This paper proposes an offline gradient method with smoothing L1/2 regularization for learning and pruning of the pi-sigma neural networks (PSNNs). The original L1/2 regularization term is not smooth at the origin, since it involves the absolute value function. This causes oscillation in the computation and difficulty in the convergence analysis. In this paper, we propose to use a smooth function to replace and approximate the absolute value function, ending up with a smoothing L1/2 regularization method for PSNN. Numerical simulations show that the smoothing L1/2 regularization method eliminates the oscillation in computation and achieves better learning accuracy. We are also able to prove a convergence theorem for the proposed learning method.
In this paper, Runge-Kutta methods are discussed for numerical solutions of conservative systems. For the energy of conservative systems being as close to the initial energy as possible, a modified version of explicit Runge-Kutta methods is presented. The order of the modified Runge-Kutta method is the same as the standard Runge-Kutta method, but it is superior in energy-preserving to the standard one. Comparing the modified Runge-Kutta method with the standard Runge-Kutta method, numerical experiments are provided to illustrate the effectiveness of the modified Runge-Kutta method.
We consider the quotient categories of two categories of modules relative to the Serre classes of modules which are bounded as abelian groups and we prove a Morita type theorem for some equivalences between these quotient categories.
A combined study of morphology, stem anatomy and isozyme patterns was used to reveal the identity of sterile plants from two rivers on the Germany/France border. A detailed morphological examination proved that the putative hybrid is clearly intermediate between Potamogeton natans and P. nodosus. The stem anatomy had characteristics of both species. The most compelling evidence came from the isozyme analysis. The additive “hybrid” banding patterns of the six enzyme systems studied indicate inheritance from P. natans and P. nodosus. In contrast, other morphologically similar hybrids were excluded: P. ×gessnacensis (= P. natans × P. polygonifolius) by all the enzyme systems, P. ×fluitans (= P. lucens × P. natans) by AAT, EST and 6PGDH, and P. ×sparganiifolius (= P. gramineus × P. natans) by AAT and EST. All samples of P. ×schreberi are of a single multi-enzyme phenotype, suggesting that they resulted from a single hybridization event and that the present-day distribution of P. ×schreberi along the Saarland/Moselle border was achieved by means of vegetative propagation and long-distance dispersal. Neither of its parental species occur with P. ×schreberi or are present upstream, which suggests that this hybrid has persisted vegetatively for a long time in the absence of its parents. The total distribution of this hybrid is reviewed and a detailed account of the records from Germany is given. P. ×schreberi appears to be a rare hybrid. The risk of incorrect determination resulting from the identification of insufficiently developed or inadequately preserved plant material is discussed.
Modern organizations tend to constitute of communities of practice to cover the side effect of standardization and centralization of knowledge. The distributed nature of knowledge in groups, teams and other departments of organization and complexity of this tacit knowledge lead us to use community of practice as an environment to share knowledge. In this paper we propose an agent mediated community of a practice system using MAS-CommonKADS methodology. We support the principle of autonomy since every single agent, even those in the same community, needs its own autonomy in order to model an organization and its individuals correctly, using this approach, the natural model for an agent based on knowledge sharing system has been resulted. We presented all models of MAS-CommonKADS methodology required for developing the multi-agent system. We found MAS-CommonKADS useful to design Knowledge Management applications. Because of detailed description of agents, a resulted design model could be simply implemented. We modeled our system using Rebeca and verified it to show that by use of our system, knowledge sharing can be satisfied.
In this paper, we propose a new economic dispatch model with random wind power, demand response and carbon tax. The specific feature of the demand response model is that the consumer's electricity demand is divided into two parts: necessary part and non-essential part. The part of the consumer's participation in the demand response is the non-essential part of the electricity consumption. The optimal dispatch objective is to obtain the minimum total cost (fuel cost, random wind power cost and emission cost) and the maximum consumer's non-essential demand response benefit while satisfying some given constraints. In order to solve the optimal dispatch objective, a multi-subpopulation bat optimization algorithm (MSPBA) is proposed by using different search strategies. Finally, a case of an economic dispatch model is given to verify the feasibility and effectiveness of the established mathematical model and proposed algorithm. The economic dispatch model includes three thermal generators, two wind turbines and two consumers. The simulation results show that the proposed model can reduce the consumer's electricity demand, reduce fuel cost and reduce the impact on the environment while considering random wind energy, non-essential demand response and carbon tax. In addition, the superiority of the proposed algorithm is verified by comparing with the optimization results of CPLEX+YALMIP toolbox for MATLAB, BA, DBA and ILSSIWBA.
Finding reducts is one of the key problems in the increasing applications of rough set theory, which is also one of the bottlenecks of the rough set methodology. The population-based reduction approaches are attractive to find multiple reducts in the decision systems, which could be applied to generate multi-knowledge and to improve decision accuracy. In this paper, we design a multi-swarm synergetic optimization algorithm (MSSO) for rough set reduction and multi-knowledge extraction. It is a multi-swarm based search approach, in which different individual trends to be encoded to different reduct. The approach discovers the best feature combinations in an efficient way to observe the change of positive region as the particles proceed throughout the search space. The performance of our approach is evaluated and compared with Standard Particle Swarm Optimization (SPSO) and Genetic Algorithms (GA). Empirical results illustrate that the approach can be applied for multiple reduct problems and multi-knowledge extraction effectively.
It is shown that if g is of bounded variation in the sense of Hardy-Krause on ∏m i=1 [ai , bi ], then gχ ∏m i=1 (ai ,bi ) is of bounded variation there. As a result, we obtain a simple proof of Kurzweil’s multidimensional integration by parts formula.
Broad-band UBV light and color observations of KY And obtained in September 1982 at the Hvar Observatory have been analyzed. It was found that no single frequency satisfied the data well enough, hence, a multifrequency fit has been determined.
Based on the randomness and fuzziness of the cloud model during the transformation from the qualitative concept to the quantitative numerical value, with the theory that any data distribution can be decompounded into several normal distributions, this paper puts forward a method of multi-classification based on the cloud model. By this method, multiple classification is transformed to a superposed cloud model with training samples as the cloud expectation, while the test samples are regarded as the `cloud droplets', and their classifications of membership degree in a cloud model can be calculated. Considering the effect of the number of training samples on the membership degree, the cloud model is weighted by the ratio of the total number of training samples to the number of training samples in a single class so that the data distribution of the samples can be balanced. The formula of multiple classification based on the cloud model has the structure identical to that of Support Vector Machines, and the hyper entropy in cloud models exerts similar punishment on the noise samples just like the loose coefficients in Support Vector Machines; therefore, the reasonability of the method is theoretically proved. Compared with Support Vector Machine, the method discussed in this paper does not require any large-scale quadratic programming, thus the algorithm of the method is simpler. Last but not the least, five types of data distribution samples are selected for the comparative experiment, and comparison is made with four other classification methods; the result shows that the accuracy and stability of the algorithm is high, and its implementations on the high dimensional multiple classifications are especially satisfactory.