Based on existing fuzzy simulation algorithms, this article presents two innovative techniques for approximating the expected values of fuzzy numbers' monotone functions, which is of utmost importance in fuzzy optimization literature. In this regard, the stochastic discretization algorithm of Liu and Liu (2002) is enhanced by updating the discretization procedure for the simulation of the membership function and the calculation formula for the expected values. This is achieved through initiating a novel uniform sampling process and employing a formula for discrete fuzzy numbers, respectively, as the generated membership function in the stochastic discretization algorithm would adversely affect its accuracy to some extent. What is more, considering that the bisection procedure involved in the numerical integration algorithm of Li (2015) is time-consuming and also, not necessary for the specified types of fuzzy numbers, a special numerical integration algorithm is proposed, which can simplify the simulation procedure by adopting the analytical expressions of α-optimistic values. Subsequently, concerning the extensive applications of regular fuzzy intervals, several theorems are introduced and proved as an extended effort to apply the improved stochastic discretization algorithm and the special numerical integration algorithm to the issues of fuzzy intervals. Throughout this article, a series of numerical experiments are conducted from which the superiority of both the two novel techniques over others are conspicuously displayed in aspects of accuracy, stability, and efficiency.

As a series of industrial Internet platforms have been launched, manufacturing facilities in the physical world, although distributed in different enterprises, are interconnected in the form of manufacturing services (MSs) in cyberspace. In this context, it makes possible for on-demand sharing of MSs as well as corresponding cross-enterprise collaboration. However, many dynamic uncertainties of both MSs and the submitted demands occur unpredictably, which seriously hinders the platforms' applications. To cope with the problem of MSs scheduling with supply-demand dual dynamic uncertainties, a three-stage approach based on an evolutionary hypernetwork model is proposed. In which, six of nine kinds of dynamic events and eighteen specific conditions are considered, and an event-condition-act mechanism is designed to guide local/global rescheduling if needed. Experimental results show the effectiveness of the proposed approach, as well as the potential of a platform employing the approach in response to different dynamic events in its application.

With the deeper application of sensor & cloud-based environment into manufacturing, deploying the industrial Internet platforms toward smart manufacturing has been more concerned. Based on the platforms, ubiquitous enterprises could participate in and support cross-enterprise collaboration, so that their distributed manufacturing facilities and capabilities could be shared and utilized in the form of manufacturing services (MSs). However, in order to achieve the successful application of the platforms, how to settle the supply demand matching (SDM) of the distributed manufacturing facilities and capabilities in the form of MSs, namely, MSs-SDM, becomes one of the most urgent problems to be solved. In addition, the trend of manufacturing socialization makes this problem much more scalable. In this context, this article aims to establish a set of hypernetwork-based models for the scalable MSs-SDM problem at first. An enterprises collaborative network is derived which is the projection of the underlying MSs-SDM situation to the upper-layer enterprises. Second, a method according to the evaluation on the cross-enterprise collaboration is proposed for this problem. In which, the created utilities, the rates of service invocation, and task allocation from both the global view of the overall network and the local view of each participated enterprise are evaluated. Finally, two steps of experiments introducing scalabilities illustrate the feasibility of the proposed models and the effectiveness of the derived method for MSs-SDM optimization, and further reveal five managerial implications to improve the operation and industrial practice of the platforms.

The paper deals with resource allocation scheduling problems in which the processing time of a job is defined by a function of its starting times and its position in a sequence. We also assume that the resource-dependent ready times of jobs are continuous functions of their consumed resource. Our objective is to minimize the resource consumption (the makespan) subject to the makespan constraint (limited resource availability). We prove that these two single-machine scheduling problems can be solved in polynomial time.

MOTIVATION: Elementary flux mode (EFM) is a useful tool in constraint-based modeling of metabolic networks. The property that every flux distribution can be decomposed as a weighted sum of EFMs allows certain applications of EFMs to studying flux distributions. The existence of biologically infeasible EFMs and the non-uniqueness of the decomposition, however, undermine the applicability of such methods. Efforts have been made to find biologically feasible EFMs by incorporating information from transcriptional regulation and thermodynamics. Yet, no attempt has been made to distinguish biologically feasible EFMs by considering their graphical properties. A previous study on the transcriptional regulation of metabolic genes found that distinct branches at a branch point metabolite usually belong to distinct metabolic pathways. This suggests an intuitive property of biologically feasible EFMs, i.e. minimal branching. RESULTS: We developed the concept of minimal branching EFM and derived the minimal branching decomposition (MBD) to decompose flux distributions. Testing in the core Escherichia coli metabolic network indicated that MBD can distinguish branches at branch points and greatly reduced the solution space in which the decomposition is often unique. An experimental flux distribution from a previous study on mouse cardiomyocyte was decomposed using MBD. Comparison with decomposition by a minimum number of EFMs showed that MBD found EFMs more consistent with established biological knowledge, which facilitates interpretation. Comparison of the methods applied to a complex flux distribution in Lactococcus lactis similarly showed the advantages of MBD. The minimal branching EFM concept underlying MBD should be useful in other applications. CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Identifying the protein coding regions in the DNA sequence is an active issue in computational biology. Presently, there are many outstanding methods in predicting the coding regions with extreme high accuracy, after conducting preceding training process. However, the training dependence may reduce adaptability of the methods, particularly for new sequences from unknown organisms with no or small training sets. In this paper, we firstly present a Self Adaptive Spectral Rotation (SASR) approach, which was first introduced in a previous work published in Nucleic Acids Research. This approach is adopted to visualize the Triplet Periodicity (TP) property, which is a simple and universal coding related property. After that, we use a segmentation technique to computationally analyze the visualization and provide a numerical prediction of the coding region candidates in the DNA sequence. This approach does not require any training process, so it can work before any extra information is available, especially is helpful when dealing with new sequences from unknown organisms. Hence, it could be an efficient tool for coding region prediction in the early stage study.

MOTIVATION: Elementary flux mode (EFM) is a fundamental concept as well as a useful tool in metabolic pathway analysis. One important role of EFMs is that every flux distribution can be decomposed into a set of EFMs and a number of methods to study flux distributions originated from it. Yet finding such decompositions requires the complete set of EFMs, which is intractable in genome-scale metabolic networks due to combinatorial explosion. RESULTS: In this article, we proposed an algorithm to decompose flux distributions into EFMs in genome-scale networks. It is an iterative scheme of a mixed integer linear program. Unlike previous optimization models to find pathways, any feasible solutions can become EFMs in our algorithm. This advantage enables the algorithm to approximate the EFM of largest contribution to an objective reaction in a flux distribution. Our algorithm is able to find EFMs of flux distributions with complex structures, closer to the realistic case in which a cell is subject to various constraints. A case of Escherichia coli growth in the Lysogeny broth (LB) medium containing various carbon sources was studied. Essential metabolites and their syntheses were located. Information on the contribution of each carbon source not obvious from the apparent flux distribution was also revealed. Our work further confirms the utility of finding EFMs by optimization models in genome-scale metabolic networks. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The forward kinematics of a parallel manipulator is so difficult that the analytical solutions of only a few parallel manipulators have been found. The forward kinematics of a three-degree-of-freedom planar parallel manipulator, where the base and the mobile platforms are two similar triangles, is studied in this paper and its analytical solution is provided. The final solution is two independent univariate quadratic equations. As well, the forward kinematics solution is simplified to the parallel manipulator where the two triangles are equilateral and a numerical example is presented.

Studies the forward kinematics of a special 6-6 Stewart platform, in which both the base and the mobile platforms are similar hexagons. A concise closed-form solution to the forward kinematics of the Stewart platform is obtained by introducing a quaternion to represent the transformation matrix. It is very interesting to find that the eight possible solutions have a very simple inner symmetry relationship. So, the solutions obtained from the approach presented in the paper are concise, represented as the squares of the four quaternion components. Besides, unnecessary complex roots are avoided automatically. Finally, only univariate quadratic equations are required to solve in this approach.