Changes In Topological Properties Research Articles

418 - Changes of topological properties of white matter network in schizophrenia with metabolic syndrome after risperidone and clozapine treatment

418 - Changes of topological properties of white matter network in schizophrenia with metabolic syndrome after risperidone and clozapine treatment

Modulation of Brain Network Topological Properties in Knee Osteoarthritis by Electroacupuncture in Rats.

Osteoarthritis is a chronic, ongoing disease that affects patients, and pain is considered a key factor affecting patients, but the brain changes during the development of osteoarthritis pain are currently unclear. In this study, we used electroacupuncture (EA) to intervene the rat model of knee osteoarthritis and analyzed the changes in topological properties of brain networks using graph theory. Sixteen SD rat models of right-knee osteoarthritis with anterior cruciate ligament transection (ACLT) were randomly divided into electroacupuncture intervention group and control group. The electroacupuncture group was intervened on Zusanli (ST36) and Futu (ST32) for 20 min each time, five times a week for 3 weeks, while the control group was applied sham stimulation. Both groups were measured for pain threshold. The small-world properties and node properties of the brain network between the two groups after the intervention were statistically analyzed by graph theory methods. The differences are mainly in the changes in node attributes between the two groups, such as degree centrality, betweenness centrality, and so on in different brain regions (P<0.05). Both groups showed no small-world characteristics in the brain networks of the two groups. The mechanical thresholds and thermal pain thresholds were significantly higher in the EA group than in the control group (P<0.05). The study demonstrated that electroacupuncture intervention enhanced the activity of nodes related to pain circuit and relieved pain in osteoarthritis, which provides a complementary basis for explaining the effect of electroacupuncture intervention on pain through graphical analysis of changes in brain network topological properties and helps to develop an imaging model for pain affected by electroacupuncture.

Topological analysis of vertebrate phylogenetic trees utilizing Horton’s first law

Phylogenetic trees visually represent evolution and diversification. While many studies have focused on the number and length of edges (branches), topological properties, such as edge connection patterns, are also important. In this study, the topological properties of phylogenetic trees were quantified, focusing on edge connection patterns. Horton’s first law was applied to quantify the overall, rather than local, topological properties of phylogenetic trees. The topological properties of vertebrate phylogenetic trees for spiny-rayed fishes, Amphibians, turtles, Squamata, Aves, and placental mammals were analyzed. The topological features discussed herein include the number of first-order edges, maximum order, and bifurcation ratio. The average bifurcation ratio of all trees was approximately 3, suggesting that phylogenetic trees for different taxa have a common mechanism of evolution. Vertebrate phylogenetic trees were compared with artificial branching objects created from neutral stochastic branching model simulations. The topological properties of the actual vertebrate phylogenetic trees agreed with those of the artificial branching objects. Our study suggests that evolutionary events do not change the overall topological properties of actual phylogenetic trees, even if the number and length of the edges change. Specifically, non-neutral events (e.g., environmental changes and mass extinction) are not main factors associated with topological properties. The results instead demonstrate a relationship between the bifurcation ratio and symmetricity in the context of temporal changes of topological properties. When the number of first-order edges increased and the maximum order remained constant, the bifurcation ratio increased and symmetricity decreased. When the number of first-order edges increased and the maximum order increased by one, the bifurcation ratio decreased and symmetricity increased.

Age-Related Changes in Topological Properties of Individual Brain Metabolic Networks in Rats.

Normal aging causes profound changes of structural degeneration and glucose hypometabolism in the human brain, even in the absence of disease. In recent years, with the extensive exploration of the topological characteristics of the human brain, related studies in rats have begun to investigate. However, age-related alterations of topological properties in individual brain metabolic network of rats remain unknown. In this study, a total of 48 healthy female Sprague–Dawley (SD) rats were used, including 24 young rats and 24 aged rats. We used Jensen-Shannon Divergence Similarity Estimation (JSSE) method for constructing individual metabolic networks to explore age-related topological properties and rich-club organization changes. Compared with the young rats, the aged rats showed significantly decreased clustering coefficient (Cp) and local efficiency (Eloc) across the whole-brain metabolic network. In terms of changes in local network measures, degree (D) and nodal efficiency (Enod) of left posterior dorsal hippocampus, and Enod of left olfactory tubercle were higher in the aged rats than in the young rats. About the rich-club analysis, the existence of rich-club organization in individual brain metabolic networks of rats was demonstrated. In addition, our findings further confirmed that rich-club connections were susceptible to aging. Relative to the young rats, the overall strength of rich-club connections was significantly reduced in the aged rats, while the overall strength of feeder and local connections was significantly increased. These findings demonstrated the age-related reorganization principle of the brain structure and improved our understanding of brain alternations during aging.

Topological transition and Majorana zero modes in 2D non-Hermitian chiral superconductor with anisotropy

We study a non-Hermitian chiral topological superconductor system on two dimensional square lattice, from which we obtained a rich topological phase diagram and established an exact relationship between topological charge flow of exceptional points in generalized Brillouin zone and change of topological properties. Its rich topological phase diagram is the result of competition between anisotropy and non-Hermitian effect. This system belongs to class D according to AZ classification of non-Hermitian systems. Each topological phase can be characterized by a 2D Z number, which indicates the number of chiral edge modes, and two 1D Z 2 numbers, which indicate the existence of zero modes at edge dislocations.

Altered Topological Properties of Static/Dynamic Functional Networks and Cognitive Function After Radiotherapy for Nasopharyngeal Carcinoma Using Resting-State fMRI.

ObjectivesThe purpose of this study was to (1) explore the changes in topological properties of static and dynamic brain functional networks after nasopharyngeal carcinoma (NPC) radiotherapy (RT) using rs-fMRI and graph theoretical analysis, (2) explore the correlation between cognitive function and changes in brain function, and (3) add to the understanding of the pathogenesis of radiation brain injury (RBI).MethodsFifty-four patients were divided into 3 groups according to time after RT: PT1 (0–6 months); PT2 (>6 to ≤12 months); and PT3 (>12 months). 29 normal controls (NCs) were included. The subjects’ topological properties were evaluated by graph-theoretic network analysis, the functional connectivity of static functional networks was calculated using network-based statistics, and the dynamic functional network matrix was subjected to cluster analysis. Finally, correlation analyses were conducted to explore the relationship between the altered network parameters and cognitive function.ResultsAssortativity, hierarchy, and network efficiency were significantly abnormal in the PT1 group compared with the NC or PT3 group. The small-world variance in the PT3 group was smaller than that in NCs. The Nodal ClustCoeff of Postcentral_R in the PT2 group was significantly smaller than that in PT3 and NC groups. Functional connectivities were significantly reduced in the patient groups. Most of the functional connectivities of the middle temporal gyrus (MTG) were shown to be significantly reduced in all three patient groups. Most of the functional connectivities of the insula showed significantly reduced in the PT1 and PT3 groups, and most of the functional connectivities in brain regions such as frontal and parietal lobes showed significantly reduced in the PT2 and PT3 groups. These abnormal functional connectivities were correlated with scores on multiple scales that primarily assessed memory, executive ability, and overall cognitive function. The frequency F of occurrence of various states in each subject differed significantly, and the interaction effect of group and state was significant.ConclusionThe disruption of static and dynamic functional network stability, reduced network efficiency and reduced functional connectivity may be potential biomarkers of RBI. Our findings may provide new insights into the pathogenesis of RBI from the perspective of functional networks.

Phase transitions between helices, vortices, and hedgehogs driven by spatial anisotropy in chiral magnets

Superpositions of spin helices can yield topological spin textures, such as two-dimensional vortices and skyrmions, and three-dimensional hedgehogs. Their topological nature and spatial dimensionality depend on the number and relative directions of the constituent helices. This allows mutual transformation between the topological spin textures by controlling the spatial anisotropy. Here we theoretically study the effect of anisotropy in the magnetic interactions for an effective spin model for chiral magnetic metals. By variational calculations for both cases with triple and quadruple superpositions, we find that the hedgehog lattices, which are stable in the isotropic case, are deformed by the anisotropy, and eventually changed into other spin textures with reduced dimension, such as helices and vortices. We also clarify the changes of topological properties by tracing the real-space positions of magnetic monopoles and antimonopoles as well as the emergent magnetic field generated by the noncoplanar spin textures. Our results suggest possible control of the topological spin textures, e.g., by uniaxial pressure and chemical substitution in chiral materials.

Reorganization of brain structural networks in aging: A longitudinal study.

Normal aging is characterized by structural and functional changes in the brain contributing to cognitive decline. Structural connectivity (SC) describes the anatomical backbone linking distinct functional subunits of the brain and disruption of this communication is thought to be one of the potential contributors for the age‐related deterioration observed in cognition. Several studies already explored brain network's reorganization during aging, but most focused on average connectivity of the whole‐brain or in specific networks, such as the resting‐state networks. Here, we aimed to characterize longitudinal changes of white matter (WM) structural brain networks, through the identification of sub‐networks with significantly altered connectivity along time. Then, we tested associations between longitudinal changes in network connectivity and cognition. We also assessed longitudinal changes in topological properties of the networks. For this, older adults were evaluated at two timepoints, with a mean interval time of 52.8 months (SD = 7.24). WM structural networks were derived from diffusion magnetic resonance imaging, and cognitive status from neurocognitive testing. Our results show age‐related changes in brain SC, characterized by both decreases and increases in connectivity weight. Interestingly, decreases occur in intra‐hemispheric connections formed mainly by association fibers, while increases occur mostly in inter‐hemispheric connections and involve association, commissural, and projection fibers, supporting the last‐in‐first‐out hypothesis. Regarding topology, two hubs were lost, alongside with a decrease in connector‐hub inter‐modular connectivity, reflecting reduced integration. Simultaneously, there was an increase in the number of provincial hubs, suggesting increased segregation. Overall, these results confirm that aging triggers a reorganization of the brain structural network.

Hard-core bosonic domain walls on a honeycomb lattice

Linelike hard-core bosonic domain walls in a staggered potential on a honeycomb lattice are studied using quantum Monte Carlo simulations. The phase diagrams of ribbons with zigzag and armchair domain walls are mapped, which contain superfluid and insulator phases at various fillings. In the $\ensuremath{\rho}=\frac{1}{2}$ insulator, the domain wall separates two charge-density-wave regions with opposite Berry curvatures. Associated with the change of topological properties, superfluid transport occurs down the domain wall. The superfluid density associated with a zigzag domain wall is much larger than that of an armchair domain wall due to the different arrangements of occupied and unoccupied sites along the domain wall. Our results provide a concrete context to study bosonic topological phenomena, which may be simulated experimentally using bosonic cold atoms trapped in optical lattices.

Self-organized bosonic domain walls

Hardcore bosons on honeycomb lattice ribbons with zigzag edges are studied using exact numerical simulations. We map out the phase diagrams of ribbons with different widths, which contain superfluid and insulator phases at various fillings. We show that charge domain walls are energetically favorable, in sharp contrast to the more typical occupation of a set of sites on a single sublattice of the bipartite geometry at $\rho=\frac{1}{2}$ filling. This `self-organized domain wall' separates two charge-density-wave (CDW) regions with opposite Berry curvatures. Associated with the change of topological properties, superfluid transport occurs down the domain wall. Our results provide a concrete context to observe bosonic topological phenomena and can be simulated experimentally using bosonic cold atoms trapped in designed optical lattices.

Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems

Dynamical quantum phase transitions (DQPTs) represent a counterpart in non-equilibrium quantum time evolution of thermal phase transitions at equilibrium, where real time becomes analogous to a control parameter such as temperature. In quenched quantum systems, recently the occurrence of DQPTs has been demonstrated, both with theory and experiment, to be intimately connected to changes of topological properties. Here, we contribute to broadening the systematic understanding of this relation between topology and DQPTs to multi-orbital and disordered systems. Specifically, we provide a detailed ergodicity analysis to derive criteria for DQPTs in all spatial dimensions, and construct basic counter-examples to the occurrence of DQPTs in multi-band topological insulator models. As a numerical case study illustrating our results, we report on microscopic simulations of the quench dynamics in the Harper-Hofstadter model. Furthermore, going gradually from multi-band to disordered systems, we approach random disorder by increasing the (super) unit cell within which random perturbations are switched on adiabatically. This leads to an intriguing order of limits problem which we address by extensive numerical calculations on quenched one-dimensional topological insulators and superconductors with disorder.

From FDI network topology to macroeconomic instability

Fragmentation of production undoubtedly constitutes a possible channel of economic contagion and could play a key role in the study of systemic risk. Investments abroad implicitly create long-range economic dependencies between investors and the economies of destination, possibly triggering contagion phenomena. Complex network theory is a primary tool for highlighting economic mutual relationships and paths of contagion, shedding light on intrinsic systemic risks. In this paper, we reconstruct the EU28 foreign direct investments network and study its evolution from 2003 to 2015. Our analysis aims at detecting the changes of topological properties during the crisis, in order to assess how they affected the architecture of economic relationships. Through a detailed study of correlations at different time lags between network measurements and macroeconomic variables, we assess systemic risks. The main findings are: (i) 2009 marks a clear break in network evolution: prior to 2009 the structure was characterized by only one or few hubs/ countries, while in later years a set of connected key nodes emerged; (ii) an increasing heterogeneity is observed in link weights during the entire period analysed (2003–2015); (iii) after 2009, a rewiring of investments is observed towards the EU28 countries that are considered more safe; (iv) time-lagged centrality measures and macroeconomic variables show a clear correlation.

Radiation-induced changes in small world network in patients with nasopharyngeal carcinoma: a three-dimensional structure MRI imaging study

Objective To investigate the radiotherapy (RT)-induced changes in the brain structural network in patients with nasopharyngeal carcinoma (NPC). Methods Three-dimensional structural magnetic resonance data (3D-T1W) was adopted to investigate the structural network in 103 patients with NPC before and after receiving RT. The structural networks were then reconstructed using 3D-T1W. The radiation-induced changes in topology properties of small world network were analyzed by using graph theoretical analysis. Results Patients showed small world properties before and after RT. Compared with the pre-RT group, the global and local efficiency were lower, the shortest path length was longer and the clustering coefficient was less in the post-RT group. In addition, the hub regions in the post-RT group were significantly different from those in the pre-RT group, mainly located in the left rolandic operculum, right inferior frontal gyrus, right parahippocampal gyrus, right lingual gyrus, bilateral supramarginal gyrus, left superior temporal gyrus and temporal pole of the right middle temporal gyrus. Conclusion It is speculated that RT leads to high efficiency of network topology and information transmission, which provides a novel perspective for exploring the RT-induced brain changes, diagnosis of RT-induced injury and evaluation of RT efficacy. Key words: Nasopharyngeal neoplasm/radiotherapy; Voxel-based morphometry; Gray matter; Small world property

The Abnormality of Topological Asymmetry in Hemispheric Brain Anatomical Networks in Bipolar Disorder.

Convergent evidences have demonstrated a variety of regional abnormalities of asymmetry in bipolar disorder (BD). However, little is known about the alterations in hemispheric topological asymmetries. In this study, we used diffusion tensor imaging to construct the hemispheric brain anatomical network of 49 patients with BD and 61 matched normal controls. Graph theory was then applied to quantify topological properties of the hemispheric networks. Although small-world properties were preserved in the hemispheric networks of BD, the degrees of the asymmetry in global efficiency, characteristic path length, and small-world property were significantly decreased. More changes in topological properties of the right hemisphere than those of left hemisphere were found in patients compared with normal controls. Consistent with such changes, the nodal efficiency in patients with BD also showed less rightward asymmetry mainly in the frontal, occipital, parietal, and temporal lobes. In contrast to leftward asymmetry, significant rightward asymmetry was found in supplementary motor area of BD, and attributed to more deficits in nodal efficiency of the left hemisphere. Finally, these asymmetry score of nodal efficiency in the inferior parietal lobule and rolandic operculum were significantly associated with symptom severity of BD. Our results suggested that abnormal hemispheric asymmetries in brain anatomical networks were associated with aberrant neurodevelopment, and providing insights into the potential neural biomarkers of BD by measuring the topological asymmetry in hemispheric brain anatomical networks.

Oxidation-Induced Topological Phase Transition in Monolayer 1T'-WTe2.

Monolayer (ML) tungsten ditelluride (WTe2) is a well-known quantum spin Hall (QSH) insulator with topologically protected gapless edge states, thus promising dissipationless electronic devices. However, experimental findings exhibit the fast oxidation of ML WTe2 in ambient conditions. To reveal the changes of topological properties of WTe2 arising from oxidation, we systematically study the surface oxidation reaction of ML 1T'-WTe2 using first-principles calculations. The calculated results indicate that the fast oxidation of WTe2 originates from the existence of H2O in air, which significantly promotes the oxidation of ML 1T'-WTe2. More importantly, this low-coverage oxidized WTe2 loses its topological features and is changed into a trivial insulator. Furthermore, we propose a fully oxidized ML WTe2 that can still possess the QSH insulatorstates. The topological phase transition induced by oxidation provides exotic insight into understanding the topological features of layered transition-metal dichalcogenide materials.

Age Related Changes in Topological Properties of Brain Functional Network and Structural Connectivity

Introduction: There are still uncertainties about the true nature of age related changes in topological properties of the brain functional network and its structural connectivity during various developmental stages. In this cross- sectional study, we investigated the effects of age and its relationship with regional nodal properties of the functional brain network and white matter integrity.Method: DTI and fMRI data were acquired from 458 healthy Chinese participants ranging from age 8 to 81 years. Tractography was conducted on the DTI data using FSL. Graph Theory analyses were conducted on the functional data yielding topological properties of the functional network using SPM and GRETNA toolbox. Two multiple regressions were performed to investigate the effects of age on nodal topological properties of the functional brain network and white matter integrity.Result: For the functional studies, we observed that regional nodal characteristics such as node betweenness were decreased while node degree and node efficiency was increased in relation to increasing age. Perversely, we observed that the relationship between nodal topological properties and fasciculus structures were primarily positive for nodal betweenness but negative for nodal degree and nodal efficiency. Decrease in functional nodal betweenness was primarily located in superior frontal lobe, right occipital lobe and the global hubs. These brain regions also had both direct and indirect anatomical relationships with the 14 fiber bundles. A linear age related decreases in the Fractional anisotropy (FA) value was found in the callosum forceps minor.Conclusion: These results suggests that age related differences were more pronounced in the functional than in structural measure indicating these measures do not have direct one-to-one mapping. Our study also indicates that the fiber bundles with longer fibers exhibited a more pronounced effect on the properties of functional network.

Research on the Topological Properties of Air Quality Index Based on a Complex Network

To analyze the dynamic characteristics of air quality for enforcing effective measures to prevent and evade air pollution harm, air quality index (AQI) time series data was selected and transformed into a symbol sequence consisting of characters (H, M, L) through the coarse graining process; then each 6-symbols series was treated as one vertex by time sequence to construct the AQI directed-weighted network; finally the centrality, clusterability, and ranking of the AQI network were analyzed. The results indicated that vertex strength and cumulative strength distribution, vertex strength and strength rank presented power law distributions, and the AQI network is a scale-free network. Only 17 vertices possessed a higher weighted clustering coefficient; meanwhile weighted clustering coefficient and vertex strength didn’t show a strong correlation. The AQI network did not have an obvious central tendency towards intermediaries in general, but 20.55% of vertices accounted for nearly 1/2 of the intermediaries, and the varieties still existed. The mean distance of 68.4932% of vertices was 6.120–9.973, the AQI network did not have obvious small-world phenomena, the conversion of AQI patterns presented the characteristics of periodicity and regularity, and 20.2055% of vertices had high proximity prestige. The vertices fell into six islands, the AQI pattern indicating heavy or serious air pollution lasting six days always lingered for a long time. The number of triads 2-012 was the largest, and the AQI network followed the transitivity model. The study has instructional significance in understanding time change regulation of air quality in Beijing, opening a new way for time series prediction research. Additionally, the factors causing the change of topological properties should be analyzed in the future research.

Radiation-Induced Changes in Structural Network in Patients with Nasopharyngeal Carcinoma

Radiation therapy (RT) is the standard radical treatment for nasopharyngeal carcinoma (NPC), and has produced excellent effects in terms of survival rate [1, 2]. However, one of the serious complications gave rise by the RT is brain injury. Previous studies have found that RT could cause brain structural abnormalities on gray matter and white matter. Nevertheless, the RT effects on the network level should be further investigated. Herein, we explored changes on the structural network for patients with NPC induced by RT. The structural magnetic resonance data (sMRI) were used to investigate the structural network in 20 NPC patients after and before radiotherapy. After constructing the structural network, we examined the radiation-induced changes in topology properties of small world network using graph theoretical analysis. Our results found that both the before and after radiotherapy groups showed small world properties. Compared with the before radiotherapy (pre-RT) group, the after radiotherapy (post-RT) group had lower global and local efficiency, longer shortest path length, and less clustering coefficient. In addition, the hub regions in the post-RT group were significantly different from the pre-RT group. Our findings exhibited the architecture of network topology and information transfer efficiency became poor in post-RT group. We speculated radiation therapy might induce the differences. The results can provide a new perspective to explore and diagnose radiation-induced brain injury and evaluate the effect of radiotherapy.

Magneto-optical mapping of elementary topological configurations of inhomogeneous magnetic fields

Magneto-optical images (MO) of projections of an inhomogeneous magnetic field on a magnetic indicator films plane were studied experimentally and by means of modeling. Inhomogeneity of the field clearly displays itself in the planar component distribution of this vector field by the presence of singular points and is clearly revealed by the MO-images in longitudinal sensitivity. The topological structure of the singular points of the field (Poincare Index) manifests itself in the peculiarities of the intensity distribution of the magneto-optical images. These peculiarities can serve as identifiers of “sink”, “source” and “saddle”-type singular points. The influence of a homogenous bias field on the change in topological properties is demonstrated. Changes in the geometry of the magnetic system also change the topology of the magnetic field; this is reflected in the number and the properties of the singular points of the MO-images.

Reconfiguration of the Brain Functional Network Associated with Visual Task Demands.

Neuroimaging studies have demonstrated that the topological properties of resting-state brain functional networks are modulated through task performances. However, the reconfiguration of functional networks associated with distinct degrees of task demands is not well understood. In the present study, we acquired fMRI data from 18 healthy adult volunteers during resting-state (RS) and two visual tasks (i.e., visual stimulus watching, VSW; and visual stimulus decision, VSD). Subsequently, we constructed the functional brain networks associated with these three conditions and analyzed the changes in the topological properties (e.g., network efficiency, wiring-cost, modularity, and robustness) among them. Although the small-world attributes were preserved qualitatively across the functional networks of the three conditions, changes in the topological properties were also observed. Compared with the resting-state, the functional networks associated with the visual tasks exhibited significantly increased network efficiency and wiring-cost, but decreased modularity and network robustness. The changes in the task-related topological properties were modulated according to the task complexity (i.e., from RS to VSW and VSD). Moreover, at the regional level, we observed that the increased nodal efficiencies in the visual and working memory regions were positively associated with the increase in task complexity. Together, these results suggest that the increased efficiency of the functional brain network and higher wiring-cost were observed to afford the demands of visual tasks. These observations provide further insights into the mechanisms underlying the reconfiguration of the brain network during task performance.