Differential Transformation Research Articles

Convective heat transfer and MHD flow through semi-porous cylindrical filters embedded in an impermeable region

• Magnetic field dominate the flow field and suppresses the flow rate. • Maximize the effect of Hartmann number leads to rise in temperature distribution for the flow. • Heat transfer in the flow is enhanced as the Darcy number increased. • A negative pressure gradient influences the flow immensely. In the present study, profound applications of agriculture, industries and engineering have motivated to report an exact solution for steady incompressible axisymmetric electrically conducting fluid flow through a semi-porous media surrounded by an impervious cylinder. The uniqueness of this paper is to propose the effect of Joule heating by incorporating convection terms which allows to improve the flow model. Further, the non-dimensional parameters applied on equations governing the flow, takes the form of non-linear differential equations. A Differential Transform Method (DTM) is employed directly to the non-linear differential equations. A succinct solution for velocity and temperature is obtained and its variation on the fluid flow is observed for different dimensionless parameters. This is an interesting phenomenon graphically revealed by Skin-friction and Nusselt number. A good agreement is found in the current paper with certain added features by making the equations compatible and well matched with the previous work of research investigators.

Circulating Tumor DNA Methylation Biomarkers for Characterization and Determination of the Cancer Origin in Malignant Liver Tumors.

Malignant liver tumors include primary malignant liver tumors and liver metastases. They are among the most common malignancies worldwide. The disease has a poor prognosis and poor overall survival, especially with liver metastases. Therefore, early detection and differentiation between malignant liver tumors are critical for patient treatment selection. The detection of cancer and the prediction of its origin is possible with a DNA methylation profile of the tumor DNA compared to that of normal cells, which reflects tissue differentiation and malignant transformation. New technologies enable the characterization of the tumor methylome in circulating tumor DNA (ctDNA), providing a variety of new ctDNA methylation biomarkers, which can provide additional information to clinical decision-making. Our review of the literature provides insight into methylation changes in ctDNA from patients with common malignant liver tumors and can serve as a starting point for further research.

Marangoni bioconvection and cross diffusion in the Casson nanofluid flow over a magnetized disk: DTM-Pade solutions

The Soret-Dufour phenomenon has been analyzed in the magnetohydrodynamic bioconvective Casson nanomaterial flow under Marangoni convection. The analysis of flow is performed under the external magnetic field influence which helps to control the nanofluid flows. The surface of the rotating disk is assumed to vary linearly with temperature, concentration and motile density. The mathematical model thus formed using partial differential equations is re-framed to nonlinear differential expressions by using suitable similarity transformations and the resulted equations are tackled via DTM (Differential Transformation Method) and Pade approximant. The results achieved by this methodology are justified by the comparison with the available data. The final outcomes are reported graphically. The liquid velocity is reduced while the temperature and concentration are enhanced against the larger magnetic parameter values. An enhancement in Marangoni parameter improved the velocity while reduced the temperature and concentration profiles. The Marangoni convection improved the fluid flow while decreased its temperature. The microorganisms density is found to decrease with an improvement in Peclet and bioconvected Schmidt numbers. The higher temperature and concentration profiles are achieved against the incrementing Dufour and Soret number values.

The Differential Transform Method as an Effective Tool to Solve Implicit Hessenberg Index-3 Differential-Algebraic Equations

Differential-algebraic equations (DAEs) are important tools to model complex problems in various application fields easily. Those DAEs with an index-3, even the linear ones, are known to cause problems when solving them numerically. The present article proposes a new algorithm together with its multistage form to efficiently solve a class of nonlinear implicit Hessenberg index-3 DAEs. This algorithm is based on the idea of applying the differential transform method (DTM) directly to the DAE without applying the traditional index reduction methods, which can be complex and often result in violations of the DAE constraints. Also, to deal with the nonlinear terms in the DAE, we approximate them using the Adomian polynomials. This new idea has given us a simple and efficient algorithm, which involves the solution of linear algebraic systems except for the initial recursion terms. This algorithm is easy to implement in Maple or Mathematica. Furthermore, to enlarge the interval of convergence of the power series solution obtained from the DTM, an algorithm for the multistage DTM is also given. Both algorithms are applied to solve two examples of highly nonlinear implicit index-3 Hessenberg DAEs. Numerical results show that the DTM can determine the exact solution in convergent power series, while the multistage DTM can compute accurate numerical solutions over large intervals.

Soil Microplastics Spectrum Based on Visible Near-Infrared Spectroscopy

As the largest "repository" of microplastics, soil is affected by soil structure, microplastics category and particle size. In this study, the method of combining indoor simulation modeling and field verification is proposed. The reflectance of soil microplastic samples was collected by ASD FieldSpec4 Hi-Res spectrometer, NOR, MSC, SNV were used for spectral pretreatment, and differential transformations of different orders are used to enhance the spectral signal-to-noise ratio. The results showed that the spectral reflectance of microplastics decreased with the increase of microplastics content in soil. After FD and SD transform, the spectral features are enhanced obviously. The regression model based on NOR transformation of reflectivity combined with first deviation is the best, Rc2, Rv2, RMSEC and RMSEPare 0.75, 0.77, 0.16, 0.12,respectively.This study can provide a scientific basis for quantitative research on microplastics in farmland soil in northern Shaanxi, China. Bangladesh J. Bot. 51(4): 971-977, 2022 (December) Special

Epigenetic Modification of Cytosines in Hematopoietic Differentiation and Malignant Transformation.

The mammalian DNA methylation landscape is established and maintained by the combined activities of the two key epigenetic modifiers, DNA methyltransferases (DNMT) and Ten-eleven-translocation (TET) enzymes. Once DNMTs produce 5-methylcytosine (5mC), TET proteins fine-tune the DNA methylation status by consecutively oxidizing 5mC to 5-hydroxymethylcytosine (5hmC) and further oxidized derivatives. The 5mC and oxidized methylcytosines are essential for the maintenance of cellular identity and function during differentiation. Cytosine modifications with DNMT and TET enzymes exert pleiotropic effects on various aspects of hematopoiesis, including self-renewal of hematopoietic stem/progenitor cells (HSPCs), lineage determination, differentiation, and function. Under pathological conditions, these enzymes are frequently dysregulated, leading to loss of function. In particular, the loss of DNMT3A and TET2 function is conspicuous in diverse hematological disorders, including myeloid and lymphoid malignancies, and causally related to clonal hematopoiesis and malignant transformation. Here, we update recent advances in understanding how the maintenance of DNA methylation homeostasis by DNMT and TET proteins influences normal hematopoiesis and malignant transformation, highlighting the potential impact of DNMT3A and TET2 dysregulation on clonal dominance and evolution of pre-leukemic stem cells to full-blown malignancies. Clarification of the normal and pathological functions of DNA-modifying epigenetic regulators will be crucial to future innovations in epigenetic therapies for treating hematological disorders.

The APPROXIMATE SOLUTIONS OF MALARIA DISEASE TRANSMISSION MODEL: USING MUTI-STEP DIFFERENTIAL TRANSFORMATION METHOD

In this paper, numerical solutions to the SPEIR-SEI Malaria disease model were obtained using the Multi-Step Differential Transformation Method (MS-DTM). MS-DTM is a semi-analytical method for solving a system of a non-linear differential equation where its exact solution is difficult to obtain. The analytical solution of MS-DTM was compared with the solution of Maple21’s in-built classical fourth-order Runge-Kutta method. The results demonstrate the reliability and efficiency of the method and the graphs show that the solutions from both methods agreed well with each other.

Sensitivity analysis of nonlinear convective heat transport of a hybrid nanoliquid sandwiched by micropolar liquid using RSM

Petroleum and polymer industries utilize a multilayer flow model for efficient heat transfer. In such applications, the linear Boussinesq approximation is not recommended as the devices used in such experiments would work at moderate or extremely high temperatures. Therefore, the flow and heat transfer in a multilayer vertical channel with a magnetic field and the nonlinear (quadratic) Boussinesq approximation are investigated, with the central region filled with a hybrid nanoliquid and the outer regions filled with an oil-based micropolar liquid. The effects of Joule heating and viscous dissipation are taken into account. The effective viscosity and thermal conductivity are modeled using the experimental data based Esfe model. The modeled equations are coupled and nonlinear, they are solved using the Differential Transform Method (DTM). Results are analyzed for various values of the material parameter, quadratic convection parameter, Brinkman number, mixed convection parameter, Hartmann number, nanoparticle volume fraction (NVF) on Nusselt number, skin friction, velocity, microrotation velocity and temperature distributions. Additionally, multi-objective optimization of Nusselt number and friction factor is performed for three different levels of the quadratic convection parameter , material parameter and the NVF using the Response Surface Methodology (RSM). The material parameter diminishes the velocity whereas enhances the microrotation velocity. Also, the quadratic convection parameter increases the flow field. Sensitivity computations reveal that the Nusselt number is more sensitive to material parameter and NVF whereas the skin friction coefficient is more sensitive to quadratic convection parameter.

Application of differential transformation and Hermite wavelet methods for micropolar flow through a permeable channel

AbstractIn this study, micropolar fluid flow in a porous channel is investigated using the differential transform method (DTM) and the Hermite wavelet method (HWM). By exploiting Berman's similarity transformation, the governing partial differential equations are transformed into a system of nonlinear coupled ordinary differential equations (ODEs). The concepts of DTM and HWM are briefly introduced and employed to derive solutions of nonlinear coupled ODEs. Our results compared with solutions already existing in the literature. When we compare DTM and HWM, HWM is more efficient and also requires less time to maintain a higher level of accuracy. The results are presented to study the velocity and microrotation profiles for various physical parameters such as Reynolds number, coupling parameter, spin‐gradient viscosity parameter, and micropolar fluid constant. As an important result, increases in the values of the coupling parameter and micropolar fluid constant have different results in comparison with the spin‐gradient viscosity parameter increasing.

AutoMA: Towards Automatic Model Augmentation for Transferable Adversarial Attacks

Recent adversarial attack works attempt to improve the transferability by applying various differentiable transformations on input images. Considering the differentiable transformations and the original model together as a new model, these methods can be regarded as model augmentation that effectively derives an ensemble of models from the single original model. Despite their impressive performance, the model augmentation policies used in these methods are manually designed by experimental attempts, leaving the design of model augmentation policy an open question. In this paper, we propose an Automatic Model Augmentation (AutoMA) approach to find a strong model augmentation policy for transferable adversarial attacks. Specifically, we design a discrete search space that contains various diffierentiable transformations with different parameters and adopt reinforcement learning to search for the strong augmentation policy. The sampled augmentation policies together with the rewards they obtain during the searching process reveal several valuable observations for designing more powerful attacks using model augmentation policy: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1) Augmentation transformations on color space are less effective; 2) The transformation type diversity matters; and 3) Using small distortion for geometric transformations while larger distortion for intensity transformations.</i> Extensive experiments show that the augmentation policy found by AutoMA achieves superior performance than existing manually designed policies in a wide range of cases.

Parallel-in-Time Power System Simulation Using a Differential Transformation Based Adaptive Parareal Method

For parallel-in-time simulation of large-scale power systems, this paper proposes a differential transformation based adaptive Parareal method for significantly improved convergence and time performance compared to a traditional Parareal method, which iterates a sequential, numerical coarse solution over extended time steps to connect parallel fine solutions within respective time steps. The new method employs the differential transformation to derive a semi-analytical coarse solution of power system differential-algebraic equations, by which the order and time step, as well as the window length with a multi-window solution strategy, can adaptively vary with the response of the system. Thus, the new method can reduce divergences and also speed up the overall simulation. Extensive tests on the IEEE 39-bus system and the Polish 2383-bus system have verified the performance of the proposed method.

Stationary Factor of Non-Stationary Random Process Based on Differential Transformation

This research studies the deviation of the output signal from stationary state by calculating stationary factor in differential filter with constant and non-stochastic coefficients, a stationary process is applied on its input. We show that this deviation is related to the degree of transformation the study range length and the form of a correlation function of the process applied on the input and the special solution of the equation LY=X and its correlation or un-correlation with that process.

Conditions for distortion-free voltage transfer in the transformer

The optimal design of low-power transformers, sonic and ultrasonic transformers, pulse transformers, differential transformers, etc. requires an in-depth study of their theory and design calculation. In this article, the influence of transformer parameters on the voltage transfer ratio is discussed, and recommendations are given for the selection of values of these parameters to reduce possible distortions. The calculation methods are illustrated by an example.

DECOMPOSITION METHODS FOR DETERMINING COMPLEX ONE-PARAMETER GENERALIZED INVERSE MOORE-PENROSE MATRICES (I)

Analytical and numerical-analytical decomposition methods for determining complex one-parameter generalized inverse Moore-Penrose matrices are suggested. Analytical methods are based on the first two Moore-Penrose conditions. It is shown that in both cases the same solution to the problem is obtained, as it should be. Numerical-analytical methods are based on the obtained analytical relations and differential Pukhov transformations. In contrast to the known methods, in which we operate with rectangular generalized inverse matrices, in all the proposed analytical and numerical-analytical methods, we operate with square generalized (ordinary) inverse matrices. In view of this circumstance, an exact but not an approximate solution to the problem is obtained. A model example with a square matrix is considered, for which an analytical solution is obtained using two approaches - the determination of the usual inverse one-parameter matrix and the decomposition method for determining the same matrix. This matrix is defined in exactly the same way as numerical-analytical decomposition methods. In this paper, exact analytical and approximate numerical-analytical computational methods for determining complex one-parameter generalized inverse Moore-Penrose matrices are proposed. Numerical-analytical computational methods are easily implemented using modern information technologies, since they are based on simple recurrent computational procedures. It is assumed that all elements of the corresponding one-parameter matrices have a sufficient degree of smoothness at the center of approximation of solutions.

Stem cell therapy: An emerging hope in regenerative medicine

In recent years, a new revolutionary giant has developed which gives high hopes, promises and proficient scientific study area is Stem cell therapy. Recent research showing the effective application of stem cell therapies to patients has enriched the hope that such regeneration methods may one day become a remedy for a variety of difficult ailments. In the past few years, clinical trials in which stem cell therapies are involved have raised pretty exponentially. Some of these trials had a notable influence on a number of ailments, such as neurological disorders, pulmonary dysfunctions, diseases related to metabolism and the endocrine system, disorders of reproduction, skin burns, and cardiovascular conditions. Although mesenchymal stem cells (MSCs) have been put to use clinically to treat autoimmune and chronic inflammatory illnesses, concerns about the field of regenerative medicine remain due to their ability to endorse cancer growth and metastasis as well as their overstated therapeutic potential. The most significant obstacle to the development of hESC-based therapeutic medicines is an ethical quandary involving the killing of a human embryo. Induced pluripotent stem cells (iPSCs), which were first developed to address this problem, have since been proven to be effective, although there are still lingering concerns regarding their efficacy for use in medicine. The unwanted differentiation and cancerous transformation are significant safety concerns, iPSCs can be employed for human reproductive cloning, however, their limitless differentiation efficiency raises concerns about the possibility of producing genetically altered human embryos and human-animal chimeras. The issue is contentious because some people claim it goes against nature, yet nature herself gives an opportunity that opens a new avenue for people who suffer from untreated ailments and disorders.

The Glioblastoma Landscape: Hallmarks of Disease, Therapeutic Resistance, and Treatment Opportunities.

Malignant brain tumors are aggressive and difficult to treat. Glioblastoma is the most common and lethal form of primary brain tumor, often found in patients with no genetic predisposition. The median life expectancy for individuals diagnosed with this condition is 6 months to 2 years and there is no known cure. New paradigms in cancer biology implicate a small subset of tumor cells in initiating and sustaining these incurable brain tumors. Here, we discuss the heterogenous nature of glioblastoma and theories behind its capacity for therapy resistance and recurrence. Within the cancer landscape, cancer stem cells are thought to be both tumor initiators and major contributors to tumor heterogeneity and therapy evasion and such cells have been identified in glioblastoma. At the cellular level, disruptions in the delicate balance between differentiation and self-renewal spur transformation and support tumor growth. While rapidly dividing cells are more sensitive to elimination by traditional treatments, glioblastoma stem cells evade these measures through slow division and reversible exit from the cell cycle. At the molecular level, glioblastoma tumor cells exploit several signaling pathways to evade conventional therapies through improved DNA repair mechanisms and a flexible state of senescence. We examine these common evasion techniques while discussing potential molecular approaches to better target these deadly tumors. Equally important, the presented information encourages the idea of augmenting conventional treatments with novel glioblastoma stem cell-directed therapies, as eliminating these harmful progenitors holds great potential to modulate tumor recurrence.

DECOMPOSITION METHODS FOR DETERMINING COMPLEX ONE-PARAMETER GENERALIZED INVERSE MOORE-PENROSE MATRICES (II)

Analytical and numerical-analytical decomposition methods for determining complex one-parameter generalized inverse Moore-Penrose matrices are suggested. Analytical methods are based on the first two Moore-Penrose conditions. It is shown that in both cases, the same solution to the problem is obtained, as it should be. Numerical-analytical methods are based on the obtained analytical relations and differential Pukhov transformations. A model example is considered.

Estimating the Texture of Purple Soils Using Vis-NIR Spectroscopy and Optimized Conversion Models

Soil texture is an indicator of soil physical structure which delivers many ecological functions of soils such as thermal regime, plant growth, and soil quality. However, traditional methods for soil texture measurement are time-consuming and labor-intensive. This study attempts to explore an indirect method for rapid estimating the texture of three subgroups of purple soils (i.e. calcareous, neutral, and acidic). 190 topsoil (0 - 10 cm) samples were collected from sloping croplands in Tongnan and Beibei Districts of Chongqing Municipality in China. Vis-NIR spectrum was measured and processed, and stepwise multiple linear regression (SMLR), partial least squares regression (PLSR), and back propagation neural network (BPNN) models were constructed to inform the soil texture. The clay fractions ranged from 4.40% to 27.12% while sand fractions ranged from 0.34% to 36.57%, hereby soil samples encompass three textural classes (i.e. silt, silt loam, and silty clay loam). For the original spectrum, the texture of calcareous and neutral purple soils was not significantly correlated with spectral reflectance and linear models (SMLR and PLSR) exhibited low prediction accuracy. The correlation coefficients and the goodness-of-fits between soil texture and the transformed spectra of all soil groups increased by continuum-removal (CR), first-order differential (R'), and second-order differential (R") transformations. Among them, the R" had the best performance in terms of improving the correlation coefficients and the goodness-of-fits. For the calcareous purple soil, the SMLR exceeds PLSR and BPNN with a higher coefficient of determination (R2) and the ratio of performance to inter-quartile distance (RPIQ) values and lower root mean square error of validation (RMSEV), but for the neutral and acidic purple soils, the PLSR model has a better prediction accuracy. In summary, the linear methods (SMLR and PLSR) are more reliable in estimating the texture of the three purple soil groups when using Vis-NIR spectroscopy inversion.

Suspected Case of MALT Lymphoma of the Nasal Turbinate in a Horse

We examined a female Kiso horse (a native Japanese horse breed) aged 2 years and 9 months with persisting nasal discharge that died due to lymphoma. Necropsy revealed masses in the left nasal cavity, left periorbital cavity, and left maxillary and mandibular areas. Histologically, the neoplastic tissues were composed of lymphoid and plasmacytoid cells, with immunoglobulin A (α and λ chains) production in the latter. The foci of large lymphoid cells were detected at some sites. All neoplastic cell types were positively stained in immunohistochemical staining for CD20. Extranodal marginal zone B-cell lymphoma of mucosa-associated lymphoid tissue (MALT lymphoma) was suspected on the basis of the presence of lymphoepithelial lesions, plasmacytic differentiation, and large-cell transformation. A history of chronic rhinitis may be linked to the development of this disorder.

ParamCrop: Parametric Cubic Cropping for Video Contrastive Learning

The central idea of contrastive learning is to discriminate between different instances and force different views from the same instance to share the same representation. To avoid trivial solutions, augmentation plays an important role in generating different views, among which random cropping is shown to be effective for the model to learn a generalized and robust representation. Commonly used random crop operation keeps the distribution of the difference between two views unchanged along the training process. In this work, we show that adaptively controlling the disparity between two augmented views along the training process enhances the quality of the learned representations. Specifically, we present a parametric cubic cropping operation, ParamCrop, for video contrastive learning, which automatically crops a 3D cubic by differentiable 3D affine transformations. ParamCrop is trained simultaneously with the video backbone using an adversarial objective, so that it learns to increase the contrastive loss and thus gradually reduces the shared contents between two cropped views. Experiments show that this adaptive and gradual increase in the disparity yielded by ParamCrop is beneficial to learning a strong and generalized representation for downstream tasks, which is shown to be effective on multiple contrastive learning frameworks and video backbones.