Set Of Topologies Research Articles

Syndetic proximal set in topological transformation group

In this paper will study the syndetic set in topological transformation group. It represents one of the most important sets in topological dynamics that Gottschak referred .We Introduce dynamical relationship between syndetic set and translation (left-right) ,In topological dynamics group present semi replet set and extensive set .We referred to the relationship of semi replet set and extensive set on the one hand, and their relationship to syndetic set on the other hand . We introduced a new concept syndetic proximal point that depended on syndetic set we indicated a relationship syndetic proximal point with proximal point and extensive proximal point , conclude a number of relationships and concepts

Dynamic Generation Method of Highway ETC Gantry Topology Based on LightGBM

In Electronic Toll Collection (ETC) systems, accurate gantry topology data are crucial for fair and efficient toll collection. Currently, inaccuracies in the topology data can cause tolls to be based on the shortest route rather than the actual distance travelled, contradicting the ETC system’s purpose. To address this, we adopt a novel Gradient Boosting Decision Tree (GBDT) algorithm, Light Gradient Boosting Machine (LightGBM), to dynamically update ETC gantry topology data on highways. We use ETC gantry and toll booth transaction data from a province in southeast China, where ETC usage is high at 72.8%. From this data, we generate a candidate topology set and extract five key characteristics. We then use Amap API and QGIS map analysis to annotate the candidate set, and, finally, apply LightGBM to train on these features, generating the dynamic topology. Our comparison of LightGBM with 14 other machine learning algorithms showed that LightGBM outperformed the others, achieving an impressive accuracy of 97.6%. This methodology can help transportation departments maintain accurate and up-to-date toll systems, reducing errors and improving efficiency.

Likelihood-Based Tests of Species Tree Hypotheses.

Likelihood-based tests of phylogenetic trees are a foundation of modern systematics. Over the past decade, an enormous wealth and diversity of model-based approaches have been developed for phylogenetic inference of both gene trees and species trees. However, while many techniques exist for conducting formal likelihood-based tests of gene trees, such frameworks are comparatively underdeveloped and underutilized for testing species tree hypotheses. To date, widely used tests of tree topology are designed to assess the fit of classical models of molecular sequence data and individual gene trees and thus are not readily applicable to the problem of species tree inference. To address this issue, we derive several analogous likelihood-based approaches for testing topologies using modern species tree models and heuristic algorithms that use gene tree topologies as input for maximum likelihood estimation under the multispecies coalescent. For the purpose of comparing support for species trees, these tests leverage the statistical procedures of their original gene tree-based counterparts that have an extended history for testing phylogenetic hypotheses at a single locus. We discuss and demonstrate a number of applications, limitations, and important considerations of these tests using simulated and empirical phylogenomic data sets that include both bifurcating topologies and reticulate network models of species relationships. Finally, we introduce the open-source R package SpeciesTopoTestR (SpeciesTopology Tests in R) that includes a suite of functions for conducting formal likelihood-based tests of species topologies given a set of input gene tree topologies.

Modeling of COVID-19 in View of Rough Topology

Rough-based topology has become an important technique for decision making in numerous real-life problems. The main purpose of this research paper is to use some topological notions in the approximation space of a rough set. Firstly, some concepts of topological near open sets and rough concepts are presented. A new approximation structure based on the topological near open sets is introduced. We debate the properties of the new approximation structure. We included an algorithm for detecting COVID-19 infection by its side effects. We believe that our approach will be helpful for any future detection.

The SIRAH force field: A suite for simulations of complex biological systems at the coarse-grained and multiscale levels

The different combinations of molecular dynamics simulations with coarse-grained representations have acquired considerable popularity among the scientific community. Especially in biocomputing, the significant speedup granted by simplified molecular models opened the possibility of increasing the diversity and complexity of macromolecular systems, providing realistic insights on large assemblies for more extended time windows.However, a holistic view of biological ensembles' structural and dynamic features requires a self-consistent force field, namely, a set of equations and parameters that describe the intra and intermolecular interactions among moieties of diverse chemical nature (i.e., nucleic and amino acids, lipids, solvent, ions, etc.). Nevertheless, examples of such force fields are scarce in the literature at the fully atomistic and coarse-grained levels. Moreover, the number of force fields capable of handling simultaneously different scales is restricted to a handful. Among those, the SIRAH force field, developed in our group, furnishes a set of topologies and tools that facilitate the setting up and running of molecular dynamics simulations at the coarse-grained and multiscale levels. SIRAH uses the same classical pairwise Hamiltonian function implemented in the most popular molecular dynamics software. In particular, it runs natively in AMBER and Gromacs engines, and porting it to other simulation packages is straightforward.This review describes the underlying philosophy behind the development of SIRAH over the years and across families of biological molecules, discussing current limitations and future implementations.

Projection-based distributed economic dispatch algorithm considering communication delays under switching topologies

In this paper, a projection-based distributed algorithm is proposed to solve the economic dispatch problem of power system with communication delays under switching topologies. The algorithm is suitable for economic dispatch problem with strongly convex cost function, and ensures that the output power of each generator is always kept within its output limit. In addition, the topology is only required to be jointly connected. Firstly, the relationship between the equilibrium point and the optimal solution of the algorithm is analyzed, and then a common Lyapunov function is introduced for a set of switching topologies. According to the Lyapunov stability theory and Cauchy convergence criterion, LMIs-based sufficient conditions for the convergence of the algorithm are obtained. Finally, the effectiveness of the algorithm under different cases are verified by MATLAB simulation results.

Formal topological description of three-dimensional topological entities based on k-dimensional pseudo-manifold

This paper clarifies the necessity of studying three-dimensional spatial data models, analyzes the research progress and existing problems of topological spatial relationship description methods, and proposes a complete and formal description framework of three-dimensional topological spatial relations based on point set topological theory and dimension expansion method. On this basis, the topological spatial relations existing in three-dimensional spatial objects are classified, and five fundamental topological spatial relations are defined. The mutual exclusivity and completeness of the minimal set of 3D topological space relations are proved. Based on point set topology and k-dimensional pseudo-manifold, this paper proposes the formal description of three-dimensional topological properties and spatial relations between spatial entities. The simplicial homology is applied to manifolds, the topological properties of three-dimensional space entities are revealed, and the formal description method of three-dimensional space entities is given through the geometric structural relationship between simplex and simplicial k-complex.

On Primal Soft Topology

In a soft environment, we investigated several (classical) structures such as ideals, filters, grills, etc. It is well known that these structures are applied to expand abstract concepts; in addition, some of them offer a vital tool to address some practical issues, especially those related to improving rough approximation operators and accuracy measures. Herein, we contribute to this line of research by presenting a novel type of soft structure, namely “soft primal”. We investigate its basic properties and describe its behaviors under soft mappings with the aid of some counterexamples. Then, we introduce three soft operators (·)⋄, Cl⋄ and (·)□ inspired by soft primals and explore their main characterizations. We show that Cl⋄ satisfies the soft Kuratowski closure operator, which means that Cl⋄ generates a unique soft topology we call a primal soft topology. Among other obtained results, we elaborate that the set of primal topologies forms a natural class in the lattice of topologies over a universal set and set forth some descriptions for primal soft topology under specific types of soft primals.

Zero programming robotics in additive manufacturing repairs

This document explains the implementation of an integral additive manufacturing system at the Canadian Centre for Welding and Joining (CCWJ). Highlighting its use to remanufacture high-value components with a streamlined workflow using an optical coordinate measuring machine and parametric programming. The resultant output robot code is embedded with control of dimensional accuracy, laser power, beam velocity, and powder feed rate. This approach centers its attention on the remanufacturing of parts and their inherent complex surface as well as the time-consuming task of programming the robot to construct tool paths for the cladding strategy. These issues are solved using a set of topologies implemented in software and hardware that deliver a system that integrates the control parameters and the tooltip toolpaths into a highly automated system offering versatility, scalability, and reproducibility. The results show the capacity of the system to directly repair worn-out parts from a 3D scanner and deliver short-time programming sequences with integrated process constraints, precision, and high dimensional accuracy.

A representation of interval orders through a bi-utility function

The elaboration of preference relations and their representations trace their source to early economic theory. Classical representations of preferences theorems rely on Debreu–Eilenberg’s theorems in the topological setting. An important class of preferences consists of interval orders. A natural question is to achieve a bi-utility representation for interval orders. We suggest to introduce a condition reminiscent of N. Wiener’s early works on the relativeness of positions. We obtain a bi-utility representation through the precedence and succession relations.

Development of superconducting model dipole magnets beyond 12 T with a combined common-coil configuration

The superconducting magnet group at IHEP (the Institute of High Energy Physics, Chinese Academy of Sciences, China) has been engaging in the R&D of high field accelerator magnets since 2014 for the pre-study of the next-generation high energy particle accelerators like CEPC-SPPC (Circular Electron Positron Collider-Super Proton Proton Collider), FCC (Future Circular Collider), etc. A superconducting model dipole magnet named LPF1 was first fabricated with NbTi and Nb3Sn in a combined common-coil configuration in 2017 and tested in 2018, a main field of 10.23 T was reached within two 10 mm apertures. The magnet was reassembled with higher pre-stress in 2019 to investigate the influence of the pre-stress loading level on the performance of common-coil dipole magnets. The main field of this upgraded magnet named LPF1-S was increased to 10.71 T within two 12 mm apertures. By improving the key processing technologies in Rutherford cable fabrication, coil winding, Nb3Sn & NbTi splices soldering and coil impregnation, the recently fabricated model dipole magnet named LPF1-U attained a 12.47 T main field in two 14 mm apertures in 2021. To fully take advantage of Nb3Sn and NbTi superconductors in different field regions, LPF1-U was still designed and developed with a combined coil configuration with Nb3Sn for the inner two coils and NbTi for the outer four coils. Additionally, graded coil topology and different coil LSS (length of straight section) settings were adopted in the optimization of LPF1-U layouts. Bladder and key technology was used for the support structure, and fiber optic sensors based on FBG (fiber Bragg grating) were utilized to monitor the stress distribution and variation in the structures and coils through the whole process from magnet assembly to cool-down and excitation. During the performance test, a relatively large number of trainings were carried out and LPF1-U became more stable after the thermal cycle. A peak field of 12.7 T in the coils (12.47 T main field in apertures) corresponds to an operating current of 6865 A and a load line ratio of 90% was finally attained. It is worth mentioning that LPF1-U is the first hybrid—Nb3Sn, NbTi—common coil dipole magnet that has achieved a main field of more than 12 T in two apertures. The design, fabrication and performance analysis of the LPF series dipole magnets are presented in this paper.

Topological properties of definable sets in ordered Abelian groups of burden 2

AbstractWe obtain some new results on the topology of unary definable sets in expansions of densely ordered Abelian groups of burden 2. In the special case in which the structure has dp‐rank 2, we show that the existence of an infinite definable discrete set precludes the definability of a set which is dense and codense in an interval, or of a set which is topologically like the Cantor middle‐third set (Theorem 2.9). If it has burden 2 and both an infinite discrete set D and a dense‐codense set X are definable, then translates of X must witness the Independence Property (Theorem 2.26). In the last section, an explicit example of an ordered Abelian group of burden 2 is given in which both an infinite discrete set and a dense‐codense set are definable.

Interpreting mereotopological connection

This paper examines ten possible topological interpretations of connection and for each interpretation, identifies sufficient conditions under which a significant class of topological spaces provides models of General Extensional Mereotopology with Closure Conditions (GEMTC) in which some key mereotopological ideas align with their topological analogues. In particular, there is an interpretation under which the non-empty sets of any symmetric topology are a model of GEMTC with alignment between the mereotopological and topological definitions of (self-)connection, open and closed entities, interior, exterior, closure, and boundary.

Subspace spanning graph topological spaces of graphs

A collection of spanning subgraphs TS, of a graph G is said to be a spanning graph topology if it satisfies the three axioms: Nn, K0 ∈ TS where, n = |V (G)|, the collection is closed under any union and finite intersection. Let (X, T) be a topological space in point set topology and Y ⊆ X then, TY = {U ∩ Y : U ∈ T} is a topological space called a subspace topology or relative topology defined by T on Y . In this paper we discusses the subspace spanning graph topology defined by the graph topology TS on a spanning subgraph H of G.

Continuous orbit equivalence rigidity for left-right wreath product actions

Drimbe and Vaes proved an orbit equivalence superrigidity theorem for left-right wreath product actions in the measurable setting. We establish the counterpart result in the topological setting for continuous orbit equivalence. This gives us minimal, topologically free actions that are continuous orbit equivalence superrigid. One main ingredient for the proof is to show continuous cocycle superrigidity for certain generalized full shifts, extending our previous result with Chung.

Groups and Dynamics: Topology, Measure, and Borel Structure

While the subjects of topological dynamics, ergodic theory, and descriptive set theory have long interacted in a variety of profitable ways, recent developments have ushered in a vigorous new phase of interplay between them, from the abstract transfer and coordinated development of ideas and methods (as in the theory of dynamical tilings) to the direct leveraging of technical points of contact (as in boundary theory). The workshop served as a platform for promoting and advancing these connections by bringing together researchers working on various facets of topological, measured, and Borel dynamics.

New Structures of Continuous Functions

Continuous functions are novel concepts in topology. Many topologists contributed to the theory of continuous functions in topology. The present authors continued the study on continuous functions by utilizing the concept of gpα-closed sets in topology and introduced the concepts of weakly, subweakly and almost continuous functions. Further, the properties of these functions are established.

Statistical Equivalence of Quantum Chemical Methods for Energy Distribution in Water Clusters.

Methods of quantum chemistry are instrumental in understanding molecular structures and properties. However, the results demonstrate significant variability, which is difficult to predict and rationalize. The fundamental question is whether some molecular systems exhibit properties invariant with respect to the computational method. The idea explored here is that collective properties of statistical ensembles should be more robust than characteristics of individual molecules and their arbitrary sets. This effect is demonstrated for the complete set of hydrogen-bond topologies of the dodecahedral water cluster (H2 O)20 . Non-Gaussian energy distributions produced by various methods have the same functional form despite strong differences in mean values and standard deviations. The conclusion is tested on methods of different complexity and origin employing a number of criteria. A linear mapping between the energies produced by different methods is discussed. The significance of the results is in establishing a collective equivalence property of quantum chemical methods.

SDN-enabled Resource Provisioning Framework for Geo-Distributed Streaming Analytics

Geographically distributed (geo-distributed) datacenters for stream data processing typically comprise multiple edges and core datacenters connected through Wide-Area Network (WAN) with a master node responsible for allocating tasks to worker nodes. Since WAN links significantly impact the performance of distributed task execution, the existing task assignment approach is unsuitable for distributed stream data processing with low latency and high throughput demand. In this paper, we propose SAFA, a resource provisioning framework using the Software-Defined Networking (SDN) concept with an SDN controller responsible for monitoring the WAN, selecting an appropriate subset of worker nodes, and assigning tasks to the designated worker nodes. We implemented the data plane of the framework in P4 and the control plane components in Python. We tested the performance of the proposed system on Apache Spark, Apache Storm, and Apache Flink using the Yahoo! streaming benchmark on a set of custom topologies. The results of the experiments validate that the proposed approach is viable for distributed stream processing and confirm that it can improve at least 1.64× the processing time of incoming events of the current stream processing systems.

Urban Congestion Avoidance Methodology Based on Vehicular Traffic Thresholding

Vehicular traffic in urban areas faces congestion challenges that negatively impact our lives. The infrastructure associated with intelligent transportation systems provides means for addressing the associated challenges in urban areas. This study proposes an effective and scalable vehicular traffic congestion avoidance methodology. It introduces a traffic thresholding mechanism to predict and avoid vehicular traffic congestion during route computation. Our methodology was evaluated and validated by employing four road network topologies, three vehicular traffic density levels and various traffic light configurations, resulting in 26 urban traffic scenarios. Using our approach, the number of vehicles that can run in free flow can be increased by up to 200%, whereas for traffic congestion scenarios, the time spent in traffic may be reduced by up to 69% and CO2 emissions by up to 61%. To the best of our knowledge, in the vehicular traffic flow prediction domain, this is the first approach that covers a set of road network topologies and a large and representative set of scenarios for simulated urban traffic congestion testing. Moreover, the comparative analysis with different other solutions in the domain, showed that we obtained the best driving time and CO2 emission reduction.