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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]

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]

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]

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]

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]

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]

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]

Corona virus disease 2019 (Covid-19) is an illness caused by a natural corona virus called severe acute respiratory syndromes corona virus 2 (SARS-COV-2 formally called Covid-19) which is respiratory illness and has been declared the Covid-19 outbreak a global pandemic by World Health Organization (WHO). Presently, Covid-19 becomes a health concern around the globe. In present article, we investigated the dynamics of Covid-19 infectious disease under the fractional order derivative from both theoretical as well as analytical aspects. Using fixed-point theory results, we developed the indispensable conditions for the existence of the solution of the proposed model. Further we have used the techniques of Laplace transform coupled with the Adomian's decomposition method to obtain the semi analytical solution for the model under consideration. Finally we have provided some graphical presentation corresponding to different fractional order derivatives via Matlab for the desired solutions. [ABSTRACT FROM AUTHOR]

We study a real data set of 7,894,947 patients who received service from the University of Michigan Health System (UMHS) from January 1, 2003 to December 31, 2008 using regression analysis to understand the dynamics of patient volume. Our objective is to find out patterns from time series of patient volume during economic crisis. We propose a contribution adjusted formula to understand the dynamics of a heterogeneous customer population. We find that the trend of patient volume for a health system is positively correlated to the trend of the underlying adjusted resident population and to the GDP rates and negatively correlated to annual unemployment rate. We also find that the percent change of patient volume in a health system depends on the threshold level curves of resident population and unemployment rate with nonlinear behavior. Our multiple regression model with quadratic response surface explains 98.9% of the variation. Moreover, the multiple regression model having lag 1 with interaction term explains 96.5% of the variation. Furthermore, we propose several models having dummy variables using localities for patient groups. Overall, our results suggest that people use more health services when they have enough income, job and health insurance. [ABSTRACT FROM AUTHOR]

The Compton camera is a gamma ray imaging device expected to provide clinically relevant images in the SPECT applications where collimated cameras are sub-optimal. Its imaging performances depend not only on the design of the detection system but also on choices related to tomographic reconstruction. The aim of this work is to show that the accuracy in modelling the acquisition largely influences the quality of the images. For this purpose, we restrict here to Doppler broadening models in conjunction with the list-mode maximum likelihood expectation maximization (LM-MLEM) algorithm. The study was carried out with Monte-Carlo simulation. We show that the reconstructed point spread function is location-dependent when the model is not accurate, and the usual elongation artefacts well-known in Compton camera imaging will appear. The model we propose allows us to reconstruct isolated point sources and more complex non-uniform sources with improved resolution even in the direction orthogonal to the camera. [ABSTRACT FROM AUTHOR]

This study explores optimal control in the case when certain input uncertainties cannot be well quantified. In these scenarios, the decision-maker prefers to have the most flexibility, which is defined to be the largest range of options for decision variables, and still achieve the objectives of the operation while satisfying all constraints. Each decision variable is generalized to be a range of potential actions. These ranges are modelled with random variables, thus uncertainty quantification techniques are employed to compute expected values of objectives and probabilities of chance constraints. The proposed framework determines optimal probability densities for the decision variables by treating the amount of flexibility as an additional objective. There is a clear trade-off between the amount of flexibility that can be allowed and the resulting expected values of the other objectives. A dimension reduction technique is employed to ensure a reasonable dimension for the search space. [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]

The GM(1,1) model has been applied widely for grey prediction. However, traditional GM(1,1) model prediction sometimes results in large errors. In recent years, the grey model GM(1,1) has been improved, and the research mainly focuses on the modification, extension, and optimization of it. Most of the methods change the basic structure of the model. The study aims to improve the model's parameter estimation without changing the model's structure by using the following four methods: (1) optimizing the generating coefficient and estimating the model's parameters in the case of the optimal generating coefficient; (2) using the approximation by polynomial to estimate the model's parameters as a whole, including the parameter estimation of initial value; (3) translating the grey differential equation into the difference equation to estimate the model's parameters with the difference equation; and (4) using the modern intelligent algorithm (that is, the improved particle swarm optimization algorithm) for parameter estimation. The study builds the GM(1,1) model of the total consumption of China's industrial crude oil using the four improved methods. The simulation and prediction results show that these methods all significantly improve the prediction accuracy of model. [ABSTRACT FROM AUTHOR]

In this article, the qualitative theory and approximate solutions for fractional order Ebola model via Atangana-Baleanu-Caputo (ABC) fractional operators are developed. Using various tools of analysis, the conditions for the existence and stability of the proposed model are established. With the help of Laplace Adomain Decomposition method, we obtain the approximate solutions for the said model. In the last part, using Matlab, we plotted various graphs to discuss the underlying model for different fractional order values of γ. [ABSTRACT FROM AUTHOR]

A method for structural damage identification based on a modified Artificial Bee Colony algorithm is presented. A new formula is introduced to the onlooker bee phase to improve the convergence rate and the Tournament Selection Strategy is adopted instead of roulette to enhance global search ability of the algorithm. Test functions are introduced as benchmarks to verify the proposed algorithm. And then two numerical examples, including a supported beam and a plate, are conducted to investigate the efficiency and correctness of the proposed method. Final estimated results show that the present technique can produce more accurate damage identification results, comparing with other evolutionary algorithms, even with a few noise contaminated measurements. [ABSTRACT FROM PUBLISHER]

For Hammerstein output-error autoregressive systems, a decomposition based multi-innovation stochastic gradient (D-MISG) identification algorithm and a data filtering based multi-innovation stochastic gradient (F-MISG) identification algorithm are derived by means of the key-term separation principle and the multi-innovation identification theory. The D-MISG algorithm uses the decomposition technique to transform a Hammerstein system into two subsystems and requires less computational cost, and the F-MISG algorithm uses a linear filter to filter the input-output data and has a higher estimation accuracy for larger innovation lengths. The simulation results show that the proposed two algorithm can give satisfactory parameter estimates. [ABSTRACT FROM PUBLISHER]

A mathematical model is used to study the dynamics of ovine brucellosis when transmitted directly from infected individual, through contact with a contaminated environment or vertically through mother to child. The model developed by Aïnsebaet al.[A model for ovine brucellosis incorporating direct and indirect transmission, J. Biol. Dyn. 4 (2010), pp. 2–11. Available athttp://www.math.u-bordeaux1.fr/∼pmagal100p/papers/BBM-JBD09.pdf. Accessed 3 July 2012] was modified to include culling and then used to determine important parameters in the spread of human brucellosis using sensitivity analysis. An optimal control analysis was performed on the model to determine the best way to control such as a disease in the population. Three time-dependent controls to prevent exposure, cull the infected and reduce environmental transmission were used to set up to minimize infection at a minimum cost. [ABSTRACT FROM PUBLISHER]

A stage-structured model for a theoretical epidemic process that incorporates immature, susceptible and infectious individuals in independent stages is formulated. In this analysis, an input interpreted as a birth function is considered. The structural identifiability is studied using the Markov parameters. Then, the unknown parameters are uniquely determined by the output structure corresponding to an observation of infection. Two different birth functions are considered: the linear case and the Beverton–Holt type to analyse the structured epidemic model. Some conditions on the parameters to obtain non-zero disease-free equilibrium points are given. The identifiability of the parameters allows us to determine uniquely the basic reproduction number ℛ0and the stability of the model in the equilibrium is studied using ℛ0in terms of the model parameters. [ABSTRACT FROM PUBLISHER]

Based on the input–output representation of one-step state-delay systems, we use the auxiliary model-based recursive least-squares algorithm to estimate the parameters of the systems and study the convergence of the proposed algorithm by using the stochastic process theory. A simulation example is provided. [ABSTRACT FROM PUBLISHER]

A maximum likelihood parameter estimation algorithm is derived for controlled autoregressive autoregressive (CARAR) models based on the maximum likelihood principle. In this derivation, we use an estimated noise transfer function to filter the input–output data. The simulation results show that the proposed estimation algorithm can effectively estimate the parameters of such class of CARAR systems and give more accurate parameter estimates than the recursive generalized least-squares algorithm. [ABSTRACT FROM PUBLISHER]

The history matching (HM) hydrocarbon reservoir inverse problem is ill-posed because its solution may be non-unique or unstable. Variability of acceptable solutions around local minima may be very large. Nonetheless, it is a common practice in HM to find a unique reservoir model, although there is no guarantee that this model represents the geology. Qualitative geological information is generally not considered because of difficulties to express them mathematically. Here, we incorporate 'smoothness' in the spatial variation of physical properties as an example of a geological qualitative constraint that can be mathematically incorporated in an objective function also honouring the data. The constraint is valid if lateral continuity exists (e.g. fluvial-deltaic siliciclastic reservoirs). We mean smoothness by conditioning the permeability and/or porosity difference between adjacent grid blocks to be small. We use a synthetic 2D water-oil model and a solution search technique allowing characterising both the optimum solution and its variability. The smoothness constraint reduces the variance of the estimates by introducing bias in the solutions still preserving good match. The key point to achieve an optimum trade-off between stability and data match is the tuning of the parameter, controlling the relative importance of the constraint in the objective function. The smoothness constraint cannot be applied to all reservoirs. However, we corroborate the idea that a 'tool box' of HM can be designed; each 'tool' can incorporate a different constraint. Therefore, the interpreter can judiciously choose a specific tool from this tool box according to the adherence of its constraint to the particular reservoir being studied. [ABSTRACT FROM AUTHOR]

The history match procedure in an oil reservoir is of paramount importance because good estimates of the reservoir parameters may lead to a better forecast of the production. The reservoir is said to be 'matched' when the discrepancies between the model predictions and the observations of the real reservoir are below a certain tolerance. The determination of the model parameters via history matching requires the minimisation of an objective function in a parameter space that may be populated by many local minima. In other words, more than one set of reservoir model parameters fits the observation. Moreover, even a solution associated to a given minimum may be unstable. In order to reduce the ambiguity, it is necessary to incorporate constraints in the reservoir parameters to be estimated. Here, we use the smoothness constraint to regularise this inverse problem using as an example a modified version of the PUNQ model. The PUNQ model is suitable for applying this constraint because the sediments were deposited in a deltaic costal plain environment where good lateral continuity of the sediments is expected. We show that it is possible to recover all important features of the spatial distribution of the permo-porosity fields in all layers of the PUNQ model. In particular, the directions and widths of the sand channels were recovered. [ABSTRACT FROM AUTHOR]