ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL DIMENSIONS

In this paper,we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions.More precisely,we show that,given a real number 1≤β≤2,any real-valued continuous function in C([0,1])can be decomposed into a product of two real-valued continuous functions,each having a graph of Hausdorff dimensionβ.In addition,a product decomposition result for the packing dimension is obtained.This work answers affirmatively two questions raised by Verma and Priyadarshi[14].

Evolution of Word-updating Dynamical Systems (WDS) on Directed Graphs

This paper continues the research on theoretical foundations for computer simulation.We introduce the concept of word-updating dynamical systems(WDS)on directed graphs,which is a kind of generalization of sequential dynamical systems(SDS)on graphs.Some properties on WDS,especially some results on NOR-WDS,which are different from that on NOR-SDS,are obtained.

Conditional Generative Adversarial Network Approach for Autism Prediction

Autism Spectrum Disorder(ASD)requires a precise diagnosis in order to be managed and rehabilitated.Non-invasive neuroimaging methods are disease markers that can be used to help diagnose ASD.The majority of available techniques in the literature use functional magnetic resonance imaging(fMRI)to detect ASD with a small dataset,resulting in high accuracy but low generality.Traditional supervised machine learning classification algorithms such as support vector machines function well with unstructured and semi structured data such as text,images,and videos,but their performance and robustness are restricted by the size of the accompanying training data.Deep learning on the other hand creates an artificial neural network that can learn and make intelligent judgments on its own by layering algorithms.It takes use of plentiful low-cost computing and many approaches are focused with very big datasets that are concerned with creating far larger and more sophisticated neural networks.Generative modelling,also known as Generative Adversarial Networks(GANs),is an unsupervised deep learning task that entails automatically discovering and learning regularities or patterns in input data in order for the model to generate or output new examples that could have been drawn from the original dataset.GANs are an exciting and rapidly changingfield that delivers on the promise of generative models in terms of their ability to generate realistic examples across a range of problem domains,most notably in image-to-image translation tasks and hasn't been explored much for Autism spectrum disorder prediction in the past.In this paper,we present a novel conditional generative adversarial network,or cGAN for short,which is a form of GAN that uses a generator model to conditionally generate images.In terms of prediction and accuracy,they outperform the standard GAN.The pro-posed model is 74%more accurate than the traditional methods and takes only around 10 min for training even with a huge dataset.

The Fractional Derivatives of a Fractal Function

The present paper investigates the fractional derivatives of Weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of the graphs of Weierstrass function.

A Novel Approach for Android Malware Detection Based on Intelligent Computing

Detecting malware on mobile devices using the Android operating system has become a critical challenge in the field of cybersecurity,in the context of the rapid increase in the number of malware variants and the frequency of attacks targeting Android devices.In this paper,we propose a novel intelligent computational method to enhance the effectiveness of Android malware detection models.The proposed method combines two main techniques:(1)constructing a malware behavior profile and(2)extracting features from the malware behavior profile using graph neural networks.Specifically,to effectively construct an Android malware behavior profile,this paper proposes an information enrichment technique for the function call graph of malware files,based on new graph-structured features and semantic features of the malware’s source code.Additionally,to extract significant features from the constructed behavior profile,the study proposes using the GraphSAGE graph neural network.With this novel intelligent computational method,a variety of significant features of the malware have been effectively represented,synthesized,and extracted.The approach to detecting Android malware proposed in this paper is a new study and has not been explored in previous research.The experimental results on a dataset of 40,819 Android software indicate that the proposed method performs well across all metrics,with particularly impressive accuracy and recall scores of 99.03%and 99.19%,respectively,which outperforms existing state-of-the-art methods.