814 results
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2. A note on a paper by Molai and Khorram
- Author
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Shieh, Bih-Sheue
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MATHEMATICAL optimization , *ALGORITHMS , *FEASIBILITY studies , *MATHEMATICAL analysis , *OPERATIONS research , *LINEAR differential equations - Abstract
Abstract: The aim of this note is to show that the optimization algorithm proposed in may not lead to the optimal solution in some cases. In fact, the optimization problem remains open if we do not apply the branch-and-bound method to solve it or compute all the objective values of minimal solutions of the feasible domain. [Copyright &y& Elsevier]
- Published
- 2010
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3. Novel adaptive zeroing neural dynamics schemes for temporally-varying linear equation handling applied to arm path following and target motion positioning.
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Wu, Wenqi and Zhang, Yunong
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LINEAR equations , *MATHEMATICAL analysis , *MOTION , *ALGORITHMS - Abstract
While the handling for temporally-varying linear equation (TVLE) has received extensive attention, most methods focused on trading off the conflict between computational precision and convergence rate. Different from previous studies, this paper proposes two complete adaptive zeroing neural dynamics (ZND) schemes, including a novel adaptive continuous ZND (ACZND) model, two general variable time discretization techniques, and two resultant adaptive discrete ZND (ADZND) algorithms, to essentially eliminate the conflict. Specifically, an error-related varying-parameter ACZND model with global and exponential convergence is first designed and proposed. To further adapt to the digital hardware, two novel variable time discretization techniques are proposed to discretize the ACZND model into two ADZND algorithms. The convergence properties with respect to the convergence rate and precision of ADZND algorithms are proved via rigorous mathematical analyses. By comparing with the traditional discrete ZND (TDZND) algorithms, the superiority of ADZND algorithms in convergence rate and computational precision is shown theoretically and experimentally. Finally, simulative experiments, including numerical experiments on a specific TVLE solving as well as four application experiments on arm path following and target motion positioning are successfully conducted to substantiate the efficacy, superiority, and practicability of ADZND algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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4. How majority-vote crossover and estimation-of-distribution algorithms cope with fitness valleys.
- Author
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Witt, Carsten
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MATHEMATICAL analysis , *ALGORITHMS , *EVOLUTIONARY computation , *VALLEYS , *EVOLUTIONARY algorithms - Abstract
The benefits of using crossover in crossing fitness gaps have been studied extensively in evolutionary computation. Recent runtime results show that majority-vote crossover is particularly efficient at optimizing the well-known Jump benchmark function that includes a fitness gap next to the global optimum. Also estimation-of-distribution algorithms (EDAs), which use an implicit crossover, are much more efficient on Jump than typical mutation-based algorithms. However, the allowed gap size for polynomial runtimes with EDAs is at most logarithmic in the problem dimension n. In this paper, we investigate variants of the Jump function where the gap is shifted and appears in the middle of the typical search trajectory. Such gaps can still be overcome efficiently in time O (n log n) by majority-vote crossover and an estimation-of-distribution algorithm, even for gap sizes almost n. However, if the global optimum is located in the gap instead of the usual all-ones string, majority-vote crossover would nevertheless approach the all-ones string and be highly inefficient. In sharp contrast, an EDA can still find such a shifted optimum efficiently. Thanks to a general property called fair sampling , the EDA will with high probability sample from almost every fitness level of the function, including levels in the gap, and sample the global optimum even though the overall search trajectory points towards the all-ones string. Finally, we derive limits on the gap size allowing efficient runtimes for the EDA. • We study 2 algorithms using majority-vote crossover and an estimation-of-distribution algorithm on modified jump functions. • We derive theorems on the algorithms' runtime using rigorous mathematical analyses. • All 3 algorithms can overcome the fitness gap of the jump functions efficiently for moderate sizes of the gap. • All but the estimation-of-distribution algorithm usually fail to find an optimum located within the gap. • The estimation-of-distribution is efficient since it samples fairly on all fitness levels towards the optimum. [ABSTRACT FROM AUTHOR]
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- 2023
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5. Notes on a paper considering nonlinear equations
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Ujević, Nenad
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NUMERICAL solutions to nonlinear differential equations , *STOCHASTIC convergence , *MATHEMATICAL analysis , *PERIODICALS , *ALGORITHMS - Abstract
Abstract: In abstract of the paper [A. Rafiq, A note on “A family of methods for solving nonlinear equations”, Appl. Math. Comput. 195 (2008) 819–821] we can find the following sentences. We cite: Ujević et al. introduced a family of methods for solving nonlinear equations. However the main Algorithm 1 put forward by Ujević et al. (p. 7) is wrong. This is the main aim of this note. We also point out some major bugs in the results of Ujević et al. – the end of the citation. Here it is shown that all of the mentioned assertions are not true. In other words, the Algorithm 1 is correct (up to an obvious misprint, which is not mentioned in the above paper) and there are no major bugs in the paper by Ujević et al. In fact, these observations, which will be given in this note, show that the main aim of the paper by Rafiq is wrong. [Copyright &y& Elsevier]
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- 2009
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6. Shifted Legendre polynomials algorithm used for the numerical analysis of viscoelastic plate with a fractional order model.
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Sun, Lin, Chen, Yiming, Dang, Rongqi, Cheng, Gang, and Xie, Jiaquan
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NUMERICAL analysis , *ALGORITHMS , *LEGENDRE'S polynomials , *MATHEMATICAL errors , *MATHEMATICAL analysis , *POLYNOMIALS - Abstract
An effective numerical algorithm is presented to analyze the fractional viscoelastic plate in the time domain for the first time in this paper. The viscoelastic behavior of the plate is described with fractional Kelvin–Voigt (FKV) constitutive model in three-dimensional space. A governing equation with three independent variables is established. Ternary unknown function in the governing equation is solved by deriving integer and fractional order differential operational matrices of the shifted Legendre polynomials. Error analysis and mathematical example are presented to verify the effectiveness and accuracy of proposed algorithm. Finally, numerical analysis of the plate under different loading conditions is carried out. Effects of the damping coefficient on vibration amplitude of the viscoelastic plate are studied. The results obtained are consistent with the current reference and actual situation. It shows that shifted Legendre polynomials algorithm is suitable for numerical analysis of fractional viscoelastic plates. • The fractional order governing equation of a viscoelastic plate is established. • Shifted Legendre polynomials algorithm is used to solve the governing equation. • The feasibility and efficiency of the proposed algorithm are verified. • Transverse displacements of viscoelastic plate are calculated directly in the time domain. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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7. On optimal joint replacement policy for deteriorating series systems.
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Cheng, Guoqing and Li, Ling
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MATHEMATICAL analysis , *ALGORITHMS - Abstract
• A general repair-replacement model for series systems is proposed. • The explicit expression of the long-run average cost rate is derived. • Some analytical results on the optimal replacement policy are obtained. • An algorithm is devised to search the optimal policy much more efficiently. • A case study is provided to illustrate the proposed model and approach. In this paper, a general repair-replacement model for a k -component series system is proposed. Components of the system may break down randomly and can be repaired immediately. Due to the imperfect repair, the successive operating times decrease stochastically while the consecutive repair times increase stochastically. A joint replacement policy is adopted based on the failure number of each component. The explicit expression of the long-run average cost rate is derived. Furthermore, we investigate the optimal policies of series system and single-component system respectively, the explicit relationship between them is determined in the form of a theorem for the first time. It shows that the optimal replacement policy of a component in a series system is not less than that when it forms a single-component system, and the former is non-decreasing with the number of components. Some other analytical results are also obtained. Based on these useful results, an efficient algorithm is devised to search the optimal joint policy which leads to an elegant, mathematical appealing analysis that is easy to use in practice. Finally, illustrative examples are provided to demonstrate the proposed model and the method. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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8. Improved average complexity for comparison-based sorting.
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Iwama, Kazuo and Teruyama, Junichi
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MATHEMATICAL analysis - Abstract
This paper studies the average complexity on the number of comparisons for sorting algorithms. Its information-theoretic lower bound is n lg n − 1.4427 n + O (log n). For many efficient algorithms, the first n lg n term is easy to achieve and our focus is on the (negative) constant factor of the linear term. The current best value is −1.3999 for the MergeInsertion sort. Our new value is −1.4106, narrowing the gap by some 25%. An important building block of our algorithm is "two-element insertion," which inserts two elements A and B , A < B , into a sorted sequence T. This insertion algorithm is still sufficiently simple for rigorous mathematical analysis and works well for a certain range of the length of T for which the simple binary insertion does not, thus allowing us to take a complementary approach together with the binary insertion. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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9. Deterministic and stochastic damage detection via dynamic response analysis.
- Author
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Oberguggenberger, Michael and Schwarz, Martin
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MONTE Carlo method , *ACOUSTIC models , *MATHEMATICAL analysis , *MARKOV chain Monte Carlo , *SOUND waves , *ALGORITHMS - Abstract
The paper proposes a method of damage detection in elastic materials, which is based on analyzing the time-dependent (dynamic) response of the material excited by an acoustic signal. A case study is presented consisting of experimental measurements and their mathematical analysis. The decisive parameters (wave speed and damping coefficient) of a mathematical model of the acoustic wave are calibrated by comparing the measurement data with the numerically evaluated exact solution predicted by the mathematical model. The calibration is done both deterministically by minimizing the square error over time and stochastically by a Bayesian approach, implemented through the Metropolis-Hastings algorithm. The resulting posterior distribution of the parameters can be used to construct a Bayesian test for damage. [ABSTRACT FROM AUTHOR]
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- 2020
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10. A novel Grouping Coral Reefs Optimization algorithm for optimal mobile network deployment problems under electromagnetic pollution and capacity control criteria.
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Salcedo-Sanz, Sancho, García-Díaz, Pilar, Del Ser, Javier, Bilbao, Miren Nekane, and Portilla-Figueras, José Antonio
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ALGORITHMS , *POLLUTION , *MATHEMATICAL optimization , *MATHEMATICAL models , *MATHEMATICAL analysis - Abstract
This paper proposes a novel optimization algorithm for grouping problems, the Grouping Coral Reefs Optimization algorithm, and describes its application to a Mobile Network Deployment Problem (MNDP) under four optimization criteria. These criteria include economical cost and coverage, and also electromagnetic pollution control and capacity constraints imposed at the base stations controllers, which are novel in this study. The Coral Reefs Optimization algorithm (CRO) is a recently-proposed bio-inspired approach for optimization, based on the simulation of the processes that occur in coral reefs, including reproduction, fight for space or depredation. This paper presents a grouping version of the CRO, which has not previously evaluated before. Grouping meta-heuristics are characterized by variable-length encoding solutions, and have been successfully applied to a number of different optimization and assignment problems. The GCRO proposed is a novel contribution to the intelligent systems field, which is able to improve results obtained by two alternative grouping algorithms such as grouping genetic algorithms and grouping Harmony Search. The performance of the proposed GCRO and the algorithms for comparison has been tested with real data in a case study of a MNDP in Alcalá de Henares, Madrid, Spain. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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11. An algorithmic approach to group decision making problems under fuzzy and dynamic environment.
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Gupta, Mahima and Mohanty, B.K.
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ALGORITHMS , *FUZZY systems , *MATHEMATICAL optimization , *MATHEMATICAL models , *MATHEMATICAL analysis - Abstract
Our paper introduces a new methodology to solve group decision-making problems under fuzzy and dynamic environment. The methodology takes group members’ linguistically defined pair wise preferences of alternatives in different time intervals and aggregates them across the intervals to obtain each member's net preference levels. Each member's net preference levels are again aggregated across the members to obtain the group's preference. Our paper attaches higher importance to the members whose involvement in the decision process is more recent than the members who opined their views in the past. The fuzzy aggregation operator, IOWA (Induced Ordered Weighted Average) is used to aggregate their views in accordance to their importance in the group. The Ranked_List algorithm, introduced in our paper, inputs the aggregated views of the members in pair wise form and produces the set of sequences of ranked list of alternatives representing the group's consensus view as output. The Ranked_List algorithm is validated and analyzed through a series of synthetic data sets and its results are compared with a movie selection case study. The methodology is illustrated with a numerical example. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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12. Dynamical analysis and robust control for dive plane of supercavitating vehicles.
- Author
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Phuc, Bui Duc Hong, You, Sam-Sang, Rathore, Natwar Singh, and Kim, Hwan-Seong
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VEHICLES , *ALGORITHMS , *MATHEMATICAL models , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
Highlights • Dynamical analysis has been provided to describe nonlinear behavior of supercavitating vehicles. • Robust H∞ loop-shaping synthesis with modified PID algorithm is proposed to control the dive plane maneuver of the HSSV. • Multi-objective control problems are solved using BMI optimization of an equivalent Schur formula. • Control scheme has the low order structure and provides robustness against uncertainties. • Integrated robust controller can deal with high parametric uncertainties and suppress exogenous disturbances and sensor noises. Abstract The high-speed supercavitating vehicle (HSSV) utilizes advanced technology that enables an underwater vehicle to reach its unprecedented high speed. The vertical motion control of the HSSV is challenging problem because of its complex dynamics with nonlinear planing force, parametric uncertainties, external disturbances, actuator saturation, and sensor noises. This paper deals with dynamical analysis and a robust H∞ loop-shaping synthesis with modified PID (proportional-integral-derivative) algorithm to control the dive plane maneuver of the HSSV. Typically, the control scheme has the low order structure and provides robustness against dynamic uncertainties, which can be implemented using the bilinear matrix inequality (BMI) optimization of an equivalent Schur formula. Simulation results show that the controlled vehicle system provides good performance and high robustness against uncertainties, ensuring no-overshoot and fast in time-domain responses. In addition, the control algorithm can decouple the dynamic interactions in the multi-input multi-output (MIMO) system, overcoming parametric uncertainty, planing force, and actuator saturation while minimizing the effect of the strong external disturbances and measurement noises. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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13. Numerical aspects of the nonstationary modified linearized Bregman algorithm.
- Author
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Buccini, Alessandro, Park, Yonggi, and Reichel, Lothar
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ALGORITHMS , *NUMERICAL analysis , *NUMERICAL solutions to differential equations , *LINEAR equations , *MATHEMATICAL analysis - Abstract
The solution of discrete ill-posed problems has been a subject of research for many years. Among the many methods described in the literature, the Bregman algorithm has attracted a great deal attention and been widely investigated. Recently, a nonstationary preconditioned version of this algorithm, referred to as the nonstationary modified linearized Bregman algorithm, was proposed. The aim of this paper is to discuss numerical aspects of this algorithm and to compare computed results with known theoretical properties. We also discuss the effect of several parameters required by the algorithm on the computed solution. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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14. Queuing search algorithm: A novel metaheuristic algorithm for solving engineering optimization problems.
- Author
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Zhang, Jinhao, Xiao, Mi, Gao, Liang, and Pan, Quanke
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ALGORITHMS , *MATHEMATICAL optimization , *MATHEMATICAL analysis , *CONSUMERS , *CUSTOMER services - Abstract
This paper presents a novel metaheuristic algorithm called queuing search (QS), which is inspired from human activities in queuing. Some common phenomena are considered in QS: (1) customers actively follow the queue that provides fast service; (2) each customer service is mainly affected by the staff or customer itself; and (3) a customer can be influenced by others during the service when the queue order is not strictly maintained. The performance of QS is tested on 30 bound-constrained benchmark functions scalable with 30 and 100 dimensions from CEC 2014, 5 standard and 4 challenging constrained engineering optimization problems. Meanwhile, comparisons are performed among the results of QS and some state-of-the-art or well-known metaheuristic algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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15. A continuum-atomistic multi-scale technique for nonlinear behavior of nano-materials.
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Khoei, A.R., Sameti, A. Rezaei, and Kazerooni, Y. Nikravesh
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KINEMATICS , *FINITE element method , *ALGORITHMS , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
Highlights • A hierarchical RVE-based continuum-atomistic multi-scale procedure is developed. • The inter-scale kinematic and energetic consistency principals are exploited. • The kinematic compatibility is applied by the atomistic periodic boundary conditions. • The energetic consistency is satisfied by the Hill-Mandel periodic boundary conditions. • Coarse-scale is modeled using the stress tensor and tangent modulus computed from atomistic RVE. Abstract In this paper, a hierarchical RVE-based continuum-atomistic multi-scale procedure is developed to model the nonlinear behavior of nano-materials. The atomistic RVE is accomplished in consonance with the underlying atomistic structure, and the inter-scale consistency principals, i.e. kinematic and energetic consistency principals, are exploited. To ensure the kinematic compatibility between the fine- and coarse-scales, the implementation of periodic boundary conditions is elucidated for the fully atomistic method. The material properties of coarse-scale are modeled with the nonlinear finite element method, in which the stress tensor and tangent modulus are computed using the Hill-Mandel principal through the atomistic RVE. In order to clearly represent the mechanical behavior of the fine-scale, the stress-strain curves of the atomistic RVE undergoing distinct type of deformation modes are delineated. These results are then assessed to obtain the proper fine-scale parameters for the multi-scale analysis. Finally, several numerical examples are solved to illustrate the capability of the proposed computational algorithm. Graphical abstract Schematically representation of the hierarchical atomistic-continuum multi-scale procedure. Image, graphical abstract [ABSTRACT FROM AUTHOR]
- Published
- 2018
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16. Equimatchable claw-free graphs.
- Author
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Akbari, Saieed, Alizadeh, Hadi, Ekim, Tınaz, Gözüpek, Didem, and Shalom, Mordechai
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GRAPH theory , *MATCHING theory , *ALGORITHMS , *DISCRETE systems , *MATHEMATICAL analysis - Abstract
A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide the first characterization of claw-free equimatchable graphs by identifying the equimatchable claw-free graph families. This characterization implies an efficient recognition algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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17. Prefix and suffix reversals on strings.
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Fertin, Guillaume, Jankowiak, Loïc, and Jean, Géraldine
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STRING , *PERMUTATIONS , *ALGORITHMS , *PARAMETERS (Statistics) , *MATHEMATICAL analysis - Abstract
The Sorting by Prefix Reversals problem consists in sorting the elements of a given permutation π using a minimum number of prefix reversals, i.e. reversals that always involve the leftmost element of π . A natural extension of this problem is to consider strings, in which any letter may appear several times, rather than permutations. In strings, three different types of problems arise: grouping (given a string S , transform it so that all identical letters are consecutive), sorting (a constrained version of grouping, in which the target string must be lexicographically ordered) and rearranging (given two strings S and T , transform S into T ). In this paper, we study these three problems, under an algorithmic viewpoint, in the setting where two operations, rather than one, are allowed: namely, prefix and suffix reversals — where a suffix reversal must always involve the rightmost element of the string. We first compare the “prefix reversals only” case to our case, before presenting a series of algorithmic results on these three problems concerning polynomiality, constant ratio approximation algorithms, NP-hardness and fixed-parameterized tractability. These results depend on the size k of the alphabet on which the strings are built, with a particular focus on small-sized alphabet instances (i.e., k = O ( 1 ) ) and big-sized alphabet instances (i.e. n − k = O ( 1 ) , where n is the length of the input string(s)). [ABSTRACT FROM AUTHOR]
- Published
- 2018
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18. Multi-objective optimization of an integrated gasification combined cycle for hydrogen and electricity production.
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Al-Zareer, Maan, Dincer, Ibrahim, and Rosen, Marc A.
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MATHEMATICAL optimization , *HYDROGEN , *ELECTRICITY , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
In this paper, an integrated coal gasification combined cycle system for the production of hydrogen and electricity is optimized in terms of energy and exergy efficiencies, and the amount and cost of the produced hydrogen and electricity. The integrated system is optimized by focusing on the conversion process of coal to syngas. A novel optimization process is developed which integrates an artificial neural network with a genetic algorithm. The gasification system is modeled and simulated with Aspen Plus for large ranges of operating conditions, where the artificial neural network method is used to represent the simulation results mathematically. The mathematical model is then optimized using a genetic algorithm method. The optimization demonstrates that the lower is the grade of coal of the three considered coals, the less expensive is the hydrogen and electricity that can be produced by the considered integrated gasification combined cycle (IGCC) system. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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19. Optimal tracking control of artificial gas-lift process.
- Author
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Shi, Jing, Al-Durra, Ahmed, and Boiko, Igor
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COMPUTER simulation , *ALGORITHMS , *CHOKED flow (Fluid dynamics) , *MATHEMATICAL optimization , *MATHEMATICAL analysis - Abstract
Artificial gas-lift (AGL) technique is commonly used to enhance oil production when the reservoir pressure in wells is not enough to sustain acceptable oil flow rate. However, the gas-lift wells are prone to instability, characterized by regular oscillations of pressure and flow. This phenomenon is known as casing-heading instability. It results in production loss and negative impact on downstream equipment, and has been a challenging problem to both industry and academia. In this paper, a novel concept of optimal tracking control is proposed for stabilization and operating mode transition in gas-lift wells when casing-heading phenomenon occurs. The stability of artificial gas-lift process is ensured by manipulating both gas lift choke and oil production choke, where the openings of both choke valves can vary from fully closed to fully open. Through the simulation of the open-loop system, a stability map of AGL process is produced. Then a trajectory optimization algorithm is developed based on this stability map, which is synthesized with a tracking controller to achieve trajectory optimization control. Also, a nonlinear state observer is designed to ensure estimation of unmeasurable variables. Through simulation studies, the effectiveness of proposed trajectory optimization control is demonstrated. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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20. On the computation and physical interpretation of semi-positive reaction network invariants.
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Alobaid, Aisha, Salami, Hossein, and Adomaitis, Raymond A.
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CHEMICAL reactions , *INVARIANTS (Mathematics) , *ALGORITHMS , *MATHEMATICAL optimization , *MATHEMATICAL analysis - Abstract
In this paper, we examine the mathematical structure of chemical reaction networks with the goals of identifying reaction invariant states and determining their physical significance. A combined species-reaction graph/convex analysis approach is developed to find semi-positive invariant states associated with a reaction network. Application of this graphical/algebraic reaction network analysis approach to four different chemical processes reveals that reaction invariants can represent conserved quantities other than elemental balances. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
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21. Mechanism design for one-facility location game with obnoxious effects on a line.
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Mei, Lili, Ye, Deshi, and Zhang, Guochuan
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UTILITY functions , *MATHEMATICAL models , *MATHEMATICAL analysis , *NUMERICAL analysis , *ALGORITHMS - Abstract
In this paper, we introduce obnoxious effects into obnoxious facility location games on a line, where each agent i has a private location x i on a closed interval [ 0 , 1 ] and one facility will be built on a location y in the interval according to the bids of all the agents. In addition, there are two thresholds d 1 and d 2 in the utility function of each agent, where 0 ≤ d 1 ≤ d 2 ≤ 1 . Denote d ( y , x i ) = | y − x i | to be the distance between agent i and the facility on the location y . The utility function of agent i is 0 if d ( y , x i ) is at most d 1 ; 1 if d ( y , x i ) is at least d 2 ; otherwise a linear increasing function between 0 and 1. Each agent attempts to get the largest utility while the social welfare is to maximize the sum of all the agents' utilities. The classic obnoxious facility game [4,11] is a special case of our problem when d 1 = 0 and d 2 = 1 . In this work, we first study the hardness of approximate mechanism design on this generalized problem, which states that our problem cannot admit any deterministic strategy-proof mechanism with bounded approximation ratio if d 1 ≥ 1 2 . Then we limit the thresholds to some ranges, both deterministic and randomized strategy-proof mechanisms are studied, and the approximation ratios vary with the specific values of d 1 and d 2 . [ABSTRACT FROM AUTHOR]
- Published
- 2018
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22. Investigating results and performance of search and construction algorithms for word-based LFSRs, [formula omitted]-LFSRs.
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Bishoi, Susil Kumar and Matyas, Vashek
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ALGORITHMS , *SEARCH algorithms , *POLYNOMIALS , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Linear feedback shift registers (LFSRs) play a significant role in communications security and we investigate design of a selected class of word-based LFSRs known as σ -LFSRs. Both the search algorithm and the construction algorithm generate efficient primitive σ -LFSRs. The search algorithm first constructs the σ -polynomial and then checks the primitiveness of the σ -polynomial, whereas the construction algorithm for the σ -LFSR, first finds a primitive polynomial f ( x ) and then constructs the primitive σ -LFSR from f ( x ) . In this paper, we present some novel results pertaining to the search algorithm for primitive σ -LFSR along with the exhaustive search space complexity of the search algorithm for σ -LFSRs. Then we investigate and compare the performance of the construction algorithm with the search algorithm for the primitive σ -LFSR. Finally, the number of σ -LFSRs similar to the σ -LFSRs generated by the construction algorithm is provided. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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23. A generalization of the rectangle condition.
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Kwon, Bo-hyun
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RECTANGLES , *MATHEMATICAL decomposition , *NUMERICAL analysis , *MATHEMATICAL analysis , *ALGORITHMS - Abstract
In this paper, we define the connecting rectangle condition to check whether or not a Heegaard splitting is strongly irreducible which is a variation of the rectangle condition by Casson and Gordon. We define a general version of the rectangle condition. Moreover, with a similar condition defined on an n -bridge decomposition, we can check whether or not the Hempel distance of an n -bridge decomposition is greater than or equal to two. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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24. Structure-preserving numerical methods for the fractional Schrödinger equation.
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Wang, Pengde and Huang, Chengming
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SCHRODINGER equation , *PARTIAL differential equations , *ALGORITHMS , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
This paper considers the long-time integration of the nonlinear fractional Schrödinger equation involving the fractional Laplacian from the point of view of symplectic geometry. By virtue of a variational principle with the fractional Laplacian, the equation is first reformulated as a Hamiltonian system with a symplectic structure. Then, by introducing a pair of intermediate variables with a fractional operator, the equation is reformulated in another form for which more conservation laws are found. When reducing to the case of integer order, they correspond to multi-symplectic conservation law and local energy conservation law for the classic Schrödinger equation. After that, structure-preserving algorithms with the Fourier pseudospectral approximation to the spatial fractional operator are constructed. It is proved that the semi-discrete and fully discrete systems satisfy the corresponding symplectic or other conservation laws in the discrete sense. Numerical tests are performed to validate the efficiency of the methods by showing their remarkable conservation properties in the long-time simulation. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
25. Advances and trends in visual crowd analysis: A systematic survey and evaluation of crowd modelling techniques.
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Zitouni, M. Sami, Bhaskar, H., Dias, J., and Al-Mualla, M.E.
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ARTIFICIAL neural networks , *ARTIFICIAL intelligence , *MATHEMATICAL optimization , *MATHEMATICAL analysis , *ALGORITHMS - Abstract
Visual recognition of crowd dynamics has had a huge impact on several applications including surveillance, situation awareness, homeland security and intelligent environments. However, the state-of-the-art in crowd analysis has become diverse due to factors such as: (a) the underlying definition of a crowd, (b) the constituent elements of the crowd processing model, (c) its application, hence (d) the dataset and (e) the evaluation criteria available for benchmarking. Although such diversity is healthy, the techniques for crowd modelling thus developed have failed to establish credibility therefore becoming unreliable and of questionable validity across different research disciplines. This paper aims to give an account of such issues by deducing key statistical evidence from the existing literature and providing recommendations towards focusing on the general aspects of techniques rather than any specific algorithm. The advances and trends in crowd analysis are drawn in the context of crowd modelling studies published in leading journals and conferences over the past 7 years. Finally, this paper shall also provide a qualitative and quantitative comparison of some existing methods using various publicly available crowd datasets to substantiate some of the theoretical claims. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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26. Semi-transitive orientations and word-representable graphs.
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Halldórsson, Magnús M., Kitaev, Sergey, and Pyatkin, Artem
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GRAPH theory , *SET theory , *LINEAR statistical models , *MATHEMATICAL analysis , *ALGORITHMS - Abstract
A graph G = ( V , E ) is a word-representable graph if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if ( x , y ) ∈ E for each x ≠ y . In this paper we give an effective characterization of word-representable graphs in terms of orientations. Namely, we show that a graph is word-representable if and only if it admits a semi-transitive orientation defined in the paper. This allows us to prove a number of results about word-representable graphs, in particular showing that the recognition problem is in NP, and that word-representable graphs include all 3-colorable graphs. We also explore bounds on the size of the word representing the graph. The representation number of G is the minimum k such that G is a representable by a word, where each letter occurs k times; such a k exists for any word-representable graph. We show that the representation number of a word-representable graph on n vertices is at most 2 n , while there exist graphs for which it is n / 2 . [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
27. Inertial/celestial-based fuzzy adaptive unscented Kalman filter with Covariance Intersection algorithm for satellite attitude determination.
- Author
-
Wang, Xiaochu, You, Zheng, and Zhao, Kaichun
- Subjects
- *
KALMAN filtering , *AEROSPACE engineering , *NUMERICAL analysis , *MATHEMATICAL analysis , *ALGORITHMS - Abstract
This paper deals with the attitude determination algorithm for the satellite with an attitude measurement unit that is comprised of one gyroscope and two star trackers installed perpendicularly. Since the data updating rate of star trackers is typically lower than that of the gyro and filter, appropriate compensation is made for star sensors, but this results in more difficulties of determining the performed noise level. A fuzzy adaptive tuning method is used to help tuning, and with modified Rodrigues parameters and rotation vector to represent attitude error, a fuzzy adaptive unscented Kalman filter with minimal skew sampling method is realized, which works as a sub-system and estimates sub-optimal attitude states and gyro bias. Two such sub-systems are federated into the framework of Covariance Intersection algorithm to achieve data fusion for an optimal attitude and gyro bias estimation in system level. Simulation is performed to verify the attitude determination algorithm presented in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
28. Ramification of local rings along valuations.
- Author
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Cutkosky, Steven Dale and Vinh, Pham An
- Subjects
- *
LOCAL rings (Algebra) , *RING theory , *MATHEMATICAL formulas , *MATHEMATICS theorems , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
In this paper we discuss stable forms of extensions of algebraic local rings along a valuation in all dimensions over a field k of characteristic zero, and generalize a formula of Ghezzi, Hà and Kashcheyeva describing the extension of associated graded rings along the valuation for stable extensions of regular algebraic local rings of dimension two to arbitrary ground fields k of characteristic zero. We discuss the failure of this result in positive characteristic. The main technique used in this paper is the algorithm for constructing generating sequences of Cutkosky and Vinh (2014) [6] . In Theorem 1.4 , we show that the stable forms of extensions of regular algebraic local rings of dimension two over arbitrary ground fields of characteristic zero have a particularly simple relation between their generating sequences. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
29. Approximate inverse preconditioners with adaptive dropping.
- Author
-
Kopal, Jiří, Rozložník, Miroslav, and Tůma, Miroslav
- Subjects
- *
ALGORITHMS , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICAL decomposition , *ORTHOGONAL decompositions - Abstract
It is well-known that analysis of incomplete Cholesky and LU decompositions with a general dropping is very difficult and of limited applicability, see, for example, the results on modified decompositions (Dupont et al., 1968; Gustafsson, 1978; Bern et al., 2006) and later results based on similar concepts. This is true not only for the dropping based on magnitude of entries but it also applies to algorithms that use a prescribed sparsity pattern. This paper deals with dropping strategies for a class of AINV-type incomplete decompositions (Benzi et al., 1996) that are based on the generalized Gram–Schmidt process. Its behavior in finite precision arithmetic has been discussed in Rozložník et al. (2012). This analysis enables better understanding of the incomplete process, and the main goal of the paper is to propose a new adaptive dropping strategy and to illustrate its efficiency for problems in structural mechanics. In addition, we add a brief comparison with another approximate inverse preconditioning strategy that is based on different principles and used in engineering applications. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
30. A three-term conjugate gradient algorithm for large-scale unconstrained optimization problems.
- Author
-
Deng, Songhai and Wan, Zhong
- Subjects
- *
MATHEMATICAL optimization , *PROBLEM solving , *APPROXIMATION theory , *ALGORITHMS , *STOCHASTIC convergence , *MATHEMATICAL analysis - Abstract
In this paper, a three-term conjugate gradient algorithm is developed for solving large-scale unconstrained optimization problems. The search direction at each iteration of the algorithm is determined by rectifying the steepest descent direction with the difference between the current iterative points and that between the gradients. It is proved that such a direction satisfies the approximate secant condition as well as the conjugacy condition. The strategies of acceleration and restart are incorporated into designing the algorithm to improve its numerical performance. Global convergence of the proposed algorithm is established under two mild assumptions. By implementing the algorithm to solve 75 benchmark test problems available in the literature, the obtained results indicate that the algorithm developed in this paper outperforms the existent similar state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
31. Impacts of memory on a regular lattice for different population sizes with asynchronous update in spatial snowdrift game.
- Author
-
Shu, Feng, Liu, Xingwen, and Li, Min
- Subjects
- *
LATTICE theory , *CRYSTAL lattices , *ALGORITHMS , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
Memory is an important factor on the evolution of cooperation in spatial structure. For evolutionary biologists, the problem is often how cooperation acts can emerge in an evolving system. In the case of snowdrift game, it is found that memory can boost cooperation level for large cost-to-benefit ratio r , while inhibit cooperation for small r . Thus, how to enlarge the range of r for the purpose of enhancing cooperation becomes a hot issue recently. This paper addresses a new memory-based approach and its core lies in: Each agent applies the given rule to compare its own historical payoffs in a certain memory size, and take the obtained maximal one as virtual payoff. In order to get the optimal strategy, each agent randomly selects one of its neighbours to compare their virtual payoffs, which can lead to the optimal strategy. Both constant-size memory and size-varying memory are investigated by means of a scenario of asynchronous updating algorithm on regular lattices with different sizes. Simulation results show that this approach effectively enhances cooperation level in spatial structure and makes the high cooperation level simultaneously emerge for both small and large r . Moreover, it is discovered that population sizes have a significant influence on the effects of cooperation. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
32. Sensor fault detection and isolation of an industrial gas turbine using partial adaptive KPCA.
- Author
-
Navi, Mania, Meskin, Nader, and Davoodi, Mohammadreza
- Subjects
- *
GAS turbines , *FAULT diagnosis , *ALGORITHMS , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
In this paper, sensor fault detection and isolation of time-varying nonlinear dynamical systems is studied by utilizing an adaptive kernel principal component analysis (KPCA) solution as a useful method to overcome the weaknesses of conventional KPCA approach in dealing with time-varying dynamical processes. Toward this goal, adaptive Hotelling's T 2 is used with KPCA to tackle the time-varying behavior of nonlinear systems. Moreover, for fault isolation, partial adaptive KPCA (AKPCA) is proposed where a set of residual signals is generated based on the structured residual set framework. The simulation studies demonstrate that using the proposed methodology, the occurrence of sensor faults in the nonlinear dynamic model of an aeroderivative gas turbine can be effectively detected and isolated in the presence of component degradation. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
33. Isolating incipient sensor fault based on recursive transformed component statistical analysis.
- Author
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Shang, Jun, Chen, Maoyin, Ji, Hongquan, and Zhou, Donghua
- Subjects
- *
DETECTORS , *FAULT diagnosis , *ALGORITHMS , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
This paper considers the isolation problem of incipient sensor fault. Based on recursive transformed component statistical analysis (RTCSA), two different isolation methods are proposed. The first method is called subspace reconstruction, where elements in specific subspaces are eliminated, and then reconstructed by minimizing the reconstructed detection index. The faulty variable is determined by the least scaled reconstructed detection index. The second method is called subblock detection, which has less online computational complexity. The subblocks of the measurement matrix are sequentially selected in each sliding window to calculate the subblock detection indices, and the faulty variable is determined by the largest subblock detection margin. Compared with the existing isolation methods such as reconstruction-based contribution (RBC) and its variant termed as average residual-difference reconstruction contribution plot (ARdR-CP), the superior isolation performances of the proposed methods are illustrated by a numerical example as well as a simulation on a continuous stirred tank reactor. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
34. Dynamic fault prognosis for multivariate degradation process.
- Author
-
Wang, Xiuli, Jiang, Bin, Lu, Ningyun, and Zhang, Chuanyu
- Subjects
- *
STOCHASTIC analysis , *MATHEMATICAL analysis , *TIME series analysis , *PHASE space , *ALGORITHMS - Abstract
Stochastic characteristics of degradation process provides a great challenge for multi-step fault prognosis. Prediction accuracy is a key feature for multivariable time series in the degradation process. In order to achieve good prediction accuracy, it is necessary to take time varying feature of time series into consideration. This paper develops a dynamic multi-step fault prognosis approach for the multivariable time series in degradation process. Firstly, a time varying dynamic model is established via multivariable phase space reconstruction (PSR) method. Then a hybrid algorithm combining iterative dynamic least square-support vector regression (LS-SVR) method and moving window mechanism is proposed for multi-step degradation evolution prediction before fault happening. Finally, a comparative case study on fault prognosis is provided to validate the effectiveness and the feasibility of the proposed algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
35. Dynamics of complex-valued neural networks with variable coefficients and proportional delays.
- Author
-
Song, Qiankun, Yu, Qinqin, Zhao, Zhenjiang, Liu, Yurong, and Alsaadi, Fuad E.
- Subjects
- *
ARTIFICIAL neural networks , *COEFFICIENTS (Statistics) , *MATHEMATICAL analysis , *ALGORITHMS , *ROBUST control - Abstract
In this paper, the dynamics including boundedness and stability for a general class of complex-valued neural networks with variable coefficients and proportional delays are investigated. By employing inequality techniques and mathematical analysis method, some sufficient criteria to guarantee boundedness and global exponential stability are established for the considered neural networks. As a special case that the coefficients of networks are constants, sufficient criteria are also derived to guarantee the existence, uniqueness and global exponential stability of the equilibrium point. This work generalizes and improves previously known results, and the obtained criteria can be tested and applied easily in practice. An illustrative example demonstrates the feasibility of the proposed results. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
36. Guided color consistency optimization for image mosaicking.
- Author
-
Xie, Renping, Xia, Menghan, Yao, Jian, and Li, Li
- Subjects
- *
ALGORITHMS , *MATHEMATICAL optimization , *MACHINE theory , *MATHEMATICAL analysis , *MACHINE translating , *SYSTEM analysis - Abstract
This paper studies the problem of color consistency correction for sequential images with diverse color characteristics. Existing algorithms try to adjust all images to minimize color differences among images under a unified energy framework, however, the results are prone to presenting a consistent but unnatural appearance when the color difference between images is large and diverse. In our approach, this problem is addressed effectively by providing a guided initial solution for the global consistency optimization, which avoids converging to a meaningless integrated solution. First of all, to obtain the reliable intensity correspondences in overlapping regions between image pairs, we creatively propose the histogram extreme point matching algorithm which is robust to image geometrical misalignment to some extents. In the absence of the extra reference information, the guided initial solution is learned from the major tone of the original images by searching some image subset as the reference, whose color characteristics will be transferred to the others via the paths of graph analysis. Thus, the final results via global adjustment will take on a consistent color similar to the appearance of the reference image subset. Several groups of convincing experiments on both the synthetic dataset and the challenging real ones sufficiently demonstrate that the proposed approach can achieve as good or even better results compared with the state-of-the-art approaches. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
37. Global LSMR(Gl-LSMR) method for solving general linear systems with several right-hand sides.
- Author
-
Mojarrab, M. and Toutounian, F.
- Subjects
- *
LINEAR systems , *ALGORITHMS , *FINITE volume method , *MATHEMATICAL models , *MATHEMATICAL analysis - Abstract
The global solvers are an attractive class of iterative solvers for solving linear systems with multiple right-hand sides. In this paper, first, a new global method for solving general linear systems with several right-hand sides is presented. This method is the global version of the LSMR algorithm presented by Fong and Saunders (2011). Then, some theoretical properties of the new method are discussed. Finally, numerical experiments from real applications are used to confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
38. Inferring strings from Lyndon factorization.
- Author
-
Nakashima, Yuto, Okabe, Takashi, I, Tomohiro, Inenaga, Shunsuke, Bannai, Hideo, and Takeda, Masayuki
- Subjects
- *
FACTORIZATION , *STRING theory , *MONOTONIC functions , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
The Lyndon factorization of a string w is a unique factorization ℓ 1 p 1 , … , ℓ m p m of w such that ℓ 1 , … , ℓ m is a sequence of Lyndon words that is monotonically decreasing in lexicographic order. In this paper, we consider the reverse-engineering problem on Lyndon factorization : Given a sequence S = ( ( s 1 , p 1 ) , … , ( s m , p m ) ) of ordered pairs of positive integers, find a string w whose Lyndon factorization corresponds to the input sequence S , i.e., the Lyndon factorization of w is in a form of ℓ 1 p 1 , … , ℓ m p m with | ℓ i | = s i for all 1 ≤ i ≤ m . Firstly, we show that there exists a simple O ( n ) -time algorithm if the size of the alphabet is unbounded, where n is the length of the output string. Secondly, we present an O ( n ) -time algorithm to compute a string over an alphabet of the smallest size. Thirdly, we show how to compute only the size of the smallest alphabet in O ( m ) time. Fourthly, we give an O ( m ) -time algorithm to compute an O ( m ) -size representation of a string over an alphabet of the smallest size. Finally, we propose an efficient algorithm to enumerate all strings whose Lyndon factorizations correspond to S . [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
39. A space efficient algorithm for the longest common subsequence in k-length substrings.
- Author
-
Zhu, Daxin, Wang, Lei, Wang, Tinran, and Wang, Xiaodong
- Subjects
- *
ALGORITHMS , *STRING theory , *COMPUTATIONAL complexity , *TOPOLOGICAL spaces , *MATHEMATICAL analysis - Abstract
Two space efficient algorithms to solve the L C S k problem and L C S ≥ k problem are presented in this paper. The algorithms improve the time and space complexities of the algorithms of Benson et al. [4] . The space cost of the first algorithm to solve the L C S k problem is reduced from O ( n 2 ) to O ( k n ) , if the size of the two input sequences are both n . The time and space costs of the second algorithm to solve the L C S ≥ k problem are both improved. The time cost is reduced from O ( k n 2 ) to O ( n 2 ) , and the space cost is reduced from O ( n 2 ) to O ( k n ) . In the case of k = O ( 1 ) , the two algorithms are both linear space algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
40. Attribute reduction based on k-nearest neighborhood rough sets.
- Author
-
Wang, Changzhong, Shi, Yunpeng, Fan, Xiaodong, and Shao, Mingwen
- Subjects
- *
MATHEMATICAL analysis , *A posteriori error analysis , *ANALYTICAL solutions , *MATHEMATICAL models , *ALGORITHMS - Abstract
Abstract Neighborhood rough sets are widely used as an effective tool to deal with numerical data. However, most of the existing neighborhood granulation models cannot well describe the neighborhoods of category-mixed samples when they are used to characterize the classification ability of a subset of attributes. In this paper, we propose a new neighborhood rough set model called k -nearest neighborhood rough sets. This model combines the advantages of both δ -neighborhood and k -nearest neighbor, and has a better ability to deal with this type of heterogeneous data than the existing models. We employ an iterative strategy to define rough approximations of a decision and discuss their monotonicity. Furthermore, an attribute reduction algorithm based on this model is designed. Experimental analysis shows that the proposed algorithm has better performance than some existing algorithms, especially the δ -neighborhood rough set model and k -nearest neighbor rough set model. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
41. State space model identification of multirate processes with time-delay using the expectation maximization.
- Author
-
Gu, Ya, Liu, Jicheng, Li, Xiangli, Chou, Yongxin, and Ji, Yan
- Subjects
- *
ALGORITHMS , *NUMERICAL analysis , *MATHEMATICAL analysis , *NONLINEAR mechanics , *COMPUTER simulation - Abstract
Abstract This paper presents the problems of state space model identification of multirate processes with unknown time delay. The aim is to identify a multirate state space model to approximate the parameter-varying time-delay system. The identification problems are formulated under the framework of the expectation maximization algorithm. Through introducing two hidden variables, a new expectation maximization algorithm is derived to estimate the unknown model parameters and the time-delays simultaneously. The effectiveness of the proposed algorithm is validated by a simulation example. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
42. Augmented complex-valued normalized subband adaptive filter: Algorithm derivation and analysis.
- Author
-
Wen, Pengwei, Zhang, Jiashu, Zhang, Sheng, and Li, Defang
- Subjects
- *
ALGORITHMS , *COMPUTER simulation , *NUMERICAL analysis , *MATHEMATICAL analysis , *ADAPTIVE filters - Abstract
Abstract In this paper, a novel augmented complex-valued normalized subband adaptive filter (ACNSAF) algorithm is proposed for processing the noncircular complex-valued signals. Based on the augmented statistics, the proposed algorithm is derived by computing a constraint cost function. Due to contain all second-order statistical properties, the ACNSAF algorithm can process the circular and noncircular complex-valued signals simultaneously. Moreover, the stability and mean square steady-state analysis of the proposed algorithm is derived by using the energy conservation principle. Computer simulation experiments on complex-valued system identification, prediction and noise cancelling show that the proposed algorithm achieves the improved mean square deviation and prediction gain compared to the ACNLMS algorithm. And the simulation results are consistent with the analysis results. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
43. A hybrid algorithm for Caputo fractional differential equations.
- Author
-
Salgado, G.H.O. and Aguirre, L.A.
- Subjects
- *
DIFFERENTIAL equations , *CAPUTO fractional derivatives , *ALGORITHMS , *HYBRID systems , *MATHEMATICAL analysis - Abstract
This paper is concerned with the numerical solution of fractional initial value problems (FIVP) in sense of Caputo’s definition for dynamical systems. Unlike for integer-order derivatives that have a single definition, there is more than one definition of non integer-order derivatives and the solution of an FIVP is definition-dependent. In this paper, the chief differences of the main definitions of fractional derivatives are revisited and a numerical algorithm to solve an FIVP for Caputo derivative is proposed. The main advantages of the algorithm are twofold: it can be initialized with integer-order derivatives, and it is faster than the corresponding standard algorithm. The performance of the proposed algorithm is illustrated with examples which suggest that it requires about half the computation time to achieve the same accuracy than the standard algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
44. An algorithm of determining T-spline classification.
- Author
-
Wang, Aizeng and Zhao, Gang
- Subjects
- *
SPLINE theory , *ALGORITHMS , *MATHEMATICAL analysis , *PROBLEM solving , *APPROXIMATION theory , *FUNCTIONAL analysis - Abstract
Highlights: [•] Aiming at the problem that how to classify T-splines this paper gives a mathematical analysis, and a sufficient condition of standard T-splines is also given. [•] Then this paper presents an algorithm of determining the T-spline classification, and we can get the inherently mathematical properties of T-splines by the algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
45. A nonhomogeneous super-twisting algorithm for systems of relative degree more than one.
- Author
-
Basin, Michael, Rodriguez-Ramirez, Pablo, Ding, Steven, and Dominic, Shane
- Subjects
- *
ALGORITHMS , *CONTINUOUS functions , *STOCHASTIC convergence , *COMPUTER simulation , *MATHEMATICAL analysis - Abstract
This paper presents a nonhomogeneous continuous super-twisting algorithm for systems of relative degree more than one. The conditions of finite-time convergence to the origin are obtained and the robustness of the designed algorithm is discussed. The paper concludes with numerical simulations illustrating performance of the designed algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
46. A second look at counting triangles in graph streams (corrected).
- Author
-
Cormode, Graham and Jowhari, Hossein
- Subjects
- *
GRAPH theory , *ALGORITHMS , *MATHEMATICAL analysis , *TOPOLOGY , *MATHEMATICAL proofs - Abstract
In this paper we present improved results on the problem of counting triangles in edge streamed graphs. For graphs with m edges and at least T triangles, we show that an extra look over the stream yields a two-pass streaming algorithm that uses O ( m ε 2.5 T polylog ( m ) ) space and outputs a ( 1 + ε ) approximation of the number of triangles in the graph. This improves upon the two-pass streaming tester of Braverman, Ostrovsky and Vilenchik, ICALP 2013, which distinguishes between triangle-free graphs and graphs with at least T triangle using O ( m T 1 / 3 ) space. Also, in terms of dependence on T , we show that more passes would not lead to a better space bound. In other words, we prove there is no constant pass streaming algorithm that distinguishes between triangle-free graphs from graphs with at least T triangles using O ( m T 1 / 2 + ρ ) space for any constant ρ ≥ 0 . [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
47. Constructions of ϵ-mono-components and mathematical analysis on signal decomposition algorithm.
- Author
-
Huang, Chao, Tan, Lihui, Zhang, Qian, and Yang, Lihua
- Subjects
- *
MATHEMATICAL analysis , *SIGNAL processing , *MATHEMATICAL decomposition , *ALGORITHMS , *TIME-frequency analysis - Abstract
The concept of mono-component is widely used in non-stationary signal processing and time-frequency analysis. A special class of mono-components, called ϵ-mono-components, were proposed in our recent publication. It was illustrated that this model coincides with the intuition of human beings on the physical mono-components very well provided that the parameter ϵ is sufficiently small. It is then very meaningful to construct desired ϵ-mono-components and design algorithms to decompose and represent non-stationary signals adaptively. This paper studies the constructions of ϵ-mono-components and makes mathematical analysis on an adaptive signal decomposition algorithm based on ϵ-mono-components. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
48. Directed hypergraphs: Introduction and fundamental algorithms—A survey.
- Author
-
Ausiello, Giorgio and Laura, Luigi
- Subjects
- *
GRAPH theory , *GEOMETRY , *HYPERGRAPHS , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Just as ordinary hypergraphs are a generalization of graphs, directed hypergraphs (DH) are a natural generalization of digraphs. A DH consists of a set of vertices V and a set of hyperarcs H , where a hyperarc is a pair < S , v > , S non empty subset of V and v ∈ V . DHs have a variety of applications: they have been used to represent functional dependency in databases, Horn formulae in propositional logic, and–or graphs, context free grammars etc. In the paper, after providing a brief historical introduction on the notion of DH and some relevant applications, various problems regarding DHs are surveyed and analyzed. In particular we consider the complexity of the reachability problem (together with its application in the related satisfiability problem for Horn CNF formulae) and the computation of transitive closure and transitive reduction of directed hypergraphs (together with its application to the computation of minimum coverings for a set of functional dependencies). Finally a short introduction to the problem of computing shortest hyperpaths in directed hypergraphs is provided. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
49. Detecting community structure in complex networks using an interaction optimization process.
- Author
-
Kim, Paul and Kim, Sangwook
- Subjects
- *
COMMUNITY organization , *MATHEMATICAL optimization , *ALGORITHMS , *MATHEMATICAL analysis , *STRUCTURAL analysis (Science) - Abstract
Most complex networks contain community structures. Detecting these community structures is important for understanding and controlling the networks. Most community detection methods use network topology and edge density to identify optimal communities; however, these methods have a high computational complexity and are sensitive to network forms and types. To address these problems, in this paper, we propose an algorithm that uses an interaction optimization process to detect community structures in complex networks. This algorithm efficiently searches the candidates of optimal communities by optimizing the interactions of the members within each community based on the concept of greedy optimization. During this process, each candidate is evaluated using an interaction-based community model. This model quickly and accurately measures the difference between the quantity and quality of intra- and inter-community interactions. We test our algorithm on several benchmark networks with known community structures that include diverse communities detected by other methods. Additionally, after applying our algorithm to several real-world complex networks, we compare our algorithm with other methods. We find that the structure quality and coverage results achieved by our algorithm surpass those of the other methods. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
50. On the Hosoya index of a family of deterministic recursive trees.
- Author
-
Chen, Xufeng, Zhang, Jingyuan, and Sun, Weigang
- Subjects
- *
RECURSION theory , *DETERMINISTIC processes , *TREE graphs , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
In this paper, we calculate the Hosoya index in a family of deterministic recursive trees with a special feature that includes new nodes which are connected to existing nodes with a certain rule. We then obtain a recursive solution of the Hosoya index based on the operations of a determinant. The computational complexity of our proposed algorithm is O ( log 2 n ) with n being the network size, which is lower than that of the existing numerical methods. Finally, we give a weighted tree shrinking method as a graphical interpretation of the recurrence formula for the Hosoya index. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
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