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.