Search Results (182)

We develop algorithms for computing permutation polynomials (PPs) using normalization, so-called F-maps and G-maps, and the Hermite criterion. This allows for a more efficient computation of PPs for larger degrees and for larger finite fields. We use this to improve some lower bounds for $M(n,D)$, the maximum number of permutations on n symbols with a pairwise Hamming distance of D. Full article

This paper expands the Mallows model for use in combinatorial domains. The Mallows model is a popular distribution used to sample permutations around a central tendency but requires a unique normalizing constant for each distance metric used in order to be computationally efficient. In this paper, closed-form expressions for the Mallows model normalizing constant are derived for the Hamming distance, symmetric difference, and the similarity coefficient in combinatorial domains. Additionally, closed-form expressions are derived for the normalizing constant of the weighted Mallows model in combinatorial domains. The weighted Mallows model increases the versatility of the Mallows model by allowing granular control over likelihoods of individual components in the domain. The derivation of the closed-form expression results in a reduction of the order of calculations required to calculate probabilities from exponential to constant. Full article

Edge computing offers low-latency and distributed processing for IoT applications but poses new security challenges, due to limited resources and decentralized data. Intrusion detection systems (IDSs) are essential for real-time threat monitoring, yet traditional IDS frameworks often struggle in edge environments, failing to meet efficiency requirements. This paper presents an efficient intrusion detection framework that integrates spatiotemporal hashing, federated learning, and fast K-nearest neighbor (KNN) retrieval. A hashing neural network encodes network traffic into compact binary codes, enabling low-overhead similarity comparison via Hamming distance. To support scalable retrieval, multi-index hashing is applied for sublinear KNN searching. Additionally, we propose an attention-guided federated aggregation strategy that dynamically adjusts client contributions, reducing communication costs. Our experiments on benchmark datasets demonstrate that our method achieves competitive detection accuracy with significantly lower computational, memory, and communication overhead, making it well-suited for edge-based deployment. Full article

Cancer is one of the most lethal diseases in the modern world. Early diagnosis significantly contributes to prolonging the life expectancy of patients. The application of intelligent systems and AI methods is crucial for diagnosing oncological diseases. Primarily, expert systems or decision support systems are utilized in such cases. This research explores early lung cancer diagnosis through protocol-based questioning, considering the impact of nuclear testing factors. Nuclear tests conducted historically continue to affect citizens’ health. A classification of regions into five groups was proposed based on their proximity to nuclear test sites. The weighting coefficient was assigned accordingly, in proportion to the distance from the test zones. In this study, existing expert systems were analyzed and classified. Approaches used to build diagnostic expert systems for oncological diseases were grouped by how well they apply to different tumor localizations. An online questionnaire based on the lung cancer diagnostic protocol was created to gather input data for the neural network. To support this diagnostic method, a functional block diagram of the intelligent system “Oncology” was developed. The following methods were used to create the mathematical model: gradient boosting, multilayer perceptron, and Hamming network. Finally, a web application architecture for early lung cancer detection was proposed. Full article

This paper addresses the challenges of testing computing systems and their hardware components, especially memory devices. It highlights the limitations of traditional random testing. Such methods often fail to use available information about the system under test and previously generated test patterns. The potential of controlled random testing, which incorporates knowledge of prior patterns, is therefore explored. A class of controlled random tests with a limited number of test patterns is identified and analyzed, including existing standard approaches. The paper introduces a novel measure of dissimilarity between test patterns. This measure is based on calculating Hamming distances for binary patterns after mapping them into different numeral systems, including quaternary, octal, and hexadecimal. We propose a method for generating controlled random tests with a guaranteed minimum Hamming distance. It is based on representing binary patterns as symbols from non-binary numeral systems. In this way, ensuring a specific Hamming distance in the symbolic domain also guarantees at least the same distance in the binary representation. We evaluate the effectiveness of the proposed method through simulations, particularly in the context of memory testing and the detection of multicell faults, i.e., errors caused by interactions between multiple memory cells. This approach can enhance the efficiency and reliability of test procedures in embedded systems, memory diagnostics, and safety-critical applications. Full article

A physical unclonable function (PUF) leverages the unclonable random variations in device behavior due to defects incurred during manufacturing to produce a unique “biometric” that can be used for authentication. Here, we show that the threshold current for the switching of a magnetic tunnel junction via spin transfer torque is sensitive to the nature of structural defects introduced during manufacturing and hence can be the basis of a PUF. We use micromagnetic simulations to study the threshold currents for six different defect morphologies at two different temperatures to establish the viability of a PUF. We also derive the challenge–response set at the two different temperatures to calculate the inter- and intra-Hamming distances for a given challenge. Full article

We consider mixed Hamming packings, addressing the maximal cardinality of codes with a minimum codeword Hamming distance. We do not rely on any algebraic structure of the alphabets. We extend known-integer linear programming models of the problem to be efficiently tractable using standard ILP solvers. This is achieved by adopting the concept of contact graphs from classical continuous sphere packing problems to the present discrete context, resulting in a reduction technique for the models which enables their efficient solution as well as their decomposition to smaller subproblems. Based on our calculations, we provide a systematic summary of all lower and upper bounds for packings in the smallest Hamming spaces. The known results are reproduced, with some bounds found to be sharp, and the upper bounds improved in some cases. Full article

This paper applies hierarchical clustering and Hamming Distance to analyze the temporal trends of infectious diseases across different regions of Uzbekistan. By leveraging hierarchical clustering, we effectively group regions based on disease similarity without requiring predefined cluster numbers. Hamming Distance further quantifies disease trajectory similarities, helping assess epidemiological patterns over time. Binary tree visualizations enhance the interpretability of clustering results, offering a novel method for identifying regional trends. The dataset includes yearly incidence rates of seven infectious diseases from 2012 to 2019, along with population, healthcare infrastructure, and geographic attributes for each region. This approach provides an interpretable framework for public health analysis and decision-making. Full article

Frequency-hopping multiple access is widely adopted to blunt narrow-band jamming and limit spectral disclosure in cyber–physical systems, yet its practical resilience depends on three sequence-level properties. First, balancedness guarantees that every carrier is occupied equally often, removing spectral peaks that a jammer or energy detector could exploit. Second, a wide gap between successive hops forces any interferer to re-tune after corrupting at most one symbol, thereby containing error bursts. Third, a no-hit zone (NHZ) window with a zero pairwise Hamming correlation eliminates user collisions and self-interference when chip-level timing offsets fall inside the window. This work introduces an algebraic construction that meets the full set of requirements in a single framework. By threading a permutation over an integer ring and partitioning the period into congruent sub-blocks tied to the desired NHZ width, we generate balanced wide gap no-hit zone frequency-hopping (WG-NHZ FH) sequence sets. Analytical proofs show that (i) each sequence achieves the Lempel–Greenberger bound for auto-correlation, (ii) the family and zone sizes satisfy the Ye–Fan bound with equality, (iii) the hop-to-hop distance satisfies a provable WG condition, and (iv) balancedness holds exactly for every carrier frequency. Full article

Let $\Sigma$ be a nonempty set of characters, called an alphabet. The run-length encoding $\left(\mathrm{RLE}\right)$ algorithm processes any nonempty string u over $\Sigma$ and produces two outputs: a k-tuple $(b_1,b_2,\dots ,b_k)$, where each $b_i$ is a character and $b_{i+1}\ne b_i$; and a corresponding k-tuple $(q_1,q_2,\dots ,q_k)$ of positive integers, so that the original string can be reconstructed as $u=b_1^{q_1}{b}_2^{q_2}\dots b_k^{q_k}$. The integer k is termed the run-length of u, and symbolized by $\rho \left(u\right)$. By convention, we let $\rho \left(\epsilon \right)=0$. In the Euclidean space $({\mathbb{R}}^n,\parallel ·{\parallel }_2)$, the volume of a sphere is determined solely by the dimension n and the radius, following well-established formulas. However, for spheres of strings under the edit metric, the situation is more complex, and no general formulas have been identified. This work intended to show that the volume of the sphere ${\mathbf{S}}_L(u,1)$, composed of all strings of Levenshtein distance 1 from u, is dependent on the specific structure of the “$\mathrm{RLE}$-decomposition” of u. Notably, this volume equals $(2\mathcal{l}\left(u\right)+1)s-\left(2\mathcal{l}\left(u\right)-\rho \left(u\right)\right)$, where $\rho \left(u\right)$ represents the run-length of u and $\mathcal{l}\left(u\right)$ denotes its length (i.e., the number of characters in u). Given an integer $p\ge 2$, we present a partial result concerning the computation of the volume $\left|{\mathbf{S}}_L(u,p)\right|$ in the specific case where the run-length $\rho \left(u\right)=1$. More precisely, for a fixed integer $n\ge 1$ and a character $a\in \Sigma$, we explicitly compute the volume of the Levenshtein sphere of radius p, centered at the string $u=a^n$. This case corresponds to the simplest run structure and serves as a foundational step toward understanding the general behavior of Levenshtein spheres. Full article

One of the most challenging problems in data analysis is visualizing patterns and extracting insights from multi-dimensional datasets that vary over time. The complexity of data and variations in the correlations between different features adds further difficulty to the analysis. In this paper, we provide a framework to analyze the temporal dynamics of such datasets. We use machine learning clustering techniques and examine the time evolution of data patterns by constructing the corresponding cluster trajectories. These trajectories allow us to visualize the patterns and the changing nature of correlations over time. The similarity and correlations of features are reflected in common cluster membership, whereas the historical dynamics are described by a trajectory in the corresponding (cluster, time) space. This allows an effective visualization of multi-dimensional data over time. We introduce several statistical metrics to measure duration, volatility, and inertia of changes in patterns. Using the Hamming distance of trajectories over multiple time periods, we propose a novel metric, the Hamming diversification index, to measure the spread between trajectories. The novel metric is easy to compute, has a simple machine learning implementation, and provides additional insights into the temporal dynamics of data. This parsimonious diversification index can be used to examine changes in pattern similarities over aggregated time periods. We demonstrate the efficacy of our approach by analyzing a complex multi-year dataset of multiple worldwide economic indicators. Full article

With the rise of the Internet of Things (IoT), smart sensors are increasingly being deployed as compact edge processing units, necessitating continuously writable memory with low power consumption and fast access times. Magnetic random-access memory (MRAM) has emerged as a promising non-volatile alternative to conventional DRAM and SDRAM, offering advantages such as faster access speeds, reduced power consumption, and enhanced endurance. However, MRAM is subject to challenges including process variations and thermal fluctuations, which can induce random bit errors and result in imbalanced probabilities of 0 and 1 bits. To address these issues, we propose a novel sparse coding scheme characterized by a minimum Hamming distance of three. During the encoding process, three check bits are appended to the user data and processed using a generator matrix. If the resulting codeword fails to satisfy the sparsity constraint, it is inverted to comply with the coding requirement. This method is based on the error characteristics inherent in MRAM to facilitate effective error correction. Furthermore, we introduce a dynamic threshold detection technique that updates bit probability estimates in real time during data transmission. Simulation results demonstrate substantial improvements in both error resilience and decoding accuracy, particularly as MRAM density increases. Full article

During the launching process of electromagnetic projectiles, radiated noise, smoke, and debris will interfere with the line of sight and affect the accuracy of initial attitude estimation. To address this issue, an enhanced method that integrates Mask R-CNN and a multi-constraint genetic algorithm was proposed. First, Mask R-CNN was utilized to perform pixel-level edge segmentation of the original image, followed by the Canny algorithm to extract the edge image. This edge image was then processed using the line segment detector (LSD) algorithm to identify the main structural components, characterized by line segments. An enhanced genetic algorithm was employed to restore the occluded edge image. A fitness function, constructed with Hamming distance (HD) constraints alongside initial parameter constraints defined by centroid displacement, was applied to boost convergence speed and avoid local optimization. The optimized search strategy minimized the HD constraint between the repaired stereo images to obtain accurate attitude output. An electromagnetic simulation device was utilized for the experiment. The proposed method was 13 times faster than the Structural Similarity Index (SSIM) method. In a single launch, the target with 70% occlusion was successfully recovered, achieving average deviations of 0.76°, 0.72°, and 0.44° in pitch, roll, and yaw angles, respectively. Full article

An artificial neural network (ANN)-based decision support system model, which aggregates intuitionistic fuzzy matrix data using a recently introduced operator, is developed in this work. Several desirable features related to distance measures of aggregation operators and artificial neural networks, including the backpropagation method, are investigated to support the application of the proposed methodologies to multiple attribute group decision-making (MAGDM) problems using intuitionistic fuzzy information. A novel and enhanced aggregation operator—the Hamming–Intuitionistic Fuzzy Power Generalized Weighted Averaging (H-IFPGWA) operator—is proposed for weight determination in MAGDM situations. Numerical examples are provided, and various ranking techniques are used to demonstrate the effectiveness of the suggested strategy. Subsequently, an identical numerical example is solved without bias using the ANN backpropagation approach. Additionally, a novel algorithm is created to address MAGDM problems using the proposed backpropagation model in an unbiased manner. Several defuzzification operators are applied to solve the numerical problems, and the efficacy of the solutions is compared. For MAGDM situations, the novel approach works better than the previous ANN approaches. Full article

This research investigates the integration of quantum hardware-assisted security into critical applications, including the Industrial Internet-of-Things (IIoT), Smart Grid, and Smart Transportation. The Quantum Physical Unclonable Functions (QPUF) architecture has emerged as a robust security paradigm, harnessing the inherent randomness of quantum hardware to generate unique and tamper-resistant cryptographic fingerprints. This work explores the potential of Quantum Computing for Security-by-Design (SbD) in the Industrial Internet-of-Things (IIoT), aiming to establish security as a fundamental and inherent feature. SbD in Quantum Computing focuses on ensuring the security and privacy of Quantum computing applications by leveraging the fundamental principles of quantum mechanics, which underpin the quantum computing infrastructure. This research presents a scalable and sustainable security framework for the trusted attestation of smart industrial entities in Quantum Industrial Internet-of-Things (QIoT) applications within Industry 4.0. Central to this approach is the QPUF, which leverages quantum mechanical principles to generate unique, tamper-resistant fingerprints. The proposed QPUF circuit logic has been deployed on IBM quantum systems and simulators for validation. The experimental results demonstrate the enhanced randomness and an intra-hamming distance of approximately 50% on the IBM quantum hardware, along with improved reliability despite varying error rates, coherence, and decoherence times. Furthermore, the circuit achieved 100% reliability on Google’s Cirq simulator and 95% reliability on IBM’s quantum simulator, highlighting the QPUF’s potential in advancing quantum-centric security solutions. Full article