**Mathematical Proof of the New Proposed Non-Coprime Moduli Set Using Forward Conversion in Residue Number System**

Mansour Bader, Al-Balqa'a Applied University, Jordan and Andraws Swidan, Jordan University, Jordan##### ABSTRACT

In this paper mathematical proof of the new Binary-to-RNS Non-Coprime moduli set in RNS of the form{ 2n – 2, 2n, 2n + 2 } is presented. The modulies 2n – 2, 2n + 2 are known to be called conjugates of each other and has been discussed in previous literature [2- 4]. Coprime moduli sets offer these benefits:1) Large dynamic ranges. 2) Fast RNS arithmetic. 3) Simple and efficient RNS processing hardware. 4) Efficient weighted-to-RNS and RNS-to-Weighted converters. When comparing the Non-Coprime ones to them the DR (Dynamic Range )is the dominant. The dynamic range achieved by the set above is defined by the least common multiple ( LCM ) of the moduli and the non-coprime set was carefully chosen to do the mathematical calculations upon. This new non-coprime moduli set is unique and the only one of its shape.

**Kurtosis: Is It An Appropriate Measure To Compare The Extent Of Fat-Tailedness Of The Degree Distribution For Any Two Real-World Networks?**

Natarajan Meghanathan, Jackson State University, USA##### ABSTRACT

"Kurtosis" has long been considered an appropriate measure to quantify the extent of fat-tailedness of the degree distribution of a complex real-world network. However, the Kurtosis values for more than one real-world network have not been studied in conjunction with other statistical measures that also capture the extent of variation in node degree. In this paper, we determine the Kurtosis values for a suite of 48 real-world networks along with measures such as SPR(K), Max(K)-Min(K), Max(K)-Avg(K), SD(K)/Avg(K), wherein SPR(K), Max(K), Min(K), Avg(K) and SD(K) represent the spectral radius ratio for node degree, maximum node degree, minimum node degree, average and standard deviation of node degree respectively. Contrary to the conceived notion in the literature, we observe that real-world networks whose degree distribution is Poisson in nature (characterized by lower values of SPR(K), Max(K)-Min(K), Max(K)-Avg(K), SD(K)/Avg(K)) could have Kurtosis values that are larger than that of real-world networks whose degree distribution is scale-free in nature (characterized by larger values of SPR(K), Max(K)-Min(K), Max(K)-Avg(K), SD(K)/Avg(K)). When evaluated for any two real-world networks among all the 48 real-world networks, the Kendall's concordance-based correlation coefficients between Kurtosis and each of SPR, Max(K)-Min(K), Max(K)-Avg(K) and SD(K)/Avg(K) are 0.40, 0.26, 0.34 and 0.50 respectively. Thus, we seriously question the appropriateness of using Kurtosis to compare the extent of fat-tailedness of the degree distribution of the vertices for any two real-world networks.

**An Auto-Scaling Virtual Resource Mechanism for Real-Time Healthcare Applications in Cloud Computing**

Tushar Bhardwaj, Mohit Kumar, and Subhash Chander Sharma, IIT Roorkee, India##### ABSTRACT

In real-time healthcare applications, the user’s requests vary dramatically which requires adequate computing resources to meet Quality of services (QoS). The conventional server side mechanisms have limitations in adaptively allocating the necessary computation resources in order to handle the variability of incoming user's requests. Cloud computing provides the infinite number of virtual resources to address the aforementioned scenario. But, the main issue in this system is to handle the over and under utilization of resources. In this paper, we propose and develop an autonomous virtual resource mechanism that automatically allocate and de-allocate (scale-up & scale-down) the virtual resources as per user requirements.The main aim of this study is to improve the response time and virtual resource's utilization with respect to conventional methods. We have formulated the problem with the help of simple heuristic, taking response time and number of virtual resources as parameters. The results show the improvement in response time with an effective utilization of virtual resources.