Trees with the most subtrees -- an algorithmic approach

When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in applications. The number of subtrees in the extremal cases constitute sequences which are of interest to number theorists. The structures which maximize or minimize the number of subtrees among general trees, binary trees and trees with a given maximum degree have been identified previously. Most recently, results of this nature are generalized to trees with a given degree sequence. In this note, we characterize the trees which maximize the number of subtrees among trees of a given order and degree sequence. Instead of using theoretical arguments, we take an algorithmic approach that explicitly describes the process of achieving an extremal tree from any random tree. The result also leads to some interesting questions and provides insight on finding the trees close to extremal and their numbers of subtrees.Comment: 12 pages, 7 figures; Journal of combinatorics, 201

Schwarz Lemma and Schwarz-Pick Lemma for solutions of the α\alpha-harmonic equation

In this paper, the Schwarz type and Schwarz-Pick type inequalities for solutions of $\alpha$-harmonic equation for $\alpha>-1$ are investigated. By making use of the integral of trigonometric functions, we obtain the two types of inequalities in terms of hypergeometric functions which improve the corresponding results due to Khalfallah et al. (Complex Var. Elliptic Equ., 2023) and Li et al. (Bull. Malays. Math. Sci. Soc., 2022).Comment: 14 pages, 1 figur

Expressions of toll-like receptors 2 and 4, and relative cellular factors in HIV patients with tuberculosis infection

Purpose: To investigate the expressions of toll-like receptor 2 (TLR2), toll-like receptor 4 (TLR4), tumor necrosis factor alpha (TNF-α), IFN-γ (IFN- gamma), interleukin 2 (IL-2), interleukin 6 (IL-6) and interleukin 10 (IL-10) in human immunodeficiency virus (HIV) patients with tuberculosis (TB) infection.Methods: Two groups of HIV patients (68 in each group) were used for this study. These were HIV with TB (HIV/TB) group and HIV without TB group. A third group (68 healthy people) served as control. Quantitative polymerase chain reaction (qPCR) was adopted to measure TLR-2 and TLR-4 expressions in peripheral blood mononuclear cells (PBMC), while the serum levels of TNF-α, IFN-γ, IL-2, IL-6 and IL-10 were determined by ELISA.Results: The △Ct values of TLR-2 and TLR-4 in HIV/TB and HIV groups were significantly lower than those in the control group (p < 0.05). Compared to control group, the serum levels of TNF-α, IL-6 and IL-10 significantly increased, while IFN-γ and IL-2 in HIV/TB and HIV groups significantly decreased (p < 0.05). However, IFN-γ and IL-2 decreased significantly in HIV/TB group (p < 0.05). Expression of TLR2 correlated positively with serum levels of TNF-α, IL-6 and IL-10, but negatively with IFN-γ and IL-2 (p < 0.05).Conclusion: TLR2 signal pathway plays a role in HIV patients with TB infection by promoting the expressions of TNF-α, IL-6 and IL-10, while inhibiting IFN-γ and IL-2 cellular factors, and thus may provide a new pathway for the treatment of patients with HIV/TB.Keywords: HIV, Tuberculosis, Toll-like receptor, Cellular factors, Tumor necrosis factor, Interleuki

Species-specific and needle age-related responses of photosynthesis in two Pinus species to long-term exposure to elevated CO2 concentration

There is, so far, no common conclusion about photosynthetic responses of trees to long-term exposure to elevated CO2. Photosynthesis and specific leaf area (SLA) of 1-year-old and current-year needles in Pinus koraiensis and P. sylvestriformis grown in open-top chambers were measured monthly for consecutive two growing seasons (2006, 2007) after 8-9years of CO2 enrichment in northeastern China, to better understand species-specific and needle age-related responses to elevated CO2 (500μmolmol−1CO2). The light-saturated photosynthetic rates (P Nsat) increased in both species at elevated CO2, but the stimulation magnitude varied with species and needle age. Photosynthetic acclimation to elevated CO2, in terms of reduced V cmax (maximum carboxylation rate) and J max (maximum electron transport rate), was found in P. koraiensis but not in P. sylvestriformis. The photosynthetic parameters (V cmax, J max, P Nsat) measured in different-aged needles within each species responded to elevated CO2 similarly, but elevated CO2 resulted in much pronounced variations of those parameters in current-year needles than in 1-year-old needles within each species. This result indicated that needle age affects the magnitude but not the patterns of photosynthetic responses to long-term CO2 enrichment. The present study indicated that different species associated with different physioecological properties responded to elevated CO2 differently. As global change and CO2 enrichment is more or less a gradual rather than an abrupt process, long-term global change experiments with different plant species are still needed to character and better predict the global change effects on terrestrial ecosystem

Prognostic value of vitamin D in patients with pneumonia: A systematic review and meta-analysis

Purpose: To investigate the prognostic role of vitamin D in pneumonia patients  through meta-analysis.Methods: PubMed and Embase were systematically searched for relevant studies that assessed the impact of vitamin D on the risk of adverse outcomes among patients with pneumonia. Risk ratios (RR) with 95 % confidence intervals (95 % CI) were pooled using meta-analysis. Q-test and I2 statistics were used to evaluate between-study heterogeneity.Results: Six studies were finally included in the meta-analysis. The results of meta-analysis of these studies indicated that low vitamin D status was associated with higher risk of mortality among pneumonia patients (RR = 2.59, 95 % CI = 1.32-5.08; p = 0.005). Results from meta-analysis of studies with adjusted estimates suggest that low vitamin D status was independently associated with higher risk of mortality among pneumonia patients (RR = 3.15, 95 % CI 1.54-6.44, p = 0.002). There was no significant risk of bias in the meta-analysis.Conclusion: This study demonstrates that low vitamin D level is associated with a higher risk of adverse outcomes in patients with pneumonia.Keywords: Pneumonia, Vitamin D, Prognosis, Meta-analysis, Systematic revie

3,3′-Dibromo-5,5′-bis­[(S)-l-menth­yloxy]-4,4′-(hexane-1,6-diyldiimino)difuran-2(5H)-one

The title compound, C34H54Br2N2O6, was obtained by the Michael addition–elimination reaction of (5S)-5-(l-menthyl­oxy)-3,4-dibromo­furan-2(5H)-one with 1,6-hexa­nediamine in the presence of triethyl­amine. The crystal structure contains two chiral five-membered furan­one rings, in twist and envelope conformations, and two six-membered cyclo­hexane rings in chair conformations

Mobility Census for the analysis of rapid urban development

Traditionally urban structure and development are monitored using infrequent high-quality datasets such as censuses. However, human culture is accelerating and aggregating, leading to ever-larger cities and an increased pace of urban development. Our modern interconnected world also provides us with new data sources that can be leveraged in the study of cities. However, these often noisy and unstructured sources of big data pose new challenges. Here we propose a method to extract meaningful explanatory variables and classifications from such data. Using movement data from Beijing, which is produced as a byproduct of mobile communication, we show that meaningful features can be extracted, revealing for example the emergence and absorption of subcenters. In the future this method will allow the analysis of urban dynamics at a high spatial resolution (here, 500m) and near real-time frequency

1-Butyl-3-(1-naphthyl­meth­yl)benzimidazolium hemi{di-μ-iodido-bis­[diiodidomercurate(II)]} dimethyl sulfoxide monosolvate

In the title compound, (C22H23N2)[Hg2I6]0.5·(CH3)2SO, the 1-butyl-3-(1-naphthyl­meth­yl)benzimidazolium anion lies across a centre of inversion. The dihedral angle between the benzimidazolium and naphthalene ring systems is 81.9 (3)°. In the crystal structure, π–π stacking inter­actions are observed between the imidazolium ring and the unsubstituted benzene ring of the naphthalene ring system, with a centroid–centroid separation of 3.510 (5) Å. In the centrosymmetric anion, the Hg(II) atoms are in a distorted tetrahedral coordination. The dimethyl sulfoxide solvent mol­ecule is disordered over two sites with occupancies of 0.615 (9) and 0.385 (9)

N-[(2S)-4-Chloro-2-(l-menthyloxy)-5-oxo-2,5-dihydro-3-furyl]-l-alanine

The title compound, C17H26ClNO5, was prepared via a tandem asymmetric Michael addition–elimination reaction of (5S)-3,4-dichloro-5-(l-menth­yloxy)furan-2(5H)-­one and l-alanine in the presence of potassium hydroxide. The five-membered furan­one ring is approximately planar while the six-membered menth­yloxy ring adopts a chair conformation. The crystal packing is stabilized by inter­molecular O—H⋯O and N—H⋯O hydrogen bonds