Anecdotal Bias in Capital Allocation Depends on Anecdote Similarity

Previous research found that anecdotes are more persuasive than statistical data—the anecdotal bias effect. Separate research found that anecdotes that are similar to a target problem are more influential on decision-making than dissimilar anecdotes. Further, previous investigations on anecdotal bias primarily focused on medical decision-making with very little focus on business decision-making. Therefore, we investigated the effect of anecdote similarity on anecdotal bias in capital allocation decisions. Participants were asked to allocate a hypothetical budget between two business projects. One of the projects (the target project) was clearly superior in terms of the provided statistical measures, but some of the participants also saw a description of a project with a conflicting outcome (the anecdotal project). This anecdotal project was always from the same industry as the target project. The anecdote description, however, either contained substantive connections to the target or not. Further, the anecdote conflicted with the statistical measures because it was either successful (positive anecdote) or unsuccessful (negative anecdote). The results showed that participants’ decisions were influenced by anecdotes only when they believed that they were actually relevant to the target project. Further, they still incorporated the statistical measures into their decision. This was found for both positive and negative anecdotes. Further, participants were given information about the way that the anecdotes were sampled that suggested that the statistical information should have been used in all cases. Participants did not use this information in their decisions and still showed an anecdotal bias effect. Therefore, people seem to appropriately use anecdotes based on their relevance, but do not understand the implications of certain statistical concepts.

Penalaran analogi siswa tipe campers dalam menyelesaikan soal persamaan logaritma

The purpose of this descriptive qualitative research is to describe the analogical reasoning from 6 students with campers type in the X-grade of IPA 1 SMA Nasional Malang. Analogical reasoning id described based on encoding, inferring, mapping and applying stage. The data collected in this research are the result of the questionnaire. The research shows that analogical reasoning of the campers students are correct in the stage of encoding, inferring and mapping. It also found that the campers students made mistake on the stage of applying in doing the target problem caused by less accuracy, having wrong concept of logarithm, and the influence of perception mapping in the source problem which is directly associated to the target problem without firstly analyzing the target problem. Tujuan penelitian deskriptif kualitatif ini adalah mendeskripsikan penalaran analogi dari 6 siswa tipe campers pada kelas X IPA 1 SMA Nasional Malang. Penalaran analogi dideskripsikan berdasarkan tahapan pengkodean (encoding), penyimpulan (inferring), pemetaan (mapping), dan penerapan (applying). Data yang dikumpulkan dalam penelitian ini adalah jawaban siswa atas soal masalah analogi serta hasil wawancara. Hasil penelitian ini menunjukkan bahwa penalaran analogi subjek tipe campers pada tahap pengkodean, penyimpulan, dan pemetaan mampu melakukan dengan benar. Sedangkan pada tahap penerapan terdapat kesalahan dalam menyelesaikan masalah target yang diakibatkan karena kurang teliti, salah konsep logaritma dan pengaruh pemetaan persepsi yang ada pada masalah sumber yang langsung disesuaikan ke dalam situasi masalah target tanpa analisis pada masalah target terlebih dahulu.

CTPPM (Context_Target_Problem_Pattern_Method): Procedure for framing and dealing with research problems

In this essay, I would like to present the CTPPM procedure of framing and dealing with research problems. ‘CTPPM’ stands for five important notions that I always considered when starting a new research project: Context, Target, Problem, Pattern (Position), and Method.

Petri Net Modeling for Ising Model Formulation in Quantum Annealing

Quantum annealing is an emerging new platform for combinatorial optimization, requiring an Ising model formulation for optimization problems. The formulation can be an essential obstacle to the permeation of this innovation into broad areas of everyday life. Our research is aimed at the proposal of a Petri net modeling approach for an Ising model formulation. Although the proposed method requires users to model their optimization problems with Petri nets, this process can be carried out in a relatively straightforward manner if we know the target problem and the simple Petri net modeling rules. With our method, the constraints and objective functions in the target optimization problems are represented as fundamental characteristics of Petri net models, extracted systematically from Petri net models, and then converted into binary quadratic nets, equivalent to Ising models. The proposed method can drastically reduce the difficulty of the Ising model formulation.

Indirect Analogical Reasoning Components

If using different instruments obtained a different analogical reasoning component. With use people-piece analogies, verbal analogies, and geometric analogies, have analogical reasoning component consists of encoding, inferring, mapping, and application. Meanwhile, with use analogical problems (algebra, source problem and target problem is equal), have analogical reasoning components consist of structuring, mapping, applying, and verifying. The instrument used was analogical problems consisting of two problems where the source problem was symbolic quadratic equation problem and the target problems were trigonometric equation problem and a word problem. This study aims to provide information analogical reasoning process in solving indirect analogical problems. in addition, to identify the analogical reasoning components in solving indirect analogical problems. Using a qualitative design approach, the study was conducted at two schools in Mataram city of Nusa Tenggara Barat, Indonesia. The results of the study provide an overview of analogical reasoning of the students in solving indirect analogical problems and there is a component the representation and mathematical model in solving indirect analogical problems. So the analogical reasoning component in solving indirect analogical problems is the representation and mathematical modeling, structuring, mapping, applying, and verifying. This means that there are additional components of analogical reasoning developed by Ruppert. Analogical reasoning components in problem-solving depend on the analogical problem is given.

Developing Written Mathematics Communication through Solving Analogous Problems

Developing mathematics communication, especially in writing is needed considering that communication is one of the objectives of learning mathematics which can describe students understanding so that effective strategies are needed to develop it. One of problem solving strategies that can measures written mathematics communication is solving the analogous problem. This research aims to describe the analogous problem in developing mathematics communication especially in written communication. This research was a qualitative type through a student-written test about solving target problem using analogous problems and interview. The result showed solving analogous problems gave students understanding to be able to do the target question correctly also easier than before and it effected students could communicate the correct solutions accurately, effectively and completely in writing. So it can be said that solving analogous problems develops written mathematics communication ability of student effectively.

A Generalised Solution to the Point to Target Problem Using the Minimum Curvature Method

An explicit solution to the general 3D point to target problem based on the minimum curvature method has been sought for more than four decades. The general case involves the trajectory's start and target points connected by two circular arcs joined by a straight line with the position and direction defined at both ends. It is known that the solutions are multi-valued and efficient iterative schemes to find the principal root have been established. This construction is an essential component of all major trajectory construction packages. However, convergence issues have been reported in cases where the intermediate tangent section is either small or vanishes and rigorous mathematical conditions under which solutions are both possible and are guaranteed to converge have not been published. An implicit expression has now been determined that enables all the roots to be identified and permits either exact, or polynomial type solution methods to be employed. Most historical attempts at solving the problem have been purely algebraic, but a geometric interpretation of related problems has been attempted, showing that a single circular arc and a tangent section can be encapsulated in the surface of a horn torus. These ideas have now been extended, revealing that the solution to the general 3D point to target problem can be represented as a 10th order self-intersecting geometric surface, characterised by the trajectory's start and end points, the radii of the two arcs and the length of the tangent section. An outline of the solution's derivation is provided in the paper together with complete details of the general expression and its various degenerate forms so that readers can implement the algorithms for practical application. Most of the degenerate conditions reduce the order of the governing equation. Full details of the critical and degenerate conditions are also provided and together these indicate the most convenient solution method for each case. In the presence of a tangent section the principal root is still most easily obtained using an iterative scheme, but the mathematical constraints are now known. It is also shown that all other cases degenerate to quadratic forms that can be solved using conventional methods. It is shown how the general expression for the general point to target problem can be modified to give the known solutions to the 3D landing problem and how the example in the published works on this subject is much simplified by the geometric, rather than algebraic treatment.

A Generalized Solution to the Point-to-Target Problem Using the Minimum Curvature Method

Summary An explicit solution to the general 3D point-to-target problem based on the minimum curvature method has been sought for more than four decades. The general case involves the trajectory's start and target points connected by two circular arcs joined by a straight line with the position and direction defined at both ends. It is known that the solutions are multivalued, and efficient iterative schemes to find the principal root have been established. This construction is an essential component of all major trajectory construction packages. However, convergence issues have been reported in cases where the intermediate tangent section is either small or vanishes and rigorous mathematical conditions under which solutions are both possible and are guaranteed to converge have not been published. An implicit expression has now been determined that enables all the roots to be identified and permits either exact or polynomial-type solution methods to be used. Most historical attempts at solving the problem have been purely algebraic, but a geometric interpretation of related problems has been attempted, showing that a single circular arc and a tangent section can be encapsulated in the surface of a horn torus. These ideas have now been extended, revealing that the solution to the general 3D point-to-target problem can be represented as a 10th-orderself-intersecting geometric surface, characterized by the trajectory's start and end points, the radii of the two arcs, and the length of the tangent section. An outline of the solution's derivation is provided in the paper together with complete details of the general expression and its various degenerate forms so that readers can implement the algorithms for practical application. Most of the degenerate conditions reduce the order of the governing equation. Full details of the critical and degenerate conditions are also provided, and together these indicate the most convenient solution method for each case. In the presence of a tangent section, the principal root is still most easily obtained using an iterative scheme, but the mathematical constraints are now known. It is also shown that all other cases degenerate to quadratic forms that can be solved using conventional methods. It is shown how the general expression for the general point-to-target problem can be modified to give the known solutions to the 3D landing problem and how the example in the published works on this subject is much simplified by the geometric, rather than algebraic treatment.

PARAMETRIC OPTIMIZATION METHOD FOR WIDE NEURAL NETWORKS USING GENETIC ALGORITHMS

In many complex technical problems, the number of parameters available for analysis is in the thousands. At the same time, depending on the specifics of the problem being solved, usually the number of key parameters, that is, parameters that have a significant impact on the processes associated with the target problem, does not exceed several tens. However, determining a subset of these parameters from those available in itself is a difficult task, which in most cases is solved with the assistance of experts in the relevant subject area. This paper proposes a parametric optimization method that can be used for wide neural networks, that is, neural networks with a large number of neurons in a layer. This method uses evolutionary optimization methods, namely, genetic algorithms, together with the method of invariant data representation in wide neural networks, using the algebra of hyperdimensional binary vectors, due to which, when the number of parameters of a neural network model changes during optimization, its topology does not change. At the same time, the more parameters are included in the model, the less accurately their values are transmitted, thus, in the course of optimization, a balance is achieved between the composition, number and accuracy of the parameters of the target problem. The proposed method does not require the participation of an expert corresponding to the subject area, allowing the process of parametric optimization to be fully automated.