A local limit theorem for the number of nodes,the height,and the number of final leaves in a critical branching process tree

Let Z_i be the number of particles in the ith generation of a non-degenerate critical Bienaymé-Galton-Watson process with offspring distribution $ p_r = P \{\hbox{a given individual has {\it r} children}\},\kern2em r\geq 0. $ Let ν = Σ^infinity₀ Z_j be the total progeny and let ζ = inf{r: Z_r = 0} be the extinction time. Equivalently, ν and ζ are the total number of nodes and (1 + the height), respectively, of the family tree of the branching process. Assume that E{Z₁} = Σ p_rr = 1 and E{Z₁^{3 + δ}} = Σ p_rr^{3 + δ} < infinity for some δ ϵ (0, 1). We find an asymptotic formula with remainder term for k⁴P{ζ = k + 1, Z_k = ℓ ν = n} when k→ infinity, which is uniform over n and ℓ. This is used to confirm a conjecture by Wilf that the number of leaves in the last generation of a randomly chosen rooted tree converges in distribution. More precisely, in the terminology introduced above, there exists a probability distribution {q₁} such that for n → infinity $ P\{Z_{\zeta-1} = l | \nu=n\} = q_l + O \left({{\log^3 n } \over {n^{1/2}}}\right), $ uniformly over ℓ ≥1. The limiting distribution is identified by means of a functional equation for the generating function Σ^infinity₁ q s^ℓ. Numerically, q₁ ≅ 0.0602, q₂ ≅ 0.248, q₃ ≅ 0.094, and q₄ ≅ 0.035. Our method can also be used to find lim _{k→ infinity} k⁴P{ζ = k + 1, Z_k = ℓ ν = n} when only E{Z₁^{2 + δ}} < infinity for some 0 ≤δ≤1, but we do not treat this case here; it goes without saying that the fewer moment assumptions one makes, the poorer the estimates become. © 1996 John Wiley & Sons, Inc.     

Hybrid Chelator-Based PSMA Radiopharmaceuticals: Translational Approach

(1) Background: Prostate-specific membrane antigen (PSMA) has been extensively studied in the last decade. It became a promising biological target in the diagnosis and therapy of PSMA-expressing cancer diseases. Although there are several radiolabeled PSMA inhibitors available, the search for new compounds with improved pharmacokinetic properties and simplified synthesis is still ongoing. In this study, we developed PSMA ligands with two different hybrid chelators and a modified linker. Both compounds have displayed a promising pharmacokinetic profile. (2) Methods: DATA^5m.SA.KuE and AAZTA⁵.SA.KuE were synthesized. DATA^5m.SA.KuE was labeled with gallium-68 and radiochemical yields of various amounts of precursor at different temperatures were determined. Complex stability in phosphate-buffered saline (PBS) and human serum (HS) was examined at 37 °C. Binding affinity and internalization ratio were determined in in vitro assays using PSMA-positive LNCaP cells. Tumor accumulation and biodistribution were evaluated in vivo and ex vivo using an LNCaP Balb/c nude mouse model. All experiments were conducted with PSMA-11 as reference. (3) Results: DATA^5m.SA.KuE was synthesized successfully. AAZTA⁵.SA.KuE was synthesized and labeled according to the literature. Radiolabeling of DATA^5m.SA.KuE with gallium-68 was performed in ammonium acetate buffer (1 M, pH 5.5). High radiochemical yields (>98%) were obtained with 5 nmol at 70 °C, 15 nmol at 50 °C, and 60 nmol (50 µg) at room temperature. [⁶⁸Ga]Ga-DATA^5m.SA.KuE was stable in human serum as well as in PBS after 120 min. PSMA binding affinities of AAZTA⁵.SA.KuE and DATA^5m.SA.KuE were in the nanomolar range. PSMA-specific internalization ratio was comparable to PSMA-11. In vivo and ex vivo studies of [¹⁷⁷Lu]Lu-AAZTA⁵.SA.KuE, [⁴⁴Sc]Sc-AAZTA⁵.SA.KuE and [⁶⁸Ga]Ga-DATA^5m.SA.KuE displayed specific accumulation in the tumor along with fast clearance and reduced off-target uptake. (4) Conclusions: Both KuE-conjugates showed promising properties especially in vivo allowing for translational theranostic use.     

A new strategy for the discovery of epimedium metabolites using high-performance liquid chromatography with high resolution mass spectrometry

In this paper, a new strategy of drug metabolite discovery and identification was established using high-performance liquid chromatography with high resolution mass spectrometry (HPLC–HRMS) and a mass spectral trees similarity filter (MTSF) technique. The MTSF technique was developed as a means to rapidly discover comprehensive metabolites from multiple active components in a complicated biological matrix. Using full-scan mass spectra as the stem and data-dependent subsequent stage mass spectra to form branches, the HRMS and multiple-stage mass spectrometric data from detected compounds were converted to mass spectral trees data. Potential metabolites were discovered based on the similarity between their mass spectral trees and that known compounds or metabolites in a mass spectra trees library. The threshold value for match similarity scores was set at above 200, allowing approximately 80% of interference to be filtered out. A total of 115 metabolites of five flavonoid monomers (epimedin A, epimedin B, epimedin C, icariin, and baohuoside I) and herbal extract of epimedium were discovered and identified in rats via this new strategy. As a result, a metabolic profile for epimedium was obtained and a metabolic pathway was proposed. In addition, comparing to the widely used neutral loss filter (NLF), product ion filter (PIF), and mass defect filter (MDF) techniques, the MTSF technique was shown superior efficiency and selectivity for discovering and identifying metabolites in traditional Chinese medicine (TCM).     

毛细管电泳核酸分析用于重大疾病诊断的研究

对毛细管电泳核酸（包括基因和核苷）分析在重大疾病诊断中的应用作了较为详细的论述,同时概括了相关的毛细管电泳方法和聚合酶链反应,并对今后的工作作了展望。     

近期微流控芯片疾病诊断技术的研究进展

微流控芯片具有液流可控、样品消耗量小、反应速度快、易于集成化等特点,在临床诊断和疾病筛查领域具有广阔的发展前景。本文针对近年来微流控芯片技术在疾病诊断方面的最新研究进展,从疾病标志物检测、细胞筛选和药物代谢研究及疾病诊断微流控芯片装置的发展现状等方面概述其在疾病诊断方面的应用和发展。     

滚动轴承早期故障的小波诊断方法

利用包络分析结合小波变换抽取强背景噪声下滚动轴承振动信号中的故障信息,对滚动轴承早期故障进行诊断,对五套３０７号轴承进行的成功诊断表明,提出的方法准确有效,适用于滚动轴承的在线监测与诊断。     

捷联惯性导航系统中二自由度陀螺故障的智能诊断

本文介绍了神经网络的联想记忆功能,讨论了四陀螺的最佳配置,并提出了基于Ｈｏｐ ｆｉｅｌｄ 网络的余度陀螺故障检测与隔离的设计方法,该方法具有较强的抗噪声能力。     

新型二维材料MXene在生物医学的应用

MXene是一类新型的二维过渡金属碳化物和氮化物的总称,通式为M_{n + 1}X_nT_x(n = 1~3),其中M为前过渡金属元素,X为碳或氮元素,T指键合在该材料表面的氟基、羟基或氧基等活性官能团。该类材料具有超薄的结构和出色的物理化学(电子、光学、磁性等)特性,从而吸引了各领域研究人员的广泛兴趣。目前,MXene在生物医学领域的应用逐渐拓展。这主要是由于其大的表面积和在近红外区域的强吸收,加之其可以通过容易的表面修饰与多种分子或者纳米颗粒结合。在这篇综述中,我们总结了MXene在生物医学应用中的最新进展。文章首先介绍MXene的相关制备方法和表面改性手段;之后重点围绕其独特的理化性质,依次介绍该材料在抗菌材料、生物成像、肿瘤诊断治疗和生物传感等生物医学领域中的应用进展;文章最后总结讨论了MXene在生物医学应用方面面临的挑战和新机遇。预期超薄MXene及精巧设计的纳米复合物将成为多种生物医学应用的最有吸引力的生物相容性无机纳米平台之一。     

机器学习在心血管疾病辅助诊断中的研究:现状与未来进展

心血管疾病具有高发病率、高住院率、高致残率、高死亡率等特征,伴随高额的治疗疾病负担,早期准确诊断心血管疾病意义重大.以机器学习(ML)为代表的人工智能心血管疾病辅助诊断技术为诊断心血管疾病提供了新方法.基于ML疾病诊断技术日趋成熟,且在各类心血管疾病中取得诸多进展,包括冠心病、心力衰竭及心律失常等.本文综述了ML在心血管疾病辅助诊断中的技术背景和研究现状,分析了该领域在临床转化应用方面的挑战,并对未来研究进行了展望.     

树的L(3,2,1)-标号问题

An L(3,2,1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all non-negative integers(labels) such that |f(u)-f(v)|≥3 if d(u,v)=1,|f(u)-f(v)≥2 if d(u,v)=2 and |f(u)-f(v)|≥1 if d(u,v)=3.For a non-negative integer k,a k-L(3,2,1)-labeling is an L(3,2,1)-labeling such that no label is greater than k.The L(3,2,1)-labeling number of G,denoted by λ_(3,2,1)(G), is the smallest number k such that G has a k-L(3,2,1)-labeling.In this article,we characterize the L(3,2,1)-labeling numbers of trees with diameter at most 6.