Leaf-to-leaf distances and their moments in finite and infinite m-ary tree graphs

We study the leaf-to-leaf distances on full and complete m-ary graphs using a recursive approach. In our formulation, leaves are ordered along a line. We find explicit analytical formulae for the sum of all paths for arbitrary leaf-to-leaf distance r as well as the average path lengths and the moments thereof. We show that the resulting explicit expressions can be recast in terms of Hurwitz-Lerch transcendants. Results for periodic trees are also given. For incomplete random binary trees, we provide first results by numerical techniques; we find a rapid drop of leaf-to-leaf distances for large r.Comment: 10 pages, 7 figure

Evolution and Taxonomic Classification of Human Papillomavirus 16 (HPV16)-Related Variant Genomes: HPV31, HPV33, HPV35, HPV52, HPV58 and HPV67

Human papillomavirus 16 (HPV16) species group (alpha-9) of the Alphapapillomavirus genus contains HPV16, HPV31, HPV33, HPV35, HPV52, HPV58 and HPV67. These HPVs account for 75% of invasive cervical cancers worldwide. Viral variants of these HPVs differ in evolutionary history and pathogenicity. Moreover, a comprehensive nomenclature system for HPV variants is lacking, limiting comparisons between studies.DNA from cervical samples previously characterized for HPV type were obtained from multiple geographic regions to screen for novel variants. The complete 8 kb genomes of 120 variants representing the major and minor lineages of the HPV16-related alpha-9 HPV types were sequenced to capture maximum viral heterogeneity. Viral evolution was characterized by constructing phylogenic trees based on complete genomes using multiple algorithms. Maximal and viral region specific divergence was calculated by global and pairwise alignments. Variant lineages were classified and named using an alphanumeric system; the prototype genome was assigned to the A lineage for all types.The range of genome-genome sequence heterogeneity varied from 0.6% for HPV35 to 2.2% for HPV52 and included 1.4% for HPV31, 1.1% for HPV33, 1.7% for HPV58 and 1.1% for HPV67. Nucleotide differences of approximately 1.0% - 10.0% and 0.5%-1.0% of the complete genomes were used to define variant lineages and sublineages, respectively. Each gene/region differs in sequence diversity, from most variable to least variable: noncoding region 1 (NCR1) /noncoding region 2 (NCR2) >upstream regulatory region (URR)> E6/E7 > E2/L2 > E1/L1.These data define maximum viral genomic heterogeneity of HPV16-related alpha-9 HPV variants. The proposed nomenclature system facilitates the comparison of variants across epidemiological studies. Sequence diversity and phylogenies of this clinically important group of HPVs provides the basis for further studies of discrete viral evolution, epidemiology, pathogenesis and preventative/therapeutic interventions

ZIP8 Zinc Transporter: Indispensable Role for Both Multiple-Organ Organogenesis and Hematopoiesis In Utero

Previously this laboratory characterized Slc39a8-encoded ZIP8 as a Zn2+/(HCO3–)2 symporter; yet, the overall physiological importance of ZIP8 at the whole-organism level remains unclear. Herein we describe the phenotype of the hypomorphic Slc39a8(neo/neo) mouse which has retained the neomycin-resistance gene in intron 3, hence causing significantly decreased ZIP8 mRNA and protein levels in embryo, fetus, placenta, yolk sac, and several tissues of neonates. The Slc39a8(neo) allele is associated with diminished zinc and iron uptake in mouse fetal fibroblast and liver-derived cultures; consequently, Slc39a8(neo/neo) newborns exhibit diminished zinc and iron levels in several tissues. Slc39a8(neo/neo) homozygotes from gestational day(GD)-11.5 onward are pale, growth-stunted, and die between GD18.5 and 48 h postnatally. Defects include: severely hypoplastic spleen; hypoplasia of liver, kidney, lung, and lower limbs. Histologically, Slc39a8(neo/neo) neonates show decreased numbers of hematopoietic islands in yolk sac and liver. Low hemoglobin, hematocrit, red cell count, serum iron, and total iron-binding capacity confirmed severe anemia. Flow cytometry of fetal liver cells revealed the erythroid series strikingly affected in the hypomorph. Zinc-dependent 5-aminolevulinic acid dehydratase, required for heme synthesis, was not different between Slc39a8(+/+) and Slc39a8(neo/neo) offspring. To demonstrate further that the mouse phenotype is due to ZIP8 deficiency, we bred Slc39a8(+/neo) with BAC-transgenic BTZIP8-3 line (carrying three extra copies of the Slc39a8 allele); this cross generated viable Slc39a8(neo/neo)_BTZIP8-3(+/+) pups showing none of the above-mentioned congenital defects–proving Slc39a8(neo/neo) causes the described phenotype. Our study demonstrates that ZIP8-mediated zinc transport plays an unappreciated critical role during in utero and neonatal growth, organ morphogenesis, and hematopoiesis

Autoignition behavior of gasoline/ethanol blends at engine-relevant conditions

Ethanol is an attractive oxygenate increasingly used for blending with petroleum-derived gasoline yielding beneficial combustion and emissions behavior for a range of internal combustion engine schemes, including stoichiometric spark-ignition and low temperature combustion (LTC). As such, it is important to fundamentally understand the autoignition behavior of gasoline/ethanol blends. This work utilizes a rapid compression machine (RCM) and a homogeneous charge compression ignition (HCCI) engine to experimentally quantify changes in fuel reactivity, through ignition delay times and preliminary heat release, for blends of 0 to 30% vol./vol. into a full boiling range research gasoline (FACE-F). Diluted/stoichiometric and undiluted/fuel-lean conditions are explored covering a wide range of compressed temperatures and pressures relevant to conventional and advanced, gasoline combustion engines. Detailed chemical kinetic modeling is undertaken using a recently updated gasoline surrogate model in conjunction with a five-component surrogate to model the RCM experiments and provide chemical insight into the perturbative effects of ethanol on the autoignition process. The diluted/stoichiometric RCM measurements reveal that within the low-temperature regime ethanol retards first-stage and main ignition delay times, and suppresses both the rates and extents of low-temperature heat release (LTHR), while within the intermediate-temperature regime ethanol only causes slight changes. Good agreement of ignition delay time and preliminary heat release prediction is found between model and experimental results. Sensitivity and flux analyses further show that ethanol blending effects are dominated by the competition between the H-atom abstraction from ethanol and other fuel components by OH radical at low temperatures, and by HO2 radical at intermediate temperatures. These findings are consistent across both fuel loading conditions explored in this study. In addition, when HCCI engine experiments are mapped onto undiluted/lean RCM measurements under a constant combustion phasing scenario, good correspondence between the two apparatuses is observed for LTHR and start of high-temperature heat release. The current study highlights the importance of characterizing LTHR in predicting fuel behaviors in high-boost/low-temperature engines, and demonstrates that RCM experiments can provide an alternative, and more-efficient avenue for such characterization