Canonical characters on quasi-symmetric functions and bivariate Catalan numbers

Every character on a graded connected Hopf algebra decomposes uniquely as a product of an even character and an odd character (Aguiar, Bergeron, and Sottile, math.CO/0310016). We obtain explicit formulas for the even and odd parts of the universal character on the Hopf algebra of quasi-symmetric functions. They can be described in terms of Legendre's beta function evaluated at half-integers, or in terms of bivariate Catalan numbers: $$C(m,n)=\frac{(2m)!(2n)!}{m!(m+n)!n!}.$$ Properties of characters and of quasi-symmetric functions are then used to derive several interesting identities among bivariate Catalan numbers and in particular among Catalan numbers and central binomial coefficients

Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras

We develop a theory of multigraded (i.e., $N^l$-graded) combinatorial Hopf algebras modeled on the theory of graded combinatorial Hopf algebras developed by Aguiar, Bergeron, and Sottile [Compos. Math. 142 (2006), 1--30]. In particular we introduce the notion of canonical $k$-odd and $k$-even subalgebras associated with any multigraded combinatorial Hopf algebra, extending simultaneously the work of Aguiar et al. and Ehrenborg. Among our results are specific categorical results for higher level quasisymmetric functions, several basis change formulas, and a generalization of the descents-to-peaks map.Comment: 49 pages. To appear in the Journal of Algebraic Combinatoric

Improved detection of Pneumocystis jirovecii in upper and lower respiratory tract specimens from children with suspected pneumocystis pneumonia using real-time PCR: a prospective study

<p>Abstract</p> <p>Background</p> <p><it>Pneumocystis </it>pneumonia (PCP) is a major cause of hospitalization and mortality in HIV-infected African children. Microbiologic diagnosis relies predominantly on silver or immunofluorescent staining of a lower respiratory tract (LRT) specimens which are difficult to obtain in children. Diagnosis on upper respiratory tract (URT) specimens using PCR has been reported useful in adults, but data in children are limited. The main objectives of the study was (1) to compare the diagnostic yield of PCR with immunofluorescence (IF) and (2) to investigate the usefulness of upper compared to lower respiratory tract samples for diagnosing PCP in children.</p> <p>Methods</p> <p>Children hospitalised at an academic hospital with suspected PCP were prospectively enrolled. An upper respiratory sample (nasopharyngeal aspirate, NPA) and a lower respiratory sample (induced sputum, IS or bronchoalveolar lavage, BAL) were submitted for real-time PCR and direct IF for the detection of <it>Pneumocystis </it><it>jirovecii</it>. A control group of children with viral lower respiratory tract infections were investigated with PCR for PCP.</p> <p>Results</p> <p>202 children (median age 3.3 [inter-quartile range, IQR 2.2 - 4.6] months) were enrolled. The overall detection rate by PCR was higher than by IF [180/349 (52%) vs. 26/349 (7%) respectively; p < 0.0001]. PCR detected more infections compared to IF in lower respiratory tract samples [93/166 (56%) vs. 22/166 (13%); p < 0.0001] and in NPAs [87/183 (48%) vs. 4/183 (2%); p < 0.0001]. Detection rates by PCR on upper (87/183; 48%) compared with lower respiratory tract samples (93/166; 56%) were similar (OR, 0.71; 95% CI, 0.46 - 1.11). Only 2/30 (6.6%) controls were PCR positive.</p> <p>Conclusion</p> <p>Real-time PCR is more sensitive than IF for the detection of <it>P. jirovecii </it>in children with PCP. NPA samples may be used for diagnostic purposes when PCR is utilised. Wider implementation of PCR on NPA samples is warranted for diagnosing PCP in children.</p

Imaging of Zebrafish In Vivo with Second-Harmonic Generation Reveals Shortened Sarcomeres Associated with Myopathy Induced by Statin

We employed second-harmonic generation (SHG) imaging and the zebrafish model to investigate the myopathy caused by statin in vivo with emphasis on the altered microstructures of the muscle sarcomere, the fundamental contractile element of muscles. This approach derives an advantage of SHG imaging to observe the striated skeletal muscle of living zebrafish based on signals produced mainly from the thick myosin filament of sarcomeres without employing exogenous labels, and eliminates concern about the distortion of muscle structures caused by sample preparation in conventional histological examination. The treatment with statin caused a significantly shortened sarcomere relative to an untreated control (1.73±0.09 µm vs 1.91±0.08 µm, P<0.05) while the morphological integrity of the muscle fibers remained largely intact. Mechanistic tests indicated that this microstructural disorder was associated with the biosynthetic pathway of cholesterol, or, specifically, with the impaired production of mevalonate by statins. This microstructural disorder exhibited a strong dependence on both the dosage and the duration of treatment, indicating a possibility to assess the severity of muscle injury according to the altered length of the sarcomeres. In contrast to a conventional assessment of muscle injury using clinical biomarkers in blood, such as creatine kinase that is released from only disrupted myocytes, the ability to determine microstructural modification of sarcomeres allows diagnosis of muscle injury before an onset of conventional clinical symptoms. In light of the increasing prevalence of the incidence of muscle injuries caused by new therapies, our work consolidates the combined use of the zebrafish and SHG imaging as an effective and sensitive means to evaluate the safety profile of new therapeutic targets in vivo

Overexpression of Akt1 Enhances Adipogenesis and Leads to Lipoma Formation in Zebrafish

<div><h3>Background</h3><p>Obesity is a complex, multifactorial disorder influenced by the interaction of genetic, epigenetic, and environmental factors. Obesity increases the risk of contracting many chronic diseases or metabolic syndrome. Researchers have established several mammalian models of obesity to study its underlying mechanism. However, a lower vertebrate model for conveniently performing drug screening against obesity remains elusive. The specific aim of this study was to create a zebrafish obesity model by over expressing the insulin signaling hub of the <em>Akt1</em> gene.</p> <h3>Methodology/Principal Findings</h3><p><em>Skin oncogenic transformation screening shows that a stable zebrafish transgenic of Tg(krt4Hsa.myrAkt1</em>)^cy18 displays severely obese phenotypes at the adult stage. In Tg(<em>krt4:Hsa.myrAkt1</em>)^cy18, the expression of exogenous human constitutively active Akt1 (myrAkt1) can activate endogenous downstream targets of mTOR, GSK-3α/β, and 70S6K. During the embryonic to larval transitory phase, the specific over expression of myrAkt1 in skin can promote hypertrophic and hyperplastic growth. From 21 hour post-fertilization (hpf) onwards, myrAkt1 transgene was ectopically expressed in several mesenchymal derived tissues. This may be the result of the integration position effect. Tg(<em>krt4:Hsa.myrAkt1</em>)^cy18 caused a rapid increase of body weight, hyperplastic growth of adipocytes, abnormal accumulation of fat tissues, and blood glucose intolerance at the adult stage. Real-time RT-PCR analysis showed the majority of key genes on regulating adipogenesis, adipocytokine, and inflammation are highly upregulated in Tg(<em>krt4:Hsa.myrAkt1</em>)^cy18. In contrast, the myogenesis- and skeletogenesis-related gene transcripts are significantly downregulated in Tg(<em>krt4:Hsa.myrAkt1</em>)^cy18, suggesting that excess adipocyte differentiation occurs at the expense of other mesenchymal derived tissues.</p> <h3>Conclusion/Significance</h3><p>Collectively, the findings of this study provide direct evidence that Akt1 signaling plays an important role in balancing normal levels of fat tissue in vivo. The obese zebrafish examined in this study could be a new powerful model to screen novel drugs for the treatment of human obesity.</p> </div

SN 2022crv: IIb, Or Not IIb: That is the Question

We present optical and near-infrared observations of SN~2022crv, a stripped envelope supernova in NGC~3054, discovered within 12 hrs of explosion by the Distance Less Than 40 Mpc Survey. We suggest SN~2022crv is a transitional object on the continuum between SNe Ib and SNe IIb. A high-velocity hydrogen feature ($\sim$$-$20,000 -- $-$16,000 $\rm km\,s^{-1}$) was conspicuous in SN~2022crv at early phases, and then quickly disappeared around maximum light. By comparing with hydrodynamic modeling, we find that a hydrogen envelope of $\sim 10^{-3}$ \msun{} can reproduce the behaviour of the hydrogen feature observed in SN~2022crv. The early light curve of SN~2022crv did not show envelope cooling emission, implying that SN~2022crv had a compact progenitor with extremely low amount of hydrogen. The analysis of the nebular spectra shows that SN~2022crv is consistent with the explosion of a He star with a final mass of $\sim$4.5 -- 5.6 \msun{} that has evolved from a $\sim$16 -- 22 \msun{} zero-age main sequence star in a binary system with about 1.0 -- 1.7 \msun{} of oxygen finally synthesized in the core. The high metallicity at the supernova site indicates that the progenitor experienced a strong stellar wind mass loss. In order to retain a small amount of residual hydrogen at such a high metallicity, the initial orbital separation of the binary system is likely larger than $\sim$1000~$\rm R_{\odot}$. The near-infrared spectra of SN~2022crv show a unique absorption feature on the blue side of He I line at $\sim$1.005~$\mu$m. This is the first time that such a feature has been observed in a Type Ib/IIb, and could be due to \ion{Sr}{2}. Further detailed modelling on SN~2022crv can shed light on the progenitor and the origin of the mysterious absorption feature in the near infrared.Comment: 33 pages, 23 figures, submitted to Ap