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In this paper, a stability analysis and the controller improvement of T-S fuzzy Descriptor system are studied. Firstly, by making full use of the related theory of fuzzy affiliation function and combining the design method of fuzzy Lyapunov function with the method of inequality deflation, a stability condition with wider admissibility and less system conservatism is proposed. The advantage of this method is that it is not necessary to ensure that each fuzzy subsystem is progressively stable. We also maximise the boundary of the derivatives of the affiliation function mined. Secondly, a PDC controller and a Non-PDC controller are designed, and the deflation conditions for the linear matrix inequalities of the two controllers are constructed. Finally, some arithmetic simulations and practical examples are given to demonstrate the effectiveness of the method studied in this paper, and the results obtained are less conservative and have larger feasible domains than previous methods. [ABSTRACT FROM AUTHOR]

The performance of underwater target detection algorithms is affected by poor imaging quality in underwater environments. Due to the arithmetic power limitation of underwater devices, existing deep learning networks are unable to provide efficient detection processes with high detection accuracy. Lightweight CNN models have been actively applied for underwater environment detection, yet their lite feature fusion networks cannot provide effective fusion effects and reduce the detection accuracy. In this paper, a lightweight algorithm based on multi-scale feature fusion was proposed, with the model parameters greatly reduced, improving the target detection accuracy. The forward propagation memory overhead is reduced by using multi-scale shared convolutional kernels and pooling operations to co-construct the query matrix in the Tansformer encoding stage. Then, the feature fusion path is optimized in order to enhance the connection of multi-scale features. A multiscale feature adaptive fusion strategy is used to enhance the detection performance and reduce the dependence on the complex feature extraction network. The feature extraction network is also reparameterized to simplify the operation. Using the UPRC offshore dataset for validation, the study results have demonstrated that the statistical mAP metrics validate the detection accuracy. Compared with SSD, RetinaNet and YOLOv5-s improved by 13%, 8.6%, and 0.8%, while the number of parameters decreased by 76.09%, 89.74%, and 87.67%. In addition, compared with the YOLOv5-lite model algorithm with the same parameter volume, the mAP is improved by 3.8%, which verifies the accuracy and efficiency of the algorithm in this paper. [ABSTRACT FROM AUTHOR]

The purpose of this article is to present three related studies that build on each other to demonstrate first the need and then the efficacy of the Blended Arithmetic Curriculum (BAC) to help students overcome both slow language processing and the environmental effects of being a student in an urban school district. The author's underlying theory is that K–3 students with slow language processing may be good at complex reasoning, but still struggle with retrieving basic computational facts. Nonetheless, if they did not learn their facts, these students would struggle with K–3 multi-digit arithmetic computation, and ultimately struggle with their hypothesized strength: seeing numeric patterns as would be needed in university level computation. To teach arithmetic facts conceptually, the author developed a paper and pencil curriculum that first teaches complex multi-digit addition with regrouping using a limited number of facts such as 5 + 5, 9 + 1, 1 + 9; 7 + 7, 7 + 8, 8 + 7, and 8 + 8 in problems such as 197 + 108 = 305 so that fact retrieval and computation are fast and accurate. At the end of 2nd grade, urban students with learning disabilities solved 42 two-digit by two-digit problems with 92 percent accuracy in an average of 7 min. The results matched those of suburban students and were significantly faster and more accurate than general education students in the same urban school. [ABSTRACT FROM AUTHOR]

To model fuzzy numbers with the confidence degree and better account for information uncertainty, Zadeh came up with the notion of Z-numbers, which can effectively combine the objective information of things with subjective human interpretation of perceptive information, thereby improving the human comprehension of natural language. Although many numbers are in fact Z-numbers, their higher computational complexity often prevents their recognition as such. In order to reduce computational complexity, this paper reviews the development and research direction of Z-numbers and deduces the operational rules for symmetric triangular Z-numbers. We first transform them into classical fuzzy numbers. Using linear programming, the extension principle of Zadeh, the convolution formula, and fuzzy number algorithms, we determine the operational rules for the basic operations of symmetric triangular Z-numbers, which are number-multiplication, addition, subtraction, multiplication, power, and division. Our operational rules reduce the complexity of calculation, improve computational efficiency, and effectively reduce the information difference while being applicable to other complex operations. This paper innovatively combines Z-numbers with classical fuzzy numbers in Z-number operations, and as such represents a continuation and innovation of the research on the operational laws of Z-numbers. [ABSTRACT FROM AUTHOR]

The rational field Q is highly desired in many applications. Algorithms using the rational number field Q algebraic number fields use only integer arithmetics and are easy to implement. Therefore, studying and designing systems and expansions with coefficients in Q or algebraic number fields is particularly interesting. This paper discusses constructing quasi-tight framelets with symmetry over an algebraic field. Compared to tight framelets, quasi-tight framelets have very similar structures but much more flexibility in construction. Several recent papers have explored the structure of quasi-tight framelets. The construction of symmetric quasi-tight framelets directly applies the generalized spectral factorization of 2 × 2 matrices of Laurent polynomials with specific symmetry structures. We adequately formulate the latter problem and establish the necessary and sufficient conditions for such a factorization over a general subfield F of C , including algebraic number fields as particular cases. Our proofs of the main results are constructive and thus serve as a guideline for construction. We provide several examples to demonstrate our main results. [ABSTRACT FROM AUTHOR]

With the rapid proliferation of the Internet of Things (IoT) in recent years, the number of IoT devices has surged exponentially. These devices collect and transmit vast amounts of data, including sensitive information. Encrypting data is a crucial means to prevent unauthorized access and potential misuse. However, the traditional cryptographic schemes offering robust security demand substantial device resources and are unsuitable for lightweight deployments, particularly in resource-constrained IoT devices. On the other hand, with the automotive industry making strides in autonomous driving, self-driving vehicles are beginning to integrate into people's daily lives. Ensuring the security of autonomous driving systems, particularly in preventing hacker infiltrations, is a paramount challenge currently facing the industry. An emerging lightweight sequence cipher—aiming to strike a balance between security and resource efficiency—has been proposed in this paper based on S-box substitution and arithmetic addition. The designed security threshold is 280. It has been verified that with a slight performance disadvantage, it can reduce memory usage while ensuring the security threshold. The key stream generated by this structure exhibits excellent pseudo-randomness. [ABSTRACT FROM AUTHOR]

The Tree-Seed Algorithm (TSA) has been effective in addressing a multitude of optimization issues. However, it has faced challenges with early convergence and difficulties in managing high-dimensional, intricate optimization problems. To tackle these shortcomings, this paper introduces a TSA variant (DTSA). DTSA incorporates a suite of methodological enhancements that significantly bolster TSA's capabilities. It introduces the PSO-inspired seed generation mechanism, which draws inspiration from Particle Swarm Optimization (PSO) to integrate velocity vectors, thereby enhancing the algorithm's ability to explore and exploit solution spaces. Moreover, DTSA's adaptive velocity adaptation mechanism based on count parameters employs a counter to dynamically adjust these velocity vectors, effectively curbing the risk of premature convergence and strategically reversing vectors to evade local optima. DTSA also integrates the trees population integrated evolutionary strategy, which leverages arithmetic crossover and natural selection to bolster population diversity, accelerate convergence, and improve solution accuracy. Through experimental validation on the IEEE CEC 2014 benchmark functions, DTSA has demonstrated its enhanced performance, outperforming recent TSA variants like STSA, EST-TSA, fb-TSA, and MTSA, as well as established benchmark algorithms such as GWO, PSO, BOA, GA, and RSA. In addition, the study analyzed the best value, mean, and standard deviation to demonstrate the algorithm's efficiency and stability in handling complex optimization issues, and DTSA's robustness and efficiency are proven through its successful application in five complex, constrained engineering scenarios, demonstrating its superiority over the traditional TSA by dynamically optimizing solutions and overcoming inherent limitations. [ABSTRACT FROM AUTHOR]

Deep neural network (DNN) inference demands substantial computing power, resulting in significant energy consumption. A large number of negative output activations in convolution layers are rendered zero due to the invocation of the ReLU activation function. This results in a substantial number of unnecessary computations that consume significant amounts of energy. This paper presents ECHO, an accelerator for DNN inference designed for computation pruning, utilizing an unconventional arithmetic paradigm known as online/most significant digit first (MSDF) arithmetic, which performs computations in a digit-serial manner. The MSDF digit-serial computation of online arithmetic enables overlapped computation of successive operations, leading to substantial performance improvements. The online arithmetic, coupled with a negative output detection scheme, facilitates early and precise recognition of negative outputs. This, in turn, allows for the timely termination of unnecessary computations, resulting in a reduction in energy consumption. The implemented design has been realized on the Xilinx Virtex-7 VU3P FPGA and subjected to a comprehensive evaluation through a rigorous comparative analysis involving widely used performance metrics. The experimental results demonstrate promising power and performance improvements compared to contemporary methods. In particular, the proposed design achieved average improvements in power consumption of up to 81 % , 82.9 % , and 40.6 % for VGG-16, ResNet-18, and ResNet-50 workloads compared to the conventional bit-serial design, respectively. Furthermore, significant average speedups of 2.39 × , 2.6 × , and 2.42 × were observed when comparing the proposed design to conventional bit-serial designs for the VGG-16, ResNet-18, and ResNet-50 models, respectively. [ABSTRACT FROM AUTHOR]

In the present paper, we address the following general question in the framework of classical first-order logic. Assume that a certain mathematical principle can be formalized in a first-order language by a set E of conditional formulas of the form α (v) → β (v) . Given a base theory T, we can use the set of conditional formulas E to extend the base theory in two natural ways. Either we add to T each formula in E as a new axiom (thus obtaining a theory denoted by T + E ) or we extend T by using the formulas in E as instances of an inference rule (thus obtaining a theory denoted by T + E – Rule ). The theory T + E will be stronger than T + E – Rule , but how much stronger can T + E be? More specifically, is T + E conservative over T + E – Rule for theorems of some fixed syntactical complexity Γ ? Under very general assumptions on the set of conditional formulas E, we obtain two main conservation results in this regard. Firstly, if the formulas in E have low syntactical complexity with respect to some prescribed class of formulas Π and in the applications of E – Rule side formulas from the class Π and can be eliminated (in a certain precise sense), then T + E is ∀ B (Π) -conservative over T + E – Rule . Secondly, if, in addition, E is a finite set with m conditional sentences, then nested applications of E – Rule of a depth at most of m suffice to obtain ∀ B (Π) conservativity. These conservation results between axioms and inference rules extend well-known conservation theorems for fragments of first-order arithmetics to a general, purely logical framework. [ABSTRACT FROM AUTHOR]

In order to improve the efficiency of the "last-mile" distribution in urban logistics and solve the problem of the difficult charging of electric logistics vehicles (ELVs), this paper proposes a charging station location optimization scheme for ELVs that takes into account time-window and load constraints (TW-LCs). Taking the optimal transportation path as the objective function and considering the time-window and vehicle load constraints, a charging station siting model was established. For the TW-LC problem, an improved genetic algorithm combining the farthest-insertion heuristic idea and local search operation was designed. Three different types of standardized arithmetic examples, C type, R type, and RC type, were used to test the proposed algorithm and compare it with the traditional genetic algorithm. The results indicate that, under the same conditions, compared to the traditional genetic algorithm, the improved genetic algorithm reduced the optimal path length by an average of 11.12%. It also decreased the number of charging stations selected, the number of vehicles in use, and the algorithm complexity by 22.97%, 13.71%, and 46.81%. Building on this, a case study was conducted on the TW-LC problem in a specific area of Chongqing, China. It resulted in a 50% reduction in the number of charging stations and a 25% reduction in the number of vehicles selected. In terms of economic indicators, the proposed algorithm improves unit electricity sales by 73.88% and reduces the total annualized cost of the logistics company by 18.81%, providing a theoretical basis for the subsequent promotion of ELVs. [ABSTRACT FROM AUTHOR]

As a novel biological computing device, the Spiking Neural P system (SNPS) has powerful computing potential. The application of SNPS in the field of arithmetic operation has been a hot research topic in recent years. Researchers have proposed methods and systems for implementing basic arithmetic operations using SNPS. This paper studies four basic arithmetic operations, improves the parallelization of addition and multiplication methods, and designs more effective natural number addition and multiplication SNPS, as well as SNPS for subtraction and for division of natural numbers based on multiple subtractions. The effectiveness of the proposed SNPS is verified by example. Compared with the same kind of SNPS, for the addition operation the number of neurons used in our system is reduced by 50% and the time overhead is reduced by 33%, while for the multiplication operation the number of neurons is reduced by 40%. [ABSTRACT FROM AUTHOR]

First-grade students often encounter challenges in understanding and solving arithmetic word problems due to their limited reading comprehension abilities. Despite these difficulties, students may employ arbitrary strategies, such as combining numbers based on specific keywords, even if they lack a full understanding of the problems. Research suggests that effective mathematical reasoning involves the use of visual mental representations during the problem-solving process. To address this, some studies have explored methods to enhance students' comprehension of word problems. Building on this, the current study explores the impact of first-grade pupils creating visual representations of problem situations on their comprehension and the number of correct solutions. In a typical math class, 45 first graders received a paper-and-pencil task, and, in a visual context, they solved similar problems after reading and illustrating the situation. The findings reveal that while most participants correctly represented the problem situations through drawing, about half struggled to determine the numeric solutions. Nevertheless, the visual context led to an increase in the number of correct problem solutions compared to the normal context, suggesting the potential benefits of incorporating visual representations in enhancing comprehension and problem-solving skills. [ABSTRACT FROM AUTHOR]

There are some drawbacks to arithmetic and logic operations of general discrete fuzzy numbers, which limit their application. For example, the result of the addition operation of general discrete fuzzy numbers defined by the Zadeh's extension principle may not satisfy the condition of becoming a discrete fuzzy number. In order to solve these problems, special discrete fuzzy numbers on countable sets are investigated in this paper. Since the representation theorem of fuzzy numbers is the basic tool of fuzzy analysis, two kinds of representation theorems of special discrete fuzzy numbers on countable sets are studied first. Then, the metrics of special discrete fuzzy numbers on countable sets are defined, and the relationship between these metrics and the uniform Hausdorff metric (i.e., supremum metric) of general fuzzy numbers is discussed. In addition, the triangular norm and triangular conorm operations (t-norm and t-conorm for short) of special discrete fuzzy numbers on countable sets are presented, and the properties of these two operators are proven. We also prove that these two operators satisfy the basic conditions for closure of operation and present some examples. Finally, the applications of special discrete fuzzy numbers on countable sets in image fusion and aggregation of subjective evaluation are proposed. [ABSTRACT FROM AUTHOR]

In this paper, an optimization approach based on an arithmetic optimization algorithm (AOA) is proposed for specifying the optimal allocation of distribution generations/generators (DGs) and capacitor banks (CBs) in radial distribution systems. The AOA is a new population-based meta-heuristic algorithm that is essentially based on using basic arithmetic operators in mathematics. The proposed approach is employed to specify the optimum placement, capacity, and power factor of DGs and CBs to decrease the distribution systems' total power loss and voltage deviation. To state the performance of the proposed approach, DGs and CBs are placed in IEEE 33-bus and 69-bus systems separately or together. When only DGs are used and the parameters of location, capacity, and power factor of DGs are determined simultaneously, the total active power loss reductions in the IEEE 33-bus and 69-bus systems are achieved at 94.42% and 98.03%, respectively. When the results of other optimization algorithms are examined, it is seen that better results are obtained with AOA. [ABSTRACT FROM AUTHOR]

The D-S evidence theory is extensively applied to manage uncertain information. However, the theory encounters challenges related to conflicts during the fusion process, impeding the precise identification of multi-subset focal elements. This paper introduces a novel method for conflicting evidence fusion that incorporates the Bray–Curtis dissimilarity, cosine distance of the included angle, and belief entropy. The method comprehensively evaluates three aspects—evidence similarity, evidence distance, and the amount of information—while considering factors like the credibility and uncertainty of evidence. Initially, the evidence undergoes conversion into single-subset focal element evidence through the improved Pignistic probability function. Subsequently, the credibility between pieces of evidence is established using the Bray–Curtis dissimilarity and angle cosine distance, while the uncertainty of the evidence is computed using belief entropy. The weighted correction coefficient of the evidence is determined by integrating the credibility and uncertainty of the evidence. Subsequently, the corrected evidence is fused using the D-S evidence theory to derive the final judgment. An analysis of two sets of arithmetic examples, considering both single-subset and multi-subset focal elements, demonstrates the faster convergence and enhanced accuracy and reliability of the proposed method in comparison to existing approaches. [ABSTRACT FROM AUTHOR]

The new arithmetic operations of non-normal fuzzy sets are studied in this paper by using the extension principle and considering the general aggregation function. Usually, the aggregation functions are taken to be the minimum function or t-norms. In this paper, we considered a general aggregation function to set up the arithmetic operations of non-normal fuzzy sets. In applications, the arithmetic operations of fuzzy sets are always transferred to the arithmetic operations of their corresponding α -level sets. When the aggregation function is taken to be the minimum function, this transformation is clearly realized. Since the general aggregation function was adopted in this paper, the concept of compatibility with α -level sets is needed and is proposed, which can cover the conventional case using minimum functions as the special case. [ABSTRACT FROM AUTHOR]

This study aims to construct some new Milne-type integral inequalities for functions whose modulus of the local fractional derivatives is convex on the fractal set. To that end, we develop a novel generalized integral identity involving first-order generalized derivatives. Finally, as applications, some error estimates for the Milne-type quadrature formula and new inequalities for the generalized arithmetic and p-Logarithmic means are derived. This paper's findings represent a significant improvement over previously published results. The paper's ideas and formidable tools may inspire and motivate further research in this worthy and fascinating field. [ABSTRACT FROM AUTHOR]

Stochastic circuits are used in applications that require low area and power consumption. The computing performed using these circuits is referred to as Stochastic computing (SC). The arithmetic operations in this computing can be realized using minimum logic circuits. The SC system allows a tradeoff of computational accuracy and area; thereby, the challenge in SC is improving the accuracy. The accuracy depends on the SC system's stochastic number generator (SNG) part. SNGs provide the appropriate stochastic input required for stochastic computation. Hence we explore the accuracy in SC for various arithmetic operations performed using stochastic computing with the help of logic circuits. The contributions in this paper are; first, we have performed stochastic computing for arithmetic components using two different SNGs. The SNGs considered are Linear Feed-back Shift Register (LFSR) -based traditional stochastic number generators and S-box-based stochastic number generators. Second, the arithmetic components are implemented in a combinational circuit for algebraic expression in the stochastic domain using two different SNGs. Third, computational analysis for stochastic arithmetic components and the stochastic algebraic equation has been conducted. Finally, accuracy analysis and measurement are performed between LFSR-based computation and S-box-based computation. The novel aspect of this work is the use of S-box-based SNG in the development of stochastic computing in arithmetic components. Also, the implementation of stochastic computing in the combinational circuit using the developed basic arithmetic components, and exploration of accuracy with respect to stochastic number generators used is presented. [ABSTRACT FROM AUTHOR]

Previous studies have shown that the application of the M-coder in the H.264/AVC and H.265/HEVC video coding standards allows for highly parallel implementations without decreasing maximal frequencies. Although the primary limitation on throughput, originating from the range register update, can be eliminated, other limitations are associated with low register processing. Their negative impact is revealed at higher degrees of parallelism, leading to a gradual throughput saturation. This paper presents optimizations introduced to the generative hardware architecture to increase throughputs and hardware efficiencies. Firstly, it can process more than one bypass-mode subseries in one clock cycle. Secondly, aggregated contributions to the codestream are buffered before the low register update. Thirdly, the number of contributions used to update the low register in one clock cycle is decreased to save resources. Fourthly, the maximal one-clock-cycle renormalization shift of the low register is increased from 32 to 64 bit positions. As a result of these optimizations, the binary arithmetic coder, configured for series lengths of 27 and 2 symbols, increases the throughput from 18.37 to 37.42 symbols per clock cycle for high-quality H.265/HEVC compression. The logic consumption increases from 205.6k to 246.1k gates when synthesized on 90 nm TSMC technology. The design can operate at 570 MHz. [ABSTRACT FROM AUTHOR]

Modern processors have improved performance but still face challenges such as power consumption, storage limitations, and the need for faster processing. The 16-bit Digital Signal Processors (DSPs) accelerate DSP applications by significantly enhancing speed and performance for tasks including audio processing, telecommunications, image and video processing, wireless communication, and consumer electronics. This paper presents a novel technique for accelerating DSP applications on a 16-bit processor by combining two methods: Block Random Access Memory (BRAM) and Distributed Arithmetic (DA). Integrating BRAM as a replacement for conventional RAM minimizes timing and critical route delays, improving processor efficiency and performance. Furthermore, the Distributed Arithmetic approach enhances performance and efficiency by utilizing precomputed lookup tables to expedite multiplication operations within the Arithmetic and Logic Unit (ALU). We use the Xilinx Vivado tool, a robust development environment for FPGA-based systems, for the design process and execute the hardware implementation using the Genesys2 Kintex board. The proposed work produces improved efficiency with a cycle per instruction of 2, where the delay is 2.009 ns, the critical path delay is 8.182 ns, and the power consumption is 4 mW. [ABSTRACT FROM AUTHOR]

In this paper, we study ⊕-sb-metric spaces, which were introduced to generalize the concept of strong b-metric spaces. In particular, we study the properties of the topology induced via an ⊕-sb metric (separation properties, countability axioms, etc.), prove the continuity of the ⊕-sb-metric, establish the metrizability of the ⊕-sb-metric spaces of countable weight, discuss the convergence structure of an ⊕-sb-metric space and prove the Baire category type theorem for such spaces. Most of the results obtained here are new already for strong b-metric spaces, i.e., in the case where an arithmetic sum "+" is taken in the role of ⊕. [ABSTRACT FROM AUTHOR]

Approximate adders are some of the fundamental arithmetic operators that are being employed in error-resilient applications, to achieve performance/energy/area gains. This improvement usually comes at the cost of some accuracy and, therefore, requires prior error analysis, to select an approximate adder variant that provides acceptable accuracy. Most of the state-of-the-art error analysis techniques for approximate adders assume input bits and operands to be independent of one another, while some also assume the operands to be uniformly distributed. In this paper, we analyze the impact of these assumptions on the accuracy of error estimation techniques, and we highlight the need to address these assumptions, to achieve better and more realistic quality estimates. Based on our analysis, we propose DAEM, a data- and application-aware error analysis methodology for approximate adders. Unlike existing error analysis models, we neither assume the adder operands to be uniformly distributed nor assume them to be independent. Specifically, we use 2D joint input probability mass functions (PMFs), populated using sample data, in order to incorporate the data and application knowledge in the analysis. These 2D joint input PMFs, along with 2D error maps of approximate adders, are used to estimate the error PMF of an adder network. The error PMF is then utilized to compute different error measures, such as the mean squared error (MSE) and mean error distance (MED). We evaluate the proposed error analysis methodology on audio and video processing applications, and we demonstrate that our methodology provides error estimates having a better correlation with the simulation results, as compared to the state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

In this paper, we establish new generalizations of the Hermite-Hadamard-type inequalities. These inequalities are formulated in terms of modules of certain powers of proper functions. Generalizations for convex functions are also considered. As applications, some new inequalities for the digamma function in terms of the trigamma function and some inequalities involving special means of real numbers are given. The results also include estimates via arithmetic, geometric and logarithmic means. The examples are derived in order to demonstrate that some of our results in this paper are more exact than the existing ones and some improve several known results available in the literature. The constants in the derived inequalities are calculated; some of these constants are sharp. As a visual example, graphs of some technically important functions are included in the text. [ABSTRACT FROM AUTHOR]

Elliptic curve (EC) based cryptographic systems are more trustworthy than the currently used cryptographic approaches since they require less computational work while providing good security. This paper shows how to use an EC to make a good cryptosystem for encrypting digital audio. As a preliminary step, the system uses an EC of a particular type over a binary extension field to distort the digital audio pixel position. It reduces the inter-correlation between pixels in the original audio, making the system resistant to statistical attacks. In creating confusion in the data, an EC over a binary extension field is used to make a different number of substitution boxes (S-boxes). The suggested design employs a unique curve that relies on efficient EC arithmetic operations in the diffusion module. As a result, it generates high-quality pseudo-random numbers (PRNs) and achieves optimal diffusion in encrypted audio files with less processing work. Audio files of various sizes and kinds can all be encrypted using the provided algorithm. Moreover, the results show that this method effectively protects many kinds of audio recordings and is more resistant to statistical and differential attacks. [ABSTRACT FROM AUTHOR]

Data centers are getting more and more attention due the rapid increase of IoT deployments, which may result in the implementation of smaller facilities being closer to the end users as well as larger facilities up in the cloud. In this paper, an arithmetic study has been carried out in order to measure a coefficient related to both the average number of hops among nodes and the average number of links among devices for a range of typical network topologies fit for data centers. Such topologies are either tree-like or graph-like designs, where this coefficient provides a balance between performance and simplicity, resulting in lower values in the coefficient accounting for a better compromise between both factors in redundant architectures. The motivation of this contribution is to craft a coefficient that is easy to calculate by applying simple arithmetic operations. This coefficient can be seen as another tool to compare network topologies in data centers that could act as a tie-breaker so as to select a given design when other parameters offer contradictory results. [ABSTRACT FROM AUTHOR]

Quantum-dot cellular automata (QCA) are a promising nanoscale computing technology that exploits the quantum mechanical tunneling of electrons between quantum dots in a cell and electrostatic interaction between dots in neighboring cells. QCA can achieve higher speed, lower power, and smaller areas than conventional, complementary metal-oxide semiconductor (CMOS) technology. Developing QCA circuits in a logically and physically reversible manner can provide exceptional reductions in energy dissipation. The main challenge is to maintain reversibility down to the physical level. A crucial component of a computer's central processing unit (CPU) is the arithmetic logic unit (ALU), which executes multiple logical and arithmetic functions on the data processed by the CPU. Current QCA ALU designs are either irreversible or logically reversible; however, they lack physical reversibility, a crucial requirement to increase energy efficiency. This paper shows a new multilayer design for a QCA ALU that can carry out 16 different operations and is both logically and physically reversible. The design is based on reversible majority gates, which are the key building blocks. We use QCADesigner-E software to simulate and evaluate energy dissipation. The proposed logically and physically reversible QCA ALU offers an improvement of 88.8% in energy efficiency. Compared to the next most efficient 16-operation QCA ALU, this ALU uses 51% fewer QCA cells and 47% less area. [ABSTRACT FROM AUTHOR]

In this paper, we present new variants of Newton–Raphson-based protocols for the secure computation of the reciprocal and the (reciprocal) square root. The protocols rely on secure fixed-point arithmetic with arbitrary precision parameterized by the total bit length of the fixed-point numbers and the bit length of the fractional part. We perform a rigorous error analysis aiming for tight accuracy claims while minimizing the overall cost of the protocols. Due to the nature of secure fixed-point arithmetic, we perform the analysis in terms of absolute errors. Whenever possible, we allow for stochastic (or probabilistic) rounding as an efficient alternative to deterministic rounding. We also present a new protocol for secure integer division based on our protocol for secure fixed-point reciprocals. The resulting protocol is parameterized by the bit length of the inputs and yields exact results for the integral quotient and remainder. The protocol is very efficient, minimizing the number of secure comparisons. Similarly, we present a new protocol for integer square roots based on our protocol for secure fixed-point square roots. The quadratic convergence of the Newton–Raphson method implies a logarithmic number of iterations as a function of the required precision (independent of the input value). The standard error analysis of the Newton–Raphson method focuses on the termination condition for attaining the required precision, assuming sufficiently precise floating-point arithmetic. We perform an intricate error analysis assuming fixed-point arithmetic of minimal precision throughout and minimizing the number of iterations in the worst case. [ABSTRACT FROM AUTHOR]

The slime mold algorithm (SMA) and the arithmetic optimization algorithm (AOA) are two novel meta-heuristic optimization algorithms. Among them, the slime mold algorithm has a strong global search ability. Still, the oscillation effect in the later iteration stage is weak, making it difficult to find the optimal position in complex functions. The arithmetic optimization algorithm utilizes multiplication and division operators for position updates, which have strong randomness and good convergence ability. For the above, this paper integrates the two algorithms and adds a random central solution strategy, a mutation strategy, and a restart strategy. A hybrid slime mold and arithmetic optimization algorithm with random center learning and restart mutation (RCLSMAOA) is proposed. The improved algorithm retains the position update formula of the slime mold algorithm in the global exploration section. It replaces the convergence stage of the slime mold algorithm with the multiplication and division algorithm in the local exploitation stage. At the same time, the stochastic center learning strategy is adopted to improve the global search efficiency and the diversity of the algorithm population. In addition, the restart strategy and mutation strategy are also used to improve the convergence accuracy of the algorithm and enhance the later optimization ability. In comparison experiments, different kinds of test functions are used to test the specific performance of the improvement algorithm. We determine the final performance of the algorithm by analyzing experimental data and convergence images, using the Wilcoxon rank sum test and Friedman test. The experimental results show that the improvement algorithm, which combines the slime mold algorithm and arithmetic optimization algorithm, is effective. Finally, the specific performance of the improvement algorithm on practical engineering problems was evaluated. [ABSTRACT FROM AUTHOR]

Flying ad hoc networks (FANETs), composed of small unmanned aerial vehicles (UAVs), possess characteristics of flexibility, cost-effectiveness, and rapid deployment, rendering them highly attractive for a wide range of civilian and military applications. FANETs are special mobile ad hoc networks (MANETs), FANETs have the characteristics of faster network topology changes and limited energy. Existing reactive routing protocols are unsuitable for the highly dynamic and limited energy of FANETs. For the lithium battery-powered UAV, flight endurance lasts from half an hour to two hours. The fast-moving UAV not only affects the packet delivery rate, average throughput, and end-to-end delay but also shortens the flight endurance. Therefore, research is urgently needed into a high-performance routing protocol with high energy efficiency. In this paper, we propose a novel routing protocol called AO-AOMDV, which utilizes arithmetic optimization (AO) to enhance the ad hoc on-demand multi-path distance vector (AOMDV) routing protocol. The AO-AOMDV utilizes a fitness function to calculate the fitness value of multiple paths and employs arithmetic optimization for selecting the optimal route for routing selection. Our experiments were conducted using NS3 with three evaluation metrics: the packet delivery ratio, network lifetime, and average end-to-end delay. We compare this algorithm to routing protocols including AOMDV and AODV. The results indicate that the proposed AO-AOMDV attained a higher packet delivery ratio, network lifetime, and lower average end-to-end delay. [ABSTRACT FROM AUTHOR]

This paper proposes a wireless channel equalization method applied to the constant modulus blind equalization system, which addresses the slow convergence and strong randomness in the initialization of equalizer weights in the constant modulus blind equalization algorithm (CMA) by introducing a hybrid arithmetic whale optimization algorithm (HAWOA). The mean square error in the CMA is utilized as the cost function for the HAWOA to obtain a more effective initial weights for the equalizer. To validate the superiority of the hybrid arithmetic whale constant modulus blind equalization algorithm, tests are conducted on the equalization system using 16QAM and 64QAM signals. The simulation results demonstrate that the proposed algorithm achieved better initial weights compared to the CMA and the constant modulus blind equalization algorithm based on the whale optimization algorithm. It can obtain the desired mean square error with a lower symbol error rate in fewer iterations. Furthermore, the hybrid arithmetic whale constant modulus blind equalization algorithm exhibited faster convergence in optimizing initial weights, effectively enhancing the equalization performance of the CMA in wireless channels while ensuring timeliness. [ABSTRACT FROM AUTHOR]

A model of set theory ZFC is defined in our recent research, in which, for a given n ≥ 3 , (A n) there exists a good lightface Δ n 1 well-ordering of the reals, but (B n) no well-orderings of the reals (not necessarily good) exist in the previous class Δ n − 1 1 . Therefore, the conjunction (A n) ∧ (B n) is consistent, modulo the consistency of ZFC itself. In this paper, we significantly clarify and strengthen this result. We prove the consistency of the conjunction (A n) ∧ (B n) for any given n ≥ 3 on the basis of the consistency of PA 2 , second-order Peano arithmetic, which is a much weaker assumption than the consistency of ZFC used in the earlier result. This is a new result that may lead to further progress in studies of the projective hierarchy. [ABSTRACT FROM AUTHOR]

The Arithmetic Optimization Algorithm (AOA) is a meta-heuristic algorithm inspired by mathematical operators, which may stagnate in the face of complex optimization issues. Therefore, the convergence and accuracy are reduced. In this paper, an AOA variant called ASFAOA is proposed by integrating a double-opposite learning mechanism, an adaptive spiral search strategy, an offset distribution estimation strategy, and a modified cosine acceleration function formula into the original AOA, aiming to improve the local exploitation and global exploration capability of the original AOA. In the proposed ASFAOA, a dual-opposite learning strategy is utilized to enhance population diversity by searching the problem space a lot better. The spiral search strategy of the tuna swarm optimization is introduced into the addition and subtraction strategy of AOA to enhance the AOA's ability to jump out of the local optimum. An offset distribution estimation strategy is employed to effectively utilize the dominant population information for guiding the correct individual evolution. In addition, an adaptive cosine acceleration function is proposed to perform a better balance between the exploitation and exploration capabilities of the AOA. To demonstrate the superiority of the proposed ASFAOA, two experiments are conducted using existing state-of-the-art algorithms. First, The CEC 2017 benchmark function was applied with the aim of evaluating the performance of ASFAOA on the test function through mean analysis, convergence analysis, stability analysis, Wilcoxon signed rank test, and Friedman's test. The proposed ASFAOA is then utilized to solve the wireless sensor coverage problem and its performance is illustrated by two sets of coverage problems with different dimensions. The results and discussion show that ASFAOA outperforms the original AOA and other comparison algorithms. Therefore, ASFAOA is considered as a useful technique for practical optimization problems. [ABSTRACT FROM AUTHOR]

Underwater sensor networks play a crucial role in collecting valuable data to monitor offshore aquaculture infrastructures. The number of deployed devices not only impacts the bandwidth for a highly constrained communication environment, but also the cost of the sensor network. On the other hand, industrial and literature current meters work as raw data loggers, and most of the calculations to determine the fundamental frequencies are performed offline on a desktop computer or in the cloud. Belonging to the edge computing research area, this paper presents an algorithm to extract the fundamental frequencies of water currents in an underwater sensor network deployed in offshore aquaculture infrastructures. The target sensor node is based on a commercial ultra-low-power microcontroller. The proposed fundamental frequency identification algorithm only requires the use of an integer arithmetic unit. Our approach exploits the mathematical properties of the finite impulse response (FIR) filtering in the integer domain. The design and implementation of the presented algorithm are discussed in detail in terms of FIR tuning/coefficient selection, memory usage and variable domain for its mathematical formulation aimed at reducing the computational effort required. The approach is validated using a shallow water current model and real-world raw data from an offshore aquaculture infrastructure. The extracted frequencies have a maximum error below a 4%. [ABSTRACT FROM AUTHOR]

Higher accuracy in cluster failure prediction can ensure the long-term stable operation of cluster systems and effectively alleviate energy losses caused by system failures. Previous works have mostly employed BP neural networks (BPNNs) to predict system faults, but this approach suffers from reduced prediction accuracy due to the inappropriate initialization of weights and thresholds. To address these issues, this paper proposes an improved arithmetic optimization algorithm (AOA) to optimize the initial weights and thresholds in BPNNs. Specifically, we first introduced an improved AOA via multi-subpopulation and comprehensive learning strategies, called MCLAOA. This approach employed multi-subpopulations to effectively alleviate the poor global exploration performance caused by a single elite, and the comprehensive learning strategy enhanced the exploitation performance via information exchange among individuals. More importantly, a nonlinear strategy with a tangent function was designed to ensure a smooth balance and transition between exploration and exploitation. Secondly, the proposed MCLAOA was utilized to optimize the initial weights and thresholds of BPNNs in cluster fault prediction, which could enhance the accuracy of fault prediction models. Finally, the experimental results for 23 benchmark functions, CEC2020 benchmark problems, and two engineering examples demonstrated that the proposed MCLAOA outperformed other swarm intelligence algorithms. For the 23 benchmark functions, it improved the optimal solutions in 16 functions compared to the basic AOA. The proposed fault prediction model achieved comparable performance to other swarm-intelligence-based BPNN models. Compared to basic BPNNs and AOA-BPNNs, the MCLAOA-BPNN showed improvements of 2.0538 and 0.8762 in terms of mean absolute percentage error, respectively. [ABSTRACT FROM AUTHOR]

To address the current difficulties and problems of short-term load forecasting (STLF), this paper proposes a combined forecasting method based on the improved sparrow search algorithm (ISSA), with fused Cauchy mutation and opposition-based learning (OBL), to optimize the hyperparameters of the long- and short-term-memory (LSTM) network. For the sparrow-search algorithm (SSA), a Sin-chaotic-initialization population, with an infinite number of mapping folds, is first used to lay the foundation for global search. Secondly, the previous-generation global-optimal solution is introduced in the discoverer-location update way, to improve the adequacy of the global search, while adaptive weights are added to reconcile the ability of the local exploitation and global search of the algorithm as well as to hasten the speed of convergence. Then, fusing the Cauchy mutation arithmetic and the OBL strategy, a perturbation mutation is performed at the optimal solution position to generate a new solution, which, in turn, strengthens the ability of the algorithm to get rid of the local space. After that, the ISSA-LSTM forecasting model is constructed, and the example is verified based on the power load data of a region, while the experimental comparison with various algorithms is conducted, and the results confirm the superiority of the ISSA-LSTM model. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a new method for image-based grammatical inference of deterministic, context-free L-systems (D0L systems) from a single sequence. This approach is characterized by first parsing an input image into a sequence of symbols and then, using a genetic algorithm, attempting to infer a grammar that can generate this sequence. This technique has been tested using our test suite and compared to similar algorithms, showing promising results, including solving the problem for systems with more rules than in existing approaches. The tests show that it performs better than similar heuristic methods and can handle the same cases as arithmetic algorithms. [ABSTRACT FROM AUTHOR]

Several metaheuristic algorithms have been implemented to solve global optimization issues. Nevertheless, these approaches require more enhancement to strike a suitable harmony between exploration and exploitation. Consequently, this paper proposes improving the arithmetic optimization algorithm (AOA) to solve engineering optimization issues based on the cuckoo search algorithm called AOACS. The developed approach uses cuckoo search algorithm operators to improve the ability of the exploitation operations of AOA. AOACS enhances the convergence ratio of the presented technique to find the optimum solution. The performance of the AOACS is examined using 23 benchmark functions and CEC-2019 functions to show the ability of the proposed work to solve different numerical optimization problems. The proposed AOACS is evaluated using four engineering design problems: the welded beam, the three-bar truss, the stepped cantilever beam, and the speed reducer design. Finally, the results of the proposed approach are compared with state-of-the-art approaches to prove the performance of the proposed AOACS approach. The results illustrated an outperformance of AOACS compared to other methods of performance measurement. [ABSTRACT FROM AUTHOR]

The goal was to address the problems of slow convergence speed, low solution accuracy and insufficient performance in solving complex functions in the search process of an arithmetic optimization algorithm (AOA). A multi-strategy improved arithmetic optimization algorithm (SSCAAOA) is suggested in this study. By enhancing the population's initial distribution, optimizing the control parameters, integrating the positive cosine algorithm with improved parameters, and adding inertia weight coefficients and a population history information sharing mechanism to the PSO algorithm, the optimization accuracy and convergence speed of the AOA algorithm are improved. This increases the algorithm's ability to perform a global search and prevents it from hitting a local optimum. Simulations of SSCAAOA using other optimization algorithms are used to examine their efficacy on benchmark test functions and engineering challenges. The analysis of the experimental data reveals that, when compared to other comparative algorithms, the improved algorithm presented in this paper has a convergence speed and accuracy that are tens of orders of magnitude faster for the unimodal function and significantly better for the multimodal function. Practical engineering tests also demonstrate that the revised approach performs better. [ABSTRACT FROM AUTHOR]

The Shor's algorithm can find solutions to the discrete logarithm problem on binary elliptic curves in polynomial time. A major challenge in implementing Shor's algorithm is the overhead of representing and performing arithmetic on binary elliptic curves using quantum circuits. Multiplication of binary fields is one of the critical operations in the context of elliptic curve arithmetic, and it is especially costly in the quantum setting. Our goal in this paper is to optimize quantum multiplication in the binary field. In the past, efforts to optimize quantum multiplication have centred on reducing the Toffoli gate count or qubits required. However, despite the fact that circuit depth is an important metric for indicating the performance of a quantum circuit, previous studies have lacked sufficient consideration for reducing circuit depth. Our approach to optimizing quantum multiplication differs from previous work in that we aim at reducing the Toffoli depth and full depth. To optimize quantum multiplication, we adopt the Karatsuba multiplication method which is based on the divide-and-conquer approach. In summary, we present an optimized quantum multiplication that has a Toffoli depth of one. Additionally, the full depth of the quantum circuit is also reduced thanks to our Toffoli depth optimization strategy. To demonstrate the effectiveness of our proposed method, we evaluate its performance using various metrics such as the qubit count, quantum gates, and circuit depth, as well as the qubits-depth product. These metrics provide insight into the resource requirements and complexity of the method. Our work achieves the lowest Toffoli depth, full depth, and the best trade-off performance for quantum multiplication. Further, our multiplication is more effective when not used in stand-alone cases. We show this effectiveness by using our multiplication to the Itoh–Tsujii algorithm-based inversion of F (x 8 + x 4 + x 3 + x + 1) . [ABSTRACT FROM AUTHOR]

The second-order system of non-stiff Initial Value Problems (IVP) is considered and, in particular, the case where the first derivatives are absent. This kind of problem is interesting since since it arises in many significant problems, e.g., in Celestial mechanics. Runge–Kutta–Nyström (RKN) pairs are perhaps the most successful approaches for solving such type of IVPs. To achieve a pair attaining orders eight and six, we have to solve a well-defined set of equations with respect to the coefficients. Here, we provide a simplified form of these equations in a robust algorithm. When creating such pairings for use in double precision arithmetic, numerous conditions are often satisfied. First and foremost, we strive to keep the coefficients' magnitudes small to prevent accuracy loss. We may, however, allow greater coefficients when working with quadruple precision. Then, we may build pairs of orders eight and six with significantly smaller truncation errors. In this paper, a novel pair is generated that, as predicted, outperforms state-of-the-art pairs of the same orders in a collection of important problems. [ABSTRACT FROM AUTHOR]

Evolutionary Population Dynamics (EPD) refers to eliminating poor individuals in nature, which is the opposite of survival of the fittest. Although this method can improve the median of the whole population of the meta-heuristic algorithms, it suffers from poor exploration capability to handle high-dimensional problems. This paper proposes a novel EPD operator to improve the search process. In other words, as the primary EPD mainly improves the fitness of the worst individuals in the population, and hence we name it the Fitness-Based EPD (FB-EPD), our proposed EPD mainly improves the diversity of the best individuals, and hence we name it the Diversity-Based EPD (DB-EPD). The proposed method is applied to the Grey Wolf Optimizer (GWO) and named DB-GWO-EPD. In this algorithm, the three most diversified individuals are first identified at each iteration, and then half of the best-fitted individuals are forced to be eliminated and repositioned around these diversified agents with equal probability. This process can free the merged best individuals located in a closed populated region and transfer them to the diversified and, thus, less-densely populated regions in the search space. This approach is frequently employed to make the search agents explore the whole search space. The proposed DB-GWO-EPD is tested on 13 high-dimensional and shifted classical benchmark functions as well as 29 test problems included in the CEC2017 test suite, and four constrained engineering problems. The results obtained by the proposal upon implemented on the classical test problems are compared to GWO, FB-GWO-EPD, and four other popular and newly proposed optimization algorithms, including Aquila Optimizer (AO), Flow Direction Algorithm (FDA), Arithmetic Optimization Algorithm (AOA), and Gradient-based Optimizer (GBO). The experiments demonstrate the significant superiority of the proposed algorithm when applied to a majority of the test functions, recommending the application of the proposed EPD operator to any other meta-heuristic whenever decided to ameliorate their performance. [ABSTRACT FROM AUTHOR]

The objective of this paper was to present a new inverse problem statement and numerical method for the Volterra integral equations with piecewise continuous kernels. For such Volterra integral equations of the first kind, it is assumed that kernel discontinuity curves are the desired ones, but the rest of the information is known. The resulting integral equation is nonlinear with respect to discontinuity curves which correspond to integration bounds. A direct method of discretization with a posteriori verification of calculations is proposed. The family of quadrature rules is employed for approximation purposes. It is shown that the arithmetic complexity of the proposed numerical method is O (N 3) . The method has first-order convergence. A generalization of the method is also proposed for the case of an arbitrary number of discontinuity curves. The illustrative examples are included to demonstrate the efficiency and accuracy of proposed solver. [ABSTRACT FROM AUTHOR]

Traditional controlled-source audio-frequency magnetotellurics (CSAMT) radiates symmetric beams using a grounded symmetric dipole (GSD). Only a tiny fraction of radiant energy is taken advantage of during the far-field (Ff) observation due to the low directivity of the GSD. In order to enhance the signal-to-noise ratio (SNR) during the Ff observation, it is necessary to reduce the transceiving distance (TD) or increase the transmitting power (TP), but both methods will cause many problems. Further, when using the tensor method for observation, GSDs in two vertical directions will be employed to radiate energy, and then a series of problems will occur such as an asymmetry of the SNR in two vertical directions if the geological conditions under the two GSDs vary widely. An arithmetic phase difference (APd) weighting asymmetric beamforming method (ABFM) in CSAMT is proposed in this paper, which uses a GSD array instead of a single GSD, and a signal with APd is transmitted to control the wavefront for beam steering. A significant enhancement (about 3 dB) of the SNR will occur by collecting the radiant energy in the region of concern (RoC) using ABFM. The analysis and simulation results demonstrate that under the premise of the same TD and TP, the ABFM has obvious advantages in improving energy utilization in CSAMT. In other words, the APd-weighted ABFM can deal with a complex noise environment in the field better than the traditional method. [ABSTRACT FROM AUTHOR]

Studying the theoretical properties of optimization algorithms such as genetic algorithms and evolutionary strategies allows us to determine when they are suitable for solving a particular type of optimization problem. Such a study consists of three main steps. The first step is considering such algorithms as Stochastic Global Optimization Algorithms (SGoals), i.e., iterative algorithm that applies stochastic operations to a set of candidate solutions. The second step is to define a formal characterization of the iterative process in terms of measure theory and define some of such stochastic operations as stationary Markov kernels (defined in terms of transition probabilities that do not change over time). The third step is to characterize non-stationary SGoals, i.e., SGoals having stochastic operations with transition probabilities that may change over time. In this paper, we develop the third step of this study. First, we generalize the sufficient conditions convergence from stationary to non-stationary Markov processes. Second, we introduce the necessary theory to define kernels for arithmetic operations between measurable functions. Third, we develop Markov kernels for some selection and recombination schemes. Finally, we formalize the simulated annealing algorithm and evolutionary strategies using the systematic formal approach. [ABSTRACT FROM AUTHOR]

Shift transformations are the fundamental operation of cryptographic algorithms, and the arithmetic unit implementing different types of shift transformations are utilized in the coarse-grain reconfigurable cryptographic architectures (CGRCA) to meet the different cryptographic algorithms. In this paper, a reconfigurable shift transformation unit (RSTU) is proposed to meet the complicated shift requirement of CGRCA, which achieves high flexibility and a good cost–performance ratio. The mathematical properties of shift transformation are analyzed, and several theorems are introduced to design a reconfigurable shifter. Furthermore, the reconfigurable data path of the proposed unit is presented to implement the random combination of shift operations in different granularity, and configuration word and routing algorithms are proposed to generate control information for RSTU. Moreover, the control information generation module is designed to invert the configuration word into the control information, according to the routing algorithms. As a proof-of-concept, the proposed RSTU is built using the CMOS 65 nm technology. The experimental results show that RSTU supports more shift operations, increases 18.2% speed at most, and reduces 13% area occupation, compared to the existing shifters. [ABSTRACT FROM AUTHOR]

Let ρ r (n r) denote the number of positive r-regular integers ( mod n r ) that are less than or equal to n r ; in this paper, we investigate some arithmetic properties of certain functions related to r-regular integers (mod n r) . Then, we study the average orders and the extremal orders of ρ r (n r) in connection with the divisor function and the generalized Dedekind function. Moreover, we also introduce an analogue of Cohen–Ramanujan's sum with respect to r-regular integers (mod n r) and show some basic properties of this function. [ABSTRACT FROM AUTHOR]

Let Γ = (V Γ , E Γ) be a simple undirected graph with finite vertex set V Γ and edge set E Γ . A total n -labeling α : V Γ ∪ E Γ → { 1 , 2 , ... , n } is called a total edge irregular labeling on Γ if for any two different edges x y and x ′ y ′ in E Γ the numbers α (x) + α (x y) + α (y) and α (x ′) + α (x ′ y ′) + α (y ′) are distinct. The smallest positive integer n such that Γ can be labeled by a total edge irregular labeling is called the total edge irregularity strength of the graph Γ. In this paper, we provide the total edge irregularity strength of some asymmetric graphs and some symmetric graphs, namely generalized arithmetic staircase graphs and generalized double-staircase graphs, as the generalized forms of some existing staircase graphs. Moreover, we give the construction of the corresponding total edge irregular labelings. [ABSTRACT FROM AUTHOR]

The arithmetic optimization algorithm (AOA) is a new metaheuristic algorithm inspired by arithmetic operators (addition, subtraction, multiplication, and division) to solve arithmetic problems. The algorithm is characterized by simple principles, fewer parameter settings, and easy implementation, and has been widely used in many fields. However, similar to other meta-heuristic algorithms, AOA suffers from shortcomings, such as slow convergence speed and an easy ability to fall into local optimum. To address the shortcomings of AOA, an improved arithmetic optimization algorithm (IAOA) is proposed. First, dynamic inertia weights are used to improve the algorithm's exploration and exploitation ability and speed up the algorithm's convergence speed; second, dynamic mutation probability coefficients and the triangular mutation strategy are introduced to improve the algorithm's ability to avoid local optimum. In order to verify the effectiveness and practicality of the algorithm in this paper, six benchmark test functions are selected for the optimization search test verification to verify the optimization search ability of IAOA; then, IAOA is used for the parameter optimization of support vector machines to verify the practical ability of IAOA. The experimental results show that IAOA has a strong global search capability, and the optimization-seeking capability is significantly improved, and it shows excellent performance in support vector machine parameter optimization. [ABSTRACT FROM AUTHOR]

Recently, numerous new meta-heuristic algorithms have been proposed for solving optimization problems. According to the Non-Free Lunch theorem, we learn that no single algorithm can solve all optimization problems. In order to solve industrial engineering design problems more efficiently, we, inspired by the algorithm framework of the Arithmetic Optimization Algorithm (AOA) and the Harris Hawks Optimization (HHO), propose a novel hybrid algorithm based on these two algorithms, named EAOAHHO in this paper. The pinhole imaging opposition-based learning is introduced into the proposed algorithm to increase the original population diversity and the capability to escape from local optima. Furthermore, the introduction of composite mutation strategy enhances the proposed EAOAHHO exploitation and exploration to obtain better convergence accuracy. The performance of EAOAHHO is verified on 23 benchmark functions and the IEEE CEC2017 test suite. Finally, we verify the superiority of the proposed EAOAHHO over the other advanced meta-heuristic algorithms for solving four industrial engineering design problems. [ABSTRACT FROM AUTHOR]

Multi-source information fusion is widely used because of its similarity to practical engineering situations. With the development of science and technology, the sources of information collected under engineering projects and scientific research are more diverse. To extract helpful information from multi-source information, in this paper, we propose a multi-source information fusion method based on the Dempster-Shafer (DS) evidence theory with the negation of reconstructed basic probability assignments (nrBPA). To determine the initial basic probability assignment (BPA), the Gaussian distribution BPA functions with padding terms are used. After that, nrBPAs are determined by two processes, reassigning the high blur degree BPA and transforming them into the form of negation. In addition, evidence of preliminary fusion is obtained using the entropy weight method based on the improved belief entropy of nrBPAs. The final fusion results are calculated from the preliminary fused evidence through the Dempster's combination rule. In the experimental section, the UCI iris data set and the wine data set are used for validating the arithmetic processes of the proposed method. In the comparative analysis, the effectiveness of the BPA determination using a padded Gaussian function is verified by discussing the classification task with the iris data set. Subsequently, the comparison with other methods using the cross-validation method proves that the proposed method is robust. Notably, the classification accuracy of the iris data set using the proposed method can reach an accuracy of 97.04%, which is higher than many other methods. [ABSTRACT FROM AUTHOR]