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The GM (1, N) model is an important prediction model among gray models, but the conventional GM (1, N) model shows big errors sometimes mainly due to the structural inconsistency between the gray differential equation for parameter estimation and the whitening equation for prediction. The paper derives the modified model of conventional gray differential equation based on the whitening equation, and the gray differential equation obtained in this way has the structure basically consistent with the structure of whitening equation. The paper estimates parameters with the gray differential equation of modified GM (1, N) model and gives three parameter estimation methods with different background values. The time response equation for conventional GM (1, N) model generally has no analytical solution, but the paper gives a specific solving method for the time response equation of modified model. The example proves that the modified GM (1, N) model given and the models built with the methods proposed improve the simulation and prediction accuracy significantly compared with the conventional model. [ABSTRACT FROM AUTHOR]

In the gray prediction, the GM(1,1) model has been applied widely, but the conventional GM(1,1) model prediction shows big errors sometimes. Many researchers improve prediction accuracy by changing the basic structure of model. The paper tries to make improvements in the models parameter estimation on the basis of new background value optimization without changing the models structure, and gives the following four methods: (1) estimating the parameter of gray model GM(1,1) with the optimized value of exponential curve as the background value; (2) estimating the parameter of gray model GM(1,1) with the optimized value of power function curve as the background value; (3) estimating the parameter of gray model GM(1,1) with the optimized value of polynomial curve as the background value; (4) estimating the parameter of gray model GM(1,1) with the optimized value of interpolation function as the background value. The last part of the paper builds the GM(1,1) model of China's total clean energy consumption with the four improved methods. The simulation and prediction results show that these methods all improve the prediction accuracy of model significantly. [ABSTRACT FROM AUTHOR]

Understanding the relation between large-scale and small-scale functionality is an acute problem in large systems. This paper presents possible structures that capture those relations. Here “structure” means a functor on a category, in this case the category of “combinatorial systems” that model manufacturing systems and supply networks. The details of the dynamics of these systems are frequently the domain of specialists and are ill understood outside such areas. Clustering activities in subsystems introduces covers as scales of analysis. This allows the development of sheaves of schedules and their properties which are analyzed by an adaptation of Čech cohomology. These are applied in supply networks to characterize the fragmentation of these networks and to characterize the conditions for local changes in schedules to extend to the whole system. The intent of this paper is to see sheaves and their cohomology as analytical probes that can enhance our understanding of large-scale systems. [ABSTRACT FROM AUTHOR]

The building industry is becoming very important in sustainable development. The recently developed policies in European Union directives on energy and their transposition to Spanish regulations make the Energy Performance Certification process for buildings mandatory. Two software tools have been developed in Spain to carry out this process: Lider and Calener. These software tools have been used in this paper to simulate energy performance in new semidetached houses after taking into account the thermal envelope of the building and facilities. This has been done in different climatic zones in Spain and for all the possible energy ratings. Based on the energy rating and construction cost variables, it has been possible to obtain mathematical models that explain the behaviour of global costs of buildings based on energy ratings and climatic zones. Depreciation costs, maintenance costs, energy consumption and CO2emissions during the service life of a house have also been modelled. [ABSTRACT FROM AUTHOR]

This paper studies some problems related to the stability and the spectral radius of a finite set of matrices. A seasonal epidemic model is given to illustrate the use of the obtained results. In this example, the relationship between the obtained results and the stability of a discrete time periodic linear system is obtained. [ABSTRACT FROM PUBLISHER]

Bregman iterative algorithms have been extensively used forand total variation regularization problems, allowing to obtain simple, fast and effective algorithms. In this paper, three already-available algorithms for geosounding inversion are modified by including them in a Bregman iterative procedure. The resulting algorithms are easy to implement and do not require any optimization package. Modelling results are presented for synthetic and field data, observing better convergence properties than the original versions, avoiding the need of any continuation descent procedure. [ABSTRACT FROM AUTHOR]

Vendor–retailer collaboration has an important role in supply chain management. Although vendor–retailer collaboration results in better supply chain profit, collaboration is difficult to realize. This is because most vendors and retailers try to optimize their own profit. This paper applies the Stackelberg game with stochastic demand for the vendor–retailer system. The vendor as a leader determines the product price, and the retailer decides order quantity and frequency of price markdown. This study develops example and sensitivity analyses to illustrate the theory. Results show that the price markdown option has a better total supply chain profit than without a price markdown policy, and the vendor receives more benefit. For different demand variances, the retailer profit is more sensitive than the vendor profit. [ABSTRACT FROM AUTHOR]

In this paper, a new reliable algorithm called the multistage homotopy analysis method (MHAM) based on an adaptation of the standard homotopy analysis method (HAM) is presented to solve a time-fractional enzyme kinetics. This enzyme–substrate reaction is formed by a system of nonlinear ordinary differential equations of fractional order. The new algorithm is only a simple modification of the HAM, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding systems. Numerical comparisons between the MHAM and the classical fourth-order Runge–Kutta method in the case of integer-order derivatives reveal that the new technique is a promising tool for nonlinear systems of integer and fractional order. [ABSTRACT FROM AUTHOR]

Student academic underachievement is a concern of paramount importance in Europe, where around 15% of the students in the last high school courses do not achieve the minimum knowledge academic requirement. In this paper, we propose a model based on a system of differential equations to study the dynamics of the students’ academic performance in the German region of the North Rhine-Westphalia. This approach is supported by the idea that both good and bad study habits, are a mixture of personal decisions and influence of classmates. This model allows us to forecast the student academic performance by means of confidence intervals over the next few years. [ABSTRACT FROM PUBLISHER]

The consistency of identification algorithms for systems with colored noises is a main topic in system identification. This paper focuses on the extended stochastic gradient (ESG) identification algorithm for the multivariable linear systems with moving average noises. By integrating the noise regression terms and the noise model parameters into the information matrix and the parameter vector, and based on the gradient search principle, the ESG algorithm is presented. The unknown noise terms in the information matrix are replaced with their estimates. The convergence analysis shows that the parameter estimation error converges to zero under a persistent excitation condition. Two simulation examples are given to illustrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

This paper focuses on identification problems for Hammerstein systems with non-uniform sampling. By using the over-parameterization technique, we derive a linear regressive identification model with different input updating rates. To solve the identification problem of Hammerstein output error systems with the unmeasurable variables in the information vector, the least-squares-based iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates. The performances of the proposed algorithm are analysed and compared by using a numerical example. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce ordinary and delay differential equations to describe the interactions between a malignant tumour and the immune systemin vivoin the presence of human immunodeficiency virus (HIV) infection of CD4+T-cells. In the delay model, we take into account the time lags required by the healthy effector cell components to recognize the pathogens and tumour cells. The models consist of four populations: tumour cells, healthy effector cells (CD4+T-cells), effector cells infected by HIVs and free viral particles. The presence of delay term in the model leads to a notable increase in the complexity of the observed behaviour. We investigate the qualitative behaviour of the models and find the conditions that guarantee the asymptotic stability of the steady states. Numerical simulations are provided to illustrate and extend the theoretical results. The obtained results are consistent with the real phenomena and give a better understanding of cancer immunity and viral oncogenesis. [ABSTRACT FROM PUBLISHER]

The efficient and reliable control of an electric arc furnace (EAF) is a challenging problem, due to the strong intercorrelation among process variables, the large dimension of the input and output space, the strong interaction among process variables, a large time delay, and a highly nonlinear behaviour. This paper presents a model that allows us to optimize the control and, therefore, the electric power consumption in an EAF. The data used for this study were collected from Bizkaia Steel Mill (Arcelor Company). Neural network and fuzzy logic techniques have been applied on these data in order to get an improved model of the casting temperature inside the furnace's hearth. First, we developed some neural network models with different topologies and input variables. Then we used the best model obtained in the previous step to combine it with a fuzzy logic technique to get the final model. Comparison with experimental data and other models is carried out to validate the proposed model. Finally, the conclusions and future studies are exposed. [ABSTRACT FROM AUTHOR]

For the purpose of energy conservation, we present in this paper an introduction to the use of support vector (SV) learning machines used as a data mining tool applied to buildings energy consumption data from a measurement campaign. Experiments using a SVM-based software tool for the prediction of the electrical consumption of a residential building is performed. The data included 1 year and 3 months of daily recordings of electrical consumption and climate data such as temperatures and humidities. The learning stage was done for a first part of the data and the predictions were done for the last month. Performances of the model and contributions of significant factors were also derived. The results show good performances for the model. The second experiment consists of model re-estimations on a 1-year daily recording dataset lagged at 1-day time intervals in such a way that we derive temporal series of influencing factors weights along with model performance criteria. Finally, we introduce a perturbation in one of the influencing variables to detect a model change. Comparing contributing weights with and without the perturbation, the sudden contributing weight change could have diagnosed the perturbation. The important point is the ease of the production of many models. This method announces future research work in the exploitation of possibilities of this 'model factory'. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel eigenface-based face recognition approach. First we describe a continuous model for facial feature extraction, involving the covariance operator associated with gradient of the 2-D image function. Then we provide a discretized version of this model. Face identification and verification procedures, using a supervised classification technique, are also proposed. [ABSTRACT FROM AUTHOR]

The problem of nonlinear dynamical system modeling, considered in this paper, is motivated by restrictions arising in real-world tasks. The restrictions are that first, a system input cannot be entirely observed for one trial. Second, the system model must be subjected to the causality principle. Third, the input is corrupted by noise so that no relationship between the reference input and noise is known. Fourth, the model should have some degrees of freedom so that the associated accuracy can be regulated by a variation of these freedom degrees. We propose and justify new procedures for the nonlinear system modeling that are initialized by these motivations. The models are nonlinear and given by so called r -degree operators that can be reduced to a matrix form presentation. To satisfy the restrictions above, the matrices have special structures that we call the lower p -band matrices. The degree r of the models is the required degree of freedom. The rigorous analysis of errors associated with the presented techniques is given. Numerical experiments with real data demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This article is the second part of a two paper series exploring the application of two advanced computing techniques: artificial neural networks (ANNs) and genetic algorithms (GAs), to the problem of structural parameter identification for an idealised model of an aircraft wing. In this article, GAs are used to determine an idealised finite element model that is representative of the wing of the Pilatus PC-9/A trainer aircraft. This is achieved through an optimisation process that attempts to match the static and dynamic response of the model to measured aircraft structural responses. A number of approaches were trialed with improvements made to each successive approach in an attempt to find a suitable unique parameter set. Structural parameters were found for a three-element model which has characteristics very similar to those of the PC-9/A wing. A comparison is also provided between the performance of the neural network and GA approaches. [ABSTRACT FROM AUTHOR]

This article is the second part of a two paper series exploring the application of two advanced computing techniques: artificial neural networks (ANNs) and genetic algorithms (GAs), to the problem of structural parameter identification for an idealised model of an aircraft wing. In this article, GAs are used to determine an idealised finite element model that is representative of the wing of the Pilatus PC-9/A trainer aircraft. This is achieved through an optimisation process that attempts to match the static and dynamic response of the model to measured aircraft structural responses. A number of approaches were trialed with improvements made to each successive approach in an attempt to find a suitable unique parameter set. Structural parameters were found for a three-element model which has characteristics very similar to those of the PC-9/A wing. A comparison is also provided between the performance of the neural network and GA approaches. [ABSTRACT FROM AUTHOR]

This paper describes a new algorithm for policy evaluation for Markov decision processes (MDP) that possess a quasi birth-death structure. The proposed algorithm is based on matrix analytic methods which use probabilistic concepts associated with restricting the underlying Markov process to certain state subsets. A telecommunications application example shows that the method offers significant computational reduction compared to a standard MDP policy evaluation approach. [ABSTRACT FROM AUTHOR]

Multidimensional (MD) systems describe relations between signals depending on two or more independent variables. They are also called distributed parameter systems, if the independent variables are time and space. The only conventional models for their description are partial differential equations. This is in contrast to onedimensional (lumped parameter) systems, where a variety of different models including transfer functions is used. This paper extends the concept of transfer function models to multidimensional systems with bounded spatial domains, i.e., systems which can be described as initial-boundary-value problems. These transfer function models are useful for system analysis and as a starting point for the derivation of numerically efficient discrete simulation models. [ABSTRACT FROM AUTHOR]