Topological Conditions Research Articles

Connection-Aware Digital Twin for Mobile Adhoc Networks in the 5G Era

5G Mobile Adhoc Networks (5G-MANETs) are a popular and agile solution for data transmission in local contexts while maintaining communication with remote entities via 5G. These characteristics have established 5G-MANETs as versatile communication infrastructures for deploying contextual applications, leveraging physical proximity while exploiting the possibilities of the Internet. As a result, there is growing interest in exploring the potential of these networks and their performance in real-world scenarios. However, the management and monitoring of 5G-MANETs are challenging due to their inherent characteristics, such as highly variable topology, unstable connections, energy consumption of individual devices, message routing, and occasional inability to connect to 5G. Considering these challenges, the proposed work aims to address real-time monitoring of 5G-MANETs using a connection-aware Digital Twin (DT). The approach provides two main functions: offering a live virtual representation of the network, even in scenarios where multiple nodes lack 5G connectivity, and estimating the performance of the infrastructure, enabling the specification of customized conditions. To achieve this, a communication architecture is proposed, analyzing its components and defining the involved processes. The DT is implemented and evaluated in a laboratory setting, assessing its accuracy in representing the physical network under varying conditions of topology and Internet availability. The results show 100% accuracy for the DT in fully connected topologies, with ultra-low latency averaging under 80 ms, and suitable performance in partially connected contexts, with latency averages below 3000 ms.

Topological conditions drive stability in meta-ecosystems

On a global level, ecological communities are being perturbed at an unprecedented rate by human activities and environmental instabilities. Yet, we understand little about what factors facilitate or impede long-term persistence of these communities. While observational studies indicate that increased biodiversity must, somehow, be driving stability, theoretical studies have argued the exact opposite viewpoint instead. This encouraged many researchers to participate in the ongoing debate. Within this context, however, there has been a severe lack of studies that consider spatial features explicitly, even though nearly all habitats are spatially embedded. To this end, we study here the linear stability of meta-ecosystems on networks that describe how discrete patches are connected by dispersal between them. By combining results from random-matrix theory and network theory, we are able to show that there are three distinct features that underlie stability: edge density, tendency to triadic closure, and isolation or fragmentation. Our results appear to further indicate that network sparsity does not necessarily reduce stability, and that connections between patches are just as important, if not more so, to consider when studying the stability of large ecological systems. Published by the American Physical Society 2024

Modern quantum materials

Quantum phenomena, including entanglement, superposition, tunneling, and spin–orbit interactions, among others, are foundational to the development of recent innovations in quantum computing, teleportation, encryption, sensing, and new modalities of electronics, such as spintronics, spin-orbitronics, caloritronics, magnonics, twistronics, and valleytronics. These emerging technologies provide disruptive influences to global commercial markets. These remarkable advances in quantum technologies are nearly always enabled by the discovery of materials and their quantum behaviors. Such advances are governed by quantum principles that are strongly influenced by environmental, physical, topological, and morphological conditions such as very small length scales, short time durations, ultrahigh pressures, ultralow temperatures, etc., which lead to quantum behaviors that manifest as quantum tunneling, entanglement, superpositioning, superfluidity, low-dimensional, high-temperature and high-pressure superconductivity, quantum fluctuations, Bose–Einstein condensates, topological effects, and other phenomena that are not yet fully understood nor adequately explored. Here, we provide a review of quantum materials developed up to 2023. Remarkable advances in quantum materials occur daily, and therefore, by the time of publication, new and exciting breakthroughs will have occurred that are regrettably not covered herein.

Lightning Network Economics: Topology

By design, the Bitcoin protocol has a low throughput. The Lightning Network (LN) is a layer-two solution built to increase throughput by cryptographically securing commitments to transactions and only occasionally converting cumulative balances into on-chain transactions. LN channels enable payments between nodes connected by a path of channels. The payment flow through a channel determines its cost. Different channel topologies can support the same underlying flows but impose different costs. This paper obtains necessary conditions for cost-minimizing topologies by identifying local cost-reducing strategies. The first local strategy entails repositioning of channels. The second entails adding hubs to handle the flows of groups of nodes. The paper also evaluates the efficiency of a global configuration, obtaining bounds on the minimum cost topology and showing the unusual circumstances in which the cost minimal structure is a hub that connects to all other nodes. This paper was accepted by Joshua Gans, business strategy. Funding: This work was partially supported by Science Foundation Ireland [Grants 16/IA/4443, 16/SPP/3347], Columbia-International Business Machines Center for Blockchain and Data Transparency, Chaire Fintech at University Paris Dauphine-Paris Sciences et Lettres, Algorand Foundation, and Simons Institute.

Effects of topological boundary conditions on Bell nonlocality

Effects of topological boundary conditions on Bell nonlocality

Topological conditions for impurity effects in carbon nanosystems

Topological conditions for impurity effects in carbon nanosystems

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.

Assessing structural homogeneity and heterogeneity in offshore wind farms: A population-based structural health monitoring approach

This paper presents an in-depth analysis of population-based structural health monitoring applied to offshore wind farms, with a specific focus on a real wind farm. The study quantifies the heterogeneity within the wind turbine population utilising advanced numerical methods. The Fréchet distance is introduced as a key metric to assess the similarity in terms of structural integrity among the turbines considering factors, such as geometry, material properties, topology, and operational conditions. The results revealed a predominant homogeneity with respect across the wind turbines, despite variations in environmental exposure and operational states. Furthermore, the scope of the study is extended to explore the implications of environmental influences, such as corrosion, scour, and marine growth, which are typically unmonitored yet crucial for comprehensive structural assessment. The present paper contributes to the field by demonstrating the feasibility of knowledge transfer in homogeneous wind turbine populations and highlighting the need for detailed similarity assessments in heterogeneous settings. The findings of this study pave the way for better-targeted, smart, and efficient structural health monitoring strategies in renewable energy systems.

On the symmetry TFT of Yang-Mills-Chern-Simons theory

Three-dimensional Yang-Mills-Chern-Simons theory has the peculiar property that its one-form symmetry defects have nontrivial braiding, namely they are charged under the same symmetry they generate, which is then anomalous. This poses a few puzzles in describing the corresponding Symmetry TFT in a four-dimensional bulk. First, the braiding between lines at the boundary seems to be ill-defined when such lines are pulled into the bulk. Second, the Symmetry TFT appears to be too trivial to allow for topological boundary conditions encoding all the different global variants. We show that both of these puzzles can be solved by including endable (tubular) surfaces in the class of bulk topological operators one has to consider. In this way, we are able to reproduce all global variants of the theory, with their symmetries and their anomalies. We check the validity of our proposal also against a top-down holographic realization of the same class of theories.

Modeling end-to-end delays in TSCH wireless sensor networks using queuing theory and combinatorics

Wireless communication offers significant advantages in terms of flexibility, coverage and maintenance compared to wired solutions and is being actively deployed in the industry. IEEE 802.15.4 standardizes the Physical and the Medium Access Control (MAC) layer for Low Power and Lossy Networks (LLNs) and features Timeslotted Channel Hopping (TSCH) for reliable, low-latency communication with scheduling capabilities. Multiple scheduling schemes were proposed to address Quality of Service (QoS) in challenging scenarios. However, most of them are evaluated through simulations and experiments, which are often time-consuming and may be difficult to reproduce. Analytical modeling of TSCH performance is lacking, as only one-hop communication with simplified traffic patterns is considered in state-of-the-art. This work proposes a new framework based on queuing theory and combinatorics to evaluate end-to-end delays in multihop TSCH networks of arbitrary topology, traffic and link conditions. The framework is validated in simulations using OMNeT++ and shows below 6% root-mean-square error (RMSE), providing quick and reliable latency estimation tool to support decision-making and enable formalized comparison of existing scheduling solutions.

The geometry of induced currents in two-dimensional media

We present a framework that allows us to clearly identify the geometric features underlying the phenomenon of superconductivity in two-dimensional materials. In particular, we show that any such medium whose response to an externally applied electromagnetic field is a geodesically flowing induced current, must be a superconductor. In this manner, we conclude that the underlying geometry of this type of media is that of a Lorentzian contact manifold. Moreover, we show that the macroscopic hallmark of their superconducting state is a purely topological condition equivalent to the geodesic nature of the induced current: the non-vanishing of its helicity.

From noise on the sites to noise on the links: Discretizing the conserved Kardar-Parisi-Zhang equationin real space.

Numerical analysis of conserved field dynamics has been generally performed with pseudospectral methods. Finite differences integration, the common procedure for nonconserved field dynamics, indeed struggles to implement a conservative noise in the discrete spatial domain. In this work we present a method to generate a conservative noise in the finite differences framework, which works for any discrete topology and boundary conditions. We apply it to numerically solve the conserved Kardar-Parisi-Zhang (cKPZ) equation, widely used to describe surface roughening when the number of particles is conserved. Our numerical simulations recover the correct scaling exponents α,β, and z in d=1 and in d=2. To illustrate the potentiality of the method, we further consider the cKPZ equationon different kinds of nonstandard lattices and on the random Euclidean graph. This is a unique numerical study of conserved field dynamics on an irregular topology, paving the way for a broad spectrum of possible applications.

Dimers on Riemann surfaces I: Temperleyan forests

This is the first article in a series of two papers in which we study the Temperleyan dimer model on an arbitrary bounded Riemann surface of finite topological type. The end goal of both papers is to prove the convergence of height fluctuations to a universal and conformally invariant scaling limit. In this part, we show that the dimer model on the Temperleyan superposition of a graph embedded on the surface and its dual is well posed, provided that we remove an appropriate number of punctures. We further show that the resulting dimer configuration is in bijection with an object which we call Temperleyan forest, whose law is characterised in terms of a certain topological condition. Finally, we discuss the relation between height differences and Temperleyan forest and prove that the convergence of the latter (which is the subject of the second paper in this series) implies the existence of a conformally invariant scaling limit of height fluctuations.

An infinite dimensional KAM theorem with normal degeneracy

In this paper, we consider a classical Hamiltonian normal form with degeneracy in the normal direction. In previous results, one needs to assume that the perturbation satisfies certain non-degenerate conditions in order to remove the degeneracy in the normal form. Instead of that, we introduce a topological degree condition and a weak convexity condition, which are easy to verify, and we prove the persistence of lower dimensional tori without any restriction on perturbation but only smallness and analyticity.

Finding regulatory modules of chemical reaction systems

Within a cell, numerous chemical reactions form chemical reaction networks (CRNs), which are the origins of cellular functions. We previously developed a theoretical method called structural sensitivity analysis (SSA), which enables us to determine, solely from the network structure, the qualitative changes in the steady-state concentrations of chemicals resulting from the perturbations to a parameter. Notably, if a subnetwork satisfies specific topological conditions, it is referred to as a buffering structure, and the effects of perturbations to the parameter within the subnetwork are localized to the subnetwork (the law of localization). A buffering structure can be the origin of modularity in the regulation of cellular functions generated from CRNs. However, an efficient method to search for buffering structures in a large CRN has not yet been established. In this study, we prove the “inverse theorem” of the law of localization, which states that a certain subnetwork exhibiting a confined response range is always a buffering structure. In other words, we are able to identify buffering structures in terms of confined responses rather than the topological conditions. By leveraging this property, we develop an algorithm to enumerate all buffering structures for a given network by calculating responses. Additionally, we show that the hierarchy of perturbed response patterns corresponds to that of buffering structures, and present a method to illustrate the hierarchy. Our method will be a powerful tool for understanding the regulation of cellular functions generated from CRNs. Published by the American Physical Society 2024

On topological conditions for enabling transient control in leader–follower networks

We derive necessary and sufficient conditions for leader–follower multi-agent systems such that we can further apply prescribed performance control to achieve the desired formation while satisfying certain transient constraints. A leader–follower framework is considered in the sense that a group of agents with external inputs are selected as leaders in order to drive the group of followers in a way that the entire system can achieve target formation within certain prescribed performance transient bounds. We first derive necessary conditions on the leader–follower graph topology under which the target formation together with the prescribed performance guarantees can be fulfilled. Afterwards, the derived necessary conditions are extended to necessary and sufficient conditions for leader–follower formation control under transient constraints. Finally, the proposed results are illustrated with simulation examples.

Learned load balancing

Effectively balancing traffic in datacenter networks is a crucial operational goal. Most existing load balancing approaches are handcrafted to the structure of the network and/or network workloads. Thus, new load balancing strategies are required if the underlying network conditions change, e.g., due to hard or grey failures, network topology evolution, or workload shifts. While we can theoretically derive the optimal load balancing strategy by solving an optimization problem given certain traffic and topology conditions, these problems take too much time to solve and makes the derived solution stale to deploy. In this paper, we describe a load balancing scheme Learned Load Balancing (LLB), which is a general approach to finding an optimal load balancing strategy for a given network topology and workload, and is fast enough in practice to deploy the inferred strategies. LLB uses deep supervised learning techniques to learn how to handle different traffic patterns and topology changes, and adapts to any failures in the underlying network. LLB leverages emerging trends in network telemetry, programmable switching, and “smart” NICs. Our experiments show that LLB performs well under failures and can be expanded to more complex, multi-layered network topologies. We also prototype neural network inference on smartNICs to demonstrate the workability of LLB.

ENHANCING 3T RETINOTOPIC MAPS USING DIFFEOMORPHIC REGISTRATION.

Retinotopic mapping aims to uncover the relationship between visual stimuli on the retina and neural responses on the visual cortical surface. This study advances retinotopic mapping by applying diffeomorphic registration to the 3T NYU retinotopy dataset, encompassing analyze-PRF and mrVista data. Diffeomorphic Registration for Retinotopic Maps (DRRM) quantifies the diffeomorphic condition, ensuring accurate alignment of retinotopic maps without topological violations. Leveraging the Beltrami coefficient and topological condition, DRRM significantly enhances retinotopic map accuracy. Evaluation against existing methods demonstrates DRRM's superiority on various datasets, including 3T and 7T retinotopy data. The application of diffeomorphic registration improves the interpretability of low-quality retinotopic maps, holding promise for clinical applications.

Topological properties and skin effects modulated by different-density nonreciprocal couplings in the Su-Schrieffer-Heeger structure

We pay attention to the topological properties and skin effects in the one-dimensional Su-Schrieffer-Heeger (SSH) structure, by considering the presence of different-density non-reciprocal couplings. We find that when only one single non-reciprocal coupling term is introduced, e.g., in the middle of the SSH structure, edge states can be induced around the sites suffering from the non-reciprocal coupling. As one non-reciprocal coupling term is introduced in each two cells, the topological phase transition is modified. Besides, new topological edge states and skin effects appear at the ends of the SSH structure, and the edge states can be differentiated by their localities, localization degrees, and the imaginary part of energy. Furthermore, if two neighboring cells of the SSH structure are coupled by the non-reciprocal coupling, the topological edge states and skin effect more well-defined, accompanied by the further change of the topological phase transition condition. These results suggest that the non-reciprocal coupling plays a unique and important role in modulating the topological properties and the skin effects of the one-dimensional SSH structure.

Thermodynamics and kinetics of interconversion between platinum nanoparticles and cations in zeolites

In metal-containing zeolites, sintering and redispersion processes exercise control over the identity of metal site structures, but the thermodynamic and kinetic factors that influence these molecular-level processes are not completely understood. Here, we assess the ability of first principles informed free energy models (for supported and unsupported nanoparticles) and kinetic models integrating Ostwald ripening with atom trapping to describe the interconversion between Pt cations and nanoparticles encapsulated in chabazite (CHA) zeolites. Density functional theory-derived thermodynamic phase diagrams show that the interconversion between cations, favored in oxidizing environments, and particles, favored in reducing environments, is fully reversible within a wide range of their respective conditions (temperatures and pressures) for CHA and several other zeolite topologies. Kinetic Monte Carlo simulations of Pt redispersion are consistent with experimentally observed redispersion kinetics of encapsulated Pt nanoparticles in CHA zeolites, and model results suggest the zeolite host imparts additional stability for Pt nanoparticles. We envision our thermodynamic and kinetic models for Pt-CHA are also capable of describing nanoparticle and cation interconversions for other zeolite frameworks under similar conditions.