Violations at the Reference Point of Discontinuity: Limitations of Prospect Theory and an Alternative Model of Risk Choices

The tilted S-shaped utility function proposed in Prospect Theory (PT) relied fundamentally on the geometrical notion that there is a discontinuity between gains and losses, and that individual preferences change relative to a reference point. This results in PT having three distinct parameters; concavity, convexity and the reference point represented as a disjoint between the concavity and convexity sections of the curve. The objective of this paper is to examine the geometrical violations of PT at the zero point of reference. This qualitative study adopted a theoretical review of PT and Markowitz’s triply inflected value function concept to unravel methodological assumptions which were not fully addressed by either PT or cumulative PT. Our findings suggest a need to account for continuity and to resolve this violation of PT at the reference point. In so doing, an alternative preference transition theory, was proposed as a solution that includes a phase change space to cojoin these three separate parameters into one continuous nonlinear model. This novel conceptual model adds new knowledge of risk and uncertainty in decision making. Through a better understanding of an individual’s reference point in decision making behaviour, we add to contemporary debate by complementing empirical studies and harmonizing research in this field. Doi: 10.28991/ESJ-2022-06-01-03 Full Text: PDF

Up and down deconvolution in complex geological scenarios

The redatuming approach, often referred to as up-down deconvolution, is well-known and applied to remove water-layer and source-signature effects in seabed seismic surveys. The upgoing wavefield can be expressed as the multidimensional convolution of the downgoing wavefield with the earth’s reflectivity. Consequently, deconvolving the downgoing wavefield from the upgoing wavefield, gives us the earth’s reflectivity response. The deconvolution process requires solving a multidimensional integral equation but, in a laterally invariant medium, after that wavefields are decomposed into plane-wave components, deconvolution can be enormously simplified if performed as a spectral division in the Fourier or Radon domain. It has been experimentally observed that deconvolution carried out one plane-wave component at a time gives good results, even in the presence of complex subsurface structures, provided that the seabed is relatively flat. When this geological condition is not satisfied, the same problem can be formulated in terms of interferometric redatuming using multidimensional deconvolution, where the integral equation solution is achieved by introducing the point-spread function concept. We present a methodology based on numerical simulations to determine when the integral equations associated with the problem of up-down deconvolution can be solved under the assumption of shift-invariant wavefields and when it requires multidimensional deconvolution. In the latter case, we propose a regularized inverse procedure that mitigates the numerical problems due to the typically ill-posed nature of the inversion and that, combined with an interpolation strategy for the downgoing, enables the application of multidimensional deconvolution within the range of sampling scenarios considered so far. We apply this methodology to synthetic data, and we discuss on the potential to extend up-down deconvolution to a broader range of geological conditions.

Didactical Design for Overcoming Students' Learning Obstacles on the Inverse Function Concept

The inverse function in secondary schools is still a difficult concept to learn. Meanwhile, in national exams or competitions this problem often arises. Didactic design is an attempt to improve the learning process. The purpose of this study is to identify the epistemological obstacle, to develop the learning designs, and to describe the students’ responses regarding the implementation of inverse function’s concept learning designs in the class. This research was held in one of Senior High School in South Tangerang of 38 people from class X. The research method is Didactical Design Research (DDR). This method is conducted from three stages, prospective analysis, metapedia didactic analysis, and retrospective analysis. The result of the study was indicated that the student’s obstacles are according to predictions and didactical design still generates some new epistemological obstacle. The revised didactical design was obtained by updating the initial didactical design to resolve the obstacle. The revised didactical design includes choosing vocabulary, adding new instructions, and expanding predictions and anticipating student responses.AbstrakFungsi invers di sekolah menengah masih merupakan konsep yang sulit dipelajari. Sedangkan dalam ujian atau kompetisi nasional masalah ini sering muncul. Desain didaktik merupakan upaya untuk meningkatkan proses pembelajaran. Tujuan penelitian ini adalah untuk mengidentifikasi hambatan epistemologis, mengembangkan desain pembelajaran, dan mendeskripsikan tanggapan siswa terkait penerapan desain pembelajaran konsep fungsi invers di kelas. Penelitian ini dilaksanakan di salah satu Sekolah Menengah Atas di Tangerang Selatan yang berjumlah 38 orang dari kelas X. Metode penelitian yang digunakan adalah Penelitian Desain Didaktik. Metode ini dilakukan dari tiga tahap yaitu analisis prospektif, analisis metapedadidaktik, dan analisis retrospektif. Hasil penelitian menunjukkan bahwa kesulitan yang dialami siswa sesuai dengan prediksi dan desain didaktis masih menimbulkan hambatan epistemologis baru. Desain didaktis yang direvisi diperoleh dengan memperbarui desain didaktis awal untuk menyelesaikan kesulitan. Desain didaktis yang direvisi terdiri atas: memilih kosakata, menambahkan instruksi baru, dan memperluas prediksi dan mengantisipasi respon siswa. How to Cite: Muin, A., Pratiwi, A. A., Satriawati, G. (2020). Didactical Design for Overcoming Students' Learning Obstacles on the Inverse Function Concept. TARBIYA: Journal of Education in Muslim Society, 7(2), 183-191. doi:10.15408/tjems.v7i2.13041.

An Advanced Extremum Seeking Scheme for the Target Trajectory in Electromagnetic Micromirror System

Now two problems result in bad control in the development of the electromagnetic micromirror system. One is that theoretical model in electromagnetic micromirror system is difficult to be determined; Another is that parameters in common control need to be tuned according to the experience. In this paper, cost function concept is proposed to determine the model order in slow-scan axis control of the electromagnetic micromirror. Then recursive least square scheme is built to off-line identify this model. Furthermore, an advanced extremum seeking scheme along with backtracking line search is exploited, which can automatically identify the best parameter value before each extremum search to improve the controllability based on this model for the target trajectory in slow-scan axis control. And the convergence of it is proved. Finally, the experiments and the simulations verify this method proposed valid.

University Mathematics Lecturing as Modelling Mathematical Discourse

The lecture format, while being the subject of much criticism, is still one of the most common formats of university mathematics teaching. This paper investigates lecturing as a means of modelling mathematical discourse, sometimes highlighted in the literature as one of its most important functions. The data analysed in the paper are taken from first-semester lectures given by seven mathematics lecturers at three Swedish universities, all concerning various aspects of the function concept. Analysis was carried out from a commognitive perspective, which distinguishes between object-level and meta-level discourse. Here I focus on two aspects of meta-level discourse: introducing new mathematical objects; and what counts as valid endorsement of a narrative. The analysis reveals a number of metarules concerning the modelling of mathematical reasoning and behaviour, both more general rules such as precision and consensus, and rules more specifically concerning construction and endorsement of narratives. The paper contributes to a small but growing body of empirical research on university mathematics teaching, and also lends empirical support to previous claims about the modelling aspect of mathematics lecturing, thus contributing to a deepened understanding of the lecture format and its potential role in future university mathematics teaching.

TAMAN BUDAYA DI MANGGA BESAR, JAKARTA BARAT

Indonesia has many kinds of ethnicities and cultures. Unfortunately, nowadays news about intolerance is often heard in Indonesia. diversity of ethnicities could cause incompatibilities. Each ethnic have their habits and lifestyle. In consequence, this project is made to provide education to all kinds of communities. The form of education is a cultural park, that adopts themes of the Betawi and the Chinese culture because both cultures have many resemblances. This cultural park at the same time can be used as a third place for the local citizens. The third place serves as an intermediary between first places (such as houses, apartments, hotels, home) and second places (such as offices, stores, working space). The third place is flexible, it could be used as a place to relax or even having work meetings with co-workers. This Cultural Park has a traditional concept, with the form that blends in with its site region. As for the methods; Site project analysis; Determining building program; Positive energy method application; Symbiosis method application; Form follows function method application; Luo shu method application; Final project result. In conclusion, Mangga Besar Cultural Park has a goal to educate local citizens about the Betawi and Chinese culture. Mangga Besar Cultural park also applies the symbiosis and form follows function concept and luo shu. In conclusion, Mangga Besar Cultural Park has a goal to provide education to citizens about the Betawi and Chinese culture. This project applies some concepts, such as symbiosis in architecture, form follows function, and luo shu. Keywords: Culture; Ethnicities; Local Citizen; Park; Third PlaceAbstrak Indonesia memiliki berbagai macam suku dan budaya. Namun, belakangan ini sering terdengar masalah mengenai intoleransi di Indonesia. Keberagaman etnis dapat menimbulkan ketidak cocokan dalam bermasyarakat. Masing-masing etnis memiliki kebiasaan dan gaya hidup mereka sendiri. Oleh karena itu, proyek ini dibuat dengan maksud untuk meminimalisir masalah tersebut, dengan memberi edukasi kepada masyarakat dari semua kalangan. Edukasi tersebut berbentuk taman budaya di Jakarta, yang memiliki tema bangunan budaya betawi dan budaya tionghoa yang digabungkan, dikarenakan kedua budaya tersebut saling berselingan. Taman budaya disini juga sekaligus dapat dijadikan sebagai third place bagi masyarakat sekitar. Third Place disini berfungsi sebagai perantara antara first place (rumah, hotel, apartemen, tempat tinggal) dan second place (kantor, pertokoan, tempat kerja). Third place disini memiliki fungsi fleksibel, dapat digunakan untuk bersantai hingga membahas pekerjaan bersama rekan kerja. Taman budaya berkonteks arsitektur tradisional, dengan bentuk yang sesuai dan membaur dengan bangunan sekitarnya. Metode perancangan; Pemahaman Kawasan Jakarta Barat; Pemahaman Mengenai Tapak Perancangan; Penetapan Program Bangunan; Penggunaan Metode Energi Positif; Penggunaan Metode Simbiosis; Penggunaan Metode Form follows function; Penggunaan Metode Luo Shu; Hasil Akhir Perancangan. Kesimpulan dari hasil perancangan adalah Taman Budaya di Mangga Besar memiliki tujuan untuk memberikan edukasi kepada masyarakat mengenai budaya Betawi dan Tionghoa. Proyek ini menerapkan beberapa konsep, seperti simbiosis dalam arsitektur, form follows function dan luo shu.

Climate-Optimized Trajectories and Robust Mitigation Potential: Flying ATM4E

Aviation can reduce its climate impact by controlling its CO2-emission and non-CO2 effects, e.g., aviation-induced contrail-cirrus and ozone caused by nitrogen oxide emissions. One option is the implementation of operational measures that aim to avoid those atmospheric regions that are in particular sensitive to non-CO2 aviation effects, e.g., where persistent contrails form. The quantitative estimates of mitigation potentials of such climate-optimized aircraft trajectories are required, when working towards sustainable aviation. The results are presented from a comprehensive modelling approach when aiming to identify such climate-optimized aircraft trajectories. The overall concept relies on a multi-dimensional environmental change function concept, which is capable of providing climate impact information to air traffic management (ATM). Estimates on overall climate impact reduction from a one-day case study are presented that rely on the best estimate for climate impact information. Specific weather situation that day, containing regions with high contrail impact, results in a potential reduction of total climate impact, by more than 40%, when considering CO2 and non-CO2 effects, associated with an increase of fuel by about 0.5%. The climate impact reduction per individual alternative trajectory shows a strong variation and, hence, also the mitigation potential for an analyzed city pair, depending on atmospheric characteristics along the flight corridor as well as flight altitude. The robustness of proposed climate-optimized trajectories is assessed by using a range of different climate metrics. A more sustainable ATM needs to integrate comprehensive environmental impacts and associated forecast uncertainties into route optimization in order to identify robust eco-efficient trajectories.