Some analytic aspects of automorphic forms on GL(2) of minimal type

27 pagesLet $\pi$ be a cuspidal automorphic representation of $PGL_2(\mathbb{A}_\mathbb{Q})$ of arithmetic conductor $C$ and archimedean parameter $T$, and let $\phi$ be an $L^2$-normalized automorphic form in the space of $\pi$. The sup-norm problem asks for bounds on $\| \phi \|_\infty$ in terms of $C$ and $T$. The quantum unique ergodicity (QUE) problem concerns the limiting behavior of the $L^2$-mass $|\phi|^2 (g) \, d g$ of $\phi$. All previous work on these problems in the conductor-aspect has focused on the case that $\phi$ is a newform. In this work, we study these problems for a class of automorphic forms that are not newforms. Precisely, we assume that for each prime divisor $p$ of $C$, the local component $\pi_p$ is supercuspidal (and satisfies some additional technical hypotheses), and consider automorphic forms $\phi$ for which the local components $\phi_p \in \pi_p$ are "minimal" vectors. Such vectors may be understood as non-archimedean analogues of lowest weight vectors in holomorphic discrete series representations of $PGL_2(\mathbb{R})$. For automorphic forms as above, we prove a sup-norm bound that is sharper than what is known in the newform case. In particular, if $\pi_\infty$ is a holomorphic discrete series of lowest weight $k$, we obtain the optimal bound $C^{1/8 -\epsilon} k^{1/4 - \epsilon} \ll_{\epsilon} |\phi|_\infty \ll_{\epsilon} C^{1/8 + \epsilon} k^{1/4+\epsilon}$. We prove also that these forms give analytic test vectors for the QUE period, thereby demonstrating the equivalence between the strong QUE and the subconvexity problems for this class of vectors. This finding contrasts the known failure of this equivalence for newforms of powerful level

Bounds for Rankin--Selberg integrals and quantum unique ergodicity for powerful levels

43 pages; various minor corrections (many thanks to the referee) and improvements in clarity and exposition. To appear in JAMS43 pages; various minor corrections (many thanks to the referee) and improvements in clarity and exposition. To appear in JAMSLet f be a classical holomorphic newform of level q and even weight k. We show that the pushforward to the full level modular curve of the mass of f equidistributes as qk -> infinity. This generalizes known results in the case that q is squarefree. We obtain a power savings in the rate of equidistribution as q becomes sufficiently "powerful" (far away from being squarefree), and in particular in the "depth aspect" as q traverses the powers of a fixed prime. We compare the difficulty of such equidistribution problems to that of corresponding subconvexity problems by deriving explicit extensions of Watson's formula to certain triple product integrals involving forms of non-squarefree level. By a theorem of Ichino and a lemma of Michel--Venkatesh, this amounts to a detailed study of Rankin--Selberg integrals int|f|^2 E attached to newforms f of arbitrary level and Eisenstein series E of full level. We find that the local factors of such integrals participate in many amusing analogies with global L-functions. For instance, we observe that the mass equidistribution conjecture with a power savings in the depth aspect is equivalent to the union of a global subconvexity bound and what we call a "local subconvexity bound"; a consequence of our local calculations is what we call a "local Lindelof hypothesis"

Wikipedia as an encyclopaedia of life

In his 2003 essay E O Wilson outlined his vision for an “encyclopaedia of life” comprising “an electronic page for each species of organism on Earth”, each page containing “the scientific name of the species, a pictorial or genomic presentation of the primary type specimen on which its name is based, and a summary of its diagnostic traits.” Although the “quiet revolution” in biodiversity informatics has generated numerous online resources, including some directly inspired by Wilson's essay (e.g., "http://ispecies.org":http://ispecies.org, "http://www.eol.org":http://www.eol.org), we are still some way from the goal of having available online all relevant information about a species, such as its taxonomy, evolutionary history, genomics, morphology, ecology, and behaviour. While the biodiversity community has been developing a plethora of databases, some with overlapping goals and duplicated content, Wikipedia has been slowly growing to the point where it now has over 100,000 pages on biological taxa. My goal in this essay is to explore the idea that, largely independent of the efforts of biodiversity informatics and well-funded international efforts, Wikipedia ("http://en.wikipedia.org/wiki/Main_Page":http://en.wikipedia.org/wiki/Main_Page) has emerged as potentially the best platform for fulfilling E O Wilson’s vision

Eosinophil and T Cell Markers Predict Functional Decline in COPD Patients

BACKGROUND. The major marker utilized to monitor COPD patients is forced expiratory volume in one second (FEV1). However, asingle measurement of FEV1 cannot reliably predict subsequent decline. Recent studies indicate that T lymphocytes and eosinophils are important determinants of disease stability in COPD. We therefore measured cytokine levels in the lung lavage fluid and plasma of COPD patients in order to determine if the levels of T cell or eosinophil related cytokines were predictive of the future course of the disease. METHODS. Baseline lung lavage and plasma samples were collected from COPD subjects with moderately severe airway obstruction and emphysematous changes on chest CT. The study participants were former smokers who had not had a disease exacerbation within the past six months or used steroids within the past two months. Those subjects who demonstrated stable disease over the following six months (ΔFEV1 % predicted = 4.7 ± 7.2; N = 34) were retrospectively compared with study participants who experienced a rapid decline in lung function (ΔFEV1 % predicted = -16.0 ± 6.0; N = 16) during the same time period and with normal controls (N = 11). Plasma and lung lavage cytokines were measured from clinical samples using the Luminex multiplex kit which enabled the simultaneous measurement of several T cell and eosinophil related cytokines. RESULTS AND DISCUSSION. Stable COPD participants had significantly higher plasma IL-2 levels compared to participants with rapidly progressive COPD (p = 0.04). In contrast, plasma eotaxin-1 levels were significantly lower in stable COPD subjects compared to normal controls (p < 0.03). In addition, lung lavage eotaxin-1 levels were significantly higher in rapidly progressive COPD participants compared to both normal controls (p < 0.02) and stable COPD participants (p < 0.05). CONCLUSION. These findings indicate that IL-2 and eotaxin-1 levels may be important markers of disease stability in advanced emphysema patients. Prospective studies will need to confirm whether measuring IL-2 or eotaxin-1 can identify patients at risk for rapid disease progression.National Heart, Lung, and Blood Institute (NO1-HR-96140, NO1-HR-96141-001, NO1-HR-96144, NO1-HR-96143; NO1-HR-96145; NO1-HR-96142, R01HL086936-03); The Flight Attendant Medical Research Institute; the Jo-Ann F. LeBuhn Center for Chest Diseas

New Selective Estrogen Receptor Modulators (SERMs) in Development

Selective estrogen receptor modulators (SERMs) or estrogen agonists/antagonists have shown promise in osteoporosis in that they have the potential to reduce the risk of fracture, and also reduce the risk of breast cancer. SERMs maybe classified according to their core structure, which is typically a variation of the 17 beta-estradiol template and subclassified according to the side chain at the helix 12 affector region. The best known are the triphenylethylenes such as tamoxifen, used in the management of breast cancer. However, the clinical application of this class of SERMs has been limited due to endometrial stimulation. A second class is the benzothiophenes such as raloxifene and arzoxifene, which have skeletal benefit with little, if any, uterine stimulation. Indole-based SERMs such as bazedoxifene have a 2-phenyl ring system that serves as a core binding unit. Other classes include benzopyrans and naphthalenes (eg, lasofoxifene). In this review article, I will discuss raloxifene and three new SERMs—arzoxifene, bazedoxifene, and lasofoxifene—that have been recently studied. I will discuss their effect on bone, breast, and the cardiovascular system, as well as on safety

Immune Correlates of Protection Against Human Cytomegalovirus Acquisition, Replication, and Disease

Human cytomegalovirus (HCMV) is the most common infectious cause of infant birth defects and an etiology of significant morbidity and mortality in solid organ and hematopoietic stem cell transplant recipients. There is tremendous interest in developing a vaccine or immunotherapeutic to reduce the burden of HCMV-associated disease, yet after nearly a half-century of research and development in this field we remain without such an intervention. Defining immune correlates of protection is a process that enables targeted vaccine/immunotherapeutic discovery and informed evaluation of clinical performance. Outcomes in the HCMV field have previously been measured against a variety of clinical end points, including virus acquisition, systemic replication, and progression to disease. Herein we review immune correlates of protection against each of these end points in turn, showing that control of HCMV likely depends on a combination of innate immune factors, antibodies, and T-cell responses. Furthermore, protective immune responses are heterogeneous, with no single immune parameter predicting protection against all clinical outcomes and stages of HCMV infection. A detailed understanding of protective immune responses for a given clinical end point will inform immunogen selection and guide preclinical and clinical evaluation of vaccines or immunotherapeutics to prevent HCMV-mediated congenital and transplant disease

Attention on Weak Ties in Social and Communication Networks

Granovetter's weak tie theory of social networks is built around two central hypotheses. The first states that strong social ties carry the large majority of interaction events; the second maintains that weak social ties, although less active, are often relevant for the exchange of especially important information (e.g., about potential new jobs in Granovetter's work). While several empirical studies have provided support for the first hypothesis, the second has been the object of far less scrutiny. A possible reason is that it involves notions relative to the nature and importance of the information that are hard to quantify and measure, especially in large scale studies. Here, we search for empirical validation of both Granovetter's hypotheses. We find clear empirical support for the first. We also provide empirical evidence and a quantitative interpretation for the second. We show that attention, measured as the fraction of interactions devoted to a particular social connection, is high on weak ties --- possibly reflecting the postulated informational purposes of such ties --- but also on very strong ties. Data from online social media and mobile communication reveal network-dependent mixtures of these two effects on the basis of a platform's typical usage. Our results establish a clear relationships between attention, importance, and strength of social links, and could lead to improved algorithms to prioritize social media content

Gravity effect on thermal-solutal convection during solidification revealed by four-dimensional synchrotron imaging with compositional mapping

The effect of gravity on thermo-solutal convection and its impact on solidification dynamics of an Al-15 wt%Cu alloy were studied using high speed synchrotron tomography. A method for mapping the composition of the solidifying samples was developed, enabling three-dimensional quantification of the time evolved solute concentration and dendrite morphology. Differences in solute segregation, dendrite morphology and fragmentation between upwards and downwards solidification were identified, which were attributed to buoyancy-modulated thermal-solutal convection

Lipids and nutrition of the southern rock lobster, Jasus edwardsii, from hatch to puerulus

We examined the lipid class and fatty-acid composition of the southern rock lobster, Jasus edwardsii, phyllosomas larvae and puerulus stage to improve understanding of their nutrition in relation to aquaculture. Lipid is critical in the nutrition of larval crustaceans, including lobsters. Specimens were from Tasmanian waters, Australia, and North Island, New Zealand, waters. Analyses were by TLC-FID and capillary GC and GC-MS. Phyllosomas larvae and nektonic pueruli were low in storage lipid (triacylglycerol), and phospholipid was the major lipid class. Sterol, mainly cholesterol, was the next most abundant class. The ratio of the essential omega-3 fatty acid eicosapentaenoic acid (EPA) to the omega-6 fatty acid arachidonic acid (AA) was lower in newly hatched phyllosomas (1.2-1.3) than in other phyllosomas (stages III-XI; 2.8-6.7) and pueruli (3.8). Ratios of the omega-3 fatty acid DHA (docosahexaenoic acid) to EPA were also lower in newly hatched phyllosomas (0.5) than in later-stage phyllosomas (1.5-2.1) and pueruli (1.2). We have followed up these compositional data by successfully enriching the live diet (Artemia) of early phyllosomas with AA, EPA and DHA. This dietary manipulation has achieved ratios of these key polyunsaturated fatty acids similar to those of wild phyllosomas. These findings will be of significance to the future of rock-lobster aquaculture