The Euler characteristic as a basis for teaching topology concepts to crystallographers

The simple Euler polyhedral formula, expressed as an alternating count of the bounding faces, edges and vertices of any polyhedron, V − E + F = 2, is a fundamental concept in several branches of mathematics. Obviously, it is important in geometry, but it is also well known in topology, where a similar telescoping sum is known as the Euler characteristic χ of any finite space. The value of χ can also be computed for the unit polyhedra (such as the unit cell, the asymmetric unit or Dirichlet domain) which build, in a symmetric fashion, the infinite crystal lattices in all space groups. In this application χ has a modified form (χm) and value because the addends have to be weighted according to their symmetry. Although derived in geometry (in fact in crystallography), χm has an elegant topological interpretation through the concept of orbifolds. Alternatively, χm can be illustrated using the theorems of Harriot and Descartes, which predate the discovery made by Euler. Those historical theorems, which focus on angular defects of polyhedra, are beautifully expressed in the formula of de Gua de Malves. In a still more general interpretation, the theorem of Gauss–Bonnet links the Euler characteristic with the general curvature of any closed space. This article presents an overview of these interesting aspects of mathematics with Euler's formula as the leitmotif. Finally, a game is designed, allowing readers to absorb the concept of the Euler characteristic in an entertaining way.

Cross-Layer Learning

Deep learning-based investigation mechanisms are available for conventional forensics, but not for IoT forensics. Dividing the system into different layers according to their functionalities, collecting data from each layer, finding the correlating factor, and using it for pattern detection is the fundamental concept behind the proposed intelligent system. The authors utilize this notion for embedding intelligence in forensics and speed up the investigation process by providing hints to the examiner. They propose a novel cross-layer learning architecture (CCLA) for IoT forensics. To the best of their knowledge, this is the first attempt to incorporate deep learning into the forensics of the IoT ecosystem.

The Concept of God According to Sa’id Nursi

The concept of God is a fundamental concept for every religion, especially Islam. The concept of God in Islam is different from other religions, even emerging from the time of the Greek philosophical tradition and Eastern and Western mystical traditions. Not a few Muslims state that all religions are the same God. This is a problem for the religions of this world. Therefore, Sa’id Nursi clearly stated that the concept of God according to Islam is different from the concept of God according to other religions. The method used by the writer is descriptive and analytical. In this case, Badi'uzzaman has a perspective on the concept of God. God, according to Badi'uzzaman, is one immanent and radiates his light into the universe, thus creating the greatness of the universe and its contents, which is often called Tauhīd. Nursi understands monotheism as the basis of ideology and epistemology viewing the universe. So, Nursi's concept of divinity emphasizes the monotheistic aspect, in contrast to the esoteric and exoteric sides.

Gamification Reloaded

Gamification can help to increase motivation for various activities. As a fundamental concept in HCI, gamification has connections with various fields involving mixed reality, health care, or education. This article presents the expertise of 106 gamification specialists who participated in four workshops called “Gam-R — Gamification Reloaded.” The extraction of current and future trends in gamification is the result of this. Four general topics, four in-depth topics, and seven emerging fields of application for gamification are depicted and enriched with the current state of research to support interested academic scholars and practitioners. Technical and less technical areas, which are the fields of work and research in gamification, are demonstrated. Some areas are already trending, while others are just beginning to show a future trend.

The Willingness to Pay for Diversification

Diversification is a fundamental concept in economics and finance. This paper argues that decision makers have an intrinsic preference for diversification that is responsive to cost and that this willingness to pay for diversification is driven by risk aversion and loss aversion. In an experiment replicating a portfolio choice problem, the value of diversification is estimated to be at 5% of the initial endowment of approximately $100. Moreover, risk-averse and loss-averse individuals are willing to pay more for diversification. These findings point to the idea that diversification is a fundamental preference and may help explain portfolio choice anomalies such as irrational diversification, the diversification bias, and overdiversification. This paper was accepted by Tomasz Piskorski, finance.

Analisis Pemahaman Konsep, Multirepresentasi, dan Kosistensi Jawaban Siswa SMA pada Konsep Hukum III Newton

Newton's third law is a fundamental concept of Physics that is still not reached by students. The tendency of students who do not understand the concept well can be observed by measuring the ability of multi-representation and solutions when solving Physics problems. Therefore, this study aims to determine the concept of Newton's third law understood by students, the multi-representation students have, and the consistency of students' answers in answering physics questions. The participants numbered 28 students from the second semester of high school, selected using the purposive sampling technique, who had just completed discussions about Newton's Law and were willing to participate in this study. Participants were given 6 two-tier question items that managed the R-FCI questions. The results of the answers were analyzed quantitatively to determine the initial percentage description and then analyzed qualitatively to determine understanding, multi-representation ability, and consistency in depth. Most of the participants had low conceptual understanding and answered the questions consistent-wrong. However, based on the analysis of the answer choices and the reasons given, most students understand the meaning of the representation of the answers given

On hate and the typology of the misfit in Dostoevsky’s and Salinger’s Works

As part of the death drive, hate, so prevalent in world literature as the natural state of so many characters, has led the creative spirits, preoccupied invariably with metamorphosis and ascension, to produce genuine masterpieces. Whether malignant or benign (socially justified), hate, along with its many shapes and forms, generates attitudes which characterize a fundamental concept in Dostoevsky’s fiction, namely the antihero. Displaying typical features that are traceable throughout literature from the great Russian author on, the character dominated by hate withdraws from the world, thus fueling his alienation.

Computational Paths and the Fundamental Groupoid of a Type

Using computational paths as the fundamental concept, we show that we can leverage Category Theory to propose the concept of fundamental groupoid of a type.

The Art of Mesenchymal Stem Cells in Liver Fibrosis Management

Liver fibrogenesisis chronic tissue damage characterized by an extracellular ac-cumulation of fibrillar matrix associated with continuous degradation and remod-elling. This scientific review describes current concepts on the pathophysiology of liver fibrosis, inflammation asa fundamental concept of liver fibrosis, mechanistic concepts of liver fibrosis, the role of mesenchymal stem cells (MSC) in liver injury, the functional effects of MSC secretome, the advantages of secretome ther-apy, and the latest research developments on MSC. The role of MSCs has been proven in many liver fibrosis studies involving experimental animals. However, it still requires further research for safety and efficacy aspects.