Appraising Science Textbooks through Quantitative Text Analysis andPsychometric Results of Students’ Reading Skills

The “primary-secondary learning gap” has long been discussedin Japan. Many students suddenly have difficulties inunderstanding subjects when they enter junior high school (7thgrade in Japan). Despite the fact that textbooks are one of themost important learning instruments, the qualitative andquantitative change in the content of textbooks has not beenexamined in light of the primary-secondary learning gap. Inthis paper, we show that students are overloaded with the steepincrease in the definitions of scientific concepts in textbooks.While the number of definition expressions in textbooksincreases rapidly toward junior high school, students’ skills inunderstanding definitions develop only gradually. Wedemonstrated this through a quantitative linguistic analysis oftextbooks and psychometric results of students’ reading skills

Two controller design procedures using SDP and QE for a Power Supply Unit

In this paper, we propose two controller design procedures using semi-definite programing (SDP) and quantifier elimination (QE), respectively. We consider to design controllers for a principal circuit in a power supply unit as an example. In general, a controller design problem is given as a problem finding a controller that satisfies given specifications in the open-loop transfer function’s frequency characteristic.This is so-called an open-loop shaping problem in linear control theory. There exist some numerical methods for solving the problem using SDP. We propose an SDP-based controller design method via generalized Kalman-Yakubovich-Popov (GKYP) lemma. These SDP-based methods are effective for finding a feasible controller efficiently, but we cannot describe exact mathematical constraints for the required specifications by these methods. In order to obtain exact controller’s feasible regions for the required specifications, we describe the specifications as exact constraints formulated by sign definite conditions (SDCs) and solve them symbolically using QE

Two controller design procedures using SDP and QE for a Power Supply Unit

In this paper, we propose two controller design procedures using semi-definite programing (SDP) and quantifier elimination (QE), respectively. We consider to design controllers for a principal circuit in a power supply unit as an example. In general, a controller design problem is given as a problem finding a controller that satisfies given specifications in the open-loop transfer function’s frequency characteristic.This is so-called an open-loop shaping problem in linear control theory. There exist some numerical methods for solving the problem using SDP. We propose an SDP-based controller design method via generalized Kalman-Yakubovich-Popov (GKYP) lemma. These SDP-based methods are effective for finding a feasible controller efficiently, but we cannot describe exact mathematical constraints for the required specifications by these methods. In order to obtain exact controller’s feasible regions for the required specifications, we describe the specifications as exact constraints formulated by sign definite conditions (SDCs) and solve them symbolically using QE

The Most Uncreative Examinee: A First Step toward Wide Coverage Natural Language Math Problem Solving

We report on a project aiming at developing a system that solves a wide range of math problems written in natural language. In the system, formal analysis of natural language semantics is coupled with automated reasoning technologies including computer algebra, using logic as their common language. We have developed a prototype system that accepts as its input a linguistically annotated problem text. Using the prototype system as a reference point, we analyzed real university entrance examination problems from the viewpoint of end-to-end automated reasoning. Further, evaluation on entrance exam mock tests revealed that an optimistic estimate of the system’s performance already matches human averages on a few test sets

An indirect search algorithm for disaster restoration with precedence and synchronization constraints

Abstract When a massive disaster occurs, to repair the damaged part of lifeline networks, planning is needed to appropriately allocate tasks to two or more restoration teams and optimize their traveling routes. However, precedence and synchronization constraints make restoration teams interdependent of one another, and impede a successful solution by standard local search. In this paper, we propose an indirect local search method using the product set of team-wise permutations as an auxiliary search space. It is shown that our method successfully avoids the interdependence problem induced by the precedence and synchronization constraints, and that it has the big advantage of non-deteriorating perturbations being available for iterated local search

An Effective Implementation of a Special Quantifier Elimination for a Sign Definite Condition by Logical Formula Simplification

This paper presents an efficient quantifier elimination algorithm tailored for a sign definite condition (SDC). The SDC for a polynomial f ∈ R[x] with parametric coefficients is written as ∀x(x ≥ 0 → f (x) > 0). To improve the algorithm, simplification of an output formula is needed. We show a necessary condition for the SDC and an approach to simplify formulae by using a logic minimization method. Experimental results show that our approach significantly simplify formulae

A Practical Implementation of a Symbolic-Numeric Cylindrical Algebraic Decomposition for Quantifier Elimination

MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」Recently quantifier elimination (QE) has been of great interest in many fields of science and engineering. In this paper an effective symbolic-numeric cylindrical algebraic decomposition (SNCAD) algorithm and its variant specially designed for QE are proposed based on the authors’ previous work and our implementation of those is reported. Based on analysing experimental performances, we are improving our design/synthesis of the SNCAD for its practical realization with existing efficient computational techniques and several newly introduced ones. The practicality of the SNCAD is now examined by experimentation on real computer, which also reveals the quality of the implementation