Fantastic Educational Gaps and Where to Find Them: LERB – A Model to Classify Inequity and Inequality

In today’s world, education is less being considered as an outcome, but more as a journey. As the adventurers, our students are facing more and more complex challenges. Previously, the socio-economic status of a student’s family seemed to be one of the biggest factors among inequality causes. Nowadays, the chaotic situation of today's VUCA world (volatility, uncertainty, complexity, and ambiguity) is generating more and more types of inequity and inequality. Thus, the purpose of the study is to develop LERB - a simple model to classify inequity and inequality, as a stepping-stone to build a gap detection framework. Through a structured literature review, the study identified the interconnection between equity and equality, as well as their transition toward students as an individual or as a group(s) and subgroup(s). The study can also be adapted to examine the correlation between different categories of equity, as well as to brainstorm and propose remedies to tackle those gaps

A Snapshot of Educational Research in 2019

2019 is a year witnessing the explosion of many high-tech applications in learning and teaching with integrated multimedia technologies (virtual reality - VR, augmented reality - AR), group and team collaboration technology, class organization, class management, and school ... It is indisputable that the application of new technology generates more interest in the learning and collaboration process. However, we are seemingly fraught with intractable problems within the transformation of a VUCA world (volatility - fragility, uncertainty, uncertainty, complexity - complexity, ambiguity - ambiguity) if we rely solely on technology. Students of today's Z generation (born around 1997 onwards) are not only more proficient with technology from birth, but also have completely different psychological characteristics and needs to be compared to the previous generation. In the 20s of the upcoming XXI century, researchers are ready a name to give birth to the generation that is about to be born? And what do we, as educators, prepare to foster contemporary generations of students? Let's take a look at some of the outstanding educational research in 2019, whether we can name a new challenge or feel the intangible challenges will suddenly come in 2020

Dấu chấm lửng của thế hệ trẻ

Cảm giác của sự thành công không thú vị bằng cảm giác của sự thấu hiểu. Thấu hiểu một câu chuyện thì không khó, thấu hiểu một thế hệ, nhất là thế hệ trẻ là không đơn giản. Hãy để tuổi trẻ thuộc về chính tuổi trẻ, dấn thân và quyết định lựa chọn tương lai của chính họ từ những sự trải nghiệm

Xu hướng ứng dụng Công nghệ trong Giáo dục: Cải tổ toàn diện vì một thế hệ người học mới

TTCT - Những đứa trẻ thuộc thế hệ Alpha (sinh từ năm 2011-2025) khi vừa chào đời đã được bủa vây bởi công nghệ. Chính vì thế, nhu cầu về ứng dụng công nghệ trong học tập không chỉ dừng lại ở công cụ lưu trữ, giao tiếp thông thường, mà trở nên bao trùm và ranh giới giữa học tập, giải trí và việc thể hiện lối sống bị xóa nhòa

TS-Reconfiguration of kk-Path Vertex Covers in Caterpillars for kgeq4k geq 4

A $k$-path vertex cover ($k$-PVC) of a graph $G$ is a vertex subset $I$ such that each path on $k$ vertices in $G$ contains at least one member of $I$. Imagine that a token is placed on each vertex of a $k$-PVC. Given two $k$-PVCs $I, J$ of a graph $G$, the $k$-Path Vertex Cover Reconfiguration ($k$-PVCR) under Token Sliding ($mathsf{TS}$) problem asks if there is a sequence of $k$-PVCs between $I$ and $J$ where each intermediate member is obtained from its predecessor by sliding a token from some vertex to one of its unoccupied neighbors. This problem is known to be $mathtt{PSPACE}$-complete even for planar graphs of maximum degree $3$ and bounded treewidth and can be solved in polynomial time for paths and cycles. Its complexity for trees remains unknown. In this paper, for $k geq 4$, we present a polynomial-time algorithm that solves $k$-PVCR under $mathsf{TS}$ for caterpillars (i.e., trees formed by attaching leaves to a path)

On The Complexity of Distance-dd Independent Set Reconfiguration

This PDF is not the same as the Accepted Paper for 'WALCOM 2023'.For a fixed positive integer $d geq 2$, a distance-$d$ independent set (D$d$IS) of a graph is a vertex subset whose distance between any two members is at least $d$. Imagine that there is a token placed on each member of a D$d$IS. Two D$d$ISs are adjacent under Token Sliding ($mathsf{TS}$) if one can be obtained from the other by moving a token from one vertex to one of its unoccupied adjacent vertices. Under Token Jumping ($mathsf{TJ}$), the target vertex needs not to be adjacent to the original one. The Distance-$d$ Independent Set Reconfiguration (D$d$ISR) problem under $mathsf{TS}/mathsf{TJ}$ asks if there is a corresponding sequence of adjacent D$d$ISs that transforms one given D$d$IS into another. The problem for $d = 2$, also known as the Independent Set Reconfiguration problem, has been well-studied in the literature and its computational complexity on several graph classes has been known. In this paper, we study the computational complexity of D$d$ISR on different graphs under $mathsf{TS}$ and $mathsf{TJ}$ for any fixed $d geq 3$. On chordal graphs, we show that D$d$ISR under $mathsf{TJ}$ is in $mathtt{P}$ when $d$ is even and $mathtt{PSPACE}$-complete when $d$ is odd. On split graphs, there is an interesting complexity dichotomy: D$d$ISR is $mathtt{PSPACE}$-complete for $d = 2$ but in $mathtt{P}$ for $d=3$ under $mathsf{TS}$, while under $mathsf{TJ}$ it is in $mathtt{P}$ for $d = 2$ but $mathtt{PSPACE}$-complete for $d = 3$. Additionally, certain well-known hardness results for $d = 2$ on general graphs, perfect graphs, planar graphs of maximum degeree three and bounded bandwidth can be extended for $d geq 3$

3D Least Squares Based Surface Reconstruction

Diese Arbeit präsentiert einen vollständig dreidimensionalen (3D) Algorithmus zur Oberflächenrekonstruktion aus Bildfolgen mit großer Basis. Die rekonstruierten Oberflächen werden durch Dreiecksgitter beschrieben, was eine einfache Integration von Bild- und Geometrie-basierten Bedingungen ermöglicht. Die vorgestellte Arbeit erweitert den erfolgreichen Ansatz von Heipke (1990) zur 2,5D Rekonstruktion zur vollständigen 3D Rekonstruktion. Verdeckung und nicht-Lambertsche Spiegelung werden durch robuste kleinste Quadrate Ausgleichung zur Schätzung des Modells berücksichtigt. Ausgangsdaten sind Bilder von verschiedenen Positionen, abgeleitete genaue Orientierungen der Bilder und eine begrenzte Zahl von 3D Punkten (Bartelsen and Mayer 2010). Die erste Neuerung des vorgestellten Ansatzes besteht in der Art und Weise, wie zusätzliche Punkte (Unbekannte) in dem Dreiecksgitter aus den vorgegebenen 3D Punkten positioniert werden. Dank den genauen Positionen dieser zusätzlichen Punkte werden präzisere und genauere rekonstruierte Oberflächen bezüglich Form und Anpassung der Bildtextur erhalten. Die zweite Neuerung besteht darin, dass individuelle Bias-Parameter für verschiedene Bilder und angepasste Gewichtungen für unterschiedliche Bildbeobachtungen verwendet werden, um damit unterschiedliche Intensitäten verschiedener Bilder als auch Ausreißer zu berücksichtigen. Die dritte Neuerung sind die verwendete Faktorisierung der Design-Matrix und die Art und Weise, wie die Gitter in Ebenen zerlegt werden, um die Laufzeit zu reduzieren. Das wesentliche Element des vorgestellten Modells besteht in der Varianz der Intensitätswerte der Bildbeobachtungen innerhalb eines Dreiecks. Mit dem vorgestellten Ansatz können genaue 3D Oberflächen für unterschiedliche Arten von Szenen rekonstruiert werden. Ergebnisse werden als VRML (Virtual Reality Modeling Language) Modelle ausgegeben, welche sowohl das Potential als auch die derzeitigen Grenzen des Ansatzes aufzeigen.This thesis presents a fully three dimensional (3D) surface reconstruction algorithm from wide-baseline image sequences. Triangle meshes represent the reconstructed surfaces allowing for an easy integration of image- and geometry-based constraints. We extend the successful approach for 2.5D reconstruction of Heipke (1990) to full 3D. To take into account occlusion and non-Lambertian reflection, we apply robust least squares adjustment to estimate the model. The input for our approach are images taken from different positions and derived accurate image orientations as well as sparse 3D points (Bartelsen and Mayer 2010). The first novelty of our approach is the way we position additional 3D points (unknowns) in the triangle meshes constructed from given 3D points. Owing to the precise positions of these additional 3D points, we obtain more precise and accurate reconstructed surfaces in terms of shape and fit of texture. The second novelty is to apply individual bias parameters for different images and adapted weights for different image observations to account for differences in the intensity values for different images as well as to consider outliers in the estimation. The third novelty is the way we factorize the design matrix and divide the meshes into layers to reduce the run time. The essential element for our model is the variance of the intensity values of image observations inside a triangle. Applying the approach, we can reconstruct accurate 3D surfaces for different types of scenes. Results are presented in the form of VRML (Virtual Reality Modeling Language) models, demonstrating the potential of the approach as well as its current shortcomings

A Note On Acyclic Token Sliding Reconfiguration Graphs of Independent Sets

We continue the study of token sliding reconfiguration graphs of independent sets initiated by the authors in an earlier paper (arXiv:2203.16861). Two of the topics in that paper were to study which graphs $G$ are token sliding graphs and which properties of a graph are inherited by a token sliding graph. In this paper we continue this study specializing on the case of when $G$ and/or its token sliding graph $mathsf{TS}_k(G)$ is a tree or forest, where $k$ is the size of the independent sets considered. We consider two problems. The first is to find necessary and sufficient conditions on $G$ for $mathsf{TS}_k(G)$ to be a forest. The second is to find necessary and sufficient conditions for a tree or forest to be a token sliding graph. For the first problem we give a forbidden subgraph characterization for the cases of $k=2, 3$. For the second problem we show that for every $k$-ary tree $T$ there is a graph $G$ for which $mathsf{TS}_{k+1}(G)$ is isomorphic to $T$. A number of other results are given along with a join operation that aids in the construction of $mathsf{TS}_k(G)$-graphs

On Reconfiguration Graphs of Independent Sets under Token Sliding

An independent set of a graph $G$ is a vertex subset $I$ such that there is no edge joining any two vertices in $I$. Imagine that a token is placed on each vertex of an independent set of $G$. The $mathsf{TS}$- ($mathsf{TS}_k$-) reconfiguration graph of $G$ takes all non-empty independent sets (of size $k$) as its nodes, where $k$ is some given positive integer. Two nodes are adjacent if one can be obtained from the other by sliding a token on some vertex to one of its unoccupied neighbors. This paper focuses on the structure and realizability of these reconfiguration graphs. More precisely, we study two main questions for a given graph $G$: (1) Whether the $mathsf{TS}_k$-reconfiguration graph of $G$ belongs to some graph class $mathcal{G}$ (including complete graphs, paths, cycles, complete bipartite graphs, connected split graphs, maximal outerplanar graphs, and complete graphs minus one edge) and (2) If $G$ satisfies some property $mathcal{P}$ (including $s$-partitedness, planarity, Eulerianity, girth, and the clique's size), whether the corresponding $mathsf{TS}$- ($mathsf{TS}_k$-) reconfiguration graph of $G$ also satisfies $mathcal{P}$, and vice versa. Additionally, we give a decomposition result for splitting a $mathsf{TS}_k$-reconfiguration graph into smaller pieces