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.

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.

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.

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.

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.

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.

Conformable and Caputo’s Derivatives in Generalized Viscoelastic Models

We study two generalized versions of a system of equations which describe the time evolution of the hydrodynamic fluctuations of density and velocity in a linear viscoelastic fluid. In the first of these versions, the time derivatives are replaced by conformable derivatives, and in the second version left-handed Caputo’s derivatives are used. We show that the solutions obtained with these two types of derivatives exhibit significant similarities, which is an interesting (and somewhat surprising) result, taking into account that the conformable derivatives are local operators, while Caputo’s derivatives are nonlocal operators. We also show that the solutions of the generalized systems are similar to the solutions of the original system, if the order α of the new derivatives (conformable or Caputo) is less than one. On the other hand, when α is greater than one, the solutions of the generalized systems are qualitatively different from the solutions of the original system.

Adomian Modification Methods for the Solution of Chebyshev’s Differential Equations

The current study examines the important class of Chebyshev’s differential equations via the application of the efficient Adomian Decomposition Method (ADM) and its modifications. We have proved the effectiveness of the employed methods by acquiring exact analytical solutions for the governing equations in most cases;while minimal noisy error terms have been observed in a particular method modification. Above all, the presented approaches have rightly affirmed the exactitude of the available literature. More to the point, the application of this methodology could be extended to examine various forms of high-order differential equations, as approximate exact solutions are rapidly attained with less computation stress.

Differentiation of rhesus adipose stem cells into dopaminergic neurons

LIM homeobox transcription factor la （Lmxla） has the capacity to initiate the development program of neuronal cells and promote the differentiation of embryonic stem cells into dopaminergic neurons. In this study, rhesus adipose stem cells were infected with recombinant adenovirus carrying the Lmxla gene and co-cultured with embryonic rat neural stem cells. Cell differentiation was induced using sonic hedgehog and fibroblast growth factor-8. Immunofluorescence staining showed that cells were positive for neuron-specific enolase and ^-tubulin II1. Reverse transcription-PCR results demonstrated that rhesus adipose stem cells were not only positive for neuron-specific enolase and I^-tubulin III, but also positive for the dopaminergic neuron marker, tyrosine hydroxylase, neurofilament, glial cell line-derived neurotrophic factor family receptor a2 and nuclear receptor related factor 1. The number of Lmxla gene-infected cells expressing the dopaminergic neuron marker was substantially greater than the number of cells not infected with Lmxla gene. These results suggest that Lmxla-mediated regulation combined with the strategy of co-culture with neural stem cells can robustly promote the differentiation of rhesus adipose stem cells into dopaminergic neurons.

EWS Knockdown and Taxifolin Treatment Induced Differentiation and Removed DNA Methylation from p53 Promoter to Promote Expression of Puma and Noxa for Apoptosis in Ewing’s Sarcoma

Ewing’s sarcoma is a pediatric tumor that mainly occurs in soft tissues and bones. Malignant characteristics of Ewing’s sarcoma are correlated with expression of EWS oncogene. We achieved knockdown of EWS expression using a plasmid vector encoding EWS short hairpin RNA (shRNA) to increase anti-tumor mechanisms of taxifolin (TFL), a new flavonoid, in human Ewing’s sarcoma cells in culture and animal models. Immunofluorescence microscopy and flow cytometric analysis showed high expression of EWS in human Ewing’s sarcoma SK-N-MC and RD-ES cell lines. EWS shRNA plus TFL inhibited 80% cell viability and caused the highest decreases in EWS expression at mRNA and protein levels in both cell lines. Knockdown of EWS expression induced morphological features of differentiation. EWS shRNA plus TFL caused more alterations in molecular markers of differentiation than either agent alone. EWS shRNA plus TFL caused the highest decreases in cell migration with inhibition of survival, angiogenic and invasive factors. Knockdown of EWS expression was associated with removal of DNA methylation from p53 promoter, promoting expression of p53, Puma, and Noxa. EWS shRNA plus TFL induced the highest amounts of apoptosis with activation of extrinsic and intrinsic pathways in both cell lines in culture. EWS shRNA plus TFL also inhibited growth of Ewing’s sarcoma tumors in animal models due to inhibition of differentiation inhibitors and angiogenic and invasive factors and also induction of activation of caspase-3 for apoptosis. Collectively, knockdown of EWS expression increased various anti-tumor mechanisms of TFL in human Ewing’s sarcoma in cell culture and animal models.

Inverse Differential Operators in Time and Space

When one function is defined as a differential operation on another function, it’s often desirable to invert the definition, to effectively “undo” the differentiation. A Green’s function approach is often used to accomplish this, but variations on this theme exist, and we examine a few such variations. The mathematical analysis of is sought in the form if such an inverse operator exists, but physics is defined by both mathematical formula and ontological formalism, as I show for an example based on the Dirac equation. Finally, I contrast these “standard” approaches with a novel exact inverse operator for field equations.

Solution of Laguerre’s Differential Equations via Modified Adomian Decomposition Method

This paper presents a technique for obtaining an exact solution for the well-known Laguerre’s differential equations that arise in the modeling of several phenomena in quantum mechanics and engineering. We utilize an efficient procedure based on the modified Adomian decomposition method to obtain closed-form solutions of the Laguerre’s and the associated Laguerre’s differential equations. The proposed technique makes sense as the attitudes of the acquired solutions towards the neighboring singular points are correctly taken care of.

Diagnostic performance of texture analysis in the differential diagnosis of perianal fistulising Crohn’s disease and glandular anal fistula

BACKGROUND Perianal fistulising Crohn's disease(PFCD)and glandular anal fistula have many similarities on conventional magnetic resonance imaging.However,many patients with PFCD show concomitant active proctitis,but only few patients with glandular anal fistula have active proctitis.AIM To explore the value of differential diagnosis of PFCD and glandular anal fistula by comparing the textural feature parameters of the rectum and anal canal in fat suppression T2-weighted imaging(FS-T2WI).METHODS Patients with rectal water sac implantation were screened from the first part of this study(48 patients with PFCD and 22 patients with glandular anal fistula).Open-source software ITK-SNAP(Version 3.6.0,http://www.itksnap.org/)was used to delineate the region of interest(ROI)of the entire rectum and anal canal wall on every axial section,and then the ROIs were input in the Analysis Kit software(version V3.0.0.R,GE Healthcare)to calculate the textural feature parameters.Textural feature parameter differences of the rectum and anal canal wall between the PFCD group vs the glandular anal fistula group were analyzed using Mann-Whitney U test.The redundant textural parameters were screened by bivariate Spearman correlation analysis,and binary logistic regression analysis was used to establish the model of textural feature parameters.Finally,diagnostic accuracy was assessed by receiver operating characteristic-area under the curve(AUC)analysis.RESULTS In all,385 textural parameters were obtained,including 37 parameters with statistically significant differences between the PFCD and glandular anal fistula groups.Then,16 texture feature parameters remained after bivariate Spearman correlation analysis,including one histogram parameter(Histogram energy);four grey level co-occurrence matrix(GLCM)parameters(GLCM energy_all direction_offset1_SD,GLCM entropy_all direction_offset4_SD,GLCM entropy_all direction_offset7_SD,and Haralick correlation_all direction_offset7_SD);four texture parameters(Correlation_all direction_offset1_SD,cluster prominence_angle 90_offset4,Inertia_all direction_offset7_SD,and cluster shade_angle 45_offset7);five grey level run-length matrix parameters(grey level nonuniformity_angle 90_offset1,grey level nonuniformity_all direction_offset4_SD,long run high grey level emphasis_all direction_offset1_SD,long run emphasis_all direction_offset4_SD,and long run high grey level emphasis_all direction_offset4_SD);and two form factor parameters(surface area and maximum 3D diameter).The AUC,sensitivity,and specificity of the model of textural feature parameters were 0.917,85.42%,and 86.36%,respectively.CONCLUSION The model of textural feature parameters showed good diagnostic performance for PFCD.The texture feature parameters of the rectum and anal canal in FS-T2WI are helpful to distinguish PFCD from glandular anal fistula.