Topological Constraints Research Articles

Combined topological and spatial constraints are required to capture the structure of neural connectomes

Abstract Volumetric brain reconstructions provide an unprecedented opportunity to gain insights into the complex connectivity patterns of neurons in an increasing number of organisms. Here, we model and quantify the complexity of the resulting neural connectomes in the fruit fly, mouse, and human and unveil a simple set of shared organizing principles across these organisms. To put the connectomes in a physical context, we also construct contactomes, the network of neurons in physical contact in each organism. With these, we establish that physical constraints—either given by pairwise distances or the contactome—play a crucial role in shaping the network structure. For example, neuron positions are highly optimal in terms of distance from their neighbors. Yet, spatial constraints alone cannot capture the network topology, including the broad degree distribution. Conversely, the degree sequence alone is insufficient to recover the spatial structure. We resolve this apparent mismatch by formulating scalable maximum entropy models, incorporating both types of constraints. The resulting generative models have predictive power beyond the input data, as they capture several additional biological and network characteristics, like synaptic weights and graphlet statistics.

Modification of Premises for the Black Hole Information Paradox Caused by Topological Constraints in the Event Horizon Vicinity

We demonstrate that at the rim of the photon sphere of a black hole, the quantum statistics transition takes place in any multi-particle system of indistinguishable particles, which passes through this rim to the inside. The related local departure from Pauli exclusion principle restriction causes a decay of the internal structure of collective fermionic systems, including the collapse of Fermi spheres in compressed matter. The Fermi sphere decay is associated with the emission of electromagnetic radiation, taking away the energy and entropy of the falling matter without unitarity violation. The spectrum and timing of the related e-m radiation agree with some observed short giant gamma-ray bursts and X-ray components of the luminosity of quasars and of short transients powered by black holes. The release of energy and entropy when passing the photon sphere rim of a black hole significantly modifies the premises of the information paradox at the falling of matter into a black hole.

Graph topology-constrained BILP for optimal PMU placements

In the monitoring and control of power systems, the deployment of Phasor Measurement Units (PMUs) is of paramount importance, yet their high installation costs have limited their widespread application. To address this issue, this paper proposes an innovative method based on graph topology constraints, known as the Graph Topology-constrained Binary Integer Linear Programming (GT-BILP) approach, aimed at achieving the optimal configuration of PMUs. This method not only takes into account cost-effectiveness but also ensures the complete observability of the system. By quantifying the contribution of each node and bus to the system's observability within the network, a novel contribution matrix is constructed. This matrix integrates the dynamic characteristics of network topology and information flow, providing precise decision support for the deployment of PMUs. By combining the matrix with the network's planning model, the GT-BILP model is obtained, which can effectively solve the PMU layout requirements for large power grids. For the special case of zero-injection buses (ZIBs), the Topology Transformation algorithm has been improved, significantly enhancing the solution efficiency and quality. Through simulation experiments on multiple IEEE standard test systems, the effectiveness and superiority of the proposed GT-BILP model have been verified. This research is of significant importance for improving the monitoring and control capabilities of power systems and provides a new perspective for technological advancement in this field.

Automatic reconstruction of semantic façade model of architectural heritage

Façade elements, such as windows, doors, balconies, sculptures, and totems, in architectural heritage images with incomplete structures should be automatically reconstructed for applications in 3D analysis, 3D modeling, virtual tourism, city planning, and the protection and reconstruction of architectural heritage. This study segments façade elements of architectural heritage semantically using YOLOv9. A parameterized expression for the semantic façade model is designed. In addition, the façade layer graph (FLG) and element layer graph (ELG) algorithms are developed based on topological, geometric, and structural constraints to automatically reconstruct the semantic façade model for architectural heritages. The results showed that the average precision (AP) and mean intersection over union (MIoU) achieved using YOLOv9 + FLG-ELG are 86.91% and 85.63%, respectively, on the dataset concerning façade elements of architectural heritages. The AP values obtained from the proposed method are 98.5% on the ECP2011 dataset and 95.3% on the Graz2012 dataset. The YOLOv9 + FLG-ELG method automatically reconstructs regular, irregular, and complex façade layouts with high accuracy and robustness.

Untangling bacterial DNA topoisomerases functions.

Topoisomerases are the main enzymes capable of resolving the topological constraints imposed by DNA transactions such as transcription or replication. All bacteria possess topoisomerases of different types. Although bacteria with circular replicons should encounter similar DNA topology issues, the distribution of topoisomerases varies from one bacterium to another, suggesting polymorphic functioning. Recently, several proteins restricting, enhancing or modifying the activity of topoisomerases were discovered, opening the way to a new area of understanding DNA topology management during the bacterial cell cycle. In this review, we discuss the distribution of topoisomerases across the bacterial phylum and current knowledge on the interplay among the different topoisomerases to maintain topological homeostasis.

TopoPIS: Topology-constrained pipe instance segmentation via adaptive curvature convolution

Precise and fast pipe instance segmentation is a critical component in industrial automatic assembly, facilitating accurate object detection and pose estimation, optimizing and supervising the assembly process. However, this problem is challenging due to topological errors on fine-scale structures caused by the pipes being complex and slender. To address these challenges, we propose a topology-constrained pipe instance segmentation network (TopoPIS) for complex stacking scene to achieve accurate segmentation with topological correctness. To better extract the features of complex and variable morphological pipes, adaptive curvature convolution is introduced to dynamically adapt to the slender pipe structure and capture critical features. To handle topological errors like broken connections, we propose a novel topological constraint loss function based on persistent homology, which greatly improves the topological continuity of the segmentation. Experimental results on real-world and unseen datasets demonstrate that our TopoPIS outperforms other methods regrading segmentation accuracy and topological continuity.

Memory-based consensus control for multi-agent systems with time-varying topology and communication constraints

This paper focuses on the design of event-triggered observer-based heterogeneous memory controllers for leader-following multi-agent systems with time-varying topology. In order to save limited on-board resources, a novel adaptive event-triggered strategy based on the nonlinear transformation law of the estimation error is proposed in this paper, which can effectively reduce some unnecessary data transmission due to small fluctuations after the estimation error converges. Then, a more general topology structure described by an interval type-2 fuzzy model is adopted, which contains both nonlinear time-varying law and uncertain parameters. Taking into account the differences in the interactions between various agents, the heterogeneous fuzzy-dependent controllers with past state measurements are constructed to further improve consensus performance. Moreover, some sufficient conditions are derived to solve the designed observers and controllers while ensuring that the desired consensus of the multi-agent systems can be achieved. Finally, two examples are given to illustrate the superiority and effectiveness of the proposed event-triggered strategy, and also to verify that introducing past state measurements into the controller helps enhance the consensus control performance.

A semi-definite optimization method for maximizing the shared band gap of topological photonic crystals

Topological photonic crystals (PCs) can support robust edge modes to transport electromagnetic energy in an efficient manner. Such edge modes are the eigenmodes of the PDE operator for a joint optical structure formed by connecting together two photonic crystals with distinct topological invariants, and the corresponding eigenfrequencies are located in the shared band gap of two individual photonic crystals. This work is concerned with maximizing the shared band gap of two photonic crystals with different topological features in order to increase the bandwidth of the edge modes. We develop a semi-definite optimization framework for the underlying optimal design problem, which enables efficient update of dielectric functions at each time step while respecting symmetry constraints and, when necessary, the constraints on topological invariants. At each iteration, we perform sensitivity analysis of the band gap function and the topological invariant constraint function to linearize the optimization problem and solve a convex semi-definite programming (SDP) problem efficiently. Numerical examples show that the proposed algorithm is superior in generating optimized optical structures with robust edge modes.

Indoor Scene Intelligent Identification System Based on Spatial Topological Relationship Constraints

Abstract. Indoor scene identification can provide prior environmental information for indoor positioning applications, achieving positioning enhancement. Due to the similarity of wireless signals in adjacent spaces, it can lead to incorrect identification in neighbouring scenario units. To address this problem, this paper first employs a Naive Bayes classifier to train and classify wireless signal strength data from different scenes, constructing a scene identification algorithm. Secondly, a topological relationship adjacency matrix and adjacency list tailored for indoor positioning are constructed, imposing spatial topological constraints to assist scene identification. Finally, an indoor scene intelligent identification system is developed and implemented. The experimental results indicate that the scene identification method based on spatial topological relationship constraints can effectively improve identification accuracy. The overall accuracy for 8 scenario units is 98.2%, and the identification accuracy is increased by 1.1% compared with the original method.

Chain relaxation of carborane segments with tailored chain length at high temperatures

High-performance thermoset polymers have good thermal stability due to their highly crosslinked network, while also represent topological constraints that restrict cooperative segmental motion, making it difficult to relax stresses even at high temperatures. Failure of most thermoset polymers at high temperatures is due to ineffective stress relaxation, which limits the use of thermoset polymers in harsh environments. Herein, we employed a cyclosiloxane hybrid polymer (CHP) containing o-carborane segments with tailored carbon chain length to relieve internal stress. The introduction of o-carborane and lengthening of carbon chain both increased the CHP fractional free volume, and reduced the activation energy required in the later stages of the curing process. The carbon chain changed the conformation to achieve chain relaxation by stretching and rotating the carbon–carbon bonds at high temperatures, which avoided cracking and increased the failure temperature of the CHP. Furthermore, the adhesion strength of the o-carborane modified CHP reached a maximum of 2.15 MPa, surpassing 1.23 MPa of the neat CHP. The o-carborane modified CHP with the longest carbon chain exhibited good stability while supporting 1 kg load for 5 min when subjected to ablation, whereas the neat CHP failed after only 47 s. The o-carborane-modified CHP exhibited enhanced high-temperature properties through chain relaxation to inhibit cracking and in situ generation of boron oxide at high temperatures to protect the resin matrix.

Improved air traffic flow prediction in terminal areas using a multimodal spatial–temporal network for weather-aware (MST-WA) model

Accurately predicting air traffic flow in terminal areas is critical for balancing demand and capacity, particularly under challenging weather conditions. However, the complex interactions between weather patterns and air traffic make reliable predictions difficult. To address this issue, we propose a novel approach called the Multimodal Spatial-Temporal network for Weather-Aware prediction (MST-WA), designed to enhance air traffic flow prediction (ATFP) in terminal areas. Our method begins by constructing a spatial–temporal graph that captures the topology of the terminal area, including airports, routes, and fixes as nodes. A weather-aware module is then introduced, leveraging a Residual Network (ResNet) and attention mechanism to model the deep spatial–temporal correlations in the Weather Avoidance Field (WAF). The proposed model architecture integrates five key branches: arrival flow, departure flow, graph network topology, weather conditions, and flow constraint control, with predictions generated via an attention-based Long Short-Term Memory (LSTM) network. Experimental results using real-world data from Guangzhou Baiyun Airport, China, show that MST-WA outperforms baseline models in ATFP. Furthermore, a case study in convective weather scenarios demonstrates the model’s adaptability and effectiveness. We believe that the proposed model can serve as a valuable tool for air traffic controllers, enhancing decision-making and improving overall air traffic management.

Edge-on anchored discotic liquid crystals in spherical shells: A computational study of the phases and defects.

The self-assembly of liquid crystal droplets and shells represents a captivating frontier in soft matter physics, promising precision engineering of functional materials. In this study, we delve into the phase behavior and investigate defect formation patterns in spherical shell-confined discotic liquid crystals (DLCs) through NpT Monte Carlo simulations. These shells are created by confining DLCs between two spherical surfaces, promoting the same anchoring. In this study, we focus on the case when both surfaces promote edge-on (planar) anchoring. Our study confirms a general result which states that, when a liquid crystal is under strong confinement, the nature of the isotropic-nematic transition changes from first order into continuous. Furthermore, as expected, topological defects at the spherical surface arise due to the topological constraints on the director field. Notably, our investigation reveals a unique topological defect configuration, characterized by the formation of four disclination lines that bridge the inner and external surfaces. Additionally, we observe a mixed ±1/2 wedge-twist disclination line that forms an arch that terminates at the outer surface. This arch decreases its length with decreasing temperature to eventually disappear.

Measuring Topological Constraint Relaxation in Ring-Linear Polymer Blends.

Polymers are an effective test bed for studying topological constraints in condensed matter due to a wide array of synthetically available chain topologies. When linear and ring polymers are blended together, emergent rheological properties are observed as the blend can be more viscous than either of the individual components. This emergent behavior arises since ring-linear blends can form long-lived topological constraints as the linear polymers thread the ring polymers. Here, we demonstrate how the Gauss linking integral can be used to efficiently evaluate the relaxation of topological constraints in ring-linear polymer blends. For majority-linear blends, the relaxation rate of topological constraints depends primarily on reptation of the linear polymers, resulting in the diffusive time τ_{d,R} for rings of length N_{R} blended with linear chains of length N_{l} to scale as τ_{d,R}∼N_{R}^{2}N_{L}^{3.4}.

Sec18 side-loading is essential for universal SNARE recycling across cellular contexts.

SNARE proteins drive membrane fusion as their core domains zipper into a parallel four-helix bundle1,2. After fusion, these bundles are disassembled by the AAA+ protein Sec18/NSF and its adaptor Sec17/ α-SNAP3,4 to make them available for subsequent rounds of membrane fusion. SNARE domains are often flanked by C-terminal transmembrane or N-terminal domains5. Previous structures of the NSF-α-SNAP-SNARE complex revealed SNARE domain threaded through the D1 ATPase ring6, posing a topological constraint as SNARE transmembrane domains would prevent complete substrate threading as suggested for other AAA+ systems7. Here, in vivo mass-spectrometry reveals N-terminal SNARE domain interactions with Sec18, exacerbating this topological issue. Cryo-EM structures of a yeast SNARE complex, Sec18, and Sec17 in a non-hydrolyzing condition shows SNARE Sso1 threaded through the D1 and D2 ATPase rings of Sec18, with its folded, N-terminal Habc domain interacting with the D2 ring. This domain does not unfold during Sec18/NSF activity. Cryo-EM structures under hydrolyzing conditions revealed substrate-released and substrate-free states of Sec18 with a coordinated opening in the side of the ATPase rings. Thus, Sec18/NSF operates by substrate side-loading and unloading topologically constrained SNARE substrates.

UCAN: U-shaped context aggregation network for thin crack segmentation under topological constraints

PurposeThin cracks on the surface, such as those found in nuclear power plant concrete structures, are difficult to identify because they tend to be thin. This paper aims to design a novel segmentation network, called U-shaped contextual aggregation network (UCAN), for better recognition of weak cracks.Design/methodology/approachUCAN uses dilated convolutional layers with exponentially changing dilation rates to extract additional contextual features of thin cracks while preserving resolution. Furthermore, this paper has developed a topology-based loss function, called ℓcl Dice, which enhances the crack segmentation’s connectivity.FindingsThis paper generated five data sets with varying crack widths to evaluate the performance of multiple algorithms. The results show that the UCAN network proposed in this study achieves the highest F1-Score on thinner cracks. Additionally, training the UCAN network with the ℓcl Dice improves the F1-Scores compared to using the cross-entropy function alone. These findings demonstrate the effectiveness of the UCAN network and the value of incorporating the ℓcl Dice in crack segmentation tasks.Originality/valueIn this paper, an exponentially dilated convolutional layer is constructed to replace the commonly used pooling layer to improve the model receptive field. To address the challenge of preserving fracture connectivity segmentation, this paper introduces ℓcl Dice. This design enables UCAN to extract more contextual features while maintaining resolution, thus improving the crack segmentation performance. The proposed method is evaluated using extensive experiments where the results demonstrate the effectiveness of the algorithm.

Innovative Tools for DNA Topology Probing in Human Cells Reveal a Build-Up of Positive Supercoils Following Replication Stress at Telomeres and at the FRA3B Fragile Site.

Linear unconstrained DNA cannot harbor supercoils since these supercoils can diffuse and be eliminated by free rotation of the DNA strands at the end of the molecule. Mammalian telomeres, despite constituting the ends of linear chromosomes, can hold supercoils and be subjected to topological stress. While negative supercoiling was previously observed, thus proving the existence of telomeric topological constraints, positive supercoils were never probed due to the lack of an appropriate tool. Indeed, the few tools available currently could only investigate unwound (Trioxsalen) or overwound (GapR) DNA topology (variations in twist) but not the variations in writhe (supercoils and plectonemes). To address this question, we have designed innovative tools aimed at analyzing both positive and negative DNA writhe in cells. Using them, we could observe the build-up of positive supercoils following replication stress and inhibition of Topoisomerase 2 on telomeres. TRF2 depletion caused both telomere relaxation and an increase in positive supercoils while the inhibition of Histone Deacetylase I and II by TSA only caused telomere relaxation. Moving outside telomeres, we also observed a build-up of positive supercoils on the FRA3B fragile site following replication stress, suggesting a topological model of DNA fragility for this site.

Constrained motion of self-propelling eccentric disks linked by a spring.

It has been supposed that the interplay of elasticity and activity plays a key role in triggering the non-equilibrium behaviors in biological systems. However, the experimental model system is missing to investigate the spatiotemporally dynamical phenomena. Here, a model system of an active chain, where active eccentric-disks are linked by a spring, is designed to study the interplay of activity, elasticity, and friction. Individual active chain exhibits longitudinal and transverse motions; however, it starts to self-rotate when pinning one end and self-beat when clamping one end. In addition, our eccentric-disk model can qualitatively reproduce such behaviors and explain the unusual self-rotation of the first disk around its geometric center. Furthermore, the structure and dynamics of long chains were studied via simulations without steric interactions. It was found that a hairpin conformation emerges in free motion, while in the constrained motions, the rotational and beating frequencies scale with the flexure number (the ratio of self-propelling force to bending rigidity), χ, as ∼(χ)4/3. Scaling analysis suggests that it results from the balance between activity and energy dissipation. Our findings show that topological constraints play a vital role in non-equilibrium synergy behaviors.

Fluidification of entangled polymers by loop extrusion

Loop extrusion is one of the main processes shaping chromosome organization across the cell cycle, yet its role in regulating deoxyribonucleic acid (DNA) entanglement and nucleoplasm viscoelasticity remains overlooked. We simulate entangled solutions of linear polymers under the action of generic loop extruding factors (LEFs) with a model that fully accounts for topological constraints and LEF-DNA uncrossability. We discover that extrusion drives the formation of bottlebrushlike structures which significantly lower the entanglement and effective viscosity of the system through an active fluidification mechanism. Interestingly, this fluidification displays an optimum at one LEF every 300–3000 base pairs. In marked contrast with entangled linear chains, the viscosity of extruded chains scales linearly with polymer length, yielding up to 1000-fold fluidification in our system. Our results illuminate how intrachain loop extrusion contributes to actively modulate genome entanglement and viscoelasticity . Published by the American Physical Society 2024

Myotube formation on micropatterns guiding by centripetal cellular motility and crowding

The physical microenvironment, including substrate rigidity and topology, impacts myoblast differentiation and myotube maturation. However, the interplay effect and physical mechanism of mechanical stimuli on myotube formation is poorly understood. In this study, we utilized elastic substrates, microcontact patterning technique, and particle image velocimetry to investigate the effect of substrate rigidity and topological constraints on myoblast behaviors. Our findings suggested the interplay of substrate stiffness and cellular confinement improved the myotube formation by inducing centripetal cellular motility. These results shed light on the impact of the topological substrate on myoblast differentiation and emphasize the critical role of asymmetrical cell motility during this process, which is highly correlated with cell movement and crowding. Our research provides insights into the intricate interplay between substrate properties, cell motility, and myotube formation during myogenesis. Understanding these mechanisms could trigger tissue engineering strategies and therapies to enhance muscle regeneration and function.

The neuroanatomical organization of the hypothalamus is driven by spatial and topological efficiency.

The hypothalamus in the mammalian brain is responsible for regulating functions associated with survival and reproduction representing a complex set of highly interconnected, yet anatomically and functionally distinct, sub-regions. It remains unclear what factors drive the spatial organization of sub-regions within the hypothalamus. One potential factor may be structural connectivity of the network that promotes efficient function with well-connected sub-regions placed closer together geometrically, i.e., the strongest axonal signal transferred through the shortest geometrical distance. To empirically test for such efficiency, we use hypothalamic data derived from the Allen Mouse Brain Connectivity Atlas, which provides a structural connectivity map of mouse brain regions derived from a series of viral tracing experiments. Using both cost function minimization and comparison with a weighted, sphere-packing ensemble, we demonstrate that the sum of the distances between hypothalamic sub-regions are not close to the minimum possible distance, consistent with prior whole brain studies. However, if such distances are weighted by the inverse of the magnitude of the connectivity, their sum is among the lowest possible values. Specifically, the hypothalamus appears within the top 94th percentile of neural efficiencies of randomly packed configurations and within one standard deviation of the median efficiency when packings are optimized for maximal neural efficiency. Our results, therefore, indicate that a combination of geometrical and topological constraints help govern the structure of the hypothalamus.