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Accompanied with the rapid increase of the amount of data registered in the databases of biological sequences, the need for a fast method of sequence comparison applicable to sequences of large size is also increasing. In general, alignment is used for sequence comparison. However, the alignment may not be appropriate for comparison of sequences of large size such as whole genome sequences due to its large time complexity. In this article, we propose a semi alignment-free method of sequence comparison based on word frequency distributions, in which we partially use the alignment to measure word frequencies along with the idea of fuzzy set theory. Experiments with ten bacterial genome sequences demonstrated that the fuzzy measurements has the effect that facilitates discrimination between close relatives and distant relatives.

Rackwitz–Fiessler (RF) method is well accepted as an efficient way to solve the uncorrelated non-Normal reliability problems by transforming original non-Normal variables into equivalent Normal variables based on the equivalent Normal conditions. However, this traditional RF method is often abandoned when correlated reliability problems are involved, because the point-by-point implementation property of equivalent Normal conditions makes the RF method hard to clearly describe the correlations of transformed variables. To this end, some improvements on the traditional RF method are presented from the isoprobabilistic transformation and copula theory viewpoints. First of all, the forward transformation process of RF method from the original space to the standard Normal space is interpreted as the isoprobabilistic transformation from the geometric point of view. This viewpoint makes us reasonably describe the stochastic dependence of transformed variables same as that in Nataf transformation (NATAF). Thus, a corresponding enhanced RF (EnRF) method is proposed to deal with the correlated reliability problems described by Pearson linear correlation. Further, we uncover the implicit Gaussian copula hypothesis of RF method according to the invariant theorem of copula and the strictly increasing isoprobabilistic transformation. Meanwhile, based on the copula-only rank correlations such as the Spearman and Kendall correlations, two improved RF (IRF) methods are introduced to overcome the potential pitfalls of Pearson correlation in EnRF. Later, taking NATAF as a reference, the computational cost and efficiency of above three proposed RF methods are also discussed in Hasofer–Lind reliability algorithm. Finally, four illustrative structure reliability examples are demonstrated to validate the availability and advantages of the new proposed RF methods.

Learning to hash is receiving increasing research attention due to its effectiveness in addressing the large-scale similarity search problem. Most of the existing hashing algorithms are focused on learning hash functions in the form of numeric quantization of some projected feature space. In this work, we propose a novel hash learning method that encodes features’ relative ordering instead of quantizing their numeric values in a set of low-dimensional ranking subspaces. We formulate the ranking-based hash learning problem as the optimization of a continuous probabilistic error function using softmax approximation and present an efficient learning algorithm to solve the problem. As a generalization of Winner-Take-All (WTA) hashing, the proposed algorithm naturally enjoys the numeric stability benefits of rank correlation measures while being optimized to achieve high precision with very compact code. Additionally, the proposed method can also be easily extended to nonlinear kernel spaces to discover ranking structures that can not be revealed in linear subspaces. We demonstrate through extensive experiments that the proposed method can achive competitive performances as compared to a number of state-of-the-art hashing methods.

The relationship between crime and economic growth, and corruption and economic growth is complex in nature. It is also difficult to compare crime rates both internationally and nationally due to variation not only in legal definition of crime but also in its reporting systems, counting methods, and data quality. In India, average number of offences during the study period is ₹54.77 lakh of which ₹18.48 lakh under Indian Penal Code and ₹36.29 lakh under special and local laws. Crime against body, crime against properties and riots are falling but crime against women and economic offences are rising. This study covers 5 Indian States representing northern, southern, eastern and western part of India including West Bengal. Kerala, a southern state has the highest crime rate but remarkably better in overall functioning of the Criminal Justice System. On the other hand, West Bengal has lowest crime rate but requires improvement in Criminal Justice System. Unlike criminality rate and economic growth, the interrelationship between corruption and economic growth is perceived to be direct and strong. The rank correlation coefficient between ‘corruption perception index’ and ‘per capita GDP rank’ is 0.78 for selected 19 countries and 0.46 for selected Indian states. But there is an inverse relationship between crime and state domestic product. In addition, the data collected from wide range of people under this study reflects that rich persons are responsible for crime and corruption. Most of the respondents are not satisfied with anticorruption measures. Lack of education, poor salary and poverty are considered to be the most important cause for corruption. People's active involvement in eradicating crime and corruption hold the key.