Hybrid Gene Selection Methods for High-Dimensional Lung Cancer Data Using Improved Arithmetic Optimization Algorithm

Lung cancer is among the most frequent cancers in the world,with over one million deaths per year.Classification is required for lung cancer diagnosis and therapy to be effective,accurate,and reliable.Gene expression microarrays have made it possible to find genetic biomarkers for cancer diagnosis and prediction in a high-throughput manner.Machine Learning(ML)has been widely used to diagnose and classify lung cancer where the performance of ML methods is evaluated to identify the appropriate technique.Identifying and selecting the gene expression patterns can help in lung cancer diagnoses and classification.Normally,microarrays include several genes and may cause confusion or false prediction.Therefore,the Arithmetic Optimization Algorithm(AOA)is used to identify the optimal gene subset to reduce the number of selected genes.Which can allow the classifiers to yield the best performance for lung cancer classification.In addition,we proposed a modified version of AOA which can work effectively on the high dimensional dataset.In the modified AOA,the features are ranked by their weights and are used to initialize the AOA population.The exploitation process of AOA is then enhanced by developing a local search algorithm based on two neighborhood strategies.Finally,the efficiency of the proposed methods was evaluated on gene expression datasets related to Lung cancer using stratified 4-fold cross-validation.The method’s efficacy in selecting the optimal gene subset is underscored by its ability to maintain feature proportions between 10%to 25%.Moreover,the approach significantly enhances lung cancer prediction accuracy.For instance,Lung_Harvard1 achieved an accuracy of 97.5%,Lung_Harvard2 and Lung_Michigan datasets both achieved 100%,Lung_Adenocarcinoma obtained an accuracy of 88.2%,and Lung_Ontario achieved an accuracy of 87.5%.In conclusion,the results indicate the potential promise of the proposed modified AOA approach in classifying microarray cancer data.

An Algorithm for Short-Circuit Current Interval in Distribution Networks with Inverter Type Distributed Generation Based on Affine Arithmetic

During faults in a distribution network,the output power of a distributed generation(DG)may be uncertain.Moreover,the output currents of distributed power sources are also affected by the output power,resulting in uncertainties in the calculation of the short-circuit current at the time of a fault.Additionally,the impacts of such uncertainties around short-circuit currents will increase with the increase of distributed power sources.Thus,it is very important to develop a method for calculating the short-circuit current while considering the uncertainties in a distribution network.In this study,an affine arithmetic algorithm for calculating short-circuit current intervals in distribution networks with distributed power sources while considering power fluctuations is presented.The proposed algorithm includes two stages.In the first stage,normal operations are considered to establish a conservative interval affine optimization model of injection currents in distributed power sources.Constrained by the fluctuation range of distributed generation power at the moment of fault occurrence,the model can then be used to solve for the fluctuation range of injected current amplitudes in distributed power sources.The second stage is implemented after a malfunction occurs.In this stage,an affine optimization model is first established.This model is developed to characterizes the short-circuit current interval of a transmission line,and is constrained by the fluctuation range of the injected current amplitude of DG during normal operations.Finally,the range of the short-circuit current amplitudes of distribution network lines after a short-circuit fault occurs is predicted.The algorithm proposed in this article obtains an interval range containing accurate results through interval operation.Compared with traditional point value calculation methods,interval calculation methods can provide more reliable analysis and calculation results.The range of short-circuit current amplitude obtained by this algorithm is slightly larger than those obtained using the Monte Carlo algorithm and the Latin hypercube sampling algorithm.Therefore,the proposed algorithm has good suitability and does not require iterative calculations,resulting in a significant improvement in computational speed compared to the Monte Carlo algorithm and the Latin hypercube sampling algorithm.Furthermore,the proposed algorithm can provide more reliable analysis and calculation results,improving the safety and stability of power systems.

Enhanced Arithmetic Optimization Algorithm Guided by a Local Search for the Feature Selection Problem

High-dimensional datasets present significant challenges for classification tasks.Dimensionality reduction,a crucial aspect of data preprocessing,has gained substantial attention due to its ability to improve classification per-formance.However,identifying the optimal features within high-dimensional datasets remains a computationally demanding task,necessitating the use of efficient algorithms.This paper introduces the Arithmetic Optimization Algorithm(AOA),a novel approach for finding the optimal feature subset.AOA is specifically modified to address feature selection problems based on a transfer function.Additionally,two enhancements are incorporated into the AOA algorithm to overcome limitations such as limited precision,slow convergence,and susceptibility to local optima.The first enhancement proposes a new method for selecting solutions to be improved during the search process.This method effectively improves the original algorithm’s accuracy and convergence speed.The second enhancement introduces a local search with neighborhood strategies(AOA_NBH)during the AOA exploitation phase.AOA_NBH explores the vast search space,aiding the algorithm in escaping local optima.Our results demonstrate that incorporating neighborhood methods enhances the output and achieves significant improvement over state-of-the-art methods.

Improved Arithmetic Optimization Algorithm with Multi-Strategy Fusion Mechanism and Its Application in Engineering Design

This article addresses the issues of falling into local optima and insufficient exploration capability in the Arithmetic Optimization Algorithm (AOA), proposing an improved Arithmetic Optimization Algorithm with a multi-strategy mechanism (BSFAOA). This algorithm introduces three strategies within the standard AOA framework: an adaptive balance factor SMOA based on sine functions, a search strategy combining Spiral Search and Brownian Motion, and a hybrid perturbation strategy based on Whale Fall Mechanism and Polynomial Differential Learning. The BSFAOA algorithm is analyzed in depth on the well-known 23 benchmark functions, CEC2019 test functions, and four real optimization problems. The experimental results demonstrate that the BSFAOA algorithm can better balance the exploration and exploitation capabilities, significantly enhancing the stability, convergence mode, and search efficiency of the AOA algorithm.

Probability Distribution of Arithmetic Average of China Aviation Network Edge Vertices Nearest Neighbor Average Degree Value and Its Evolutionary Trace Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of arithmetic average of edge vertices nearest neighbor average degree values of China aviation network were studied based on the statistics data of China civil aviation network in 1988,1994,2001,2008 and 2015.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network.Based on the statistical data,the arithmetic averages of edge vertices nearest neighbor average degree values of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Using the probability statistical analysis method,it was found that the arithmetic average of edge vertices nearest neighbor average degree values had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.

The Formalization of The Arithmetic System on The Ground of The Atomic Logic

This paper is a continuation of the paper [16]. Namely, in [16] we have introduced, among others, the definition of the N atomic entailment and we have constructed the system S, which is based on the atomic entailment. In this paper we show that the classical Arithmetic can be based on the Atomic Logic （see [17]）.

Calculation connectivity reliability of road networks based on recursive decomposition arithmetic

In order to decrease the calculation complexity of connectivity reliability of road networks, an improved recursive decomposition arithmetic is proposed. First, the basic theory of recursive decomposition arithmetic is reviewed. Then the characteristics of road networks, which are different from general networks, are analyzed. Under this condition, an improved recursive decomposition arithmetic is put forward which fits road networks better. Furthermore, detailed calculation steps are presented which are convenient for the computer, and the advantage of the approximate arithmetic is analyzed based on this improved arithmetic. This improved recursive decomposition arithmetic directly produces disjoint minipaths and avoids the non-polynomial increasing problems. And because the characteristics of road networks are considered, this arithmetic is greatly simplified. Finally, an example is given to prove its validity.

1 + 1 = 3: Synergy Arithmetic in Economics

Counting has always been one of the most important operations for human be-ings. Naturally, it is inherent in economics and business. We count with the unique arithmetic, which humans have used for millennia. However, over time, the most inquisitive thinkers have questioned the validity of standard arithmetic in certain settings. It started in ancient Greece with the famous philosopher Zeno of Elea, who elaborated a number of paradoxes questioning popular knowledge. Millennia later, the famous German researcher Herman Helmholtz (1821-1894) [1] expressed reservations about applicability of conventional arithmetic with respect to physical phenomena. In the 20th and 21st century, mathematicians such as Yesenin-Volpin (1960) [2], Van Bendegem (1994) [3], Rosinger (2008) [4] and others articulated similar concerns. In validation, in the 20th century expressions such as 1 + 1 = 3 or 1 + 1 = 1 occurred to reflect important characteristics of economic, business, and social processes. We call these expressions synergy arithmetic. It is common notion that synergy arithmetic has no meaning mathematically. However in this paper we mathematically ground and explicate synergy arithmetic.

On the Consistency of the Arithmetic System

In this paper we establish that the well-known Arithmetic System is consistent in the traditional sense. The proof is done within this Arithmetic System.

Reversible Natural Language Watermarking Using Synonym Substitution and Arithmetic Coding

For protecting the copyright of a text and recovering its original content harmlessly,this paper proposes a novel reversible natural language watermarking method that combines arithmetic coding and synonym substitution operations.By analyzing relative frequencies of synonymous words,synonyms employed for carrying payload are quantized into an unbalanced and redundant binary sequence.The quantized binary sequence is compressed by adaptive binary arithmetic coding losslessly to provide a spare for accommodating additional data.Then,the compressed data appended with the watermark are embedded into the cover text via synonym substitutions in an invertible manner.On the receiver side,the watermark and compressed data can be extracted by decoding the values of synonyms in the watermarked text,as a result of which the original context can be perfectly recovered by decompressing the extracted compressed data and substituting the replaced synonyms with their original synonyms.Experimental results demonstrate that the proposed method can extract the watermark successfully and achieve a lossless recovery of the original text.Additionally,it achieves a high embedding capacity.

Maintenance decision-making method for manufacturing system based on cost and arithmetic reduction of intensity model

A cost-based selective maintenance decision-making method was presented.The purpose of this method was to find an optimal choice of maintenance actions to be performed on a selected group of machines for manufacturing systems.The arithmetic reduction of intensity model was introduced to describe the influence on machine failure intensity by different maintenance actions (preventive maintenance,minimal repair and overhaul).In the meantime,a resolution algorithm combining the greedy heuristic rules with genetic algorithm was provided.Finally,a case study of the maintenance decision-making problem of automobile workshop was given.Furthermore,the case study demonstrates the practicability of this method.

A Comparison of Arithmetic Operations for Dynamic Process Optimization Approach

A comparison of arithmetic operations of two dynamic process optimization approaches called quasi-sequential approach and reduced Sequential Quadratic Programming(rSQP)simultaneous approach with respect to equality constrained optimization problems is presented.Through the detail comparison of arithmetic operations,it is concluded that the average iteration number within differential algebraic equations(DAEs)integration of quasi-sequential approach could be regarded as a criterion.One formula is given to calculate the threshold value of average iteration number.If the average iteration number is less than the threshold value,quasi-sequential approach takes advantage of rSQP simultaneous approach which is more suitable contrarily.Two optimal control problems are given to demonstrate the usage of threshold value.For optimal control problems whose objective is to stay near desired operating point,the iteration number is usually small.Therefore,quasi-sequential approach seems more suitable for such problems.

Interval arithmetic operations for uncertainty analysis with correlated interval variables

A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional parallelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation,and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addition, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.

Vertical 2D Modeling of Free Surface Flow with Hydrodynamic Pressure Using SIMPLE Arithmetic in σ Coordinates

A numerical model for shallow water flow has been developed based on the unsteady Reynolds-averaged Navier-Stokes equations with the hydrodynamic pressure instead of hydrostatic pressure assumption. The equations are transformed into the σ-coordinate system and the eddy viscosity is calculated with the standard k-ε turbulence model. The control volume method is used to discrete the equations, and the boundary conditions at the bed for shallow water models only include vertical diffusion terms expressed with wall functions. And the semi-implicit method for pressure linked equation arithmetic is adopted to solve the equations. The model is applied to the 2D vertical plane flow of a current over two steep-sided trenches for which experiment data are available for comparison and good agreement is obtained. And the model is used to predicting the flow in a channel with a steep-sided submerged breakwater at the bottom, and the streamline is drawn.

Cryptanalysis of a chaos-based cryptosystem with an embedded adaptive arithmetic coder

In this paper, we analyse a new chaos-based cryptosystem with an embedded adaptive arithmetic coder, which was proposed by Li Heng-Jian and Zhang J S （Li H J and Zhang J S 2010 Chin. Phys. B 19 050508）. Although this new method has a better compression performance than its original version, it is found that there are some problems with its security and decryption processes. In this paper, it is shown how to obtain a great deal of plain text from the cipher text without prior knowledge of the secret key. After discussing the security and decryption problems of the Li Heng-Jian et al. algorithm, we propose an improved chaos-based cryptosystem with an embedded adaptive arithmetic coder that is more secure.

Design of area and power efficient Radix-4 DIT FFT butterfly unit using floating point fused arithmetic

In this work, power efficient butterfly unit based FFT architecture is presented. The butterfly unit is designed using floating-point fused arithmetic units. The fused arithmetic units include two-term dot product unit and add-subtract unit. In these arithmetic units, operations are performed over complex data values. A modified fused floating-point two-term dot product and an enhanced model for the Radix-4 FFT butterfly unit are proposed. The modified fused two-term dot product is designed using Radix-16 booth multiplier. Radix-16 booth multiplier will reduce the switching activities compared to Radix-8 booth multiplier in existing system and also will reduce the area required. The proposed architecture is implemented efficiently for Radix-4 decimation in time(DIT) FFT butterfly with the two floating-point fused arithmetic units. The proposed enhanced architecture is synthesized, implemented, placed and routed on a FPGA device using Xilinx ISE tool. It is observed that the Radix-4 DIT fused floating-point FFT butterfly requires 50.17% less space and 12.16% reduced power compared to the existing methods and the proposed enhanced model requires 49.82% less space on the FPGA device compared to the proposed design. Also, reduced power consumption is addressed by utilizing the reusability technique, which results in 11.42% of power reduction of the enhanced model compared to the proposed design.

An Adaptive Joint Source/Channel Coding Using Error Correcting Arithmetic Codes

An approximately optimal adaptive arithmetic coding (AC) system using a forbidden symbol (FS) over noisy channels was proposed which allows one to jointly and adaptively design the source decoding and channel correcting in a single process, with superior performance compared with traditional separated techniques. The concept of adaptiveness is applied not only to the source model but also to the amount of coding redundancy. In addition, an improved branch metric computing algorithm and a faster sequential searching algorithm compared with the system proposed by Grangetto were proposed. The proposed system is tested in the case of image transmission over the AWGN channel, and compared with traditional separated system in terms of packet error rate and complexity. Both hard and soft decoding were taken into account.

On the Distribution of Values of Euler＇s Function over Integers in Arithmetic Progressions

Let φ(n) denote the Euler-totient function, we study the distribution of solutions of φ(n) ≤ x in arithmetic progressions, where n ≡ l(mod q) and an asymptotic formula was obtained by Perron formula.

PARALLEL ARITHMETIC NUMERICAL SIMULATION AND APPLICATION OF SECONDARY MIGRATION- ACCUMULATION OF OIL RESOURCES

From such actual conditions as the effects of characteristics of miltilayer petroleum geology and permeation fluid mechanics, a new numerical model is put forward and coupling splitting-up implicit interactive scheme is formed. For the actual situation of Dongying hollow (four-layer) and Tanhai region (three-layer) of Shengli Petroleum Field, the numerical simulation test results and the actual conditions are coincident.

INTERVAL ARITHMETIC AND STATIC INTERVAL FINITE ELEMENT METHOD

When the uncertainties of structures may be bounded in intervals, through some suitable discretization, interval finite element method can be constructed by combining the interval analysis with the traditional finite element method (FEM). The two parameters, median and deviation, were used to represent the uncertainties of interval variables. Based on the arithmetic rules of intervals, some properties and arithmetic rules of interval variables were demonstrated. Combining the procedure of interval analysis with FEM, a static linear interval finite element method was presented to solve the non-random uncertain structures. ne solving of the characteristic parameters of n-freedom uncertain displacement field of the static governing equation was transformed into 2 n-order linear equations. It is shown by a numerical example that the proposed method is practical and effective.