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A critical part of supporting the development of students' algorithmic thinking is understanding the challenges that emerge when students engage with algorithmatizing tasks--tasks that require the creation of an algorithm. Knowledge of these challenges can serve as a basis upon which educators can build effective strategies for enhancing students' algorithmic thinking skills. This paper presents three illustrative cases of emergent challenges evident as students grapple with the process of creating an algorithm. The first challenge highlights discrepancies between the method with which students solve a problem and the algorithm they create, and claim would, when implemented, solve the same problem. The second challenge pertains to the persistence of students' normatively incorrect algorithms, despite going through multiple iterations of testing and revising. Finally, the third challenge concerns issues around the use of test problems for supporting students in their creation of generalized algorithms. These three challenges are discussed using student data (illustrative cases) from three different mathematical algorithmatizing tasks. Suggestions are put forth for addressing some of these challenges, with a particular emphasis on practical pedagogical suggestions for cultivating students' mathematical thinking in the context of algorithmatizing tasks.

This paper presents an application of the Kalman filter in signal processing in instrumentation systems when the conditions of the environment generate a large amount of interference for the acquisition of signals from measurement systems. The unwanted interferences make important use of the instrumentation system resources and do not represent useful information under any aspect. A simulation is presented using the Matlab tool, which remarkably facilitates the information processing so that the corresponding actions are taken according to the information obtained, taking advantage of the current resources offered by the embedded systems and the required measurements are obtained with enough accuracy.

This study explores student flexibility in mathematics by examining the relationship between accuracy and strategy use for solving arithmetic and algebra problems. Core to procedural flexibility is the ability to select and accurately execute the most appropriate strategy for a given problem. Yet the relationship between strategy selection and accurate execution is nuanced and poorly understood. In this paper, this relationship was examined in the context of an assessment where students were asked to complete the same problem twice using different approaches. In particular, we explored (a) the extent to which students were more accurate when selecting standard or better-than-standard strategies, (b) whether this accuracy-strategy use relationship differed depending on whether the student solved a problem for the first time or the second time, and (c) the extent to which students were more accurate when solving algebraic versus arithmetic problems. Our results indicate significant associations between accuracy and all of these aspects--we found differences in accuracy based on strategy, problem type, and a significant interaction effect between strategy and assessment part. These findings have important implications both for researchers investigating procedural flexibility as well as secondary mathematics educators who seek to promote this capacity among their students.

Both cost-sensitive classification and online learning have been extensively studied in data mining and machine learning communities, respectively. However, very limited study addresses an important intersecting problem, that is, “Cost-Sensitive Online Classification”. In this paper, we formally study this problem, and propose a new framework for Cost-Sensitive Online Classification by directly optimizing cost-sensitive measures using online gradient descent techniques. Specifically, we propose two novel cost-sensitive online classification algorithms, which are designed to directly optimize two well-known cost-sensitive measures: (i) maximization of weighted sum of sensitivity and specificity, and (ii) minimization of weighted misclassification cost. We analyze the theoretical bounds of the cost-sensitive measures made by the proposed algorithms, and extensively examine their empirical performance on a variety of cost-sensitive online classification tasks. Finally, we demonstrate the application of the proposed technique for solving several online anomaly detection tasks, showing that the proposed technique could be a highly efficient and effective tool to tackle cost-sensitive online classification tasks in various application domains. [ABSTRACT FROM AUTHOR]

A fourth-order hybrid implicit and explicit finite-difference time-domain Method has been presented in this paper. This new method investigates the use of a second-order accurate in time and a fourth-order accurate in space. The 2D formulation of the method is presented and the time stability condition of the method is certified. The maximum time step size in this method is only determined by one spatial discretization. The numerical dispersion is discussed. Numerical examples demonstrate that when this method is used to solve electromagnetic problems, higher computational efficiency and less dispersion error can be obtained by comparing with the traditional finite-difference time-domain algorithm. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Classifier learning with data-sets that suffer from imbalanced class distributions is a challenging problem in data mining community. This issue occurs when the number of examples that represent one class is much lower than the ones of the other classes. Its presence in many real-world applications has brought along a growth of attention from researchers. In machine learning, the ensemble of classifiers are known to increase the accuracy of single classifiers by combining several of them, but neither of these learning techniques alone solve the class imbalance problem, to deal with this issue the ensemble learning algorithms have to be designed specifically. In this paper, our aim is to review the state of the art on ensemble techniques in the framework of imbalanced data-sets, with focus on two-class problems. We propose a taxonomy for ensemble-based methods to address the class imbalance where each proposal can be categorized depending on the inner ensemble methodology in which it is based. In addition, we develop a thorough empirical comparison by the consideration of the most significant published approaches, within the families of the taxonomy proposed, to show whether any of them makes a difference. This comparison has shown the good behavior of the simplest approaches which combine random undersampling techniques with bagging or boosting ensembles. In addition, the positive synergy between sampling techniques and bagging has stood out. Furthermore, our results show empirically that ensemble-based algorithms are worthwhile since they outperform the mere use of preprocessing techniques before learning the classifier, therefore justifying the increase of complexity by means of a significant enhancement of the results. [ABSTRACT FROM PUBLISHER]

What is called numerical reproducibility is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing units, execution environments, computational loads, etc. This problem is especially stringent for HPC numerical simulations. In what follows, we identify the problems encountered when implementing interval routines in floating-point arithmetic. Some are well-known and common in numerical computations, some are specific to interval computations. We propose here a classification of floating-point issues by distinguishing their severity with respect to correctness and tightness of the computed interval result. In fact, interval computation can accommodate the lack of numerical reproducibility as long as it does not affect the inclusion property, which is the main property of interval arithmetic. Several ways to preserve the inclusion property are presented, on the example of the product of matrices with interval coefficients. [ABSTRACT FROM AUTHOR]

Finding a universal description of the algorithm optimization is one of the key challenges in personalized recommendation. In this article, for the first time, we introduce a scaling-based algorithm (SCL) independent of recommendation list length based on a hybrid algorithm of heat conduction and mass diffusion, by finding out the scaling function for the tunable parameter and object average degree. The optimal value of the tunable parameter can be abstracted from the scaling function, which is heterogeneous for the individual object. Experimental results obtained from three real datasets, Netflix, MovieLens and RYM, show that the SCL is highly accurate in recommendation. More importantly, compared with a number of excellent algorithms, including the mass diffusion method, the original hybrid method, and even an improved version of the hybrid method, the SCL algorithm remarkably promotes the personalized recommendation in three other aspects: solving the accuracy-diversity dilemma, presenting a high novelty, and solving the key challenge of cold start problem. [ABSTRACT FROM AUTHOR]

Unscented particle filter (UPF) struggles to completely cover the target state space when handling the maneuvering target tracing problem, and the tracking performance can be affected by the low sample diversity and algorithm redundancy. In order to solve this problem, the method of divide-and-conquer sampling is applied to the UPF tracking algorithm. By decomposing the state space, the descending dimension processing of the target maneuver is realized. When dealing with the maneuvering target, particles are sampled separately in each subspace, which directly prevents particles from degeneracy. Experiments and a comparative analysis were carried out to comprehensively analyze the performance of the divide-and-conquer sampling unscented particle filter (DCS-UPF). The simulation result demonstrates that the proposed algorithm can improve the diversity of particles and obtain higher tracking accuracy in less time than the particle swarm algorithm and intelligent adaptive filtering algorithm. This algorithm can be used in complex maneuvering conditions. [ABSTRACT FROM AUTHOR]