Modeling as a means for making powerful ideas accessible to children at an early age

The SimCalc Vision and Contributions Advances in Mathematics Education 2013, pp 419-436 Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age Richard Lesh, Lyn English, Serife Sevis, Chanda Riggs … show all 4 hide » Look Inside » Get Access Abstract In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to describe situations that involve continuous quantities (inches, feet, pounds, etc.), signed quantities, quantities that have both magnitude and direction, locations (coordinates, or ordinal quantities), transformations (actions), accumulating quantities, continually changing quantities, and other kinds of mathematical objects. Furthermore, if we ask, what kind of situations can children use numbers to describe? rather than restricting attention to situations where children should be able to calculate correctly, then this study shows that average ability children in grades K-2 are (and need to be) able to productively mathematize situations that involve far more than simple counts. Similarly, whereas nearly the entire K-16 mathematics curriculum is restricted to situations that can be mathematized using a single input-output rule going in one direction, even the lives of primary school children are filled with situations that involve several interacting actions—and which involve feedback loops, second-order effects, and issues such as maximization, minimization, or stabilizations (which, many years ago, needed to be postponed until students had been introduced to calculus). …This brief paper demonstrates that, if children’s stories are used to introduce simulations of “real life” problem solving situations, then average ability primary school children are quite capable of dealing productively with 60-minute problems that involve (a) many kinds of quantities in addition to “counts,” (b) integrated collections of concepts associated with a variety of textbook topic areas, (c) interactions among several different actors, and (d) issues such as maximization, minimization, and stabilization.

Molecular dynamics simulation of fracture strength and morphology of defective graphene

Different types of defects can be introduced into graphene during material synthesis, and significantly influence the properties of graphene. In this work, we investigated the effects of structural defects, edge functionalisation and reconstruction on the fracture strength and morphology of graphene by molecular dynamics simulations. The minimum energy path analysis was conducted to investigate the formation of Stone-Wales defects. We also employed out-of-plane perturbation and energy minimization principle to study the possi-ble morphology of graphene nanoribbons with edge-termination. Our numerical results show that the fracture strength of graphene is dependent on defects and environmental temperature. However, pre-existing defects may be healed, resulting in strength recovery. Edge functionalization can induce compressive stress and ripples in the edge areas of gra-phene nanoribbons. On the other hand, edge reconstruction contributed to the tensile stress and curved shape in the graphene nanoribbons.

CASNS - A heuristic algorithm for the nesting of irregular-shaped sheet-metal blanks

This article reports on the design and implementation of a computer-aided sheet nesting system (CASNS) for the nesting of two-dimensional irregular-shaped sheet-metal blanks on a given sheet stock or coil stock. The system is designed by considering several constraints of sheet-metal stamping operations, such as bridge width and grain orientation, and design requirements such as maximizing the strength of the part hen subsequent bending is involved, minimization of scrap, and economic justification for'a single or multiple station operation. Through many practical case studies, the system proves its efficiency, effectiveness and usefulness.

Molecular dynamics simulation of fracture strength and morphology of defective graphene

Different types of defects can be introduced into graphene during material synthesis, and significantly influence the properties of graphene. In this work, we investigated the effects of structural defects, edge functionalisation and reconstruction on the fracture strength and morphology of graphene by molecular dynamics simulations. The minimum energy path analysis was conducted to investigate the formation of Stone-Wales defects. We also employed out-of-plane perturbation and energy minimization principle to study the possible morphology of graphene nanoribbons with edge-termination. Our numerical results show that the fracture strength of graphene is dependent on defects and environmental temperature. However, pre-existing defects may be healed, resulting in strength recovery. Edge functionalization can induce compressive stress and ripples in the edge areas of graphene nanoribbons. On the other hand, edge reconstruction contributed to the tensile stress and curved shape in the graphene nanoribbons.

Fairness aware resource allocation in multi-hop OFDM systems

This thesis presents an analysis of the resource allocation problem in Orthogonal Frequency Division Multiplexing based multi-hop wireless communications systems. The study analyzed the tractable nature of the problem and designed several heuristic and fairness-aware resource allocation algorithms. These algorithms are fast and efficient and therefore can improve power management in wireless systems significantly.

The use of acoustic indices to determine avian species richness in audio-recordings of the environment

Interpreting acoustic recordings of the natural environment is an increasingly important technique for ecologists wishing to monitor terrestrial ecosystems. Technological advances make it possible to accumulate many more recordings than can be listened to or interpreted, thereby necessitating automated assistance to identify elements in the soundscape. In this paper we examine the problem of estimating avian species richness by sampling from very long acoustic recordings. We work with data recorded under natural conditions and with all the attendant problems of undefined and unconstrained acoustic content (such as wind, rain, traffic, etc.) which can mask content of interest (in our case, bird calls). We describe 14 acoustic indices calculated at one minute resolution for the duration of a 24 hour recording. An acoustic index is a statistic that summarizes some aspect of the structure and distribution of acoustic energy and information in a recording. Some of the indices we calculate are standard (e.g. signal-to-noise ratio), some have been reported useful for the detection of bioacoustic activity (e.g. temporal and spectral entropies) and some are directed to avian sources (spectral persistence of whistles). We rank the one minute segments of a 24 hour recording in descending order according to an "acoustic richness" score which is derived from a single index or a weighted combination of two or more. We describe combinations of indices which lead to more efficient estimates of species richness than random sampling from the same recording, where efficiency is defined as total species identified for given listening effort. Using random sampling, we achieve a 53% increase in species recognized over traditional field surveys and an increase of 87% using combinations of indices to direct the sampling. We also demonstrate how combinations of the same indices can be used to detect long duration acoustic events (such as heavy rain and cicada chorus) and to construct long duration (24 h) spectrograms.

On the allocation of a takeover purchase price under AASB1013

The purpose of this paper is to document and explain the allocation of takeover purchase price to identifiable intangible assets (IIAs), purchased goodwill, and/or target net tangible assets in an accounting environment unconstrained with respect to IIA accounting policy choice. Using a sample of Australian acquisitions during the unconstrained accounting environment from 1988 to 2004, we find the percentage allocation of purchase price to IIAs averaged 19.09%. The percentage allocation to IIAs is significantly positively related to return on assets and insignificantly related to leverage, contrary to opportunism. Efficiency suggests an explanation: profitable firms acquire and capitalise a higher percentage of IIAs in acquisitions. The target's investment opportunity set is significantly positively related to the percentage allocation to IIAs, consistent with information-signalling. The paper contributes to the accounting policy choice literature by showing how Australian firms make the one-off accounting policy choice in regards allocation of takeover purchase price (which is often a substantial dollar amount to) in an environment where accounting for IIAs was unconstrained.

Application of lean production to reducing operational waste in a tile manufacturing process

Roofing tile manufacturing is a mass production process with high operational and inventory wastes and costs. Due to huge operational costs, excessive inventory and wastes, and quality problems, roofing tile manufacturers are trying to implement lean manufacturing practice in their operations in order to remain competitive in an ncreasingly competitive global market. The aim of this research is to evaluate the possibility of reducing the operational and inventory costs of the tile manufacturing process through waste minimization. This paper analyses the current waste situation in a tile manufacturing process and develops current and future value stream mapping for such a process with a view to implementing lean principles in manufacturing. The focus of the approach is on cost reduction by eliminating non-value-added activities.

Analysis of interrelationships between critical waste factors in office building retrofit projects using interpretive structural modelling

The number of office building retrofit projects is increasing. These projects are characterised by processes which have a close relationship with waste generation and therefore demand a high level of waste management. In a preliminary study reported separately, we identified seven critical factors of on-site waste generation in office building retrofit projects. Through semi-structured interviews and Interpretive Structural Modelling, this research further investigated the interrelationships among these critical waste factors, to identify each factor’s level of influence on waste generation and propose effective solutions for waste minimization. “Organizational commitment” was identified as the fundamental issue for waste generation in the ISM system. Factors related to plan, design and construction processes were found to be located in the middle levels of the ISM model but still had significant impacts on the system as a whole. Based on the interview findings and ISM analysis results, some practical solutions were proposed for waste minimization in building retrofit projects: (1) reusable and adaptable fit-out design; (2) a system for as-built drawings and building information; (3) integrated planning for retrofitting work process and waste management; and (4) waste benchmarking development for retrofit projects. This research will provide a better understanding of waste issues associated with building retrofit projects and facilitate enhanced waste minimization.

Constrained control design for dynamic positioning of marine vehicles with control allocation

In this paper, we address the control design problem of positioning of over-actuated marine vehicles with control allocation. The proposed design is based on a combined position and velocity loops in a multi-variable anti-windup implementation together with a control allocation mapping. The vehicle modelling is considered with appropriate simplifications related to low-speed manoeuvring hydrodynamics and vehicle symmetry. The control design is considered together with a control allocation mapping. We derive analytical tuning rules based on requirements of closed-loop stability and performance. The anti- windup implementation of the controller is obtained by mapping the actuator-force constraint set into a constraint set for the generalized forces. This approach ensures that actuation capacity is not violated by constraining the generalized control forces; thus, the control allocation is simplified since it can be formulated as an unconstrained problem. The mapping can also be modified on-line based on actuator availability to provide actuator-failure accommodation. We provide a proof of the closed-loop stability and illustrate the performance using simulation scenarios for an open-frame underwater vehicle.

Output feedback optimal control with contraints

In Chapters 1 through 9 of the book (with the exception of a brief discussion on observers and integral action in Section 5.5 of Chapter 5) we considered constrained optimal control problems for systems without uncertainty, that is, with no unmodelled dynamics or disturbances, and where the full state was available for measurement. More realistically, however, it is necessary to consider control problems for systems with uncertainty. This chapter addresses some of the issues that arise in this situation. As in Chapter 9, we adopt a stochastic description of uncertainty, which associates probability distributions to the uncertain elements, that is, disturbances and initial conditions. (See Section 12.6 for references to alternative approaches to model uncertainty.) When incomplete state information exists, a popular observer-based control strategy in the presence of stochastic disturbances is to use the certainty equivalence [CE] principle, introduced in Section 5.5 of Chapter 5 for deterministic systems. In the stochastic framework, CE consists of estimating the state and then using these estimates as if they were the true state in the control law that results if the problem were formulated as a deterministic problem (that is, without uncertainty). This strategy is motivated by the unconstrained problem with a quadratic objective function, for which CE is indeed the optimal solution (˚Astr¨om 1970, Bertsekas 1976). One of the aims of this chapter is to explore the issues that arise from the use of CE in RHC in the presence of constraints. We then turn to the obvious question about the optimality of the CE principle. We show that CE is, indeed, not optimal in general. We also analyse the possibility of obtaining truly optimal solutions for single input linear systems with input constraints and uncertainty related to output feedback and stochastic disturbances.We first find the optimal solution for the case of horizon N = 1, and then we indicate the complications that arise in the case of horizon N = 2. Our conclusion is that, for the case of linear constrained systems, the extra effort involved in the optimal feedback policy is probably not justified in practice. Indeed, we show by example that CE can give near optimal performance. We thus advocate this approach in real applications.

Numerical estimation of 3D mechanical forces exerted by cells on non-linear materials

The exchange of physical forces in both cell-cell and cell-matrix interactions play a significant role in a variety of physiological and pathological processes, such as cell migration, cancer metastasis, inflammation and wound healing. Therefore, great interest exists in accurately quantifying the forces that cells exert on their substrate during migration. Traction Force Microscopy (TFM) is the most widely used method for measuring cell traction forces. Several mathematical techniques have been developed to estimate forces from TFM experiments. However, certain simplifications are commonly assumed, such as linear elasticity of the materials and/or free geometries, which in some cases may lead to inaccurate results. Here, cellular forces are numerically estimated by solving a minimization problem that combines multiple non-linear FEM solutions. Our simulations, free from constraints on the geometrical and the mechanical conditions, show that forces are predicted with higher accuracy than when using the standard approaches.

Aircraft dynamic navigation for unmanned aerial vehicles

This thesis describes the investigation of an Aircraft Dynamic Navigation (ADN) approach, which incorporates an Aircraft Dynamic Model (ADM) directly into the navigation filter of a fixed-wing aircraft or UAV. The result is a novel approach that offers both performance improvements and increased reliability during short-term GPS outages. This is important in allowing future UAVs to achieve routine, unconstrained, and safe operations in commercial environments. The primary contribution of this research is the formulation Unscented Kalman Filter (UKF) which incorporates a complex, non-linear, laterally and longitudinally coupled, ADM, and sensor suite consisting of a Global Positioning System (GPS) receiver, Inertial Measurement Unit (IMU), Electronic Compass (EC), and Air Data (AD) Pitot Static System.

Anti-wind-up designs for dynamic positioning of marine vehicles with control allocation

This paper presents a framework for the design of a joint motion controller and a control allocation strategy for dynamic positioning of marine vehicles. The key aspects of the proposed designs are a systematic approach to deal with actuator saturation and to inform the motion controller about saturation. The proposed system uses a mapping that translates the actuator constraint sets into constraint sets at the motion controller level. Hence, while the motion controller addresses the constraints, the control allocation algorithm can solve an unconstrained optimisation problem. The constrained control design is approached using a multivariable anti-wind-up strategy for strictly proper controllers. This is applicable to the implementation of PI and PID type of motion controllers.

Locating people in video from semantic descriptions : a new database and approach

The location of previously unseen and unregistered individuals in complex camera networks from semantic descriptions is a time consuming and often inaccurate process carried out by human operators, or security staff on the ground. To promote the development and evaluation of automated semantic description based localisation systems, we present a new, publicly available, unconstrained 110 sequence database, collected from 6 stationary cameras. Each sequence contains detailed semantic information for a single search subject who appears in the clip (gender, age, height, build, hair and skin colour, clothing type, texture and colour), and between 21 and 290 frames for each clip are annotated with the target subject location (over 11,000 frames are annotated in total). A novel approach for localising a person given a semantic query is also proposed and demonstrated on this database. The proposed approach incorporates clothing colour and type (for clothing worn below the waist), as well as height and build to detect people. A method to assess the quality of candidate regions, as well as a symmetry driven approach to aid in modelling clothing on the lower half of the body, is proposed within this approach. An evaluation on the proposed dataset shows that a relative improvement in localisation accuracy of up to 21 is achieved over the baseline technique.