Improving controllability of complex networks by rewiring links regularly

Network science have constantly been in the focus of research for the last decade, with considerable advances in the controllability of their structural. However, much less effort has been devoted to study that how to improve the controllability of complex networks. In this paper, a new algorithm is proposed to improve the controllability of complex networks by rewiring links regularly which transforms the network structure. Then it is demonstrated that our algorithm is very effective after numerical simulation experiment on typical network models (Erd\"os-R\'enyi and scale-free network). We find that our algorithm is mainly determined by the average degree and positive correlation of in-degree and out-degree of network and it has nothing to do with the network size. Furthermore, we analyze and discuss the correlation between controllability of complex networks and degree distribution index: power-law exponent and heterogeneit

Navigating the Seas of Mathematics Education: New Waves in Research to Improve Student Learning

This issue focuses on research in the domain of mathematics education. Although mathematics has been a subject of study for many centuries, mathematics education is a relatively new field of scholarly inquiry, having been established as an independent field of research only in the early twentieth century. The most significant milestone was the establishment of the International Commission on Mathematical Instruction (ICMI) in 1908. Since 1969, ICMI has organized the International Congress on Mathematical Education, a quadrennial international meeting whose aim is to present the current states and trends in mathematics education research and in the practice of mathematics teaching at all levels

Mathematical Problem Posing as a Measure of Curricular Effect on Students\u27 Learning

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students\u27 learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evidence of strengths one might expect of students who used the standards-based reform curriculum but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of employing a qualitative rubric to assess different characteristics of students\u27 responses to the posing tasks. Instructional and methodological implications of this study, as well as future directions for research, are discussed

Impact of Curriculum Reform: Evidence of Change in Classroom Instruction in the United States

The purpose of the study reported in this article is to examine the impact of curriculum on instruction. Over a three-year period, we observed 579 algebra-related lessons in grades 6–8. Approximately half the lessons were taught in schools that had adopted a Standards-based mathematics curriculum called the Connected Mathematics Program (CMP), and the remainder of the lessons were taught in schools that used more traditional curricula (non-CMP). We found many significant differences between the CMP and non-CMP lessons. The CMP lessons, emphasized the conceptual aspects of instruction to a greater extent than the non-CMP lessons and the non-CMP lessons emphasized the procedural aspects of instruction to a greater extent than the CMP lessons. About twice as many CMP lessons as non-CMP lessons were structured to use group work as a method of instruction. During lessons, non-CMP students worked individually on homework about three times as often as CMP students. When it came to text usage, CMP teachers were more likely than non-CMP teachers to work problems from the text and to follow lessons as laid out in the text. However, non-CMP students and teachers were more likely than CMP students and teachers to review examples or find formulas in the text. Surprisingly, only small proportions of the CMP lessons utilized calculators (16%) or manipulatives (11%)

Longitudinal investigation of the curricular effect: An analysis of student learning outcomes from the LieCal Project in the United States

In this article, we present the results from a longitudinal examination of the impact of a Standards-based or reform mathematics curriculum (called CMP) and traditional mathematics curricula (called non-CMP) on students’ learning of algebra using various outcome measures. Findings include the following: (1) students did not sacrifice basic mathematical skills if they are taught using a Standards-based or reform mathematics curriculum like CMP; (2) African American students experienced greater gain in symbol manipulation when they used a traditional curriculum; (3) the use of either the CMP or a non-CMP curriculum improved the mathematics achievement of all students, including students of color; (4) the use of CMP contributed to significantly higher problem-solving growth for all ethnic groups; and (5) a high level of conceptual emphasis in a classroom improved the students’ ability to represent problem situations. (However, the level of conceptual emphasis bears no relation to students’ problem solving or symbol manipulation skills.

Phylogenetic analysis, structural evolution and functional divergence of the 12-oxo-phytodienoate acid reductase gene family in plants

BACKGROUND: The 12-oxo-phytodienoic acid reductases (OPRs) are enzymes that catalyze the reduction of double-bonds in α, β-unsaturated aldehydes or ketones and are part of the octadecanoid pathway that converts linolenic acid to jasmonic acid. In plants, OPRs belong to the old yellow enzyme family and form multigene families. Although discoveries about this family in Arabidopsis and other species have been reported in some studies, the evolution and function of multiple OPRs in plants are not clearly understood. RESULTS: A comparative genomic analysis was performed to investigate the phylogenetic relationship, structural evolution and functional divergence among OPR paralogues in plants. In total, 74 OPR genes were identified from 11 species representing the 6 major green plant lineages: green algae, mosses, lycophytes, gymnosperms, monocots and dicots. Phylogenetic analysis showed that seven well-conserved subfamilies exist in plants. All OPR genes from green algae were clustered into a single subfamily, while those from land plants fell into six other subfamilies, suggesting that the events leading to the expansion of the OPR family occurred in land plants. Further analysis revealed that lineage-specific expansion, especially by tandem duplication, contributed to the current OPR subfamilies in land plants after divergence from aquatic plants. Interestingly, exon/intron structure analysis showed that the gene structures of OPR paralogues exhibits diversity in intron number and length, while the intron positions and phase were highly conserved across different lineage species. These observations together with the phylogenetic tree revealed that successive single intron loss, as well as indels within introns, occurred during the process of structural evolution of OPR paralogues. Functional divergence analysis revealed that altered functional constraints have occurred at specific amino acid positions after diversification of the paralogues. Most notably, significant functional divergence was also found in all pairs, except for the II/IV, II/V and V/VI pairs. Strikingly, analysis of the site-specific profiles established by posterior probability revealed that the positive-selection sites and/or critical amino acid residues for functional divergence are mainly distributed in α-helices and substrate binding loop (SBL), indicating the functional importance of these regions for this protein family. CONCLUSION: This study highlights the molecular evolution of the OPR gene family in all plant lineages and indicates critical amino acid residues likely relevant for the distinct functional properties of the paralogues. Further experimental verification of these findings may provide valuable information on the OPRs' biochemical and physiological functions