Approximate Analytical Solutions of Space-Fractional Telegraph Equations by Sumudu Adomian Decomposition Method

The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases

Socio-demographic characteristics and tobacco use among the adults in urban slums of Dhaka, Bangladesh

Background: Use of tobacco has become one of the major causes of premature deaths in most developing countries, including Bangladesh. The poorest and most disadvantaged populations, such as those living in slums, are considered to be extremely vulnerable to non-communicable diseases and their risk factors, especially tobacco use. The objective of this study was to assess the current status of tobacco consumption among slum dwellers and its association with socio-demographic factors. Methods: A cross-sectional study was conducted in three slums of Dhaka city. Information about tobacco use as well as socio-demographic characteristics was collected from adult slum dwellers via face to face interviews using WHO STEPS questionnaire. Result: Overall proportion of smoking, smokeless tobacco consumption and dual use of tobacco was 35% [95% CI: 31.6-39.8], 40.6% [95% CI: 36.5-45.2] and 12% [95% CI: 9.3-15.0] respectively. Elderly people (55-64 years) were more likely to smoke (OR: 2.34, 95% CI: 1.21-4.49) than younger people (aged 25-34 years). On the other hand, those who had no schooling history (OR: 2.95, 95% CI: 1.66-5.25) were more likely to consume smokeless tobacco than those who had higher education (secondary or above). At the same time, manual workers were more likely to indulge in dual use of tobacco (OR: 5.17, 95% CI: 2.82-9.48) as compared to non-manual workers. Conclusion: The urban slum population of Dhaka city has a high prevalence of tobacco use, which increases their likelihood of developing non-communicable diseases. Proper attention needs to be directed towards addressing the risk factors related to non-communicable diseases within this vulnerable population

On existence results for solutions of a coupled system of hybrid boundary value problems with hybrid conditions

Abstract We investigate sufficient conditions for existence and uniqueness of solutions for a coupled system of fractional order hybrid differential equations (HDEs) with multi-point hybrid boundary conditions given by D ω ( x ( t ) H ( t , x ( t ) , z ( t ) ) ) = − K 1 ( t , x ( t ) , z ( t ) ) , ω ∈ ( 2 , 3 ] , D ϵ ( z ( t ) G ( t , x ( t ) , z ( t ) ) ) = − K 2 ( t , x ( t ) , z ( t ) ) , ϵ ∈ ( 2 , 3 ] , x ( t ) H ( t , x ( t ) , z ( t ) ) | t = 1 = 0 , D μ ( x ( t ) H ( t , x ( t ) , z ( t ) ) ) | t = δ 1 = 0 , x ( 2 ) ( 0 ) = 0 , z ( t ) G ( t , x ( t ) , z ( t ) ) | t = 1 = 0 , D ν ( z ( t ) G ( t , x ( t ) , z ( t ) ) ) | t = δ 2 = 0 , z ( 2 ) ( 0 ) = 0 , $$\begin{aligned}& \mathcal{D}^{\omega}\biggl(\frac{x(t)}{\mathcal{H}(t,x(t),z(t))}\biggr)=-\mathcal {K}_{1}\bigl(t,x(t),z(t)\bigr), \quad\omega\in(2,3], \\& \mathcal{D}^{\epsilon}\biggl(\frac{z(t)}{\mathcal {G}(t,x(t),z(t))}\biggr)=-\mathcal{K}_{2} \bigl(t,x(t),z(t)\bigr), \quad\epsilon\in (2,3],\\& \frac{x(t)}{\mathcal{H}(t,x(t),z(t))}\bigg|_{t=1}=0,\qquad \mathcal{D}^{\mu}\biggl( \frac{x(t)}{\mathcal{H}(t,x(t),z(t))}\biggr)\bigg|_{t= \delta_{1} }=0,\qquad x^{(2)}(0)=0, \\& \frac{z(t)}{\mathcal{G}(t,x(t),z(t))}\bigg|_{t=1}=0, \qquad\mathcal{D}^{\nu}\biggl( \frac{z(t)}{\mathcal{G}(t,x(t),z(t))}\biggr)\bigg|_{t= \delta_{2}}=0,\qquad z^{(2)}(0)=0, \end{aligned}$$ where t ∈ [ 0 , 1 ] $t\in[0,1]$ , δ 1 , δ 2 , μ , ν ∈ ( 0 , 1 ) $\delta_{1}, \delta_{2}, \mu, \nu\in(0,1)$ , and D ω $\mathcal{D}^{\omega}$ , D ϵ $\mathcal{D}^{\epsilon}$ , D μ $\mathcal{D}^{\mu}$ and D ν $\mathcal{D}^{\nu}$ are Caputo’s fractional derivatives of order ω, ϵ, μ and ν, respectively, K 1 , K 2 ∈ C ( [ 0 , 1 ] × R × R , R ) $\mathcal{K}_{1}, \mathcal{K}_{2}\in C([0,1]\times\mathcal{R}\times \mathcal{R},\mathcal{R} )$ and G , H ∈ C ( [ 0 , 1 ] × R × R , R − { 0 } ) $\mathcal{G},\mathcal{H}\in C([0,1]\times\mathcal{R}\times\mathcal {R},\mathcal{R} - \{0\} )$ . We use classical results due to Dhage and Banach’s contraction principle (BCP) for the existence and uniqueness of solutions. For applications of our results, we include examples

A Comparative Study of AHP and Fuzzy AHP Method for Inconsistent Data

In various cases of decision analysis we use two popular methods – Analytical Hierarchical Process (AHP) and Fuzzy based AHP or Fuzzy AHP. Both the methods deal with stochastic data and can determine decision result through Multi Criteria Decision Making (MCDM) process. Obviously resulting values of the two methods are not same though same set of data is fed into them. In this research work, we have tried to observe similarities and dissimilarities between two methods’ outputs. Almost same trend or fluctuations in outputs have been seen for both methods’ for same set of input data which are not consistent. Both method outputs’ ups and down fluctuations are same for fifty percent cases

Addressing Uncertainty in Imbalanced Histopathology Image Classification of HER2 Breast Cancer: An interpretable Ensemble Approach with Threshold Filtered Single Instance Evaluation (SIE)

Breast Cancer (BC) is among women's most lethal health concerns. Early diagnosis can alleviate the mortality rate by helping patients make efficient treatment decisions. Human Epidermal Growth Factor Receptor (HER2) has become one the most lethal subtype of BC. According to the College of American Pathologists/American Society of Clinical Oncology (CAP/ASCO), the severity level of HER2 expression can be classified between 0 and 3+ range. HER2 can be detected effectively from immunohistochemical (IHC) and, hematoxylin \& eosin (HE) images of different classes such as 0, 1+, 2+, and 3+. An ensemble approach integrated with threshold filtered single instance evaluation (SIE) technique has been proposed in this study to diagnose BC from the multi-categorical expression of HER2 subtypes. Initially, DenseNet201 and Xception have been ensembled into a single classifier as feature extractors with an effective combination of global average pooling, dropout layer, dense layer with a swish activation function, and l2 regularizer, batch normalization, etc. After that, extracted features has been processed through single instance evaluation (SIE) to determine different confidence levels and adjust decision boundary among the imbalanced classes. This study has been conducted on the BC immunohistochemical (BCI) dataset, which is classified by pathologists into four stages of HER2 BC. This proposed approach known as DenseNet201-Xception-SIE with a threshold value of 0.7 surpassed all other existing state-of-art models with an accuracy of 97.12\%, precision of 97.15\%, and recall of 97.68\% on H\&E data and, accuracy of 97.56\%, precision of 97.57\%, and recall of 98.00\% on IHC data respectively, maintaining momentous improvement. Finally, Grad-CAM and Guided Grad-CAM have been employed in this study to interpret, how TL-based model works on the histopathology dataset and make decisions from the data

Piecewise mABC fractional derivative with an application

In this study, we give the notion of a piecewise modified Atangana-Baleanu-Caputo (mABC) fractional derivative and apply it to a tuberculosis model. This novel operator is a combination of classical derivative and the recently developed modified Atangana-Baleanu operator in the Caputo's sense. For this combination, we have considered the splitting of an interval $[0, t_2]$ for $t_2\in\mathbb{R}^+$, such that, the classical derivative is applied in the first portion $[0, t_1]$ while the second differential operator is applied in the interval $[t_1, t_2]$. As a result, we obtained the piecewise mABC operator. Its corresponding integral is also given accordingly. This new operator is then applied to a tuberculosis model for the study of crossover behavior. The existence and stability of solutions are investigated for the nonlinear piecewise modified ABC tuberculosis model. A numerical scheme for the simulations is presented with the help of Lagrange's interpolation polynomial is then applied to the available data

Shapes2Toon: Generating Cartoon Characters from Simple Geometric Shapes

Cartoons are an important part of our entertainment culture. Though drawing a cartoon is not for everyone, creating it using an arrangement of basic geometric primitives that approximates that character is a fairly frequent technique in art. The key motivation behind this technique is that human bodies - as well as cartoon figures - can be split down into various basic geometric primitives. Numerous tutorials are available that demonstrate how to draw figures using an appropriate arrangement of fundamental shapes, thus assisting us in creating cartoon characters. This technique is very beneficial for children in terms of teaching them how to draw cartoons. In this paper, we develop a tool - shape2toon - that aims to automate this approach by utilizing a generative adversarial network which combines geometric primitives (i.e. circles) and generate a cartoon figure (i.e. Mickey Mouse) depending on the given approximation. For this purpose, we created a dataset of geometrically represented cartoon characters. We apply an image-to-image translation technique on our dataset and report the results in this paper. The experimental results show that our system can generate cartoon characters from input layout of geometric shapes. In addition, we demonstrate a web-based tool as a practical implication of our work.Comment: Accepted as a full paper in AICCSA2022 (19th ACS/IEEE International Conference on Computer Systems and Applications

On ABC coupled Langevin fractional differential equations constrained by Perov's fixed point in generalized Banach spaces

Nonlinear differential equations are widely used in everyday scientific and engineering dynamics. Problems involving differential equations of fractional order with initial and phase changes are often employed. Using a novel norm that is comfortable for fractional and non-singular differential equations containing Atangana-Baleanu-Caputo fractional derivatives, we examined a new class of initial values issues in this study. The Perov fixed point theorems that are utilized in generalized Banach spaces form the foundation for the new findings. Examples of the numerical analysis are provided in order to safeguard and effectively present the key findings