Topological Description Research Articles

Understanding disorder and linker deficiency in porphyrinic zirconium-based metal\u2013organic frameworks by resolving the Zr8O6 cluster conundrum in PCN-221

Porphyrin-based metal–organic frameworks (MOFs), exemplified by MOF-525, PCN-221, and PCN-224, are promising systems for catalysis, optoelectronics, and solar energy conversion. However, subtle differences between synthetic protocols for these three MOFs give rise to vast discrepancies in purported product outcomes and description of framework topologies. Here, based on a comprehensive synthetic and structural analysis spanning local and long-range length scales, we show that PCN-221 consists of Zr6O4(OH)4 clusters in four distinct orientations within the unit cell, rather than Zr8O6 clusters as originally published, and linker vacancies at levels of around 50%, which may form in a locally correlated manner. We propose disordered PCN-224 (dPCN-224) as a unified model to understand PCN-221, MOF-525, and PCN-224 by varying the degree of orientational cluster disorder, linker conformation and vacancies, and cluster–linker binding. Our work thus introduces a new perspective on network topology and disorder in Zr-MOFs and pinpoints the structural variables that direct their functional properties.

Simplicial and topological descriptions of human brain dynamics

While brain imaging tools like functional magnetic resonance imaging (fMRI) afford measurements of whole-brain activity, it remains unclear how best to interpret patterns found amid the data’s apparent self-organization. To clarify how patterns of brain activity support brain function, one might identify metric spaces that optimally distinguish brain states across experimentally defined conditions. Therefore, the present study considers the relative capacities of several metric spaces to disambiguate experimentally defined brain states. One fundamental metric space interprets fMRI data topographically, that is, as the vector of amplitudes of a multivariate signal, changing with time. Another perspective compares the brain’s functional connectivity, that is, the similarity matrix computed between signals from different brain regions. More recently, metric spaces that consider the data’s topology have become available. Such methods treat data as a sample drawn from an abstract geometric object. To recover the structure of that object, topological data analysis detects features that are invariant under continuous deformations (such as coordinate rotation and nodal misalignment). Moreover, the methods explicitly consider features that persist across multiple geometric scales. While, certainly, there are strengths and weaknesses of each brain dynamics metric space, wefind that those that track topological features optimally distinguish experimentally defined brain states.

Persistence of hierarchical network organization and emergent topologies in models of functional connectivity

Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well known to be organized in hierarchical and modular way. While it is assumed that structural networks shape their functional counterparts, it is also hypothesized that alterations of brain dynamics come with transformations of functional connectivity. In this computational study, we introduce a novel methodology to monitor the persistence and breakdown of hierarchical order in functional networks, generated from computational models of activity spreading on both synthetic and real structural connectomes. We show that hierarchical connectivity appears in functional networks in a persistent way if the dynamics is set to be in the quasi-critical regime associated with optimal processing capabilities and normal brain function, while it breaks down in other (supercritical) dynamical regimes, often associated with pathological conditions. Our results offer important clues for the study of optimal neurocomputing architectures and processes, which are capable of controlling patterns of activity and information flow. We conclude that functional connectivity patterns achieve optimal balance between local specialized processing (i.e. segregation) and global integration by inheriting the hierarchical organization of the underlying structural architecture.

A Progressive Approach to Scalar Field Topology.

This article introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices, which are vertices that have no impact on the topological description of the data and for which we show that no computation is required as they are introduced in the hierarchy. This enables the definition of efficient coarse-to-fine topological algorithms, which leverage fast update mechanisms for ordinary vertices and avoid computation for the topologically invariant ones. We demonstrate our approach with two examples of topological algorithms (critical point extraction and persistence diagram computation), which generate interpretable outputs upon interruption requests and which progressively refine them otherwise. Experiments on real-life datasets illustrate that our progressive strategy, in addition to the continuous visual feedback it provides, even improves run time performance with regard to non-progressive algorithms and we describe further accelerations with shared-memory parallelism. We illustrate the utility of our approach in batch-mode and interactive setups, where it respectively enables the control of the execution time of complete topological pipelines as well as previews of the topological features found in a dataset, with progressive updates delivered within interactive times.

Maritime Traffic as a Complex Network: a Systematic Review

This article proposes a systematic review of papers dealing with maritime traffic whose methodology is based on a Complex Network Analysis (CNA) approach. The papers selected have been categorised, reviewed and analysed, extracting the most important characteristics of each, namely sources of information, geographical scope and network modelling characteristics, and then grouped according to the specific topics covered. The literature is classified according to two main streams: Papers dealing with a topological description of maritime networks, and papers applying a CNA approach to specific topics. In each case, an analysis is carried out, highlighting the most interesting concepts and methodologies of the selected papers, summarising the most important findings and proposing further topics for investigation. An additional analysis has been carried out with the keywords of the selected papers, creating a network and identifying seven communities representing and grouping the main research interest topics in the selected literature.

Lightweight finite element mesh database in Julia

A simple, lightweight, and flexible, package in the programming language Julia for managing finite element mesh data structures is presented. The key role in the design of the data structures is granted to the incidence relation. This concept has some interesting implications for the simplicity and efficiency of the implementation. The entire library has less than 500 executable lines. The low memory requirements are also notable. The design of the data structures is not fixed a priori. The user of the library is given the power over the decisions which mesh entities should be represented explicitly in the data structures, and which of the topological relationships should be computed and stored. This enables a small memory footprint, yet affords a sufficiently rich topology description capability.

A new level set based multi-material topology optimization method using alternating active-phase algorithm

This paper proposes a new level set based multi-material topology optimization method, where a difference-set-based multi-material level set (DS-MMLS) model is developed for topology description and an alternating active-phase algorithm is implemented. Based on the alternating active-phase algorithm, a multi-material topology optimization problem with N + 1 phases is split into N(N + 1)/2 binary-phase topology optimization sub-problems. Compared with the initial multi-material problem, each sub-problem involves fewer design variables and volume constraints. In the DS-MMLS model, N + 1 phases are represented by the sequential difference set of N level set functions. Based on this model, the topological evolution of two active phases can be easily achieved by updating a single level set function in a fixed domain, which contributes a great convenience to the implementation of the alternating active-phase algorithm with level set method. Therefore, the proposed method can be easily extended to topology optimization problems with more material phases. To demonstrate its effectiveness, some 2D and 3D numerical examples with different material phases are presented. The results reveal that the proposed method is effective for multi-material topology optimization problems.

Floquet–Dirac fermions in monolayer graphene by Wannier functions

Wannier functions have been widely applied in the study of topological properties and Floquet–Bloch bands of materials. Usually, the real-space Wannier functions are linked to the k-space Hamiltonian by two types of Fourier transform (FT), namely lattice-gauge FT (LGFT) and atomic-gauge FT (AGFT), but the differences between these two FTs on Floquet–Bloch bands have rarely been addressed. Taking monolayer graphene as an example, we demonstrate that LGFT gives different topological descriptions on the Floquet–Bloch bands for the structurally equivalent directions which are obviously unphysical, while AGFT is immune to this dilemma. We introduce the atomic-laser periodic effect to explain the different Floquet–Bloch bands between the LGFT and AGFT. Using AGFT, we showed that linearly polarized laser could effectively manipulate the properties of the Dirac fermions in graphene, such as the location, generation and annihilation of Dirac points. This proposal offers not only deeper understanding on the role of Wannier functions in solving the Floquet systems, but also a promising platform to study the interaction between the time-periodic laser field and materials.

Optimization of Generatively Encoded Multi-Material Lattice Structures for Desired Deformation Behavior

Natural systems achieve favorable mechanical properties through coupling significantly different elastic moduli within a single tissue. However, when it comes to man-made materials and structures, there are a lack of methods which enable production of artifacts inspired by these phenomena. In this study, a method for design automation based on alternate deposition of soft and stiff struts within a multi-material 3D lattice structure with desired deformation behavior is proposed. These structures, once external forces are applied, conform to the geometry given in advance. For that purpose, a population-based algorithm was proposed and integrated with a multi-material physics simulator. To reduce the amount of data processed during optimization, a generative encoding method based on discrete cosine transform (DCT) was proposed. This enabled a compressed topological description and promoted symmetry in material distribution. The simulation results showed different three-dimensional lattice structures designed with proposed algorithm to meet a set of desired deformation behaviors. The relation between residual deformation error, targeted deformation geometry, and material distribution is discussed.

Models and Methods for Discovery of Local Area Network Topology with Incomplete Data

A lot of network management tasks require a description of the logical and physical computer network topology. Obtaining such a description in an automatic way is complicated due to the possibility of incompleteness and incorrectness of the initial data on the network structure. This article provides a study on the properties of incomplete initial data on network device connectivity on the link layer. Methods for generalized handling of the heterogeneous input data on the link layer are included. We describe models and methods for deriving a missing part of the data, as well as the condition in which it is possible to get a single correct network topology description. The article includes algorithms for building a link layer topology description from incomplete data when this data is possible to fulfill up to the required level. Also, we provide methods for detecting and resolving an ambiguity in the data and methods for improving incorrect initial data. The tests and evaluations provided in the article demonstrate the applicability and effectiveness of the build methods for discovering various heterogeneous real-life networks. Additionally, we show the advantages of the provided methods over the previous analogs: our methods are able to derive up to 99% data on link layer connectivity in polynomial time; able to provide a correct solution from an ambiguous data.

Models and methods for local area network topology discovery with incomplete data

A lot of network management tasks require a description of the logical and physical computer network topology. Obtaining such a description in an automatic way is complicated due to the possibility of incompleteness and incorrectness of the initial data on the network structure. This article provides a study on the properties of incomplete initial data on network device connectivity on the link layer. Methods for generalized handling of the heterogeneous input data on the link layer are included. We describe models and methods for deriving a missing part of the data, as well as the condition in which it is possible to get a single correct network topology description. The article includes algorithms for building a link layer topology description from incomplete data when this data is possible to fulfill up to the required level. Also, we provide methods for detecting and resolving an ambiguity in the data and methods for improving incorrect initial data. Tests and evaluations provided in the article demonstrate the applicability and effectiveness of the build methods for discovering various heterogeneous real-life networks. Additionally, we show advantages of the provided methods over the previous analogs: our methods are able to derive up to 99\% data on link layer connectivity in polynomial time; able to provide a correct solution from an ambiguous data.

Characterising the structural pattern of urban road networks in Ghana using geometric and topological measures

Road networks are an integral part of any human settlement, facilitating the movement of people, goods, and information. The structural arrangement of a road network can have a profound impact on its performance, mobility and access to critical infrastructure. This study takes advantage of a computational network science approach to examine the structural configuration of road networks using geometric and topological descriptions in districts covering 10 regional capitals in Ghana. The majority of urban road networks were found to follow a radial pattern at the global scale, with either a gridded or a branching configuration at the local scale. Only road networks in Accra and Kumsi are fine grained and of comparable density to other global cities, based on intersection and street densities. Structural indicators such as circuity, clustering, page rank, degree centrality, and betweenness centrality for urban roads in Ghana were found to be comparable to other global cities. Given the lack of adequate infrastructure for traffic monitoring in Ghana, the spatial distribution of betweenness centrality could be part of the critical resource to provide insight for traffic management. These findings provide the basis to inform transportation planning and management on critical issues, particularly, based on the spatial distribution of betweenness centrality it is possible to identify problematic locations within the road network which are most vulnerable to traffic congestion.

A Persistent Homology-Based Topological Loss Function for Multi-class CNN Segmentation of Cardiac MRI.

With respect to spatial overlap, CNN-based segmentation of short axis cardiovascular magnetic resonance (CMR) images has achieved a level of performance consistent with inter observer variation. However, conventional training procedures frequently depend on pixel-wise loss functions, limiting optimisation with respect to extended or global features. As a result, inferred segmentations can lack spatial coherence, including spurious connected components or holes. Such results are implausible, violating the anticipated topology of image segments, which is frequently known a priori. Addressing this challenge, published work has employed persistent homology, constructing topological loss functions for the evaluation of image segments against an explicit prior. Building a richer description of segmentation topology by considering all possible labels and label pairs, we extend these losses to the task of multi-class segmentation. These topological priors allow us to resolve all topological errors in a subset of 150 examples from the ACDC short axis CMR training data set, without sacrificing overlap performance.

Resolvent, heat kernel, and torsion under degeneration to fibered cusps

Manifolds with fibered cusps are a class of complete noncompact Riemannian manifolds including all locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold undergoing degeneration to a manifold with fibered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with fibered cusps in terms of the R-torsion of the underlying manifold with boundary.

A Modular Active Balancing Circuit for Redox Flow Battery Applied in Energy Storage System

To improve the operation performance and energy conversion efficiency of the redox flow battery (RFB), a modular active balancing circuit for redox flow battery applied in the energy storage system is proposed in this paper. Detailed topology description, parameter design, characteristic analysis, operation principle and control strategy of the proposed circuit are presented and discussed in the paper. Different from the conventional battery balancing circuit, the key point of the proposed balancing circuit is that it integrates the circulating pump driving circuit and the state-of-charge (SOC) equalization circuit of the redox flow battery. It uses the energy consumption of the pump driving to balance the SOCs of different battery stacks, which provides a new SOC balancing mechanism for RFB. Based on the proposed circuit, an active balancing control strategy using the time-sharing energy transmission method is proposed, in which the sub-modules of the circuit are alternatively configured in charge-state and discharge-state for absorbing energy or releasing energy to achieve the SOC balancing control for RFB. Compared with the conventional balancing solution or circuit, the proposed modular active balancing circuit simplifies the complexity of the battery management system for RFB, which has the advantages of high efficiency, high reliability, and good scalability. Simulations on Matlab/Simulink and experiments on a downscaled prototype were carried out to verify the feasibility and effectiveness of the proposed circuit and control strategy.

Construction of a 3D Stratum Model Based on a Solid Model

A three-dimensional stratum model stratum model is a useful auxiliary tool for geotechnical engineering and other exploration work. The existing methods for stratum model construction lack complete topological descriptions of entities, so it is difficult to apply them to 3D geological modeling with complex geometric structures and complex topological relationships between modules. To solve the above problem, in this paper, the boundary representation method is used to represent the arbitrarily-shaped geological entities, and the half winged-edge-face structure topological structure is proposed to describe the topological information of the stratum model for a complex entity. The topological structure can record the topological information of the solid stratum model completely, thereby providing the basis for operations with the model and the applications of various algorithms. Based on this topological structure, the construction process for a 3D solid stratum model is proposed. The reliability and effectiveness of the constructed 3D solid stratum model are verified by an engineering case. The solid stratum model not only solves the geological modeling problem with respect to complex geometric and topological relations, but also provides a new method and idea for 3D geological modeling.

MODELLING AND CONTROL OF RURAL PV MICRO GRID USING FUZZY LOGIC CONTROLLER

This paper proposes an approach for the hybrid solar photovoltaic and Battery management for stand-alone applications. Battery charging process is non-linear, time-varying with a considerable time delay so it is difficult to achieve the best energy management performance by using traditional control approaches. A fuzzy control strategy for battery charging or discharging used in a renewable power generation system is analyzed in the paper. To improve the life cycle of the battery, fuzzy control manages the desired state of charge. A fuzzy logic-based controller to be used for the Battery SOC control of the designed hybrid system is proposed. This paper presents a general description of the implemented microgrid topology. The exact linearization theory adapted for power converters is applied to both a Single-Ended PrimaryInductor converter (SEPIC) to extract energy from PV modules and to a Boost converter to increase the voltage. The entire designed system is modeled and simulated using MATLAB/Simulink environment.

Topology generation and optimization of boundary cable nets for the mesh reflector antenna

The mesh reflector antenna is an ideal large deployable structure for on-orbit service. Surface accuracy and tension uniformity are two important performance indicators of it. The cable net topology, especially boundary cable net topology has great effects on the tension uniformity and also surface accuracy. The boundary cable net topology can vary with the design parameters and supporting truss. Finding the most suitable boundary cable net topology from a large number of potential topologies is a challenging task. At present, topology generation considered both the surface accuracy and tension uniformity is seldom studied. In this paper, the boundary cable net topology generation and optimization method (BGO) which can be applied for different mesh reflector antennas is proposed. Firstly, a generalized topology description method is developed based on the concepts of graph and adjacency matrix in graph theory. Secondly, three criteria are proposed according to the common sense in the generation of potential boundary cable net topologies. Thirdly, the topology optimization strategy setting the tension uniformity as the optimization objective is proposed based on the equilibrium matrix method. Lastly, numerical examples are given, and the results show that with the optimized boundary cable net topologies, better tension uniformity is achieved.

Real Springer fibers and odd arc algebras

We give a topological description of the two-row Springer fiber over the real numbers. We show its cohomology ring coincides with the oddification of the cohomology ring of the complex Springer fiber introduced by Lauda-Russell. We also realize Ozsv\'ath-Rasmussen-Szab\'o odd TQFT from pullbacks and exceptional pushforwards along inclusion and projection maps between hypertori. Using these results, we construct the odd arc algebra as a convolution algebra over components of the real Springer fiber, giving an odd analogue of a construction of Stroppel-Webster.

Shape-Driven Difference Electrical Impedance Tomography.

This work proposes a novel shape-driven reconstruction approach for difference electrical impedance tomography (EIT). In the proposed approach, the reconstruction problem is formulated as a shape reconstruction problem and solved via an explicit and geometrical methodology, where the geometry of the embedded inclusions is represented by a shape and topology description function (STDF). To incorporate more geometry and prior information directly into the reconstruction and to provide better flexibility in the solution process, the concept of a moving morphable component (MMC) is applied here implying that MMC is treated as the basic building block of the embedded inclusions. Simulations, phantom studies, and in vivo pig data are used to test the proposed approach for the most popular biomedical application of EIT - lung imaging - and the performance is compared with the conventional linear approach. In addition, the modality's robustness is studied in cases where (i) modeling errors are caused by inhomogeneity in the background conductivity, and (ii) uncertainties in the contact impedances and reference state are present. The results of this work indicate that the proposed approach is tolerant to modeling errors and is fairly robust to typical EIT uncertainties, producing greatly improved image quality compared to the conventional linear approach.