中立型Caputo分数阶泛函微分方程解的存在性和Hyers-Ulam稳定性

考虑具有无穷时滞和多个Caputo分数阶导数的中立型分数阶泛函微分方程解的存在性和Hyers-Ulam稳定性。利用压缩映射原理及无穷时滞的相空间理论得到方程解的存在性,并利用分数阶微积分的广义Gronwal型不等式及分数阶积分算子的单调性得到解的Hyers-Ulam稳定性。

Differential diagnosis of Crohn’s disease and intestinal tuberculosis based on ATR-FTIR spectroscopy combined with machine learning

BACKGROUND Crohn’s disease(CD)is often misdiagnosed as intestinal tuberculosis(ITB).However,the treatment and prognosis of these two diseases are dramatically different.Therefore,it is important to develop a method to identify CD and ITB with high accuracy,specificity,and speed.AIM To develop a method to identify CD and ITB with high accuracy,specificity,and speed.METHODS A total of 72 paraffin wax-embedded tissue sections were pathologically and clinically diagnosed as CD or ITB.Paraffin wax-embedded tissue sections were attached to a metal coating and measured using attenuated total reflectance fourier transform infrared spectroscopy at mid-infrared wavelengths combined with XGBoost for differential diagnosis.RESULTS The results showed that the paraffin wax-embedded specimens of CD and ITB were significantly different in their spectral signals at 1074 cm^(-1) and 1234 cm^(-1) bands,and the differential diagnosis model based on spectral characteristics combined with machine learning showed accuracy,specificity,and sensitivity of 91.84%,92.59%,and 90.90%,respectively,for the differential diagnosis of CD and ITB.CONCLUSION Information on the mid-infrared region can reveal the different histological components of CD and ITB at the molecular level,and spectral analysis combined with machine learning to establish a diagnostic model is expected to become a new method for the differential diagnosis of CD and ITB.

Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.

一类ψ-Caputo分数阶微分方程解的存在性和Ulam-Hyers稳定性

主要讨论在有限闭区间[a,b]上关于另一个函数的非线性Caputo分数阶微分方程.首先,给出了初值问题解的存在性和唯一性的充分条件.其次,利用Krasnoselskii不动点定理证明了该方程解的存在唯一性.最后,分两种情况讨论了系统的Ulam-Hyers-Rassias稳定性.

Genetic diversity and differentiation of the Dybowski's frog(Rana dybowskii) in Northeast China

The genetic diversity and population structure of the Dybowski＇s frog（Rana dybowskii） were investigated by using 11 polymorphic microsatellite loci.Total 75 individuals were sampled from six populations in Lesser Khingan Mountains and Changbai Mountains,China.Results showed that allele number of the 11 microsatellite loci was in the range of 2-10 in all populations,with the mean of 5.6.The average expected heterozygosity（HE） was 0.572,indicating a moderate polymorphism.The results of genetic differentiation coefficient（FST） showed that population genetic differentiation was significant between Changbai and Lesser Khingan Mountains（p〈0.001）.This result was verified further by Nei＇s genetic distance（DA） based on UPGMA phy-logenetic trees and by AMOVA analysis.In conclusion,the populations distributed in Lesser Khingan Mountains and Changbai Mountain are proposed to be two distinct management units（MUs） for their protection and management.

基于GPU的大状态密码S盒差分性质评估方法

大状态的密码S盒能够为对称密码算法提供更好的混淆性,但对大状态S盒的性质评估开销巨大。为高效评估大状态密码S盒的差分性质,提出基于GPU并行计算的大状态密码S盒差分性质评估方法。该方法基于现有的差分均匀度计算方法,针对16比特S盒的差分均匀度和32比特S盒的差分性质,分别设计GPU并行方案,通过优化GPU并行粒度和负载均衡提高了核函数和GPU的执行效率,并缩短了计算时间。测试结果表明,相较于CPU方法和GPU并行方法,所提方法大幅降低了大状态S盒差分性质评估的计算时间,提高了对大状态S盒差分性质的评估效率:对16比特S盒差分均匀度的计算时间为0.3 min;对32比特S盒的单个输入差分的最大输出差分概率计算时间约5 min,对它的差分性质计算时间约2.6 h。

混合差分和多种群粒子群算法的T-S模糊模型辨识

为提高T-S模型的辨识精度,针对基本粒子群优化(particle swarm optimization,PSO)算法T-S模型全局优化辨识问题,提出混合差分和多种群粒子群算法的T-S模糊模型辨识方法,将T-S模型前件参数和后件参数整体编码进行全局优化辨识.为避免基本粒子群的早熟收敛和后期收敛速度慢的缺陷对T-S模型辨识精度和速度的影响,算法将种群分为若干个子群,每个子群根据粒子适应度值自适应调整惯性权重,平衡了算法的开发和探索能力,对子群最优粒子,进行差分操作以增强算法的全局搜索能力,采用全局最优粒子替代随机子群的最优粒子以加强子群间的信息交流,维持粒子多样性.典型非线性系统和混沌系统的仿真结果表明,采用混合差分和多种群粒子群算法辨识的T-S模型具有更高的辨识精度.

On the partial stability of nonlinear impulsive Caputo fractional systems

In this work,stability with respect to part of the variables of nonlinear impulsive Caputo fractional differential equations is investigated.Some effective sufficient conditions of stability,uniform stability,asymptotic uniform stability and Mittag Leffler stability.The approach presented is based on the specially introduced piecewise continuous Lyapunov functions.Furthermore,some numerical examples are given to show the effectiveness of our obtained theoretical results.

On Time Fractional Partial Differential Equations and Their Solution by Certain Formable Transform Decomposition Method

This paper aims to investigate a new efficient method for solving time fractional partial differential equations.In this orientation,a reliable formable transform decomposition method has been designed and developed,which is a novel combination of the formable integral transform and the decomposition method.Basically,certain accurate solutions for time-fractional partial differential equations have been presented.Themethod under concern demandsmore simple calculations and fewer efforts compared to the existingmethods.Besides,the posed formable transformdecompositionmethod has been utilized to yield a series solution for given fractional partial differential equations.Moreover,several interesting formulas relevant to the formable integral transform are applied to fractional operators which are performed as an excellent application to the existing theory.Furthermore,the formable transform decomposition method has been employed for finding a series solution to a time-fractional Klein-Gordon equation.Over and above,some numerical simulations are also provided to ensure reliability and accuracy of the new approach.

On Fractional Differential Inclusion for an EpidemicModel via L-Fuzzy Fixed Point Results

The real world is filled with uncertainty,vagueness,and imprecision.The concepts we meet in everyday life are vague rather than precise.In real-world situations,if a model requires that conclusions drawn from it have some bearings on reality,then two major problems immediately arise,viz.real situations are not usually crisp and deterministic;complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously,process and understand.Conventional mathematical tools which require all inferences to be exact,are not always efficient to handle imprecisions in a wide variety of practical situations.Following the latter development,a lot of attention has been paid to examining novel L-fuzzy analogues of conventional functional equations and their various applications.In this paper,new coincidence point results for single-valued mappings and an L-fuzzy set-valued map in metric spaces are proposed.Regarding novelty and generality,the obtained invariant point notions are compared with some well-known related concepts via non-trivial examples.It is observed that our principal results subsume and refine some important ones in the corresponding domains.As an application,one of our results is utilized to discussmore general existence conditions for realizing the solutions of a non-integer order inclusion model for COVID-19.

Comparison of human amniotic fluid-derived and umbilical cord Wharton＇s Jelly-derived mesenchymal stromal cells： Characterization and myocardial differentiation capacity

Objective To compare the characterization and myocardial differentiation capacity of arnniotic fluid-derived mesenchymal stromal cells （AF MSCs） and umbilical cord Wharton＇s Jelly-derived mesenchymal stromal cells （WJ MSCs）. Methods The human AF MSCs were cultured from amniotic fluid samples obtained by amniocentesis. The umbilical cord WJ MSCs were obtained from Wharton＇s Jelly of umbilical cords of infants delivered full-term by normal labor. The morphology, growth curves, and analyses by flow cytometry of cell surface markers were compared between the two types of cells. Myocardial genes （GATA-4, c-TnT, a-actin, and Cx43） were detected by real-time PCR and the corresponding protein expressions were detected by Western blot analysis after myocardial induced in AF MSCs and WJ MSCs. Results Our findings revealed AF MSCs and WJ MSCs shared similar morphological characteristics of the fibroblastoid shape. The AF MSCs were easily obtained than the WJ MSCs and had a shorter time to reach adherence of 2.7 ± 1.6 days to WJ MSCs of 6.5 ± 1.8 days. The growth curves by MTT cytotoxic assay showed the AF MSCs had a similar proliferative capacity at passage 5 and passage 10. However, the proliferative capacities ofWJ MSCs were decreased at 5 passage relative to 10 passage. Both AF stem cells and WJ stem cells had the characteristics of mesenchymal stromal cells with some characteristics of embryonic stem cells. They express CD29 and CD105, but not CD34. They were positive for Class I major histocompatibility （MHC I） antigens （HLA-ABC）, and were negative, or mildly positive, for MHC Class II （HLA-DR） antigen. Oct-4 was positive in all the two cells types. Both AF MSCs and WJ MSCs could differentiate along myocardium. The differentiation capacities were detected by the expression of GATA-4, c-TnT, a-actin, Cx43 after myocardial induction. Conclusions Both AF MSCs and WJ MSCs have the potential clinical application for myogenesis in cardiac regenerative therapy.

Thyroid carcinoma showing thymus-like differentiation: Case presentation of a young man

Ectopic thymic tissue can be present in the thyroid gland and a carcinoma showing thymus-like differentiation(CASTLE) may arise from such tissue. We are reported the case of a 26-year-old man with CASTLE, with cervical subcutaneous nodules relapse, who showed a good response to treatment with surgery, chemotherapy and radiotherapy. The problematic aspect of this case was the diagnosis; only on review were we able to make a final diagnosis. CASTLE is a very rare neoplasm. It is important to differentiate this cancer from others tumors such as primary or metastatic squamous cell carcinoma of the head and neck or squamous cell thyroid carcinoma, because the therapy and prognosis are different.Diagnosis is complicated and requires careful histological analysis(CD5- and P63-positive with presence of Hassall's corpuscles); unfortunately there is no gold standard treatment so, in this case, we administered a sandwich of chemotherapy and radiotherapy.

Caveolin-1 downregulation promotes the dopaminergic neuron-like differentiation of human adipose-derived mesenchymal stem cells

Previous studies have shown that caveolin-1 is involved in regulating the differentiation of mesenchymal stem cells.However,its role in the differentiation of human adipose mesenchymal stem cells into dopaminergic neurons remains unclear.The aim of this study was to investigate whether caveolin-1 regulates the differentiation of human adipose mesenchymal stem cells into dopaminergic-like neurons.We also examined whether the expression of caveolin-1 could be modulated by RNA interference technology to promote the differentiation of human adipose mesenchymal stem cells into dopaminergic-like neurons.The differentiation of human adipose mesenchymal stem cells into dopaminergic neurons was evaluated morphologically and by examining expression of the markers tyrosine hydroxylase,Lmx1a and Nurr1.The analyses revealed that during the differentiation of human adipose mesenchymal stem cells into dopaminergic neurons,the expression of caveolin-1 is decreased.Notably,the downregulation of caveolin-1 promoted the differentiation of human adipose mesenchymal stem cells into dopaminergic-like neurons,and it increased the expression of tyrosine hydroxylase,Lmx1a and Nurr1.Together,our findings suggest that caveolin-1 plays a negative regulatory role in the differentiation of dopaminergic-like neurons from stem cells,and it may therefore be a potential molecular target for strategies for regulating the differentiation of these cells.This study was approved by the Medical Ethics Committee of the First Affiliated Hospital of Dalian Medical University of China(approval No.PJ-KS-KY-2020-54)on March 7,2017.

On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse Laplace Transform Methods

Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analyticalmeans.Thus,we need numerical inversionmethods to convert the obtained solution fromLaplace domain to a real domain.In this paper,we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with orderα,β.Our proposed numerical scheme is based on three main steps.First,we convert the given fractal-fractional differential equation to fractional-differential equation in Riemann-Liouville sense,and then into Caputo sense.Secondly,we transformthe fractional differential equation in Caputo sense to an equivalent equation in Laplace space.Then the solution of the transformed equation is obtained in Laplace domain.Finally,the solution is converted into the real domain using numerical inversion of Laplace transform.Three inversion methods are evaluated in this paper,and their convergence is also discussed.Three test problems are used to validate the inversion methods.We demonstrate our results with the help of tables and figures.The obtained results show that Euler’s and Talbot’s methods performed better than Stehfest’s method.

一类Caputo-Katugampola型分数阶微分方程耦合系统边值问题

利用Leray-Schauder二择一定理和Schauder不动点定理,研究了一类具有Caputo-Katugampola型导数的分数阶微分方程耦合系统边值问题解的存在唯一性,再利用Banach不动点定理和Ulam-Hyers稳定性的定义,讨论了该边值问题的Ulam-Hyers稳定性.

一类具有推广的Caputo分数阶导数的微分方程的Ulam稳定性

本文研究一类具有推广的Caputo分数阶导数的微分方程,推广的Caputo分数阶导数可由Conformable导数与经典的Caputo导数结合而得或是推广的分数阶算子.我们利用拉普拉斯变换研究了线性方程的Ulam-Hyers稳定性,分别利用Banach不动点定理和Guonwall不等式研究了非线性方程解的存在唯一性和Ulam-Hyers-Rassis稳定性,获得了几个充分条件的定理,并给出一个例子作为所得结果的应用.

Effect of transforming growth factor beta and bone morphogenetic proteins on rat hepatic stellate cell proliferation and transdifferentiation

AIM: To explore different roles of TGF-β (transforming growth factor beta) and bone morphogenetic proteins (BMPs)in hepatic stellate cell proliferation and trans-differentiation.METHODS: Hepatic stellate cells were isolated from male Sprague-Dawley rats. Sub-cultured hepatic stellate cells were employed for cell proliferation assay with WST-1 reagent and Western blot analysis with antibody against smooth muscle alpha actin (SMA).RESULTS: The results indicated that TGF-β1 significantly inhibited cell proliferation at concentration as low as 0.1 ng/ml, but both BMP-2 and BMP-4 did not affect cell proliferation at concentration as high as 10 ng/ml. The effect on hepatic stellate cell trans-differentiation was similar between TGFβ1 and BMPs. However, BMPs was more potent at transdifferentiation of hepatic stellate cells than TGF-β1. In addition, we observed that TGF-β1 transient reduced the abundance of SMA in hepatic stellate cells.CONCLUSION: TGF-β may be more important in regulation of hepatic stellate cell proliferation while BMPs may be the major cytokines regulating hepatic stellate cell transdifferentiation.

Research on Federated Learning Data Sharing Scheme Based on Differential Privacy

To realize data sharing,and to fully use the data value,breaking the data island between institutions to realize data collaboration has become a new sharing mode.This paper proposed a distributed data security sharing scheme based on C/S communication mode,and constructed a federated learning architecture that uses differential privacy technology to protect training parameters.Clients do not need to share local data,and they only need to upload the trained model parameters to achieve data sharing.In the process of training,a distributed parameter update mechanism is introduced.The server is mainly responsible for issuing training commands and parameters,and aggregating the local model parameters uploaded by the clients.The client mainly uses the stochastic gradient descent algorithm for gradient trimming,updates,and transmits the trained model parameters back to the server after differential processing.To test the performance of the scheme,in the application scenario where many medical institutions jointly train the disease detection system,the model is tested from multiple perspectives by taking medical data as an example.From the testing results,we can know that for this specific test dataset,when the parameters are properly configured,the lowest prediction accuracy rate is 90.261%and the highest accuracy rate is up to 94.352.It shows that the performance of the model is good.The results also show that this scheme realizes data sharing while protecting data privacy,completes accurate prediction of diseases,and has a good effect.

Neural differentiation of human Wharton＇s jelly-derived mesenchymal stem cells improves the recovery of neurological function after transplantation in ischemic stroke rats

Human Wharton＇s jelly-derived mesenchymal stem cells（h WJ-MSCs）have excellent proliferative ability,differentiation ability,low immunogenicity,and can be easily obtained.However,there are few studies on their application in the treatment of ischemic stroke,therefore their therapeutic effect requires further verification.In this study,h WJ-MSCs were transplanted into an ischemic stroke rat model via the tail vein 48 hours after transient middle cerebral artery occlusion.After 4 weeks,neurological functions of the rats implanted with h WJ-MSCs were significantly recovered.Furthermore,many h WJ-MSCs homed to the ischemic frontal cortex whereby they differentiated into neuron-like cells at this region.These results confirm that h WJ-MSCs transplanted into the ischemic stroke rat can differentiate into neuron-like cells to improve rat neurological function and behavior.

Total saponins of Panax ginseng effects on proliferation and differentiation of human embryonic neural stem cells and in a Parkinson's disease mouse model

BACKGROUND： Total saponins of Panax ginseng （TSPG） exhibits neuroprotection against Parkinson＇s disease in the substantia nigra. OBJECTIVE： To investigate the effects of TSPG on human embryonic neural stem cells （NSCs） proliferation and differentiation into dopaminergic neurons using in vitro studies, and to observe NSC differentiation in a mouse model of Parkinson＇s disease, as well as behavioral changes before and after transplantation. DESIGN, TIME AND SETTING： In vitro neural cell biology trial and in vivo randomized, controlled animal trial were performed at the Institute of Basic Medical Sciences, Chongqing Medical University between September 2004 and December 2007. MATERIALS： TSPG （purity 〉 95%） was isolated, extracted, and identified by Chongqing Academy of Chinese Materia Medica. Recombinant human basic fibroblast growth factor （bFGF） and recombinant human epidermal growth factor （EGF） were purchased from PeproTech, USA. A total of 25 C57/BL6J mice, aged 18-20 weeks were included. Twenty were used to establish a Parkinson＇s disease model with i.p. injection of MPTP （1-methyl-4-phenyl-1, 2, 3, 6-tetrahydropyridine） and TSPG alone or combined with interleukin-1 （IL-1）-treated NSCs prior to transplantation into the corpus striatum. The remaining five mice were pretreated for 3 days with TSPG prior to MPTP injection, serving as the TSPG prevention group. METHODS： Primary NSCs were isolated, cultured and purified from embryonic cerebral cortex. Immunocytochemistry was employed to detect specific antigen expression in the NSCs. In vitro experiment： （1） to induce proliferation, NSCs were treated with TSPG, EGF＋bFGF, or TSPG＋EGF＋bFGF, respectively; （2） to induce dopaminergic neuronal differentiation, NSCs were treated with TSPG, IL-1, or TSPG＋IL-1, respectively. MAIN OUTCOME MEASURES： In vitro experiment： the effects of TSPG on NSCs proliferation were evaluated with flow cytometry and MTT assay. Tyrosine hydroxylase expression was determined by immunocytochemistry assay to observe effects of TSPG on dopaminergic neuronal differentiation. In vivo experiment： differentiation of grafted NSCs in the mouse brain was determined by immunohistochemical staining. Behavioral changes were evaluated by spontaneous activity frequency, memory function, and score of paralysis agitans. RESULTS： （1） NSCs were cultured and passaged for more than three passages. Immunocytochemistry revealed positive nestin staining, as well as neurofilament protein and glial fibrillary acidic protein. （2） TSPG significantly increased NSC proliferation, in particular when combined with EGF and bFGF, which was twice as effective as FGF or bFGF alone. TSPG also induced dopaminergic differentiation in NSCs, in particular when TSPG was added together with IL-1, resulting in an effect five times greater than that of IL-1 alone. （3） At day 30 following transplantation, most NSCs in the TSPG prevention group differentiated into dopaminergic neurons, and the scores of paralysis agitans, spontaneous activity, and memory function were significantly increased compared with TSPG alone or TSPG＋IL-1 groups （P 〈 0.05）. CONCLUSION： TSPG stimulated NSC proliferation, in particular when combined with FGF and bFGF. TSPG significantly induced dopaminergic neuronal differentiation of NSCs, and the effect was greater when combined with IL-1. In addition, TSPG greatly improved behavior in the Parkinson＇s disease mouse model following NSC transplantation. Following NSC transplantation, TSPG pretreatment exhibited superior efficacy over either TSPG alone or TSPG in combination with IL-1, in terms of behavioral improvements in the Parkinson＇s disease mouse model.