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Fractional calculus is closer to reality and has the same memory characteristics as memristor. Therefore, a fractional-order multistable locally active memristor is proposed for the first time in this paper, which has infinitely many coexisting pinched hysteresis loops under different initial states and wide locally active regions. Through the theoretical and numerical analysis, it is found that the fractional-order memristor has stronger locally active and memory characteristics and wider nonvolatile ranges than the integer-order memristor. Furthermore, this fractional-order memristor is applied in a chaotic system. It is found that oscillations occur only within the locally active regions. This chaotic system not only has complex and rich nonlinear dynamics such as infinitely many discrete equilibrium points, multistability and anti-monotonicity but also produces two new phenomena that have not been found in other chaotic systems. The first one is transient transition: the behavior of local chaos and local period transition alternately occurring. The second is state jump: the behavior of local period-4 oscillation or local chaotic oscillation jumping to local period-2 oscillation. Finally, the circuit simulation of the fractional-order multistable locally active memristive chaotic system using PSIM is carried out to verify the validity of the numerical simulation results. [ABSTRACT FROM AUTHOR]

This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behaviour of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and doublescroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronisation of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master–slave synchronisation is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme. [ABSTRACT FROM AUTHOR]

Considering users' access order, the recommendation approach based on sequential patterns is becoming one hot topic in the field of recommender system. To improve the level of personalization, we propose a recommender algorithm named personalized recommendation based on weighted sequential patterns(PRWSP). We first present a new weighted sequential pattern model, in which the different importance degrees of the items in different sequences are considered. Furthermore, by approximation, the rationale of anti-monotonicity in mining weighted sequential patterns is discussed, thus the searching space is reduced. Finally, the measurement metrics of the matching degree of the sequential patterns are defined. Experimental results show that the PRWSP algorithm has higher mining efficiency and recommendation accuracy. [ABSTRACT FROM AUTHOR]

A discrete data augmentation scheme together with two different parameterizations yields two Gibbs samplers for sampling from the posterior distribution of the hyperparameters of the Dirichlet-multinomial hierarchical model under a default prior distribution. The finite-state space nature of this data augmentation permits us to construct two perfect samplers using bounding chains that take advantage of monotonicity and anti-monotonicity in the target posterior distribution, but both are impractically slow. We demonstrate that a composite algorithm that strategically alternates between the two samplers’ updates can be substantially faster than either individually. The speed gains come because the composite algorithm takes a divide-and-conquer approach in which one update quickly shrinks the bounding set for the augmented data, and the other update immediately coalesces on the parameter, once the augmented-data bounding set is a singleton. We theoretically bound the expected time until coalescence for the composite algorithm, and show via simulation that the theoretical bounds can be close to actual performance. [ABSTRACT FROM AUTHOR]

In graph mining, a frequency measure for graphs is anti-monotonic if the frequency of a pattern never exceeds the frequency of a subpattern. The efficiency and correctness of most graph pattern miners relies critically on this property. We study the case where frequent subgraphs have to be found in one graph. Vanetik et al. (Data Min Knowl Disc 13(2):243-260, ) already gave sufficient and necessary conditions for anti-monotonicity of graph measures depending only on the edge-overlaps between the instances of the pattern in a labeled graph. We extend these results to homomorphisms, isomorphisms and homeomorphisms on both labeled and unlabeled, directed and undirected graphs, for vertex- and edge-overlap. We show a set of reductions between the different morphisms that preserve overlap. As a secondary contribution, we prove that the popular maximum independent set measure assigns the minimal possible normalized frequency and we introduce a new measure based on the minimum clique partition that assigns the maximum possible normalized frequency. In that way, we obtain that all normalized anti-monotonic overlap graph measures are bounded from above and below. We also introduce a new measure sandwiched between the former two based on the polynomial time computable Lovász θ-function. [ABSTRACT FROM AUTHOR]