Development of mathematical models to elaborate strategies, to select alternatives and the development of plans for the adaptation of communities to climate change in different geographical areas including costs to implement it

Climate change is on the policy agenda at the global level, with the aim of understanding and reducing its causes and to mitigate its consequences. In most of the countries and international organisms UNO, OECD, EC, etc … the efforts and debates have been directed to know the possible causes, to predict the future evolution of some variable conditioners, and trying to make studies to fight against the effects or to delay the negative evolution of such. Nevertheless, the elaboration of a global model was not boarded that can help to choose the best alternative between the feasible ones, to elaborate the strategies and to evaluate the costs. As in all natural, technological and social changes, the best-prepared countries will have the best bear and the more rapid recover. In all the geographic areas the alternative will not be the same one, but the model should help us to make the appropriated decision. It is essential to know those areas that are more sensitive to the negative effects of climate change, the parameters to take into account for its evaluation, and comprehensive plans to deal with it. The objective of this paper is to elaborate a mathematical model support of decisions, that will allow to develop and to evaluate alternatives of adaptation to the climatic change of different communities in Europe and Latin-America, mainly, in vulnerable areas to the climatic change, considering in them all the intervening factors. The models will take into consideration criteria of physical type (meteorological, edaphic, water resources), of use of the ground (agriculturist, forest, mining, industrial, urban, tourist, cattle dealer), economic (income, costs, benefits, infrastructures), social (population), politician (implementation, legislation), educative (Educational programs, diffusion), sanitary and environmental, at the present moment and the future.

ANN and Fuzzy c-Means applied to environmental pollution prediction

Salamanca, situated in center of Mexico is among the cities which suffer most from the air pollution in Mexico. The vehicular park and the industry, as well as orography and climatic characteristics have propitiated the increment in pollutant concentration of Sulphur Dioxide (SO2). In this work, a Multilayer Perceptron Neural Network has been used to make the prediction of an hour ahead of pollutant concentration. A database used to train the Neural Network corresponds to historical time series of meteorological variables and air pollutant concentrations of SO2. Before the prediction, Fuzzy c-Means and K-means clustering algorithms have been implemented in order to find relationship among pollutant and meteorological variables. Our experiments with the proposed system show the importance of this set of meteorological variables on the prediction of SO2 pollutant concentrations and the neural network efficiency. The performance estimation is determined using the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). The results showed that the information obtained in the clustering step allows a prediction of an hour ahead, with data from past 2 hours.

Functional modeling applied to HAZOP automation

In this paper we present a new tool to perform guided HAZOP analyses. This tool uses a functional model of the process that merges its functional and its structural information in a natural way. The functional modeling technique used is called D-higraphs. This tool solves some of the problems and drawbacks of other existing methodologies for the automation of HAZOPs. The applicability and easy understanding of the proposed methodology is shown in an industrial case.

A Monitoring Infrastructure for FPGA Self-Awareness and Dynamic Adaptation

Variabilities associated with CMOS evolution affect the yield and performance of current digital designs. FPGAs, which are widely used for fast prototyping and implementation of digital circuits, also suffer from these issues. Proactive approaches start to appear to achieve self-awareness and dynamic adaptation of these devices. To support these techniques we propose the employment of a multi-purpose sensor network. This infrastructure, through adequate use of configuration and automation tools, is able to obtain relevant data along the life cycle of an FPGA. This is realised at a very reduced cost, not only in terms of area or other limited resources, but also regarding the design effort required to define and deploy the measuring infrastructure. Our proposal has been validated by measuring inter-die and intra-die variability in different FPGA families.

Multiprotocol Android Application for Smart Control and Monitoring in Buildings

This paper presents a multiprotocol mobile application for building automation which supports and enables the integration of the most representative control technologies such as KNX, LonWorks and X-10. The application includes a real-time monitoring service. Finally, advanced control functionalities based on gestures recognition and predefined scenes have been implemented. This application has been developed and tested in the Energy Efficiency Research Facility located at CeDInt-UPM, where electrical loads, blinds and HVAC and lighting systems can be controlled.

Smart Spaces and Smart Objects interoperability Architecture (S3OiA)

The presented work aims to contribute towards the standardization and the interoperability off the Future Internet through an open and scalable architecture design. We present S³OiA as a syntactic/semantic Service-Oriented Architecture that allows the integration of any type of object or device, not mattering their nature, on the Internet of Things. Moreover, the architecture makes possible the use of underlying heterogeneous resources as a substrate for the automatic composition of complex applications through a semantic Triple Space paradigm. Created applications are dynamic and adaptive since they are able to evolve depending on the context where they are executed. The validation scenario of this architecture encompasses areas which are prone to involve human beings in order to promote personal autonomy, such as home-care automation environments and Ambient Assisted Living.

Search strategies and the automated control of plant diseases

We propose the use of the "infotaxis" search strategy as the navigation system of a robotic platform, able to search and localize infectious foci by detecting the changes in the profile of volatile organic compounds emitted by and infected plant. We builded a simple and cost effective robot platform that substitutes odour sensors in favour of light sensors and study their robustness and performance under non ideal conditions such as the exitence of obstacles due to land topology or weeds.

Risk analysis for UAV safe operations: a rationalization for an agricultural environment

The road to the automation of the agricultural processes passes through the safe operation of the autonomous vehicles. This requirement is a fact in ground mobile units, but it still has not well defined for the aerial robots (UAVs) mainly because the normative and legislation are quite diffuse or even inexistent. Therefore, to define a common and global policy is the challenge to tackle. This characterization has to be addressed from the field experience. Accordingly, this paper presents the work done in this direction, based on the analysis of the most common sources of hazards when using UAV's for agricultural tasks. The work, based on the ISO 31000 normative, has been carried out by applying a three-step structure that integrates the identification, assessment and reduction procedures. The present paper exposes how this method has been applied to analyze previous accidents and malfunctions during UAV operations in order to obtain real failure causes. It has allowed highlighting common risks and hazardous sources and proposing specific guards and safety measures for the agricultural context.

Response threshold models and stochastic learning automata for self-coordination of heterogeneous multi-task distribution in multi-robot systems.

This paper focuses on the general problem of coordinating multiple robots. More specifically, it addresses the self-selection of heterogeneous specialized tasks by autonomous robots. In this paper we focus on a specifically distributed or decentralized approach as we are particularly interested in a decentralized solution where the robots themselves autonomously and in an individual manner, are responsible for selecting a particular task so that all the existing tasks are optimally distributed and executed. In this regard, we have established an experimental scenario to solve the corresponding multi-task distribution problem and we propose a solution using two different approaches by applying Response Threshold Models as well as Learning Automata-based probabilistic algorithms. We have evaluated the robustness of the algorithms, perturbing the number of pending loads to simulate the robot’s error in estimating the real number of pending tasks and also the dynamic generation of loads through time. The paper ends with a critical discussion of experimental results.

Detection and Tracking of Dynamic Objects. A MultiRobot approach to Critical Infrastructures Surveillance.

Despite that Critical Infrastructures (CIs) security and surveillance are a growing concern for many countries and companies, Multi Robot Systems (MRSs) have not been yet broadly used in this type of facilities. This dissertation presents a novel study of the challenges arisen by the implementation of this type of systems and proposes solutions to specific problems. First, a comprehensive analysis of different types of CIs has been carried out, emphasizing the influence of the different characteristics of the facilities in the design of a security and surveillance MRS. One of the most important needs for the surveillance of a CI is the detection of intruders. From a technical point of view this problem can be abstracted as equivalent to the Detection and Tracking of Mobile Objects (DATMO). This dissertation proposes algorithms to solve this specific problem in a CI environment. Using 3D range images of the environment as input data, two detection algorithms for ground robots have been developed. These detection algorithms provide a list of moving objects in the robot detection area. Direct image differentiation and computer vision techniques are used when the robot is static. Alternatively, multi-layer ground reconstructions are compared to detect the dynamic objects when the robot is moving. Since CIs usually spread over large areas, it is very useful to incorporate aerial vehicles in the surveillance MRS. Therefore, a moving object detection algorithm for aerial vehicles has been also developed. This algorithm compares the real optical flow obtained from a down-face oriented camera with an artificial optical flow computed using a RANSAC based homography matrix. Two tracking algorithms have been developed to follow the moving objects trajectories. These algorithms can efficiently handle occlusions and crossings, as well as exchange information among robots. The multirobot tracking can be applied to any type of communication structure: centralized, decentralized or a combination of both. Even more, the developed tracking algorithms are independent of the detection algorithms and could be potentially used with other detection procedures or even with static sensors, such as cameras. In addition, using the 3D point clouds available to the robots, a relative localization algorithm has been developed to improve the position estimation of a given robot with observations from other robots. All the developed algorithms have been extensively tested in different simulated CIs using the Webots robotics simulator. Furthermore, the algorithms have also been validated with real robots operating in real scenarios. In conclusion, this dissertation presents a multirobot approach to Critical Infrastructure Surveillance, mainly focusing on Detecting and Tracking Dynamic Objects.

Implementation of a building automation system based on semantic modeling

This paper presents an Ontology-Based multi-technology platform designed to avoid some issues of Building Automation Systems. The platform allows the integration of several building automation protocols, eases the development and implementation of different kinds of services and allows sharing information related to the infrastructure and facilities within a building. The system has been implemented and tested in the Energy Efficiency Research Facility at CeDInt-UPM.

An introduction to swarm robotics

Swarm robotics is a field of multi-robotics in which large number of robots are coordinated in a distributed and decentralised way. It is based on the use of local rules, and simple robots compared to the complexity of the task to achieve, and inspired by social insects. Large number of simple robots can perform complex tasks in a more efficient way than a single robot, giving robustness and flexibility to the group. In this article, an overview of swarm robotics is given, describing its main properties and characteristics and comparing it to general multi-robotic systems. A review of different research works and experimental results, together with a discussion of the future swarm robotics in real world applications completes this work.

MIA - a free and open source software for gray scale medical image analysis

Background Gray scale images make the bulk of data in bio-medical image analysis, and hence, the main focus of many image processing tasks lies in the processing of these monochrome images. With ever improving acquisition devices, spatial and temporal image resolution increases, and data sets become very large. Various image processing frameworks exists that make the development of new algorithms easy by using high level programming languages or visual programming. These frameworks are also accessable to researchers that have no background or little in software development because they take care of otherwise complex tasks. Specifically, the management of working memory is taken care of automatically, usually at the price of requiring more it. As a result, processing large data sets with these tools becomes increasingly difficult on work station class computers. One alternative to using these high level processing tools is the development of new algorithms in a languages like C++, that gives the developer full control over how memory is handled, but the resulting workflow for the prototyping of new algorithms is rather time intensive, and also not appropriate for a researcher with little or no knowledge in software development. Another alternative is in using command line tools that run image processing tasks, use the hard disk to store intermediate results, and provide automation by using shell scripts. Although not as convenient as, e.g. visual programming, this approach is still accessable to researchers without a background in computer science. However, only few tools exist that provide this kind of processing interface, they are usually quite task specific, and don’t provide an clear approach when one wants to shape a new command line tool from a prototype shell script. Results The proposed framework, MIA, provides a combination of command line tools, plug-ins, and libraries that make it possible to run image processing tasks interactively in a command shell and to prototype by using the according shell scripting language. Since the hard disk becomes the temporal storage memory management is usually a non-issue in the prototyping phase. By using string-based descriptions for filters, optimizers, and the likes, the transition from shell scripts to full fledged programs implemented in C++ is also made easy. In addition, its design based on atomic plug-ins and single tasks command line tools makes it easy to extend MIA, usually without the requirement to touch or recompile existing code. Conclusion In this article, we describe the general design of MIA, a general purpouse framework for gray scale image processing. We demonstrated the applicability of the software with example applications from three different research scenarios, namely motion compensation in myocardial perfusion imaging, the processing of high resolution image data that arises in virtual anthropology, and retrospective analysis of treatment outcome in orthognathic surgery. With MIA prototyping algorithms by using shell scripts that combine small, single-task command line tools is a viable alternative to the use of high level languages, an approach that is especially useful when large data sets need to be processed.

User Experience in Human-Technology Interaction. Communication, context and evaluation methodology

En esta Tesis se presentan dos líneas de investigación relacionadas y que contribuyen a las áreas de Interacción Hombre-Tecnología (o Máquina; siglas en inglés: HTI o HMI), lingüística computacional y evaluación de la experiencia del usuario. Las dos líneas en cuestión son el diseño y la evaluación centrada en el usuario de sistemas de Interacción Hombre-Máquina avanzados. En la primera parte de la Tesis (Capítulos 2 a 4) se abordan cuestiones fundamentales del diseño de sistemas HMI avanzados. El Capítulo 2 presenta una panorámica del estado del arte de la investigación en el ámbito de los sistemas conversacionales multimodales, con la que se enmarca el trabajo de investigación presentado en el resto de la Tesis. Los Capítulos 3 y 4 se centran en dos grandes aspectos del diseño de sistemas HMI: un gestor del diálogo generalizado para tratar la Interacción Hombre-Máquina multimodal y sensible al contexto, y el uso de agentes animados personificados (ECAs) para mejorar la robustez del diálogo, respectivamente. El Capítulo 3, sobre gestión del diálogo, aborda el tratamiento de la heterogeneidad de la información proveniente de las modalidades comunicativas y de los sensores externos. En este capítulo se propone, en un nivel de abstracción alto, una arquitectura para la gestión del diálogo con influjos heterogéneos de información, apoyándose en el uso de State Chart XML. En el Capítulo 4 se presenta una contribución a la representación interna de intenciones comunicativas, y su traducción a secuencias de gestos a ejecutar por parte de un ECA, diseñados específicamente para mejorar la robustez en situaciones de diálogo críticas que pueden surgir, por ejemplo, cuando se producen errores de entendimiento en la comunicación entre el usuario humano y la máquina. Se propone, en estas páginas, una extensión del Functional Mark-up Language definido en el marco conceptual SAIBA. Esta extensión permite representar actos comunicativos que realizan intenciones del emisor (la máquina) que no se pretende sean captadas conscientemente por el receptor (el usuario humano), pero con las que se pretende influirle a éste e influir el curso del diálogo. Esto se consigue mediante un objeto llamado Base de Intenciones Comunicativas (en inglés, Communication Intention Base, o CIB). La representación en el CIB de intenciones “no claradas” además de las explícitas permite la construcción de actos comunicativos que realizan simultáneamente varias intenciones comunicativas. En el Capítulo 4 también se describe un sistema experimental para el control remoto (simulado) de un asistente domótico, con autenticación de locutor para dar acceso, y con un ECA en el interfaz de cada una de estas tareas. Se incluye una descripción de las secuencias de comportamiento verbal y no verbal de los ECAs, que fueron diseñados específicamente para determinadas situaciones con objeto de mejorar la robustez del diálogo. Los Capítulos 5 a 7 conforman la parte de la Tesis dedicada a la evaluación. El Capítulo 5 repasa antecedentes relevantes en la literatura de tecnologías de la información en general, y de sistemas de interacción hablada en particular. Los principales antecedentes en el ámbito de la evaluación de la interacción sobre los cuales se ha desarrollado el trabajo presentado en esta Tesis son el Technology Acceptance Model (TAM), la herramienta Subjective Assessment of Speech System Interfaces (SASSI), y la Recomendación P.851 de la ITU-T. En el Capítulo 6 se describen un marco y una metodología de evaluación aplicados a la experiencia del usuario con sistemas HMI multimodales. Se desarrolló con este propósito un novedoso marco de evaluación subjetiva de la calidad de la experiencia del usuario y su relación con la aceptación por parte del mismo de la tecnología HMI (el nombre dado en inglés a este marco es Subjective Quality Evaluation Framework). En este marco se articula una estructura de clases de factores subjetivos relacionados con la satisfacción y aceptación por parte del usuario de la tecnología HMI propuesta. Esta estructura, tal y como se propone en la presente tesis, tiene dos dimensiones ortogonales. Primero se identifican tres grandes clases de parámetros relacionados con la aceptación por parte del usuario: “agradabilidad ” (likeability: aquellos que tienen que ver con la experiencia de uso, sin entrar en valoraciones de utilidad), rechazo (los cuales sólo pueden tener una valencia negativa) y percepción de utilidad. En segundo lugar, este conjunto clases se reproduce para distintos “niveles, o focos, percepción del usuario”. Éstos incluyen, como mínimo, un nivel de valoración global del sistema, niveles correspondientes a las tareas a realizar y objetivos a alcanzar, y un nivel de interfaz (en los casos propuestos en esta tesis, el interfaz es un sistema de diálogo con o sin un ECA). En el Capítulo 7 se presenta una evaluación empírica del sistema descrito en el Capítulo 4. El estudio se apoya en los mencionados antecedentes en la literatura, ampliados con parámetros para el estudio específico de los agentes animados (los ECAs), la auto-evaluación de las emociones de los usuarios, así como determinados factores de rechazo (concretamente, la preocupación por la privacidad y la seguridad). También se evalúa el marco de evaluación subjetiva de la calidad propuesto en el capítulo anterior. Los análisis de factores efectuados revelan una estructura de parámetros muy cercana conceptualmente a la división de clases en utilidad-agradabilidad-rechazo propuesta en dicho marco, resultado que da cierta validez empírica al marco. Análisis basados en regresiones lineales revelan estructuras de dependencias e interrelación entre los parámetros subjetivos y objetivos considerados. El efecto central de mediación, descrito en el Technology Acceptance Model, de la utilidad percibida sobre la relación de dependencia entre la intención de uso y la facilidad de uso percibida, se confirma en el estudio presentado en la presente Tesis. Además, se ha encontrado que esta estructura de relaciones se fortalece, en el estudio concreto presentado en estas páginas, si las variables consideradas se generalizan para cubrir más ampliamente las categorías de agradabilidad y utilidad contempladas en el marco de evaluación subjetiva de calidad. Se ha observado, asimismo, que los factores de rechazo aparecen como un componente propio en los análisis de factores, y además se distinguen por su comportamiento: moderan la relación entre la intención de uso (que es el principal indicador de la aceptación del usuario) y su predictor más fuerte, la utilidad percibida. Se presentan también resultados de menor importancia referentes a los efectos de los ECAs sobre los interfaces de los sistemas de diálogo y sobre los parámetros de percepción y las valoraciones de los usuarios que juegan un papel en conformar su aceptación de la tecnología. A pesar de que se observa un rendimiento de la interacción dialogada ligeramente mejor con ECAs, las opiniones subjetivas son muy similares entre los dos grupos experimentales (uno interactuando con un sistema de diálogo con ECA, y el otro sin ECA). Entre las pequeñas diferencias encontradas entre los dos grupos destacan las siguientes: en el grupo experimental sin ECA (es decir, con interfaz sólo de voz) se observó un efecto más directo de los problemas de diálogo (por ejemplo, errores de reconocimiento) sobre la percepción de robustez, mientras que el grupo con ECA tuvo una respuesta emocional más positiva cuando se producían problemas. Los ECAs parecen generar inicialmente expectativas más elevadas en cuanto a las capacidades del sistema, y los usuarios de este grupo se declaran más seguros de sí mismos en su interacción. Por último, se observan algunos indicios de efectos sociales de los ECAs: la “amigabilidad ” percibida los ECAs estaba correlada con un incremento la preocupación por la seguridad. Asimismo, los usuarios del sistema con ECAs tendían más a culparse a sí mismos, en lugar de culpar al sistema, de los problemas de diálogo que pudieran surgir, mientras que se observó una ligera tendencia opuesta en el caso de los usuarios del sistema con interacción sólo de voz. ABSTRACT This Thesis presents two related lines of research work contributing to the general fields of Human-Technology (or Machine) Interaction (HTI, or HMI), computational linguistics, and user experience evaluation. These two lines are the design and user-focused evaluation of advanced Human-Machine (or Technology) Interaction systems. The first part of the Thesis (Chapters 2 to 4) is centred on advanced HMI system design. Chapter 2 provides a background overview of the state of research in multimodal conversational systems. This sets the stage for the research work presented in the rest of the Thesis. Chapers 3 and 4 focus on two major aspects of HMI design in detail: a generalised dialogue manager for context-aware multimodal HMI, and embodied conversational agents (ECAs, or animated agents) to improve dialogue robustness, respectively. Chapter 3, on dialogue management, deals with how to handle information heterogeneity, both from the communication modalities or from external sensors. A highly abstracted architectural contribution based on State Chart XML is proposed. Chapter 4 presents a contribution for the internal representation of communication intentions and their translation into gestural sequences for an ECA, especially designed to improve robustness in critical dialogue situations such as when miscommunication occurs. We propose an extension of the functionality of Functional Mark-up Language, as envisaged in much of the work in the SAIBA framework. Our extension allows the representation of communication acts that carry intentions that are not for the interlocutor to know of, but which are made to influence him or her as well as the flow of the dialogue itself. This is achieved through a design element we have called the Communication Intention Base. Such r pr s ntation of “non- clar ” int ntions allows th construction of communication acts that carry several communication intentions simultaneously. Also in Chapter 4, an experimental system is described which allows (simulated) remote control to a home automation assistant, with biometric (speaker) authentication to grant access, featuring embodied conversation agents for each of the tasks. The discussion includes a description of the behavioural sequences for the ECAs, which were designed for specific dialogue situations with particular attention given to the objective of improving dialogue robustness. Chapters 5 to 7 form the evaluation part of the Thesis. Chapter 5 reviews evaluation approaches in the literature for information technologies, as well as in particular for speech-based interaction systems, that are useful precedents to the contributions of the present Thesis. The main evaluation precedents on which the work in this Thesis has built are the Technology Acceptance Model (TAM), the Subjective Assessment of Speech System Interfaces (SASSI) tool, and ITU-T Recommendation P.851. Chapter 6 presents the author’s work in establishing an valuation framework and methodology applied to the users’ experience with multimodal HMI systems. A novel user-acceptance Subjective Quality Evaluation Framework was developed by the author specifically for this purpose. A class structure arises from two orthogonal sets of dimensions. First we identify three broad classes of parameters related with user acceptance: likeability factors (those that have to do with the experience of using the system), rejection factors (which can only have a negative valence) and perception of usefulness. Secondly, the class structure is further broken down into several “user perception levels”; at the very least: an overall system-assessment level, task and goal-related levels, and an interface level (e.g., a dialogue system with or without an ECA). An empirical evaluation of the system described in Chapter 4 is presented in Chapter 7. The study was based on the abovementioned precedents in the literature, expanded with categories covering the inclusion of an ECA, the users’ s lf-assessed emotions, and particular rejection factors (privacy and security concerns). The Subjective Quality Evaluation Framework proposed in the previous chapter was also scrutinised. Factor analyses revealed an item structure very much related conceptually to the usefulness-likeability-rejection class division introduced above, thus giving it some empirical weight. Regression-based analysis revealed structures of dependencies, paths of interrelations, between the subjective and objective parameters considered. The central mediation effect, in the Technology Acceptance Model, of perceived usefulness on the dependency relationship of intention-to-use with perceived ease of use was confirmed in this study. Furthermore, the pattern of relationships was stronger for variables covering more broadly the likeability and usefulness categories in the Subjective Quality Evaluation Framework. Rejection factors were found to have a distinct presence as components in factor analyses, as well as distinct behaviour: they were found to moderate the relationship between intention-to-use (the main measure of user acceptance) and its strongest predictor, perceived usefulness. Insights of secondary importance are also given regarding the effect of ECAs on the interface of spoken dialogue systems and the dimensions of user perception and judgement attitude that may have a role in determining user acceptance of the technology. Despite observing slightly better performance values in the case of the system with the ECA, subjective opinions regarding both systems were, overall, very similar. Minor differences between two experimental groups (one interacting with an ECA, the other only through speech) include a more direct effect of dialogue problems (e.g., non-understandings) on perceived dialogue robustness for the voice-only interface test group, and a more positive emotional response for the ECA test group. Our findings further suggest that the ECA generates higher initial expectations, and users seem slightly more confident in their interaction with the ECA than do those without it. Finally, mild evidence of social effects of ECAs was also found: the perceived friendliness of the ECA increased security concerns, and ECA users may tend to blame themselves rather than the system when dialogue problems are encountered, while the opposite may be true for voice-only users.

Design and kinematic analysis of 3PSS-1S wrist for needle insertion guidance

In this work it is presented a complete kinematic analysis of the 3PSS-1S parallel mechanism for its implementation as a spherical wrist for a needle insertion guidance robot. The spherical 3PSS-1S mechanism is a low weight and reduced dimension parallel mechanism that allows spherical movements providing the requirements needed for the serial–parallel robotic arm for needle insertion guidance. The solution of its direct kinematic is computed with a numerical method based on the Newton–Raphson formulation and a constraint function of the mechanism. The input–output velocity equation is obtained with the use of screw theory. Three types of singular postures are identified during simulations and verified in the real prototype. The 3PSS-1S can perform pure rotations of ±45°±45°, ±40°±40°, ±60°±60° along the View the MathML sourcex, View the MathML sourcey, View the MathML sourcez axes respectively.