Topological Constraints Research Articles

Structural basis of DNA crossover capture by Escherichia coli DNA gyrase.

DNA supercoiling must be precisely regulated by topoisomerases to prevent DNA entanglement. The interaction of type IIA DNA topoisomerases with two DNA molecules, enabling the transport of one duplex through the transient double-stranded break of the other, remains elusive owing to structures derived solely from single linear duplex DNAs lacking topological constraints. Using cryo-electron microscopy, we solved the structure of Escherichia coli DNA gyrase bound to a negatively supercoiled minicircle DNA. We show how DNA gyrase captures a DNA crossover, revealing both conserved molecular grooves that accommodate the DNA helices. Together with molecular tweezer experiments, the structure shows that the DNA crossover is of positive chirality, reconciling the binding step of gyrase-mediated DNA relaxation and supercoiling in a single structure.

Topological constraint model of modified telluro‐vanadate glasses

AbstractTopological constraint theory has emerged as a rapid, predictive method to quantify the relationship between structural rigidity and glass properties. Understanding the structure of telluro‐vanadate (TeO2–V2O5) glasses has remained difficult owing to their complex mixture of structural units. Here, we propose a topological model that accurately captures the glass structure and can be used to predict properties such as glass transition temperature and hardness. The experimentally obtained properties are in agreement with predicted properties by the model suggesting that this simplified structural model accurately describes the V2O5–TeO2 structure.

Hydrogen Bonding-Induced Alleviation of Topological Constraints in Acrylic Polymers Mixed with Small Molecules

Hydrogen Bonding-Induced Alleviation of Topological Constraints in Acrylic Polymers Mixed with Small Molecules

Origin of Melt Memory Effects in Poly(ethylene oxide): The Crucial Role of Entanglements.

The melt memory effect on crystallization is an intriguing phenomenon displayed by semicrystalline polymers, as opposed to low molar mass molecules. It concerns the effect of melt temperature on nucleation upon recrystallization. Typically, polymer crystals must be considerably superheated to erase the effect of previous morphology on the subsequent crystallization, avoiding an acceleration of the process. Despite being known for decades, its origin is still not fully understood. Investigating model poly(ethylene oxide) covering a wide range of molar mass, it is demonstrated that melt memory originates from topological constraints among the chains, i.e., entanglements, for PEO in which weak intermolecular interactions are present due to the ether groups. In fact, no memory is observed for samples below the critical molar mass for the formation of entanglements (about 1 kg mol-1). The increase in molar mass raises the number of entanglements and induces the formation of folded chains crystals, both factors leading to a topologically complex amorphous phase, enhancing the melt memory effect. The molecular origin of the melt memory effect in polymers with weak intermolecular interactions is thus ascribed to a slower isotropization in the melt of the chain segments originally contained in the crystals, due to the presence of entanglements among the chains. This study defines the distinction between small molecules and polymers from the point of view of melt memory.

Salient object detection via multi-grained refinement polygon topology positive feedback

Despite significant progress in current salient object detection (SOD) tasks, they are limited by overlapping regions, broken connections, voids and neglecting explicit exploration of background regions. In this paper, we propose a multi-grained refinement polygonal topology network (MPT) that explores two important components of background mining information and the impact of topological segmentation errors. (1) Unlike existing models that focus on inter-image relationships, we introduce a multi-grained refinement module to discriminate between saliency objects and background information, and introduce inter-image relationships into the pixel-by-pixel segmentation features to enhance the discrimination of segmentation features, and this Multi-grained refinement is the basis for mining saliency objects. (2) Based on the multi-grained refinement features, we introduce a polygonal topology-aware module and add topological constraints as penalty terms to regularize the focus loss to effectively resolve topological errors to enhance the quality of the performance of salient object detection. Meanwhile, we introduce a measurements-based on positive feedback model to integrate the decision fusion of multi-model perception results to obtain higher accuracy of saliency prediction while ensuring that the prediction results will not deteriorate. Extensive experiments on six benchmark and extended datasets demonstrate that our proposed MPTNet exhibits excellent performance both qualitatively and quantitatively and outperforms state-of-the-art saliency detectors.

Optimizing Truss Dynamics: A Multi-Objective Approach to Modify Natural Frequencies and Mode Shapes with Geometric Constraints

This article presents a comprehensive optimization approach to dynamically enhance a truss structure. The optimization problem addresses the systematic modification of the truss dynamics, focusing on achieving a specific set of natural frequencies without compromising the geometrical integrity. The truss structure is redesigned through the exploration of diverse cost functions, considering both minimization and maximization strategies for targeted subsets of natural frequencies and mode shape elements but also preserving essential geometric properties including dimensional intervals, symmetry conditions, and adherence to topological constraints. A dual-objective optimization paradigm is adopted; concurrently pursuing the minimization and maximization objectives together with various constraints are introduced to enforce geometric limits on each truss member, providing a holistic solution for effectively tailoring the dynamic characteristics of the truss structure. This study represents a nuanced understanding of dynamic optimization in truss design. The article's main contribution is improving balance between optimizing the dynamic requirements of the truss structure and considering the essential geometry constraints that ensures its practical utility. By doing so, the research not only advances the understanding of truss dynamics but also provides a framework for approaching similar optimization challenges in mechanical engineering.

Walkability defined neighborhoods for sustainable cities

The concept of 15-min cities has recently received a lot of attention in recent research. However, the clear definition of a measurement for this concept has not yet been done at a neighborhood and city level across all continents and encompassing topological constraints. Yielding the question if 15 min is even the right indicator. In this study, we propose a method for determining how closely a city adheres to this concept using Open Data. We also propose an optimized method for generating communities that will assist us in discriminating walkability needs and validating generated communities. We discover that the number of communities meeting the 15-min target is inversely related to population growth and city area.

Curvature conservation and conduction modulation for symmetric charged ferroelectric domain walls

Curvature conservation is a common feature for the physical properties with topological constraints, from the macroscopic cosmic string loops to the microscopic quantized vortex rings in the superfluid. Interestingly, ferroelectric domain-wall curvature is important to determine its conduction, which is the key parameter for designing domain-wall nanoelectronic devices. Here, we demonstrate the curvature conservation of the charged domain walls confined in ferroelectric topological structures with specific domain symmetry by combining piezoelectric force microscopy, conducting atomic force microscopy, and phase-field simulations. Significantly, the intrinsic conductivity of the charged domain walls exhibits an inverse functional relationship with the local domain-wall curvature in the ferroelectric BiFeO3 nano-islands, which can also be precisely and continuously modulated by applying an electric field. This work provides us with an insightful understanding of the conduction mechanism of charged domain walls confined in ferroelectric topological structures with a high degree of spatial symmetry, which paves the way for the application of charged domain walls as flexible conducting channels with continuously changing resistance states to be used for ferroelectric domain-wall memristors.

Hartle-Hawking state and its factorization in 3d gravity

We study 3d quantum gravity with two asymptotically anti-de Sitter regions, in particular, using its relation with coupled Alekseev-Shatashvili theories and Liouville theory. Expressions for the Hartle-Hawking state, thermal 2n-point functions, torus wormhole correlators and Wheeler-DeWitt wavefunctions in different bases are obtained using the ZZ boundary states in Liouville theory. Exact results in 2d Jackiw-Teitelboim (JT) gravity are uplifted to 3d gravity, with two copies of Liouville theory in 3d gravity playing a similar role as Schwarzian theory in JT gravity. The connection between 3d gravity and the Liouville ZZ boundary states are manifested by viewing BTZ black holes as Maldacena-Maoz wormholes, with the two wormhole boundaries glued along the ZZ boundaries. In this work, we also study the factorization problem of the Hartle-Hawking state in 3d gravity. With the relevant defect operator that imposes the necessary topological constraint for contractibility, the trace formula in gravity is modified in computing the entanglement entropy. This trace matches with the one from von Neumann algebra considerations, further reproducing the Bekenstein-Hawking area formula from entanglement entropy. Lastly, we propose a calculation for off-shell geometrical quantities that are responsible for the ramp behavior in the late time two-point functions, which follows from the understanding of the Liouville FZZT boundary states in the context of 3d gravity, and the identification between Verlinde loop operators in Liouville theory and “baby universe” operators in 3d gravity.

Optimization optical and radiation shielding properties via controlling the Hirshfeld topological constraints: A case study of carbonate-based crystals

This work explores the potential of carbonate-based ceramics (CBC) as materials for optical and radiation shielding applications. The results reveal the distinctive behavior of various CBC materials in shielding γ-rays. At an intermediate energy of E = 0.5 MeV, SiO2 has a MAC value of 0.087, whereas the MAC values for the CBCs are as follows: (CMs, MAC (g/cm2)): (CaCO3, 0.088), (MgCO3, 0.087), (SrCO3, 0.086), (BaCO3, 0.096), (ZnCO3, 0.086), (CdCO3, 0.091), and (PbCO3, 0.145). Also, the effective atomic numbers (Zeff) found to range from 11.03 to 78.82. These values surpass those of silicon dioxide (SiO2), highlighting the superior γ-ray attenuation capabilities of CBC. The work also delves also into the optical properties of CBC materials, highlighting the interplay between density (2.61 < ρ < 6.72 g/cm3), band gap energy (2.680<Eg < 5.050 eV), and refractive index (1.99254 < n < 2.48905). Furthermore, the study delves into the impact of charge density within Hirshfeld voids on these properties, revealing that as the interatomic interactions increase: 2.1% < O⋯C<26.8%, 9.3% < O⋯O<26.3%, or 63.3% < O … A2⁺<86.4% (A = Ca, Mg, Sr, Ba, Zn, Cd) due to higher charge density, thus the LAC and n values may tune among the studied CBC. The fine-tuning of topological and charge density distributions within the crystal's voids offers a promising avenue to optimize these materials for enhanced radiation shielding effectiveness or optical properties. This interplay between crystal structure, composition, charge distribution, Hirshfeld topological constraints as key factors in determining their radiation attenuation and optical capabilities was explored.

Applicability of Kroon network theory for biaxial mechanics in rubber through multiscale approach

In this paper, we address the problem of the multiscale prediction of the multiaxial hyperelastic behavior of rubber. Our goal is to test the predictive capabilities of a hyperelastic model grounded in the principles of continuum mechanics, bridging the gap between continuum-level mechanics and molecular-level descriptions. This constitutive model posits that macroscopic behavior results from the non-affine deformation of the molecular network, influenced by topological constraints. We employ molecular dynamics methods to measure the mechanical behavior of a rubber network structure under various deformation modes. The study includes an analysis of the molecular network deformation during the straining process, shedding light on the deformation mechanisms at the molecular level. By examining how the total network stress in our specifically designed molecular structure responds to biaxial strain ratios, we are able to assess the effectiveness of the hyperelastic constitutive model.

Line simplification with sidedness relationship consistency using the constrained total least squares method

AbstractThe simplification of lines plays a crucial role in map generalization and multiscale representation; however, addressing inconsistent sidedness relationships between the simplified lines and their neighboring features poses a persistent challenge. In order to preserve correct and consistent sidedness relationships following simplification, this study introduces a novel line simplification method. This method incorporates topological constraints pertaining to left–right sidedness relationships, formulated as an optimization procedure based on the proposed partial total least squares method with constraints. The primary objective is to minimize the positional difference between the line features before and after simplification, with the sidedness relationship represented as an inequality constraint. Moreover, an optimization algorithm is derived to address the simplification problem effectively while adhering to the specified constraints. The proposed method is then applied to simplify the lines within three distinct datasets. Experimental results validate the efficacy of the proposed method in maintaining sidedness consistency across all tested datasets. In comparison to the Douglas–Peucker (DP) method, the proposed method exhibits minimal vertical displacement variance in the line feature points post‐simplification. Additionally, it achieves a smaller overall positional difference between the simplified and original lines compared to the DP method. These findings underscore the superior performance of the proposed method in maintaining sidedness relationships and minimizing positional differences during the line simplification process.

Study of the matrix–particle interactions of polymer nanocomposites in the low‐frequency regime

AbstractIn this study, the dynamic moduli, in a wide frequency scale, of two series of polymer nanocomposites were qualitatively discussed. The dynamic mechanical analysis experimental results of polylactic acid (PLA)/silica nanocomposites, as well as PLA/graphene oxide‐carbon nanotubes hybrid nanocomposites, were employed. The study has been focused on the low‐frequency regime, estimating the terminal incline of the storage and loss modulus. In addition, the relative position of the two dynamic moduli was examined and results about the nanofiller's dispersion quality, as well as their interaction with the matrix were extracted. The consequence of nanofiller kind, loading, and distribution quality on the mechanical enhancement was thoroughly studied. In addition, the storage modulus master curves could be simulated by a model from the literature, considering the topological constraints of an entangled polymer reinforced by nanoparticles. It was shown that by adopting the linear contribution of the free and adsorbed chains to the relaxation function, the details of the master curves could be captured in the entire frequency range, quite effectively. The estimated model parameter values confirmed the analysis of the matrix–particle interactions.Highlights The SiO2 size effect on the terminal zone slope of the dynamic moduli. Successful description of the dynamic moduli by the tube reptation concept. Analysis of the physical meaning of the model parameter values. Relation between SiO2 dispersion quality and molecular motion restriction. Matrix‐particle interactions is the governing mechanism of enhancement.

A deep pedestrian trajectory generator for complex indoor environments

AbstractPedestrian trajectory data, which can be used to mine pedestrian motion patterns or to model pedestrian dynamics, is crucial for indoor location‐based service studies and applications. However, researchers are faced with the challenges of data shortage and privacy restrictions when using pedestrian trajectory data. We present an Indoor Pedestrian Trajectory Generator (IPTG), which is a novel deep learning model to synthesize pedestrian trajectory data. IPTG first produces feature sequences that encode the spatial–temporal and semantic features of the walking process and then interpolates them into complete trajectories using A* and perturbation algorithms. IPTG has specially designed loss functions that preserve topological constraints and semantic characteristics. Incorporating the prior knowledge of environment constraints and pedestrian walking patterns, the IPTG model is capable of generating topologically and logically sound indoor pedestrian trajectories. We evaluated the synthesized trajectories based on multiple metrics and examined the generated trajectories qualitatively. The results show that IPTG outperforms several baselines, demonstrating its ability to generate semantically meaningful and spatiotemporally coherent trajectories.

Co-Operatively Increasing Smoothing and Mapping Based on Switching Function

Collaborative localization is a technique that utilizes the exchange of information between multiple sensors or devices to improve localization accuracy and robustness. It has a wide range of applications in autonomous driving and unmanned aerial vehicles (UAVs). In the field of UAVs, collaborative localization can help UAVs perform autonomous navigation and mission execution in complex environments. However, when GNSS is not available, it becomes challenging to position the UAV swarm relative to each other. This is because the swarm loses its perception and constraint of the position relationship between each member. Consequently, the swarm faces the problem of the serious drift of relative accuracy for an extended period. Furthermore, when the environment is faced with complex obstruction challenges or a camera with low texture scenes, noise can make it more difficult to solve the relative position relationship between drones, and a single UAV may lose positioning capability. To solve these specific problems, this paper studies a swarm co-operative localization method in a GNSS-denied environment with loud noise interference. In this paper, we proposed a method that utilizes a distributed scheme based on an incremental smoothing and mapping (iSAM) algorithm for state estimation. It incorporates new anchor-free topological constraints to prevent positioning failures and significantly improve the system’s robustness. Additionally, a new switching function is applied in front of each factor of the loss function, which adjusts the switches in real time in response to the input information to improve observably the accuracy of the system. A novel co-operative incremental smoothing and mapping (CI-SAM) method is proposed and the method does not require a complete relative position measurement, which reduces the need for vehicle measurement equipment configuration. The effectiveness of the method is verified by simulation.

Discrete variable topology optimization for maximizing single/multiple natural frequencies and frequency gaps considering the topological constraint

AbstractFinding optimized structural topology design for maximizing natural frequencies and frequency gaps of continuum structures is crucial for engineering applications. However, two significant numerical issues must be addressed: non‐smoothness caused by multiple frequencies and Artificial Localized Rigid Motion (ALRM) modes due to the violation of the topological constraint related to isolated islands and point‐connections. The above two issues are solved by employing the discrete variable topology optimization method based on Sequential Approximate Integer Programming (SAIP). First, the directional differentiability and multiple frequencies preservation constraints are formulated as the linear integer constraints. And then, the integer programming with these linear integer constraints is established and solved by the discrete variable linear or quadratic programming solver with multi‐constraint Canonical Relaxation Algorithm (CRA). We also prove that the popular Average Modal Frequencies (AMF) strategy, like the Kreisselmeier‐Steinhauser (KS) function, cannot rigorously tackle this non‐smoothness caused by multiple frequencies. Furthermore, to eliminate the ALRM modes and concentrate on the real structural global modes, the burning method is employed to impose the topological constraint of the first Betti number that represents the number of isolated islands and point‐connections. Numerical examples, including 2D and 3D, two‐fold and three‐fold multiple frequencies, natural frequencies and frequency gaps, are presented to show the effectiveness of the proposed method.

Steric repulsion introduced by loop constraints modulates the microphase separation of chromatins.

Within the confines of a densely populated cell nucleus, chromatin undergoes intricate folding, forming loops, domains, and compartments under the governance of topological constraints and phase separation. This coordinated process inevitably introduces interference between different folding strategies. In this study, we model interphase chromatins as block copolymers with hetero-hierarchical loops within a confined system. Employing dissipative particle dynamics simulations and scaling analysis, we aim to explain how the structure and distribution of loop domains modulate the microphase separation of chromatins. Our results highlight the correlation between the microphase separation of the copolymer and the length, heterogeneity, and hierarchically nested levels of the loop domains. This correlation arises from steric repulsion intrinsic to loop domains. The steric repulsion induces variations in chain stiffness (including local orientation correlations and the persistence length), thereby influencing the degree of phase separation. Through simulations of block copolymers with distinct groups of hetero-hierarchical loop anchors, we successfully reproduce changes in phase separation across diverse cell lines, under fixed interaction parameters. These findings, in qualitative alignment with Hi-C data, suggest that the variations of loop constraints alone possess the capacity to regulate higher-order structures and the gene expressions of interphase chromatins.

Segmentation of Low-Light Optical Coherence Tomography Angiography Images under the Constraints of Vascular Network Topology.

Optical coherence tomography angiography (OCTA) offers critical insights into the retinal vascular system, yet its full potential is hindered by challenges in precise image segmentation. Current methodologies struggle with imaging artifacts and clarity issues, particularly under low-light conditions and when using various high-speed CMOS sensors. These challenges are particularly pronounced when diagnosing and classifying diseases such as branch vein occlusion (BVO). To address these issues, we have developed a novel network based on topological structure generation, which transitions from superficial to deep retinal layers to enhance OCTA segmentation accuracy. Our approach not only demonstrates improved performance through qualitative visual comparisons and quantitative metric analyses but also effectively mitigates artifacts caused by low-light OCTA, resulting in reduced noise and enhanced clarity of the images. Furthermore, our system introduces a structured methodology for classifying BVO diseases, bridging a critical gap in this field. The primary aim of these advancements is to elevate the quality of OCTA images and bolster the reliability of their segmentation. Initial evaluations suggest that our method holds promise for establishing robust, fine-grained standards in OCTA vascular segmentation and analysis.

The Role of Lanthanum Stearate on Strain-Induced Crystallization and the Mechanical Properties of Whole Field Latex Rubber.

Natural rubber (NR) is extensively utilized in numerous industries, such as aerospace, military, and transportation, because of its exceptional elasticity and all-around mechanical qualities. However, commercial NR made using various techniques typically has distinct mechanical characteristics. For instance, whole field latex rubber (SCR-WF) cured with accelerator 2-Mercaptobenzothiazole exhibits poor mechanical properties. This work attempts to enhance the mechanical property of SCR-WF via the addition of lanthanum stearate (LaSt). The influence of LaSt on strain-induced crystallization (SIC) and the mechanical properties of SCR-WF were investigated. The results of crosslinking density measured by the equilibrium swelling method demonstrate that the presence of LaSt significantly increases the crosslinking density of SCR-WF with lower loading of LaSt. The results of the mechanical properties show that the introduction of LaSt can enhance the tensile strength and fracture toughness of SCR-WF. To reveal the mechanism of LaSt improving the mechanical properties of SCR-WF, synchrotron radiation wide-angle X-ray diffraction (WAXD) experiments were used to investigate the SIC behaviors of SCR-WF. We found that the LaSt leads to higher crystallinity of SIC for the strain higher than 3.5. The tube model indicates the contribution of LaSt in both crosslinking and topological constraints. This work may provide an instruction for developing SCR-WF with superior mechanical properties.

Self–dual solutions of a field theory model of two linked rings

In this work the connection established in [7,8] between a model of two linked polymers rings with fixed Gaussian linking number forming a 4-plat and the statistical mechanics of non-relativistic anyon particles is explored. The excluded volume interactions have been switched off and only the interactions of entropic origin arising from the topological constraints are considered. An interpretation from the polymer point of view of the field equations that minimize the energy of the model in the limit in which one of the spatial dimensions of the 4-plat becomes very large is provided. It is shown that the self-dual contributions are responsible for the long-range interactions that are necessary for preserving the global topological properties of the system during the thermal fluctuations. The non self-dual part is also related to the topological constraints, and takes into account the local interactions acting on the monomers in order to prevent the breaking of the polymer lines. It turns out that the energy landscape of the two linked rings is quite complex. Assuming as a rough approximation that the monomer densities of half of the 4-plat are constant, at least two points of energy minimum are found. Classes of non-trivial self-dual solutions of the self-dual field equations are derived. One of these classes is characterized by densities of monomers that are the squared modulus of holomorphic functions. The second class is obtained under some assumptions that allow to reduce the self-dual equations to an analog of the Gouy-Chapman equation for the charge distribution of ions in a double layer capacitor. In the present case, the spatial distribution of the electric potential of the ions is replaced by the spatial distribution of the fictitious magnetic fields associated with the presence of the topological constraints. In the limit in which two of the spatial dimensions are large in comparison with the third one, we provide exact formulas for the conformations of the monomer densities of the 4-plat by using the elliptic, hyperbolic and trigonometric solutions of the sinh-Gordon and cosh-Gordon equations which have been used for instance in the construction of classical string solutions in AdS3 and dS3 [9].