一类生物流体力学模型的稳定性

在研究颅内压集中参数模型的基础上，改进自适应的龙格-库塔法对一类生物流体力学模型进行数值模拟。通过合理控制计算量，得到了微分方程近似解的局部截断误差的估计。使用矩阵特征值分析微分方程的稳定性，在实际生理范围内变化模型参数，得到特征值随参数变化的关系，指出模型中存在实部为正的特征值。文章还讨论了控制矩阵特征值的变化对数值方法稳定步长的影响，并得到步长的取值范围。通过理论分析。得到控制方程的解随时间的发展和模型中生理参数的选取相关。分析了特征值变化的稳定性和参数的关系，并对模型进行改进，讨论其稳定性的情况。     

Missing value imputation strategies for metabolomics data

The origin of missing values can be caused by different reasons and depending on these origins missing values should be considered differently and dealt with in different ways. In this research, four methods of imputation have been compared with respect to revealing their effects on the normality and variance of data, on statistical significance and on the approximation of a suitable threshold to accept missing data as truly missing. Additionally, the effects of different strategies for controlling familywise error rate or false discovery and how they work with the different strategies for missing value imputation have been evaluated. Missing values were found to affect normality and variance of data and k‐means nearest neighbour imputation was the best method tested for restoring this. Bonferroni correction was the best method for maximizing true positives and minimizing false positives and it was observed that as low as 40% missing data could be truly missing. The range between 40 and 70% missing values was defined as a “gray area” and therefore a strategy has been proposed that provides a balance between the optimal imputation strategy that was k‐means nearest neighbor and the best approximation of positioning real zeros.     

Enzyme-regulated the changes of pH values for assembling a colorimetric and multistage interconnection logic network with multiple readouts

Based on enzymatic reactions-triggered changes of pH values and biocomputing, a novel and multistage interconnection biological network with multiple easy-detectable signal outputs has been developed. Compared with traditional chemical computing, the enzyme-based biological system could overcome the interference between reactions or the incompatibility of individual computing gates and offer a unique opportunity to assemble multicomponent/multifunctional logic circuitries. Our system included four enzyme inputs: β-galactosidase (β-gal), glucose oxidase (GOx), esterase (Est) and urease (Ur). With the assistance of two signal transducers (gold nanoparticles and acid–base indicators) or pH meter, the outputs of the biological network could be conveniently read by the naked eyes. In contrast to current methods, the approach present here could realize cost-effective, label-free and colorimetric logic operations without complicated instrument. By designing a series of Boolean logic operations, we could logically make judgment of the compositions of the samples on the basis of visual output signals. Our work offered a promising paradigm for future biological computing technology and might be highly useful in future intelligent diagnostics, prodrug activation, smart drug delivery, process control, and electronic applications.     

Entire functions sharing one small function CM with their shifts and difference operators

In this article, we mainly devote to proving uniqueness results for entire functions sharing one small function CM with their shift and difference operator simultaneously. Let f(z) be a nonconstant entire function of finite order, c be a nonzero finite complex constant,and n be a positive integer. If f(z), f(z + c), and ?_c~n f(z) share 0 CM, then f(z + c) ≡ Af(z),where A(= 0) is a complex constant. Moreover, let a(z), b(z)( ≡ 0) ∈ S(f) be periodic entire functions with period c and if f(z)-a(z), f(z + c)-a(z), ?_c~n f(z)-b(z) share 0 CM, then f(z + c) ≡ f(z).     

Evaluation of a proficiency test on cadmium and lead in herbal material using assigned reference values

This paper presents an international proficiency testing program (APLAC T065) on two trace elements, cadmium and lead, in an herbal sample, Herba Desmodii Styracifolii. The program was registered with a total of 109 laboratories from 42 countries. The assigned reference values of the analytes for performance assessment were provided by the organizers using an accurate gravimetric isotope dilution inductively coupled plasma-mass spectrometry technique. z-Score was used as the numerical indicator to interpret participants' competence. The between-laboratory variations for cadmium and lead were respectively 18.7% and 19.8% and the consensus values were found to be consistent with the assigned reference values. Twenty-two participants gave at least one unsatisfactory z-score, but the performance of the majority of participants on the analysis of cadmium and lead in herbal matrix was generally good when compared with the assigned reference values.     

Element assessment in whole blood, serum and urine of three Italian healthy sub-populations by INAA

This research, that is a framework of a big project regarding the knowledge of human metabolism in patients affected by renal disease, is aimed to assess the levels of some selected essential (Co, Fe, K, Na, Rb, Se and Zn) and non-essential elements (Br Cr, Cs, Hg, Ni and Sb) in different biological matrices such as whole blood, serum and urine, of three Italian sub-populations.The analytical methodology involved is the Instrumental Neutron Activation Analysis (INAA), a primary analytical technique: the samples (totally 144) were irradiated in the Triga nuclear reactor at the R.C.-Casaccia ENEA for 12 h at a neutron flux of 2.6 × 10¹² n × cm^{− 2} × s^{− 1}.The results show a similar distribution for essential elements whereas quite different for non-essential elements. The statistical treatment has evidenced no differences among the samples grouping the subpopulations into unique one. In this way, the levels found can be considered “reference values” in the investigated matrices.     

A new biosynthetic tracer for the inline measurement of virus retention in membrane processes: part II. Biochemical and physicochemical characterizations of the new tracer

In a previous work, a reproducible procedure to produce a new biosynthetic tracer was developed. This new tracer is an MS2 bacteriophage with enzymatic probes grafted on its surface, which can induce enzymatic activity of the tracer. In this paper, the biochemical and physicochemical characteristics of this new tracer are determined. A protocol was developed to determine the specific enzymatic activity kcat_TRACER of the tracer, which was found to be 2.93 ± 0.78 × 10⁴ min⁻¹ on average. Physicochemical characterizations of this new tracer showed that it is representative of viruses and may thus be used as a virus surrogate to assess the virus retention of membrane systems inline. Notably, the mean diameter and molecular weight of the tracer were found to be respectively 64.1 ± 0.3 nm and 12140 ± 3654 kDa, which are within the size and molecular weight ranges of pathogenic viruses carried by water. The tracer surface was also studied and revealed the considerable porosity of the grafted probe layer, with a mean porosity of 88%, which could explain why the zeta potential of the tracers (−14.34 ± 1.66 mV) was nearly the same as that of the native MS2 phages. Finally, a comparison between filtration of the reference microorganism used for membrane performance assessment (the MS2 phage) and the tracer suspensions showed the same filtration behaviour.     

A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach

The Proper Generalized Decomposition (PGD) is a methodology initially proposed for the solution of partial differential equations (PDE) defined in tensor product spaces. It consists in constructing a separated representation of the solution of a given PDE. In this paper we consider the mathematical analysis of this framework for a larger class of problems in an abstract setting. In particular, we introduce a generalization of Eckart and Young theorem which allows to prove the convergence of the so-called progressive PGD for a large class of linear problems defined in tensor product Hilbert spaces.