Search

Structure learning is the core of graph model Bayesian Network learning, and the current mainstream single search algorithm has problems such as poor learning effect, fuzzy initial network, and easy falling into local optimum. In this paper, we propose a heuristic learning algorithm HC-PSO combining the HC (Hill Climbing) algorithm and PSO (Particle Swarm Optimization) algorithm, which firstly uses HC algorithm to search for locally optimal network structures, takes these networks as the initial networks, then introduces mutation operator and crossover operator, and uses PSO algorithm for global search. Meanwhile, we use the DE (Differential Evolution) strategy to select the mutation operator and crossover operator. Finally, experiments are conducted in four different datasets to calculate BIC (Bayesian Information Criterion) and HD (Hamming Distance), and comparative analysis is made with other algorithms, the structure shows that the HC-PSO algorithm is superior in feasibility and accuracy. [ABSTRACT FROM AUTHOR]

Quantum approximate optimization algorithm (QAOA) is a promising hybrid quantum-classical algorithm to solve combinatorial optimization problems in the era of noisy intermediate-scale quantum computers. Recently it has been revealed that warm-start approaches can improve the performance of QAOA, where approximate solutions are obtained by classical algorithms in advance and incorporated into the initial state and/or unitary ansatz. In this work, we study in detail how the accuracy of approximate solutions affects the performance of the warm-start QAOA (WS-QAOA). We numerically find that in typical MAX-CUT problems, WS-QAOA achieves higher fidelity (probability that exact solutions are observed) and approximation ratio than QAOA as the Hamming distance of approximate solutions to the exact ones becomes smaller. We reveal that this could be quantitatively attributed to the initial state of the ansatz. We also solve MAX-CUT problems by WS-QAOA with approximate solutions obtained via QAOA, having higher fidelity and approximation ratio than QAOA especially when the circuit is relatively shallow. We believe that our study may deepen understanding of the performance of WS-QAOA and also provide a guide as to the necessary quality of approximate solutions. [ABSTRACT FROM AUTHOR]

Sequence motif discovery algorithms enhance the identification of novel deoxyribonucleic acid sequences with pivotal biological significance, especially transcription factor (TF)-binding motifs. The advent of assay for transposase-accessible chromatin using sequencing (ATAC-seq) has broadened the toolkit for motif characterization. Nonetheless, prevailing computational approaches have focused on delineating TF-binding footprints, with motif discovery receiving less attention. Herein, we present Cis rEgulatory Motif Influence using de Bruijn Graph (CEMIG), an algorithm leveraging de Bruijn and Hamming distance graph paradigms to predict and map motif sites. Assessment on 129 ATAC-seq datasets from the Cistrome Data Browser demonstrates CEMIG's exceptional performance, surpassing three established methodologies on four evaluative metrics. CEMIG accurately identifies both cell-type-specific and common TF motifs within GM12878 and K562 cell lines, demonstrating its comparative genomic capabilities in the identification of evolutionary conservation and cell-type specificity. In-depth transcriptional and functional genomic studies have validated the functional relevance of CEMIG-identified motifs across various cell types. CEMIG is available at https://github.com/OSU-BMBL/CEMIG , developed in C++ to ensure cross-platform compatibility with Linux, macOS and Windows operating systems. [ABSTRACT FROM AUTHOR]

While the theoretical analysis of evolutionary algorithms (EAs) has made significant progress for pseudo-Boolean optimization problems in the last 25 years, only sporadic theoretical results exist on how EAs solve permutation-based problems. To overcome the lack of permutation-based benchmark problems, we propose a general way to transfer the classic pseudo-Boolean benchmarks into benchmarks defined on sets of permutations. We then conduct a rigorous runtime analysis of the permutation-based (1 + 1) EA proposed by Scharnow et al. (J Math Model Algorithm 3:349–366, 2004) on the analogues of the LeadingOnes and Jump benchmarks. The latter shows that, different from bit-strings, it is not only the Hamming distance that determines how difficult it is to mutate a permutation σ into another one τ , but also the precise cycle structure of σ τ - 1 . For this reason, we also regard the more symmetric scramble mutation operator. We observe that it not only leads to simpler proofs, but also reduces the runtime on jump functions with odd jump size by a factor of Θ (n) . Finally, we show that a heavy-tailed version of the scramble operator, as in the bit-string case, leads to a speed-up of order m Θ (m) on jump functions with jump size m. A short empirical analysis confirms these findings, but also reveals that small implementation details like the rate of void mutations can make an important difference. [ABSTRACT FROM AUTHOR]

This paper presents a method for unsupervised classification of entities by a group of agents with unknown domains and levels of expertise. In contrast to the existing methods based on majority voting ("wisdom of the crowd") and their extensions by expectation-maximization procedures, the suggested method first determines the levels of the agents' expertise and then weights their opinions by their expertise level. In particular, we assume that agents will have relatively closer classifications in their field of expertise. Therefore, the expert agents are recognized by using a weighted Hamming distance between their classifications, and then the final classification of the group is determined from the agents' classifications by expectation-maximization techniques, with preference to the recognized experts. The algorithm was verified and tested on simulated and real-world datasets and benchmarked against known existing algorithms. We show that such a method reduces incorrect classifications and effectively solves the problem of unsupervised collaborative classification under uncertainty, while outperforming other known methods. [ABSTRACT FROM AUTHOR]

Modern applications of graph algorithms often involve the use of the output sets (usually, a subset of edges or vertices of the input graph) as inputs to other algorithms. Since the input graphs of interest are large and dynamic, it is desirable for an algorithm's output to not change drastically when a few random edges are removed from the input graph, so as to prevent issues in postprocessing. Alternately, having such a guarantee also means that one can revise the solution obtained by running the algorithm on the original graph in just a few places in order to obtain a solution for the new graph. We formalize this feature by introducing the notion of average sensitivity of graph algorithms, which is the average earth mover's distance between the output distributions of an algorithm on a graph and its subgraph obtained by removing an edge, where the average is over the edges removed and the distance between two outputs is the Hamming distance. In this work, we initiate a systematic study of average sensitivity of graph algorithms. After deriving basic properties of average sensitivity such as composition, we provide efficient approximation algorithms with low average sensitivities for concrete graph problems, including the minimum spanning forest problem, the global minimum cut problem, the minimum s-t cut problem, and the maximum matching problem. In addition, we prove that the average sensitivity of our global minimum cut algorithm is almost optimal, by showing a nearly matching lower bound. We also show that every algorithm for the 2-coloring problem has average sensitivity linear in the number of vertices. One of the main ideas involved in designing our algorithms with low average sensitivity is the following fact: if the presence of a vertex or an edge in the solution output by an algorithm can be decided locally, then the algorithm has a low average sensitivity, allowing us to reuse the analyses of known subline artime algorithms and local computation algorithms. Using this fact in conjunction with our average sensitivity lower bound for 2-coloring, we show that every local computation algorithm for 2-coloring has query complexity linear in the number of vertices, thereby answering an open question. [ABSTRACT FROM AUTHOR]

We thoroughly study a novel but basic combinatorial matrix completion problem: Given a binary incomplete matrix, fill in the missing entries so that every pair of rows in the resulting matrix has a Hamming distance within a specified range. We obtain an almost complete picture of the complexity landscape regarding the distance constraints and the maximum number of missing entries in any row. We develop polynomial-time algorithms for maximum diameter three based on Deza's theorem (1973) [11] from extremal set theory. We also prove NP-hardness for diameter at least four. For the number of missing entries per row, we show polynomial-time solvability when there is only one and NP-hardness when there can be at least two. In many of our algorithms, we heavily rely on Deza's theorem to identify sunflower structures. This paves the way towards polynomial-time algorithms which are based on finding graph factors and solving 2-SAT instances. [ABSTRACT FROM AUTHOR]

Motivation Comparing single-stranded nucleic acids (ssNAs) secondary structures is fundamental when investigating their function and evolution and predicting the effect of mutations on their structures. Many comparison metrics exist, although they are either too elaborate or not sensitive enough to distinguish close ssNAs structures. Results In this context, we developed AptaMat, a simple and sensitive algorithm for ssNAs secondary structures comparison based on matrices representing the ssNAs secondary structures and a metric built upon the Manhattan distance in the plane. We applied AptaMat to several examples and compared the results to those obtained by the most frequently used metrics, namely the Hamming distance and the RNAdistance, and by a recently developed image-based approach. We showed that AptaMat is able to discriminate between similar sequences, outperforming all the other here considered metrics. In addition, we showed that AptaMat was able to correctly classify 14 RFAM families within a clustering procedure. Availability and implementation The python code for AptaMat is available at https://github.com/GEC-git/AptaMat.git. Supplementary information Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

The affine scale-invariant feature transform (ASIFT) algorithm is a feature extraction algorithm with affinity and scale invariance, which is suitable for image feature matching using unmanned aerial vehicles (UAVs). However, there are many problems in the matching process, such as the low efficiency and mismatching. In order to improve the matching efficiency, this algorithm firstly simulates image distortion based on the position and orientation system (POS) information from real-time UAV measurements to reduce the number of simulated images. Then, the scale-invariant feature transform (SIFT) algorithm is used for feature point detection, and the extracted feature points are combined with the binary robust invariant scalable keypoints (BRISK) descriptor to generate the binary feature descriptor, which is matched using the Hamming distance. Finally, in order to improve the matching accuracy of the UAV images, based on the random sample consensus (RANSAC) a false matching eliminated algorithm is proposed. Through four groups of experiments, the proposed algorithm is compared with the SIFT and ASIFT. The results show that the algorithm can optimize the matching effect and improve the matching speed. [ABSTRACT FROM AUTHOR]

Trace reconstruction considers the task of recovering an unknown string $\mathbf {x}\in \{0,1\}^{n}$ given a number of independent “traces”, i.e., subsequences of $\mathbf {x}$ obtained by randomly and independently deleting every symbol of $\mathbf {x}$ with some probability $p$. The information-theoretic limit of the number of traces needed to recover a string of length $n$ is still unknown. This limit is essentially the same as the number of traces needed to determine, given strings $\mathbf {x}$ and $\mathbf {y}$ and traces of one of them, which string is the source. The most-studied class of algorithms for the worst-case version of the problem are “mean-based” algorithms. These are a restricted class of distinguishers that only use the mean value of each coordinate on the given samples. In this work we study limitations of mean-based algorithms on strings at small Hamming or edit distance. We show that, on the one hand, distinguishing strings that are nearby in Hamming distance is “easy” for such distinguishers. On the other hand, we show that distinguishing strings that are nearby in edit distance is “hard” for mean-based algorithms. Along the way, we also describe a connection to the famous Prouhet-Tarry-Escott (PTE) problem, which shows a barrier to finding explicit hard-to-distinguish strings: namely such strings would imply explicit short solutions to the PTE problem, a well-known difficult problem in number theory. Furthermore, we show that the converse is also true, thus, finding explicit solutions to the PTE problem is equivalent to the problem of finding explicit strings that are hard-to-distinguish by mean-based algorithms. Our techniques rely on complex analysis arguments that involve careful trigonometric estimates, and algebraic techniques that include applications of Descartes’ rule of signs for polynomials over the reals. [ABSTRACT FROM AUTHOR]

To solve the low accuracy of image feature matching in horticultural robot visual navigation, an innovative and effective image feature matching algorithm was proposed combining the improved Oriented FAST and Rotated BRIEF (ORB) and Lucas–Kanade (LK) optical flow algorithm. First, image feature points were extracted according to the adaptive threshold calculated using the Michelson contrast. Then, the extracted feature points were uniformed by the quadtree structure, which can reduce the calculated amount of feature matching, and the uniform ORB feature points were roughly matched to estimate the position of the feature points in the matched image using the improved LK optical flow. Finally, the Hamming distance between rough matching points was calculated for precise matching. Feature extraction and matching experiments were performed in four typical scenes: normal light, low light, high texture, and low texture. Compared with the traditional algorithm, the uniformity and accuracy of the feature points extracted by the proposed algorithm were enhanced by 0.22 and 50.47%, respectively. Meanwhile, the results revealed that the matching accuracy of the proposed algorithm increased by 14.59%, whereas the matching time and total time decreased by 39.18% and 44.79%, respectively. The proposed algorithm shows great potential for application in the visual simultaneous localization and mapping (V-SLAM) of horticultural robots to achieve higher accuracy of real-time positioning and map construction. [ABSTRACT FROM AUTHOR]

Smoke detection is an advance caution to the unforeseen great damage events. Therefore, it is required to identify the smoke in the course of initial stages for preventing fire events. A new technique is proposed to lessen the rate of incorrect alarm by identify the smoke and examine its distinctive texture attributes. Initially, the smoke-colored regions are segmented based on color at the YUV color locality. Then the tentative frame differencing is used to segment the candidate smoke region from the smoke-colored region. In the next phase, the candidate distinctive texture attributes in the smoke region are extracted using Co-occurrence of Hamming Distance based Local Binary pattern (CoHDLBP) and Co-occurrence of Local Binary pattern (CoLBP); these features include homogeneity, energy, correlation and contrast. Finally, the ELM classifier is proficient for the take-out features from the candidate smoke region, and then the decision has been taken with the assistance of a smoke alarm. Investigational outcomes proved that the suggested smoke recognition process executes better compared with all the usual smoke recognition methods by achieving better detection accuracy and processing time. [ABSTRACT FROM AUTHOR]

The rapid and accurate identification of photovoltaic (PV) model parameters is of great significance in solving practical engineering problems such as PV power prediction, maximum power point tracking and battery failure model recognition. Aiming at the shortcomings of low accuracy and poor reliability and being easy to fall into local optimization when standard intelligent optimization algorithms identify PV model parameters, a novel drunken adaptive walking chaotic wolf swarm algorithm is proposed, which is named DCWPA for short. The DCWPA uses the chaotic map sequence to initialize the population, thus to improve the diversity of the initial population. It adopts the walking direction mechanism based on the drunk walking model and the adaptive walking step size to increase the randomness of walking, enhance the individual's ability to explore and develop and improve the ability of algorithm optimization. It also designs the judgment conditions for half siege in order to accelerate the convergence of the algorithm and improve the speed of the algorithm. In the iterative process, according to the change of the optimal solution, the Hamming Distance is used to judge the similarity of individuals in the population, and the individuals in the population are constantly updated to avoid the algorithm from stopping evolution prematurely due to falling into local optimization. This paper firstly analyzes the time complexity of the algorithm, and then selects eight standard test functions (Benchmark) with different characteristics to verify the performance of the DCWPA algorithm for continuous optimization, and finally the improved algorithm is applied for parameter identification of PV models. The experiments show that the DCWPA has higher identification accuracy than other algorithms, and the results are more consistent with the measured data. Thus, the effectiveness and superiority of the improved algorithm in identifying solar cell parameters are verified, and the identification effect of the improved algorithm on solar cell parameters under different illumination is shown. This research provides a new idea and method for parameter identification of a PV module model. [ABSTRACT FROM AUTHOR]

An improved ORB feature point purification method has been proposed to address the problem of large feature point matching error and low image registration rate in the oriented FAST and rotated BRIEF (ORB) feature point color image matching algorithm. Pure virtual quaternions were used to represent the color image pixels in this method, and an improved FAST algorithm was used to detect the color feature points at first. The firework algorithm has been used to divide the detected feature points into key areas, auxiliary areas, and small influence areas, depending on the degree of attachment. The feature points of the key area and the subsidiary area are the required feature points. In order to further improve the efficiency of matching the color image feature points, the firework explosion radius formula and the explosion number formula in the firework algorithm have been improved, and an improved firework algorithm is proposed. This improved algorithm purifies the quaternion-represented color image feature points. For feature matching, the hamming distance was used. Experiments show that, when compared to the traditional ORB algorithm, the improved algorithm retains the key feature points of the color image with high accuracy, removes a large number of irrelevant feature points and noise points, and provides significantly higher accuracy and efficiency of color image matching. [ABSTRACT FROM AUTHOR]

Mining clusters from data is an important endeavor in many applications. The k‐means method is a popular, efficient, and distribution‐free approach for clustering numerical‐valued data, but does not apply for categorical‐valued observations. The k‐modes method addresses this lacuna by replacing the Euclidean with the Hamming distance and the means with the modes in the k‐means objective function. We provide a novel, computationally efficient implementation of k‐modes, called Optimal Transfer Quick Transfer (OTQT). We prove that OTQT finds updates to improve the objective function that are undetectable to existing k‐modes algorithms. Although slightly slower per iteration due to algorithmic complexity, OTQT is always more accurate and almost always faster (and only barely slower on some datasets) to the final optimum. Thus, we recommend OTQT as the preferred, default algorithm for k‐modes optimization. [ABSTRACT FROM AUTHOR]

Line-of-sight (LOS) is a critical requirement for mmWave wireless communications. In this work, we explore the use of access point (AP) infrastructure mobility to optimize indoor mmWave WiFi network performance based on the discovery of LOS connectivity to stations (STAs). We consider a ceiling-mounted mobile (CMM) AP as the infrastructure mobility framework. Within this framework, we propose two heuristic algorithms (basic and weighted) derived from Hamming distance computation and a machine learning (ML) solution fully exploiting available network state information to address the LOS discovery problem. Based on the ML solution, we then propose a systematic solution WiMove , which can decide if and where the AP should move to for optimizing network performance. Using both ns-3 based simulation and experimental prototype implementation, we show that the throughput and fairness performance of WiMove is up to 119% and 15% better compared with single static AP and brute force search. • We focus on line of sight discovery for mmWave WiFi with access point mobility. • We propose two heuristic algorithms and a machine learning (ML) solution. • Based on the ML solution, we provide a systematic solution called WiMove. • WiMove outperforms conventional methods (e.g., static AP and brute force). [ABSTRACT FROM AUTHOR]

Due to the advantage of capacity-achieving, polar codes have been extended to the block fading channel whereas most constructions involve complex iterative-calculation. In this paper, we establish a systematic framework to analyze the error performance of polar codes in the case of block mapping and random mapping. For both the mappings, by introducing the new concept, named split polar spectrum, we derive the upper bound on the error probability of polarized channel which explicitly reveals the relationship between the diversity order $L$ and the block-wise weight distribution of the codeword. For the special case $L=2$ in the block mapping, we design the enumeration algorithm to calculate the exact split polar spectrum based on the general MacWilliams identities. For arbitrary diversity order in the random mapping, with the help of uniform interleaving, we derive the approximate split polar spectrum by combining the polar spectrum and the probability of fading pattern for a specific weight. Furthermore, we propose the design criteria to construct polar codes over the block fading channel. The full diversity criterion is the primary target to achieve the diversity gain and the product distance criterion requires to maximize the product of the block-wise Hamming distance whereby obtain the coding gain. Guided by these design criteria, the construction metrics, respectively named polarized diversity weight (PDW) and simplified PDW (SPDW) are proposed to designpolar codes in both mappings. Such simple metrics can construct polar codes with similar or better performance over those based on traditional methods in block fading channel. [ABSTRACT FROM AUTHOR]

In order to satisfy the rapidly increasing demand for data volume, large data center networks (DCNs) have been proposed. In 2019, Zhang et al. proposed a new highly scalable DCN architecture named HSDC (Highly Scalable Data Center Network), which can achieve greater incremental scalability. In this paper, we give the definition of the logical graph of HSDC, named H n , which can be treated as a compound graph of hypercube and complete graph of the same dimension. First, we prove that the connectivity and tightly super connectivity of H n are both n. Then, we give an O(n) shortest unicast algorithm to find a shortest path between any two distinct nodes in H n , and prove the correctness of this algorithm. In fact, we also prove that the length of the shortest path constructed by this algorithm is no more than 2 d + 1 if d < n and at most 2d if d = n , where d is the Hamming distance between the start and end nodes, and the diameter of H n is 2n. [ABSTRACT FROM AUTHOR]

In an inverse combinatorial optimization problem, a feasible solution is given and is not optimal under the current parameters. The aim is to make the feasible solution optimal by modifying the current parameters as little as possible. The modification cost can be measured by different norms, such as weighted l 1 norm, weighted l 2 norm, weighted l ∞ norm, weighted Hamming distance and so on. In this paper, we focus on the constrained inverse minimum flow problems under the weighted Hamming distance. Three different models are considered: the general problem under the weighted bottleneck-type Hamming distance and two cases under the mixed of sum-type and bottleneck type. Strongly polynomial algorithms are presented for the models we studied. [ABSTRACT FROM AUTHOR]

The development of information technology has produced massive amounts of data, which has brought severe challenges to information storage. Traditional electronic storage media cannot keep up with the ever-increasing demand for data storage, but in its place DNA has emerged as a feasible storage medium with high density, large storage capacity and strong durability. In DNA data storage, many different approaches can be used to encode data into codewords. DNA coding is a key step in DNA storage and can directly affect storage performance and data integrity. However, since errors are prone to occur in DNA synthesis and sequencing, and non-specific hybridization is prone to occur in the solution, how to effectively encode DNA has become an urgent problem to be solved. In this article, we propose a DNA storage coding method based on the equilibrium optimization random search (EORS) algorithm, which meets the Hamming distance, GC content and no-runlength constraints and can reduce the error rate in storage. Simulation experiments have shown that the size of the DNA storage code set constructed by the EORS algorithm that meets the combination constraints has increased by an average of 11% compared with previous work. The increase in the code set means that shorter DNA chains can be used to store more data. [ABSTRACT FROM AUTHOR]

Graphs such as de Bruijn graphs and OLC (overlap-layout-consensus) graphs have been widely adopted for the de novo assembly of genomic short reads. This work studies another important problem in the field: how graphs can be used for high-performance compression of the large-scale sequencing data. We present a novel graph definition named Hamming-Shifting graph to address this problem. The definition originates from the technological characteristics of next-generation sequencing machines, aiming to link all pairs of distinct reads that have a small Hamming distance or a small shifting offset or both. We compute multiple lexicographically minimal k-mers to index the reads for an efficient search of the weight-lightest edges, and we prove a very high probability of successfully detecting these edges. The resulted graph creates a full mutual reference of the reads to cascade a code-minimized transfer of every child-read for an optimal compression. We conducted compression experiments on the minimum spanning forest of this extremely sparse graph, and achieved a 10 − 30% more file size reduction compared to the best compression results using existing algorithms. As future work, the separation and connectivity degrees of these giant graphs can be used as economical measurements or protocols for quick quality assessment of wet-lab machines, for sufficiency control of genomic library preparation, and for accurate de novo genome assembly. Author summary: We present a novel graph-based algorithm to compress next-generation short sequencing reads. The novelty of the algorithm is attributed to a new definition of genomic sequence graph named Hamming-Shifting graph. It consists of edges between distinct reads that have a small Hamming distance or a small shifting offset or both. Efficient construction of Hamming-Shifting graphs is challenging. We introduce a heuristic technique to detect the weight-lightest edges through multiple minimizers from each read, then search the minimum spanning trees and forests of the Hamming-Shifting graph for a high-performance compression of the reads. Our method achieves an additional 10 − 30% file size reduction compared to contemporary compression techniques. [ABSTRACT FROM AUTHOR]

This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming distance from codeword estimates to the received sequence in the reprocessing stages of the OSD algorithm. We prove that the Hamming distance and weighted Hamming distance distributions can be characterized as mixture models capturing the decoding error probability and code weight enumerator. Simulation and numerical results show that our proposed statistical approaches can accurately describe the distance distributions. Based on these distributions and with the aim to reduce the decoding complexity, several techniques, including stopping rules and discarding rules, are proposed, and their decoding error performance and complexity are accordingly analyzed. Simulation results for decoding various eBCH codes demonstrate that the proposed techniques can significantly reduce the decoding complexity with a negligible loss in the decoding error performance. [ABSTRACT FROM AUTHOR]

To improve the imperceptibility without decreasing the steganographic capacity when steganography by a modification to an audio is carried out, this paper proposes an optimal matching path algorithm to reduce the modification to achieve it. A steganography operation unit is defined, which is composed of every N consecutive audio frames and each frame includes M LPC parameters. All these parameters in the same steganography operation unit will form an M × N matrix. A traversal path is a sequence of all these parameters in the matrix. Each parameter in the matrix will be converted into a one-bit binary digit based on two subcodebooks divided by the complementary neighbor vertex (CNV) method. Thus, every traversal path will have a corresponding binary string named PathBinStr. Steganography is performed by computing the Hamming distance between the binary secret and the corresponding PathBinStr and selecting the traversal path with minimal hamming distance expected value to hide the secret via the CNV embedding method. The experimental results show that the proposed steganography algorithm has better performance in audio quality and the modified bit rate decreases from 50 to 37.4% when only 6 traversal paths are predefined, and its processing time can satisfy the real-time requirement of VoIP services. Also, it does not change the audio size, and the theoretical analysis and experiments show its undetectability is good. [ABSTRACT FROM AUTHOR]

Differential Convolutional Codes with designed Hamming distance are defined, and an algebraic decoding algorithm, inspired by Peterson–Gorenstein–Zierler's algorithm, is designed for them. [ABSTRACT FROM AUTHOR]

We consider the circular pattern matching with k mismatches (k -CPM) problem in which one is to compute the minimal Hamming distance of every length- m substring of T and any cyclic rotation of P , if this distance is no more than k. It is a variation of the well-studied k -mismatch problem. A multitude of papers has been devoted to solving the k -CPM problem, but only average-case upper bounds are known. In this paper, we present the first non-trivial worst-case upper bounds for this problem. Specifically, we show an O (n k) -time algorithm and an O (n + n m k 4) -time algorithm. The latter algorithm applies in an extended way a technique that was very recently developed for the k -mismatch problem Bringmann et al. (2019) [10]. A preliminary version of this work appeared at FCT 2019 [35]. In this version we improve the time complexity of the second algorithm from O (n + n m k 5) to O (n + n m k 4). [ABSTRACT FROM AUTHOR]

Analogs of balls in n -dimensional Euclidean space are defined in the monoid of strings composed of letters of an alphabet if a metric is defined on the monoid. These analogs are not only balls in the monoid of strings but also regular languages. Since the Levenshtein distance, a reasonable metric between strings, was introduced in 1965, researchers have aimed to determine a formula for computing the volumes of balls of strings under this distance and their growth rate. However, this problem remains open. In this paper, we first derive a formula for the volumes of balls of strings under a metric obtained by extending the Hamming distance as a metric on the whole monoid and subsequently reveal the growth rate of balls of strings under the Levenshtein distance using this formula. Furthermore, we describe a conjecture on the formula for the volumes of spheres of strings under the Levenshtein distance. Next, we construct an efficient randomized algorithm that computes estimates of the volumes of the balls whose estimation errors are less than a given value with a probability greater than a specified value. Finally, we examine the validity of the proposed conjecture, using the (true) volumes obtained by exhaustive searches for small spheres and estimates of the volumes obtained by this algorithm for large ones. [ABSTRACT FROM AUTHOR]

The Oriented FAST and Rotated BRIEF (ORB) algorithm has the problem that the extracted feature points are overconcentrated or even overlapped, leading to information loss of local image features. A homogenized ORB algorithm using dynamic thresholds and improved quadtree method is proposed in this paper, named Quadtree ORB (QTORB). In the feature point extraction stage, a new dynamic local threshold calculation method is proposed to enhance the algorithm's ability to extract feature points at homogeneous regions. Then, a quadtree method is improved and adopted to manage and optimize feature points to eliminate those excessively concentrated and overlapping feature points. Meanwhile, in the feature points optimization process, different quadtree depths are set at different image pyramid levels to prevent excessive splitting of the quadtree and increase calculation speed. In the feature point description stage, local gray difference value information is introduced to enhance the saliency of the feature description. Finally, the Hamming distance is used to match points and RANSAC is used to avoid mismatches. Two datasets, namely, the optical image dataset and SAR image dataset, are used in the experiment. The experimental result shows that, considering accuracy and real-time efficiency, the QTORB can effectively improve the distribution uniformity of feature points. [ABSTRACT FROM AUTHOR]

Background: The Damerau-Levenshtein (DL) distance metric has been widely used in the biological science. It tries to identify the similar region of DNA,RNA and protein sequences by transforming one sequence to the another using the substitution, insertion, deletion and transposition operations. Lowrance and Wagner have developed an O(mn) time O(mn) space algorithm to find the minimum cost edit sequence between strings of length m and n, respectively. In our previous research, we have developed algorithms that run in O(mn) time using only O(s∗min{m,n}+m+n) space, where s is the size of the alphabet comprising the strings, to compute the DL distance as well as the corresponding edit sequence. These are so far the fastest and most space efficient algorithms. In this paper, we focus on the development of algorithms whose asymptotic space complexity is linear. Results: We develop linear space algorithms to compute the Damerau-Levenshtein (DL) distance between two strings and determine the optimal trace (corresponding edit operations.)Extensive experiments conducted on three computational platforms–Xeon E5 2603, I7-x980 and Xeon E5 2695–show that, our algorithms, in addition to using less space, are much faster than earlier algorithms. Conclusion: Besides using less space than the previously known algorithms,significant run-time improvement was seen for our new algorithms on all three of our experimental platforms. On all platforms, our linear-space cache-efficient algorithms reduced run time by as much as 56.4% and 57.4% in respect to compute the DL distance and an optimal edit sequences compared to previous algorithms. Our multi-core algorithms reduced the run time by up to 59.3% compared to the best previously known multi-core algorithms. [ABSTRACT FROM AUTHOR]

The huge amount of data acquired by high-throughput sequencing requires data reduction for effective analysis. Here we give a clustering algorithm for genome-wide open chromatin data using a new data reduction method. This method regards the genome as a string of 1s and 0s based on a set of peaks and calculates the Hamming distances between the strings. This algorithm with the systematically optimized set of peaks enables us to quantitatively evaluate differences between samples of hematopoietic cells and classify cell types, potentially leading to a better understanding of leukemia pathogenesis. Author summary: High-throughput sequencing provides us huge amounts of data about gene regulation. In order to extract useful information from the data, data reduction is needed. Although RNA-seq data analysis has been extensively studied, where the focus is mainly on genetic loci, tools for epigenetic sequencing data, such as ATAC-seq data which represent chromatin accessibility, are comparatively lacking. Since the binding of transcription factors mainly occurs in open chromatin regions, it is presumably important to understand how chromatin accessibility landscape affects cell phenotype. In this context, we developed a systematic algorithm to select a set of peaks representing the open state of chromatin for a given sample of ATAC-seq data. This algorithm quantifies the difference between samples by regarding the genome as a string of 1s and 0s with Hamming distances and then performs hierarchical clustering. This algorithm has less computational cost and gives a reasonable cell type classification compared to a previous method. In this work, as an application of this algorithm, we present a comparative analysis of leukemia samples with healthy hematopoietic cells and provide new insights about the relationship between chromatin structures, cell surface proteins, and symptoms in leukemia. [ABSTRACT FROM AUTHOR]

In the nonbinary low-density parity check (NB-LDPC) codes decoding algorithms, the iterative hard reliability based on majority logic decoding (IHRB-MLGD) algorithm has poor error correction performance. The essential reason is that the hard information is used in the initialization and iterative processes. For the problem of partial loss of information, when the reliability is assigned during initialization, the error correction performance is improved by modifying the assignment of reliability at initialization. The initialization process is determined by the probability of occurrence of the number of erroneous bits in the symbol and the Hamming distance. In addition, the IHRB-MLGD decoding algorithm uses the hard decision in the iterative decoding process. The improved algorithm adds soft decision information in the iterative process, which improves the error correction performance while only slightly increasing the decoding complexity, and improves the reliability accumulation process which makes the algorithm more stable. The simulation results indicate that the proposed algorithm has a better decoding performance than IHRB algorithm. [ABSTRACT FROM AUTHOR]

Models of sequence evolution typically assume that all sequences are possible. However, restriction enzymes that cut DNA at specific recognition sites provide an example where carrying a recognition site can be lethal. Motivated by this observation, we studied the set of strings over a finite alphabet with taboos, that is, with prohibited substrings. The taboo-set is referred to as T and any allowed string as a taboo-free string. We consider the so-called Hamming graph Γ n (T) , whose vertices are taboo-free strings of length n and whose edges connect two taboo-free strings if their Hamming distance equals one. Any (random) walk on this graph describes the evolution of a DNA sequence that avoids taboos. We describe the construction of the vertex set of Γ n (T) . Then we state conditions under which Γ n (T) and its suffix subgraphs are connected. Moreover, we provide an algorithm that determines if all these graphs are connected for an arbitrary T . As an application of the algorithm, we show that about 87 % of bacteria listed in REBASE have a taboo-set that induces connected taboo-free Hamming graphs, because they have less than four type II restriction enzymes. On the other hand, four properly chosen taboos are enough to disconnect one suffix subgraph, and consequently connectivity of taboo-free Hamming graphs could change depending on the composition of restriction sites. [ABSTRACT FROM AUTHOR]

Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. Sampled string matching is an efficient approach recently introduced in order to overcome the prohibitive space requirements of an index construction, on the one hand, and drastically reduce searching time for the online solutions, on the other hand. In this paper we present a new algorithm for the sampled string matching problem, based on a characters distance sampling approach. The main idea is to sample the distances between consecutive occurrences of a given pivot character and then to search online the sampled data for any occurrence of the sampled pattern, before verifying the original text. From a theoretical point of view we prove that, under suitable conditions, our solution can achieve both linear worst-case time complexity and optimal average-time complexity. From a practical point of view it turns out that our solution shows a sub-linear behaviour in practice and speeds up online searching by a factor of up to 9, using limited additional space whose amount goes from 11 to 2.8% of the text size, with a gain up to 50% if compared with previous solutions. [ABSTRACT FROM AUTHOR]

Effective resistance to intellectual property (IP) piracy, overproduction and reverse engineering are becoming more and more necessary in the integrated circuit (IC) supply chain. To protect the hardware, the obfuscation methodology hides the original function by adding a large number of redundant states. However, existing hardware obfuscation approaches have hardware overhead and efficiency of obfuscation limitations. This paper proposed a novel methodology for IP security using the minimum spanning tree finite state machine (MST-FSM) obfuscation. In the minimum spanning tree (MST) algorithm, the Hamming distance defines the cost of obfuscated states. The Kruskal algorithm optimizes the connection relationship of obfuscated states by computing the Hamming distance of the MST-FSM. The proposed MST-FSM is automatically generated and embedded in the hardware IP with the self-building program. Finally, the MST-FSM is applied on the itc99 benchmark circuits and encryption standard IP cores. Compared with other state-of-the-arts, the obfuscation potency is improved by 3.57%, and the average hardware cost is decreased by about 6.01%. [ABSTRACT FROM AUTHOR]

It was demonstrated that, as a nonlinear implementation of Slepian-Wolf Coding, Distributed Arithmetic Coding (DAC) outperforms traditional Low-Density Parity-Check (LPDC) codes for short code length and biased sources. This fact triggers research efforts into theoretical analysis of DAC. In our previous work, we proposed two analytical tools, Codebook Cardinality Spectrum (CCS) and Hamming Distance Spectrum, to analyze DAC for independent and identically-distributed (i.i.d.) binary sources with uniform distribution. This article extends our work on CCS from uniform i.i.d. binary sources to biased i.i.d. binary sources. We begin with the final CCS and then deduce each level of CCS backwards by recursion. The main finding of this article is that the final CCS of biased i.i.d. binary sources is not uniformly distributed over [0, 1). This article derives the final CCS of biased i.i.d. binary sources and proposes a numerical algorithm for calculating CCS effectively in practice. All theoretical analyses are well verified by experimental results. [ABSTRACT FROM AUTHOR]

The computational efficiency of large-scale unit commitment (UC) is still a critical issue in power system and electricity market operations. To reduce the computation time of UC, relaxation-based neighborhood search (RBNS) and improved relaxation inducement (IRI) are proposed in this article. RBNS explores the neighborhood of the linear program (LP) relaxation optimal solution for a high-quality feasible solution. A new distance function, termed relaxation distance (RD), is proposed to measure the distance between the current solution and the tendency of the LP relaxation optimal solution. RBNS can substantially reduce the optimization space, and thus improve the efficiency. IRI has been developed to effectively induce binary variables towards the tendency of the relaxed solution. In contrast to a conventional relaxation inducement method, the binary variables are symmetrically and bi-directionally induced. The ratio between the inducing functions and the original objective function is optimized. IRI can induce more binary variables to integrality, and fewer binary variables need to be branched. Therefore, the size of the branch-and-bound tree can be reduced significantly. Modified IEEE-300 bus system and Polish 2746 bus system are used to demonstrate the effectiveness and performance of the proposed RBNS and IRI methods. [ABSTRACT FROM AUTHOR]

In a real-world cloud server, a speech signal is prone to suffer various attacks, such as malicious muting and tampering. In such a context, the privacy security of the speech owner will not be guaranteed. In order to achieve content authentication of encrypted speech in the cloud server, an efficient encrypted speech authentication method based on uniform subband spectrum variance and perceptual hashing is proposed. Firstly, the original speech is scrambled by Henon mapping to construct an encrypted speech library in the cloud, through extracting uniform subband spectrum variance of the encrypted speech and constructing a hashing sequence to generate a hashing template of the cloud. In this way, a one-to-one correspondence between the encrypted speech and the hashing sequence is built. Secondly, the authentication digest of encrypted speech is extracted according to the inquiry result. Finally, the authentication digest and the hashing sequence in the cloud are matched by the Hamming distance algorithm. The experimental results demonstrate that the proposed method has great security and efficiency, and it can directly extract the authentication digest from encrypted speech. The authentication digest not only has good discrimination and robustness, but it accurately locates the tampered area for malicious substitution and mute attacks. [ABSTRACT FROM AUTHOR]

A closed string contains a proper factor occurring as both a prefix and a suffix but not elsewhere in the string. Closed strings were introduced by Fici (WORDS 2011) as objects of combinatorial interest. This paper addresses a new problem by extending the closed string problem to the k -closed string problem, for which a level of approximation is permitted up to a number of Hamming distance errors, set by the parameter k. We address the problem of deciding whether or not a given string of length n over an integer alphabet is k -closed and additionally specifying the border resulting in the string being k -closed. Specifically, we present an 𝒪 (k n) -time and 𝒪 (n) -space algorithm to achieve this along with the pseudocode of an implementation and proof-of-concept experimental results. [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]

In the k -mappability problem, we are given a string x of length n and integers m and k , and we are asked to count, for each length- m factor y of x , the number of other factors of length m of x that are at Hamming distance at most k from y. We focus here on the version of the problem where k = 1. There exists an algorithm to solve this problem for k = 1 requiring time O (m n log ⁡ n / log ⁡ log ⁡ n) using space O (n). Here we present two new algorithms that require worst-case time O (m n) and O (n log ⁡ n log ⁡ log ⁡ n) , respectively, and space O (n) , thus greatly improving the previous result. Moreover, we present another algorithm that requires average-case time and space O (n) for integer alphabets of size σ if m = Ω (log σ ⁡ n). Notably, we show that this algorithm is generalizable for arbitrary k , requiring average-case time O (k n) and space O (n) if m = Ω (k log σ ⁡ n) , assuming that the letters are independent and uniformly distributed random variables. Finally, we provide an experimental evaluation of our average-case algorithm demonstrating its competitiveness to the state-of-the-art implementation. [ABSTRACT FROM AUTHOR]

We study the problem of similarity self-join and similarity join size estimation in a streaming setting where the goal is to estimate, in one scan of the input and with sublinear space in the input size, the number of record pairs that have a similarity within a given threshold. The problem has many applications in data cleaning and query plan generation, where the cost of a similarity join may be estimated before actually doing the join. On unary input where two records either match or don’t match, the problem becomes join and self-join size estimation for which one-pass algorithms are readily available. Our work addresses the problem for $d$ d -ary input, for $d \geq 1$ d ≥ 1 , where the degree of similarity can vary from 1 to $d$ d . We show that our proposed algorithm gives an accurate estimate and scales well with the input size. We provide error bounds and time and space costs, and conduct an extensive experimental evaluation of our algorithm, comparing its estimation accuracy to a few competitors, including some multi-pass algorithms. Our results show that given the same space, the proposed algorithm has an order of magnitude less error for a large range of similarity thresholds. [ABSTRACT FROM AUTHOR]

A border p of a string x is an enhanced cover of x if the number of positions of x that lie within some occurrence of p is the maximum among all borders of x. (String p is a border of x if p is both a proper prefix and a suffix of x.) In this paper, two more general notions based on enhanced covers are introduced: a k -approximate enhanced cover and a relaxed k -approximate enhanced cover, where a fixed maximum number of errors k under the Hamming distance is considered. The k -approximate enhanced cover of x is its border, and its k -approximate occurrences are also considered in the covered number of positions of x. The relaxed k -approximate enhanced cover of x is a factor of x and a k -approximate border of x. Algorithms that compute all the variations of k -approximate enhanced covers mentioned above are presented in this paper. [ABSTRACT FROM AUTHOR]

Given a set of n strings of length L and a radius d , the closest string problem (CSP for short) asks for a string t s o l that is within a Hamming distance of d to each of the given strings. It is known that the problem is NP-hard and its optimization version admits a polynomial time approximation scheme (PTAS). A number of parameterized algorithms have been then developed to solve the problem when d is small. Among them, the relatively new ones have not been implemented before and their performance in practice was unknown. In this study, we implement all of them by careful engineering. For those that have been implemented before, our implementation is much faster. For some of those that have not been implemented before, our experimental results show that there exist huge gaps between their theoretical and practical performances. We also design a new parameterized algorithm for the binary case of CSP. The algorithm is deterministic and runs in O (n 2 L + n 2 d ⋅ 6.16 d) time, while the previously best deterministic algorithm runs in O (n L + n d 3 ⋅ 6.731 d) time. [ABSTRACT FROM AUTHOR]

Given n vectors x 0 , x 1 , ... , x n − 1 in { 0 , 1 } m , how to find two vectors whose pairwise Hamming distance is minimum? This problem is known as the Closest Pair Problem. If these vectors are generated uniformly at random except two of them are correlated with Pearson-correlation coefficient ρ , then the problem is called the Light Bulb Problem. In this work, we propose a novel coding-based scheme for the Closest Pair Problem. We design both randomized and deterministic algorithms, which achieve the best-known running time when the length of input vectors m is small and the minimum distance is very small compared to m. Specifically, the running time of our randomized algorithm is O (n log 2 ⁡ n ⋅ 2 c m ⋅ poly (m)) and the running time of our deterministic algorithm is O (n log ⁡ n ⋅ 2 c ′ m ⋅ poly (m)) , where c and c ′ are constants depending only on the (relative) distance of the closest pair. When applied to the Light Bulb Problem, our result yields state-of-the-art deterministic running time when the Pearson-correlation coefficient ρ is very large. Specifically, when ρ ≥ 0.9933 , our deterministic algorithm runs faster than the previously best deterministic algorithm (Alman, SOSA 2019). [ABSTRACT FROM AUTHOR]

Because of their high recognition rates, coding-based approaches that use multispectral palmprint images have become one of the most popular palmprint recognition methods. This paper describes a new multispectral palmprint recognition method that aims to further improve the performance of coding-based approaches by focusing on the local binary pattern (LBP) filters and spiral moments features. The final feature map is derived through a staged process of creating a composite of spiral and LBP features by fusing them together and passing the features through the minimum redundancy maximum relevance transformers. Using Hamming distances, the inter- and intra-similarities of the palmprint feature maps are determined. The experimental technique was evaluated using the available data on the IITD, MSPolyU and PolyU PPDB databases. The results indicate that the method achieved high levels of accuracy in the identification and verification modes. Furthermore, this method outperforms the existing advanced techniques. [ABSTRACT FROM AUTHOR]

Given a binary word relation τ onto A ⁎ and a finite language X ⊆ A ⁎ , a τ -Gray cycle over X consists in a permutation (w [ i ]) 0 ≤ i ≤ | X | − 1 of X such that each word w [ i ] is an image under τ of the previous word w [ i − 1 ]. We define the complexity measure λ A , τ (n) , equal to the largest cardinality of a language X having words of length at most n , and st. some τ -Gray cycle over X exists. The present paper is concerned with τ = σ k , the so-called k -character substitution, st. (u , v) ∈ σ k holds if, and only if, the Hamming distance of u and v is k. We present loopless (resp., constant amortized time) algorithms for computing specific maximum length σ k -Gray cycles. [ABSTRACT FROM AUTHOR]

In fact, compression and computation are two sides of the same coin, as they exploit the same underlying structure both for storing and operating on data. The study in [[4]] establishes new upper bounds and a conditional lower bound on the indexed regular expression matching problem and [[5]] improves existing analyses on the approximation ratios for common grammar-based compressors. As the production of massive data has outpaced Moore's law in many scientific areas, the very notion of algorithms is transforming. [Extracted from the article]

Mutually uncorrelated (MU) codes are a class of codes in which no proper prefix of one codeword is a suffix of another codeword. These codes were originally studied for synchronization purposes and recently, Yazdi et al. showed their applicability to enable random access in DNA storage. In this paper,we follow the research of Yazdi et al. and study MU codes along with their extensions to correct errors and balanced codes. We first review a well-known construction of MU codes and study the asymptotic behavior of its cardinality. This task is accomplished by studying a special class of run-length limited codes that impose the longest run of zeros to be at most some function of the codewords length. We also present an efficient algorithm for this class of constrained codes and show how to use this analysis for MU codes. Next, we extend the results on the run-length limited codes in order to study $(d_{h},d_{m})$ -MU codes that impose a minimum Hamming distance of $d_{h}$ between different codewords and $d_{m}$ between prefixes and suffixes. In particular, we show an efficient construction of these codes with nearly optimal redundancy. We also provide similar results for the edit distance and balanced MU codes. Last, we draw connections to the problems of comma-free and prefix synchronized codes. [ABSTRACT FROM AUTHOR]