On single processor scheduling problems with learning dependent on the number of processed jobs

The importance of the role that learning plays in manufacturing, industry and computer systems is undeniable as well as the profit that can be increased if this phenomenon is taken into consideration for short- and long-term optimization. In this paper, we focus on scheduling jobs on a single processor, where its effectiveness can increase with the number of processed jobs, to minimize one of the following objectives: the maximum completion time with the release dates, the maximum lateness and the number of late jobs. It is proved that these well known polynomially solvable problems become at least NP-hard with the considered learning models. To solve them we provide some elimination procedures that are used to construct a branch and bound algorithm. Furthermore, we propose some fast heuristics for the problem of minimizing the number of late jobs with the general model of the learning effect.     

Single machine scheduling with resource allocation and learning effect considering the rate-modifying activity

This paper addresses a single machine scheduling problem in which the actual job processing times are determined by resource allocation function, its position in a sequence and a rate-modifying activity simultaneously. We discuss two objective functions with two resource allocation functions under the consideration of a rate-modifying activity. We show that the problems are solvable in O(n⁴)$O(n^4)$ time for a linear resource allocation function and are solvable in O(n²logn)$O(n^2\mathit{logn})$ time for a convex resource allocation function.     

Parallel-machine scheduling with past-sequence-dependent delivery times and learning effect

This paper considers identical parallel-machine scheduling problem with past-sequence-dependent (psd) delivery times and learning effect. In electronic manufacturing industry, an electronic component may be exposed to certain electromagnetic field and requires an extra time for eliminating adverse effect after the main processing. The extra time is modeled as past-sequence-dependent delivery time in the literature, which is proportional to the waiting time in the system. It is also observed that the learning process reflects a decrease in the processing time as a function of the number of repetitions, i.e., as a function of the job position in the sequence. In practice, one often has to deal with the scheduling problems with psd delivery times and learning effect. Identical parallel-machine setting is considered because the occurrence of resources in parallel is common in the real world. In this paper, three objectives are the minimization of the total absolute deviation of job completion times, the total load on all machines and the total completion time. We develop polynomial algorithms to optimally solve these problems.     

Constructs of engagement emerging in an ethnomathematically-based teacher education course

This paper presents a case study, in which we apply and develop theoretical constructs to analyze motivating desires observed in an unconventional, culturally contextualized teacher education course. Participants, Israeli students from several different cultures and backgrounds (pre-service and in-service teachers, Arabs and Jews, religious and secular) together studied geometry through inquiry into geometric ornaments drawn from diverse cultures, and acquired knowledge and skills in multicultural education. To analyze affective behaviors in the course we applied the methodology of engagement structures recently proposed by Goldin and his colleagues. Our study showed that engagement structures were a powerful tool for examining motivating desires of the students. We found that the constructivist ethnomathematical approach highlighted the structures that matched our instructional goals and diminished those related to students’ feelings of dissatisfaction and inequity. We propose a new engagement structure “Acknowledge my culture” to embody motivating desires, arising from multicultural interactions, that foster mathematical learning.     

A Note on Existence and Convergence of Best Proximity Points for Pointwise Cyclic Contractions

We introduce a notion of pointwise cyclic contraction T satisfying TA ? B and TB ? A to obtain the existence of a point x ∈ A, such that d(x, Tx) = dist(A, B), known as a best proximity point for such a map. We also prove that for any x ∈ A, the Picard iteration {T²ⁿx} converges to a best proximity point.     

我国青少年科学教育的历史与展望

本文回顾了我国科学教育的历史;论述了科学教育是基础教育阶段的核心课程以及在国际上受到的重视;分析了我国科学教育的现状,并提出加强科学教育的建议.     

Learning Bayesian Networks with the Combination of Evolutionary Algorithm and EMI Method

Most Bayesian network （BN） learning algorithms use EMI algorithm to deal with incomplete data. But EMI algorithm is of low efficiency due to its iterative parameter refinement, and the problem will become even worse when multiple runs of EMI algorithm are needed. Besides, EMI algorithm usually converges to local maxima, which also degrades the accuracy of EMI based BN learning algorithms. In this paper, we replace EMI algorithm used in BN learning tasks with EMI method to deal with incomplete data. EMI is a very efficient method, which estimates probability distributions directly from incomplete data rather than performs iterative refinement of parameters. Base on EMI method, we propose an effec- tive algorithm, namely EMI-EA. EMI-EA algorithm uses EMI method to estimate probability distribution over local structures in BNs, and evaluates BN structures with a variant of MDL scoring function. To avoid getting into local maxima of the search process, EMI-EA evolves BN struc- tures with an Evolutionary algorithm （EA）. The experi- mental results on Alarm, Asia and an examplar network show that EMI-EA algorithm outperforms EMI-EA for all samples and E-TPDA algorithms for small and middle size of samples in terms of accuracy. In terms of efficiency, EMI-EA is comparable with E-TPDA algorithm and much more efficient than EMI-EA algorithm. EMI-EA also out- performs EMI-EA and M-V algorithm when learning BNs with hidden variables.     

Imprecise probability models for learning multinomial distributions from data. Applications to learning credal networks

This paper considers the problem of learning multinomial distributions from a sample of independent observations. The Bayesian approach usually assumes a prior Dirichlet distribution about the probabilities of the different possible values. However, there is no consensus on the parameters of this Dirichlet distribution. Here, it will be shown that this is not a simple problem, providing examples in which different selection criteria are reasonable. To solve it the Imprecise Dirichlet Model (IDM) was introduced. But this model has important drawbacks, as the problems associated to learning from indirect observations. As an alternative approach, the Imprecise Sample Size Dirichlet Model (ISSDM) is introduced and its properties are studied. The prior distribution over the parameters of a multinomial distribution is the basis to learn Bayesian networks using Bayesian scores. Here, we will show that the ISSDM can be used to learn imprecise Bayesian networks, also called credal networks when all the distributions share a common graphical structure. Some experiments are reported on the use of the ISSDM to learn the structure of a graphical model and to build supervised classifiers.     

DFD-SS: Document Forgery Detection using Spectral – Spatial Features for Hyperspectral Images

In the present era of machines and edge-cutting technologies, still document frauds persist. They are done intuitively by using almost identical inks, that it becomes challenging to detect them—this demands an approach that efficiently investigates the document and leaves it intact. Hyperspectral imaging is one such a type of approach that captures the images from hundreds to thousands of spectral bands and analyzes the images through their spectral and spatial features, which is not possible by conventional imaging. Deep learning is an edge-cutting technology known for solving critical problems in various domains. Utilizing supervised learning imposes constraints on its usage in real scenarios, as the inks used in forgery are not known prior. Therefore, it is beneficial to use unsupervised learning. An unsupervised feature extraction through a Convolutional Autoencoder (CAE) followed by Logistic Regression (LR) for classification is proposed (CAE-LR). Feature extraction is evolved around spectral bands, spatial patches, and spectral-spatial patches. We inspected the impact of spectral, spatial, and spectral-spatial features by mixing inks in equal and unequal proportion using CAE-LR on the UWA writing ink hyperspectral images dataset for blue and black inks. Hyperspectral images are captured at multiple correlated spectral bands, resulting in information redundancy handled by restoring certain principal components. The proposed approach is compared with eight state-of-art approaches used by the researchers. The results depicted that by using the combination of spectral and spatial patches, the classification accuracy enhanced by 4.85% for black inks and 0.13% for blue inks compared to state-of-art results. In the present scenario, the primary area concern is to identify and detect the almost similar inks used in document forgery, are efficiently managed by the proposed approach.     

The impact of a conceptual model-based mathematics computer tutor on multiplicative reasoning and problem-solving of students with learning disabilities

The study explored the impact of Please Go Bring Me-COnceptual Model-based Problem Solving (PGBM-COMPS) computer tutoring system on multiplicative reasoning and problem solving of students with learning disabilities. The PGBM-COMPS program focused on enhancing the multiplicative reasoning and problem solving through nurturing fundamental mathematical ideas and moving students above and beyond the concrete level of operation. This is achieved by taking advantages of the constructivist approach from mathematics education and explicit conceptual model-based problem solving approach from special education. Participants were three elementary students with learning disabilities (LD). A mixed method design was employed to investigate the effect of the PGBM-COMPS program on enhancing students’ multiplicative reasoning and problem solving. It was found that the PGBM-COMPS program significantly improved participating students’ problem solving performance not only on researcher developed criterion tests but also on a norm-referenced standardized test. Qualitative and quantities data from this study indicate that, in addition to nurturing fundamental concept of composite units, it is necessary to help students to understand underlying problem structures and move toward mathematical model-based problem representation and solving for generalized problem solving skills.