Topological Framework Research Articles

ML Model Coverage Assessment by Topological Data Analysis Exploration

The increasing complexity of deep learning models necessitates advanced methods for model coverage assessment, a critical factor for their reliable deployment. In this study, we introduce a novel approach leveraging topological data analysis to evaluate the coverage of a couple dataset & classification model. By using tools from topological data analysis, our method identifies underrepresented regions within the data, thereby enhancing the understanding of both model performances and data completeness. This approach simultaneously evaluates the dataset and the model, highlighting areas of potential risk. We report experimental evidence demonstrating the effectiveness of this topological framework in providing a comprehensive and interpretable coverage assessment. As such, we aim to open new avenues for improving the reliability and trustworthiness of classification models, laying the groundwork for future research in this domain.

Investigation of the risk influential factors of maritime accidents: A novel topology and robustness analytical framework

This study aims to develop a novel and fully data-driven approach to analyse the maritime accidents risk influential factors (RIFs) by integrating Association Rule Mining (ARM) and Complex Network (CN) modelling. Firstly, a comprehensive dataset comprising 21,206 maritime accident records from Marine Accident Investigation Branch and Transportation Safety Board is collected and processed to serve as the foundational data source supporting the development of the new approach. Secondly, a novel Combined Association Rule Mining method is proposed to extract the interconnections among RIFs, with the mined results mapped into a CN framework. Finally, two importance ranking algorithms, namely the PageRank-Information-Entropy algorithm and edge betweenness centrality, are applied to identify the key RIFs and their information transmission paths. By simulating deliberate and random attacks within networks, a robustness analysis is conducted to further explore the evolution of RIFs. The findings reveal that ship-related factors demonstrate greater centrality and connectivity, exerting a more substantial influence on information propagation within the network structure. The robustness analysis illustrates that strategic node and edge removals are effective in preventing risk propagation. It therefore makes contributions to the development of a theoretical basis for stakeholders to develop cost-effective preventive measures against specific RIFs, ultimately enhancing maritime safety.

Neutrosophic Topological Framework for Uncertainty Management in Smartphone Data Extraction Applications

Neutrosophic Topological Framework for Uncertainty Management in Smartphone Data Extraction Applications

Fe-MOF-74 Reactivity Explored: Comprehensive Computational Assessment of O and S Atom Influence on CO2 and CO Reduction Reactions

The conversion of carbon dioxide (CO2) and carbon monoxide (CO) into higher-value materials is crucial for addressing escalating levels of greenhouse gases in Earth’s atmosphere. Employing first-principles methods, we investigated the electrocatalytic reduction of CO2 and CO on two Fe-based MOFs: Fe2DOBDC and Fe2DSBDC. By directly comparing these MOFs, we aimed to discern the impact of introducing S atoms into the framework without changing the topological framework. Several chemical properties such as electronegativity, atomic radius, polarizability, and charge density are expected to lead to significant changes for the reduction reactions upon the replacement of O atoms with S atoms. CM5 atomic charge analysis highlights some of these differences by showing the equatorial Fe-O/S bonds of Fe2DSBDC are less polarized and result in smaller positive and negative charges on the Fe and O/S atoms, respectively. Additionally, the larger S atoms are expected to weaken adsorbate binding due to less favorable van der Waals interactions near the open-metal Fe site. Consequently, the less electropositive Fe site and the larger S atoms of Fe2DSBDC impede the adsorption of reduced CO2 and CO products, while the more electropositive Fe site and smaller O atoms of Fe2DOBDC strongly favor product adsorption. This implies that CO2 and CO reduction on Fe2DSBDC is likely to yield only 2e- products (HCOOH and CH2O, respectively), whereas Fe2DOBDC is expected to produce deeper reduction products (CH2O and CH4, respectively). This insight offers a foundation for constructing novel MOFs with tunable reaction behaviors by strategically replacing O atoms with heavier S atoms in the MOF scaffold.

Automatic topology and capacity generation framework for urban drainage systems with deep learning-based land use segmentation and hydrological characterization

This paper proposed a comprehensive and automated framework that integrates the entire urban drainage design process, from refined land use segmentation, to catchment subdivision and characterization, to network topology generation, and finally to hydraulic estimation of pipeline capacity, based on multiple open-source datasets. The method incorporated deep learning-based semantic segmentation, GIS-based hydrological characterization, topology generation and hydraulic calculation algorithms. The performance and applicability of the method were validated through case studies of two cities. The results showed that the deep learning model with prior knowledge could accurately segment urban land use to obtain the detailed shape and boundary description, and achieved higher detection accuracy for water bodies, buildings, and roads. The stormwater drainage topology and conveyance capacity were automatically generated based on subcatchment division and hydrological characterization under a set of topological parameter conditions. In the optimal Critical Success Index (CSI) scenario, only 8% and 21% of the generated pipelines were inconsistent with the expert-designed networks. Compared to the traditional manual design process, the automated approach can save significant time and resources and reduce the reliance on field surveys and empirical/expert work. At the same time, the tool can be employed for system layout and capacity optimization, providing important support for the automation, design, and rehabilitation of stormwater drainage systems.

Employing hydrogen-bonded organic frameworks in optoelectronic applications

Compared to other topological crystalline frameworks, HOFs offer unique advantages for sensors, memristors, neuromorphic computing, and artificial synapses.

Topological hydrogen-bonded organic frameworks (HOFs) and their electronic applications in sensor, memristor, and neuromorphic computing

Recently, an emerging class of hydrogen-bonded organic frameworks (HOFs) has become an appealing member of organic material family, attributed to their layered self-assembly structures, high-crystalline, and environmentally friendly characteristics, which have rapidly propelled their development in the field of electronic devices. In this context, we focus on the latest category of topological HOFs, with particular attention given to cutting-edge experimental demonstrations, exceptional electrical performances, and promising applications. First, a concise concept and fundamental mechanism of HOFs are provided, elucidating the potential correlation between structural designs and material properties. Subsequently, a comprehensive summary is presented on the preparation and synthesis methods, such as hydrothermal techniques, epitaxial growth, electro-deposition, among others. Notably, the latest advancements in HOFs-based electronics are thoroughly introduced and discussed, along with their applications in sensors, memristors, artificial synapses, neuromorphic computing, and human perception systems. Finally, the future challenges and prospects of topological HOFs are elaborated upon with the aim of providing valuable guidance for high-performance HOF-based electronics.

Innovative two-dimensional porphyrin-integrated metal-organic frameworks for enhanced photocatalytic hydrogen peroxide generation in pure water

In the quest for eco-friendly and efficient synthesis of hydrogen peroxide (H2O2), a chemical with extensive applications, photocatalytic production emerges as a promising clean technique. Metal-organic frameworks (MOFs), known for their exceptional porosity and geometric customizability, stand at the forefront of potential photocatalytic materials. Yet, the conventional three-dimensional topologies of MOFs pose a challenge, impeding the swift transit of photogenerated electrons and thereby curbing performance enhancements. In this vein, we have engineered novel 2D porphyrin-based MOFs, specifically Ce-TCPP and La-TCPP, utilizing diverse metal sources while maintaining a consistent topological framework. This design strategy streamlines the electron and hole transport pathways, thus elevating the photocatalytic activity. Delving into the structural nuances of these MOFs, our research unveiled that the photocatalytic activity experienced a marked shift upon altering the metal cluster types. Notably, La-TCPP, as an efficacious catalyst, demonstrated an H2O2 yield of 79.75 μmol/g/h in pure water, sans any sacrificial agents. Rigorous testing confirmed the robust stability of both MOFs. This study marks the inaugural design and synthesis of a single crystal structure of La-TCPP. By strategically varying metal cluster compositions, we have fine-tuned the architecture of two-dimensional MOFs. This approach sheds light on the intricate structure-activity relationship governing the photocatalytic synthesis of H2O2, paving the way for future advancements in the field.

A Zn(II) Coordination Polymer for Fluorescent Turn-Off Selective Sensing of Heavy Metal Cation and Toxic Inorganic Anions.

A novel coordination polymer [Zn(atyha)2]n (1) (Hatyha = 2-(2-aminothiazole-4-yl)-2- hydroxyiminoacetic acid) was constructed by hydrothermal reaction of Zn2+ with Hatyha ligand. CP 1 exhibits a 2D (4,4)-connected topological framework with Schläfli symbol of {44·62}, where atyha- anions serve as tridentate ligands, bridging with Zn2+ through carboxylate, thiazole and oxime groups. CP 1 displays a strong ligand-based photoluminescence at 390 nm in the solid state, and remains significantly structurally stable in water. Interestingly, it can be utilized as a fluorescent probe for selective and sensitive sensing of Fe3+, Cr2O72- and MnO4- through the fluorescent turn-off effect with limit of detection (LOD) of 3.66 × 10-6, 2.38 × 10-5 and 2.94 × 10-6 M, respectively. Moreover, the efficient recyclability for detection of Fe3+ and Cr2O72- is better than that for MnO4-. The mechanisms of fluorescent quenching involve reversible overlap of UV-Vis absorption bands of the analytes (Fe3+, Cr2O72- and MnO4-) with fluorescence excitation and emission bands for CP 1, respectively.

New approach for efficient malicious multiparty private set intersection

The Multiparty Private Set Intersection (MPSI) protocol allows untrusted parties to compute the intersection of their sets without revealing any additional information. MPSI has found wide applications in fields such as advertising, vertical federated learning, privacy-preserving data mining, and private contact tracing. However, existing MPSI solutions face challenges in terms of security and efficiency. Some MPSI schemes are secure only against semi-honest adversaries and cannot effectively defend against malicious adversaries. Other schemes, while capable of withstanding malicious adversaries, exhibit efficiency problems, especially as the number of corrupt participants increases. A practical MPSI solution must maintain high security and efficiency, even when handling large-scale data and a majority of corrupted participants.This paper introduces a novel MPSI scheme named TH-PSI, built upon a new star-shaped topological network communication framework based on the trusted execution environment. TH-PSI has been rigorously proven to be secure within the standard Universal Composability framework, capable of thwarting malicious adversaries. To demonstrate the efficiency of TH-PSI, we conduct a comprehensive series of experiments. We implement the TH-PSI scheme and tested it in both LAN and WAN settings, involving up to 30 participants and datasets as large as 222. We compare TH-PSI with state-of-the-art MPSI schemes, ENOC21 and NTY21, with a specific focus on their efficiency in the presence of malicious adversaries. Our experiments show that TH-PSI is an efficient solution capable of delivering results within a matter of seconds, even when dealing with data at the million-level and a majority of corrupted participants.

Topo: Towards a fine-grained topological data processing framework on Tianhe-3 supercomputer

Big data frameworks are widely deployed in supercomputers for analyzing large-scale datasets. Topological data processing is an emerging approach that focuses on analyzing the topological structures in high-dimensional scientific data. However, incorporating topological data processing into current big data frameworks presents three main challenges: (1) The frequent data exchange poses challenges to the traditional coarse-grained parallelism. (2) The spatial topology makes parallel programming harder using oversimplified MapReduce APIs. (3) The massive intermediate data and NUMA architecture hinder resource utilization and scalability on novel supercomputers and many-core processors.In this paper, we present Topo, a generic distributed framework that enhances topological data processing on many-core supercomputers. Topo relies on three concepts. (1) It employs fine-grained parallelism, with awareness of topological structures in datasets, to support interactions among collaborative workers before each shuffle phase. (2) It provides intuitive APIs for topological data operations. (3) It implements efficient collective I/O and NUMA-aware dynamic task scheduling to improve multi-threading and load balancing. We evaluate Topo's performance on the Tianhe-3 supercomputer, which utilizes state-of-the-art ARM many-core processors. Experimental results of execution time show that compared to popular frameworks, Topo achieves an average speedup of 5.3× and 6.3×, with a maximum speedup of 8.4× and 20×, on HPC workloads and big data benchmarks, respectively. Topo further reduces total execution time on processing skewed datasets by 41%.

Enhancing Flow Batteries: Topology Optimization of Electrode Porosity and Shape Optimization of Cell Design

This research focuses on the improvement of porosity distribution within the electrode of an all‐vanadium redox flow battery (VRFB) and on optimizing novel cell designs. A half‐cell model, coupled with topology and shape optimization framework, is introduced. The multiobjective functional in both cases aims to minimize pressure drop while maximizing reaction rate within the cell. Topology optimization results reveal dependencies on initial value, porosity constraint, and flow rate. The distribution with lower porosity is preferred downstream of the inlet manifold. This design enhances active surface area, thus facilitating more effective conversion of incoming educts and improving mass transport of products. Compared to homogeneous electrodes, two‐part design demonstrates superior performance at specific porosity values. For combined porosities of 0.7 and 0.95, optimized distribution results in 81 % reduction in pressure drop, while conversion rate decreases by 7%. As regards various cell designs, optimization suggests a need to reconsider the vertical format of a rectangular cell. Horizontal cells are favored for nearly all porosities and flow rates. Trapezoidal and radial designs characterized by reduced downstream cross sections lead to higher pressure drops and are not preferred. This work provides further valuable insight into optimizing VRFB electrodes and challenges conventional cell design assumptions.

The Dataveillance and Care in Teachers’ Work with Early Warning Systems

It has now become a widespread practice in both public and private organisations to analyse data collected through digital systems and tools. Datafication in schools has resulted in additional work tasks for teachers and an increased level of accountability on their part. One of these data-work-related tasks of teachers is to proactively recognize students who may be at risk of dropping out of school and help them. Machine learning holds significant promise in the creation of advanced early warning systems (EWS) for predicting such student dropouts. Such systems are in line with a positive discourse supporting teachers’ effective decision making and a deeper understanding of student behaviour. In contrast, critical scholars raise concerns about the impact of data-driven practices in education on the teaching profession. This study adds to this body of literature by exploring how teachers are regulated by and regulating EWS as part of their work practice.In this study as part of a larger working life funded project, we focus on one digital tool used in Swedish upper secondary schools called StudyBee, integrated with Google Classroom and connected to the Swedish National Agency for Education. We conducted a combination of ethnographic methods such as desktop research of application’s website and social media posts to gain a deeper knowledge on the StudyBee’s Graphical User Interface, interviews with teachers and principals, as well as go-alongs with teachers to understand their interactions with EWSs. Based on Decuypere’s (2021) topological framework, we analyse what is happening on, with, behind, and beyond EWS.To argue that teacher work is shaped by accountability mechanisms, we use a critical perspective on teacher work within the digital platform/accountability discourse, aiming to reveal underlying power dynamics. We apply the concept of dataveillance (datafied surveillance, Clarke in Lyon, 2022) to illustrate how power operates, encouraging teachers to self-regulate in alignment with school accountability. Furthermore, we utilize the concept of care (Zakharova & Jarke, 2022) to understand technology-related aspects and care for students.

Topological awareness towards collision-free multi-axis curved layer additive manufacturing

We present a topology-aware computational framework that enables global collision-free and support-structure-free material extrusion for curved layer multi-axis printing of a range of high-genus and simply connected models. The nature of multi-axis additive manufacturing facilitates continuous variation of build direction, which paves the way for numerous approaches of geometry-based curved layer design. However, due to unawareness of global topological features, prevention of collision between the printer nozzle and the workpiece can either remain uncertain or demand for exhaustive algorithmic approaches, depending on the topological and geometrical complexity of a given mesh model. In this paper, we present a topological analysis framework that draws inspiration from the concepts of Reeb graph and Morse theory, to distinguish between collision-prone and collision-free regions of mesh models. We provide an exact definition for global collision-inducing features in regions of risk and optimise the nozzle orientation vector field to avoid global collisions whilst adhering to the overhang angle constraints. A new shape analysis method is then proposed to find the model orientation which maximises the manufacturability of bifurcating simply connected models. To validate our algorithmic framework, several high-genus and bifurcating simply connected models are printed using a robotic multi-axis printer. The experimental results demonstrate the feasibility and effectiveness of our framework for minimising global collisions in multi-axis curved layer additive manufacturing for a range of mesh models.

Brain chains as topological signatures for Alzheimer’s disease

AbstractTopology is providing new insights for neuroscience. For instance, graphs, simplicial complexes, directed graphs, flag complexes, persistent homology and convex covers have been used to study functional brain networks, synaptic connectivity, and hippocampal place cell codes. We propose a topological framework to study the evolution of Alzheimer’s disease, the most common neurodegenerative disease. The modeling of this disease starts with the representation of the brain connectivity as a graph and the seeding of a toxic protein in a specific region represented by a vertex. Over time, the accumulation of toxic proteins at vertices and their propagation along edges are modeled by a dynamical system on this graph. These dynamics provide an order on the edges of the graph according to the damage created by high concentrations of proteins. This sequence of edges defines a filtration of the graph. We consider different filtrations given by different disease seeding locations. To study these filtrations we propose a new combinatorial and topological method. A filtration defines a maximal chain in the partially ordered set of spanning subgraphs ordered by inclusion. To identify similar graphs, and define a topological signature, we quotient this poset by graph homotopy equivalence, which gives maximal chains in a smaller poset. We provide an algorithm to compute this direct quotient without computing all subgraphs and then propose bounds on the total number of graphs up to homotopy equivalence. To compare the maximal chains generated by this method, we extend Kendall’s $$d_K$$ d K metric for permutations to more general graded posets and establish bounds for this metric. We then demonstrate the utility of this framework on actual brain graphs by studying the dynamics of tau proteins on the structural connectome. We show that the proposed topological brain chain equivalence classes distinguish different simulated subtypes of Alzheimer’s disease.

Alchemical Enhanced Sampling with Optimized Phase Space Overlap.

An alchemical enhanced sampling (ACES) method has recently been introduced to facilitate importance sampling in free energy simulations. The method achieves enhanced sampling from Hamiltonian replica exchange within a dual topology framework while utilizing new smoothstep softcore potentials. A common sampling problem encountered in lead optimization is the functionalization of aromatic rings that exhibit distinct conformational preferences when interacting with the protein. It is difficult to converge the distribution of ring conformations due to the long time scale of ring flipping events; however, the ACES method addresses this issue by modeling the syn and anti ring conformations within a dual topology. ACES thereby samples the conformer distributions by alchemically tunneling between states, as opposed to traversing a physical pathway with a high rotational barrier. We demonstrate the use of ACES to overcome conformational sampling issues involving ring flipping in ML300-derived noncovalent inhibitors of SARS-CoV-2 Main Protease (Mpro). The demonstrations explore how the use of replica exchange and the choice of softcore selection affects the convergence of the ring conformation distributions. Furthermore, we examine how the accuracy of the calculated free energies is affected by the degree of phase space overlap (PSO) between adjacent states (i.e., between neighboring λ-windows) and the Hamiltonian replica exchange acceptance ratios. Both of these factors are sensitive to the spacing between the intermediate states. We introduce a new method for choosing a schedule of λ values. The method analyzes short "burn-in" simulations to construct a 2D map of the nonlocal PSO. The schedule is obtained by optimizing an alchemical pathway on the 2D map that equalizes the PSO between the λ intervals. The optimized phase space overlap λ-spacing method (Opt-PSO) leads to more numerous end-to-end single passes and round trips due to the correlation between PSO and Hamiltonian replica exchange acceptance ratios. The improved exchange statistics enhance the efficiency of ACES method. The method has been implemented into the FE-ToolKit software package, which is freely available.

Refinement and Computation Method for Line/Body Topological Relationships

Three-dimensional topological relationships serve as a theoretical foundation for quality control, update processing, and spatial analysis of three-dimensional spatial data in real-world three-dimensional GIS. The existing 3D topological relationship models are all basic relationship models that cannot distinguish the refined topological relationship between the line and the body with multiple intersections. In this study, we develop a 3D refined topological relationship description framework that draws from the two-dimensional refined topological relationship model, defines the unit intersection between the line and the body based on manifold topology, and proposes a method for describing the unit intersections between the line and the body considering Euler numbers and adjacency types. In total, 23 basic types between the line and the body are deduced. An example is provided to illustrate the distinguished refined topological relationship between the line and the body with multiple intersections. Subsequently, an algorithm for determining the basic type of line/body is developed. Finally, a line/body refined topological relationship computation prototype system is developed using the Nef polyhedron model, C++ language, and an open-source geometric algorithm library, and the effectiveness of our method is verified using actual building and pedestrian data.

Concept and Development of Algebraic Topological Framework Nucleic Acids.

Nucleic acids are considered as promising materials for developing exquisite nanostructures from one to three dimensions. The advances of DNA nanotechnology facilitate ingenious design of DNA nanostructures with diverse shapes and sizes. Especially, the algebraic topological framework nucleic acids (ATFNAs) are functional DNA nanostructures that engineer guest molecules (e. g., nucleic acids, proteins, small molecules, and nanoparticles) stoichiometrically and spatially. The intrinsic precise properties and tailorable functionalities of ATFNAs hold great promise for biological applications, such as cell recognition and immunotherapy. This Perspective highlights the concept and development of precisely assembled ATFNAs, and outlines the new frontiers and opportunities for exploiting the structural advantages of ATFNAs for biological applications.

Development of a multi-layer network model for characterizing energy cascade behavior on turbulent mixing

Eddies of various sizes are visible to the naked eye in turbulent flow. Each eddy scale corresponds to a fraction of the total energy released by the turbulence cascade. Understanding the dynamic mechanism of the energy cascade is crucial to the study of turbulent mixing. In this paper, an energy cascade multi-layer network (ECMN) based on the complex network algorithm is proposed to investigate the spatio-temporal evolution of the energy cascade, covering both the inertial and dispersive ranges. The dynamic process of energy cascade is transformed into a topological structure based on the node definition and edge determination. The topological structure allows for the exploration of eddies interaction and chaotic energy transfer across scales. The model results show the intermittent and non-uniform nature of the energy cascade. Meanwhile, the scale gap found in the model verifies the fractal property of the energy evolution. We also found that scales of the generated eddies in energy cascade process are stochastic, and a synchronous energy cascade pattern is demonstrated according to the constructed framework. Furthermore, it provides a topological way to evaluate the contribution of large and small scale eddies. In addition, a network structure coefficient κ is proposed to evaluate the energy transfer strength. It agrees very well with the fluctuation of dissipation rates. All of this shows that the network model can effectively reveal the inhomogeneous properties of the energy cascade and quantify the turbulent mixing intensity based on the intermittent scale interaction. This also provides new insights into the study of fractal scales of nonlinear complex systems and the bridging of chaotic dynamics with topological frameworks.

Correction to: A topological framework for identifying phenomenological bifurcations in stochastic dynamical systems

Correction to: A topological framework for identifying phenomenological bifurcations in stochastic dynamical systems