously fresh. This salinity pattern, which has held since at least 2004, suggests an increase in the hydrological cycle. Sea ice conditions in the Arctic were significantly different than those in the Antarctic during the year. The annual minimum ice extent in the Arctic reached in September was the third lowest on record since 1979. In the Antarctic, zonally averaged sea ice extent reached an all-time record maximum from mid-June through late August and again from mid-November through early December. Corresponding record positive Southern Hemisphere Annular Mode Indices influenced the Antarctic sea ice extents. Greenland glaciers lost more mass than any other year in the decade-long record. The Greenland Ice Sheet lost a record amount of mass, as the melt rate was the highest since at least 1958, and the area and duration of the melting was greater than any year since at least 1978. High summer air temperatures and a longer melt season also caused a continued increase in the rate of ice mass loss from small glaciers and ice caps in the Canadian Arctic. Coastal sites in Alaska show continuous permafrost warming and sites in Alaska, Canada, and Russia indicate more significant warming in relatively cold permafrost than in warm permafrost in the same geographical area. With regional differences, permafrost temperatures are now up to 2 C warmer than they were 20 to 30 years ago. Preliminary data indicate there is a high probability that 2010 will be the 20th consecutive year that alpine glaciers have lost mass. Atmospheric greenhouse gas concentrations continued to rise and ozone depleting substances continued to decrease. Carbon dioxide increased by 2.60 ppm in 2010, a rate above both the 2009 and the 1980-2010 average rates. The global ocean carbon dioxide uptake for the 2009 transition period from La Nina to El Nino conditions, the most recent period for which analyzed data are available, is estimated to be similar to the long-term average. The 2010 Antarctic ozone hole was among the lowest 20% compared with other years since 1990, a result of warmer-than-average temperatures in the Antarctic stratosphere during austral winter between mid-July and early September

State of the Climate in 2016

In 2016, the dominant greenhouse gases released into Earth's atmosphere-carbon dioxide, methane, and nitrous oxide-continued to increase and reach new record highs. The 3.5 +/- 0.1 ppm rise in global annual mean carbon dioxide from 2015 to 2016 was the largest annual increase observed in the 58-year measurement record. The annual global average carbon dioxide concentration at Earth's surface surpassed 400 ppm (402.9 +/- 0.1 ppm) for the first time in the modern atmospheric measurement record and in ice core records dating back as far as 800000 years. One of the strongest El Nino events since at least 1950 dissipated in spring, and a weak La Nina evolved later in the year. Owing at least in part to the combination of El Nino conditions early in the year and a long-term upward trend, Earth's surface observed record warmth for a third consecutive year, albeit by a much slimmer margin than by which that record was set in 2015. Above Earth's surface, the annual lower troposphere temperature was record high according to all datasets analyzed, while the lower stratospheric temperature was record low according to most of the in situ and satellite datasets. Several countries, including Mexico and India, reported record high annual temperatures while many others observed near-record highs. A week-long heat wave at the end of April over the northern and eastern Indian peninsula, with temperatures surpassing 44 degrees C, contributed to a water crisis for 330 million people and to 300 fatalities. In the Arctic the 2016 land surface temperature was 2.0 degrees C above the 1981-2010 average, breaking the previous record of 2007, 2011, and 2015 by 0.8 degrees C, representing a 3.5 degrees C increase since the record began in 1900. The increasing temperatures have led to decreasing Arctic sea ice extent and thickness. On 24 March, the sea ice extent at the end of the growth season saw its lowest maximum in the 37-year satellite record, tying with 2015 at 7.2% below the 1981-2010 average. The September 2016 Arctic sea ice minimum extent tied with 2007 for the second lowest value on record, 33% lower than the 1981-2010 average. Arctic sea ice cover remains relatively young and thin, making it vulnerable to continued extensive melt. The mass of the Greenland Ice Sheet, which has the capacity to contribute similar to 7 m to sea level rise, reached a record low value. The onset of its surface melt was the second earliest, after 2012, in the 37-year satellite record. Sea surface temperature was record high at the global scale, surpassing the previous record of 2015 by about 0.01 degrees C. The global sea surface temperature trend for the 21st century-to-date of +0.162 degrees C decade(-1) is much higher than the longer term 1950-2016 trend of +0.100 degrees C decade(-1). Global annual mean sea level also reached a new record high, marking the sixth consecutive year of increase. Global annual ocean heat content saw a slight drop compared to the record high in 2015. Alpine glacier retreat continued around the globe, and preliminary data indicate that 2016 is the 37th consecutive year of negative annual mass balance. Across the Northern Hemisphere, snow cover for each month from February to June was among its four least extensive in the 47-year satellite record. Continuing a pattern below the surface, record high temperatures at 20-m depth were measured at all permafrost observatories on the North Slope of Alaska and at the Canadian observatory on northernmost Ellesmere Island. In the Antarctic, record low monthly surface pressures were broken at many stations, with the southern annular mode setting record high index values in March and June. Monthly high surface pressure records for August and November were set at several stations. During this period, record low daily and monthly sea ice extents were observed, with the November mean sea ice extent more than 5 standard deviations below the 1981-2010 average. These record low sea ice values contrast sharply with the record high values observed during 2012-14. Over the region, springtime Antarctic stratospheric ozone depletion was less severe relative to the 1991-2006 average, but ozone levels were still low compared to pre-1990 levels. Closer to the equator, 93 named tropical storms were observed during 2016, above the 1981-2010 average of 82, but fewer than the 101 storms recorded in 2015. Three basins-the North Atlantic, and eastern and western North Pacific-experienced above-normal activity in 2016. The Australian basin recorded its least active season since the beginning of the satellite era in 1970. Overall, four tropical cyclones reached the Saffir-Simpson category 5 intensity level. The strong El Nino at the beginning of the year that transitioned to a weak La Nina contributed to enhanced precipitation variability around the world. Wet conditions were observed throughout the year across southern South America, causing repeated heavy flooding in Argentina, Paraguay, and Uruguay. Wetter-than-usual conditions were also observed for eastern Europe and central Asia, alleviating the drought conditions of 2014 and 2015 in southern Russia. In the United States, California had its first wetter-than-average year since 2012, after being plagued by drought for several years. Even so, the area covered by drought in 2016 at the global scale was among the largest in the post-1950 record. For each month, at least 12% of land surfaces experienced severe drought conditions or worse, the longest such stretch in the record. In northeastern Brazil, drought conditions were observed for the fifth consecutive year, making this the longest drought on record in the region. Dry conditions were also observed in western Bolivia and Peru; it was Bolivia's worst drought in the past 25 years. In May, with abnormally warm and dry conditions already prevailing over western Canada for about a year, the human-induced Fort McMurray wildfire burned nearly 590000 hectares and became the costliest disaster in Canadian history, with $3 billion (U.S. dollars) in insured losses