Search

In 2018, Luca and Patel conjectured that the largest perfect power representable as the sum of two Fibonacci numbers is 38642 = F36 + F12. In other words, they conjectured that the equation has no solutions with a ≥ 2 and ya > 38642 While this is still an open problem, there exist several partial results. For example, recently Kebli, Kihel, Larone and Luca proved an explicit upper bound for ya, which depends on the size of y. In this paper, we find an explicit upper bound for ya, which only depends on the Hamming weight of y with respect to the Zeckendorf representation. More specifically we prove the following: If y = Fn1 + · · · + Fnk and equation (*) is satisfied by y and some non-negative integers n, m and a ≥ 2, then Here, ϵ > 0 can be chosen arbitrarily and C(ϵ) is an effectively computable constant. [ABSTRACT FROM AUTHOR]

Multimedia security is important as privacy and protection has to be ensured when images from military, medical and other confidential services are sent through the unprotected channel. In this paper, an attempt to develop reconfigurable hardware for an encryption scheme using FPGA has been carried out and tested successfully for its features. In this proposed encryption scheme, chaos and a novel artificial neural network-based diffusion have been used along with zig-zag permutation for pixel level and novel enhanced Fisher-Yates permutation for bit level. The ANN is composed of additive and multiplicative convolution and the 2D cellular automata as an activation function for diffusion. A novel key generation algorithm is adopted to produce the key values for generating the chaos sequence. Every image gets a new key, hence differential attack possibility is negligible. The encryption algorithm is designed in MATLAB and coded in Verilog HDL to develop it as reconfigurable hardware. The hamming distance is analyzed to know the difference between the key sequence generated. The average hamming distance is 0.5111 and the highest value is 0.8796 to show that the randomness of the sequence. Similarly, equidistribution, autocorrelation and periodicity analysis are performed. The NIST SP 800–22 randomness test was also performed on keys and encrypted images to analyze its randomness. The results obtained from the encryption process are tested for their efficiency related to statistical and differential attacks. It gives better results when compared with a few encryption algorithms in the literature. [ABSTRACT FROM AUTHOR]

Feature allocation models postulate a sampling distribution whose parameters are derived from shared features. Bayesian models place a prior distribution on the feature allocation, and Markov chain Monte Carlo is typically used for model fitting, which results in thousands of feature allocations sampled from the posterior distribution. Based on these samples, we propose a method to provide a point estimate of a latent feature allocation. First, we introduce FARO loss, a function between feature allocations which satisfies quasi-metric properties and allows for comparing feature allocations with differing numbers of features. The loss involves finding the optimal feature ordering among all possible orderings, but computational feasibility is achieved by framing this task as a linear assignment problem. We also introduce the FANGS algorithm to obtain a Bayes estimate by minimizing the Monte Carlo estimate of the posterior expected FARO loss using the available samples. FANGS can produce an estimate other than those visited in the Markov chain. We provide an investigation of existing methods and our proposed methods. Our loss function and search algorithm are implemented in the fangs package in R. [ABSTRACT FROM AUTHOR]

Abstract Orthogonal arrays (OAs) are widely applied in the statistical design of experiments. The Hamming distances of OAs play an increasingly important role in various areas; however, it is difficult to use Hamming distances, especially for tight and mixed orthogonal arrays (MOAs). For example, two OAs with the same parameters may have distinct Hamming distances due to their different structures and constructions. In addition, studies on Hamming distances of tight OAs are scant, with the exception of a study indicating that a tight symmetrical OA of strength 2 has a constant Hamming distance. In this article, we calculate Hamming distances for high-strength OAs, including all tight symmetrical OAs of strength 3, 4, and 5. Interestingly, the Hamming distances do not depend on the constructions or structures of the arrays. Additionally, we study the Hamming distances of several classes of MOAs of strength 2 and 3, some of which are not related to the structures of the arrays. [ABSTRACT FROM AUTHOR]

Mixed-membership unsupervised clustering is widely used to extract informative patterns from data in many application areas. For a shared dataset, the stochasticity and unsupervised nature of clustering algorithms can cause difficulties in comparing clustering results produced by different algorithms, or even multiple runs of the same algorithm, as outcomes can differ owing to permutation of the cluster labels or genuine differences in clustering results. Here, with a focus on inference of individual genetic ancestry in population-genetic studies, we study the cost of misalignment of mixed-membership unsupervised clustering replicates under a theoretical model of cluster memberships. Using Dirichlet distributions to model membership coefficient vectors, we provide theoretical results quantifying the alignment cost as a function of the Dirichlet parameters and the Hamming permutation difference between replicates. For fixed Dirichlet parameters, the alignment cost is seen to increase with the Hamming distance between permutations. Datasets with low variance across individuals of membership coefficients for specific clusters generally produce high misalignment costs—so that a single optimal permutation has far lower cost than suboptimal permutations. Higher variability in data, as represented by greater variance of membership coefficients, generally results in alignment costs that are similar between the optimal permutation and suboptimal permutations. We demonstrate the application of the theoretical results to data simulated under the Dirichlet model, as well as to membership estimates from inference of human-genetic ancestry. The results can contribute to improving cluster alignment algorithms that seek to find optimal permutations of replicates. for this article are available online. [ABSTRACT FROM AUTHOR]

This article studies the Hamming distances and association schemes of orthogonal arrays. We present a general method of constructing mixed schematic saturated orthogonal arrays of strength two produced from saturated symmetric orthogonal arrays by using the expansive replacement method. As applications of the method, we obtain many new mixed schematic saturated orthogonal arrays. Some examples are given to illustrate this construction method. [ABSTRACT FROM AUTHOR]

Two fractional factorial designs are called isomorphic if one can be obtained from the other by relabeling the factors, reordering the runs and switching the levels of factors. Given a set of all orthogonal designs (ODs) with n runs, q levels and s factors, it may have several non-isomorphic subclasses. Once a new OD with this design size is generated, it is interesting to know which subclass it belongs to. In this paper, we review several existing methods, which can classify newly generated ODs to the correct non-isomorphic subclass. We also propose two new non-isomorphic detection methods. They can be utilized for the design classification purpose and take some advantages over the existing methods in terms of computation efficiency and classification capability. [ABSTRACT FROM AUTHOR]

Performing successful experiments is a crucial topic for scientists. The selection of factors and levels that have significant effects on the outputs is the most hard problem they may face. For a perfect procedure, a small number of runs (trials) are preferred as an initial-stage experiment (ISExp) for gaining prior information about the influence (importance) of the suggested factors and levels. After analysing the ISExp, the following prior information may arise: (i) the number of parameters in the used model is much larger than the expected number of runs and thus more runs need to be added; (ii) some of the ignored or fixed factors may be active and need further investigations; (iii) extending the levels of some active factors is necessary for optimising the outputs; and/or (iv) the impacts of the active factors are not equally important and thus different weights need be assigned to the factors to identify their importance. Therefore, follow-up experiments (FuExps) need to be conducted for adding new active factors, levels, runs, and/or factor-weights to the ISExps. This paper provides novel techniques for designing FuExps to deal with these real-life scenarios for ISExp with a mixture of two-level factors and four-level factors. To clarify the power and efficiency of the proposed techniques, numerical and theoretical justifications are given. [ABSTRACT FROM AUTHOR]

Genome subsequence assembly plays an important role in personalized medicine and genome variation. Third generation sequencing mechanisms were very crucial problems of subsequence assembly. For example mapping the subsequences or finding the identical positions in them is one of the rigid challenges in Bioinformatics. In this paper, we introduce a novel methodology of MapReduce Maximum Exact Matches (MR-MEM) which effectively utilizes the MapReduce program while finding and mapping between genome subsequences using parallel suffix and prefix index structure. The proposed technique works by aligning fragments according to the reference genome. A fragment subsequence is initially matched with the genome to identify the probable matching locations. These identified locations are then analyzed for complete matches. We find the best matching fragment that is assigned to the location by finding the hamming distance between the query sequence and genome reference. The implementation results show that the proposed approach exhibits faster and accurate alignments by providing very low gaps and very high exact alignments. [ABSTRACT FROM AUTHOR]

This paper considers a new method for obtaining an S-box, which is one of the nonlinear transformations used in modern block-symmetric cipher systems. This method is based on modular arithmetic, that is, exponentiation modulo polynomial in extended Galois fields GF 28 ð Þ. The indicators and criteria of efficiency of the obtained S-box (balance, Hamming distance, distribution criteria, autocorrelation, algebraic immunity, cyclic structure of the S-box) are analyzed. The cryptographic characteristics are presented in comparison with the substitution boxes of known modern block ciphers. In addition, the resulting S-box was investigated by the methods of linear and differential cryptanalysis. In the future, the proposed Sbox will be used in the developed encryption algorithm designed for the preencryption of confidential information. [ABSTRACT FROM AUTHOR]

Companies face a number of management challenges, and decision makers must adopt new approaches that consider sustainable development in their operations. In this context, the article aims to address sustainable supply chain management and propose solutions based on a fuzzy logic. Three distance measurement algorithms are applied to evaluate and classify suppliers in a consumer goods industry. The results demonstrate the usefulness of the algorithms in decision-making and bring a contribution to the sustainable development of companies. Furthermore, it supports future studies on sustainable management, the supply chain, and the application of algorithms to sustainability. [ABSTRACT FROM AUTHOR]

In the inverse optimization problem, we modify parameters of the original problem at minimum total cost so as to make a prespecified solution optimal with respect to new parameters. We extend in this paper a class of inverse single facility problems on trees, including inverse balance point, inverse 1-median and inverse 1-center problem, and call it the inverse stable point problem. For the general situation where variables are both edge lengths and vertex weights under an extension of Chebyshev norm and bottleneck Hamming distance, we first derive an algorithm that reduces the corresponding problem to the one under either Chebyshev norm or bottleneck Hamming distance and then develop an approximation approach for the problem. Special cases concerning the problem under this extension with strongly polynomial time algorithms are also discussed. [ABSTRACT FROM AUTHOR]

This article considers quantum annealing in the Ising framework for solving combinatorial optimization problems. The path-integral Monte Carlo simulation approach is often used to approximate quantum annealing and implement the approximation by classical computers, which refers to simulated quantum annealing (SQA). In this article, we introduce a data augmentation scheme into SQA and develop a new algorithm for its implementation. The proposed algorithm reveals new insights on the sampling behaviors in SQA. Theoretical analyses are established to justify the algorithm, and numerical studies are conducted to check its performance and to confirm the theoretical findings. for this article are available online. [ABSTRACT FROM AUTHOR]

Orthogonal arrays have many connections to other combinatorial designs and are applied in coding theory, the statistical design of experiments, cryptography, various types of software testing and quality control. In this paper, we present some general methods to find the Hamming distances for saturated asymmetrical orthogonal arrays (SAOAs) with strength 2. As applications of our methods, the Hamming distances of SAOA parents of size less than or equal to 100 are obtained. We also provide the Hamming distances of the SAOAs constructed from difference schemes or by the expansive replacement method. The feasibility of Hamming distances is discussed. [ABSTRACT FROM AUTHOR]

In this article we propose indices for technological breadth and depth of patent documents. We conceptually compare and contrast several indices that have been used in the existing literature, explaining main limitations. Motivated by the drawbacks of those we demonstrate how Rao's Quadratic Entropy, a statistical index used in ecology for measuring biodiversity, can be decomposed to separately measure technological breadth and depth. The properties of breadth and depth are then investigated using patents for business data processing. For the technological domains with the highest patenting activity, we show how the novel measures of technological breadth and depth can be used to rank the patenting entities by average breadth, and identify ones with inventions that on average exceed the domain-specific average depth. Practical implications of the proposed indices are also exemplified and discussed in the context of competitor analysis for entrepreneurial ventures in the area of network security for business data processing. [ABSTRACT FROM AUTHOR]

The early stages of many real-life experiments involve a large number of factors among which only a few factors are active. Unfortunately, the optimal full-dimensional designs of those early stages may have bad low-dimensional projections and the experimenters do not know which factors turn out to be important before conducting the experiment. Therefore, designs with good projections are desirable for factor screening. In this regard, significant questions are arising such as whether the optimal full-dimensional designs have good projections onto low dimensions? How experimenters can measure the goodness of a full-dimensional design by focusing on all of its projections?, and are there linkages between the optimality of a full-dimensional design and the optimality of its projections? Through theoretical justifications, this paper tries to provide answers to these interesting questions by investigating the construction of optimal (average) projection designs for screening either nominal or quantitative factors. The main results show that: based on the aberration and orthogonality criteria the full-dimensional design is optimal if and only if it is optimal projection design; the full-dimensional design is optimal via the aberration and orthogonality if and only if it is uniform projection design; there is no guarantee that a uniform full-dimensional design is optimal projection design via any criterion; the projection design is optimal via the aberration, orthogonality and uniformity criteria if it is optimal via any criterion of them; and the saturated orthogonal designs have the same average projection performance. [ABSTRACT FROM AUTHOR]

Here, we propose a clustering technique for general clustering problems including those that have nonconvex clusters. For a given desired number of clusters K, we use three stages to find clusters. The first stage uses a hybrid clustering technique to produce a series of clusterings of various sizes (randomly selected). The key step in this stage is to find a K-means clustering using clusters where and then join these small clusters by using single linkage clustering. The second stage stabilizes the result of stage one by reclustering via the "membership matrix" under Hamming distance to generate a dendrogram. The third stage is to cut the dendrogram to get clusters where and then prune back to K to give a final clustering. A variant on our technique also gives a reasonable estimate for KT, the true number of clusters. We provide arguments to justify the steps in the stages of our methods and we provide examples involving simulated and published data to compare our technique with other techniques. An R library, GHC, implementing our method is available from Github. [ABSTRACT FROM AUTHOR]

The distance spectral radius of a connected hypergraph is the largest eigenvalue of its distance matrix. We determine the unique connectedk-uniform hypergraphs with minimum distance spectral radius when the number of pendant edges is given, the uniquek-uniform non-hyperstar-like hypertrees (non-hyper-caterpillars, respectively) with minimum distance spectral radius, and the uniquek-uniform non-hyper-caterpillars with maximum distance spectral radius for. [ABSTRACT FROM AUTHOR]

We present a technique for clustering categorical data by generating many dissimilarity matrices and combining them. We begin by demonstrating our technique on low-dimensional categorical data and comparing it to several other techniques that have been proposed. We show through simulations and examples that our method is both more accurate and more stable. Then we give conditions under which our method should yield good results in general. Our method extends to high-dimensional categorical data of equal lengths by ensembling over many choices of explanatory variables. In this context, we compare our method with two other methods. Finally, we extend our method to high-dimensional categorical data vectors of unequal length by using alignment techniques to equalize the lengths. We give an example to show that our method continues to provide useful results, in particular, providing a comparison with phylogenetic trees. Supplementary material for this article is available online. [ABSTRACT FROM AUTHOR]

This paper presents a general method of constructing schematic saturated orthogonal arrays of strength two. We consider a class of mixed saturated orthogonal arrays produced from saturated symmetric orthogonal arrays by using the contractive replacement method, study the Hamming distances of the rows, construct their association schemes, and prove that they are schematic. Some examples are given to illustrate this construction method. [ABSTRACT FROM AUTHOR]

A nonparametric technique based on the Hamming distance is proposed in this research by recognizing that once the attribute vector is known, or correctly estimated with high probability, one can determine the item-by-attribute vectors for new items undergoing calibration. We consider the setting whereQis known for a large item bank, and theq-vectors of additional items are estimated. The method is studied in simulation under a wide variety of conditions, and is illustrated with the Tatsuoka fraction subtraction data. A consistency theorem is developed giving conditions under which nonparametricQcalibration can be expected to work. [ABSTRACT FROM AUTHOR]

With widespread development of biometrics, concerns about security and privacy are rapidly increasing. Homomorphic encryption enables us to operate on encrypted data without decryption, and it can be applied to construct a privacy-preserving biometric system. In this article, we apply two homomorphic encryption schemes based on ideal-lattice and ring-LWE (Learning with Errors), which both have homomorphic correctness over the ring of integers of a cyclotomic field. We compare the two schemes in applying them to privacy-preserving biometrics. In biometrics, the Hamming distance is used as a metric to compare two biometric feature vectors for authentication. We propose an efficient method for secure Hamming distance. Our method can pack a biometric feature vector into a single ciphertext, and it enables efficient computation of secure Hamming distance over our packed ciphertexts. [ABSTRACT FROM AUTHOR]

Linguistic hesitant fuzzy sets (LHFSs), which can be used to represent decision-makers’ qualitative preferences as well as reflect their hesitancy and inconsistency, have attracted a great deal of attention due to their flexibility and efficiency. This paper focuses on a multi-criteria decision-making approach that combines LHFSs with the evidential reasoning (ER) method. After reviewing existing studies of LHFSs, a new order relationship and Hamming distance between LHFSs are introduced and some linguistic scale functions are applied. Then, the ER algorithm is used to aggregate the distributed assessment of each alternative. Subsequently, the set of aggregated alternatives on criteria are further aggregated to get the overall value of each alternative. Furthermore, a nonlinear programming model is developed and genetic algorithms are used to obtain the optimal weights of the criteria. Finally, two illustrative examples are provided to show the feasibility and usability of the method, and comparison analysis with the existing method is made. [ABSTRACT FROM AUTHOR]

This paper addresses all possible equivalence classes of 1-variable Boolean functions and from these classes using recursion and Cartesian product of sets, 15 different ways of classifications ofn-variable Boolean functions are obtained. The properties with regard to the size and the number of classes for these 15 different ways are also elaborated. [ABSTRACT FROM AUTHOR]

Digital truncated and obstructed Hamming apertures are used in confocal laser scanning microscope (CLSM) to improve the resolution. The resultant point spread function (RPSF) and the coherent transfer function of the defined microscope, using the modified Hamming apertures, are computed. The mammographic images are used in the CLSM to test resolution of the investigated apertures. The image is computed from the modulus square of the convolution product of the RPSF and the complex amplitude of the object. A comparison with the images obtained in case of circular uniform apertures is investigated. Another application on holography allows the recognition of the modulated Hamming apertures. [ABSTRACT FROM AUTHOR]

Two symmetrical fractional factorial designs are said to be combinatorially equivalent if one design can be obtained from another by reordering the runs, relabeling the factors and relabeling the levels of one or more factors. This article presents concepts of ordered distance frequency matrix, distance frequency vector, and reduced distance frequency vector for a design. Necessary conditions for two designs to be combinatorial equivalent based on these concepts are presented. A new algorithm based on the results obtained is proposed to check combinatorial non-equivalence of two factorial designs and several illustrating examples are provided. [ABSTRACT FROM AUTHOR]

Recently, hesitant fuzzy sets (HFSs) have been studied by many researchers as a powerful tool to describe and deal with uncertain data, but relatively, very few studies focus on the clustering analysis of HFSs. In this paper, we propose a novel hesitant fuzzy agglomerative hierarchical clustering algorithm for HFSs. The algorithm considers each of the given HFSs as a unique cluster in the first stage, and then compares each pair of the HFSs by utilising the weighted Hamming distance or the weighted Euclidean distance. The two clusters with smaller distance are jointed. The procedure is then repeated time and again until the desirable number of clusters is achieved. Moreover, we extend the algorithm to cluster the interval-valued hesitant fuzzy sets, and finally illustrate the effectiveness of our clustering algorithms by experimental results. [ABSTRACT FROM PUBLISHER]

With the increasing needs in security systems, hand vein recognition is reliable as one of the important solutions for biometrics-based identification systems. This work presents an effective approach for dorsal hand vein recognition by analysing vein patterns. The methodology involves extraction of dorsal hand vein features based on Gaussian filter. In order to obtain effective pattern of dorsal hand vein vascular, we propose an innovative and robust Gaussian directional filter method to extract the dorsal hand vein patterns and to encode the vein features in binary code. A new coding scheme, namely Gaussian directional binary code, is then proposed for dorsal hand vein recognition. To evaluate the efficacy of the proposed approach, the normalised Hamming distance used in recognition is adopted. A total of 5120 dorsal hand vein images were collected from 256 persons to verify the validity of the proposed dorsal hand vein recognition approach. High accuracies (>99%) and low equal error rate (0·95%) have been obtained by the proposed method. Experimental results demonstrate that our proposed approach is feasible and effective for dorsal hand vein recognition. [ABSTRACT FROM AUTHOR]

Hand vein patterns are among the biometric traits being investigated today for identification purposes, attracting interest from both the research community and industry. A reliable and robust personal verification approach using dorsal hand vein patterns is presented in this paper. This approach needs less computational and memory requirements and has a higher recognition accuracy than similar methods. In our work, a near-infrared charge-coupled device camera is adopted as an input device for capturing dorsal hand vein images, due to its advantages of the low-cost and non-contact imaging. In the proposed approach, two finger-peaks are automatically selected to define the region of interest in the dorsal hand vein images. In order to obtain effective pattern of dorsal hand vein vascular, we proposed an innovative and robust adaptive Gabor filter method to extract the dorsal hand vein patterns and encode the vein features in bit string representation. The bit string representation, called VeinCode, offers speedy template matching and enables more effective template storage and retrieval. The similarity of two VeinCodes is measured by normalised Hamming distance. A total of 6160 dorsal hand vein images were collected from 308 persons to verify the validity of the proposed dorsal hand vein recognition approach. High accuracies (>99%) have been obtained by the proposed method, and the speed of the method (responding time <0·8 s) is rapid enough for real-time recognition. Experimental results demonstrate that our proposed approach is feasible and effective for dorsal hand vein recognition. [ABSTRACT FROM AUTHOR]

Secret keys are usually stored in a nonvolatile memory, which can be hard to secure. An alternative is to generate the keys “on-the-fly” by using the inherent uniqueness of a device based on the manufacturing process variations. This is realized by physical unclonable functions (PUFs). A promising approach is to construct an intrinsic PUF based on SRAM memory, since many electronic devices have embedded SRAM. However, using a SRAM as PUF requires the stability of the SRAM fingerprint under a wide variety of conditions, and the SRAM fingerprint must be unique. In this paper, we show that a 16Kbyte SRAM fingerprint contains sufficient entropy to uniquely identify each chip. In addition, if a postprocessing error correction is applied, the fingerprint can be used to generate a stable 4Kbit key. [ABSTRACT FROM AUTHOR]

In the context of technological convergence between television and internet, users can access a multitude of audiovisual contents in television sets or by searching on line. This article attempts to analyze advertising effectiveness in this new context. The objective of this research is verifying that interactive advertising formats in television are more effective than non-interactive formats to inform, persuade and remember. This study reveals that interactive advertising formats add efficacy to media to inform and remember, highlighting the interactive spot, the TV site, and the microsite. [ABSTRACT FROM PUBLISHER]

A bottleneck optimization problem (BOP) is to find a feasible solution that minimizes the maximum weight w of edges. While in an inverse (BOP), a candidate solution F * is first given, and the aim is to modify weights w to w* under some measure such that F * becomes an optimal bottleneck solution with respect to w*. The constrained inverse problem (CIBOP) is first discussed under weighted bottleneck Hamming distance (HD), where an upper-bound constraint on the sum-HD between w and w* is added. It is shown that (CIBOP) can be reduced to O(mlog m) minimum cut problems, where m = |E|. A class of lexicographic bicriteria inverse problems (BIBOP) are also studied, in which the first objective function can be measured by weighted bottleneck-HD (BIBOP bH ) and weighted l ∞ norm (BIBOP∞), and the second objective function can be measured by (weighted) sum-HD and weighted l 1 norm, respectively. It is shown that (BIBOP bH ) and (BIBOP∞) can be solved in time O((m + T cf ) log m + T c ) and O(m 2(log m + T bc ) + T c ), respectively, where T cf is the time of checking feasibility of a cut, T c and T bc are the time to find a minimum cut and a minimum bottleneck cut, respectively. [ABSTRACT FROM PUBLISHER]

Face authentication, also called face verification, is used to confirm the identity of a person by classifying the person as either the person he or she claims to be or not. For face authentication, the user generally provides a user name (and in some cases a password as well) to an authentication system that allows access to an area or system. Stored models associated with the provided username are used to verify the person's identity and then allow or deny access. This paper proposes a fast and robust method for face authentication with variant illumination, scaling, rotation, blur, and difference in emotions (smiling, angry, and screaming). Techniques introduced in this work are composed of two stages. First, the feature of the face is to be detected by a combination of Trace transform and Fourier transform. Then, in the second stage, the Hamming distance is employed to measure and determine the similarity between models and test images. Finally, our method is evaluated with experiments on the AR and XM2VTS face databases and compared with other related works (e.g., eigenface, Hausdorff-ARTMAP, Enhance-EBGH). The extensive experimental results show that the average of the accuracy rate of face authentication with variant illumination, scaling, rotation and different emotions is higher than 88%, and it was found that our proposed method performed better than the other compared methods in all cases. [ABSTRACT FROM AUTHOR]

High-dimensional categorical data models, often with inadequately large sample sizes, crop up in many fields of application. The SARS epidemic, originating in southern China in 2002, had an identified single-stranded and positive-sense RNA virus with large genome size and moderate mutation rate. The present genomic study is used as a prime illustration for motivating appropriate statistical methodology for comprehending the genomic variation in such high-dimensional categorical data models. Because of underlying restraints, a pseudomarginal approach based on Hamming distance is considered in a constrained statistical inference setup. The union-intersection principle and jackknifing methods are incorporated in exploring appropriate statistical procedures. [ABSTRACT FROM AUTHOR]

The research discusses the design philosophy for product development. It emphasizes the importance of independent evaluation with non-expert knowledge base in a commercial product design. To resolve the issues with the raised design philosophy, a fuzzy mathematic model with modified Hamming distance fuzzy set method is proposed to conduct such a non-expert evaluation for achieving better product design in industrial practices. This modified fuzzy model is able to coordinate and to deal with the tangled fuzzy and non-fuzzy issues involved in the product design to carry out a comprehensive and effective non-expert evaluation. With the model, a simple and effective tool can be built for engineers to conduct sophisticated product design. [ABSTRACT FROM AUTHOR]

Similarity searches in multidimensional Non-ordered Discrete Data Spaces (NDDS)are becoming increasingly important for application areas such as bioinformatics, biometrics, data mining and E-commerce. Efficient similarity searches require robust indexing techniques. Unfortunately, existing indexing methods developed for multidimensional (ordered) Continuous Data Spaces (CDS) such as the R-tree cannot be directly applied to an NDDS. This is because some essential geometric concepts/properties such as the minimum bounding region and the area of a region in a CDS are no longer valid in an NDDS. Other indexing methods based on metric spaces such as the M-tree and the Slim-trees are too general to effectively utilize the special characteristics of NDDSs, resulting in nonoptimized performance. In this article, we propose a new dynamic data-partitioning-based indexing technique, called the ND-tree, to support efficient similarity searches in an NDDS. The key idea is to extend the relevant geometric concepts as well as some indexing strategies used in CDSs to NDDSs. Efficient algorithms for ND-tree construction and techniques to solve relevant issues such as handling dimensions with different alphabets in an NDDS are presented. Our experimental results on synthetic data and real genome sequence data demonstrate that the ND-tree outperforms the linear scan, the M-tree and the Slim-trees for similarity searches in multidimensional NDDSs. A theoretical model is also developed to predict the performance of the ND-tree for random data. [ABSTRACT FROM AUTHOR]

We introduce a novel statistical procedure for clustering categorical data based on Hamming distance (HD) vectors. The proposed method is conceptually simple and computationally straightforward, because it does not require any specific statistical models or any convergence criteria. Moreover, unlike most currently existing algorithms that compute the class membership or membership probability for every data point at each iteration, our algorithm sequentially extracts clusters from the given dataset. That is, at each iteration our algorithm strives to identify only one cluster, which will then be deleted from the dataset at the next iteration; this procedure repeats until there are no more significant clusters in the remaining data. Consequently, the number of clusters can be determined automatically by the algorithm. As for the identification and extraction of a cluster, we first locate the cluster center by using a Pearson chi-squared-type statistic on the basis of HD vectors. The partition of the dataset produced by our algorithm is unique and insensitive to the input order of data points. The performance of the proposed algorithm is examined using both simulated and real world datasets. Comparisons with two well-known clustering algorithms, K-modes and AutoClass, show that the proposed algorithm substantially outperforms these competitors, with the classification rate or the information gain typically improved by several orders of magnitude. Computational complexity and run time comparisons are also provided. [ABSTRACT FROM AUTHOR]

Nonregular fractional factorial designs, such as Plackett-Burman designs, are widely used in industrial experiments for run size economy and flexibility. A novel criterion, called moment aberration projection, is proposed to rank and classify nonregular designs. It measures the goodness of a design through moments of the number of coincidences between the rows of its projection designs. The new criterion is used to rank and classify designs of 16, 20, and 27 runs. Examples are given to illustrate that the ranking of designs is supported by other design criteria. [ABSTRACT FROM AUTHOR]

The problem of approximate string searching comprises two classes of problems: string searching with k mismatches and string searching with k differences. In this paper we present a short survey and experimental results for well known sequential approximate string searching algorithms. We consider algorithms based on different approaches including dynamic programming, deterministic finite automata, filtering, counting and bit parallelism. We compare these algorithms in terms of running time against pattern length and for several values of k for four different kinds of text: binary alphabet, alphabet of size 8, English alphabet and DNA alphabet. Finally, we compare the experimental results of the algorithms with their theoretical complexities. [ABSTRACT FROM AUTHOR]

A review of the article "Finding Correlations in Subquadratic Time, with Applications to Learning Parities and the Closest Pair Problem" by Gregory Valiant, which appeared in the periodical "Journal of the ACM" on May 2015, is presented.