Characterization of metabolites of tanshinone IIA in rats by liquid chromatography/tandem mass spectrometry

The metabolism of tanshinone IIA was studied in rats after a single-dose intravenous administration. In the present study, 12 metabolites of tanshinone IIA were identified in rat bile, urine and feces with two LC gradients using LC-MS/MS. Seven phase I metabolites and five phase II metabolites of tanshinone IIA were characterized and their molecular structures proposed on the basis of the characteristics of their precursor ions, product ions and chromatographic retention time. The seven phase I metabolites were formed, through two main metabolic routes, which were hydroxylation and dehydrogenation metabolism. M1, M4, M5 and M6 were supposedly tanshinone IIB, hydroxytanshinone IIA, przewaquinone A and dehydrotanshinone IIA, respectively, by comparing their HPLC retention times and mass spectral patterns with those of the standard compounds. The five phase II metabolites identified in this research were all glucuronide conjugates, all of which showed a neutral loss of 176 Da. M9 and M12 were more abundant than other identified metabolites in the bile, which was the main excretion path of tanshinone IIA and the metabolites. M12 was the main metabolite of tanshinone IIA. M9 and M12 were proposed to be the glucuronide conjugates of two different semiquinones and these semiquinones were the hydrogenation products of dehydrotanshinone IIA and tanshinone IIA, respectively. This hydrogenized reaction may be catalyzed by the NAD(P)H: quinone acceptor oxidoreductase (NQO). The biotransformation pathways of tanshinone IIA were proposed on the basis of this research.     

The recognition of similarities in trace elements content in medicinal plants using MLP and RBF neural networks

The objective of the paper was to verify if the content of some elements provides enough information for proper classification of the medicinal plant raw materials. Such information could be helpful in standardization process of herbal products. Four elements—zinc, copper, lead and cadmium were determined using inverse voltammetry in commercially available medicinal herbal raw materials. Initially, principal component analysis (PCA) was employed to investigate the relationships among the analyzed trace elements. In the next stage of the study, two different types of feed-forward artificial neural networks (FANNs)—multilayer perceptron (MLP) and radial basis function (RBF) were applied. The concentrations of the elements were used as input variables to neural networks models, which were to recognize the taxonomy of the plant and the anatomical part it originated from. Although full recognition of the samples with use of FANNs on the basis of some trace elements content was not achieved, it was possible to identify two elements—cadmium and lead as the most important in the classification analysis of medicinal plants.     

Non-self-adjoint Jacobi matrices with a rank-one imaginary part

We develop direct and inverse spectral analysis for finite and semi-infinite non-self-adjoint Jacobi matrices with a rank-one imaginary part. It is shown that given a set of n not necessarily distinct nonreal numbers in the open upper (lower) half-plane uniquely determines an n×n Jacobi matrix with a rank-one imaginary part having those numbers as its eigenvalues counting algebraic multiplicity. Algorithms of reconstruction for such finite Jacobi matrices are presented. A new model complementing the well-known Livsic triangular model for bounded linear operators with a rank-one imaginary part is obtained. It turns out that the model operator is a non-self-adjoint Jacobi matrix. We show that any bounded, prime, non-self-adjoint linear operator with a rank-one imaginary part acting on some finite-dimensional (respectively separable infinite-dimensional Hilbert space) is unitarily equivalent to a finite (respectively semi-infinite) non-self-adjoint Jacobi matrix. This obtained theorem strengthens a classical result of Stone established for self-adjoint operators with simple spectrum. We establish the non-self-adjoint analogs of the Hochstadt and Gesztesy-Simon uniqueness theorems for finite Jacobi matrices with nonreal eigenvalues as well as an extension and refinement of these theorems for finite non-self-adjoint tri-diagonal matrices to the case of mixed eigenvalues, real and nonreal. A unique Jacobi matrix, unitarily equivalent to the operator of integration in the Hilbert space L₂[0,l] is found as well as spectral properties of its perturbations and connections with the well-known Bernoulli numbers. We also give the analytic characterization of the Weyl functions of dissipative Jacobi matrices with a rank-one imaginary part.     

Inverse scattering for the magnetic Schrödinger operator

We show that fixed energy scattering measurements for the magnetic Schrödinger operator uniquely determine the magnetic field and electric potential in dimensions n?3. The magnetic potential, its first derivatives, and the electric potential are assumed to be exponentially decaying. This improves an earlier result of Eskin and Ralston (1995) [5] which considered potentials with many derivatives. The proof is close to arguments in inverse boundary problems, and is based on constructing complex geometrical optics solutions to the Schrödinger equation via a pseudodifferential conjugation argument.     

The h-Laplace and q-Laplace transforms

Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the particular concepts of the h-Laplace and q-Laplace transforms. The convolution and inversion problems for these transforms are considered in some detail.     

Resource-saving infinite-horizon tracking under uncertain input

A feedback controller for approximate tracking a prescribed trajectory of an inaccurately observed dynamical system effected by uncertain non-observable input disturbances over an infinite time interval is constructed. The controller is “resource-saving” in a sense that control resources spent for approximate tracking do not exceed (with some small gaps) those needed for exact tracking in an “ideal” situation where the current values of the input disturbance are fully observable.     

Inverse integer optimization with an imperfect observation

This study develops and evaluates methods for inverse integer optimization problems with an imperfect observation where the unknown parameters are the cost coefficients. We propose a cutting plane algorithm for this problem and compare it to a heuristic which solves the inverse of the linear relaxation of the forward problem. We then propose a hybrid approach that initializes the cutting plane algorithm from the solution of the heuristic.     

Optimal strategies for mitigating the HIV/AIDS epidemic in the Philippines

The human immunodeficiency virus (HIV) impairs a person's immune system against many infections and some types of cancer, leading to acquired immunodeficiency syndrome (AIDS), which is characterized by severe illnesses. The number of HIV infections in the Philippines has increased, more than doubled, within the last decade. This alarming HIV crisis in the country requires urgent actions. In this study, a mathematical model is developed to describe the disease transmission in the Philippines. Disease-free and endemic equilibria are obtained, stability analysis is performed, and the basic reproduction number is computed. Sensitivity analyses and subset selection are performed to identify influential parameters and to determine an identifiable parameter set given measurements, respectively. Available data on the number of asymptomatic aware infectious, those who are in the AIDS stage, and those under treatment are utilized to estimate key epidemiological parameters such as transmission, treatment, and screening rates. Uncertainty of these parameter estimates is quantified through bootstrapping method. Furthermore, intervention strategies are investigated in the framework of optimal control theory. Control measures include precaution, HIV screening, antiretroviral treatment, and pre-exposure prophylaxis (PrEP) treatment. These various control efforts are compared with regard to cost efficiency and effectiveness in reducing the number of infected individuals. Given limited available control measures, the PrEP-only scenario is shown to be the most cost-effective, followed by other scenarios that combine PrEP with other controls.     

Studies on the Interaction Mechanism between the mRNA Vaccine against SARS-CoV-2 and the Immune System

Vaccines are an effective tool in the fight against infectious diseases. However, mathematical models of SARS-CoV-2 focus on the macroscopic situation, while articles on vaccines focus on effectiveness and safety. We develop four mathematical models to investigate the immune system and the microdynamics of antigens and viruses in individuals injected with mRNA vaccines. We first theoretically analyze the optimal model, calculate all equilibria, and prove that the disease-free equilibrium is globally asymptotically stable while the others are unstable. This suggests that after a certain period after vaccination, the infected cells and antigens will no longer exist in vivo and will be eliminated by the immune system over time or will die naturally. This theoretically proves the safety of the mRNA vaccines. Then, we use the differential algebra to analyze the structural identifiability of the models. We find that two of them are globally identifiable while the other two are unidentifiable, but once a certain parameter is fixed, then they are identifiable as well. To select the optimal model among four models, we use the Affine Invariant Ensemble Markov Chain Monte Carlo algorithm for data fitting and parameter estimation. We find that the roles of memory cells in killing infected cells and promoting immune cells and neutralizing antibodies in the process of mRNA vaccination are not significant and can be ignored in the modeling. On the other hand, the innate immunity of the human body plays an important role in this process. In addition, we also analyze the practical identifiability of the parameters of the optimal model. The results show that even if the structure of the system is globally identifiable, it does not ensure that all the parameters are practically identifiable. After random sampling and simulating the four unidentifiable parameters, we find that only two variables, infected cells II and antibodies, are sensitive to these unidentifiable parameters, but the results are still within acceptable ranges. This suggests that our fitting results are generally reliable. Finally, we simulate multiple booster injections and find that booster injections are indeed effective in maintaining antibody levels in vivo, which could otherwise gradually die off over time. Therefore, booster injections are beneficial to help the human body increase and maintain immunity.     

基于弹性力学第一性原理的数据驱动力学建模

提出了一种基于弹性力学第一性原理的数据驱动力学建模方法,其能够从基于弹性力学方程的数值计算结果建立简洁且能准确捕捉变形机制的力学模型。基于有限元计算得到的高精度数据和无监督数据驱动控制方程识别方法Seq-SVF,从梁的载荷和位移数据中自动识别出了Timoshenko梁形式的弯曲控制微分方程,得到了三种不同加载条件下剪切影响系数关于结构尺寸和力学参数的函数表达式。揭示了经典模型适用的加载条件,同时还给出了一种未发现的新模型。通过将基于弹性力学的第一性原理计算与数据驱动范式相结合,克服了传统建模方法的局限性和对人类经验的强依赖性,为建立简洁的力学模型提供了一种新途径。