Topological Definition Research Articles

MPCC: strong stability of weakly nondegenerate S-stationary points

ABSTRACT In this paper, we consider the class of mathematical programmes with complementarity constraints (MPCC). Specifically, we focus on strong stability of M- and S-stationary points for MPCC. Kojima introduced this concept for standard nonlinear optimization problems. It refers to several well-posedness properties of the underlying problem. Besides its topological definition, the challenge is to state an algebraic characterization of strong stability. We obtain such a description for S-stationary points whose components of Lagrange vectors corresponding to bi-active constraints do not mutually vanish. We call these points weakly nondegenerate. Moreover, we show that a particular constraint qualification is necessary for strong stability.

Recurrent sets for endomorphisms of topological groups

This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent points and chain transitive component of the identity are topological subgroups. Furthermore, we show that some dynamical properties are induced by the original system on quotient spaces. These results link an algebraic property to a dynamical property.

A Deformable Constraint Transport Network for Optimal Aortic Segmentation From CT Images.

Aortic segmentation from computed tomography (CT) is crucial for facilitating aortic intervention, as it enables clinicians to visualize aortic anatomy for diagnosis and measurement. However, aortic segmentation faces the challenge of variable geometry in space, as the geometric diversity of different diseases and the geometric transformations that occur between raw and measured images. Existing constraint-based methods can potentially solve the challenge, but they are hindered by two key issues: inaccurate definition of properties and inappropriate topology of transformation in space. In this paper, we propose a deformable constraint transport network (DCTN). The DCTN adaptively extracts aortic features to define intra-image constrained properties and guides topological implementation in space to constrain inter-image geometric transformation between raw and curved planar reformation (CPR) images. The DCTN contains a deformable attention extractor, a geometry-aware decoder and an optimal transport guider. The extractor generates variable patches that preserve semantic integrity and long-range dependency in long-sequence images. The decoder enhances the perception of geometric texture and semantic features, particularly for low-intensity aortic coarctation and false lumen, which removes background interference. The guider explores the geometric discrepancies between raw and CPR images, constructs probability distributions of discrepancies, and matches them with inter-image transformation to guide geometric topology in space. Experimental studies on 267 aortic subjects and four public datasets show the superiority of our DCTN over 23 methods. The results demonstrate DCTN's advantages in aortic segmentation for different types of aortic disease, for different aortic segments, and in the measurement of clinical indexes.

Stable Neutrosophic Crisp Topological Space

The significance and influence of neutrosophic crisp set theory in numerous scientific domains, particularly topology, led us to construct a new definition of topology based on neutrosophic crisp sets, allowing us to regulate its key mathematical ideas. Therefore, we constructed this definition and dubbed it stable neutrosophic crisp topology, where we went over the key idea which is the interior with the vital features.

The hidden quantum origin of gauge connections

A fibre bundle viewpoint of gauge field theories is reviewed with focus on a possible quantum interpretation. The fundamental quantum properties of non-separability of state spaces is considered in the context of defining the connection on the fibre bundle, leading to an application of the quantum principles to the geometrical and topological definition of gauge theories. As a result, one could justifiably ask oneself if all interactions of the standard model, and perhaps even classical gravity have some quantum component after all. I employ a standard fibre bundle approach to introduce gauge theories, albeit it is known that a quantum bundle exists, simply because the main scope is to show that in the usual way in which we formulate classical gauge theories one can find quantum aspects that have been unknown until now. In a sense, I will try to justify the assessment that if we are to allow for gauge fields and parallel transport, we may have to allow at least some level of quantumness even in our classical gauge theories. The main statement is that propagation of interactions in spacetime is a quantum phenomenon. After writing the first draft of this article I noticed Y Shen C. Rosales-Guzman 2022 Laser & Photonics Reviews, 16,2100533 where the authors device entanglement of what they call ‘classical light’. This experiment supports my theoretical developments with the distinction that I interpret such phenomena also as fundamentally quantum. The distinction comes from the fact that the quantum nature of the experiments is manifested in a different way. My view on this is that there is no purely classical reality, no matter what the scale is at which we consider the description. I also discuss the fact that observing a quantum nature of ‘classical’ light propagation would amount to the requirement of modifying the causal structure defined in terms of the speed of light in a vacuum, on stronger grounds, based on the quantum interpretation of gauge connections.

Properties of function space under Cauchy convergence topology

In 2020, Peng and Sun modified the definition of the Cauchy convergence topology, defined on the space of continuous functions from a metric space X to the real line R that is denoted by Cch(d)(X). In continuation of this study we examine some of the important properties of this space. First, we prove that the space Cch(d)(X) is not dense in RX. Further we find the necessary and sufficient condition for the openness of the restriction map on the space Cch(d)(X). Apart from these we find the condition for the space Cch(d)(X) to be Frechet-Uryshon space.

Diversity of 'simple' multicellular eukaryotes: 45 independent cases and six types of multicellularity.

Multicellularity evolved multiple times in the history of life, with most reviewers agreeing that it appeared at least 20 times in eukaryotes. However, a specific list of multicellular eukaryotes with clear criteria for inclusion has not yet been published. Herein, an updated critical review of eukaryotic multicellularity is presented, based on current understanding of eukaryotic phylogeny and new discoveries in microbiology, phycology and mycology. As a result, 45 independent multicellular lineages are identified that fall into six distinct types. Functional criteria, as distinct from a purely topological definition of a cell, are introduced to bring uniformity and clarity to the existing definitions of terms such as colony, multicellularity, thallus or plasmodium. The category of clonal multicellularity is expanded to include: (i) septated multinucleated thalli found in Pseudofungi and early-branching Fungi such as Chytridiomycota and Blastocladiomycota; and (ii) multicellular reproductive structures formed by plasmotomy in intracellular parasites such as Phytomyxea. Furthermore, (iii) endogeneous budding, as found in Paramyxida, is described as a form of multicellularity. The best-known case of clonal multicellularity, i.e. (iv) non-separation of cells after cell division, as known from Metazoa and Ochrophyta, is also discussed. The category of aggregative multicellularity is expanded to include not only (v) pseudoplasmodial forms, such a sorocarp-forming Acrasida, but also (vi) meroplasmodial organisms, such as members of Variosea or Filoreta. A common set of topological, geometric, genetic and life-cycle criteria are presented that form a coherent, philosophically sound framework for discussing multicellularity. A possibility of a seventh type of multicellularity is discussed, that of multi-species superorganisms formed by protists with obligatory bacterial symbionts, such as some members of Oxymonada or Parabasalia. Its inclusion is dependent on the philosophical stance taken towards the concepts of individuality and organism in biology. Taxa that merit special attention are identified, such as colonial Centrohelea, and a new speculative form of multicellularity, possibly present in some reticulopodial amoebae, is briefly described. Because of insufficient phylogenetic and morphological data, not all lineages could be unequivocally identified, and the true total number of all multicellular eukaryotic lineages is therefore higher, likely close to a hundred.

Тhe concept of topological well-ordered space

UDC 515.12 Since the general definition of topology is based on the characteristics of the standard Euclidean topology, the relationships between the ordering on real numbers and its topology have been generalized over time and studied in numerous aspects. The compatibility of partially ordered sets with the topology on them was studied by many researchers. On the other hand, well-orderedness is an important concept of the set theory. We define the concept of topological well-orderedness, which can be regarded as a topological generalization of well-orderedness in the set theory, and analyze its basic properties. In this way, the relationship between well-orderedness and topology is established from a different point of view. Finally, some basic applications of the concept of topological well-orderedness to the graph theory are investigated.

PI16+ reticular cells in human palatine tonsils govern T cell activity in distinct subepithelial niches

Fibroblastic reticular cells (FRCs) direct the interaction and activation of immune cells in discrete microenvironments of lymphoid organs. Despite their important role in steering innate and adaptive immunity, the age- and inflammation-associated changes in the molecular identity and functional properties of human FRCs have remained largely unknown. Here, we show that human tonsillar FRCs undergo dynamic reprogramming during life and respond vigorously to inflammatory perturbation in comparison to other stromal cell types. The peptidase inhibitor 16 (PI16)-expressing reticular cell (PI16+ RC) subset of adult tonsils exhibited the strongest inflammation-associated structural remodeling. Interactome analysis combined with ex vivo and in vitro validation revealed that T cell activity within subepithelial niches is controlled by distinct molecular pathways during PI16+ RC–lymphocyte interaction. In sum, the topological and molecular definition of the human tonsillar stromal cell landscape reveals PI16+ RCs as a specialized FRC niche at the core of mucosal immune responses in the oropharynx.

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.

Hybridization of a Backhoe Loader: Electric Drive System Design

Heavy machinery is critical to agriculture, construction, mining, and other sectors of a country’s economy. However, such vehicles consume a high amount of fuel, increasing production costs and the emission of polluting gases into the atmosphere. One of the alternatives to reduce fuel consumption is the electrification of these vehicles, but the definition of an optimal topology for the electrification of heavy vehicles is still under study, and works with electric drive systems projects for these machines are scarce. This paper presents the main characteristics of the design of an electric drive system for the electrification of a backhoe, including the control and simulation of the motor drive system, and presents a prototype bench and experimental tests carried out in the context of the hybridization topology presented. Based in these results, improvements are proposed and discussed with aid of computational simulation.

Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices

A weave is the lift to the thickened Euclidean plane of a particular type of quadrivalent planar connected graph with an over or under crossing information to each vertex and such that the lifted components are non-intersecting simple open curves. In this paper, we introduce a formal topological definition of weaves as three-dimensional entangled structures and characterize the equivalence classes of doubly periodic untwisted [Formula: see text]-weaves by introducing a new invariant, called crossing matrix. Finally, we suggest a combinatorial approach to classify this specific class of weaves by their crossing number.

Identification of Local Accessibility Hubs and Leisure Amenities in Suburbanized Settlements: Case Study on the Suburban Zone of Prague

This paper focuses on the topological definition of the system of public spaces in suburbanized settlements. It identifies hubs with the best local accessibility within the system of public open spaces using the Space syntax method and analyses their leisure amenities. The topological investigation was performed on the example of the suburban zone of Prague, the immediate surroundings of which have been developing dramatically in recent decades. About 44 rapidly developing settlements in this area were included in the study and their system of public open spaces was analyzed using the Integration HH metric and local accessibility hubs (those with the highest Integration HH value) were identified. Subsequently, the placement of existing leisure amenities with respect to these accessibility hubs was evaluated. Only 32% of leisure amenities were located in the accessibility hubs, which indicates an unfulfilled potential of locally well-accessible places. At the same time, the placement of leisure amenities within new developments in areas difficult-to-access from other parts of the settlement poses a threat to the integration of the population from these new developments with those from other parts of the settlement. This paper offers solutions for preventing these issues, for identifying natural centers with the best accessibility, and proposes possible measures for mitigation of the identified problems.

Bounding Memory Access Times in Multi-Accelerator Architectures on FPGA SoCs

Modern FPGA System-on-Chips (SoCs) embed large FPGA logics capable of hosting multiple hardware accelerators. Typically, hardware accelerators require direct access to the shared DRAM memory for reaching the high performance demanded by modern applications. In commercial FPGA SoCs, this goal is achieved by interconnecting the hardware accelerators on an interconnect based on AMBA AXI, which is the de-facto industrial standard for on-chip communications. The AXI standard provides great flexibility in the definition of the network topology. Nevertheless, such flexibility generates a significant unpredictability when attempting to bound the hardware accelerators’ response time when executing under contention. This work focus on bounding the worst-case memory access time of hardware accelerators deployed on commercial FPGA SoCs. We propose a modeling and analysis technique to bound the response time of the hardware accelerators and evaluate the schedulability of a system applicable to arbitrary AXI-based bus structures deployed on FPGA SoCs. Our results are validated on real execution traces collected on two popular FPGA SoCs belonging to the Xilinx ZYNQ-7000 and Zynq-Ultrascale+ families and by simulated results.

Hole Inpainting Algorithm for Half-Organized Point Cloud Obtained by Structured-Light Section System

The advances in sensors and data processing technologies enrich the types of 3D point clouds acquirement, empowering numerous extensive and novel applications such as 3D reconstruction in various scenarios. However, the hole defects affect the accuracy and fidelity of the acquired point clouds, hindering further development and application of 3D point clouds. Aiming at the hole defects in point clouds, a Bayesian hole inpainting algorithm for the half-organized point cloud is proposed, where the point cloud is obtained by a structured-light section system. The algorithm establishes a Bayesian probability model in the hole region, which adopts specific distributions of the point cloud to estimate the maximum likelihood parameter. Simulation and experimental results show that the proposed approach outperforms other competing algorithms significantly in repairing various types of holes, both in objective and subjective qualities. In addition, the proposed algorithm has better scalabilities in the cases of wrong topology definition and self-intersection confusion. This is the first algorithm specially designed for hole inpainting in half-organized point clouds, which maximizes the comprehensive consideration of local features and global optimization, supplemented by targeted prior knowledge of density, Riemannian manifold, and discrete attributes.

An Improved Method Based on Bluetooth Low-Energy Fingerprinting for the Implementation of PEPS System.

In the automotive field, the introduction of keyless access systems is revolutionizing car entry techniques currently dominated by a physical key. In this context, this paper investigates the possible use of smartphones to create a PEPS (Passive Entry Passive Start) system using the BLE (Bluetooth Low-Energy) Fingerprinting technique that allows, along with a connection to a low-cost BLE micro-controllers network, determining the driver's position, either inside or outside the vehicle. Several issues have been taken into account to assure the reliability of the proposal; in particular, (i) spatial orientation of each microcontroller-based BLE node which ensures the best performance at 180° and 90° referred to as the BLE scanner and the advertiser, respectively; (ii) data filtering techniques based on Kalman Filter; and (iii) definition of new network topology, resulting from the merger of two standard network topologies. Particular attention has been paid to the selection of the appropriate measurement method capable of assuring the most reliable positioning results by means of the adoption of only six embedded BLE devices. This way, the global accuracy of the system reaches 98.5%, while minimum and maximum accuracy values relative to the individual zones equal, respectively, to 97.3% and 99.4% have been observed, thus confirming the capability of the proposed method of recognizing whether the driver is inside or outside the vehicle.

Ambient topologies in the museum route (light, sound, and thermal): the method of analysis and visualization

ABSTRACT Defining architectural space comes with multiple and diverse aspects. Our theoretical reflection aims at establishing the base for a new definition, in the sense that theoretical topology, like geometry, is an effective means to define the form of architectural spatiality based on the notion of ambiences. Topological definitions already developed by several renowned architects allow us to build a better understanding of route and sequence and thereby help the development of our analytical model. This research is focused on the museum, which is a public-facing architectural construction. According to the approach, thirty European museums were examined. The data collected for these museums were statistically analysed. Based, on the ambience discontinuities, the sequential analysis allowed us to create ambient topologies by transforming them into ambient events that are linked to the displacement of the user in connection with ambiance change. We endeavor to develop a micro study to reflect on the interaction between different environmental sources as a means to comprehend the influence on the future spatial-energetic behavior. This study lays the groundwork for a novel approach of defining architectural space based on differences in users’ perceptions and the environment of a given space.

New Concepts of To Separation Axioms in Fuzzy Topology

Fuzzy set was introduced by Zadeh in his classical paper of 1965. Three years later, Chang gave the definition of fuzzy topology, which is a family of fuzzy set satisfying the three classical axioms. In this paper, we have introduced and studied some new notions of To separation axioms in fuzzy topological spaces by using quasi-coincident relation for fuzzy set. Every ordinary (crisp) topological space vacuously satisfies condition of being quasi-To. In this paper concept of quasi coincident relation used to introduce and investigate some quasi separation axioms such as To, T1, & T2. Concerning quasi-To space in the general frame work of fuzzy topological spaces.

An automatic graph-based method for characterizing multichannel networks

Assessment and quantitative description of river morphology using widely recognized river planview measures (e.g., length, width and sinuosity of channels, bifurcation angles and island shape) for multichannel rivers are regarded as fundamental parts of the toolkit of geomorphologists and river engineers. However, conventional assessment methods including field surveys or exiting algorithms for the extraction of multichannel planviews might be suboptimal. More recently, the potential for the application of complex network analysis to the study of river morphology has led to emphasis on the accurate characterization and definition of multichannel network topology. Therefore, we developed a novel algorithm called RivMACNet (River Morphological Analysis based on Complex Networks) that enables the extraction of multichannel network topology using satellite sensor images as the input. We applied RivMACNet to a meandering reach of the Yangtze River and a strongly anastomosing reach of the Indus River to construct their network topologies, and then calculated a series of common topological measures including weighted degree (WD), clustering coefficient (CC) and weighted characteristic path length (WCPL). The network analysis indicated that both networks exhibit poor transitivity with small clustering coefficients. The topological properties of the Indus at the reach scale are independent of flow conditions, while they vary across space at the subnetwork scale. In addition, comparison between RivMACNet and an alternative common river network analysis engine (RivaMap) demonstrated that RivMACNet is superior in terms of representation accuracy and network connectivity and, thus, is more suitable for multichannel fluvial systems with complex planviews. RivMACNet is, thus, a useful tool to support further investigation of multichannel river networks using graph theory.

P-points, MAD families and Cardinal Invariants

P-points, MAD families and Cardinal Invariants