Real analysis Stein, Elias M; Shakarchi, Rami
2005., 20091128, 2009, 2005, 2009-11-28, Volume:
3
eBook
Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the ...development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises.
The genetic gain in yield and quality are two major targets of wheat breeding programs around the world. In this study, a high density genetic map consisting of 10,172 SNP markers identified a total ...of 43 genomic regions associated with three quality traits, three yield traits and two agronomic traits in hard red spring wheat (HRSW). When compared with six grain shape and size traits, the quality traits showed mostly independent genetic control (~18% common loci), while the yield traits showed moderate association (~53% common loci). Association of genomic regions for grain area (GA) and thousand-grain weight (TGW), with yield suggests that targeting an increase in GA may help enhancing wheat yield through an increase in TGW. Flour extraction (FE), although has a weak positive phenotypic association with grain shape and size, they do not share any common genetic loci. A major contributor to plant height was the Rht8 locus and the reduced height allele was associated with significant increase in grains per spike (GPS) and FE, and decrease in number of spikes per square meter and test weight. Stable loci were identified for almost all the traits. However, we could not find any QTL in the region of major known genes like GPC-B1, Ha, Rht-1, and Ppd-1. Epistasis also played an important role in the genetics of majority of the traits. In addition to enhancing our knowledge about the association of wheat quality and yield with grain shape and size, this study provides novel loci, genetic information and pre-breeding material (combining positive alleles from both parents) to enhance the cultivated gene pool in wheat germplasm. These resources are valuable in facilitating molecular breeding for wheat quality and yield improvement.
To study whether preimplantation genetic screening with comprehensive chromosome screening (PGS-CCS) improves clinical implantation rates (IR) and sustained IR (beyond 20 weeks) compared with routine ...care for embryo selection in IVF cycles.
Meta-analysis of randomized controlled trials (RCTs) and observational studies (OSs).
University-affiliated teaching hospital.
Infertile couples undergoing IVF.
PGS-CCS with the use of different genetic platforms performed on polar body (PB), cleavage embryo, or blastocyst following embryo biopsy.
Clinical IR and sustained IR in RCTs as well as OSs comparing PGS-CCS and routine care were determined after a complete review of the literature. Pooled estimates of risk ratios (RRs) with their 95% confidence intervals (CIs) according to a fixed-effects model with the use of the Mantel-Haenszel method were calculated after the meta-analysis. Forest plots are provided for comparative purposes.
Out of 763 citations identified, 29 articles met initial eligibility criteria and were further analyzed. Of these, only three RCTs and eight OSs met full inclusion criteria, allowing direct comparison of PGS-CCS and routine IVF care based on embryo morphology selection. In the RCTs, all embryo biopsies were performed on day 5-6 of embryo development. In the OSs, biopsies were performed on different stages of embryo development, including PB, day 3, or day 5-6. Meta-analysis of the RCTs (3 studies; n = 659) showed that PGS-CCS was associated with a significantly higher clinical IR, with a pooled RR of 1.29 (95% CI 1.15-1.45), as well as a significantly higher sustained IR, with a pooled RR of 1.39 (95% CI 1.21-1.60). Similar findings were shown in the OSs, where the pooled RR for clinical IR was 1.78 (95% CI 1.60-1.99; 7 studies; n = 2,993) and for sustained IR was 1.75 (95% CI 1.48-2.07; 4 studies; n = 1,124). Statistical heterogeneity (I(2)) was minimal for RCTs and substantial among OSs.
PGS with the use of CCS technology increases clinical and sustained IRs, thus improving embryo selection, particularly in patients with normal ovarian reserve. Results from ongoing RCTs conducted on different patient populations (e.g., decreased ovarian reserve) and different embryo stage biopsy (e.g., PB, day 3) may further clarify the role of this technology.
OBJECTIVE: To determine the independent effects of obesity and hypertension on cognitive functioning. METHODS: Using a prospective design, male (n=551) and female (n=872) participants of the ...Framingham Heart Study were classified by presence or absence of obesity and hypertension based on data collected over an 18-y surveillance period. All subjects were free from dementia, stroke, and clinically diagnosed cardiovascular disease up to the time of cognitive testing. Statistical models were adjusted for age, education, occupation, cigarette smoking, alcohol consumption, total cholesterol, and a diagnosis of type II diabetes. Body mass index status (nonobese or obese) and blood pressure status (normotensive or hypertensive) were then related to cognitive performance (learning, memory, executive functioning, and abstract reasoning) on tests administered 4-6 y later. RESULTS: Adverse effects of obesity and hypertension on cognitive performance were observed for men only. Obese and hypertensive men performed more poorly than men classified as either obese or hypertensive, and the best performance was observed in nonobese, normotensive men. CONCLUSIONS: The adverse effects of obesity and hypertension in men are independent and cumulative with respect to cognitive deficit.
Preimplantation genetic testing for aneuploidy was developed as an invasive embryo-selection technique and is extensively used in in vitro fertilization (IVF) cycles. Around 95,000 preimplantation ...genetic testing cycles were carried out in the United States between 2014 and 2016, the majority of which were performed for aneuploidy. The objective of preimplantation genetic testing for aneuploidy is to select for transfer a euploid embryo, after embryo biopsy and cytogenetic analysis. The current technique consists of applying comprehensive chromosome screening on trophectoderm cells after blastocyst-stage embryo biopsy. This article reviews all the published randomized controlled trials on preimplantation genetic testing for aneuploidy with comprehensive chromosome screening and comments on the subject of embryo mosaicism detected by this technique. Most of these trials have been criticized because they only included good prognosis patients having normal ovarian reserve producing a high number of embryos available for biopsy. Preimplantation genetic testing for aneuploidy does not improve ongoing pregnancy rates per cycle started when routinely applied on the general IVF population but seems to be a good tool of embryo selection for a selected category of patients with normal ovarian reserve, yet should be only practiced by experienced IVF clinics. If no euploid embryo is available after preimplantation genetic testing for aneuploidy, a low-level mosaic embryo can be considered and prioritized for transfer after appropriate genetic counseling.
The development of glutamatergic synapses involves changes in the number and type of receptors present at the postsynaptic density. To elucidate molecular mechanisms underlying these changes, we ...combine in utero electroporation of constructs that alter the molecular composition of developing synapses with dual whole-cell electrophysiology to examine synaptic transmission during two distinct developmental stages. We find that SAP102 mediates synaptic trafficking of AMPA and NMDA receptors during synaptogenesis. Surprisingly, after synaptogenesis, PSD-95 assumes the functions of SAP102 and is necessary for two aspects of synapse maturation: the developmental increase in AMPA receptor transmission and replacement of NR2B-NMDARs with NR2A-NMDARs. In PSD-95/PSD-93 double-KO mice, the maturational replacement of NR2B- with NR2A-NMDARs fails to occur, and PSD-95 expression fully rescues this deficit. This study demonstrates that SAP102 and PSD-95 regulate the synaptic trafficking of distinct glutamate receptor subtypes at different developmental stages, thereby playing necessary roles in excitatory synapse development.
The major function of the skin is to form a barrier between the internal milieu and the hostile external environment. A permeability barrier that prevents the loss of water and electrolytes is ...essential for life on land. The permeability barrier is mediated primarily by lipid enriched lamellar membranes that are localized to the extracellular spaces of the stratum corneum. These lipid enriched membranes have a unique structure and contain approximately 50% ceramides, 25% cholesterol, and 15% free fatty acids with very little phospholipid. Lamellar bodies, which are formed during the differentiation of keratinocytes, play a key role in delivering the lipids from the stratum granulosum cells into the extracellular spaces of the stratum corneum. Lamellar bodies contain predominantly glucosylceramides, phospholipids, and cholesterol and following the exocytosis of lamellar lipids into the extracellular space of the stratum corneum these precursor lipids are converted by beta glucocerebrosidase and phospholipases into the ceramides and fatty acids, which comprise the lamellar membranes. The lipids required for lamellar body formation are derived from de novo synthesis by keratinocytes and from extra-cutaneous sources. The lipid synthetic pathways and the regulation of these pathways are described in this review. In addition, the pathways for the uptake of extra-cutaneous lipids into keratinocytes are discussed. This article is part of a Special Issue entitled The Important Role of Lipids in the Epidermis and their Role in the Formation and Maintenance of the Cutaneous Barrier. Guest Editors: Kenneth R. Feingold and Peter Elias.
•The permeability barrier is mediated by lipid membranes in the stratum corneum.•Lamellar bodies deliver the lipids to the stratum corneum extracellular spaces.•In the stratum corneum precursor lipids are converted to ceramides and fatty acids.•Epidermal lipid synthesis provides the lipids for lamellar body formation.•Uptake of extracutaneous lipids also provides lipids for lamellar body formation.
The stratum corneum extracellular matrix (ECM) is enriched in lipids that are organized into lamellar bilayers, whose molecular architecture is now known. Although these bilayers are important for ...the permeability barrier, the ECM contains not only lipids but also enzymes, structural proteins, and antimicrobial peptides that impact barrier function. Yet, how such diverse components affect barrier function remains largely unknown. Static models of the epidermis may not do justice to the ECM, which is metabolically active, as it changes both structure and function as it transits to the surface.
Local‐scale microclimatic conditions in forest understoreys play a key role in shaping the composition, diversity and function of these ecosystems. Consequently, understanding what drives variation ...in forest microclimate is critical to forecasting ecosystem responses to global change, particularly in the tropics where many species already operate close to their thermal limits and rapid land‐use transformation is profoundly altering local environments. Yet our ability to characterize forest microclimate at ecologically meaningful scales remains limited, as understorey conditions cannot be directly measured from outside the canopy. To address this challenge, we established a network of microclimate sensors across a land‐use intensity gradient spanning from old‐growth forests to oil‐palm plantations in Borneo. We then combined these observations with high‐resolution airborne laser scanning data to characterize how topography and canopy structure shape variation in microclimate both locally and across the landscape. In the processes, we generated high‐resolution microclimate surfaces spanning over 350 km2, which we used to explore the potential impacts of habitat degradation on forest regeneration under both current and future climate scenarios. We found that topography and vegetation structure were strong predictors of local microclimate, with elevation and terrain curvature primarily constraining daily mean temperatures and vapour pressure deficit (VPD), whereas canopy height had a clear dampening effect on microclimate extremes. This buffering effect was particularly pronounced on wind‐exposed slopes but tended to saturate once canopy height exceeded 20 m—suggesting that despite intensive logging, secondary forests remain largely thermally buffered. Nonetheless, at a landscape‐scale microclimate was highly heterogeneous, with maximum daily temperatures ranging between 24.2 and 37.2°C and VPD spanning two orders of magnitude. Based on this, we estimate that by the end of the century forest regeneration could be hampered in degraded secondary forests that characterize much of Borneo's lowlands if temperatures continue to rise following projected trends.
Written Summary:Local‐scale microclimatic conditions in forest understoreys play a key role in shaping the composition, diversity and function of these ecosystems. Yet our ability to capture microclimate at scales relevant for management and conservation remains inherently limited. By combining a network of microclimate sensors with high‐resolution airborne laser scanning data acquired across a land‐use intensity gradient in Borneo, here we characterise how topography and canopy structure shape variation in microclimate in human‐modified tropical landscapes. We estimate that by 2080 forest regeneration could be hampered in large tracts of degraded secondary forest that make up much of Borneo’s lowlands.
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