On a Generalization of the Frobenius Number

We consider a generalization of the Frobenius Problem where the object of interest is the greatest integer which has exactly $j$ representations by a collection of positive relatively prime integers. We prove an analogue of a theorem of Brauer and Shockley and show how it can be used for computation.Comment: 5 page

Dual GPCR and GAG mimicry by the M3 chemokine decoy receptor

Viruses have evolved a myriad of evasion strategies focused on undermining chemokine-mediated immune surveillance, exemplified by the mouse γ-herpesvirus 68 M3 decoy receptor. Crystal structures of M3 in complex with C chemokine ligand 1/lymphotactin and CC chemokine ligand 2/monocyte chemoattractant protein 1 reveal that invariant chemokine features associated with G protein–coupled receptor binding are primarily recognized by the decoy C-terminal domain, whereas the N-terminal domain (NTD) reconfigures to engage divergent basic residue clusters on the surface of chemokines. Favorable electrostatic forces dramatically enhance the association kinetics of chemokine binding by M3, with a primary role ascribed to acidic NTD regions that effectively mimic glycosaminoglycan interactions. Thus, M3 employs two distinct mechanisms of chemical imitation to potently sequester chemokines, thereby inhibiting chemokine receptor binding events as well as the formation of chemotactic gradients necessary for directed leukocyte trafficking

Two-step thermochemical solar-to-fuel efficiency computation of strontium and chromium doped lanthanum manganite perovskite oxides using CALPHAD

Reducing greenhouse gas emissions and profiting on novel synthetic fuels to store and buffer energy from renewable sources (such as solar or wind) is a prime strategy to encounter the global energy challenge. Here, two-step thermochemical fuel production is an energy technology utilizing intermittent solar power to convert water and carbon dioxide into syngas, a renewable fuel that can be stored easily and mitigate CO2 emissions. Success of the technology relies on the discovery of materials with a high thermochemical solar-to-fuel efficiency. Perovskites have attracted much attention recently due to impressive fuel productivity[1, 2]. Although a high fuel productivity shows the feasibility of a material, it does not imply that it is the optimum and most efficient material as it depends largely on the operation of the solar-to-fuel reactor [3, 4]. Literature on thermochemical solar-to-fuel efficiency of perovskites is limited and none of the existing studies measures the thermodynamic properties in the entire temperature range relevant for solar-to-fuel production, namely 1000-1800K. In this work, we use oxygen nonstoichiometry from CALPHAD data libraries on A-site doped La1-xSrxMnO3-δ and B-site doped perovskite La0.6Sr0.4Mn1-yCryO3-δ in a relevant temperature range of 1073-1873K to determine the solar thermochemical efficiency. The oxygen nonstoichiometry and thermodynamic properties extracted from CALPHAD libraries are compared to earlier studies of La1-xSrxMnO3-δ for thermochemical fuel production. We discuss diffferences between the earlier extrapolated models and the CALPHAD descriptions on the presented material examples. Specifically, we show thermochemical equilibrium models of fuel productivity supplemented by validations with experimental results on La1-xSrxMnO3-δ in literature. We make predictions on the most efficient material in the composition space La1-xSrxMn1-yCryO3-δ for different conditions. It is shown that the amount of experimental work can be reduced substantially by using the CALPHAD approach and further making predictions for multi-component systems that would be practically unattainable without this method. The solar-to-fuel field will benefit directly from additional thermodynamic data on perovskites in the relevant temperature range. Further, we provide guidelines in terms of key CALPHAD experiments that enables a mapping of the thermodynamic properties of a wide compositional space of perovskites to find materials with a high thermochemical efficiency. 1. McDaniel, A.H., et al., Sr-and Mn-doped LaAlO3−δ for solar thermochemical H2 and CO production. Energy & Environmental Science, 2013. 6(8): p. 2424-2428. 2. Bork, A.H., et al., Perovskite La0.6Sr 0.4Cr1− xCoxO3−δ solid solutions for solar-thermochemical fuel production: strategies to lower the operation temperature. Journal of Materials Chemistry A, 2015. 3(30): p. 15546-15557. 3. Scheffe, J.R., D. Weibel, and A. Steinfeld, Lanthanum–Strontium–Manganese Perovskites as Redox Materials for Solar Thermochemical Splitting of H2O and CO2. Energy & Fuels, 2013. 27(8): p. 4250-4257. 4. Yang, C.-K., et al., Thermodynamic and kinetic assessments of strontium-doped lanthanum manganite perovskites for two-step thermochemical water splitting. Journal of Materials Chemistry A, 2014. 2(33): p. 13612-13623

On the generalized Bykovskii presentation of Steinberg modules

We study presentations of the virtual dualizing modules of special linear groups of number rings, the Steinberg modules. Bykovskii gave a presentation for the Steinberg modules of the integers, and our main result is a generalization of this presentation to the Gaussian integers and the Eisenstein integers. We also show that this generalization does not give a presentation for the Steinberg modules of several Euclidean number rings.Comment: Minor revisions based on referee's comments. Accepted for publication at IMR

Human Vault Nanoparticle Targeted Delivery of Antiretroviral Drugs to Inhibit Human Immunodeficiency Virus Type 1 Infection.

"Vaults" are ubiquitously expressed endogenous ribonucleoprotein nanoparticles with potential utility for targeted drug delivery. Here, we show that recombinant human vault nanoparticles are readily engulfed by certain key human peripheral blood mononuclear cells (PBMC), predominately dendritic cells, monocytes/macrophages, and activated T cells. As these cell types are the primary targets for human immunodeficiency virus type 1 (HIV-1) infection, we examined the utility of recombinant human vaults for targeted delivery of antiretroviral drugs. We chemically modified three different antiretroviral drugs, zidovudine, tenofovir, and elvitegravir, for direct conjugation to vaults. Tested in infection assays, drug-conjugated vaults inhibited HIV-1 infection of PBMC with equivalent activity to free drugs, indicating vault delivery and drug release in the cytoplasm of HIV-1-susceptible cells. The ability to deliver functional drugs via vault nanoparticle conjugates suggests their potential utility for targeted drug delivery against HIV-1

B-type Natriuretic Peptide: Perioperative Patterns in Congenital Heart Disease

B-type natriuretic peptide (BNP) has diagnostic, prognostic, and therapeutic roles in adults with heart failure. BNP levels in children undergoing surgical repair of congenital heart disease (CHD) were characterized broadly, and distinguishable subgroup patterns delineated.Prospective, blinded, observational case series.Academic, tertiary care, free-standing pediatric hospital.Children with CHD; controls without cardiopulmonary disease.None.Preoperative cardiac medications/doses, CHD lesion types, perioperative BNP levels, intraoperative variables (lengths of surgery, bypass, cross-clamp), postoperative outcomes (lengths of ventilation, hospitalization, open chest; averages of inotropic support, central venous pressure, perfusion, urine output; death, low cardiac output syndrome (LCOS), cardiac arrest; readmission; and discharge medications).Median BNP levels for 102 neonatal and non-neonatal controls were 27 and 7 pg/mL, respectively. Serial BNP measures from 105 patients undergoing CHD repair demonstrated a median postoperative peak at 12 hours. The median and interquartile postoperative 24-hour average BNP levels for neonates were 1506 (782–3784) pg/mL vs. 286 (169–578) pg/mL for non-neonates ( P < 0.001). Postoperative BNP correlated with inotropic requirement, durations of open chest, ventilation, intensive care unit stay, and hospitalization (r = 0.33–0.65, all P < 0.001). Compared with biventricular CHD, Fontan palliations demonstrated lower postoperative BNP (median 150 vs. 306 pg/mL, P < 0.001), a 3-fold higher incidence of LCOS ( P < 0.01), and longer length of hospitalization (median 6.0 vs. 4.5 days, P = 0.01).Perioperative BNP correlates to severity of illness and lengths of therapy in the CHD population, overall. Substantial variation in BNP across time as well as within and between CHD lesions limits its practical utility as an isolated point-of-care measure. BNP commonly peaks 6–12 hours postoperatively, but the timing and magnitude of BNP elevation demonstrates notable age-dependency, peaking earlier and rising an order of magnitude higher in neonates. In spite of higher clinical acuity, non-neonatal univentricular CHD paradoxically demonstrates lower BNP levels compared with biventricular physiologies.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79231/1/j.1747-0803.2010.00396.x.pd

Analysis of Fcγ receptor haplotypes in rheumatoid arthritis: FCGR3A remains a major susceptibility gene at this locus, with an additional contribution from FCGR3B

The Fcγ receptors play important roles in the initiation and regulation of many immunological and inflammatory processes, and genetic variants (FCGR) have been associated with numerous autoimmune and infectious diseases. The data in rheumatoid arthritis (RA) are conflicting and we previously demonstrated an association between FCGR3A and RA. In view of the close molecular proximity with FCGR2A, FCGR2B and FCGR3B, additional polymorphisms within these genes and FCGR haplotypes were examined to refine the extent of association with RA. Biallelic polymorphisms in FCGR2A, FCGR2B and FCGR3B were examined for association with RA in two well characterized UK Caucasian and North Indian/Pakistani cohorts, in which FCGR3A genotyping had previously been undertaken. Haplotype frequencies and linkage disequilibrium were estimated across the FCGR locus and a model-free analysis was performed to determine association with RA. This was followed by regression analysis, allowing for phase uncertainty, to identify the particular haplotype(s) that influences disease risk. Our results reveal that FCGR2A, FCGR2B and FCGR3B were not associated with RA. The haplotype with the strongest association with RA susceptibility was the FCGR3A–FCGR3B 158V-NA2 haplotype (odds ratio 3.18, 95% confidence interval 1.13–8.92 [P = 0.03] for homozygotes compared with all genotypes). The association was stronger in the presence of nodules (odds ratio 5.03, 95% confidence interval 1.44–17.56; P = 0.01). This haplotype was also more common in North Indian/Pakistani RA patients than in control individuals, but not significantly so. Logistic regression analyses suggested that FCGR3A remained the most significant gene at this locus. The increased association with an FCGR3A–FCGR3B haplotype suggests that other polymorphic variants within FCGR3A or FCGR3B, or in linkage disequilibrium with this haplotype, may additionally contribute to disease pathogenesis