The deterministic fractals play an important role in computer graphics and mathematical sciences. The understanding of construction of such fractals, especially an ability of fractals construction from various types of polytopes is of crucial importance in several problems related both to the pure mathematical issues as well as some issues of theoretical physics. In the present paper the possibility of construction of fractals based on the Catalan solids is presented and discussed. The method and algorithm of construction of polyhedral strictly deterministic fractals is presented. It is shown that the fractals can be constructed only from a limited number of the Catalan solids due to the specific geometric properties of these solids. The contraction ratios and fractal dimensions are presented for existing fractals with adjacent contractions constructed based on the Catalan solids.

AI algorithms have been applied in a wide spectrum of articles across different domains with great success in finding solutions. There is an increasing trend of applying these techniques on newer problems. However, the numerous numbers of algorithms that are classified as AI algorithm hinder the ability of any researcher to select which algorithm is suitable for his problem. The invention of new algorithms increases the difficulty for researchers to be updated about AI algorithms. This paper is intended to provide a multi-facet comparison between various AI algorithms in order to aid researchers in understanding the differences between some of the popular algorithms and select the suitable candidate for their problems.

In the present paper first and foremost we introduce a generalization of a classical Fibonacci sequence which is called a Fibonacci-Like sequence and at hindmost we obtain some relationships between Lucas sequence and Fibonacci-Like sequence by using two cross two matrix representation to the Fibonacci-Like sequence. The most worth noticing cause of this article is our proof method, since all the identities are proved by using matrix methods.

One distress of network and data security professionals and advisers globally is about the abilities of infectious malicious agents (Malware) to invade the entire network terminals to wreak havoc extending from identity theft, financial fraud to systemic digital assault on critical national resources. This work studies the behavioural dynamics of the susceptible, infected, the recovered terminals on the mobile wireless network and the effective use of antivirus security signature as countermeasure. Solving for stability state, we found out that its Eigen value gives a positive value which means that the stability is at an unstable state. Using Homotopy perturbation to calculate the approximate solution of the system. The expression derived was simulated using a mathematical tool (mat lab).

Association rule mining is a data mining technique which is used to identify decision-making patterns by analyzing datasets. Many association rule mining techniques exist to find various relationships among itemsets. The techniques proposed in the literature are processed using non-distributed platform in which the entire dataset is sustained till all transactions are processed and the transactions are scanned sequentially. They require more space and are time consuming techniques when large amounts of data are considered. An efficient technique is needed to find association rules from big data set to minimize the space as well as time. Thus, this paper aims to enhance the efficiency of association rule mining of big transaction database both in terms of memory and speed by processing the big transaction database as distributed file system in Map-Reduce framework. The proposed method organizes the transactions into clusters and the clusters are distributed among many parallel processors in a distributed platform. This distribution makes the clusters to be processed simultaneously to find itemsets which enhances the performance both in memory and speed. Then, frequent itemsets are discovered using minimum support threshold. Associations are generated from frequent itemsets and finally interesting rules are found using minimum confidence threshold. The efficiency of the proposed method is enhanced in a noticeably higher level both in terms of memory and speed.