Set Of Topologies Research Articles

Topological insulators and K-theory

We analyze topological invariants, in particular Z2 invariants, which characterize time reversal invariant topological insulators, in the framework of index theory and K-theory. After giving a careful study of the underlying geometry and K-theory, we formalize topological invariants as elements of KR theory. To be precise, the strong topological invariants lie in the higher KR groups of spheres; KR̃−j−1(SD+1,d). Here j is a KR-cycle index, as well as an index counting off the Altland-Zirnbauer classification of Time Reversal Symmetry (TRS) and Particle Hole Symmetry (PHS)—as we show. In this setting, the computation of the invariants can be seen as the evaluation of the natural pairing between KR-cycles and KR-classes. This fits with topological and analytical index computations as well as with Poincaré Duality and the Baum–Connes isomorphism for free Abelian groups. We provide an introduction starting from the basic objects of real, complex and quaternionic structures which are the mathematical objects corresponding to TRS and PHS. We furthermore detail the relevant bundles and K-theories (Real and Quaternionic) that lead to the classification as well as the topological setting for the base spaces.

Auto-Routing Systems (ARSs) with 3D Piping for Sustainable Plant Projects Based on Artificial Intelligence (AI) and Digitalization of 2D Drawings and Specifications

The engineering sector is undergoing digital transformation (DT) alongside shifts in labor patterns. This study concentrates on piping design within plant engineering, aiming to develop a system for optimal piping route design using artificial intelligence (AI) technology. The objective is to overcome limitations related to time and costs in traditional manual piping design processes. The ultimate aim is to contribute to the digitalization of engineering processes and improve project performance. Initially, digital image processing was utilized to digitize piping and instrument diagram (P&ID) data and establish a line topology set (LTS). Subsequently, three-dimensional (3D) modeling digital tools were employed to create a user-friendly system environment that visually represents piping information. Dijkstra’s algorithm was implemented to determine the optimal piping route, considering various priorities during the design process. Finally, an interference avoidance algorithm was used to prevent clashes among piping, equipment, and structures. Hence, an auto-routing system (ARS), equipped with a logical algorithm and 3D environment for optimal piping design, was developed. To evaluate the effectiveness of the proposed model, a comparison was made between the bill of materials (BoM) from Company D’s chemical plant project and the BoM extracted from the ARS. The performance evaluation revealed that the accuracy in matching pipe weight and length was 105.7% and 84.9%, respectively. Additionally, the accuracy in matching the weight and quantity of fittings was found to be 99.7% and 83.9%, respectively. These findings indicate that current digitalized design technology does not ensure 100% accurate designs. Nevertheless, the results can still serve as a valuable reference for attaining optimal piping design. This study’s outcomes are anticipated to enhance work efficiency through DT in the engineering piping design sector and contribute to the sustainable growth of companies.

Some new open sets in bipolar N-neutrosophic supra topological spaces

The primary focus of this work is to develop the concept of bipolar N-neutrosophic supra topological spaces. Also, extended some concepts such as closure and interior operators of N-neutrosophic supra topological spaces to Bipolar N-neutrosophic supra topological spaces. The properties and relationship between weak forms of bipolar N-neutrosophic supra topological open sets are also established. Further, suggested several separations amongst bipolar N-neutrosophic supra sets. Some distance between bipolar N-neutrosophic sets is introduced and an efficient approachfor group multi-criteria decision making based on bipolar N-neutrosophic sets is proposed.

OMNeT++ Simulation Framework for Avionics Full-Duplex Switched Ethernet

Avionics Full-Duplex Switched Ethernet (AFDX) is a popular network technology for integrated modular avionics (IMA). When designing an AFDX network, it is important to fulfill the real-time communication requirements of avionic systems. To this end, simulation tools offer a low-cost solution for the performance evaluation of a given AFDX network and message set configuration at the design stage. In this paper, we develop an improved AFDX model for the widely used OMNeT++ (extensible, modular, component-based C++ simulation library and framework) network simulator. Our model exhibits high fidelity to the standard, adds detailed parameter configuration and data logging capabilities, and is compatible with the most recent OMNeT++ version. Our model is accepted by the OMNeT++ community and published as the current AFDX simulation model. Moreover, we propose a complete AFDX simulation framework by augmenting our improved OMNeT++ models with a new network configuration and analysis software tool that we call ANCAT. ANCAT enables users who lack familiarity with the OMNeT++ interface and specific file formats to provide simulation parameters in generic file formats such as.xlsx. Subsequently, ANCAT runs the simulation and generates reports for the results. We first systematically verify the correctness of our AFDX simulation framework by custom-designed experiments. Then, we investigate the practicability of our proposed framework with the performance analysis of a realistic AFDX network topology and message set. In particular, we demonstrate that our proposed framework can be efficiently used to explore the real-time capabilities and relevant features of AFDX networks, as well as provide basic guidelines for network configuration.

MAST: Phylogenetic Inference with Mixtures Across Sites and Trees.

Hundreds or thousands of loci are now routinely used in modern phylogenomic studies. Concatenation approaches to tree inference assume that there is a single topology for the entire dataset, but different loci may have different evolutionary histories due to incomplete lineage sorting (ILS), introgression, and/or horizontal gene transfer; even single loci may not be treelike due to recombination. To overcome this shortcoming, we introduce an implementation of a multi-tree mixture model that we call mixtures across sites and trees (MAST). This model extends a prior implementation by Boussau et al. (2009) by allowing users to estimate the weight of each of a set of pre-specified bifurcating trees in a single alignment. The MAST model allows each tree to have its own weight, topology, branch lengths, substitution model, nucleotide or amino acid frequencies, and model of rate heterogeneity across sites. We implemented the MAST model in a maximum-likelihood framework in the popular phylogenetic software, IQ-TREE. Simulations show that we can accurately recover the true model parameters, including branch lengths and tree weights for a given set of tree topologies, under a wide range of biologically realistic scenarios. We also show that we can use standard statistical inference approaches to reject a single-tree model when data are simulated under multiple trees (and vice versa). We applied the MAST model to multiple primate datasets and found that it can recover the signal of ILS in the Great Apes, as well as the asymmetry in minor trees caused by introgression among several macaque species. When applied to a dataset of 4 Platyrrhine species for which standard concatenated maximum likelihood (ML) and gene tree approaches disagree, we observe that MAST gives the highest weight (i.e., the largest proportion of sites) to the tree also supported by gene tree approaches. These results suggest that the MAST model is able to analyze a concatenated alignment using ML while avoiding some of the biases that come with assuming there is only a single tree. We discuss how the MAST model can be extended in the future.

Higher derivative corrections to string inflation

We quantitatively estimate the leading higher derivative corrections to N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supergravity derived from IIB string compactifications and study how they may affect moduli stabilisation and LVS inflation models. Using the Kreuzer-Skarke database of 4D reflexive polytopes and their triangulated Calabi-Yau database, we present scanning results for a set of divisor topologies corresponding to threefolds with 1 ≤ h1,1 ≤ 5. In particular, we find several geometries suitable to realise blow-up inflation, fibre inflation and poly-instantons inflation, together with a classification of the divisors topologies for which the leading higher derivative corrections to the inflationary potential vanish. In all other cases, we instead estimate numerically how these corrections modify the inflationary dynamics, finding that they do not destroy the predictions for the main cosmological observables.

Seismic 3D full-horizon tracking based on a knowledge graph to represent the stratigraphic sequence relationship

Seismic 3D full-horizon tracking is a fundamental and crucial step in sequence analysis and reservoir modeling. Existing automatic full-horizon tracking approaches lack effective methods for representing the stratigraphic sequence relationships in seismic data. However, the inability to represent the stratigraphic sequence relationships fully and accurately makes it challenging to address discontinuous areas affected by faults and unconformities. To address this issue, we develop a knowledge graph representing the stratigraphic sequence relationship, which enables the simultaneous extraction of all horizon surfaces once the stratigraphic distribution of the seismic data is obtained. This method first generates horizon patches and calculates the fault attributes, followed by the construction of an initial knowledge graph that characterizes the overall distribution of horizon patches and faults. The initial knowledge graph comprises nodes and edges. The nodes represent horizon patches, and their attributes cover the geographical location information of the patches and faults. Simultaneously, the edges represent the relationship between the horizon patches, including the stratigraphic sequence relationship, and their attributes illustrate the potential for connecting these patches. Furthermore, we introduce a multilayer knowledge graph based on the point-set topology to fuse the nodes. This allows for the continuous merging of the horizon patches to obtain horizon surfaces across discontinuities with the constraints of fault attributes and stratigraphic sequence relationships in 3D space. Synthetic and field examples demonstrate that our approach can effectively represent stratigraphic sequence relationships and accurately track horizons located in discontinuous areas with faults and unconformities.

Directed sets of topology: Tukey representation and rejection

Directed sets of topology: Tukey representation and rejection

Distributed Augmentation, Hypersweeps, and Branch Decomposition of Contour Trees for Scientific Exploration.

Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale using highperformance computing. To address this challenge, recent work has introduced distributed hierarchical contour trees for distributed computation and storage of contour trees. However, effective use of these distributed structures in analysis and visualization requires subsequent computation of geometric properties and branch decomposition to support contour extraction and exploration. In this work, we introduce distributed algorithms for augmentation, hypersweeps, and branch decomposition that enable parallel computation of geometric properties, and support the use of distributed contour trees as query structures for scientific exploration. We evaluate the parallel performance of these algorithms and apply them to identify and extract important contours for scientific visualization.

Some Properties of α^g-Closed Sets in Fuzzy Neutrosophic Topology

The present paper offers a new notion of sets known as fuzzy neutrosophic ^g-closed sets in fuzzy neutrosophic topology. It is an extended form of work conducted by Fatimah et.al. [1-3]. It investigates several properties of fuzzy neutrisophic ^ g- closed sets and explores a number of examples as to shed the light on the new characteristics of ^g-closed sets as well as some associated relations between them with other sets.

Betam-Closed Sets in Fuzzy Neutrosophic Topological Spaces

The current work offers a new concept of sets and called uzzy eutrosophic m-closed sets in fuzzy neutrosophic topology. In fact, the research is an extended form of a research conducted by F. M. Mohammed et.al. [1-7]. It explores a number of noteworthy examples to shed the light on the new characteristics and attributes of these recently formed conceptions, as well as some associated interactions between them.

Forecasting-Aided Joint Topology/State Estimation for Distribution Systems via Bayesian Non-Parametric Modeling

To ensure the validity of distribution system state estimation (DSSE) in case of frequent topology changes, it is important to develop DSSE methods with topology identification capability. This paper proposes a forecasting-aided joint topology/state estimation method for distribution systems considering topology changes. The joint estimation problem is formulated under the Dirichlet-process hidden-Markov-model (DP-HMM), which requires establishing state-space models for a partial set of topologies (i.e., predefined topologies) and constructing probability distribution of the other possible topologies (i.e., unseen topologies). A particle filter (PF)-based method is proposed to resolve this joint estimation problem, which augments the particles to include both topology-related variables and nodal voltages. Its robustness against measurement outliers is enhanced by adopting the anti-zero bias modification. The base distribution for unseen topologies are constructed via probabilistic neural networks (PNNs). To improve the accuracy of PNNs, the synthetic minority oversampling technique is employed to rebalance the training data. Aiming at efficiency enhancement, a rule-based candidate set reduction method is proposed for the unseen topologies to improve topology sampling validity. Test results on the IEEE 33-bus, IEEE 123-bus, and a modified 2516-bus distribution systems show that the proposed method has good state and topology estimation accuracy while achieving good scalability.

Thermodynamic topology of black holes from bulk-boundary, extended, and restricted phase space perspectives

In this article, we investigate the thermodynamic topology of some black holes, namely AdS Reissner Nordstrom (R–N), AdS Einstein–Gauss–Bonnet (EGB), and AdS Einstein-power-Yang–Mills (EPYM), from different frameworks: bulk-boundary (BB) and restricted phase space (RPS). Using the generalized off-shell Helmholtz free energy method, we calculate the thermodynamic topology of the selected black holes in each space separately and determine their topological classifications. We show that the addition of GB terms, dimensions, and other factors do not affect the topological classes of black holes in both spaces. The calculations and plots indicate that the AdS R–N and AdS EGB black holes show similar behavior and their topological numbers sets in both spaces, i.e., BB and RPS, are similar and equal to (W=+1). However, AdS EPYM black holes show an interesting behavior. In addition to BBT and RPS, we also consider the extended phase space thermodynamics (EPST) and evaluate the thermodynamic topology for AdS EPYM black hole. The changing (r−τ) in both spaces shows similar behavior. Also, the topological number and the total topological numbers for this black hole in the BB, RPS and EPS thermodynamics are completely same, i,e., (ωBBT=ωRPS=ωEPST=+1,−1) or WBBT=WRPS=WEPST=0. An important point is that the Einstein–Yang–Mills black hole has thermodynamic topology equivalence in three spaces. The present result may be due to the non-linear YM charge parameter and the difference between the gauge and gravity corrections in the above black holes.

An efficient MATLAB code for stress-constrained level set topology optimization method

An efficient MATLAB code for stress-constrained level set topology optimization method

Algebraic and order properties of maps and structures related to dependence relations arising in topology, algebra and rough set theory

In this paper, given an arbitrary set [Formula: see text], we study the main order and algebraic properties of some maps and set structures that are strictly related to dependence set relations on [Formula: see text], which are binary relations between subsets of [Formula: see text] naturally arising when [Formula: see text] is a topological space or an attribute set in rough set theory and granular computing based on information systems. The previous maps, that we call granular maps, have the families of the set systems, set operators, binary set relations or also of information systems on the ground set [Formula: see text] as their domain and codomain. We make use of various algebraic methodologies on granular maps to determine the main order-theoretic and combinatorial properties of specific sub-collections of set systems, binary set relations and set operators naturally arising in the investigation of dependence set relations and of rough set theory. We introduce, in more detail, the notion of granular sub-bijection to formalize in all these situations the undefined notion of cryptomorphism, and through which we exhibit new equivalences between specific families of set systems, binary set relations and set operators strictly related to dependence set relations. By means of suitable granular maps we determine three granular sub-bijections between the family of all the closure operators, that of all the Moore set systems and that of all dependence set relations on the same ground set [Formula: see text]. Next, through a property of adjunctivity, we see that in order to generate a dependence set relation it suffices to consider pointed relations on [Formula: see text], namely collections of pairs in [Formula: see text] ℘([Formula: see text]). Because of that, we study order-theoretical properties of some relevant subclasses of pointed relations and analyze the granular maps on [Formula: see text] which determine two nontrivial granular sub-bijections between two subclasses of set operators and two corresponding subclasses of pointed relations. Next, we show that any dependence set relation has the form [Formula: see text] that is a dependence set relation induced by an information system [Formula: see text] on [Formula: see text] and generalizes the Pawlak dependence set relation frequently used in rough set theory. With regard to this representation result, we characterize some set systems of minimal subsets with respect to the Pawlak indiscernibility relation on information systems. Finally, given an arbitrary binary set relation [Formula: see text] on [Formula: see text], we consider the smallest dependence set relation [Formula: see text] on [Formula: see text] containing [Formula: see text] and call it dependence closure of [Formula: see text]. Then, when [Formula: see text] is a finite set, we show how to generate [Formula: see text] in four different and recursive ways by starting from [Formula: see text]. Moreover, again in the finite case, given an information system [Formula: see text] on [Formula: see text], we also determine a binary set relation [Formula: see text] on [Formula: see text] for which [Formula: see text] agrees with [Formula: see text] and whose cardinality is minimum with respect to that of all binary set relations whose dependence closure agrees with [Formula: see text].

Designing of Edge Infrastructure for Establishing Signal Transmission in Palm Oil Field

Edge computing is real-time processing that gathers, analyses, and transports data at the edge of the network using sensor technologies. It has become one of the IoT era's computing solutions because it improves signal transmission while preventing network problems like delay, congestion, or latency. It is advantageous for farm management to be able to monitor farm activities like cropping and fertilization in real-time, which helps increase palm oil production. However, the farm's remote location limits the amount of signal transmission available from its current Internet service providers, which prevents real-time processing. Hence, suitable edge infrastructure must be designed for establishing signal accessibility for data communication. It also required determining the optimal number of edge nodes to be allocated in the palm field due to different terrain and various tree sizes. The number of edge nodes will have an impact on cost utilization because it relates to setup costs and parameters. In response to data communication issues in the palm oil field, our work focuses on developing the edge computing infrastructure to maintain stable signal transmission for real-time processing. A network topology is designed to identify suitable parameters and settings that aligned with topography of the sample palm oil field. Furthermore, by having the right topology and signal frequency settings, the number of edge nodes required in the field can be determined. In our simulated design, the appropriate setting is to add a router with less than 4K million instructions per second (MIPS) compared to connecting through three mobile hot spots. Note that different palm oil fields will have different settings for their edge infrastructure. Optimistically, our study can provide guidance for promoting signal transmission in areas with limited network accessibility.

Congruence Representations via Soft Ideals in Soft Topological Spaces

This article starts with a study of the congruence of soft sets modulo soft ideals. Different types of soft ideals in soft topological spaces are used to introduce new weak classes of soft open sets. Namely, soft open sets modulo soft nowhere dense sets and soft open sets modulo soft sets of the first category. The basic properties and representations of these classes are established. The class of soft open sets modulo the soft nowhere dense sets forms a soft algebra. Elements in this soft algebra are primarily the soft sets whose soft boundaries are soft nowhere dense sets. The class of soft open sets modulo soft sets of the first category, known as soft sets of the Baire property, is a soft σ-algebra. In this work, we mainly focus on the soft σ-algebra of soft sets with the Baire property. We show that soft sets with the Baire property can be represented in terms of various natural classes of soft sets in soft topological spaces. In addition, we see that the soft σ-algebra of soft sets with the Baire property includes the soft Borel σ-algebra. We further show that soft sets with the Baire property in a certain soft topology are equal to soft Borel sets in the cluster soft topology formed by the original one.

A novel discrete adjoint-based level set topology optimization method in B-spline space

A novel discrete adjoint-based level set topology optimization method in B-spline space

Nearly open sets in infra topology and related infra continuity

Nearly open sets in infra topology and related infra continuity

Large Scale Energy Efficient Sensor Network Routing using a Quantum Processor Unit.

The sensor network energy conservation method, which is a usage hybrid of a classical computer and quantum processor, has proved to perform better than the heuristic algorithm using a classical computer. In this manuscript, the technical context for the significance of the method is presented and justified. Then the experimental steps are demonstrated in an operational sequence with illustrations if ever needed. The method has been validated by positive results across a randomly generated sample set of network topologies. The successful experimental results of this method have provided a better approach for sensor network lifetime maximization problems and demonstrated that the current state of art quantum processor has been able to solve large practical engineering problems with merits that override current methods in the literature. In other words, quantum advantage can be exploited to best efforts. It has gone beyond the stage of proof of concept to proof of feasibility.