ALBERT

Description: With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the existence of multiple positive periodic solutions of delayed predator-prey systems with type IV functional responses on time scales. Our results not only unify the existing ones but also widen the range of applications.

Description: This paper deals with the investigation of the following more general rational difference equation: yn+1=αyn/(β+γ∑i=0kyn-(2i+1)p∏i=0kyn-(2i+1)), n=0,1,2,…, where α,β,γ,p∈(0,∞) with the initial conditions x0,x-1,…,x-2k,x-2k-1∈(0,∞). We investigate the existence of the equilibrium points of the considered equation and then study their local and global stability. Also, some results related to the oscillation and the permanence of the considered equation have been presented.

Description: Through analyzing the data about the releases, comment, and forwarding of 120,000 microblog messages in a year, this paper finds out that the intervals between information releases and comment follow a power law; besides, the analysis of data in each 24 hours reveals obvious differences between microblogging and website visit, email, instant communication, and the use of mobile phone, reflecting how people use fragments of time via mobile internet technology. The paper points out the significant influence of the user's activity on the intervals of information releases and thus demonstrates a positive correlation between the activity and the power exponent. The paper also points out that user's activity is influenced by social identity in a positive way. The simulation results based on the social identity mechanism fit well with the actual data, which indicates that this mechanism is a reasonable way to explain people's behavior in the mobile Internet.

Description: Two types of coronary artery system N-type and S-type, are investigated. The threshold conditions for the occurrence of Smale horseshoe chaos are obtained by using Melnikov method. Numerical simulations including phase portraits, potential diagram, homoclinic bifurcation curve diagrams, bifurcation diagrams, and Poincaré maps not only prove the correctness of theoretical analysis but also show the interesting bifurcation diagrams and the more new complex dynamical behaviors. Numerical simulations are used to investigate the nonlinear dynamical characteristics and complexity of the two systems, revealing bifurcation forms and the road leading to chaotic motion. Finally the chaotic states of the two systems are effectively controlled by two control methods: variable feedback control and coupled feedback control.

Description: In many applications, it is natural to use interval data to describe various kinds of uncertainties. This paper is concerned with an interval neural network with a hidden layer. For the original interval neural network, it might cause oscillation in the learning procedure as indicated in our numerical experiments. In this paper, a smoothing interval neural network is proposed to prevent the weights oscillation during the learning procedure. Here, by smoothing we mean that, in a neighborhood of the origin, we replace the absolute values of the weights by a smooth function of the weights in the hidden layer and output layer. The convergence of a gradient algorithm for training the smoothing interval neural network is proved. Supporting numerical experiments are provided.

Description: This paper deals with the problem of selective harvesting in a chemostat model. Here, we have taken the purifying effort as a dynamic variable and tax as a control instrument. The existence of the possible steady states along with their globally stable equilibrium is discussed. The optimal tax policy is also discussed with the help of Pontryagin's maximum principle. Finally, numerical examples are taken to illustrate some of the key results.

Description: Combining probability and first-order logic has been the subject of intensive research during the last 10 years. This artical introduces first-order probabilistic conditional logic (FO-PCL), a first-order extension of a propositional probabilistic logic formalism, which allows for the adequate representation of probabilistic if - then -rules. We demonstrate that our novel formalism allows to represent uncertain knowledge that cannot easily be represented by other formalisms combining first-order logic and probability. Furthermore, as the representation of the models of FO-PCL requires solving a complex entropy-optimization problem, we develop syntactic conditions for its simplification.

Description: This article presents KR eator , a versatile integrated development environment for probabilistic inductive logic programming currently under development. The area of probabilistic inductive logic programming (or statistical relational learning) aims at applying probabilistic methods of inference and learning in relational or first-order representations of knowledge. In the past ten years the community brought forth a lot of proposals to deal with problems in that area, which mostly extend existing propositional probabilistic methods like Bayes Nets and Markov Networks on relational settings. Only few developers provide prototypical implementations of their approaches and the existing applications are often difficult to install and to use. Furthermore, due to different languages and frameworks used for the development of different systems the task of comparing various approaches becomes hard and tedious. KR eator aims at providing a common and simple interface for representing, reasoning and learning with different relational probabilistic approaches. It is a general integrated development environment which enables the integration of various frameworks within the area of probabilistic inductive logic programming and statistical relational learning. Currently, KR eator implements Bayesian logic programs, Markov logic networks and relational maximum entropy under grounding semantics. More approaches will be implemented in the near future or can be implemented by researchers themselves as KR eator is open-source and available under public license. In this article, we provide some background on probabilistic inductive logic programming and statistical relational learning and illustrate the usage of KR eator on several examples using the three approaches currently implemented in KR eator . Furthermore, we give an overview on its system architecture.

Description: A special feature of programs in the action language Golog are non-deterministic constructs such as non-deterministic choice of actions or arguments. It has been shown that in the presence of stochastic actions and rewards reinforcement learning techniques can be applied to obtain optimal choices for those choice-points. In order to avoid an explosion of the state space, an abstraction mechanism is employed that computes first-order state descriptions for the given program. Intuitively, the idea is to generate abstract descriptions that group together states for which the expected reward of executing the program is the same. A current limitation is that a non-deterministic choice of arguments can be handled only if the possible candidates are known in advance. In this article we show how this restriction can be lifted. We also show how a first-order variant of binary decision diagrams can be used to efficiently compute first-order state abstractions. Moreover, we give a completely declarative specification of a learning Golog interpreter that incorporates the presented state-abstraction mechanisms.