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Aim: Hip fractures are highly frequent and severe problem, increasing incidence and severity with aging and high disability and mortality rates. Hence, the ability to predict this condition can be of high value for preventive healthcare. The present work explores clinical biomarkers' application for hip fracture risk evaluation and prediction, using an information-theoretical methodology. Material and Method: A dataset on geriatric patients, with and without hip fracture, was analyzed, including blood biomarkers routinely available to physicians: albumin, urea, hemoglobin, calcium, and white blood cells. This research comprised geriatric patients hospitalized at the Shmuel Harofe Geriatric Medical Center, Israel. The patients' data, collected during 2012-2017, were accessed retrospectively. Normalized mutual information was utilized to establish correlations between the parameters, and the nearest neighbor rule with the weighted Hamming distance was used for the construction of a diagnostic decision rule for hip fracture risk evaluation. Results: We developed an algorithm (decision tree) for hip fracture risk group attribution for subjects under 80 years old. The algorithm provided the sensitivity of 0.581 with the 95% confidence interval (0.505, 0.653), and specificity of 0.540 with the 95% confidence interval (0.479, 0.604). This performance was comparable with the results of other common methods for hip fracture risk evaluation, yet the present method may be preferable in terms of data accessibility and the ability to determine the possible time of the fracture. Conclusion: The use of this method has been piloted in the clinic, and with further development and application, can help evaluate the risks of hip fracture in older subjects (aged 60 years or over) to optimize preventive interventions. [ABSTRACT FROM AUTHOR]

To analyse and compare hyperspectral signatures, features extraction and matching are two key issues. In this letter, hyperspectral absorption features and the corresponding matching algorithm are discussed. First, an absorption detection method is applied to catch all necessary spectral absorptions with improved reliability. Then, a weighted Hamming distance is proposed to match the binary absorption‐features. Next, an elastic matching scheme is designed to classify the hyperspectral data. Experiments of classification are carried out on six classes of vegetation from the Salinas data‐set. Results show that the proposed method not only increased the overall classification accuracy to 73.13% from back propagation neural network's 71.86% and support vector machine's 73.06%, but also improved the error distributions among different classes. [ABSTRACT FROM AUTHOR]

Hamming codes are of primary concern in information theory and its applications. Despite a number of researches that have been conducted on such codes and their characterizations, dealing with the properties of previously introduced codes in a BCK-algebraic framework has not been considered in earlier works. This paper investigates a code constructed based on BCK-algebraic models and proposes an algorithm corresponding to the presented code. It is noticeable that the suggested rendered algorithm is also established on the basis of the elements of a BCK-algebra. In fact, both the Hamming distance and dimension, associated with the presented code, can be estimated through a BCK-algebra structure due to the mechanism of its algorithm which is heavily dependent on the parity check matrix. In addition, the way in which the codes are designed contributes substantially to classification of them and to extract greater number of their attributes compared to the previous works. The highlight of the proposed method is that the number of atoms of the BCK-algebra plays a key role in calculation of the Hamming distance and dimension of these codes. Moreover, the obtained codes possess specified and recognizable Hamming distance which are essential in performing error-correcting, error-detecting and decoding tasks. [ABSTRACT FROM AUTHOR]

We investigate the complexity of three optimization problems in Boolean propositional logic related to information theory: Given a conjunctive formula over a set of relations, find a satisfying assignment with minimal Hamming distance to a given assignment that satisfies the formula (NearestOtherSolution, NOSol) or that does not need to satisfy it (NearestSolution, NSol). The third problem asks for two satisfying assignments with a minimal Hamming distance among all such assignments (MinSolutionDistance, MSD). For all three problems we give complete classifications with respect to the relations admitted in the formula. We give polynomial time algorithms for several classes of constraint languages. For all other cases we prove hardness or completeness regarding APX, poly-APX, or equivalence to well-known hard optimization problems. [ABSTRACT FROM AUTHOR]

We (people) are memory machines. Our decision processes, emotions, and interactions with the world around us are based on and driven by associations to our memories. This natural association paradigm will become critical in future memory systems, namely, the key question will not be “How do I store more information?” but rather “Do I have the relevant information? How do I retrieve it?” The focus of this paper is to make a first step in this direction. We define and solve a very basic problem in associative retrieval. Given a word $W$ , the words in the memory, which are $t$ -associated with $W$ , are the words in the ball of radius $t$ around $W$. In general, given a set of words, say $W$ , $X$ , and $Y$ , the words that are $t$ -associated with $\{W,X,Y\}$ are those in the memory that are within distance $t$ from all the three words. Our main goal is to study the maximum size of the $t$ -associated set as a function of the number of input words and the minimum distance of the words in memory—we call this value the uncertainty of an associative memory. In this paper, we consider the Hamming distance and derive the uncertainty of the associative memory that consists of all the binary vectors with an arbitrary number of input words. In addition, we study the retrieval problem, namely, how do we get the $t$ -associated set given the inputs? We note that this paradigm is a generalization of the sequences reconstruction problem that was proposed by Levenshtein (2001). In this model, a word is transmitted over multiple channels. A decoder receives all the channel outputs and decodes the transmitted word. Levenshtein computed the minimum number of channels that guarantee a successful decoder—this value happens to be the uncertainty of an associative memory with two input words. [ABSTRACT FROM AUTHOR]

Interval neutrosophic linguistic sets (INLSs) take the advantages of interval neutrosophic sets (INSs) and linguistic variables (LVs), which can be better to handle the indeterminate and inconsistent information existing in the real world, and the power operator can consider all the decision arguments and their relationship. But the traditional power aggregation operator cannot handle interval neutrosophic linguistic sets. Motivated by these, firstly, the operations of interval neutrosophic linguistic numbers (INLNs) based on Einstein operations are defined, and the Hamming distance measure for INLNs is also explored in this paper. Secondly, some novel power aggregation operators based on Einstein operations are proposed, including the interval neutrosophic linguistic power weighted average (INLPWA) operator and the interval neutrosophic linguistic power weighted geometric (INLPWG) operator, and their properties are also studied. Thirdly, an illustrative example is illustrated to show the feasibility and practicality of the proposed method. [ABSTRACT FROM AUTHOR]

Codes that can correct up to $t$ symmetric errors and detect all unidirectional errors, known as $t$ -EC-AUED codes, are studied in this paper. Given positive integers $q$ , $a$ , and $t$ , let $n_{q}(a,t+1)$ denote the length of the shortest $q$ -ary $t$ -EC-AUED code of size $a$. We introduce combinatorial constructions for $q$ -ary $t$ -EC-AUED codes via one-factorizations of complete graphs, and concatenation of MDS codes and codes from resolvable set systems. Consequently, we determine the exact values of $n_{q}(a,t+1)$ for several new infinite families of $q,a$ , and $t$. [ABSTRACT FROM AUTHOR]

The bounded storage model restricts the memory of an adversary in a cryptographic protocol, rather than restricting its computational power, making information theoretically secure protocols feasible. We present the first protocols for commitment and oblivious transfer in the bounded storage model with errors, i.e., the model where the public random sources available to the two parties are not exactly the same, but instead are only required to have a small Hamming distance between themselves. Commitment and oblivious transfer protocols were known previously only for the error-free variant of the bounded storage model, which is harder to realize. [ABSTRACT FROM AUTHOR]

A reversible function is isomorphic to a permutation and an arbitrary permutation can be represented by a series of cycles. A new synthesis algorithm for 3-qubit reversible circuits was presented. It consists of two parts, the first part used the Number of reversible function’s Different Bits (NDBs) to decide whether the NOT gate should be added to decrease the Hamming distance of the input and output vectors; the second part was based on the idea of exploring properties of the cycle representation of permutations, decomposed the cycles to make the permutation closer to the identity permutation and finally turn into the identity permutation, it was realized by using totally controlled Toffoli gates with positive and negative controls. [ABSTRACT FROM AUTHOR]

Image segmentation is an essential step for many computer vision tasks. Evaluating the quality of image segmentations becomes indispensable for choosing an appropriate output of the image segmentation algorithms. To quantitatively evaluate the segmentation quality, various evaluation measures have been proposed to produce a quality map, and a spatial pooling algorithm is followed to combine the quality map into a single quality score. In this paper, we propose two pooling strategies instead of using the conventional spatial average operation. By assigning perceptual meaningful weights to the quality maps, we obtain evaluation measures that are correlated with the human perception of segmentation quality. Specifically, a quality-based and a visual importance-based pooling strategies are designed and tested on some popular evaluation measures, respectively. To the best of our knowledge, this is the first work that applies perceptual pooling strategies for segmentation evaluation. Extensive experiments are conducted on a subjective evaluation benchmark and the Berkeley Segmentation Dataset (BSDS500). The results indicate that the proposed strategies can improve the performance of existing evaluation measures and produce a more perceptually meaningful judgment on the segmentation quality. [ABSTRACT FROM AUTHOR]

Different forms of turbo codes (TCs) have already been used in the contemporary message transferring system for transmission of the protected information because of their astonishing bit error rate (BER) behavior. However, it suffers from poor 'flattening effect' performance. To overcome this limitation, component encoders having higher memory elements or more number of component encoders may be considered. At the initial segment of this article, the proposal of binary 4-dimensional turbo code (4D-TC) with appropriate 'generator polynomial' combination and suitable interleaver arrangement has been abridged in Third-Generation Partnership Project standard. This is an amended form of 3-dimensional turbo code where some part of the 'parity bits' is re-encoded by the third encoder, and rest part is re-encoded by the fourth encoder consisting of single memory component. Afterwards, performance of the proposed structure has been assessed by varying block length, number of component encoders, puncturing rate, and channel condition. At the consequent segment, 'constricted upper bound' on the BER performances of the 4D-TC has been assessed by adopting an approach called simplified augmented state diagram. Moreover, an exhaustive analysis has been performed on the novel simplified augmented state diagram approach-based 4D-TC by fluctuating several internal parameters of the code structure like generator polynomial combination, block length, puncturing rate, interleaver combination, and permeability rate. In this regard, the existing augmented state diagram approach has been considered for comparative analysis as well. [ABSTRACT FROM AUTHOR]

In information theory, linguistics and computer science are important distinct string metrics for measuring the difference between two given strings (sequences). In distinct domains of research are well known the distances of Hamming and Graev-Levenshtein between two strings. For any string distance there are distinct geometrical compute problems. Some of them are as follows: - the calculation of the median of two strings; - the calculation of the weighted means of two strings; - the problem of the convexity of the weighted mean set. In the present article the above geometrical problems are examined for the Hamming and Graev-Levenshtein string distances. [ABSTRACT FROM AUTHOR]

In information theory, linguistics and computer science are important distinct string metrics for measuring the difference between two given strings (sequences). In distinct domains of research are well known the distances of Hamming and Graev between two strings. For any string distance there are distinct geometrical compute problems, one of them being the calculation of the bisector of two strings. In the present article the problem of the bisector of two strings is examined for the Hamming and Graev string distances. [ABSTRACT FROM AUTHOR]

We define a variable-length code having the property that no (non-empty) prefix of each its codeword is a suffix of any other one, and vice versa. This kind of code can be seen as an extension of two well-known codes in the literature, called, respectively, fix-free code and non-overlapping code. In this paper we present constructive algorithms for such codes and some numerical results about their cardinality. [ABSTRACT FROM PUBLISHER]

We consider the question of interactive communication, in which two remote parties perform a computation, while their communication channel is (adversarially) noisy. We extend here the discussion into a more general and stronger class of noise, namely, we allow the channel to perform insertions and deletions of symbols. These types of errors may bring the parties “out of sync,” so that there is no consensus regarding the current round of the protocol. In this more general noise model, we obtain the first interactive coding scheme that has a constant rate and tolerates noise rates of up to $1/18- \varepsilon $ . To this end, we develop a novel primitive we name edit-distance tree code. The edit-distance tree code is carefully designed to replace the Hamming distance constraints in Schulman’s tree codes (IEEE Trans. Inf. Theory, 1996), with a stronger edit-distance requirement. [ABSTRACT FROM PUBLISHER]

We propose a decoding algorithm for a class of convolutional codes called skew Reed-Solomon convolutional codes. These are convolutional codes of designed Hamming distance endowed with a cyclic structure yielding a left ideal of a non-commutative ring (a quotient of a skew polynomial ring). In this setting, right and left division algorithms exist, so our algorithm follows the guidelines of the Sugiyama’s procedure for finding the error locator and error evaluator polynomials for Goppa block codes. [ABSTRACT FROM PUBLISHER]

The idea of the inverse optimization problem is to adjust the value of the parameters such that the observed feasible solution becomes optimal. The modification cost can be measured by different norms, such as l 1 , l 2 , l ∞ norms and the Hamming distance, and the goal is to adjust the parameters as little as possible. In this paper, we consider the inverse minimum flow problem under the weighted sum-type Hamming distance, where the lower and upper bounds for the arcs should be changed as little as possible under the weighted sum-type Hamming distance such that a given feasible flow becomes a minimum flow. Two models are considered: the unbounded case and the general bounded case. We present their respective combinatorial algorithms that both run in O ( n m ) time in terms of the minimum cut method. Computational examples are presented to illustrate our algorithms. [ABSTRACT FROM AUTHOR]

Rotation symmetric bent functions and their generation two-rotation symmetric bent functions are two classes of cryptographically significant Boolean functions. However, few constructions have been presented in the literature, which either have restriction on integer $n$ or have algebraic degree no more than 4. In this paper, for any even integer $n\ge 4$ , three classes of bent functions are presented respectively. Most notably, the proposed $n$ -variable rotation symmetric bent functions and two-rotation symmetric bent functions can have any possible algebraic degree ranging from 2 to $n/2$ . Besides, we obtain bent idempotent functions with the maximal algebraic degree $n/2$ . [ABSTRACT FROM PUBLISHER]

Locality sensitive hashing (LSH) is an efficient method for solving the problem of approximate similarity search in high-dimensional spaces. Through LSH, a high-dimensional similarity join can be processed in the same way as hash join, making the cost of joining two large datasets linear. By judicially analyzing the properties of multiple LSH algorithms, we propose a generic method to speed up the process of joining two large datasets using LSH. The crux of our method lies in the way which we identify a set of representative points to reduce the number of LSH lookups. Theoretical analyzes show that our proposed method can greatly reduce the number of lookup operations and retain the same result accuracy compared to executing LSH lookups for every query point. Furthermore, we demonstrate the generality of our method by showing that the same principle can be applied to LSH algorithms for three different metrics: the Euclidean distance (QALSH), Jaccard similarity measure (MinHash), and Hamming distance (sequence hashing). Results from experimental studies using real datasets confirm our error analyzes and show significant improvements of our method over the state-of-the-art LSH method: to achieve over 0.95 recall, we only need to operate LSH lookups for at most 15 percent of the query points. [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]

Point matching under illumination changes is significant for many vision information applications. However, the uneven and dramatic illumination variations model is rarely considered in existing point matching algorithms. Therefore, a method to match features efficiently under uneven and dramatic illumination changes is presented. This method extracts and describes illumination invariant interesting points from matched multibright-ness layers that are obtained by a set of contrast stretching functions and prior information based on original images. Layers matching is insensitive to large unevenness of illumination changes and provides similar images in brightness and structure, so the effects of large uneven illumination changes can be reduced greatly. This algorithm is compatible with most detectors and descriptors. To accelerate the computing speed, the features from the accelerated segment test detector and the improved speeded up robust features descriptor are chosen in this paper. In addition, the combination of priority Hamming distance matching and Lowe's matching algorithms is first proposed to increase the matching speed. This method is generic and can be used in most point matching under all varying illumination conditions. Experimental results demonstrate that the proposed method improves the quality of matched points significantly. [ABSTRACT FROM AUTHOR]

We present an in-depth analysis of the problem of lossy compression of binary sources in the presence of correlated side information, where the correlation is given by a generic binary asymmetric channel and the Hamming distance is the distortion metric. Our analysis is motivated by systematic rate-distortion gains observed when applying asymmetric correlation models in Wyner-Ziv video coding. First, we derive for the first time the rate-distortion function for conventional predictive coding in the binary-asymmetric-correlation-channel scenario. Second, we propose a new bound for the case where the side information is only available at the decoder—Wyner-Ziv coding. We conjecture this bound to be tight. We show that the maximum rate needed to encode as well as the maximum rate-loss of Wyner-Ziv coding relative to predictive coding corresponds to uniform sources and symmetric correlations. Importantly, we show that the upper bound on the rate-loss established by Zamir is not tight and that the maximum value is actually significantly lower. Moreover, we prove that the only binary correlation channel that incurs no rate-loss for Wyner-Ziv coding compared with predictive coding is the Z-channel. Finally, we complement our analysis with new compression performance results obtained with our state-of-the-art Wyner-Ziv video coding system. [ABSTRACT FROM AUTHOR]

Hash-based nearest neighbor search has become attractive in many applications. However, the quantization in hashing usually degenerates the discriminative power when using Hamming distance ranking. Besides, for large-scale visual search, existing hashing methods cannot directly support the efficient search over the data with multiple sources, and while the literature has shown that adaptively incorporating complementary information from diverse sources or views can significantly boost the search performance. To address the problems, this paper proposes a novel and generic approach to building multiple hash tables with multiple views and generating fine-grained ranking results at bitwise and tablewise levels. For each hash table, a query-adaptive bitwise weighting is introduced to alleviate the quantization loss by simultaneously exploiting the quality of hash functions and their complement for nearest neighbor search. From the tablewise aspect, multiple hash tables are built for different data views as a joint index, over which a query-specific rank fusion is proposed to rerank all results from the bitwise ranking by diffusing in a graph. Comprehensive experiments on image search over three well-known benchmarks show that the proposed method achieves up to 17.11% and 20.28% performance gains on single and multiple table search over the state-of-the-art methods. [ABSTRACT FROM PUBLISHER]

This paper considers a linear quasi-cyclic product code of two given quasi-cyclic codes of relatively prime lengths over finite fields. We give the spectral analysis of a quasi-cyclic product code in terms of the spectral analysis of the row and column codes. Moreover, we provide a new lower bound on the minimum Hamming distance of a given quasi-cyclic code and present a new algebraic decoding algorithm. More specifically, we prove an explicit (unreduced) basis of an \ell A {\ell B} -quasi-cyclic product code in terms of the generator matrix in reduced Gröbner basis with respect to the position-over-term (RGB/POT) order form of the \ell A -quasi-cyclic row code and the \ell B -quasi-cyclic column code, respectively. This generalizes the work of Burton and Weldon for the generator polynomial of a cyclic product code (where \ell A= {\ell B}=1 ). Furthermore, we derive the generator matrix in Pre-RGB/POT form of an \ell A {\ell B} -quasi-cyclic product code for two special cases: i) for \ell A=2 and \ell B=1 and ii) if the row code is a one-level \ell A -quasi-cyclic code (for arbitrary \ell A ) and \ell B=1 . For arbitrary \ell A and \ell B , the Pre-RGB/POT form of the generator matrix of an \ell A {\ell B} -quasi-cyclic product code is conjectured. The spectral analysis is applied to the generator matrix of the product of an \ell -quasi-cyclic and a cyclic code, and we propose a new lower bound on the minimum Hamming distance of a given \ell -quasi-cyclic code. In addition, we develop an efficient syndrome-based decoding algorithm for \ell -phased burst errors with guaranteed decoding radius. [ABSTRACT FROM AUTHOR]

This paper investigates the relation between three different notions of privacy: identifiability, differential privacy, and mutual-information privacy. Under a unified privacy-distortion framework, where the distortion is defined to be the expected Hamming distance between the input and output databases, we establish some fundamental connections between these three privacy notions. Given a maximum allowable distortion D , we define the privacy-distortion functions \epsilon _{\mathrm{ i}}^{*}(D) , \epsilon _{\mathrm{ d}}^{*}(D) , and \epsilon \mathrm{ m}^{*}(D) to be the smallest (most private/best) identifiability level, differential privacy level, and mutual information between the input and the output, respectively. We characterize \epsilon \mathrm{ i}^{*}(D) and \epsilon \mathrm{ d}^{*}(D) , and prove that \epsilon \mathrm{ i}^{*}(D)-\epsilon X\le \epsilon \mathrm{ d}^{*}(D)\le \epsilon \mathrm{ i}^{*}(D) for D within certain range, where \epsilon _{X} is a constant determined by the prior distribution of the original database X , and diminishes to zero when X is uniformly distributed. Furthermore, we show that \epsilon _{\mathrm{ i}}^{*}(D) and \epsilon _{\mathrm{ m}}^{*}(D)$ can be achieved by the same mechanism for D$ within certain range, i.e., there is a mechanism that simultaneously minimizes the identifiability level and achieves the best mutual-information privacy. Based on these two connections, we prove that this mutual-information optimal mechanism satisfies \epsilon $ -differential privacy with . The results in this paper reveal some consistency between two worst case notions of privacy, namely, identifiability and differential privacy, and an average notion of privacy, mutual-information privacy. [ABSTRACT FROM PUBLISHER]

The physical unclonable function (PUF) is a promising innovative hardware security primitive that leverages the inherent randomness in the physical systems to produce unique responses upon the inquiry of challenges, thus the PUF could serve as a fingerprint for device authentication. In this paper, we propose a novel PUF implementation exploiting the sneak paths in the resistive cross-point (X-point) array, as a hardware security primitive. The entanglement of the sneak paths in the X-point array greatly enhances the entropy of the physical system, thereby increasing the space of challenge-response pairs to make a strong PUF. The X-point PUF characteristics, such as uniqueness and reliability, are experimentally evaluated on the fabricated $12 \times 12$ cross-point arrays based on the Pt/HfOx/TiN structure. The measurement results show that the average inter-Hamming distance of the response bits is around 46.2% across 28 different arrays, showing sufficient uniqueness. The measurement results also demonstrate that 0% intra-Hamming distance (or 100% reliability) of the response bits can be maintained more than 7.2 h at 100 °C (or equivalently ten years at 40 °C). This paper demonstrates the feasibility of using X-point PUF as a lightweight and reliable PUF for device authentication. [ABSTRACT FROM PUBLISHER]

We use self-reduction methods to prove strong information lower bounds on two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product (IP). In our first result we affirm the conjecture that the information cost of GHD is linear even under the uniform distribution, which strengthens the Ω( n) bound recently shown by Kerenidis et al. (), and answers an open problem from Chakrabarti et al. (). In our second result we prove that the information cost of I P is arbitrarily close to the trivial upper bound n as the permitted error tends to zero, again strengthening the Ω( n) lower bound recently proved by Braverman and Weinstein (Electronic Colloquium on Computational Complexity (ECCC) 18, 164 ). Our proofs demonstrate that self-reducibility makes the connection between information complexity and communication complexity lower bounds a two-way connection. Whereas numerous results in the past (Chakrabarti et al. ; Bar-Yossef et al. J. Comput. Syst. Sci. 68(4), 702-732 ; Barak et al. ) used information complexity techniques to derive new communication complexity lower bounds, we explore a generic way in which communication complexity lower bounds imply information complexity lower bounds in a black-box manner. [ABSTRACT FROM AUTHOR]

This paper describes a procedure that computes seeds for LFSR-based generation of partially-functional broadside tests. Existing LFSR-based test data compression methods compute seeds based on incompletely-specified test cubes. Functional broadside tests are fully-specified, and they have fully-specified scan-in states. This is the main challenge that the test generation procedure described in this paper needs to address. It addresses it by using a process that modifies an initial seed si in order to reduce the Hamming distance between the scan-in state pi that si creates and a reachable state rj . When the Hamming distance is reduced to zero, the seed can be used for generating functional broadside tests. When the distance is larger than zero, the tests are partially-functional. Experimental results are presented for transition faults in benchmark circuits to demonstrate the resulting distances and fault coverage. [ABSTRACT FROM AUTHOR]

Motif finding is an important and a challenging problem in many biological applications such as discovering promoters, enhancers, locus control regions, transcription factors, and more. The ( l, d)-planted motif search, PMS, is one of several variations of the problem. In this problem, there are n given sequences over alphabets of size , each of length m, and two given integers l and d. The problem is to find a motif m of length l, where in each sequence there is at least an l-mer at a Hamming distance of of m. In this article, we propose ET-Motif, an algorithm that can solve the PMS problem in time and space. The time bound can be further reduced by a factor of m with space. In case the suffix tree that is built for the input sequences is balanced, the problem can be solved in time and space. Similarly, the time bound can be reduced by a factor of m using space. Moreover, the variations of the problem, namely the edit distance PMS and edited PMS (Quorum), can be solved using ET-Motif with simple modifications but upper bands of space and time. For edit distance PMS, the time and space bounds will be increased by , while for edited PMS the increase will be of in the time bound. [ABSTRACT FROM AUTHOR]

In computer science, approximate string matching is the technique of finding strings that match a pattern approximately (rather than exactly). Most often when we need to match a pattern exact matching is not possible, due to insufficient data, broken data, or other such reasons. So we try to find a close match instead of an exact match. And for this we need to find the distance between two strings. We have different approaches for the same such as edit distance in the form of Hamming distance, Levenshstien distance, Dameru-Levenshstein distance, Jaro-Winkler distance and Longest Common Subsequence (LCS). Different algorithms have been made for these different approaches, and we will try to analyze some of these algorithms. [ABSTRACT FROM AUTHOR]

The Minkowski distance is a distance measure that generalizes a wide range of other distances such as the Euclidean and the Hamming distance. In this paper, we develop a new decision making model using induced ordered weighted averaging operators and the Minkowski distance of the fuzzy linguistic variables. Then, the authors introduce a new aggregation operator called the fuzzy linguistic induced ordered weighted averaging Minkowski distance (FLIOWAMD) operator by defining a fuzzy linguistic variable distance. It is an induced generalized aggregation operator that utilizes induced OWA operator, Minkowski distance measures and uncertain information represented as fuzzy linguistic variables. Some of its main properties and particular cases are studied. And a further generalization that uses quasi-arithmetic means also is presented. A method based on the FLIOWAMD operator for decision making is presented. At last, we end the paper with a numerical example of the new method. [ABSTRACT FROM AUTHOR]

We demonstrate how adversaries with large computing resources can break quantum key distribution (QKD) protocols which employ a particular message authentication code suggested previously. This authentication code, featuring low key consumption, is not information-theoretically secure (ITS) since for each message the eavesdropper has intercepted she is able to send a different message from a set of messages that she can calculate by finding collisions of a cryptographic hash function. However, when this authentication code was introduced, it was shown to prevent straightforward man-in-the-middle (MITM) attacks against QKD protocols. In this paper, we prove that the set of messages that collide with any given message under this authentication code contains with high probability a message that has small Hamming distance to any other given message. Based on this fact, we present extended MITM attacks against different versions of BB84 QKD protocols using the addressed authentication code; for three protocols, we describe every single action taken by the adversary. For all protocols, the adversary can obtain complete knowledge of the key, and for most protocols her success probability in doing so approaches unity. Since the attacks work against all authentication methods which allow to calculate colliding messages, the underlying building blocks of the presented attacks expose the potential pitfalls arising as a consequence of non-ITS authentication in QKD post-processing. We propose countermeasures, increasing the eavesdroppers demand for computational power, and also prove necessary and sufficient conditions for upgrading the discussed authentication code to the ITS level. [ABSTRACT FROM AUTHOR]

Local binary descriptors are attracting increasingly attention due to their great advantages in computational speed, which are able to achieve real-time performance in numerous image/vision applications. Various methods have been proposed to learn data-dependent binary descriptors. However, most existing binary descriptors aim overly at computational simplicity at the expense of significant information loss which causes ambiguity in similarity measure using Hamming distance. In this paper, by considering multiple features might share complementary information, we present a novel local binary descriptor, referred as ring-based multi-grouped descriptor (RMGD), to successfully bridge the performance gap between current binary and floated-point descriptors. Our contributions are twofold. First, we introduce a new pooling configuration based on spatial ring-region sampling, allowing for involving binary tests on the full set of pairwise regions with different shapes, scales, and distances. This leads to a more meaningful description than the existing methods which normally apply a limited set of pooling configurations. Then, an extended Adaboost is proposed for an efficient bit selection by emphasizing high variance and low correlation, achieving a highly compact representation. Second, the RMGD is computed from multiple image properties where binary strings are extracted. We cast multi-grouped features integration as rankSVM or sparse support vector machine learning problem, so that different features can compensate strongly for each other, which is the key to discriminativeness and robustness. The performance of the RMGD was evaluated on a number of publicly available benchmarks, where the RMGD outperforms the state-of-the-art binary descriptors significantly. [ABSTRACT FROM AUTHOR]

Polar codes are constructed based on kernels with polarizing properties. The performance of a polar code is characterized asymptotically in terms of the exponent of its kernel. The pioneering work of Arıkan on polar codes is based on a linear kernel of dimension two and exponent 0.5. In this paper, constructions of linear and nonlinear binary kernels of dimensions up to 16 are presented. The kernels are obtained using computer search or by shortening longer kernels obtained by computer search and a computer program is used to determine their exponents. It is proved that the constructed kernels have maximum exponents except in the case of nonlinear kernels of dimension 12 where it is demonstrated that the maximum exponent either equals that of the presented construction or assumes another specified value. The results show that the minimum dimension for which there exists a linear kernel with exponent greater than 0.5, i.e., exceeds the exponent of the linear kernel proposed by Arıkan, is 15, while this minimum dimension is 14 for nonlinear kernels. Furthermore, it is shown that there is a linear kernel with maximum exponent up to dimension 11. For dimensions 13, 14, 15, and 16, there are nonlinear kernels with exponents larger than any of that of a linear kernel. The kernels of these dimensions that have maximum exponent, although nonlinear over \textrm GF(2) , are \mathbb Z4 -linear or \mathbb Z2\mathbb Z4 -linear. [ABSTRACT FROM PUBLISHER]

We extend the 'straight-line' region of transmission rates for which the BSC reliability function is known exactly. [ABSTRACT FROM AUTHOR]

This paper provides new constructions and lower bounds for subspace codes, using Ferrers diagram rank-metric codes from matchings of the complete graph and pending blocks. We present different constructions for constant dimension codes with minimum injection distance 2 or $k-1$ , where $k$ is the constant dimension. Furthermore, we present a construction of new codes from old codes for any minimum distance. Then, we construct nonconstant dimension codes from these codes. Some examples of codes obtained by these constructions are the largest known codes for the given parameters. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel dynamic sparsity-based classification scheme to analyze various interaction actions between persons. To address the occlusion problem, this paper represents an action in an over-complete dictionary to makes errors (caused by lighting changes or occlusions) sparsely appear in the training library if the error cases are well collected. Because of this sparsity, it is robust to occlusions and lighting changes. In addition, a novel Hamming distance classification (HDC) scheme is proposed to classify action events to various types. Because the nature of Hamming code is highly tolerant to noise, the HDC scheme is also robust to environmental changes. The difficulty of complicated action modeling can be easily tackled by adding more examples to the over-complete dictionary. More importantly, the HDC scheme is very efficient and suitable for real-time applications because no minimization process is involved to calculate the reconstruction error. [ABSTRACT FROM AUTHOR]

We present new constructions of codes for asymmetric channels for both binary and nonbinary alphabets, based on methods of generalized code concatenation. For the binary asymmetric channel, our methods construct nonlinear single-error-correcting codes from ternary outer codes. We show that some of the Varshamov–Tenengol’ts–Constantin–Rao codes, a class of binary nonlinear codes for this channel, have a nice structure when viewed as ternary codes. In many cases, our ternary construction yields even better codes. For the nonbinary asymmetric channel, our methods construct linear codes for many lengths and distances which are superior to the linear codes of the same length capable of correcting the same number of symmetric errors. [ABSTRACT FROM AUTHOR]

In a series of remarkable papers, Babadi and Tarokh proved the randomness of matrices and product of two matrices arising from binary linear block codes with respect to the empirical spectral distribution, provided that their dual distances are sufficiently large. However, numerical experiments conducted by Babadi and Tarokh revealed that Gold codes, which have a dual distance of 5, also possess such a randomness property. Hence, the interesting question was raised as to whether or not the stringent requirement of large dual distances can be relaxed in the theorems in order to explain the mysterious randomness of Gold sequences. In this paper, we improve the results of Babadi and Tarokh on several fronts and provide an affirmative answer to this question. [ABSTRACT FROM PUBLISHER]

As generalize of the hesitant fuzzy sets, hesitant interval-valued fuzzy sets (HIVFSs), which permits the memberships of an element to a given set having a few different interval values in [0,1] rather than real numbers, can be considered as a powerful tool to express uncertain information in the human decision making process. Based on the traditional Hamming distance, Euclidean distance, Hausdorff distance, and generalized distance, in this paper, we propose a variety of distance measures for hesitant interval-valued fuzzy sets, based on which the corresponding similarity measures can be obtained. We investigate the connections of the aforementioned distance measures and further develop a number of hesitant interval-valued ordered weighted distance measures and hesitant interval-valued ordered weighted similarity measures. They can alleviate the influence of unduly large (or small) deviations on the aggregation results by assigning them low (or high) weights. Finally, we shall present a numerical example to show potential evaluation of emerging technology commercialization with hesitant interval-valued fuzzy information in order to illustrate the method proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new fuzzy decision making technique called the fuzzy induced heavy ordered weighted averaging distance (FIHOWAD) operator. It is an extension of the ordered weighted averaging (OWA) operator that uses the main characteristics of the induced OWA (IOWA), the Hamming distance, the heavy OWA (HOWA) and uncertain information represented as fuzzy numbers. A key feature of the FIHOWAD operator is that it generalizes a wide range of aggregation operators such as the fuzzy minimum distance, the fuzzy weighted Hamming distance (FWHD), the fuzzy OWA distance (FOWAD), the fuzzy IOWA distance (FIOWAD) and the fuzzy heavy OWA distance (FHOWAD) operators. We studied some of its main properties and different particular cases. Finally, we present a numerical example to illustrate the new approach in a financial decision making problem. [ABSTRACT FROM AUTHOR]

Selection and scheduling are an important topic in production systems. To tackle the order acceptance and scheduling problem on a single machine with release dates, tardiness penalty, and sequence-dependent setup times, in this paper a diversity controlling genetic algorithm (DCGA) is proposed, in which a diversified population is maintained during the whole search process through survival selection considering both the fitness and the diversity of individuals. To measure the similarity between individuals, a modified Hamming distance without considering the unaccepted orders in the chromosome is adopted. The proposed DCGA was validated on 1500 benchmark instances with up to 100 orders. Compared with the state-of-the-art algorithms, the experimental results show that DCGA improves the solution quality obtained significantly, in terms of the deviation from upper bound. [ABSTRACT FROM AUTHOR]

Finger vein recognition is a promising biometric recognition technology, which verifies identities via the vein patterns in the fingers. Binary pattern based methods were thoroughly studied in order to cope with the difficulties of extracting the blood vessel network. However, current binary pattern based finger vein matching methods treat every bit of feature codes derived from different image of various individuals as equally important and assign the same weight value to them. In this paper, we propose a finger vein recognition method based on personalized weight maps (PWMs). The different bits have different weight values according to their stabilities in a certain number of training samples from an individual. Firstly we present the concept of PWM, and then propose the finger vein recognition framework, which mainly consists of preprocessing, feature extraction, and matching. Finally, we design extensive experiments to evaluate the effectiveness of our proposal. Experimental results show that PWM achieves not only better performance, but also high robustness and reliability. In addition, PWM can be used as a general framework for binary pattern based recognition. [ABSTRACT FROM AUTHOR]

A coordinate of a binary code of size M is said to be balanced if the number of zero and ones in the coordinate is either $$\lfloor M/2\rfloor $$ or $$\lceil M/2 \rceil $$ (that is, exactly $$M/2$$ for even M). Since good codes (of various types) tend to be balanced in all coordinates, various conjectures have been made regarding the existence of such codes. It is here shown that there are parameters for which there are no optimal binary error-correcting codes with a balanced coordinate. This is proved by the code attaining $$A(17,8) = 36$$ , which is shown to be unique here; $$A(n,d)$$ denotes the maximum size of a binary code of length n and minimum distance d. It is further shown that $$A(18,8) \le 68$$ . [ABSTRACT FROM AUTHOR]

We prove an optimal Ω(n) lower bound on the randomized communication complexity of the much-studied gap-hamming-distance problem. As a consequence, we obtain essentially optimal multipass space lower bounds in the data stream model for a number of fundamental problems, including the estimation of frequency moments. The gap-hamming-distance problem is a communication problem, wherein Alice and Bob receive n-bit strings x and y, respectively. They are promised that the Hamming distance between x and y is either at least n/2 +√n or at most n/2 - √n, and their goal is to decide which of these is the case. Since the formal presentation of the problem by Indyk and Woodruff [Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, 2003, pp. 283-289], it had been conjectured that the naive protocol, which uses n bits of communication, is asymptotically optimal. The conjecture was shown to be true in several special cases, e.g., when the communication is deterministic or when the number of rounds of communication is limited. The proof of our aforementioned result, which settles this conjecture fully, is based on a new geometric statement regarding correlations in Gaussian space, related to a result of Borell [Z. Wahrsch. Verw. Gebiete, 70 (1985), pp. 1-13]. To prove this geometric statement, we show that random projections of not-too-small sets in Gaussian space are close to a mixture of translated normal variables. [ABSTRACT FROM AUTHOR]

Constant-weight codes (CWCs) play an important role in coding theory. The problem of determining the sizes for optimal ternary CWCs with length n, weight 4, and minimum Hamming distance 5 ((n,5,4)3 code) has been settled for all positive integers n\leq 10 or n > 10 and n\equiv 1\pmod 3 with n\in \13,52,58\ undetermined. In this paper, we investigate the problem of constructing optimal (n,5,4)3 codes for all lengths n with the tool of group divisible codes. We determine the size of an optimal (n,5,4)3 code for each integer n\geq 4 leaving the lengths n\in \12,13,21,27,33,39,45,52\ unsolved. [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]

Abstract: We analyze the use of the ordered weighted averaging (OWA) operator in the selection of human resources in sport management. We use different business decision-making techniques for doing so. We consider the use of the Hamming distance, the adequacy coefficient and the index of maximum and minimum level. That is, we use the OWA distance (OWAD), the OWA adequacy coefficient (OWAAC) and the OWA index of maximum and minimum level (OWAIMAM) operator. By using the OWA operator, we can parameterize these decision-making techniques from the maximum to the minimum result according to the interests of the decision-maker. We develop an illustrative example regarding the decision-making process to follow in the selection of a football player for a team. [Copyright &y& Elsevier]

Various kinds of distances of all negacyclic codes of length 2s over are completely determined. Using our structure theorems of negacyclic codes of length 2s over Z2a, we first calculate the Hamming distances of all such negacyclic codes, which particularly lead to the Hamming weight distributions and Hamming weight enumerators of several codes. These Hamming distances are then used to obtain their homogeneous, Lee, and Euclidean distances. Our techniques are extendable to the more general class of constacyclic codes, namely, the λ-constacyclic codes of length 2s over Z2a, where λ is any unit of Z2a with the form 4k - 1. We establish the Hamming, homogeneous, Lee, and Euclidean distances of all such constacyclic codes. [ABSTRACT FROM AUTHOR]

A new general upper bound is derived on the sum of the Hamming distances between sequences when mapping from one set of sequences to another. It is shown that a similar upper bound for mappings from binary sequences to permutation sequences is a special case of this upper bound and this is used to evaluate known mappings. Also, new distance-preserving mappings (DPMs) from binary sequences to permutation sequences are presented, based on a multilevel construction. In addition to explicit distance-conserving mappings, distance-increasing, and distance-reducing mappings are also presented. Several of the new DPMs attain the upper bound. [ABSTRACT FROM AUTHOR]