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Network slicing (NS) and multi-access edge computing (MEC) are new paradigms which play key roles in 5G and beyond networks. NS allows network operators (NOs) to divide the available network resources into multiple logical NSs for providing dedicated virtual networks tailored to the specific service/business requirements. MEC enables NOs to provide diverse ultra-low latency services for supporting the needs of different industry verticals by moving computing facilities to the network edge. NS can be constructed by instantiating a set of virtual network functions (VNFs) on top of MEC cloud servers for provisioning diverse latency-sensitive communication services (e.g., autonomous driving and augmented reality) on demand at a lesser cost and time. However, VNFs, MEC cloud servers, and communication links are subject to failures due to software bugs, misconfiguration, overloading, hardware faults, cyber attacks, power outage, and natural/man-made disaster. Failure of a critical network component disrupts services abruptly and leads to users' dissatisfaction, which may result in revenue loss for the NOs. In this paper, we present a novel approach based on multi-connectivity in 5G networks to tackle this problem and our proposed approach is resilient against i) failure of VNFs, ii) failure of local servers within MEC, iii) failure of communication links, and iv) failure of an entire MEC cloud facility in regional level. To this end, we formulate the problem as a binary integer programming (BIP) model in order to optimally deploy NSs with the minimum cost, and prove it is NP-hard. To overcome time complexity, we propose an efficient genetic algorithm based heuristic to obtain near-optimal solution in polynomial time. By extensive simulations, we show that our proposed approach not only reduces resource wastage, but also improves throughput while providing high resiliency against failures.

Network Functions Virtualization (NFV) and Multi-access Edge Computing (MEC) play crucial roles in 5G networks for dynamically provisioning diverse communication services with heterogeneous service requirements. In particular, while NFV improves flexibility and scalability by softwarizing physical network functions as Virtual Network Functions (VNFs), MEC enables to provide delay-sensitive/time-critical services by moving computing facilities to the network edge. However, these new paradigms introduce challenges in terms of latency, availability, and resource allocation. In this paper, we first explore MEC cloud facility location selection and then latency-aware placement of VNFs in different selected locations of NFV enabled MEC cloud facilities in order to meet the ultra-low latency requirements of different applications (e.g., Tactile Internet, virtual reality, and mission-critical applications). Furthermore, we also aim to guarantee the survivability of VNFs and an edge server against failures in resource limited MEC cloud facility due to software bugs, configuration faults, etc. To this end, we formulate the problem of latency-aware and survivable mapping of VNFs in different MEC cloud facilities as an Integer Linear Programming (ILP) to minimize the overall service provisioning cost, and show that the problem is NP-hard. Owing to the high computational complexity of solving the ILP, we propose a simulated annealing based heuristic algorithm to obtain near-optimal solution in polynomial time. With extensive simulations, we show the effectiveness of our proposed solution in a real-world network topology, which performs close to the optimal solution.

Network Functions Virtualization (NFV) allows flexibility, scalability, agility, and easy manageability of networks by leveraging the features of virtualization and cloud computing technologies. However, softwarization of network functions imposes many challenges. Reliability and latency are major challenges in NFV-enabled 5G networks that can lead to customer dissatisfaction and revenue loss. In general, redundancy is used to improve the reliability of communication services. However, redundancy requires the same amount of additional resources and thus increases cost. In this work, we address the reliability-aware, delay guaranteed, and resource efficient Service Function Chain (SFC) placement problem in softwarized 5G networks. First, we propose a novel SFC subchaining method to enhance the reliability of an SFC without backups. If reliability requirement is not met after subchaining method, we add backups to VNFs to meet the reliability requirement. Then, we formulate the reliable SFC placement problem as an Integer Linear Programming (ILP) problem in order to solve it optimally. Owing to high computational complexity of the ILP problem for solving large input instances, we propose a modified stable matching algorithm to provide near-optimal solution in polynomial time. By extensive simulations we show that our proposed solutions consume lesser physical resources compared to state-of-the-art solutions for provisioning reliable communication services., Comment: 17 pages

Although network functions virtualization and software-defined networking offer many dynamic features such as flexibility, scalability, and programmability for easy provisioning of services at a lesser cost and time through service function chaining, it introduces new challenges in terms of reliability, availability, and latency of services. Particularly, softwarization of network and service functions (e.g., virtualization, anything as a service, dynamic virtual chaining, and routing) impose high possibility of network failures due to software issues than hardware. In this letter, we propose a novel solution called eRESERV to enhance the reliability of service chains in 5G while meeting the service level agreements., Comment: 4 pages, 10 figures

Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the variables, and they often perform poorly if the dependence among the variables is highly non-monotone in nature. In this article, we propose a copula based measure of dependency and use it to construct some new distribution-free tests of independence. The proposed measure and the resulting tests, all are invariant under permutations and monotone transformations of the variables. Our dependency measure involves a kernel function, and we use the Gaussian kernel for that purpose. We adopt a multi-scale approach, where we look at the results obtained for several choices of the bandwidth parameter associated with the Gaussian kernel and aggregate them judiciously. Large sample properties of the dependency measure and the resulting tests are derived under appropriate regularity conditions. Several simulated and real data sets are analyzed to compare the performance of the proposed tests with some popular tests available in the literature., Comment: arXiv admin note: text overlap with arXiv:1708.07485

The existing biclustering algorithms for finding feature relation based biclusters often depend on assumptions like monotonicity or linearity. Though a few algorithms overcome this problem by using density-based methods, they tend to miss out many biclusters because they use global criteria for identifying dense regions. The proposed method, RelDenClu uses the local variations in marginal and joint densities for each pair of features to find the subset of observations, which forms the bases of the relation between them. It then finds the set of features connected by a common set of observations, resulting in a bicluster. To show the effectiveness of the proposed methodology, experimentation has been carried out on fifteen types of simulated datasets. Further, it has been applied to six real-life datasets. For three of these real-life datasets, the proposed method is used for unsupervised learning, while for other three real-life datasets it is used as an aid to supervised learning. For all the datasets the performance of the proposed method is compared with that of seven different state-of-the-art algorithms and the proposed algorithm is seen to produce better results. The efficacy of proposed algorithm is also seen by its use on COVID-19 dataset for identifying some features (genetic, demographics and others) that are likely to affect the spread of COVID-19.

In this work, we propose an ensemble of classification trees (CT) and artificial neural networks (ANN). Several statistical properties including universal consistency and upper bound of an important parameter of the proposed classifier are shown. Numerical evidence is also provided using various real life data sets to assess the performance of the model. Our proposed nonparametric ensemble classifier doesn't suffer from the `curse of dimensionality' and can be used in a wide variety of feature selection cum classification problems. Performance of the proposed model is quite better when compared to many other state-of-the-art models used for similar situations.

We propose a new multivariate dependency measure. It is obtained by considering a Gaussian kernel based distance between the copula transform of the given d-dimensional distribution and the uniform copula and then appropriately normalizing it. The resulting measure is shown to satisfy a number of desirable properties. A nonparametric estimate is proposed for this dependency measure and its properties (finite sample as well as asymptotic) are derived. Some comparative studies of the proposed dependency measure estimate with some widely used dependency measure estimates on artificial datasets are included. A non-parametric test of independence between two or more random variables based on this measure is proposed. A comparison of the proposed test with some existing nonparametric multivariate test for independence is presented., Comment: This work is postponed

This article examines the application of a popular measure of sparsity, Gini Index, on network graphs. A wide variety of network graphs happen to be sparse. But the index with which sparsity is commonly measured in network graphs is edge density, reflecting the proportion of the sum of the degrees of all nodes in the graph compared to the total possible degrees in the corresponding fully connected graph. Thus edge density is a simple ratio and carries limitations, primarily in terms of the amount of information it takes into account in its definition. In this paper, we have provided a formulation for defining sparsity of a network graph by generalizing the concept of Gini Index and call it sparsity index. A majority of the six properties (viz., Robin Hood, Scaling, Rising Tide, Cloning, Bill Gates and Babies) with which sparsity measures are commonly compared are seen to be satisfied by the proposed index. A comparison between edge density and the sparsity index has been drawn with appropriate examples to highlight the efficacy of the proposed index. It has also been shown theoretically that the two measures follow similar trend for a changing graph, i.e., as the edge density of a graph increases its sparsity index decreases. Additionally, the paper draws a relationship, analytically, between the sparsity index and the exponent term of a power law distribution, a distribution which is known to approximate the degree distribution of a wide variety of network graphs. Finally, the article highlights how the proposed index together with Gini index can reveal important properties of a network graph., Comment: 15 pages with 6 figures

Time series data on cropping pattern at disaggregated level were analysed and its implications on geospatial drought assessment were demonstrated. An index of Cropping Pattern Dissimilarity (CP-DI) between a pair of years, developed in this study, proved that the cropping pattern of a year has a higher degree of similarity with that of recent past years only and tends to be dissimilar with longer time difference. The temporal divergence in cropping pattern has direct implications on geospatial approach of drought assessment, in which, time series NDVI data are compared for drought interpretation. It was found that, seasonal NDVI profiles of drought year and normal year did not show any anomaly when the cropping patterns were dissimilar and two normal years having dissimilar cropping pattern showed different NDVI profiles. Therefore, it is suggested that such temporal comparisons of NDVI are better restricted to recent past years to achieve more objective interpretation., Comment: 9 pages, 14 figures

Monthly rainfall data from June to October for 39 years was used to generate Standardized Precipitation Index (SPI) values based on Gamma distribution for a low rainfall and a high rainfall district of Andhra Pradesh state, India. Comparison of SPI, with actual rainfall and rainfall deviation from the mean indicated that SPI values under-estimate the intensity of dryness/wetness when the rainfall is very low/very high respectively. As a result, the SPI in the worst drought years of 2002 and 2006 in the low rainfall district has indicated only moderate dryness instead of extreme dryness. The range of SPI values of the high rainfall district indicated better stretching, compared to that of the low rainfall district. Further, the SPI values of longer time scale (2-, 3- and 4- months) showed an extended range compared to 1-month, but the sensitivity in drought years has not improved significantly. To ascertain whether non normality of SPI is a possible reason, normality tests were conducted. The Shapiro-Wilk statistic, p-values and absolute value of the median confirmed normal distribution of SPI in both the districts whereas cumulative probability distribution of SPI indicated deviation from normal probability in the lower and upper ranges. Therefore, it is suggested that SPI as a stand alone indicator needs to be interpreted with caution to assess the intensity of drought. Further investigations should include; sensitivity of SPI to the estimated shape and scale at lower and upper bounds of gamma and impact of other distributions such as Pearson III on SPI computation, to complement the above results., Comment: 22 pages, 8 figures

Grid (1{\deg} latitude x 1{\deg} longitude) level daily rainfall data over India from June to September for the years 1951 to 2007, generated by India Meteorological Department, was analyzed to build monthly time series of Standardized Precipitation Index (SPI). Analysis of SPI was done to study the spatial and temporal patterns of drought occurrence in the country. Geographic spread of SPI derived Area under Dryness (AUD) in different years revealed the uniqueness of 2002 drought with wide spread dryness in July. Mann-Kendal trend analysis and moving average based trends performed on AUD indicated increasing trend in July. The area under moderate drought frequency has increased in the most recent decade. Ranking of years based on Drought Persistency Score (DPS) indicated that the year 1987 was the severe-most drought year in the country. The results of the study have revealed various aspects of drought climatology in India. A similar analysis with the SPI of finer spatial resolution and relating it to crop production would be useful in quantifying the impact of drought in economic terms.

This article proposes a new method to estimate an existing mutual information based dependence measure using histogram density estimates. Finding a suitable bin length for histogram is an open problem. We propose a new way of computing the bin length for histogram using a function of maximum separation between points. The chosen bin length leads to consistent density estimates for histogram method. The values of density thus obtained are used to calculate an estimate of an existing dependence measure. The proposed estimate is named as Mutual Information Based Dependence Index (MIDI). Some important properties of MIDI have also been stated. The performance of the proposed method has been compared to generally accepted measures like Distance Correlation (dcor), Maximal Information Coefficient (MINE) in terms of accuracy and computational complexity with the help of several artificial data sets with different amounts of noise. The proposed method is able to detect many types of relationships between variables, without making any assumption about the functional form of the relationship. The power statistics of proposed method illustrate their effectiveness in detecting non linear relationship. Thus, it is able to achieve generality without a high rate of false positive cases. MIDI is found to work better on a real life data set than competing methods. The proposed method is found to overcome some of the limitations which occur with dcor and MINE. Computationally, MIDI is found to be better than dcor and MINE, in terms of time and memory, making it suitable for large data sets., Comment: International Journal of Machine Learning and Cybernetics, Springer Berlin Heidelberg, 10-Sep-2015