Theory Diagrams Research Articles

Visualizing research trends and research theme evolution in E-learning field: 1999\u20132018

This paper aims to provide a comprehensive understanding of the evolution of major research themes and trends in e-learning research. A co-word analysis is applied for the analysis of the 21,656 keywords collected from 7214 articles published in 10 journals in the field of e-learning from the years 1999 to 2018. Specifically, a cluster analysis, social network analysis, strategic diagram, and graph theory were applied in the analysis for two time periods: 1999–2008 and 2009–2018. The study detects the bridging, popular, and core topics in e-learning research for the two periods. The research results indicate that e-learning research has undergone a health evolution over the past two decades. There is a temporal continuity of e-learning research because some research topics have kept their continuity over the studied 20 years. Meanwhile, the research traditions in the e-learning field are also continuously evolving with the development of new technologies. The results also offer useful hints on the future direction of how the field may evolve.

Homogeneous Einstein metrics on non-Kähler C-spaces

We study homogeneous Einstein metrics on indecomposable non-Kähler C-spaces, i.e. even-dimensional torus bundles M=G∕H with rankG>rankH over flag manifolds F=G∕K of a compact simple Lie group G. Based on the theory of painted Dynkin diagrams we present the classification of such spaces. Next we focus on the family Mℓ,m,n≔SU(ℓ+m+n)∕SU(ℓ)×SU(m)×SU(n),ℓ,m,n∈Z+and examine several of its geometric properties. We show that invariant metrics on Mℓ,m,n are not diagonal and beyond certain exceptions their parametrization depends on six real parameters. By using such an invariant Riemannian metric, we compute the diagonal and the non-diagonal part of the Ricci tensor and present explicitly the algebraic system of the homogeneous Einstein equation. For general positive integers ℓ,m,n, by applying mapping degree theory we provide the existence of at least one SU(ℓ+m+n)-invariant Einstein metric on Mℓ,m,n. For ℓ=m we show the existence of two SU(2m+n)-invariant Einstein metrics on Mm,m,n, and for ℓ=m=n we obtain four SU(3n)-invariant Einstein metrics on Mn,n,n. We also examine the isometry problem for these metrics, while for a plethora of cases induced by fixed ℓ,m,n, we provide the numerical form of all non-isometric invariant Einstein metrics.

CFT unitarity and the AdS Cutkosky rules

We derive the Cutkosky rules for conformal field theories (CFTs) at weak and strong coupling. These rules give a simple, diagrammatic method to compute the double-commutator that appears in the Lorentzian inversion formula. We first revisit weakly-coupled CFTs in flat space, where the cuts are performed on Feynman diagrams. We then generalize these rules to strongly-coupled holographic CFTs, where the cuts are performed on the Witten diagrams of the dual theory. In both cases, Cutkosky rules factorize loop diagrams into on-shell sub-diagrams and generalize the standard S-matrix cutting rules. These rules are naturally formulated and derived in Lorentzian momentum space, where the double-commutator is manifestly related to the CFT optical theorem. Finally, we study the AdS cutting rules in explicit examples at tree level and one loop. In these examples, we confirm that the rules are consistent with the OPE limit and that we recover the S-matrix optical theorem in the flat space limit. The AdS cutting rules and the CFT dispersion formula together form a holographic unitarity method to reconstruct Witten diagrams from their cuts.

ADG: Automated generation and evaluation of many-body diagrams II. Particle-number projected Bogoliubov many-body perturbation theory

We describe the second version (v2.0.0) of the code ADG that automatically (1) generates all valid off-diagonal Bogoliubov many-body perturbation theory diagrams at play in particle-number projected Bogoliubov many-body perturbation theory (PNP-BMBPT) and (2) evaluates their algebraic expression to be implemented for numerical applications. This is achieved at any perturbative order p for a Hamiltonian containing both two-body (four-legs) and three-body (six-legs) interactions (vertices). All valid off-diagonal BMBPT diagrams of order p are systematically generated from the set of diagonal, i.e.,unprojected, BMBPT diagrams. The production of the latter were described at length in Arthuis et al. (2019) dealing with the first version of ADG. The automated evaluation of off-diagonal BMBPT diagrams relies both on the application of algebraic Feynman’s rules and on the identification of a powerful diagrammatic rule providing the result of the remaining p-tuple time integral. The new diagrammatic rule generalizes the one already identified in Arthuis et al. (2019) to evaluate diagonal BMBPT diagrams independently of their perturbative order and topology. The code ADG is written in Python3 and uses the graph manipulation package NetworkX. The code is kept flexible enough to be further expanded throughout the years to tackle the diagrammatics at play in various many-body formalisms that already exist or are yet to be formulated. Program summaryProgram Title:ADGCPC Library link to program files:https://doi.org/10.17632/6h4xrydwfb.2Licensing provisions: GPLv3Programming language: Python3Journal reference of previous version: P. Arthuis, T. Duguet, A. Tichai, R.-D. Lasseri and J.-P. Ebran, ”ADG: Automated generation and evaluation of many-body diagrams I. Bogoliubov many-body perturbation theory”, Computer Physics Communications 240 (2019), pp. 202-227.Does the new version supersede the previous version?: Yes.Reasons for the new version: Incorporation of a new formalism into the program.Summary of revisions: Addition of off-diagonal BMBPT to the formalisms for which diagrams can be generated, fix of a wrong symmetry factor, move of the codebase from Python2 to Python3 while maintaining support for Python2, various optimizations to reduce the time and memory necessary to the program.Nature of problem: As formal and numerical developments in many-body-perturbation-theory-based ab initio methods make higher orders reachable, manually producing and evaluating all the diagrams becomes rapidly untractable as both their number and complexity grow quickly, making it prone to mistakes and oversights.Solution method: Diagonal BMBPT diagrams are encoded as square matrices known as oriented adjacency matrices in graph theory, and then turned into graph objects using the NetworkX package. Off-diagonal BMBPT diagrams can then be generated from those graphs. Checks on the diagrams and evaluation of their time-integrated expression are eventually done on a purely diagrammatic basis. HF-MBPT diagrams are produced and evaluated as well using the same principle.

Deformation-obstruction theory for diagrams of algebras and applications to geometry

Let X be an algebraic variety over an algebraically closed field of characteristic 0 and let \operatorname{Coh} (X) denote its Abelian category of coherent sheaves. By the work of W. Lowen and M. Van den Bergh, it is known that the deformation theory of \operatorname{Coh}(X) as an Abelian category can be seen to be controlled by the Gerstenhaber–Schack complex associated to the restriction of the structure sheaf \mathcal O_X \vert_{\mathfrak U} to a cover of affine open sets. We construct an explicit L _\infty algebra structure on the Gerstenhaber–Schack complex controlling the higher deformation theory of \mathcal O_X \vert_{\mathfrak U} or \operatorname{Coh}(X) in case X can be covered by two acyclic open sets, giving an explicit deformation-obstruction calculus for such deformations. For smooth X , such deformations recover the deformation of complex structures and deformation quantizations of X as degenerate cases, as we show by means of concrete examples.

Reism, Concretism and Schopenhauer Diagrams

Abstract Reism or concretism are the labels for a position in ontology and semantics that is represented by various philosophers. As Kazimierz Ajdukiewicz and Jan Woleński have shown, there are two dimensions with which the abstract expression of reism can be made concrete: The ontological dimension of reism says that only things exist; the semantic dimension of reism says that all concepts must be reduced to concrete terms in order to be meaningful. In this paper we argue for the following two theses: (1) Arthur Schopenhauer has advocated a reistic philosophy of language which says that all concepts must ultimately be based on concrete intuition in order to be meaningful. (2) In his semantics, Schopenhauer developed a theory of logic diagrams that can be interpreted by modern means in order to concretize the abstract position of reism. Thus we are not only enhancing Jan Woleński’s list of well-known reists, but we are also adding a diagrammatic dimension to concretism, represented by Schopenhauer.

Hot Workability of Ultra-Supercritical Rotor Steel Using a 3-D Processing Map Based on the Dynamic Material Model.

As a new-type of ultra-supercritical HI-IP rotor steel, X12CrMoWVNbN10-1-1 alloy steel has excellent integrative performance, which can effectively improve the power generation efficiency of the generator set. In this paper, uniaxial thermal compression tests were carried out over a temperature range of 950–1200 °C and strain rates of 0.05–5 s−1 with a Gleeble-1500D thermal simulation testing machine. Moreover, based on hot compression experimental data and the theory of processing diagrams, in combination with the dynamic material model, a three-dimensional (3-D) thermal processing map considering the effect of strain was constructed. It was concluded that optimum thermal deformation conditions were as follows: the temperature range of 1150–1200 °C, the strain rate range of 0.05–0.634 s−1. Through secondary development of the finite element (FE) software FORGE®, three-dimensional thermal processing map data were integrated into finite element software FORGE®. The distributions of instability coefficient and power dissipation coefficient were obtained over various strain rates and temperatures of the Ø 8 × 12 mm cylinder specimen by using finite element simulation. It is shown that simulation results are consistent with the microstructure photos. The method proposed in this paper, which integrates the three-dimensional processing map into the finite element software FORGE® (Forge NxT 2.1, Transvalor, Nice, France), can effectively predict the formability of X12CrMoWVNbN10-1-1 alloy steel.

Coordinated Perimeter Control for Multiregion Heterogeneous Networks Based on Optimized Transfer Flows

Exploring efficient control strategies for heterogeneously congested urban networks remains a big research challenge. The theory of macroscopic fundamental diagram (MFD) provides a new perspective for network-wide congestion control decisions. This paper proposes a coordinated perimeter control strategy for multiregion heterogeneous networks based on optimized transfer flows. First, a two-layer network partitioning method is presented to capture spatial heterogeneity dynamics of urban networks. For this partition, traffic flow equilibrium model based on MFD and multiagent based hierarchical traffic management scheme are built. Then, an improved multinomial logit model is developed for deriving optimized transfer flows among multiple congested regions. A coordinated perimeter control strategy using model predictive control is further proposed, which is aimed at tracking desired accumulations of each congested region. As a case study, the proposed control strategy is applied to the downtown network of Jinan, China, using simulation analysis. The results demonstrate that it can achieve balanced network flow distribution and increased mobility.

Hasse diagrams for 3d mathcal{N} = 4 quiver gauge theories \u2014 Inversion and the full moduli space

We study Hasse diagrams of moduli spaces of 3d mathcal{N} = 4 quiver gauge theories. The goal of this work is twofold: 1) We introduce the notion of inverting a Hasse diagram and conjecture that the Coulomb branch and Higgs branch Hasse diagrams of certain theories are related through this operation. 2) We introduce a Hasse diagram to map out the entire moduli space of the theory, including the Coulomb, Higgs and mixed branches. For theories whose Higgs and Coulomb branch Hasse diagrams are related by inversion it is straight forward to generate the Hasse diagram of the entire moduli space. We apply inversion of the Higgs branch Hasse diagram in order to obtain the Coulomb branch Hasse diagram for bad theories and obtain results consistent with the literature. For theories whose Higgs and Coulomb branch Hasse diagrams are not related by inversion it is nevertheless possible to produce the Hasse diagram of the full moduli space using different methods. We give examples for Hasse diagrams of the entire moduli space of theories with enhanced Coulomb branches.

Thermodynamic analysis of the phase equilibrium of the polystyrene‐poly(vinyl methyl ether) system

AbstractThe phase diagrams of polystyrene (PS)‐poly(vinyl methyl ether) (PVME) system obtained via optical interferometry in the study of polymer interdiffusion are presented. The influence of molecular weight of the PS on the position of the binodal curve dome and the critical point is shown. Paired interaction parameters and their temperature dependences are calculated in the framework of Flory‐Huggins theory both for the present experimental diagrams and for the ones, previously obtained by different authors. It is shown that the generalized temperature dependence of the Flory‐Huggins parameter can be used to model phase equilibrium in a wide range of temperatures and compositions. For the first time for PS‐PVME system, the generalized phase state diagram characterized by both lower and upper critical solution temperatures is calculated and constructed.

Impact of microalloying element Ga on the glass-forming ability (GFA), mechanical properties and corrosion behavior of Mg–Zn–Ca bulk metallic glass

By virtue of its high corrosion resistance and desirable mechanical properties, Mg-based bulk metallic glass (BMG) is a promising candidate material for the biodegradable implants. To investigate the impact of microalloying element Ga on the glass-forming ability (GFA) and its effect on the mechanical properties and corrosion behaviors of Mg–Zn–Ca BMG, a series alloys of (Mg66Zn30Ca4)100-xGax (x = 0, 0.25, 0.5, 0.75, 1.0 and 1.25) were synthesized and investigated in this study. According to the XRD results and SEM (backscattered electron) images, the critical diameter (Dc) of Mg66Zn30Ca4 BMG is about 3.5 mm, and 1.0 at.% Ga addition improves the Dc to about 5 mm. Meanwhile, the 1.0 at.% Ga addition improves the fracture strength of Mg–Zn–Ca BMG from 651 MPa to 752 MPa. The corrosion behavior and mechanism of different metallic glass samples were investigated. According to the results of electrochemical tests and immersion test, the addition of Ga can help to form the passive film on the metallic glass substrate and improve its corrosion resistance. Besides, the relationship between the alloy composition and glass-forming ability (GFA) was postulated and interpreted by the theory of binary alloy phase diagrams.

THE ANALYSIS OF PREPOSITIONAL PHRASE IN NOVEL ‘THE PERFECT NANY’ WRITTEN BY LEILA SLIMANI

Prepositional Phrase is the part of preposition and absolutely it is the part of grammar too. It has rules and deregulations that must be obeyed. Without a correct replacement of preposition, the meaning of the sentence can make the people confused. Hence, the research questions of this research are: 1) What are the positions of prepositions phrase of sentences found in Novel The Perfect Nany written by Leila Slimani?. 2) What are the patterns of tree diagram for a prepositional phrase of sentences found in Novel The Perfect Nany written by Leila Slimani?. The researcher use Position of Prepositional Phrase theory by Frank (1972) and theory of a tree diagram by Delahunty and Garvey (2010) to analyze the data. The findings show that the position of prepositional phrase in novel The Perfect Nany written by Leila Slimani is dominated by position in adverbial function (34 data). And the position in adjectival function is only found with 16 data. Base on the data analysis, it can be concluded that prepositional phrase adverbial function is more widely used than prepositional phrase adjectival function, because it can modify the verb, adverb, and adjectival that are mostly found in sentences. It is was also concluded that in one sentence there could be more than one prepositional phrase through the tree diagram that have been analyzed.Key words: Prepositional Phrase, Adverbial Function, Adjectival Function

Climatically and culturally responsive typologies using mathematical permutation

PurposeThis research introduces a hypothesis for establishing typologies and patterns for architectural plans based on their climate, culture and orientation. The repetition and reproduction of spaces in architectural plans are rooted in mathematical equations. Factorial and permutation formulae are the type of equations used as scientific tools to define typology. In addition, a new perspective on culture and privacy in line with the Arabic house is included to illustrate the practicality of restricted plans according to cultural needs.Design/methodology/approachTo make the approach accessible, the theory is integrated into a software using C++ as the programming tool. Accordingly, all patterns and typologies are reproduced by inserting digits or numbers to simulate the process of using permutations and factorials for the creation of diagrammatic patterns and, subsequently, architectural plans.FindingsThe authors recommend that this method be integrated in future housing studies at earlier stages to obtain a high number of alternatives for architectural plans. The results of mathematical permutation of this study will help architects and designers to evolve their methods and processes through creating alternative patterns and culture (and climate)-specific typologies to provide more design possibilities.Originality/valueThis study is set to improve the adjacency diagram theory into the adjacency diagram with orientation theory, which accounts for the geographical orientation to obtain more comprehensive and climate-responsive patterns.

Voronoi diagram based simulation and experimental validation of austenite in C22 and C35 steels

This paper examines the ability of power Voronoi diagram assisted simulation in microstructure modeling during heat treatment. A model is developed for predicting fraction of austenite evolved during continuous heating of steel to austenite range, by integrating geometrical features of power Voronoi diagram and classical nucleation theory. From the simulation results, it is possible to predict the transformed fraction. The simulation results are validated using experiments conducted on two varieties of steels. The maximum error obtained is 2.08%. Thus, power Voronoi assisted simulation can be considered as an effective tool in modeling microstructure evolution during austenitization.

Tropical diagrams of probability spaces

After endowing the space of diagrams of probability spaces with an entropy distance, we study its large-scale geometry by identifying the asymptotic cone as a closed convex cone in a Banach space. We call this cone the tropical cone, and its elements tropical diagrams of probability spaces. Given that the tropical cone has a rich structure, while tropical diagrams are rather flexible objects, we expect the theory of tropical diagrams to be useful for information optimization problems in information theory and artificial intelligence. In a companion article, we give a first application to derive a statement about the entropic cone.

Generic Sequences and the Generic Tonnetz

This article employs concepts from diatonic set theory, transformation theory, and neo-Riemannian theory in an investigation of sequences in generic (mod-7) pitch space. Sequences may be described using generic transposition operators, mod-7 analogs of the more familiar mod-12 chromatic transposition operators, and may be mapped in a generic Tonnetz analogous to the Tonnetz diagrams of neo-Riemannian theory. A complete classification of generic sequences with two-chord transposition blocks is derived from the paths described by the sequences in the Tonnetz. While it is tempting to regard generic space as “diatonic,” the examples demonstrate that generic structure governs many sequences that are not actually diatonic at all. The examples also show that the sequences found in the literature include many more types than are widely recognized and that generic sequence structure may apply in numerous other contexts besides patterns of chord roots.

POLARIS: Path of Least Action Analysis on Energy Landscapes.

Free-energy landscapes are a powerful tool for analyzing dynamical processes - capable of providing a complete mapping of a system's configurations in state space while articulating its energetics topologically in the form of sprawling hills and valleys. Within this mapping, the path of least action can be derived - representing the most probable sequence of transitions taken between any two states in the landscape. In this article, POLARIS (Path of Least Action Recursive Survey) is presented as a dynamic, global approach that efficiently automates the discovery of the least action path on previously determined 2D energy landscapes. Important built-in features of this program include plotting of landscape trajectories and transition state theory diagrams, generation of text files with least action coordinates and respective energies, and bifurcation analysis tools that provide downstream versatility for comparing most probable paths and reaction rates.

Methods and guidelines for the choice of shell theories

This paper provides an overview of the modeling approaches adopted over the years to develop shell theories for composite structures. Furthermore, it presents a method to assess any structural theory concerning the accuracy and computational efficiency and trigger informed decisions on the structural theory to use for a given problem. This method exploits the synergies between the Carrera unified formulation and the axiomatic/asymptotic method. Typical outcomes are the best theory diagrams or the estimation of accuracy of a theory as compared to quasi-3D solutions. The proposed framework can be useful to provide guidelines on the construction of structural theories and can serve as a trainer for the deep learning of neural networks.

A novel classification tree based on local minimum Gini index and attribute partial order structure diagram

Decision tree is not only an important machine learning method, but also the basis of ensemble learning methods such as random forest and deep forest. Based on the theory of Formal Concept Analysis (FCA) and Attribute Partial Order Structure Diagram (APOSD), a new decision tree for classification is proposed in this paper. Firstly, the local minimum of Gini index is used to complete the data granulation, and the Formal Decision Mode Information Table (FDMIT) is constructed. Then, the Attribute Partial Order Classification Tree (APOCT) is generated based on APOSD to complete the pattern recognition and rule extraction. The method of APOCT separates the process of granulation and visualisation, and the granulation process is easy to parallelise and efficient. The experimental results show that APOCT is effective.

Power Voronoi assisted modelling and simulation of austenite formation during continuous heating in C35 steel

In the development of materials with desired properties, modelling of transformation kinetics is an important aspect. Ability of power Voronoi assisted simulation in predicting transformation kinetics is examined in this work. Initially, a mathematical model is derived incorporating the geometrical properties of power Voronoi diagram and classical nucleation theory. This is the governing equation for the power Voronoi assisted simulation. Transformed fractions at different temperatures are calculated using this equation. Simulation of microstructure evolution is carried out using power Voronoi diagram by giving nucleation rate and interface velocity as input. From the resultant geometry, it is possible to calculate the transformed fraction. The results are validated and verified using the available experimental results in literature. On comparison, it is evident that, transformed fraction can be predicted with less than 4% error using power Voronoi assisted simulation model with the derived governing equation. Thus, power Voronoi diagram can be used to simulate microstructure evolution during austenitisation with reasonably good accuracy in phase fraction.