Lung cancer clustering by identification of similarities and discrepancies of DNA copy numbers using maximal information coefficient.

Lung cancer is the second most diagnosed cancer and the first cause of cancer related death for men and women in the United States. Early detection is essential as patient survival is not optimal and recurrence rate is high. Copy number (CN) changes in cancer populations have been broadly investigated to identify CN gains and deletions associated with the cancer. In this research, the similarities between cancer and paired peripheral blood samples are identified using maximal information coefficient (MIC) and the spatial locations with substantially high MIC scores in each chromosome are used for clustering analysis. The results showed that a sizable reduction of feature set can be obtained using only a subset of locations with high MIC values. The clustering performance was evaluated using both true rate and normalized mutual information (NMI). Clustering results using the reduced feature set outperformed the performance of clustering using entire feature set in several chromosomes that are highly associated with lung cancer with several identified oncogenes.

Numerical simulation and mathematical modeling for heat and mass transfer in MHD stagnation point flow of nanofluid consisting of entropy generation.

The primary goal of this article is to explore the radiative stagnation point flow of nanofluid with cross-diffusion and entropy generation across a permeable curved surface. Moreover, the activation energy, Joule heating, slip condition, and viscous dissipation effects have been considered in order to achieve realistic results. The governing equations associated with the modeling of this research have been transformed into ordinary differential equations by utilizing appropriate transformation variable. The resulting system of equations was solved numerically by using Bvp4c built-in package in MATLAB. The impact of involved parameters have been graphically examined for the diverse features of velocity, temperature, and concentration profiles. Throughout the analysis, the volume fraction is assumed to be less than [Formula: see text] while the Prandtl number is set to be [Formula: see text]. In addition, the entropy generation, friction drag, Nusselt, and Sherwood numbers have been plotted for describing the diverse physical aspects of the underlying phenomena. The major outcomes reveal that the curvature parameter reduces the velocity profile and skin friction coefficient whereas the magnetic parameter, temperature difference parameter, and radiation parameter intensify the entropy generation.

Computational analysis of radiative engine oil-based Prandtl-Eyring hybrid nanofluid flow with variable heat transfer using the Cattaneo-Christov heat flux model.

In the present analysis, we study the energy transference through engine oil-based Prandtl-Eyring nanofluid flow through a heated stretching surface. The nanofluid is prepared by adding copper (Cu) and titanium dioxide (TiO2) nanoparticles (NPs) to the base fluid engine oil. The flow mechanism and thermal transmission are observed by exposing the nanofluid flow through the heated slippery surface. The influences of permeable surface, radiative flux and heat absorption/generation are also elaborated in this study. The flow of nanofluids has been designed using a PDEs system, which are then transformed into a set of ODEs via resemblance modification. The numerical technique "shooting method" is used to solve the acquired nonlinear set of non - dimensional ODEs. The results are physically exemplified through tables and plots. It has been detected that the accumulation of nanomaterials in the engine oil, reduces the skin friction while accelerating the energy transfer rate. The velocity field significantly decelerates with the encouragement of the porosity factor, and volume fraction of NPs. However, the temperature profile significantly escalates with the encouragement of the porosity factor, and volume fraction of NPs.

Magnetized mixed convection hybrid nanofluid with effect of heat generation/absorption and velocity slip condition.

Through a vertically shrinking sheet, a two-dimensional magnetic nanofluid is numerically analyzed for convection, heat generation and absorption, and the slip velocity effect. In this research, Al2O3-Cu/water composite nanofluid is studied, where water is deemed the base liquid and copper (Cu) and alumina (Al2O3) are the solid nanoparticles. Modern composite nanofluids improve heat transfer efficiency. Using the Tiwari-Das model, the current study examines the effects of the solid volume fraction of copper, heat generation/absorption, MHD, mixed convection, and velocity slip parameters on velocity and temperature distributions. Introducing exponential similarity variables converts nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). MATLAB bvp4c solver is used to solve ODEs. Results showed dual solutions for suction with 0%-10% copper nanoparticles and 1%-500% heat generation/absorption. As copper (Cu) solid volume percentage increases from 0% to 10%, reduced skin friction f ″ ( 0 ) boosts in the first solution but falls in the second. When Cu is added to both solutions, heat transport - θ ' ( 0 ) decreases. As heat generation/absorption increases 1%-500%, - θ ' ( 0 ) decreases in both solutions. In conclusion, solution dichotomy exists when suction parameter S ≥ S c i in assisting flow case, while no fluid flow is possible when S < S c i .

Statistical modeling for Ree-Eyring nanofluid flow in a conical gap between porous rotating surfaces with entropy generation and Hall Effect.

The attention of the current study is on the flow of a non-Newtonian incompressible Cu-Water nanofluid flow. The water is assumed as base fluid, while copper is used as nanoparticles. The Ree-Eyring prototype describes the performance of non-Newtonian nanofluids. There is a conical gap that nanofluid flow fills among the plane disc and the cone's stationary/rotational porous faces. Additionally taken into account are heat, mass transfer, and entropy production. The given mathematical model is unique due to the effects of a vertically applied Hall Effect, Ohmic dissipation, viscous dissipation, and chemical processes. The Ree-Eyring fluid constitutive equations, as well as the cylindrical coordinates, have been interpreted. The model equations for motion, heat, and concentration can be changed in the collection of non-linear ODEs by employing the applicable similarity transform. This method allocates a couple of nonlinear ODEs relating to velocity, temperature, and concentration distributions. The shooting scheme (bvp4c technique) is used to solve these equations numerically. Statistical analysis like probable error, correlation, and regression are exploited. The probable error is estimated to compute the consistency of the calculated correlation features. The theoretical data is analyzed in both graphical and tabular forms. The modeled parameters like, magnetic number, porosity parameter, Eckert number, chemical reaction parameter, Brownian motion parameter, thermophoretic parameter, Schmidt number, Hall recent parameter, radiation parameter, and volume fraction are discussed in details graphically and theoretically. The outcomes indicate that the velocity components are greater for greater values of nanoparticle volume fraction and Weissenberg number, whereas for enormous values of magnetic and porosity parameters, the velocity components fall.

Entropy Generation and Thermal Analysis on MHD Second-Grade Fluid with Variable Thermophysical Properties over a Stratified Permeable Surface of Paraboloid Revolution.

Stratification is used in a wide range of energy storage fields, including solar thermal energy systems. This paper investigates entropy optimization and the effects of heat production, magnetic field, and various fluid parameters on the flow of second-grade fluid through unstratified and stably stratified paraboloids of revolution. In the heat transfer equation, stratification, linear thermal radiation, and Joule dissipation have all been explored. The similarity transformation is used to convert the governing PDEs into nonlinear ODEs. The HAM (homotopy analysis method) is used to solve dimensionless nonlinear ODEs. The impact of significant elements on various profiles is exposed and explored. Graphical results are used to examine the influence of the velocity profile, temperature, concentration, and entropy formation rate using tables to indicate the characteristics of skin friction, Nusselt number, and Sherwood number for numerous parameters. It is noticed that the velocity is enhanced by raising the stratification parameter, while the opposite behavior is observed for temperature distribution. The concentration profile declined as the solute stratification parameter was enhanced. For both the unstratified and stratified regions, incremental values of the Brinkman number and magnetic parameter depict augmentation in entropy production, while entropy production drops for a large value of the temperature ratio parameter.

Effect of Thermal Radiation on Three-Dimensional Magnetized Rotating Flow of a Hybrid Nanofluid.

The effect of thermal radiation on the three-dimensional magnetized rotating flow of a hybrid nanofluid has been numerically investigated. Enhancing heat transmission is a contemporary engineering challenge in a range of sectors, including heat exchangers, electronics, chemical and biological reactors, and medical detectors. The main goal of the current study is to investigate the effect of magnetic parameter, solid volume fraction of copper, Eckert number, and radiation parameter on velocity and temperature distributions, and the consequence of solid volume fraction on declined skin friction and heat transfer against suction and a stretching/shrinking surface. A hybrid nanofluid is a contemporary type of nanofluid that is used to increase heat transfer performance. A linear similarity variable is−applied to convert the governing partial differential equations (PDEs) into corresponding ordinary differential equations (ODEs). Using the three-stage Labatto III-A method included in the MATLAB software's bvp4c solver, the ODE system is solved numerically. In certain ranges of involved parameters, two solutions are received. The temperature profile θη upsurges in both solutions with growing values of EC and Rd. Moreover, the conclusion is that solution duality exists when the suction parameter S≥Sci, while no flow of fluid is possible when S

Modeling and Analysis of Breast Cancer with Adverse Reactions of Chemotherapy Treatment through Fractional Derivative.

The abnormal growth of cells in the breast is called malignancy or breast cancer; it is a life-threatening and dangerous cancer in women around the world. In the treatment of cancer, the doctors apply different techniques to stop cancer cell development, remove cancer cells through surgery, or kill cancer cells. In chemotherapy treatment, powerful drugs are used to kill abnormal cells; however, it has adverse reactions on the patient heart which is called cardiotoxicity. In this paper, we formulate the dynamics of cancer in the breast with adverse reactions of chemotherapy treatment on the heart of a patient in the fractional framework to visualize its dynamical behaviour. We listed the fundamental results of the fractional calculus for the analysis of our model. The model is then analyzed for the basic properties, and the existence and uniqueness of the proposed breast cancer system are investigated through fixed point theory. Furthermore, the Adams-Bashforth numerical technique is presented for the solution of fractional-order system to illustrate the time series of breast cancer model. The dynamical behaviour of different stages of breast cancer is then highlighted numerically to show the effect of fractional-order ϑ and to visualize the role of input parameter on the dynamics of breast cancer.

Fractional-calculus analysis of the transmission dynamics of the dengue infection.

In this research paper, a novel approach in dengue modeling with the asymptomatic carrier and reinfection via the fractional derivative is suggested to deeply interrogate the comprehensive transmission phenomena of dengue infection. The proposed system of dengue infection is represented in the Liouville-Caputo fractional framework and investigated for basic properties, that is, uniqueness, positivity, and boundedness of the solution. We used the next-generation technique in order to determine the basic reproduction number R0 for the suggested model of dengue infection; moreover, we conduct a sensitivity test of R0 through a partial rank correlation coefficient technique to know the contribution of input factors on the output of R0. We have shown that the infection-free equilibrium of dengue dynamics is globally asymptomatically stable for R0<1 and unstable in other circumstances. The system of dengue infection is then structured in the Atangana-Baleanu framework to represent the dynamics of dengue with the non-singular and non-local kernel. The existence and uniqueness of the solution of the Atangana-Baleanu fractional system are interrogated through fixed-point theory. Finally, we present a novel numerical technique for the solution of our fractional-order system in the Atangana-Baleanu framework. We obtain numerical results for different values of fractional-order ϑ and input factors to highlight the consequences of fractional-order ϑ and input parameters on the system. On the basis of our analysis, we predict the most critical parameters in the system for the elimination of dengue infection.

Silhouette Analysis for Performance Evaluation in Machine Learning with Applications to Clustering.

Grouping the objects based on their similarities is an important common task in machine learning applications. Many clustering methods have been developed, among them k-means based clustering methods have been broadly used and several extensions have been developed to improve the original k-means clustering method such as k-means ++ and kernel k-means. K-means is a linear clustering method; that is, it divides the objects into linearly separable groups, while kernel k-means is a non-linear technique. Kernel k-means projects the elements to a higher dimensional feature space using a kernel function, and then groups them. Different kernel functions may not perform similarly in clustering of a data set and, in turn, choosing the right kernel for an application could be challenging. In our previous work, we introduced a weighted majority voting method for clustering based on normalized mutual information (NMI). NMI is a supervised method where the true labels for a training set are required to calculate NMI. In this study, we extend our previous work of aggregating the clustering results to develop an unsupervised weighting function where a training set is not available. The proposed weighting function here is based on Silhouette index, as an unsupervised criterion. As a result, a training set is not required to calculate Silhouette index. This makes our new method more sensible in terms of clustering concept.

Second-order slip effect on bio-convectional viscoelastic nanofluid flow through a stretching cylinder with swimming microorganisms and melting phenomenon.

The uses of nanofluid in cooling technology is growing. The nanofluid is made up of metallic and nonmetallic particles that are distributed in a base fluid. This research provides a summary of fuel cell models, uses, and how they function. Researchers have made significant contributions in the following era due to the importance of bioconvection in nanotechnology and a variety of biological systems. The idea of the recent work is to evaluate the aspects of the Cattaneo-Christov (C-C) heat and mass flux model, the second-order boundary with melting phenomenon on the bioconvective flow of viscoelastic nanofluid across a cylinder. The nature of the activation energy, thermal conductivity is also taken into account. Appropriate similarity transformations are utilized to reframe the PDEs of the modeled system into a system of ODEs. The governing equations for the renovated system of ODEs are treated by a shooting function. Here bvp4c built-in function computational tool MATLAB is used. The two-dimensional flow has ceased application in several areas, such as polymer industry, material synthesis technology, nano-biopolymer computer graphics processing, industry, mechanical engineering, airplane structures, and scientific research, which is much more useful in nanotechnology. The results of emerging important flow-field parameters are investigated with the aid of graphs and numerical results.

Fractional Dynamics of HIV with Source Term for the Supply of New CD4+ T-Cells Depending on the Viral Load via Caputo-Fabrizio Derivative.

Human immunodeficiency virus (HIV) is a life life-threatening and serious infection caused by a virus that attacks CD4+ T-cells, which fight against infections and make a person susceptible to other diseases. It is a global public health problem with no cure; therefore, it is highly important to study and understand the intricate phenomena of HIV. In this article, we focus on the numerical study of the path-tracking damped oscillatory behavior of a model for the HIV infection of CD4+ T-cells. We formulate fractional dynamics of HIV with a source term for the supply of new CD4+ T-cells depending on the viral load via the Caputo-Fabrizio derivative. In the formulation of fractional HIV dynamics, we replaced the constant source term for the supply of new CD4+ T-cells from the thymus with a variable source term depending on the concentration of the viral load, and introduced a term that describes the incidence of the HIV infection of CD4+ T-cells. We present a novel numerical scheme for fractional view analysis of the proposed model to highlight the solution pathway of HIV. We inspect the periodic and chaotic behavior of HIV for the given values of input factors using numerical simulations.

Weighted Mutual Information for Aggregated Kernel Clustering.

Background: A common task in machine learning is clustering data into different groups based on similarities. Clustering methods can be divided in two groups: linear and nonlinear. A commonly used linear clustering method is K-means. Its extension, kernel K-means, is a non-linear technique that utilizes a kernel function to project the data to a higher dimensional space. The projected data will then be clustered in different groups. Different kernels do not perform similarly when they are applied to different datasets. Methods: A kernel function might be relevant for one application but perform poorly to project data for another application. In turn choosing the right kernel for an arbitrary dataset is a challenging task. To address this challenge, a potential approach is aggregating the clustering results to obtain an impartial clustering result regardless of the selected kernel function. To this end, the main challenge is how to aggregate the clustering results. A potential solution is to combine the clustering results using a weight function. In this work, we introduce Weighted Mutual Information (WMI) for calculating the weights for different clustering methods based on their performance to combine the results. The performance of each method is evaluated using a training set with known labels. Results: We applied the proposed Weighted Mutual Information to four data sets that cannot be linearly separated. We also tested the method in different noise conditions. Conclusions: Our results show that the proposed Weighted Mutual Information method is impartial, does not rely on a single kernel, and performs better than each individual kernel specially in high noise.

Author Correction: A comprehensive study to the assessment of Arrhenius activation energy and binary chemical reaction in swirling flow.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Nano zinc elicited biochemical characterization, nutritional assessment, antioxidant enzymes and fatty acid profiling of rapeseed.

The use of nanomaterials in agriculture is a current need and could be helpful in overcoming food security risks. Brassica napus L. is the third most important crop for edible oil, having double low unsaturated fatty acids. In the present study, we investigated the effects of green synthesized Zn NPs on biochemical effects, antioxidant enzymes, nutritional quality parameters and on the fatty acid profile of rapeseed (B. napus). Plant-mediated synthesis of zinc nanoparticles (Zn NPs) was carried out using Mentha arvensis L. leaf extract followed by characterization through ultraviolet-visible spectroscopy (UV-vis), scanning electron microscopy (SEM), transmission electron microscopy (TEM), energy dispersive X-Ray (EDX), and X-Ray diffraction (XRD). NPs exhibited irregular shapes ranging in size from 30-70 nm and EDX analysis confirmed 96.08% of Zn in the sample. The investigated biochemical characterization (protein content, proline content, total soluble sugar (TSS), total flavonoid content (TFC), and total phenolic content (TPC) showed a substantial change on exposure to Zn NPs. A dose-dependent gradual increase was observed in the antioxidant enzymes, superoxide dismutase (SOD), peroxidase (POD), and catalase (CAT). Oil and moisture contents dropped significantly from the control level in the rapeseed (B. napus) varieties. However, different trends in nutritional (Zn, Na+, K+) and fatty acid profiling of B. napus have been noted. This study demonstrates that Zn NPs have the potential to improve the biochemical, nutritional, antioxidant enzymes, and fatty acid profile of B. napus varieties.

A comprehensive study to the assessment of Arrhenius activation energy and binary chemical reaction in swirling flow.

Nanotechnology research has a huge impact upon biomedicine and at the forefront of this area are micro and nano devices that use active/controlled motion. In this connection, it is focus to investigate steady three dimensional rotating flow with heat and mass transfer incorporating gyrotactic microorganisms. Buongiorno's nanofluid formulation is followed for thermophoresis and Brownian motion, porous space, Arrhenius activation energy and binary chemical reaction with some other effects. An enhanced analytical method is applied to solve the nondimensional equations. The non-dimensional parameters effects on the fields of velocity, temperature, nanoparticles concentration and gyrotactic microorganisms concentration are shown graphically. Velocity decreases while temperature and nanoparticles concentration increase with magnetic field strength. Gyrotatic microorganisms motion becomes slow with rotation parameter. Due to rotation, the present problem can be applied in microbial fuel cells, food processing, microbiology, biotechnology and environmental sciences, electric power generating and turbine systems, computer disk drives, mass spectromentries and jet motors.

Brownian Motion and Thermophoresis Effects on MHD Three Dimensional Nanofluid Flow with Slip Conditions and Joule Dissipation Due to Porous Rotating Disk.

This paper examines the time independent and incompressible flow of magnetohydrodynamic (MHD) nanofluid through a porous rotating disc with velocity slip conditions. The mass and heat transmission with viscous dissipation is scrutinized. The proposed partial differential equations (PDEs) are converted to ordinary differential equation (ODEs) by mean of similarity variables. Analytical and numerical approaches are applied to examine the modeled problem and compared each other, which verify the validation of both approaches. The variation in the nanofluid flow due to physical parameters is revealed through graphs. It is witnessed that the fluid velocities decrease with the escalation in magnetic, velocity slip, and porosity parameters. The fluid temperature escalates with heightening in the Prandtl number, while other parameters have opposite impacts. The fluid concentration augments with the intensification in the thermophoresis parameter. The validity of the proposed model is presented through Tables.

Discriminant Analysis of Lung Cancer Using Nonlinear Clustering of Copy Numbers.

Background: Patient survival is not optimal for non-small cell lung cancer (NSCLC) patients, recurrence rate is high, and hence, early detection is crucial to increase the patient's survival. Gene-cancer mapping intends to discover associated genes with cancers and due to advances in high-throughput genotyping, screening for disease loci on a genome-wide scale is now possible. DNA copy numbers can potentially be used to identify cancer from normal cells in early detection of cancer.Methods: We use a nonlinear clustering method, so-called kernel K-means to separate cancer from normal samples. Kernel K-means is applied to the copy numbers obtained for each chromosome to cluster 63 paired cancer-blood samples (total of 126 samples) into two groups. Clustering performance is evaluated using true and false-positive rates, true and false-negative rates, and a nonlinear criterion, normalized mutual information (NMI).Results: Copy numbers of paired cancer-blood samples for 63 NSCLC patients are used in this study. Kernel K-means was applied to cluster 126 samples in two groups using copy numbers on each chromosome separately. The clustering results for 22 chromosomes are evaluated and discriminant power of them in identifying cancer is computed. We identified the top five and bottom five chromosomes based on their discriminant power.Conclusions: The results reveal high discriminant power of chromosomes 8, 5, 1, 3, and 19 for identifying cancer with the highest sensitivity of 75% yielded by chromosome 5. Bottom 5 chromosomes 9, 6, 4, 13, and 21 show low discriminant power with the accuracy of below 54% where true cancer and normal samples are grouped into substantially overlapping groups using copy numbers. This indicates the similarities of copy numbers obtained for cancer and normal samples on these chromosomes.