Topological Properties Research Articles

Unraveling the mesoscale organization induced by network-driven processes

Complex systems are characterized by emergent patterns created by the nontrivial interplay between dynamical processes and the networks of interactions on which these processes unfold. Topological or dynamical descriptors alone are not enough to fully embrace this interplay in all its complexity, and many times one has to resort to dynamics-specific approaches that limit a comprehension of general principles. To address this challenge, we employ a metric-that we name Jacobian distance-which captures the spatiotemporal spreading of perturbations, enabling us to uncover the latent geometry inherent in network-driven processes. We compute the Jacobian distance for a broad set of nonlinear dynamical models on synthetic and real-world networks of high interest for applications from biological to ecological and social contexts. We show, analytically and computationally, that the process-driven latent geometry of a complex network is sensitive to both the specific features of the dynamics and the topological properties of the network. This translates into potential mismatches between the functional and the topological mesoscale organization, which we explain by means of the spectrum of the Jacobian matrix. Finally, we demonstrate that the Jacobian distance offers a clear advantage with respect to traditional methods when studying human brain networks. In particular, we show that it outperforms classical network communication models in explaining functional communities from structural data, therefore highlighting its potential in linking structure and function in the brain.

Maldistributed sequences in metric spaces

Let a kind of measure μ be given on the set of all positive integers N. By a μ-maldistributed sequence in a metric space (X,d) we mean any sequence possessing μ-extremely many points in each nonempty open subspace of (X,d). Let s(X) denote the metric space of all sequences in (X,d) endowed with the Fréchet metric. In this paper we study topological properties of the set of all maldistributed sequences in X as a subspace s(X). We show that if (X,d) is separable then this set is residual for a large class of commonly used measures μ on N.

Flexibility, toughness, and load bearing of 3D-printed chiral kerf composite structures

Chiral kerf structures are formed by arranging chiral and coiled unit cells which allows for multi-dimensional and multi-scale shape configurations under mechanical loadings. In this study, we investigate how the mechanical properties of materials and microstructural topologies interact to control the flexibility, toughness, and load bearing of 3D-printed chiral kerf structures. We explore chiral kerf structures with two different kerf patterns, i.e., square and hexagon, and three coiling densities. We consider three materials, namely brittle Polylactic Acid (PLA), compliant thermoplastic polyurethane (TPU), and a ductile composite made by alternating PLA and TPU, referred to as a programmable composite. The chiral kerf structures undergo two deformation mechanisms when subjected to mechanical loadings. The first one results from reconfigurations of kerf cells such as uncoiling, rotation of cells, and cell packing, and the second mechanism arises from nonlinear and inelastic material responses. The use of brittle material limits cell reconfigurations before material failure, reducing the overall flexibility and toughness of kerf structures. While the compliant material enables full cell reconfigurations, it results in low load bearing. The use of PLA:TPU composite allows for cell reconfigurations and inelastic material response, enhancing flexibility and toughness while maintaining a relatively high load bearing. We demonstrate that stress distribution in kerf structures can be controlled by using multiple materials or coil densities. This strategy can delay failure and improve the toughness and load-bearing capabilities of kerf structures.

Composite photonic lattice with a broad channel to sustain topological interface states

In the field of topological photonics, one goal is to seek specialized structures with topological protection that can support the stable propagation of light. We have designed a topological configuration featuring a broad channel to sustain edge or interface states. The topological properties are elucidated by analyzing the energy spectrum, eigenstates, and winding numbers. Furthermore, the propagation characteristics of light within our structure are examined through the computation of intensities derived from the coupled mode equations. Our findings reveal that the structure is capable of confining light to the central region, facilitating stable and robust propagation for large-sized beams. Additionally, simulations conducted using commercial software have substantiated the theoretical analysis. Our finding may have significant implications for the modulation of structured light and the development of photonic devices with wide channel capabilities.

GeneSPIDER2: large scale GRN simulation and benchmarking with perturbed single-cell data.

Single-cell data is increasingly used for gene regulatory network (GRN) inference, and benchmarks for this have been developed based on simulated data. However, existing single-cell simulators cannot model the effects of gene perturbations. A further challenge lies in generating large-scale GRNs that often struggle with computational and stability issues. We present GeneSPIDER2, an update of the GeneSPIDER MATLAB toolbox for GRN benchmarking, inference, and analysis. Several software modules have improved capabilities and performance, and new functionalities have been added. A major improvement is the ability to generate large GRNs with biologically realistic topological properties in terms of scale-free degree distribution and modularity. Another major addition is a simulation of single-cell data, which is becoming increasingly popular as input for GRN inference. Specifically, we introduced the unique feature to generate single-cell data based on genetic perturbations. Finally, the simulated single-cell data was compared to real single-cell Perturb-seq data from two cell lines, showing that the synthetic and real data exhibit similar properties.

Data-driven topology optimization using a multitask conditional variational autoencoder with persistent homology

Topology optimization is crucial for the mechanical design of vehicles and aircraft, allowing changes in the shape of structures and the placement of features. Recent advances have integrated deep generative models, particularly convolutional neural networks, to streamline this process.to streamline this process. However, these models struggle to preserve subtle structural features. To overcome these limitations, this study introduced a generative model adept at identifying the topological features inherent in real shapes, such as connectivity and holes, to enhance the effectiveness of topology optimization. A conditional variational autoencoder (CVAE) was employed to predict both the shape and compliance simultaneously. This model, CVAE with persistent homology, generates optimal material distributions by considering topological properties. The learning process introduced a term that minimizes the difference in topological features between true and reconstructed shapes. The proposed model can generate optimal material distributions by considering topological properties, eliminating the need for iterative calculations. This approach was validated using two numerical examples. The accuracy of the generated material distributions was compared with conventional methods using the mean-squared error. An average improvement in accuracy of approximately 36.85% was observed across the two results. This confirms that shapes considering compliance and connectivity can be accurately predicted.

Common functional mechanisms underlying dynamic brain network changes across five general anesthetics: A rat fMRI study.

Reversible loss of consciousness is the primary therapeutic endpoint of general anesthesia; however, the drug-invariant mechanisms underlying anesthetic-induced unconsciousness are still unclear. This study aimed to investigate the static, dynamic, topological and organizational changes in functional brain network induced by five clinically-used general anesthetics in the rat brain. Male Sprague-Dawley rats (n = 57) were randomly allocated to received propofol, isoflurane, ketamine, dexmedetomidine, or combined isoflurane plus dexmedetomidine anesthesia. Resting-state functional magnetic resonance images were acquired under general anesthesia and analyzed for changes in dynamic functional brain networks compared to the awake state. Different general anesthetics induced distinct patterns of functional connectivity inhibition within brain-wide networks, resulting in multi-level network reorganization primarily by impairing the functional connectivity of cortico-subcortical networks as well as by reducing information transmission capacity, intrinsic connectivity, and network architecture stability of subcortical regions. Conversely, functional connectivity and topological properties were preserved within cortico-cortical networks, albeit with fewer dynamic fluctuations under general anesthesia. Our findings highlighted the effects of different general anesthetics on functional brain network reorganization, which might shed light on the drug-invariant mechanism of anesthetic-induced unconsciousness.

On \(\beta-\gamma\)-connectedness and \( \beta_{(\gamma,\delta)}\)-continuous functions

The aim of the paper is to introduce the notion of \(\beta-\gamma\)-separated sets and study their properties in topological spaces,then we introduce the notation of \(\beta-\gamma\)-connected and \(\beta-\gamma\)-disconnectedness. Also, \(\beta-\gamma\)-disconnected spaces are defined through \(\beta-\gamma\)-separated sets and their topological properties are studied. The characterizations of \(\beta-\gamma\)-connected spaces and their behaviour under \( \beta_{(\gamma,\delta)}\)-continuous functions are analysed. The notions of \(\beta-\gamma\)-components in a space \(X\) and \(\beta-\gamma\)-locally connected spaces are also introduced.

Molecular structure of DNA via Zagreb connection descriptors.

Topological indices quantify the connectivity and structural properties of chemical compounds. We use the topological indices for predicting and evaluating the numerous properties of molecules, such as boiling temperatures, toxicity, and biological activity. Zagreb connection indices are a useful tool for studying the structural characteristics of the DNA backbone network. These indices provide important information on the arrangement and connections between nucleotide bases inside the DNA molecule. These indices show compactness, complexity, and topological properties in order to predict DNA bending propensity, DNA-protein interaction, and DNA stability. DNA folding patterns and the impact of mutations on DNA networks are areas of further research for these topological indices. In this study, we calculate Zagreb connection indices and modified Zagreb connection indices for backbone DNA network and subdivided backbone DNA network. Furthermore, we compute the hyper-Zagreb connection index, the inverse sum connection index, and the harmonic connection index.

A learning-based framework for topology-preserving segmentation using quasiconformal mappings

We propose the Topology-Preserving Segmentation Network, a deformation-based model that can extract objects in an image while maintaining their topological properties. This network generates segmentation masks that have the same topology as the template mask, even when trained with limited data. The network consists of two components: the Deformation Estimation Network, which produces a deformation map that warps the template mask to enclose the region of interest, and the Beltrami Adjustment Module, which ensures the bijectivity of the deformation map by truncating the associated Beltrami coefficient based on Quasiconformal theories. The proposed network can also be trained in an unsupervised manner, eliminating the need for labeled training data. This is achieved by incorporating an unsupervised segmentation loss. Our experimental results on various image datasets show that TPSN achieves better segmentation accuracy than state-of-the-art models with correct topology. Furthermore, we demonstrate TPSN’s ability to handle multiple object segmentation.

Distinguishing the topological charge of vortex beam via Fourier back plane imaging with chiral windmill structure

In recent years, research on the interaction between orbital angular momentum (OAM) of light and matter has shown a continuous influx of investigations. OAM possesses distinct properties, such as a degree of freedom with multiple states, vortex characteristics, and topological properties, which expand its applications in optical communication, optical sensing, and optical manipulation. We have observed different phenomena in the chiral metal windmill structure under excitation of spin angular momentum (SAM)-OAM beam generated by Q-plate than under SAM excitation. Fourier back focal plane (FBP) imaging under SAM beam excitation easily identifies the chirality and geometric properties of the structure. When the SAM-OAM beam excites the structure, FBP not only identifies its chirality and geometric properties but also distinguishes different OAM topological charges and signs, as well as the degree of elliptic polarization. The Stokes parametric FBP imaging reveals asymmetric polarization distribution resulting from the interaction between a vortex beam and the chiral structure. Moreover, it clearly reflects the conversion process of SAM to OAM. The experimental results match well with simulation results. These findings hold valuable insights for the advancement of optical information storage and communication using OAM, opening up new possibilities for further exploration in this field.

مونويدات جزئية من الزمر الباراتبولوجية الآبيلية

One of the important subclasses of abelian paratopological groups is called the free abelian paratopological group on a topological space. It was introduced in 2003 by Remaguara, Sanchis, and Tkachenko. In this paper, we introduce a single submonoid of the free abelian paratopological group on Alexandroff space, then we prove that this submonoid is a base at the identity element of the free topology of the abelian group. The main result of this paper is to give applications of this submonoid such as studying separation axioms, compactness, and other properties of the free topology on the abelian group. Keywords: free group, Abelian paratopological group, free abelian paratopological group, Alexandroff space, neighborhood base at an identity.

Asymmetric energy barrier induced magnetic skyrmion diodes in synthetic antiferromagnetic nanotracks

Magnetic skyrmions are nanoscale spin textures with topological protection properties, which are regarded as promising information carriers. When skyrmions move along nanotracks, their trajectories will shift if affected by skyrmion Hall effect and pinning effect. In this work, the influence of trapezoidal notches in synthetic antiferromagnetic nanotracks on the dynamics of skyrmions is investigated through micromagnetic simulation. The results exhibit that the asymmetric energy barrier induced by the asymmetric geometric structure can hinder reverse motion of skyrmions to realize the unidirectional conduction function of the diodes. Adjusting the height and inclination angle of the trapezoidal notch can effectively expand the current operating windows of the diodes, and the larger the height or inclination angle, the higher the threshold current density to overcome the pinning effect of the geometric energy barrier. Furthermore, the failure mode has a crucial impact on the implementation of skyrmion diodes. By utilizing the asymmetric structure, the forward conduction and reverse cutoff of skyrmion-based diodes can be achieved within 4 ns, with lower energy consumption than traditional diodes, resulting in high efficiency and low energy consumption of diodes. This work proposes a method for realizing the diode functionality by simply altering the geometric structure of the nanotracks, which may play an important role in the design and application of skyrmion-based diodes.

Microstructural and transport characteristics of triply periodic bicontinuous materials

Three-dimensional (3D) bicontinuous two-phase materials are increasingly gaining interest because of their unique multifunctional characteristics and advancements in techniques to fabricate them. Because of their complex topological and structural properties, it still has been nontrivial to develop explicit microstructure-dependent formulas to predict accurately their physical properties. A primary goal of the present paper is to ascertain various microstructural and transport characteristics of five different models of triply periodic bicontinuous porous materials at a porosity ϕ1=1/2: those in which the two-phase interfaces are the Schwarz P, Schwarz D and Schoen G minimal surfaces as well as two different pore-channel structures. We ascertain their spectral densities, pore-size distribution functions, local volume-fraction variances, and hyperuniformity order metrics and then use this information to estimate certain effective steady-state as well as time-dependent transport properties via closed-form microstructure–property formulas. Specifically, the recently introduced time-dependent diffusion spreadability is determined exactly from the spectral density. Moreover, we accurately estimate the fluid permeability of such porous materials from a closed-form formula that depends on the second moment of the pore-size function and the formation factor, a measure of the tortuosity of the pore space, which is exactly obtained for the three minimal-surface structures. We also rigorously bound the permeability from above using the spectral density. For the five models with identical cubic unit cells, we find that the permeability, inverse of the specific surface, hyperuniformity order metric, pore-size second moment and long-time spreadability behavior are all positively correlated and rank order the structures in exactly the same way. We also conjecture what structures maximize the fluid permeability for arbitrary porosities and show that this conjecture must be true in the extreme porosity limits by identifying the corresponding optimal structures.

Topological properties of fractals via M-polynomial

Sierpiński graphs are frequently related to fractals, and fractals apply in several fields of science, i.e., in chemical graph theory, computer networking, biology, and physical sciences. Functions and polynomials are powerful tools in computer mathematics for predicting the features of networks. Topological descriptors, frequently graph constraints, are absolute values that characterize the topology of a computer network. In this essay, Firstly, we compute the M-polynomials for Sierpiński-type fractals. We derive some degree-dependent topological invariants after applying algebraic operations on these M-polynomials.

Investigation of electronic and topological properties of S/Bi-terminated short stanene nanoribbons: A DFT study

Investigation of electronic and topological properties of S/Bi-terminated short stanene nanoribbons: A DFT study

Identifying Hub Genes Related to Vascular Endothelial Cell Permeability Through Bioinformatics and Verification.

In this study, we aimed to identify the hub genes responsible for increased vascular endothelial cell permeability. We applied the weighted Gene Expression Omnibus (GEO) database to mine dataset GSE178331 and ob-tained the most relevant high-throughput sequenced genes for an increased permeability of vascular endothelial cells due to inflammation. We constructed two weighted gene co-expression network analysis (WGCNA) networks, and the differential expression of high-throughput sequenced genes related to endothelial cell permeability were screened from the GEO database. Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analysis were performed on the differential genes. Their degree values were obtained from the topological properties of protein-protein interaction (PPI) networks of differential genes, and the hub genes associated with an increased endothelial cell permeability were analyzed. Reverse transcription-polymerase chain reaction (RT-PCR) and western blotting techniques were used to detect the presence of these hub genes in TNF-α induced mRNA and the protein expression in endothelial cells. In total, 1,475 differential genes were mainly enriched in the cell adhesion and TNF-α signaling pathway. With TNF-α inducing an increase in the endothelial cell permeability and significantly increasing mRNA and protein expression levels, we identified three hub genes, namely PTGS2, ICAM1, and SNAI1. There was a significant difference in the high-dose TNF-α group and in the low-dose TNF-α group compared to the control group, in the endothelial cell permeability experiment (p = 0.008 vs. p = 0.02). Measurement of mRNA and protein levels of PTGS2, ICAM1, and SNAI1 by western blotting analysis showed that there was a significant impact on TNF-α and that there was a significant dose-dependent relationship (p < 0.05 vs. p < 0.01). The three hub genes identified through bioinformatics analyses in the present study may serve as biomarkers of increased vascular endothelial cell permeability. The findings offer valuable insights into the progress and mechanism of vascular endothelial cell permeability.

Prediction of disease progression in individuals with subjective cognitive decline using brain network analysis.

The objective of this study is to explore potential differences in brain functional networks at baseline between individuals with progressive subjective cognitive decline (P-SCD) and stable subjective cognitive decline (S-SCD), as well as to identify potential indicators that can effectively distinguish between P-SCD and S-SCD. Alzheimer's Disease Neuroimaging Initiative (ADNI) database was utilized to enroll SCD individuals with a follow-up period of over 3 years. This study included 39 individuals with S-SCD, 15 individuals with P-SCD, and 45 cognitively normal (CN) individuals. Brain functional networks were constructed based on the AAL template, and graph theory analysis was performed to determine the topological properties. For global metric, the S-SCD group exhibited stronger small-worldness with reduced connectivity among nearby nodes and accelerated compensatory information transfer capacity. For nodal efficiency, the S-SCD group showed increased connectivity in bilateral posterior cingulate gyri (PCG). However, for nodal local efficiency, the P-SCD group exhibited significantly reduced connectivity in the right cerebellar Crus I compared with the S-SCD group. There are differences in brain functional networks at baseline between P-SCD and S-SCD groups. Furthermore, the right cerebellar Crus I region may be a potentially useful brain area to distinguish between P-SCD and S-SCD.

Magnetic field enhanced critical current in Ge–Si nanowire Josephson junctions

Anomalous critical current enhancement was observed with increasing magnetic field in Josephson junctions based on Ge–Si core-shell nanowires. Despite the predicted topological properties of these nanowires, which could potentially lead to non-trivial superconducting order parameter symmetries, our investigation unveils a more generalized, non-topological explanation for the observed critical current enhancement in these devices. Our findings suggest that the enhancement arises from a thermalization process induced by the magnetic field, wherein in-gap quasiparticles are generated. These quasiparticles play a crucial role in enhancing the cooling of the device, thereby lowering the effective temperature and resulting in an increased critical current. Furthermore, we elucidate how this thermalization effect varies with device geometry and measurement configuration.

Higher-order topological Dirac phase in Y3InC: a first-principles study

Higher-order topological insulators hosting intriguing topologically protected hinge or corner states are of significant research interest. However, materials that possess higher-order topological hinge states associated with gapless bulk Dirac phases still need to be explored. Using first-principles calculations with hybrid exchange functional, we explore the electronic structure and topological properties of Y3InC and a few of its sister compounds, totaling 16 bulk materials. A symmetry-protected triple point phase, with dominated d-t 2g character, is observed in Y3InC without spin–orbit coupling (SOC). Interestingly, the SOC induces a twin Dirac node phase in the bulk Y3InC. Furthermore, the computed Z 4 topological invariant reveals the higher-order topological nature of investigated materials. To demonstrate the gapless hinge states, we conduct edge state calculations using a rod-shaped geometry of Y3InC. Remarkably, Y3InC is identified to host multi-Dirac nodes in the bulk and surface phases together with the higher-order hinge states. These results lay the groundwork for further experimental and theoretical investigations into cubic antiperovskite materials for higher-order topological phases.