Search

Partial differential equation (PDE) occurs in the mathematical modeling of many physical phenomena arising in science and engineering. In this paper, we present wavelet-based lifting scheme for the numerical solution of nonlinear PDEs using different wavelet filter coefficients. The numerical results obtained by this scheme are compared with the exact solution to demonstrate the accuracy and also speeds up convergence in lesser computational time as compared with the existing schemes. Some test problems are presented for the validity and applicability of the scheme. [ABSTRACT FROM AUTHOR]

The extended invertible Logistic map and its properties are investigated in this paper. It is demonstrated that initial conditions of the extended invertible Logistic map can yield trajectories of three different types. Dedicated algorithms are used to prove the existence of transient Wada-type boundaries in the phase plane of initial conditions. An adaptive control technique for the temporary control of the divergence of the extended invertible Logistic map is proposed. This control technique is based on short impulses and exploits the properties of the Wada-type boundaries. Computational experiments are used to illustrate the efficacy of the proposed technique. [ABSTRACT FROM AUTHOR]

The seismic behavior of the structures equipped with ATMD is often investigated based on the rigid base assumption without considering soil-structure interaction (SSI) effects. The SSI effects significantly modify the dynamic characteristics of the structures, while these changes may be ignored in the design process of the controllers. The present paper aims to address the issue of the SSI effects on the seismic behavior of the structures and performance of the adopted controllers. For this purpose, a mathematical model is developed for the time domain analysis of tall building equipped with ATMD including SSI effects. Considering the fixed base case and three types of ground states, namely soft, medium and dense soil, the numerical studies are carried out on a 40-story structure subjected to different earthquake excitations. Two well-known controllers, proportional-integral-derivative (PID) and linear-quadratic regulator (LQR) controllers, are employed for tuning control force of ATMD in different conditions of ground state. A particle swarm optimization (PSO) algorithm is used for the optimum design of Tuned mass damper (TMD) parameter and the gain matrices of the controllers in both cases without and with SSI effects. It is found that TMDs are more effective for the higher soil stiffness and their efficiencies are degraded in soft soils. Furthermore, the SSI significantly affects on the optimum design of the PID and LQR controllers. The adopted controllers are significantly able to mitigate the peak top floor displacement of the tall building. In addition that the PID controller is a simple strategy with design variables much less than LQR controller, it performs better than the LQR controller in most earthquakes for different conditions of ground state. The performance of the controllers decreases with increasing soil softness, so that ignoring the SSI effects may result in incorrect and unrealistic results of the seismic behavior of the structures. [ABSTRACT FROM AUTHOR]

In this paper, we propose a prior fusion and feature transformation-based principal component analysis (PCA) method for saliency detection. It relies on the inner statistics of the patches in the image for identifying unique patterns, and all the processes are done only once. First, three low-level priors are incorporated and act as guidance cues in the model; second, to ensure the validity of PCA distinctness model, a linear transform for the feature space is designed and needs to be trained; furthermore, an extended optimization framework is utilized to generate a smoothed saliency map based on the consistency of the adjacent patches. We compare three versions of our model with seven previous methods and test them on several benchmark datasets. Different kinds of strategies are adopted to evaluate the performance and the results demonstrate that our model achieves the state-of-the-art performance. [ABSTRACT FROM AUTHOR]

The option-pricing problem is an important topic in modern finance. In this paper, we propose a stock model with varying stock diffusion based on uncertainty theory. The European option pricing formulas are derived from the proposed uncertain stock model, and some mathematical properties of these formulas are investigated. Moreover, extended uncertain stock models are introduced and discussed. Finally, numerical examples are given to illustrate the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, an order induced by implications on a bounded lattice under some more lenient conditions than the ones given former studies is defined and some of its properties are discussed. By giving an order based on uninorms on a bounded lattice, the relationships between such generated orders are investigated. [ABSTRACT FROM AUTHOR]

In the paper 'Some Open Problems in Chaos Theory and Dynamics' by Zeraoulia and Sprott, the two-dimensional map was considered and the problem on the analytical study of the boundedness of its attractors was formulated. In the present paper, the boundedness of its attractors is studied, the corresponding analytical estimation of absorbing set is obtained, and thus an answer to the problem is given. [ABSTRACT FROM AUTHOR]

Since Zadeh introduced fuzzy sets, a lot of extensions of this concept have been proposed, such as type-2 fuzzy sets, nonstationary fuzzy sets, and cloud models, to represent higher levels of uncertainty. This paper provides a comparative investigation of type-2 fuzzy sets, nonstationary fuzzy sets, and cloud models. Type-2 fuzzy sets study the fuzziness of the membership function (MF) using primary MF and secondary MF based on analytic mathematical methods; nonstationary fuzzy sets study the randomness of the MF using primary MF and variation function based on type-1 fuzzy sets theory; cloud models study the randomness of the distribution of samples in the universe and generate random membership grades (MGs) using two random variables based on probability and statistic mathematical methods. They all concentrate on dealing with the uncertainty of the MF or the MG which type-1 fuzzy sets do not consider, and thus have many similarities. Moreover, we find out that, the same qualitative concept 'moderate amount' can be represented by an interval type-2 fuzzy set, a nonstationary fuzzy set or a normal cloud model, respectively. Then, we propose a unified mathematical expression for the interval type-2 fuzzy set, nonstationary fuzzy set and normal cloud model. On the other hand, we also find out that, the theory fundament and underlying motivations of these models are quite different. Therefore, We summarize detailed comparisons of distinctive properties of type-2 fuzzy sets, nonstationary fuzzy sets, and cloud models. Further, we study their diverse characteristics of distributions of MGs across vertical slices. The comparative investigation shows that these models are complementary to describe the uncertainty from different points of view. Thus, this paper provides a fundamental contribution and makes a basic reference for knowledge representation and other applications with uncertainty. [ABSTRACT FROM AUTHOR]

Reversible circuit is of interest due to the characteristics of low energy consumption. This paper proposes a new scheme for synthesizing fault tolerant reversible circuits. A two-step method is put forward to convert an irreversible function into a parity-preserving reversible circuit. By introducing model checking for linear temporal logic, we construct a finite state machine to synthesize small reversible gates from elementary 1-qubit and 2-qubit gates, which is more automatic than the methods proposed previously. Constrains are increased so as to reduce the synthesis time in the two step method. The parity-preserving gate constructed by the two-step method has characteristics of low quantum cost because the quantum representation obtained from the counterexample for a given function in each step has the minimum quantum cost. In order to further reduce the quantum cost and decrease the synthesis time, the semi parity-preserving gates are put forward for the first time. These gates are parity-preserving when the auxiliary input is set to 0 and opposite parity when 1. Maintaining good robustness of the system in performing specific function, semi parity-preserving gate is conducive to detecting the stuck-at fault and partial gate fault in reversible circuits. The innovation of this paper is introducing the formal method to synthesis small fault tolerant gate, so as to construct the circuit with robust (semi) parity-preserving gates. [ABSTRACT FROM AUTHOR]

After a 3D Lorenz-like system has been revisited, more rich hidden dynamics that was not found previously is clearly revealed. Some more precise mathematical work, such as for the complete distribution and the local stability and bifurcation of its equilibrium points, the existence of singularly degenerate heteroclinic cycles as well as homoclinic and heteroclinic orbits, and the dynamics at infinity, is carried out in this paper. In particular, another possible new mechanism behind the creation of chaotic attractors is presented. Based on this mechanism, some different structure types of chaotic attractors are numerically found in the case of small b > 0. All theoretical results obtained are further illustrated by numerical simulations. What we formulate in this paper is to not only show those dynamical properties hiding in this system, but also (more mainly) present a kind of way and means - both "locally" and "globally" and both "finitely" and "infinitely" - to comprehensively explore a given system. [ABSTRACT FROM AUTHOR]

Trust models play an important role in computational environments. One of the main aims of the work undertaken in this domain is to provide a model that can better describe the socio-technical nature of computational trust. It has been recently shown that quantum-like formulations in the field of human decision making can better explain the underlying nature of these types of processes. Based on this research, the aim of this paper is to propose a novel model of trust based on quantum probabilities as the underlying mathematics of quantum theory. It will be shown that by using this new mathematical framework, we will have a powerful mechanism to model the contextuality property of trust. Also, it is hypothesized that many events or evaluations in the context of trust can be and should be considered as incompatible, which is unique to the noncommutative structure of quantum probabilities. The main contribution of this paper will be that, by using the quantum Bayesian inference mechanism for belief updating in the framework of quantum theory, we propose a biased trust inference mechanism. This mechanism allows us to model the negative and positive biases that a trustor may subjectively feel toward a certain trustee candidate. It is shown that by using this bias, we can model and describe the exploration versus exploitation problem in the context of trust decision making, recency effects for recently good or bad transactions, filtering pessimistic and optimistic recommendations that may result in good-mouthing or bad-mouthing attacks, the attitude of the trustor toward risk and uncertainty in different situations and the pseudo-transitivity property of trust. Finally, we have conducted several experimental evaluations in order to demonstrate the effectiveness of the proposed model in different scenarios. [ABSTRACT FROM AUTHOR]

Orthogonal frequency division multiplexing (OFDM) modulation is proposed in 4G wireless communication systems, and is under consideration for the next generation 5G systems. This is due to the higher spectral efficiency (SE) and the better immunity to channel distortions. One of the shortcomings in OFDM is its high peak-to-average power ratio (PAPR). Several schemes have been proposed to reduce the PAPR in OFDM systems. This includes clipping, coding, and pre/post-distortion schemes with or without side information. In this paper, we experimentally demonstrate one of the most promising method, to mitigate the effect of PAPR, entitled the partial orthogonal selective mapping (POSLM). The experimental results show a comparable performance with respect to the simulation results in terms of PAPR reduction, power spectral density (PSD), and bit error rate (BER) metrics. [ABSTRACT FROM AUTHOR]

In the two articles in Appl. Math. Comput., J. Giné [2012a, 2012b] studied the number of small limit cycles bifurcating from the origin of the system: ẋ=−y+Pn(x,y), ẏ=x+Qn(x,y), where Pn and Qn are homogeneous polynomials of degree n. It is shown that the maximal number of the small limit cycles, denoted by Mh(n), satisfies Mh(n)≥2n−1 for n=4,5,6,7; and Mh(8)≥13, Mh(9)≥16. It seems that the correct answer for their case n=9 should be Mh(9)≥15. In this paper, we apply Hopf bifurcation theory and normal form computation, and perturb the isolated, nondegenerate center (the origin) to prove that Mh(n)≥2n for n=4,5,6,7; and Mh(n)≥2(n−1) for n=8,9, which improve Giné’s results with one more limit cycle for each case. [ABSTRACT FROM AUTHOR]

In the last few years, many known works in learning theory stepped over the classical assumption that samples are independent and identical distribution and investigated learning performance based on non-independent samples, as mixing sequences (e.g., -mixing, -mixing, -mixing etc.), they derived similar results with the investigation based on classical sample assumption. Negative association (NA) sequence is a kind of significant dependent random variables and plays an important role in non-independent sequences. It is widely applied to various subjects such as probability theory, statistics and stochastic processes. Therefore, it is essential to study the learning performance of learning process for dependent samples drawn from NA process. Obviously, samples in this learning process are not independent and identical distribution. The results in classical learning theory are not applied directly. In this paper, we study the consistency of least-square regularized regression with NA samples. We establish the error bound of least-square regularized regression for NA samples, and prove that the learning rate of least-square regularized regression for NA samples is , which is tend to when arbitrarily close to 0, where denote the number of the samples. The simulation experiment of convergence rate on NA samples reveals that the least-square regularized regression algorithm for NA samples is consistent. This result generalizes the classical result of independent and identical distribution. [ABSTRACT FROM AUTHOR]

The emerging data explosion in sports field has created new opportunities to practice data science and analytics for deeper and larger scale analysis of games. With collaborating and competing 22 players on the field, soccer is often considered as a complex system. More specifically, each game is usually modeled as a network with players as nodes and passes between them as the edges. The number of passes usually define the weight of each edge, and these weights are employed to identify the key players using network modeling theory. However, the number of passes metric considers each pass the same and cannot differentiate players who are making ordinary passes, usually in their own pitch to a close teammate, from those who make key passes that start or improve an attack. As a solution, in this paper, we present a descriptive model to quantify the effectiveness of passes in soccer to differentiate between key passes and regular passes with not much contribution to the play of a team. Our model captures the perception of domain experts with a careful combination of risk and gain assessments. We have implemented our model in a soccer data analytics software. We performed a user study with domain experts, and the results show that our model captures domain expert evaluations of a number of example scenarios with 94% accuracy. The proposed model is not computationally demanding which allows real-time pass assessment during games on commodity hardware as demonstrated by our software prototype. [ABSTRACT FROM AUTHOR]

In this paper, we present new results of natural frequencies for the functionally graded beams based on Chebyshev collocation method and the third-order shear deformation theory (TSDT), without requiring any shear correction factors. The beams are assumed to be elastically supported by translational and rotational springs, or simply known as elastically restrained ends. The material compositions of the beams across the gradient direction are described by different mathematical models including the simple power law, exponential and Mori-Tanaka models, and their effects on the response of beams are analyzed. We first present the Chebyshev collocation formulation of the coupled differential equations of motion for free vibration of FGM beams considering different boundary conditions, and then verify the results obtained by the proposed approach against reference ones. A parametric study is also performed for parameters such as thickness, spring constant factor, material volume fraction index, etc. The present numerical results reveal that the proposed method can offer accurate frequency results for the FGM beams as compared with those available in the literature. The results also indicate that the spring constant factors have a significant effect on the frequencies of the beams. [ABSTRACT FROM AUTHOR]

This paper proposes an uncertain multi-period bi-level network interdiction problem with uncertain arc capacities. It is proved that there exists an equivalence relationship between uncertain multi-period network interdiction problem and the obtained deterministic correspondent. Application of the generalized Benders' decomposition algorithm is considered as the solution approach to the resulting mixed-integer nonlinear programming problem. Finally, a numerical example is presented to illustrate the model and the algorithm. [ABSTRACT FROM AUTHOR]

The focus of this paper is to investigate the dynamics of seizure activities by using the Epileptor coupled model. Based on the coexistence of seizure-like event (SLE), refractory status epilepticus (RSE), depolarization block (DB), and normal state, we first study the dynamical behaviors of two coupled oscillators in different activity states with Epileptor model by linking them with slow permittivity coupling. Our research has found that when one oscillator in normal states is coupled with any oscillator in SLE, RSE or DB states, these two oscillators can both evolve into SLE states under appropriate coupling strength. And then these two SLE oscillators can perform epileptiform synchronization or epileptiform anti-synchronization. Meanwhile, SLE can be depressed when considering the fast electrical or chemical coupling in Epileptor model. Additionally, a two-dimensional reduced model is also given to show the effect of coupling number on seizures. Those results can help to understand the dynamical mechanism of the initiation, maintenance, propagation and termination of seizures in focal epilepsy. [ABSTRACT FROM AUTHOR]

The broadcast of awareness programs through TV and radio advertisements (ads) makes people aware and brings behavioral changes among the individuals regarding the risk of infection and its control mechanisms. In this paper, we propose and analyze a nonlinear mathematical model for the control of infectious diseases due to impact of TV and radio advertisements. It is assumed that susceptible individuals are vulnerable to infection as well as information through TV and radio ads and they contract infection via direct contact with infected individuals. In the model formulation, it is also assumed that the growth rates in cumulative number of TV and radio ads are proportional to the number of infected individuals with decreasing function of aware individuals. Further, it is assumed that awareness among susceptible individuals induces behavioral changes and they form separate aware classes, which are fully protected from infection as they use precautionary measures for their protection during the infection period. The feasibility of equilibria and their stability properties are discussed. It is shown that the augmentation in dissemination rate of awareness among susceptible individuals due to TV and radio ads may cause stability switches through Hopf-bifurcation. The analytical findings are supported through numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of nonlocal dispersal problem with a nonlocal term arising in population dynamics: where is a bounded domain, , represents the nonlocal dispersal operator with continuous and non-negative dispersal kernel. The kernel is assumed to be non-negative and is allowed to have a degeneracy in a smooth subdomain of . When is either positive or vanishes in a subdomain, we respectively investigate the existence, multiplicity and asymptotical stability of positive steady states under the local/global variation of parameter by means of sub-supersolution method, Lyapunov-Schmidt reduction, and bifurcation theory. [ABSTRACT FROM AUTHOR]

Many multiprocessor systems have interconnection networks as underlying topologies and an interconnection network is usually represented by a graph where nodes represent processors and links represent communication links between processors. No faulty set can contain all the neighbors of any fault-free node in the system, which is called the nature diagnosability of the system. Diagnosability of a multiprocessor system is one important study topic. As a favorable topology structure of interconnection networks, the n-dimensional alternating group graph AGn has many good properties. In this paper, we prove the following. (1) The nature diagnosability of AGn is 4 n − 10 for n − 5 under the PMC model and MM* model. (2) The nature diagnosability of the 4-dimensional alternating group graph AG4 under the PMC model is 5. (3) The nature diagnosability of AG4 under the MM* model is 4. [ABSTRACT FROM AUTHOR]

In this paper we study aggregation operators that are point-sensitive which means that their values depend on the point where the functions to be aggregated are defined, as well as on the values of those functions at that point. This analysis gives rise to consider several functional equations that appear in a natural way. Further applications in mathematical social choice also appear as a by-product. In particular, we characterize the representation of certain social choice rules by means of specific numerical functions. [ABSTRACT FROM AUTHOR]

High reliability against undesirable effects is one of the key objectives in the design for Network-on-Chip (NoC). As a result, designing reliable and efficient routing method is highly desirable. This paper presents a novel turn model called NMad-y using one and two virtual channels along the - and -dimensions, respectively, and Adaptive and Fault-tolerant Routing Method (AFRM) which is designed based on the NMad-y turn model. AFRM can effectively tolerate multiple faulty routers and links in more complicated faulty situations by the link status of neighbor routers within two hops. AFRM is able to impose the reliability of network without losing the performance of network. Simulation results show that AFRM achieves better saturation throughput (0.83% on average) than a state-of-the-art fault-tolerant routing method and maintains high reliability of more than 97.43% on average. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of removing striping noise in hyperspectral images (HSI). To this end, we develop a novel destriping method by taking advantage of the spectral and spatial information of the hyperspectral image simultaneously. To obtain satisfactory destriped results, our consideration is two-fold: (1) To model the spectral information of HSI, we utilize low-rank representation to exploit the low-rank property of HSI; (2) To incorporate the spatial information into our method, we adopt the Huber-Markov random field (HMRF) prior model to preserve the edge information of HSI while reducing the striping noise. Finally, we integrate the spectral and spatial model into a unified objective function. In addition, we also devise an effective optimization algorithm to minimize the objective function. The experimental results on real-world HSI data validate the efficacy of the proposed scheme for destriping of HSI. [ABSTRACT FROM AUTHOR]

The SrBaTiO3 (SBT) memristor is prepared using the monolayer SrBaTiO3 nano-film structure. In order to apply it into the nonlinear circuit design, the SBT memristor is modeled in the paper. The voltage-controlled physical model of the SBT memristor is established based on its working mechanism. Due to the difficulty in determining the accurate parameters of the voltage-controlled physical model, a flux-controlled mathematical model of the SBT memristor is proposed, and its equivalence relation with the voltage-controlled physical model is proved. Moreover, the parameters of the flux-controlled mathematical model are determined by means of the quadratic polynomial interpolation method using the experimentally measured voltage and current data of the SBT memristor. The simulated - characteristic curve using the flux-controlled mathematical model coincides well with the measured - characteristic curves. The result indicates that the flux-controlled mathematical model with the definite parameters can be used to characterize the behaviors of the physical SBT memristor and guide its application to nonlinear circuit design. [ABSTRACT FROM AUTHOR]

In this paper, we named the composition by a real-valued measurable function and an uncertain variable as a composite uncertain variable. We focused on the uncertainty distribution for two kinds of composite uncertain variables. The conclusions show: (1) it exists a lower bound when the composed function is continuous and strictly monotonically decreasing at first and then strictly monotonically increasing (e.g. convex downward functions); (2) it exists an upper bound when the composed function is continuous and strictly monotonically increasing at first and then strictly monotonically decreasing (e.g. convex upward functions). [ABSTRACT FROM AUTHOR]

In this paper, we have proposed a dual-channel supply chain model in uncertain environment to analyze the demand of manufacturer and retailer demand in which the profit being maximized. Linguistic terms are also utilized to establish two fuzzy systems for estimating the demand in direct and retail channels. In order to do that, a mathematical model is proposed based on decentralized situation of supply chain. To solve the model, we have developed a hybrid solution method of genetic algorithm, fuzzy system, and L-P metric. Finally, several test problems are first generated; then, the computational results are analyzed. [ABSTRACT FROM AUTHOR]

Trajectory representation model has been proposed to describe non-rigid deformation. An optimal trajectory space finding algorithm for 3D non-rigid structure from motion (OTSF-NRSFM) based on this model also has been proposed. However, the influence of the wavelet basis selection on the OTSF-NRSFM algorithm has still not been studied. To help OTSF-NRSFM researchers select wavelet basis properly, we investigated the influences of wavelet basis selection. Two typical wavelet bases, DCT basis and WHT basis, are discussed in this paper. The spectrum properties of wavelet basis and feature point trajectory, trajectory representation results on synthetic shark data, OTSF-NRSFM reconstruction results on synthetic data and real data are analyzed. The results show that the wavelet selection has much influence on OTSF-NRSFM reconstruction results of some non-rigid feature points, which have complicated trajectory. This paper gives researchers some inspiration about wavelet basis selection in OTSF-NRSFM algorithm. [ABSTRACT FROM AUTHOR]

This paper solves the image fusion problem by using a multi-object optimization strategy and a key energy function. The energy function mainly consists of two components. One ensures injection of more correlated detailed spatial information. The detailed information is extracted from gradient representation of the image to be fused. The other one guarantees that the spectral information is preserved by a data fitting term. By minimizing the proposed energy function, the fusion result can be obtained. Moreover, a key parameter is used in the energy function to adjust the weights of the spectral and spatial information during the image fusion. In this paper, a multi-object optimization is constructed to determine such a key parameter. The image fusion performance is evaluated through visional perception and some fusion indexes. Experimental results further demonstrate advantages of the proposed technique over the conventional fusion techniques. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of efficiency in reinforcement learning of Single Robot Hose Transport (SRHT) by training an Extreme Learning Machine (ELM) from the state-action value Q-table, obtaining large reduction in data space requirements because the number of ELM parameters is much less than the Q-table's size. Moreover, ELM implements a continuous map which can produce compact representations of the Citable, and generalizations to increased space resolution and unknown situations. In this paper we evaluate empirically three strategies to formulate ELM learning to provide approximations to the Q-table, namely as classification, multi-variate regression and several independent regression problems. [ABSTRACT FROM AUTHOR]

This paper presents theoretical and historical backgrounds related to neural network rule extraction. It also investigates approaches for neural network rule extraction by ensemble concepts. Bologna pointed out that although many authors had generated comprehensive models from individual networks, much less work had been done to explain ensembles of neural networks. This paper carefully surveyed the previous work on rule extraction from neural network ensembles since 1988. We are aware of three major research groups i.e., Bologna' group, Zhou' group and Hayashi' group. The reason of these situations is obvious. Since the structures of previous neural network ensembles were quite complicated, the research on the efficient rule extraction algorithm from neural network ensembles was few although their learning capability was extremely high. Thus, these issues make rule extraction algorithm for neural network ensemble difficult task. However, there is a practical need for new ideas for neural network ensembles in order to realize the extremely high-performance needs of various rule extraction problems iu real life. This paper successively explain nature of artificial neural networks, origin of neural network rule extraction, incorporating fuzziness in neural network rule extraction, theoretical foundation of neural network rule extraction, computational complexity of neural network rule extraction, neuro-fuzzy hybridization, previous rule extraction from neural network ensembles and difficulties of previous neural network ensembles. Next, this paper address three principles of proposed neural network rule extraction: to increase recognition rates, to extract rules from neural network ensembles, and to minimize the use of computing resources. We also propose an ensemble-recursive-rule extraction (E-Re-RX) by two or three standard backpropagation to train multi-layer perceptrons (MLPs), which enabled extremely high recognition accuracy and the extraction of comprehensible rules. Furthermore, this enabled rule extraction that resulted in fewer rules than those in previously proposed methods. This paper summarizes experimental results of rule extraction using E-Re-RX by multiple standard backpropagation MLPs and provides deep discussions. The results make it possible for the output from a neural network ensemble to be in the form of rules, thus open the "black box" of trained neural networks ensembles. Finally, we provide valuable conclusions and as future work, three open questions on the E-Re-RX algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a study of two-dimensional hexagonal cellular automata (CA) with periodic boundary. Although the basic construction of a cellular automaton is a discrete model, its global level behavior at large times and on large spatial scales can be a close approximation to a continuous system. Meanwhile CA is a model of dynamical phenomena that focuses on the local behavior which depends on the neighboring cells in order to express their global behavior. The mathematical structure of the model suggests the importance of the algebraic structure of cellular automata. After modeling the dynamical behaviors, it is sometimes an important problem to be able to move backwards on CAs in order to understand the behaviors better. This is only possible if cellular automaton is a reversible one. In the present paper, we study two-dimensional finite CA defined by hexagonal local rule with periodic boundary over the field ℤ3 (i.e. 3-state). We construct the rule matrix corresponding to the hexagonal periodic cellular automata. For some given coefficients and the number of columns of hexagonal information matrix, we prove that the hexagonal periodic cellular automata are reversible. Moreover, we present general algorithms to determine the reversibility of 2D 3-state cellular automata with periodic boundary. A well known fact is that the determination of the reversibility of a two-dimensional CA is a very difficult problem, in general. In this study, the reversibility problem of two-dimensional hexagonal periodic CA is resolved completely. Since CA are sufficiently simple to allow detailed mathematical analysis, also sufficiently complex to produce chaos in dynamical systems, we believe that our construction will be applied many areas related to these CA using any other transition rules. [ABSTRACT FROM AUTHOR]

Immunotherapy is one of the most recent approaches in cancer therapy. In this paper, a mathematical model of tumor-immune interaction with periodically pulsed immunotherapy, which is described by impulsive differential equations, is considered. The ODE system is turned into a discrete-time dynamical system for bifurcation analysis. A mathematical analysis is performed to determine the minimum dosage for successful treatment. An adaptive grid method is then developed to identify the fixed points and their bifurcations. The effects of continuous and pulsed treatment strategies are compared. The interindividual variability is studied by one-parameter and two-parameter bifurcation diagrams. Increasing the strength of the immune response improves the outcome of the treatment if the immune response is weak. However, it becomes a drawback when the strength of the immune response increases over a certain threshold. Multiple attractors exist so that a treatment may result in a tumor-free state, a large tumor, or a middle-sized tumor depending on initial conditions. It is believed that the numerical method proposed in this paper can be applied to a class of mathematical models of periodically pulsed drug therapies. [ABSTRACT FROM AUTHOR]

Supply chain system is a complex system in which node enterprises play important roles and exert great influence. This paper proposes an output game model among multiple oligopolistic manufacturers under the circumstances of information asymmetry and analyzes the Nash equilibrium in the model. The manufacturers usually base their production decision making on the volume of order from distributors and the production decisions made by other manufacturers. They also suitably adjust the output. If the adjustment speed accelerates, chaos will be caused in the manufacturers' production decision. This paper analyzes the proposed model from a perspective of complex dynamics and discusses the impact of system parameter on the complexity of this discrete chaotic system. The measures to retain chaos among manufacturers are suggested. [ABSTRACT FROM AUTHOR]

This paper describes the sequence of construction of a cell nuclei classification model by the analysis, the characterization and the classification of shape and texture. We describe first the elaboration of dedicated shape indexes and second the construction of the associated classification submodel. Then we present a new method of texture characterization, based on the construction and the analysis of statistical matrices encoding the texture. The various characterization techniques developed in this paper are systematically compared to previous approaches. In particular, we paid special attention to the results obtained by a versatile classification method using a large range of descriptors dedicated to the characterization of shapes and textures. Finally, the last classifier built with our methods achieved 88% of classification out of the 94% possible. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of obtaining stable and robust oscillations of underactuated mechanical systems. It is concerned with the Hopf bifurcation analysis of a Controlled Inertia Wheel Inverted Pendulum (C-IWIP). Firstly, the stabilization was achieved with a control law based on the Interconnection, Damping, Assignment Passive Based Control method (IDA-PBC). Interestingly, the considered closed-loop system exhibits both supercritical and subcritical Hopf bifurcation for certain gains of the control law. Secondly, we used the center manifold theorem and the normal form technique to study the stability and instability of limit cycles emerging from the Hopf bifurcation. Finally, numerical simulations were conducted to validate the analytical results in order to prove that with IDA-PBC we can control not only the unstable equilibrium but also some trajectories such as limit cycles. [ABSTRACT FROM AUTHOR]

The existence of heteroclinic orbits of a chaotic system is a difficult yet interesting mathematical problem. Nowadays, a rigorous analytical proof for the existence of a heteroclinic orbit can be carried out only for some special chaotic and hyperchaotic systems, and few results are known for the complex systems. In this paper, by revisiting a complex Lorenz system, it is found that this system possesses an infinite set of heteroclinic orbits to the origin and its circle equilibria. However, it is impossible for the corresponding real Lorenz system to have infinitely many heteroclinic orbits. The theoretical tools for proving the main results are Lyapunov functions and the definitions of -limit set and -limit set. Numerical simulations show the effectiveness and correctness of the theoretical conclusions. The investigations not only enrich the related results for the complex Lorenz system, but also find the essential difference between the complex Lorenz system and its corresponding real version: the complex Lorenz system has infinitely many heteroclinic orbits whereas its corresponding real one does not. [ABSTRACT FROM AUTHOR]

In this paper, we study the bifurcations and exact traveling wave solutions of the celebrated Green-Naghdi equations by using the qualitative theory of differential equations and the bifurcation theory of dynamical systems. We obtain all possible phase portraits of bifurcations of the system under various conditions about the parameters associated with the planar dynamical system. Then we show the existence of traveling wave solutions including solitary wave solutions, blow-up solutions, periodic wave solutions and periodic blow-up solutions, and give their exact explicit expressions. These results can help to understand the dynamical behavior of the traveling wave solutions of the system. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of lossy compression for hyperspectral images and presents an efficient compression algorithm based on distributed source coding. The proposed algorithm employs a block-based quantizer followed by distributed lossless coding, which is implemented through the use of multilevel coset codes. First, a bitrate allocation algorithm is proposed to assign the rational bitrate for each block. Subsequently, the multilinear regression model is employed to construct the side information of each block, and the optimal quantization step size of each block is obtained under the assigned bitrate while minimizing the distortion. Finally, the quantized version of each block is encoded by distributed lossless compression. Experimental results show that the compression performance of the proposed algorithm is competitive with that of state-of-the-art transform-based compression algorithms. Moreover, the proposed algorithm provides both low encoder complexity and error resilience, making it suitable for onboard compression. [ABSTRACT FROM AUTHOR]

Evaluation on curvature variation is a significant problem in the field of curve fairing, and traditional evaluation is generally performed by observing curvature plots qualitatively. By using the theory of B-spline wavelet, the concept of curvature variation factor (CVF) is put forth in this paper to describe curvature variation quantitatively. It is verified that the quantitative evaluation results by the CVF method agree well with the traditional qualitative judgments. Based on CVF, a new curve-fairing algorithm is further put forward, whose validness is verified by an example. The advantage of the CVF-based algorithm is that it can realize different fairing effect to meet different requirements under diverse circumstances only by adjusting the shape error. [ABSTRACT FROM AUTHOR]

Control-based continuation (CBC) is a means of applying numerical continuation directly to a physical experiment for bifurcation analysis without the use of a mathematical model. CBC enables the detection and tracking of bifurcations directly, without the need for a post-processing stage as is often the case for more traditional experimental approaches. In this paper, we use CBC to directly locate limit-point bifurcations of a periodically forced oscillator and track them as forcing parameters are varied. Backbone curves, which capture the overall frequency-amplitude dependence of the system's forced response, are also traced out directly. The proposed method is demonstrated on a single-degree-of-freedom mechanical system with a nonlinear stiffness characteristic. Results are presented for two configurations of the nonlinearity - one where it exhibits a hardening stiffness characteristic and one where it exhibits softening-hardening. [ABSTRACT FROM AUTHOR]

A drillbit-rock vibro-impact system with a linear rock contact law is considered in this paper. This system is a simplified model to study the drillbit oscillation in a percussive drilling system. The main purpose of this work is to explore the optimized vibration condition of the drillbit to improve the drilling efficiency in practical drilling applications. In order to eliminate the influences of drilling progression on the dynamic analysis of drillbit oscillation, the drillbit oscillation is separated from its drift via oscillation reconstruction. The obtained bounded mathematical model is analyzed by numerical integration and numerical continuation. Based on the codimension-one bifurcations detected by TC-HAT during one-parameter continuation, the two-parameter bifurcation curves are traced by two-parameter continuation. These explored two-parameter bifurcation curves constitute the parameter boundaries for the period-one one-impact oscillation of drillbit, which is verified as the optimal oscillation with the highest drilling efficiency. [ABSTRACT FROM AUTHOR]

M. M. Hadjiandreou, R. Conejeros and V. S. Vassiliadis ( Math. Biosci. Eng. 4 (2007) 489-504) proposed an ODE model of long-term HIV infection dynamics. This model considers all important population compartments including macrophages, latently-infected CD4+ T cells and cytotoxic T lymphocytes (CTLs), which in many respects is novel in the field of mathematical modeling of HIV infection. The purpose of the paper is to simplify their model into a five-dimensional HIV dynamics model, and give a detailed classification on the existence of the equilibria of the reduced model by introducing four reproductive numbers. Then the global asymptotic stability of each equilibrium is analyzed by constructing suitable Lyapunov functions. The results in the paper extend and improve the understanding of the dynamics of HIV latency. [ABSTRACT FROM AUTHOR]

In this paper, we study the generalized thermoelastic vibration of a bounded nano-beam resonator under fractional order theory of thermoelasticity. The theory of generalized thermoelasticity with one relaxation time can be established in the limit as the special cases of the present model. The effect of fractional parameter is investigated on the nano-beam resonator for beams with clamped ends. Analytical expressions for the deflection, temperature change, frequency shift, and thermoelastic damping have been derived for the beam. The effect of the fractional parameter on the variation of frequency shifts and thermoelastic damping is analyzed graphically. [ABSTRACT FROM AUTHOR]

Uncertainty and its imposed risk have significant impacts on decision-making. However, both are disregarded in many trust-based applications. In this paper, we propose a risk-aware approach to explicitly take uncertainty of trust and its effects into account. Our approach consists of a trust, a confidence, and a risk model. We do not prescribe a specific trust model, and any probabilistic trust model can be empowered by our approach. The confidence model calculates the uncertainty of the trust model in the form of a confidence interval, and is independent of the inner-workings of the trust model. This interval is used by the utility-based risk model which assesses the effects of uncertainty on trust-based decisions. We evaluated our approach by a four-state HMM-based simulated trustee, and employed the Beta, HMM and evidence-based trust models. We proposed and compared different methods for calculating confidence intervals, as well as methods for determining the risk and opportunity of a trust-based interaction. The results demonstrate how our approach should be used to improve the correctness of decision-making in trust-based applications. According to the statistical analysis of the simulation results, confidence intervals can properly represent the trust value and its uncertainty, and strongly improve trust-based decisions. [ABSTRACT FROM AUTHOR]

In this paper, a new electro-mechanical chaotic oscillator is presented. The system is based on the motion of the metal tip of a beam in a double-well potential generated by two magnets, and works thanks to the vibrations generated in the flexible mechanical structure by two rotating coils that produce noise-like signals. As the source of vibration is internal, the system may be considered an autonomous oscillator. Chaotic motion is experimentally observed and verified with a mathematical model of the phenomenon. [ABSTRACT FROM AUTHOR]

The pre-Bötzinger complex of the mammalian brain stem plays a crucial role in the respiratory rhythms generation. Neurons within the pre-Bötzinger complex have been found experimentally to yield different firing activities. In this paper, we study the spiking and bursting activities related to the respiratory rhythms in the pre-Bötzinger complex based on a mathematical model proposed by Butera. Using the one-dimensional first recurrence map induced by dynamics, we investigate the different bursting patterns and their transition of the pre-Bötzinger complex neurons based on the Butera model, after we derived a one-dimensional map from the dynamical characters of the differential equations, and we obtained conditions for the transition of different bursting patterns. These analytical results were verified through numerical simulations. We conclude that the one-dimensional map contains similar rhythmic patterns as the Butera model and can be used as a simpler modeling tool to study fast-slow models like pre-Bötzinger complex neural circuit. [ABSTRACT FROM AUTHOR]

This paper reports on an investigation of the two-dimensional parameter-space of a generalized Nosé-Hoover oscillator. It is a mathematical model of a thermostated harmonic oscillator, which consists of a set of three autonomous first-order nonlinear ordinary differential equations. By using Lyapunov exponents to numerically characterize the dynamics of the model at each point of this parameter-space, it is shown that dissipative quasiperiodic structures are present, embedded in a chaotic region. The same parameter-space is also used to confirm the multistability phenomenon in the investigated mathematical model. [ABSTRACT FROM AUTHOR]

Crew scheduling of the passenger dedicated line is the daily work plan of train attendants, and crew scheduling problem is one of the key problems of the train crew management. Considering the actual condition of China's railway and crew rules, a crew scheduling model is established in this paper to minimize rest time between two consecutive shifts in all roundtrips. In order to solve the scheduling model, in this paper a serial-parallel ant colony optimization algorithm (SP-ACO) is provided. The SP-ACO proposed two improvements: (1) a serial-parallel ant grouping strategy, it means that we let every group of ants find the solution one group by one group for reflecting the positive feedback in a generation; (2) the transition method based on the roulette wheel selection, it means that we randomly select between the certain search and the roulette wheel to make the diversity of solutions for avoiding all ants toward the same part of the search space. Finally, two application cases of the scheduling model are represented. The two cases results show that the methods can not only automatically set roundtrips, but also decrease the number of roundtrips, and the results also show that the feasibility of model and the validity of improved ant colony algorithm for crew scheduling. [ABSTRACT FROM AUTHOR]

According to human vision theory, the image is conveyed from human visual system to brain when people have a look at. Different from previous work, the study reported in this paper attempts to simulate a more real and complex method for region of interest (ROI) detection and quantitatively analyze the correlation between users' visual perception and ROI. In this paper, a visual perception model-based ROI detection is proposed, which can be realized with an ordinary web camera. Visual perception model employs a combination of visual attention model and gaze tracking data to objectively detect ROIs. The work includes pre-ROI estimation using visual attention model, gaze data collection and ROI detection. Pre-ROIs are segmented by the visual attention model. Since eye feature extraction is critical to the accuracy and performance of gaze tracking, adaptive eye template and neural network are employed to predict gaze points. By computing the density of the gaze points, ROIs are ranked. Experimental results show that the accuracy of our ROI detection method can be raised as high as 97% and it is also demonstrated that our model can efficiently adapt to users' interests and match the objective ROI. [ABSTRACT FROM AUTHOR]