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This paper proposes a user-biometric-based image encryption using chaotic dynamical systems, SHA-256 hash function, and zigzag transformation. Three chaotic systems, namely, the Henon map, logistic map, and Lorenz system, are used to apply the chaotic properties to the encryption system. The hash value of the user biometric image is used to generate the initial value of the Henon map. The initial values for the logistic map and Lorenz system are generated from the hash value of the plain image. SHA-256 hash algorithm generates the hash values of the biometric and plain images. The plain image is scrambled using the two-dimensional chaotic values generated by the Henon map first. Next, the first scrambled image's pixels are XORed with the one-dimensional chaotic values generated from the logistic map and produce the second scrambled image. Finally, take the second scrambled image's pixels, and XOR them with the three-dimensional chaotic values generated from the Lorenz system and create the final encrypted image. The robustness and flexibility of the encryption system are analyzed using various security and performance analyses. The experiment results are compared with the existing algorithms to prove the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose two decomposition dynamical systems for solving strongly pseudomonotone variational inequalities given by a sum of two mappings. We prove that trajectories of these dynamical systems converge to the unique solution of the variational inequality. Also, we extend these algorithms for equilibrium problems and study their convergence rate. This approach is novel and the new algorithms can be considered as continuous-time versions of existing decomposition algorithms for variational inequalities and equilibrium problems. [ABSTRACT FROM AUTHOR]

Companies are eager to have a smart supply chain especially when they have a dynamic system. Industry 4.0 is a concept which concentrates on mobility and real-time integration. Thus, it can be considered as a necessary component that has to be implemented for a dynamic vehicle routing problem. The aim of this research is to solve large-scale DVRP (LSDVRP) in which the delivery vehicles must serve customer demands from a common depot to minimize transit costs while not exceeding the capacity constraint of each vehicle. In LSDVRP, it is difficult to get an exact solution and the computational time complexity grows exponentially. To find near-optimal answers for this problem, a hierarchical approach consisting of three stages: "clustering, route-construction, route-improvement" is proposed. The major contribution of this paper is dealing with LSDVRP to propose the three-stage algorithm with better results. The results confirmed that the proposed methodology is applicable. [ABSTRACT FROM AUTHOR]

An optimal feedback input design method for active parameter identification of dynamic nonlinear systems is presented. The problem is formulated in a receding horizon framework where extended Kalman filter is used for system identification and the optimal input is designed in a nonlinear model predictive control framework. Towards this end, a suitable optimality criterion related to the unknown parameters is proposed and motivated as an information measure. The aim of the optimal input design is to yield maximal information from the unknown system by minimising the cost related to the unknown parameters while maintaining some process performance and satisfying the possible constraints. Simulations are performed to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Monte Carlo computation has been widely applied in the field of dynamic systems. This paper focuses on the general framework in the implementation of sequential importance sampling by combining redrawing, resampling and rejection control simultaneously. The proposed algorithm is named as Redrawing Resampling Rejection Controlled Sequential Importance Sampling (RR-RC-SIS). It can reduce sampling computation and meanwhile maintain the diversity of random samples. Theoretical basis is given to prove that RR-RC-SIS has advantages in comparison with Rejection Controlled Sequential Importance Sampling. It also has practical value as illustrated in numerical simulation on blind deconvolution problem in digital communications. [ABSTRACT FROM AUTHOR]

In this article, mixed-effects state space models (MESSM, [Liu D, Lu T, Niu X-F, et al. Mixed-effects state-space models for analysis of longitudinal dynamic systems. Biometrics. 2011;67(2):476–485.]) are revisited. MESSM can be considered as an alternative to study the HIV dynamic in a longitudinal data environment, defining the mixed-effects component into state-space models setup. As in Liu et al.[Liu D, Lu T, Niu X-F, et al. Mixed-effects state-space models for analysis of longitudinal dynamic systems. Biometrics. 2011;67(2):476–485.], we consider a hierarchical structure to capture possible differences between the immune systems for different patients. We extend MESSM, allowing observational errors to follow a more flexible distribution to take account for heavy tails. Using the Bayesian paradigm, an efficient Markov Chain Monte Carlo (MCMC) algorithm based on McCausland et al. [McCausland WJ, Miller S, Pelletier D. Simulation smoothing for state.space models: A computational efficiency analysis. Comput Stat Data Anal. 2011;55(1):199–212.] is introduced for parameter and latent variables estimation. Moreover, the mixing variables obtained as a by-product of the scale mixture representation can be used to identify outliers. The methodology is illustrated using artificial and real datasets in order to investigate the properties and performance of the proposed model. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of H ∞ fault estimation observer design for T-S fuzzy nonlinear discrete-time descriptor systems in the finite frequency domain. First, a novel fault estimation observer for the augmented descriptor system is given. Based on Parseval's theorem and Lyapunov theory, the performance in the finite frequency domain is derived via time-domain method. Then, new sufficient conditions of admissibility and robust performance index for the dynamic error system are obtained as bilinear matrix inequalities. Meanwhile, an iterative linear matrix inequality algorithm is given to obtain the optimal solution. Finally, an example is given to demonstrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new algorithm for solving a variational inequality problem in a Hilbert space. The algorithm originates from an explicit discretization of a dynamical system in time. We establish the convergence of the algorithm for a class of non-monotone and Lipschitz continuous operators, provided by the sequentially weak-to-weak continuity of cost operators. The rate of convergence of the algorithm is also proved under some standard hypotheses. Moreover, the new algorithm uses variable step-sizes which are updated at each iteration by a cheap computation without linesearch. This step-size rule allows the resulting algorithm to work more easily without the prior knowledge of Lipschitz constant of operator. Also, it is particularly interesting in the case where the Lipschitz constant is unknown or difficult to approximate. Several numerical experiments are implemented to illustrate the theoretical results and also to compare with existing algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model is presented to numerically simulate the dynamical responses in a multi-cable suspension platform taking into account the slack cables and guiding devices. The state change of the cable (slack versus tensioned) is considered and is described mathematically by a complementary condition equation, and the interactions between the guiding wheels and the shaft wall are described by the Heaviside step function. The Lagrange's equation with constraints is used to derive the dynamic equations of the system, and a non-smooth generalized-α algorithm for non-smooth phenomena of multibody dynamics is applied to numerically solve the equations. The simulation results have shown the dynamic responses of the platform and the cable tension characters when different cables are excited by different longitudinal excitations. Moreover, the results have illustrated how the cable tension differences may affect the pressure on the shaft wall applied by the guiding devices. [ABSTRACT FROM AUTHOR]

This paper develops a parameter estimation algorithm for linear continuous-time systems based on the hierarchical principle and the parameter decomposition strategy. Although the linear continuous-time system is a linear system, its output response is a highly nonlinear function with respect to the system parameters. In order to propose a direct estimation algorithm, a criterion function is constructed between the response output and the observation output by means of the discrete sampled data. Then a scheme by combining the Newton iteration and the least squares iteration is builded to minimise the criterion function and derive the parameter estimation algorithm. In light of the different features between the system parameters and the output function, two sub-algorithms are derived by using the parameter decomposition. In order to remove the associate terms between the two sub-algorithms, a Newton and least squares iterative algorithm is deduced to identify system parameters. Compared with the Newton iterative estimation algorithm without the parameter decomposition, the complexity of the hierarchical Newton and least squares iterative estimation algorithm is reduced because the dimension of the Hessian matrix is lessened after the parameter decomposition. The experimental results show that the proposed algorithm has good performance. [ABSTRACT FROM AUTHOR]

Due to the great importance of the performance of load frequency controllers in power systems, a lot of effort have been performed to improve the performance of these controllers by fine tuning them. Evolutionary algorithms are the most popular techniques used to optimally tune the controllers. In this article, wind driven optimization (WDO) algorithm which is a newly developed evolutionary algorithm is used for tuning load frequency controllers. Based on simulation studies, the impact of different objective functions on the performance of the evolutionary algorithms in tuning the controllers is investigated. Also, using simulation studies carried out in a three areas interconnected power system, the effectiveness of the proposed optimization algorithm in comparison to other newly proposed evolutionary algorithms is demonstrated. Furthermore, the robustness of the proposed method in case of power system parameters and configuration variations is confirmed. [ABSTRACT FROM AUTHOR]

In this contribution, a new framework for -optimal reduction is presented, motivated by the local nature of both (tangential) interpolation and -optimal approximations. The main advantage is given by a decoupling of the cost of reduction from the cost of optimization, resulting in a significant speedup in -optimal reduction. In addition, a middle-sized surrogate model is produced at no additional cost and can be used e.g. for error estimation. Numerical examples illustrate the new framework, showing its effectiveness in producing -optimal reduced models at a far lower cost than conventional algorithms. Detailed discussions and optimality proofs are presented for applying this framework to the reduction of multiple-input, multiple-output linear dynamical systems. The paper ends with a brief discussion on how this framework could be extended to other system classes, thus indicating how this truly is a general framework for interpolatory reduction. [ABSTRACT FROM AUTHOR]

In engineering applications, one of the major challenges today is to develop reliable and robust control algorithms for complex networked systems. Controllability and observability of such systems play a crucial role in the design process. The underlying network structure may contain symmetries – caused, for example, by the coupling of identical building blocks – and these symmetries lead to repeated eigenvalues in a generic way. This complicates the design of controllers since repeated eigenvalues decrease the controllability of the system. In this paper, we will analyze the relationship between the controllability and observability of complex networked systems and symmetries using results from group representation theory. Furthermore, we will propose an algorithm to compute sparse input and output matrices based on projections onto corresponding isotypic components. We will illustrate our results with the aid of two guiding examples, a network withD4symmetry and the Petersen graph. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive gain algorithm for second-order sliding-mode control (2-SMC), specifically a super-twisting (STW)-like controller, with uniform finite/fixed convergence time, that is robust to perturbations with unknown bounds. It is shown that a second-order sliding mode is established as exact finite-time convergence to the origin if the adaptive gain does not have the ability to get reduced and converge to a small vicinity of the origin if the adaptation algorithm does not overestimate the control gain. The estimate of fixed convergence time of the studied adaptive STW-like controller is derived based on the Lyapunov analysis. The efficacy of the proposed adaptive algorithm is illustrated in a tutorial example, where the adaptive STW-like controller with uniform finite/fixed convergence time is compared to the adaptive STW controller with non-uniform finite convergence time. [ABSTRACT FROM AUTHOR]

In dynamical systems saddle points partition the domain into basins of attractions of the remaining locally stable equilibria. This situation is rather common especially in population dynamics models, like prey–predator or competition systems. Focusing on squirrels population models with niche, in this paper we design algorithms for the detection and the refinement of points lying on the separatrix manifold partitioning the phase space. We consider both the two populations and the three populations cases. To reconstruct the separatrix curve and surface, we apply the Partition of Unity method, which makes use of Wendland's functions as local approximants. [ABSTRACT FROM PUBLISHER]

Mathematical ideas from number theory, group theory, dynamical systems, and computer science have often been used to explain card tricks. Conversely, playing cards have been often used to illustrate the mathematical concepts of probability distributions and group theory. In this paper, we describe how the 21-card trick may be used to illustrate concepts such as a discrete dynamical system, a fixed point, and the stability of a fixed point. The 21-card trick is a way of dealing cards in order to predict a card that is selected by a volunteer, within three moves. The 21-card trick and its two generalizations are examples of piece-wise linear, non-homogeneous, discrete dynamical systems, all of which have a global stable fixed point. [ABSTRACT FROM PUBLISHER]

The purpose of this article is to provide validation for the approximate algebraic propagation algorithms to accommodate non-Gaussian dynamic processes. These algorithms have been developed to carry out Bayesian analysis based on conjugate forms and presented with detailed examples of response distributions such as Poisson and Lognormal. The validity of the approximation algorithms can be checked by introducing a metric (Hellinger divergence measure) over the distribution of the states (parameters) and use it to judge the approximation. Theoretical bounds for the efficacy of such procedure are discussed. [ABSTRACT FROM PUBLISHER]

As a wavefront sensor, the Shack–Hartmann wavefront sensor plays an important role in the wavefront measurement of human eyes. However, the low measurement accuracy and the small dynamic range of Shack–Hartmann wavefront sensor limit its application. In this paper, we present a matched-filter algorithm to improve the measurement accuracy by more than an order of magnitude. Moreover, we also introduce a new algorithm to extend the dynamic range of Shack–Hartmann wavefront sensor. With this method, the recorded spots of Shack–Hartmann wavefront sensor are not constrained to stay in the corresponding pixel area of the microlens. The result shows that the dynamic range can be extended from 57.1 to 160% for the first 24 items of Zernike wavefronts, respectively. The improvement by our methods makes the Shack–Hartmann more suitable for the measurement of highly aberrated eyes. [ABSTRACT FROM AUTHOR]

Cooperative trajectory planning is crucial for networked vehicles to respond rapidly in cluttered environments and has a significant impact on many applications such as air traffic or border security monitoring and assessment. One of the challenges in cooperative planning is to find a computationally efficient algorithm that can accommodate both the complexity of the environment and real hardware and configuration constraints of vehicles in the formation. Inspired by a local pursuit strategy observed in foraging ants, feasible and optimal trajectory planning algorithms are proposed in this paper for a class of nonlinear constrained cooperative vehicles in environments with densely populated obstacles. In an iterative hierarchical approach, the local behaviours, such as the formation stability, obstacle avoidance, and individual vehicle's constraints, are considered in each vehicle's (i.e. follower's) decentralised optimisation. The cooperative-level behaviours, such as the inter-vehicle collision avoidance, are considered in the virtual leader's centralised optimisation. Early termination conditions are derived to reduce the computational cost by not wasting time in the local-level optimisation if the virtual leader trajectory does not satisfy those conditions. The expected advantages of the proposed algorithms are (1) the formation can be globally asymptotically maintained in a decentralised manner; (2) each vehicle decides its local trajectory using only the virtual leader and its own information; (3) the formation convergence speed is controlled by one single parameter, which makes it attractive for many practical applications; (4) nonlinear dynamics and many realistic constraints, such as the speed limitation and obstacle avoidance, can be easily considered; (5) inter-vehicle collision avoidance can be guaranteed in both the formation transient stage and the formation steady stage; and (6) the computational cost in finding both the feasible and optimal solutions is low. In particular, the feasible solution can be computed in a very quick fashion. The minimum energy trajectory planning for a group of robots in an obstacle-laden environment is simulated to showcase the advantages of the proposed algorithms. [ABSTRACT FROM PUBLISHER]

The aim of this study was to identify differences in time–motion, modified training impulse, body load and movement behaviour between defenders, midfielders and forwards, during an 11-a-side simulated football game. Twenty elite youth male footballers from the same squad participated in this study (age: 18.1 ± 0.7 years old, body mass: 70.5 ± 4.3 kg, height: 1.8 ± 0.3 m and playing experience: 9.4 ± 1.3 years). All data were collected using GPS units (SPI-Pro, GPSports, Canberra, Australia). The movement behaviour was measured with kinematic data, used to calculate position-specific centroids (defenders, midfielders and forwards), and processed with non-linear statistical procedures (approximate entropy normalised and relative phase). There were significant effects and interactions in all variables across the players’ positions. The results showed that displacements of all players (defenders, midfielders and forwards) were nearer and more coordinated with their own position-specific centroids than with the other centroids. However, this coupling effect was stronger in midfield players and weaker in forwards. All players’ dynamical positioning showed more irregularity when related to the forwards’ centroid, as a consequence of their need to be less predictable when playing. The time–motion and physiological variables showed lower activity in forward players. Adding together, the results may contribute to a better understanding of players’ specific performances and football complexity. [ABSTRACT FROM AUTHOR]

Metabolic P (MP) grammars are a particular class of multiset rewriting grammars introduced in the MP theory for modelling metabolic processes. In this paper, a new algebraic formulation of inverse problems, based on MP grammars and Kronecker product, is given, for further motivating the correctness of the LGSS (Log-Gain Stoichiometric Stepwise) algorithm, introduced in 2010s for solving inverse problems in the MP framework. At the end of the paper, a section is included that introduces the problem of multicollinearity, which could arise during the execution of LGSS, and that defines an algorithm, based on a hierarchical clustering technique, that solves it in a suitable way. [ABSTRACT FROM PUBLISHER]

The main objective of this article is to mechanize the procedure of tracking and describing the various phases of deformation of a biological circular cell during micromanipulation. The devised vision-based methodology provides a real-time strategy to track and describe the cell deformation by extracting a geometric feature called dimple angle. An algorithm based on Snake was established to acquire the boundary of the indenting cell and measure the aforementioned feature. Micromanipulation experiments were conducted for zebrafish embryos. Experimental results were used to characterize the deformation of the manipulating embryo by the devised geometric parameter. The results demonstrated the high capability of the methodology. The proposed method is applicable to the micromanipulation of other circular biological embryos such as injection of the mouse oocyte/embryo. Supplemental materials are available for this article. Go to the publisher's online edition of theInternational Journal of Optomechatronicsto view the supplemental files. [ABSTRACT FROM AUTHOR]

Two different descriptions are used in the literature to formulate the optimal dynamic output feedback control problem for linear dynamical systems with white stochastic parameters and quadratic criteria, called the optimal compensation problem. One describes the matrix valued white stochastic processes involved, using a sum of deterministic matrices each one multiplied by a scalar stochastic process that is independent of the others. Another, that is more general and concise, uses Kronecker products instead. This article relates the statistics of both descriptions and shows their advantages and disadvantages. As to the first description, an important result that comes out is the minimum number of matrices multiplied by scalar, independent, stochastic processes needed to represent a certain matrix valued white stochastic process, together with an associated minimal representation. As to the second description, an important result concerns the generation of all Kronecker products that represent relevant statistics. Both results facilitate the specification of statistics of systems with white stochastic parameters. The second part of this article further exploits these results to perform an U–D factorisation of an algorithm to compute optimal dynamic output feedback controllers (optimal compensators) for linear discrete-time systems with white stochastic parameters and quadratic sum criteria. U–D factorisation of this type of algorithm is new. By solving several numerical examples, the U–D factored algorithm is compared with a conventional algorithm. [ABSTRACT FROM AUTHOR]

In this article, we give some comments on the article ‘Numerical approach to the non-linear diofantic equations with applications to the controllability of infinite dimensional dynamical systems’. The article gives an algorithm for the controllability analysis of the parabolic dynamical system defined in the n-D rectangular prism. The severe drawback of that algorithm is multiple nested, time-consuming loops which are necessary to perform. In the comments, we propose how to avoid performing sophisticated algorithms in that problem thanks to involving new advanced results of the number theory. [ABSTRACT FROM PUBLISHER]

In this literature survey, different aspects of dynamics of two-phase flow in porous media are discussed. This review is based on the results of developed dynamic pore-network models and their applications. Thus, those concepts of dynamics of two-phase systems are addressed that have been already discussed in previous studies. Since it is not always possible to study different aspects of laboratory experiments, dynamic pore-network models were developed to gain new insights into the process. This characteristic is the major advantage of pore-network models, which give a better understanding of the physics of a process at pore scale as well as at the scale of representative elementary volume. Dynamic pore-network models are reviewed under different classifications; structure, computational algorithm, and local rules and applications. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the strange star product. This product may be used to locate non-infinitely renormalizable unimodal maps f where is topologically conjugate to an adding machine. Given any sequence , with each , the strange star product can precisely construct the kneading sequence of a unimodal map with an embedded copy of the associated α-adic adding machine. [ABSTRACT FROM AUTHOR]

An emerging research area in computational biology and biotechnology is devoted to modelling and prediction of gene-expression patterns. In this article, after a short review of recent achievements we deepen and extend them, especially, by emphasizing and analysing the elegant means of matrix algebra. Based on experimental data, ordinary differential equations with nonlinearities on the right-hand side and a generalized treatment of the absolute shift term, representing the environmental effects, are investigated. Then, the genetic process is studied by a time-discretization, in particular, Runge-Kutta type discretization. By a utilization of the combinatorial algorithm of Brayton and Tong, which is based on the orbits of polyhedra, the possibility of detecting stability and instability regions has been shown. The time-continuous and -discrete systems can be represented by means of matrices allowing biological implications, such as thresholds, and interpretations; which are motivated by our gene-environment networks. A specific contribution of this article consists of a careful but rigorous integration of the environment into modelling and dynamics, and in further new sights. Relations to the parameter estimation within modelling, especially, by using optimization, are indicated, and future research is addressed. [ABSTRACT FROM AUTHOR]

We present two new algorithms for computing Nash equilibria of stochastic games. One is a global random start algorithm based on nonlinear programming, while the other combines a dynamical system with nonlinear programming to find stable equilibria. Promising numerical results are presented. [ABSTRACT FROM AUTHOR]

We consider a generalization of Fiedler's notion of algebraic connectivity to directed graphs. We show that several properties of Fiedler's definition remain valid for directed graphs and present properties peculiar to directed graphs. We prove inequalities relating the algebraic connectivity to quantities such as the bisection width, maximum directed cut and the isoperimetric number. Finally, we illustrate an application to the synchronization in networks of coupled chaotic systems. [ABSTRACT FROM AUTHOR]