Integer Algorithm Research Articles

Optimization approach of berth-quay crane-truck allocation by the tide, environment and uncertainty factors based on chaos quantum adaptive seagull optimization algorithm

The post-epidemic era has led to the accumulation of cargo, which has brought greater pressure to container ports. Since traditional methods cannot simultaneously consider the effect of tidal, uncertain, and environmental factors on the allocation plan. To relieve this pressure, firstly, considering tidal factors, formulating time window rules, thinking out uncertain factors, and determining constraints from three perspectives of vessel berthing process, quay crane and container truck operation, a new berth-quay crane-truck joint scheduling model is constructed by minimizing three aspects of vessels turnaround time, the carbon emissions of quay cranes and trucks, namely TEU-BQCT model. Then, aiming at obtaining a relatively high-quality solution, combining chaotic mapping and quantum entanglement, a new chaotic quantum adaptive seagull optimization algorithm is proposed, namely CQASOA, exclusive coding rules suitable for the TEU-BQCT model is formulated, a feasible integer algorithm is developed, the external penalty function is constructed to limit constraints, and a novel joint scheduling solution method of berth-quay crane-truck is proposed, namely TEU-BQCT_CQASOA. Subsequently, two ports of different scales in South China are used to test the constructed solution method feasibility. The simulation results indicate that the constructed TEU-BQCT model can obtain a more suitable scheduling scheme. The proposed CQASOA has better performance than other comparison algorithms selected in this paper, which can obtain a better solution when solving the TEU-BQCT model.

Applications of chaotic quantum adaptive satin bower bird optimizer algorithm in berth-tugboat-quay crane allocation optimization

With the advent of the post-pandemic era, the global economic situation has tightened, and the economic benefits of container ports have also been affected. This paper attempts to build a novel berth-tugboat-quay crane joint scheduling method for container ports to reduce the economic cost of container ports. Firstly, from the perspective of the economic cost of container ports, considering random economic factors, this paper proposes a new berth-tugboat-quay crane joint dispatch optimization model, namely E-BUQC, by taking the minimum time cost of vessels in port, the cost of additional freight distance for trucks, the cost of tugboat operation, and the minimum operation cost of quay cranes as the objective function. Then, in order to obtain a relatively high-quality solution, based on chaotic mapping and quantum computing, this paper constructs a new chaotic quantum adaptive satin bower bird optimizer algorithm, namely CQASBO, formulates exclusive coding rules for the E-BUQC model, develops a feasible integer algorithm, and proposes a new joint scheduling solution method of berth-tugboat-quay crane, named E-BUQC_CQASBO. Subsequently, based on the simulation examples of two ports in northern China, the new solution method is tested. The simulation test results show that the E-BUQC model obtains an appropriate solution; The CQASBO constructed in this paper has better performance than other traditional comparison algorithms selected in this paper and can provide a better solution when solving the E-BUQC model.

Integer Algorithm: A Useful Tool for Fault Diagnosis of Analog Circuits

This paper presents an efficient numerical method to solve systems of nonlinear algebraic equations. The method uses a homotopy simplicial approach associated with an integer algorithm. The integer algorithm is discussed in detail and supplemented with original procedures that play an essential role during computation. The fundamental problem of initial simplex generation was solved using the bounded variable simplex optimization method. Efficient root finding of nonlinear equations has wide applications in numerical mathematics and various engineering problems. The proposed method was applied to solve nonlinear equations that arise during the diagnostics of multiple parametric faults in electronic circuits. Circuits made with surface mount technology were considered, as well as circuits designed in complementary metal-oxide-semiconductor and bipolar technology. A universal diagnostic procedure enables testing different circuit classes using standard measurement equipment. Laboratory and numerical experiments demonstrate that the proposed diagnostic procedure is effective.

Integer factorization as subset-sum problem

This paper elaborates on a sieving technique that has first been applied in 2018 for improving bounds on deterministic integer factorization. We will generalize the sieve in order to obtain a polynomial-time reduction from integer factorization to a specific instance of the multiple choice subset-sum problem. As an application, we will improve upon special purpose factorization algorithms for integers composed of divisors with small difference. In particular, we will refine the runtime complexity of Fermat's factorization algorithm by a large subexponential factor. Our first procedure is deterministic, rigorous, easy to implement and has negligible space complexity. Our second procedure is heuristically faster than the first, but has non-negligible space complexity.

Thermal Analysis Based on Dynamic Performance of Rocker Arm Full-Type Needle Bearings

Based on a dynamic analysis of rolling bearings, the equations for rocker arm full-type needle bearings were established by considering the traction coefficients of FVA-M reference lubricating oil, and then they were solved by the GSTIFF (Gear Stiff) integer algorithm with variable steps. The influence of working conditions on friction power consumption and the lubricant’s convective coefficients were investigated. Then, on the basis of the heat generation and heat transfer mechanisms, the frictional power consumption was used as the boundary condition of the bearings’ simulation model. Finally, temperature fields were calculated by the finite element method. The results showed that the overall value of frictional power consumption increased gradually with the increase in either the radial load or the rotation speed. The presence or absence of lubricating oil film in the contact area affected the heat conduction of the bearing, resulting in a temperature difference. Compared with the temperature of the radial load exerted on the bearing, the maximum temperature was more sensitive to the variations in the rotation speed. When running under the conditions of a fatigue life test, the steady-state temperature value of the bearing gradually decreased from the outer raceway to the needle roller and the outer ring surface, and then to the central shaft. The maximum temperature rise was 25.9 °C relative to the ambient temperature.

Demonstration of Shor’s factoring algorithm for N = 21 on IBM quantum processors

We report a proof-of-concept demonstration of a quantum order-finding algorithm for factoring the integer 21. Our demonstration involves the use of a compiled version of the quantum phase estimation routine, and builds upon a previous demonstration. We go beyond this work by using a configuration of approximate Toffoli gates with residual phase shifts, which preserves the functional correctness and allows us to achieve a complete factoring of N=21. We implemented the algorithm on IBM quantum processors using only five qubits and successfully verified the presence of entanglement between the control and work register qubits, which is a necessary condition for the algorithm’s speedup in general. The techniques we employ may be useful in carrying out Shor’s algorithm for larger integers, or other algorithms in systems with a limited number of noisy qubits.

A Practical Analysis of the Fermat Factorization and Pollard Rho Method for Factoring Integers

The development of public-key cryptography generation using the factoring method is very important in practical cryptography applications. In cryptographic applications, the urgency of factoring is very risky because factoring can crack public and private keys, even though the strength in cryptographic algorithms is determined mainly by the key strength generated by the algorithm. However, solving the composite number to find the prime factors is still very rarely done. Therefore, this study will compare the Fermat factorization algorithm and Pollard rho by finding the key generator public key algorithm's prime factor value. Based on the series of test and analysis factoring integer algorithm using Fermat's Factorization and Pollards' Rho methods, it could be concluded that both methods could be used to factorize the public key which specifically aimed to identify the prime factors. During the public key factorizing process within 16 bytes – 64 bytes, Pollards' Rho's average duration was significantly faster than Fermat's Factorization.

Speeding up the Multiplication Algorithm for Large Integers

Multiplication is one of the basic operations that influence the performance of many computer applications such as cryptography. The main challenge of the multiplication operation is the cost of the operation as compared to other basic operations such as addition and subtraction, especially when the size of the numbers is large. In this work, we investigate the use of the window strategy for multiplying a sequence of large integers to design an efficient sequential algorithm in order to reduce the number of bit-multiplication operations involved in multiplying a sequence of large integers. In our implementation, several parameters are considered and measured for their effect on the proposed algorithm and the best-known sequential algorithm in the literature. These parameters are the size of the sequence of integers, the size of the integers, the size of the window, and the distribution of the data. The experimental results prove the effectiveness of the proposed algorithm are compared to the ones of the best-known sequential algorithm, and the proposed algorithm is able to achieve a reduction in computing time greater than 50% in most cases.

МЕТОД РЕАЛИЗАЦИИ ГОМОМОРФНОГО ДЕЛЕНИЯ

The article deals with the problems of homomorphic cryptography. Homomorphic cryptographyis one of the young directions of cryptography. Its peculiarity lies in the fact that it is possibleto process encrypted data without preliminary decryption in such a way that the result of operationson encrypted data is equivalent, after decryption, to the result of operations on open data.The article provides a brief overview of the areas of application of homomorphic encryption. Tosolve various applied problems, support for all mathematical operations is required, including thedivision operation, and the ability to perform this operation homomorphically will expand thepossibilities of using homomorphic encryption. The paper proposes a method of homomorphicdivision based on an abstract representation of the ciphertext in the form of an ordinary fraction.The paper describes in detail the proposed method. In addition, the article contains an example ofthe practical implementation of the proposed method. It is proposed to divide the levels of dataprocessing into 2 levels – cryptographic and mathematical. At the cryptographic level, a completely homomorphic encryption algorithm is used and the basic homomorphic mathematical operationsare performed – addition, multiplication and difference. The mathematical level is a superstructureon top of the cryptographic level and expands its capabilities. At the mathematical level,the ciphertext is represented as a simple fraction and it becomes possible to perform thehomomorphic division operation. The paper also provides a practical example of applying thehomomorphic division method based on the Gentry algorithm for integers. Conclusions and possibleways of further development are given.

Safety Characteristic Evaluation of Cage in Cylindrical Roller Bearing at the Stage of Start-Up and Stop

The dynamics model of cylindrical roller bearing (CRB) in aeroengine main shaft was promoted and solved by Hilber–Hughes–Taylor (HHT) integer algorithm with variable step in combination with symmetric multiprocessing (SMP) parallel solving technology, and a finite element model of roller to cage contact was built. The dynamic characteristics of CRB at the stage of start-up and stop were analyzed firstly, and then, the collision forces between rollers and cage were used as the boundary conditions of the finite element model to discuss the influences of working conditions, structural parameters, and materials on the stress distribution and safety characteristic of cage at the stage of start-up and stop. The findings will provide the theoretical basis for the designing of CRB in aeroengine main shaft.

Development of the planning model of the production and cutting of the paper web ensuring the quality of the finished products

The problem of the planning of pulp and paper production has been investigated, a complex of model and algorithmic programs as well as a software of an automated system of planning and calculating of the cutting methods on a longitudinal slitting machine (LSM) is expected to be a result of this planning. An integrated model for planning paper production and multi-stage cutting of rolled and sheet products has been proposed based on methods, models and algorithms of optimal cutting from the condition of the ensuring the products orders fulfillment with minimal losses. A scientifically based method and algorithm of generating a set of acceptable ways of rolls cutting, criteria of generating a set of acceptable ways of rolls cutting as well as an integer algorithm of the result of the problem solving have been considered. All real restrictions encountered in the manufacturing sector have been taken into account. The results of the planning models usage for real production process have been presented.

Joint Resource Allocation and Computation Offloading With Time-Varying Fading Channel in Vehicular Edge Computing

Vehicular edge computing (VEC) is considered as a novel paradigm to enhance the safety of automated vehicles and intelligent transportation systems (ITS). The computation offloading strategies are the key point of VEC, and the effect of time-varying channels cannot be ignored during the task transmission period. This paper investigates the utility maximization problem with task delay requirement constraints, in which the influence of time-varying channel on the task offloading strategies during the task offloading period is considered. The time-varying fading channel leads to the time-varying spectrum efficiency (SE), so the previous offloading strategies are questionable when the additional uncertain allocated bandwidth is taken into account. To deal with it, we first propose a linearization based Branch and Bound (LBB) algorithm to solve the fixed SE problem without considering the time-varying channel characteristics. Considering the complexity of the LBB algorithm, a closest rounding integer (CRI) algorithm is proposed to solve the fixed SE problem. Then, based on the resource allocation strategies of the fixed SE problem, we propose the LBB based computation offloading (LBBCO) algorithm and the CRI based computation offloading (CRICO) algorithm to solve the original problem for both the static tasks and dynamic tasks. The proposed LBBCO/CRICO algorithms are also applicable to multi-vehicle and multi-task scenarios. Furthermore, we analyze the effect of small-scale fading on the proposed offloading strategies. The simulation results show that the average utilities of LBBCO and CRICO algorithms have a small gap by 3.93% and 6.13% only to the upper bound, respectively. Meanwhile, the proposed LBBCO and CRICO algorithms can outperform the previous state-of-the-art solution by 4.52% and 2.38%, respectively.

Efficient GPU Implementation of Multiple-Precision Addition based on Residue Arithmetic

In this work, the residue number system (RNS) is applied for efficient addition of multiple-precision integers using graphics processing units (GPUs) that support the Compute Unified Device Architecture (CUDA) platform. The RNS allows calculations with the digits of a multiple-precision number to be performed in an element-wise fashion, without the overhead of communication between them, which is especially useful for massively parallel architectures such as the GPU architecture. The paper discusses two multiple-precision integer algorithms. The first algorithm relies on if-else statements to test the signs of the operands. In turn, the second algorithm uses radix complement RNS arithmetic to handle negative numbers. While the first algorithm is more straightforward, the second one avoids branch divergence among threads that concurrently compute different elements of a multiple-precision array. As a result, the second algorithm shows significantly better performance compared to the first algorithm. Both algorithms running on an NVIDIA RTX 2080 Ti GPU are faster than the multi-core GNU MP implementation running on an Intel Xeon 4100 processor.

Research on Data Acquisition Algorithms Based on Image Processing and Artificial Intelligence

At present, image recognition processing technology has been playing a decisive role in the field of pattern recognition, of which automatic recognition of bank notes is an important research topic. Due to the limitation of the size of bill layout and printing method, many invoice layouts are not clear, skewed or distorted, and even there are irregular handwritten signature contents, which lead to the problem of recognition of digital characters on bill surface. In this regard, this paper proposes a data acquisition and recognition algorithm based on improved BP neural network for ticket number identification, which is based on the theory of image processing and recognition, combined with improved bill information recognition technology. First, in the pre-processing stage of bill image, denoising and graying of bill image are processed. After binarization of bill image, the tilt detection method based on Bresenham integer algorithm is used to correct the tilted bill image. Secondly, character localization and feature extraction are carried out for par characters, and the target background is separated from the interference background in order to extract the desired target characters. Finally, the improved BP neural network-based bill digit data acquisition and recognition algorithm is used to realize the classification and recognition of bill characters. The experimental results show that the improved method has better classification and recognition effect than other data acquisition and recognition algorithms.

Basic approaches to air traffic and airport slots allocation

Purpose- The purpose of the study is to determine the basic approaches to air traffic and airport slots allocation. It has been admitted that demand on aviation has been doubled many times in the last years. This has necessitated creating new models and strategies to tackle the problems of congested airports/airspace. Methodology- Literature review method was used. In this review article, some theoretical and practical studies to overcome this problem have been presented. In addition, new models and simulations have been analyzed. Findings- Many problems have been made. Some researchers have applied analytical algorithms; In addition, others have used integer algorithms. However, while researching the literature, the airspace congestion studies are all about the airspace. Conclusion- A review of the literature. The different methods, algorithms, approaches. In addition, the airport congestion was at. Moreover, it was a comprehensive comparison of all presented.

Fraction-free computation of the unit-circle resultant with any singularity profile

We show that an algorithm established in a recent publication in this journal to provide a fraction-free version for the Bistritz test can also be used to compute the unit-circle resultant. The consequence is an effective new algorithm to find this resultant for any complex polynomial that is also an efficient integer algorithm for polynomial with real or Gaussian integer coefficients. The algorithm ends always with the resultant expressed as the minimal degree multivariate polynomial of the polynomial's (indeterminate) coefficients. A simpler form of the algorithm, that equally reaches this expression in all circumstances, but is not guaranteed to stay over integers during possible intermediate abnormal gaps, is also suggested along with the simplest form that the algorithm takes in the strongly regular case.

Self-contained, passive, non-contact, photoplethysmography: Real-time extraction of heart rates from live view within a Canon Powershot

Photoplethysmography (PPG) is the detection of blood flow or pressure by optical means. The most common method involves direct skin-contact measurement of light from an LED. However, the small color changes in skin under normal lighting conditions, as recorded by conventional video, potentially allow passive, non-contact, PPG. A variety of methods have been applied to extract heartrate from such a video. In another paper submitted to this conference by the same authors, a new processing algorithm based on autocorrelation is shown to be effective without needing extensive video preprocessing to enhance the signal. That method was implemented using floating-point arithmetic in MatLab to analyze complete videos. However, the algorithm’s structure suggested that it might be possible to create a simplified, integer-only, approximation that is entirely incremental: updating a heart rate estimate as each frame is captured. This new, simplified, incremental algorithm allows a reprogrammed Canon PowerShot camera to function as a stand-alone, passive, non-contact, PPG device. The incremental integer algorithm and implementation are explained and evaluated in this paper.

A fraction-free unit-circle zero location test for a polynomial with any singularity profile

ABSTRACTThis paper presents a fraction-free (FF) version of the Bistritz test to determine the zero location (ZL) of a polynomial with respect to the unit circle. The test has the property that when it is invoked on a polynomial with Gaussian or real integer coefficients, it is an efficient integer algorithm completed without fractions over the respective integral domain. The test is not restricted to integers but remains integer preserving (IP) in all possible encounters of abnormalities and singularities. We define a symmetric subresultant polynomial sequence (SSPS) for the Sylvester matrix of two symmetric polynomials. We then show that the sequence of polynomials produced by the FF test coincides with the SSPS of its first two polynomials when the test is normal and the SSPS is strongly nonsingular, or else its polynomials match the non-singular subresultant polynomial and pass over intermediate gaps of singular subresultants in an IP and efficient manner. This relationship (interesting in its own right) is used to show that the test is IP and normally attains integers of minimal size.

ALGORITHMS FOR FACTORIZATION AND IRREDUCIBILITY TESTING OF POLYNOMIALS USING ELLIPTIC CURVES

In this article irreducibility criteria and factorization algorithms are formulated and proved, that are generalizations of correspondent criteria and algorithms for integers. Generalization of Lenstra’s theorem is of especial interest. It provides correct calculations of multiple points on elliptic curve that is used in Lenstra algorithm. Note that the generalization of this theorem in case of finite field of characteristic 2 is completely different from the classical case and is very non-trivial. Using the criteria obtained, we construct a series of algorithms for factoring and testing of irreducibility of polynomials over finite field. We should note that their performance isn’t their main advantage, but the main advantage is using some abelian group built on elliptic curve. So in case of failure of algorithm we can just chose the other elliptic curve over the corresponding field and repeat the algorithm. These algorithms have no large advantage in speed, like their preimages – analogical algorithms for integers, but they demonstrate new approaches to the solutions of important problem of irreducibility testing and also are very interesting from mathematical point of view.

Cage slip characteristics of a cylindrical roller bearing with a trilobe-raceway

Based on dynamic analysis of rolling bearings, the nonlinear dynamic differential equations of a cylindrical roller bearing with a trilobe-raceway were established and solved by the GSTIFF (gear stiff) integer algorithm with a variable step. The influences of structural parameters and the tolerance of the trilobe-raceway, working conditions of the bearing, and the outer ring installation method on cage slip characteristics were investigated. The results show that: (i) The cage slip ratio and bearing rating life of a cylindrical roller bearing with a trilobe-raceway would reduce when the low-radius (radius of the outer raceway contour at the lowest point) and D-value (difference value between the high and low points of the outer raceway contour) decrease, and the former (low-radius) contributes more significantly. (ii) The cage slip ratio of a cylindrical roller bearing with a trilobe-raceway rises with the increase of the bearing speed, and decreases with the increase of the radial force; the variation range increases with the increase of the low-radius. (iii) When the installation angle of the outer ring increases in a period, the cage slip ratio remains unchanged while the bearing rating life rises up a little. Therefore, when installing a cylindrical roller bearing with a trilobe-raceway, the location of the maximum radius shall be under that of the radial force to improve the bearing rating life. (iv) With the increase of the roundness of the base circle where the radius of the lowest points of the trilobe-raceway contour locates, the cage slip ratio rises gradually and the bearing rating life decreases.