Primary school teacher’s noticing of students’ mathematical thinking in problem solving

Professional noticing of students’ mathematical thinking in problem solving involves the identification of noteworthy mathematical ideas of students’ mathematical thinking and its interpretation to make decisions in the teaching of mathematics. The goal of this study is to begin to characterize pre-service primary school teachers’ noticing of students’ mathematical thinking when students solve tasks that involve proportional and non-proportional reasoning. From the analysis of how pre-service primary school teachers notice students’ mathematical thinking, we have identified an initial framework with four levels of development. This framework indicates a possible trajectory in the development of primary teachers’ professional noticing.

GE models and algorithms for condensed phase equilibrium data regression in ternary systems: limitations and proposals

Phase equilibrium data regression is an unavoidable task necessary to obtain the appropriate values for any model to be used in separation equipment design for chemical process simulation and optimization. The accuracy of this process depends on different factors such as the experimental data quality, the selected model and the calculation algorithm. The present paper summarizes the results and conclusions achieved in our research on the capabilities and limitations of the existing GE models and about strategies that can be included in the correlation algorithms to improve the convergence and avoid inconsistencies. The NRTL model has been selected as a representative local composition model. New capabilities of this model, but also several relevant limitations, have been identified and some examples of the application of a modified NRTL equation have been discussed. Furthermore, a regression algorithm has been developed that allows for the advisable simultaneous regression of all the condensed phase equilibrium regions that are present in ternary systems at constant T and P. It includes specific strategies designed to avoid some of the pitfalls frequently found in commercial regression tools for phase equilibrium calculations. Most of the proposed strategies are based on the geometrical interpretation of the lowest common tangent plane equilibrium criterion, which allows an unambiguous comprehension of the behavior of the mixtures. The paper aims to show all the work as a whole in order to reveal the necessary efforts that must be devoted to overcome the difficulties that still exist in the phase equilibrium data regression problem.

A memetic algorithm for the delineation of local labour markets

Given a territory composed of basic geographical units, the delineation of local labour market areas (LLMAs) can be seen as a problem in which those units are grouped subject to multiple constraints. In previous research, standard genetic algorithms were not able to find valid solutions, and a specific evolutionary algorithm was developed. The inclusion of multiple ad hoc operators allowed the algorithm to find better solutions than those of a widely-used greedy method. However, the percentage of invalid solutions was still very high. In this paper we improve that evolutionary algorithm through the inclusion of (i) a reparation process, that allows every invalid individual to fulfil the constraints and contribute to the evolution, and (ii) a hillclimbing optimisation procedure for each generated individual by means of an appropriate reassignment of some of its constituent units. We compare the results of both techniques against the previous results and a greedy method.

An application of fuzzy logic for hardware/software partitioning in embedded systems

Hardware/Software partitioning (HSP) is a key task for embedded system co-design. The main goal of this task is to decide which components of an application are to be executed in a general purpose processor (software) and which ones, on a specific hardware, taking into account a set of restrictions expressed by metrics. In last years, several approaches have been proposed for solving the HSP problem, directed by metaheuristic algorithms. However, due to diversity of models and metrics used, the choice of the best suited algorithm is an open problem yet. This article presents the results of applying a fuzzy approach to the HSP problem. This approach is more flexible than many others due to the fact that it is possible to accept quite good solutions or to reject other ones which do not seem good. In this work we compare six metaheuristic algorithms: Random Search, Tabu Search, Simulated Annealing, Hill Climbing, Genetic Algorithm and Evolutionary Strategy. The presented model is aimed to simultaneously minimize the hardware area and the execution time. The obtained results show that Restart Hill Climbing is the best performing algorithm in most cases.

Algoritmos metaheurísticos en el problema del particionado hardware/software de sistemas embebidos

El particionado hardware/software es una tarea fundamental en el co-diseño de sistemas embebidos. En ella se decide, teniendo en cuenta las métricas de diseño, qué componentes se ejecutarán en un procesador de propósito general (software) y cuáles en un hardware específico. En los últimos años se han propuesto diversas soluciones al problema del particionado dirigidas por algoritmos metaheurísticos. Sin embargo, debido a la diversidad de modelos y métricas utilizadas, la elección del algoritmo más apropiado sigue siendo un problema abierto. En este trabajo se presenta una comparación de seis algoritmos metaheurísticos: Búsqueda aleatoria (Random search), Búsqueda tabú (Tabu search), Recocido simulado (Simulated annealing), Escalador de colinas estocástico (Stochastic hill climbing), Algoritmo genético (Genetic algorithm) y Estrategia evolutiva (Evolution strategy). El modelo utilizado en la comparación está dirigido a minimizar el área ocupada y el tiempo de ejecución, las restricciones del modelo son consideradas como penalizaciones para incluir en el espacio de búsqueda otras soluciones. Los resultados muestran que los algoritmos Escalador de colinas estocástico y Estrategia evolutiva son los que mejores resultados obtienen en general, seguidos por el Algoritmo genético.

A methodology for evacuation route planning inside buildings using geospatial technology

Evacuation route planning is a fundamental task for building engineering projects. Safety regulations are established so that all occupants are driven on time out of a building to a secure place when faced with an emergency situation. As an example, Spanish building code requires the planning of evacuation routes on large and, usually, public buildings. Engineers often plan these routes on single building projects, repeatedly assigning clusters of rooms to each emergency exit in a trial-and-error process. But problems may arise for a building complex where distribution and use changes make visual analysis cumbersome and sometimes unfeasible. This problem could be solved by using well-known spatial analysis techniques, implemented as a specialized software able to partially emulate engineer reasoning. In this paper we propose and test an easily reproducible methodology that makes use of free and open source software components for solving a case study. We ran a complete test on a building floor at the University of Alicante (Spain). This institution offers a web service (WFS) that allows retrieval of 2D geometries from any building within its campus. We demonstrate how geospatial technologies and computational geometry algorithms can be used for automating the creation and optimization of evacuation routes. In our case study, the engineers’ task is to verify that the load capacity of each emergency exit does not exceed the standards specified by Spain’s current regulations. Using Dijkstra’s algorithm, we obtain the shortest paths from every room to the most appropriate emergency exit. Once these paths are calculated, engineers can run simulations and validate, based on path statistics, different cluster configurations. Techniques and tools applied in this research would be helpful in the design and risk management phases of any complex building project.

Partición hardware software de un codificador JPEG utilizando escalador de colinas estocástico

La partición hardware/software es una etapa clave dentro del proceso de co-diseño de los sistemas embebidos. En esta etapa se decide qué componentes serán implementados como co-procesadores de hardware y qué componentes serán implementados en un procesador de propósito general. La decisión es tomada a partir de la exploración del espacio de diseño, evaluando un conjunto de posibles soluciones para establecer cuál de estas es la que mejor balance logra entre todas las métricas de diseño. Para explorar el espacio de soluciones, la mayoría de las propuestas, utilizan algoritmos metaheurísticos; destacándose los Algoritmos Genéticos, Recocido Simulado. Esta decisión, en muchos casos, no es tomada a partir de análisis comparativos que involucren a varios algoritmos sobre un mismo problema. En este trabajo se presenta la aplicación de los algoritmos: Escalador de Colinas Estocástico y Escalador de Colinas Estocástico con Reinicio, para resolver el problema de la partición hardware/software. Para validar el empleo de estos algoritmos se presenta la aplicación de este algoritmo sobre un caso de estudio, en particular la partición hardware/software de un codificador JPEG. En todos los experimentos es posible apreciar que ambos algoritmos alcanzan soluciones comparables con las obtenidas por los algoritmos utilizados con más frecuencia.

Logic-Based Outer-Approximation Algorithm for Solving Discrete-Continuous Dynamic Optimization Problems

We present an extension of the logic outer-approximation algorithm for dealing with disjunctive discrete-continuous optimal control problems whose dynamic behavior is modeled in terms of differential-algebraic equations. Although the proposed algorithm can be applied to a wide variety of discrete-continuous optimal control problems, we are mainly interested in problems where disjunctions are also present. Disjunctions are included to take into account only certain parts of the underlying model which become relevant under some processing conditions. By doing so the numerical robustness of the optimization algorithm improves since those parts of the model that are not active are discarded leading to a reduced size problem and avoiding potential model singularities. We test the proposed algorithm using three examples of different complex dynamic behavior. In all the case studies the number of iterations and the computational effort required to obtain the optimal solutions is modest and the solutions are relatively easy to find.