Nodal Topology Research Articles

Aberrant hippocampal intrinsic morphological connectivity patterns in Neuromyelitis optica spectrum disorder with cognitive impairment: Insights from an individual-based morphological brain network

BackgroundAlthough several clinical studies have demonstrated that hippocampus volume loss in neuromyelitis optica spectrum disorder (NMOSD) may be a significant predictor of cognition, no consensus has been reached. To investigate the alterations of the intrinsic ,hippocampal morphological networks in cognitively impaired NMOSD patients and their correlations with cognitive performance. Methods38 NMOSD patients and 39 healthy controls (HC) were enrolled. NMOSD patients were categorized into two groups based on neuropsychological assessment, including the cognitively impaired (CI) group (n = 21) and the cognitively preserved (CP) group (n = 17). Brain high-resolution 3D-T1WI MR images were evaluated, and individual-based intrinsic hippocampus morphological networks were constructed. The between-group differences in global and nodal network topology profiles were estimated, and correlations between the nodal network metrics and cognitive scores were further analyzed. ResultsCompared to the HC and CP groups, the CI group shows significant differences in nodal network metrics of the left hippocampal tail and left hippocampal cornu ammonis (CA) 1-body. Nodal network metrics of the left hippocampal tail were significantly correlated with neurocognitive scores across the entire NMOSD group. ConclusionsNMOSD patients with cognitive impairment exhibit abnormal intrinsic hippocampal morphological networks. Nodal network property measurements can help identify those with cognitive impairment.

Towards investigating influencers in complex social networks using electric potential concept from a centrality perspective

Influencers in complex social networks are crucial for shaping the dynamics of information dissemination, viral marketing strategies, and controlling public opinion. This raises an important question: which influencers wield the most power within these networks, and how can we effectively identify and strategically utilize a key group of disseminators to maximize their influence across various domains? To address this, various heuristic strategies have been developed, targeting specific scenarios. However, these strategies often fall short by focusing solely on nodal topology and ignoring the intricate interconnections among nodes. This oversight can lead to imprecise evaluations and reduce the effectiveness of information spread. To overcome these limitations, a comprehensive approach that considers both the local and global topological dynamics of networks is essential. This paper introduces a novel centrality measure, electric potential centrality (EPC), which incorporates both the degree of nodes and the distances between them. Inspired by the concept of electric potential, EPC is designed to identify key influencers by extensively analyzing topological features, including local connections and the overall network structure. The effectiveness of EPC is rigorously evaluated through experiments on both synthesized and real-world networks, which are undirected and unweighted. Our findings reveal that EPC significantly surpasses existing methodologies, exhibiting the strongest correlation with baseline metrics within the susceptible–infected–recovered model.

Signature of nodal topology in nonlinear quantum transport across junctions in Weyl and multi-Weyl semimetals

Signature of nodal topology in nonlinear quantum transport across junctions in Weyl and multi-Weyl semimetals

Changes of brain structure and structural covariance networks in Parkinson's disease associated cognitive impairment.

Cognitive impairment (CI) is common in Parkinson's disease (PD). Multiple brain regions and their interactions are involved in PD associated CI. Magnetic resonance imaging (MRI) technology is a non-invasive method in investigating brain structure and inter-regional connections. In this study, by comparing cortical thickness, subcortical volume, and brain network topology properties in PD patients with and without CI, we aimed to understand the changes of brain structure and structural covariance network properties in PD associated CI. A total of 18 PD patients with CI and 33 PD patients without CI were recruited. Movement Disorder Society Unified Parkinson's Disease Rating Scale, Hoehn and Yahr stage, Mini Mental State Examination Scale, Non-motor Symptom Rating Scale, Hamilton Anxiety Scale, and Hamilton Depression Scale were assessed. All participants underwent structural 3T MRI. Cortical thickness, subcortical volume, global and nodal network topology properties were measured. Compared with PD patients without CI, the volumes of white matter, thalamus and hippocampus were lower in PD patients with CI. And decreased whole-brain local efficiency is associated with CI in PD patients. While the cortical thickness and nodal network topology properties were comparable between PD patients with and without CI. Our findings support the alterations of brain structure and disruption of structural covariance network are involved in PD associated CI, providing a new insight into the association between graph properties and PD associated CI.

Network Robustness Based Transient Stability Optimisation via Scheduling and Switching

Security and transient stability (TS) constrained OPFs do not include network switching and often require excessive computation time due to discretization of the TS model. This paper proposes a non-simulation methodology to optimize active power dispatching and network switching to ensure TS and system security in the preventive control mode. Network switching is introduced in the security constrained OPF and classical TS models, giving a general <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dynamic</i> security and TS constrained OPF. To ensure TS constraints are manageable in the optimization framework, TS is assessed by using proposed non-simulation based proxy measures. To this end, the key factors impacting TS are investigated and new composite robustness metrics for TS assessment are proposed; they consist of two terms, the nodal and network topology metrics. The former models generator features just before a fault, whilst the second considers impact of a fault on units. The general problem is then decomposed into two stages, the first being economic dispatching and the second optimization of network topology for TS via developed network robustness metrics. The minimum cost topology solutions are ranked by the TS performance. The proposed approach is tested on the IEEE68 Bus test system and compared with time-domain TS results.

Entanglement entropy as an order parameter for strongly coupled nodal line semimetals

Topological semimetals are a class of many-body systems exhibiting novel macroscopic quantum phenomena at the interplay between high energy and condensed matter physics. They display a topological quantum phase transition (TQPT) which evades the standard Landau paradigm. In the case of Weyl semimetals, the anomalous Hall effect is a good non-local order parameter for the TQPT, as it is proportional to the separation between the Weyl nodes in momentum space. On the contrary, for nodal line semimetals (NLSM), the quest for an order parameter is still open. By taking advantage of a recently proposed holographic model for strongly-coupled NLSM, we explicitly show that entanglement entropy (EE) provides an optimal probe for nodal topology. We propose a generalized c-function, constructed from the EE, as an order parameter for the TQPT. Moreover, we find that the derivative of the renormalized EE with respect to the external coupling driving the TQPT diverges at the critical point, signaling the rise of non-local quantum correlations. Finally, we show that these quantum information quantities are able to characterize not only the critical point but also features of the quantum critical region at finite temperature.

Identifying and Constructing Complex Magnon Band Topology.

Magnetically ordered materials tend to support bands of coherent propagating spin wave, or magnon, excitations. Topologically protected surface states of magnons offer a new path toward coherent spin transport for spintronics applications. In this work we explore the variety of topological magnon band structures and provide insight into how to efficiently identify topological magnon bands in materials. We do this by adapting the topological quantum chemistry approach that has used constraints imposed by time reversal and crystalline symmetries to enumerate a large class of topological electronic bands. We show how to identify physically relevant models of gapped magnon band topology by using so-called decomposable elementary band representations, and in turn discuss how to use symmetry data to infer the presence of exotic symmetry enforced nodal topology.

Clinical factors associated with microstructural connectome related brain dysmaturation in term neonates with congenital heart disease.

Term congenital heart disease (CHD) neonates display abnormalities of brain structure and maturation, which are possibly related to underlying patient factors, abnormal physiology and perioperative insults. Our primary goal was to delineate associations between clinical factors and postnatal brain microstructure in term CHD neonates using diffusion tensor imaging (DTI) magnetic resonance (MR) acquisition combined with complementary data-driven connectome and seed-based tractography quantitative analyses. Our secondary goal was to delineate associations between mild dysplastic structural brain abnormalities and connectome and seed-base tractography quantitative analyses. These mild dysplastic structural abnormalities have been derived from prior human infant CHD MR studies and neonatal mouse models of CHD that were collectively used to calculate to calculate a brain dysplasia score (BDS) that included assessment of subcortical structures including the olfactory bulb, the cerebellum and the hippocampus. Neonates undergoing cardiac surgery for CHD were prospectively recruited from two large centers. Both pre- and postoperative MR brain scans were obtained. DTI in 42 directions was segmented into 90 regions using a neonatal brain template and three weighted methods. Clinical data collection included 18 patient-specific and 9 preoperative variables associated with preoperative scan and 6 intraoperative (e.g., cardiopulmonary bypass and deep hypothermic circulatory arrest times) and 12 postoperative variables associated with postoperative scan. We compared patient specific and preoperative clinical factors to network topology and tractography alterations on a preoperative neonatal brain MRI, and intra and postoperative clinical factors to network topology alterations on postoperative neonatal brain MRI. A composite BDS was created to score abnormal findings involving the cerebellar hemispheres and vermis, supratentorial extra-axial fluid, olfactory bulbs and sulci, hippocampus, choroid plexus, corpus callosum, and brainstem. The neuroimaging outcomes of this study included (1) connectome metrics: cost (number of connections) and global/nodal efficiency (network integration); (2) seed based tractography methods of fractional anisotropy (FA), radial diffusivity, and axial diffusivity. Statistics consisted of multiple regression with false discovery rate correction (FDR) comparing the clinical risk factors and BDS (including subcortical components) as predictors/exposures and the global connectome metrics, nodal efficiency, and seed based- tractography (FA, radial diffusivity, and axial diffusivity) as neuroimaging outcome measures. A total of 133 term neonates with complex CHD were prospectively enrolled and 110 had analyzable DTI. Multiple patient-specific factors including d-transposition of the great arteries (d-TGA) physiology and severity of impairment of fetal cerebral substrate delivery (i.e., how much the CHD lesion alters typical fetal circulation such that the highest oxygen and nutrient rich blood from the placenta are not directed toward the fetal brain) were predictive of preoperative reduced cost (p < 0.0073) and reduced global/nodal efficiency (p < 0.03). Cardiopulmonary bypass time predicted postoperative reduced cost (p < 0.04) and multiple postoperative factors [extracorporeal membrane oxygenation (ECMO), seizures and cardiopulmonary resuscitation (CPR)] were predictive of postoperative reduced cost and reduced global/nodal efficiency (p < 0.05). Anthropometric measurements (weight, length, and head size) predicted tractography outcomes. Total BDS was not predictive of brain network topology. However, key subcortical components of the BDS score did predict key global and nodal network topology: abnormalities of the cerebellum predicted reduced cost (p < 0.0417) and of the hippocampus predicted reduced global efficiency (p < 0.0126). All three subcortical structures predicted unique alterations of nodal efficiency (p < 0.05), including hippocampal abnormalities predicting widespread reduced nodal efficiency in all lobes of the brain, cerebellar abnormalities predicting increased prefrontal nodal efficiency, and olfactory bulb abnormalities predicting posterior parietal-occipital nodal efficiency. Patient-specific (d-TGA anatomy, preoperative impairment of fetal cerebral substrate delivery) and postoperative (e.g., seizures, need for ECMO, or CPR) clinical factors were most predictive of diffuse postnatal microstructural dysmaturation in term CHD neonates. Anthropometric measurements (weight, length, and head size) predicted tractography outcomes. In contrast, subcortical components (cerebellum, hippocampus, olfactory) of a structurally based BDS (derived from CHD mouse mutants), predicted more localized and regional postnatal microstructural differences. Collectively, these findings suggest that brain DTI connectome and seed-based tractography are complementary techniques which may facilitate deciphering the mechanistic relative contribution of clinical and genetic risk factors related to poor neurodevelopmental outcomes in CHD.

The effect of large-scale forcing on small-scale dynamics of incompressible turbulence

The subtle but crucial effects of large-scale forcing on the small-scale velocity-gradient (VG) dynamics is examined using direct numerical simulation (DNS) data of incompressible turbulence. The interplay among large-scale forcing, inertia, pressure and viscous effects is characterised as a function of local streamline geometry and VG magnitude (Frobenius norm). When conditioned on local topology, forcing: (i) counteracts inertial and viscous action in the strain-dominated nodal topologies; and (ii) balances pressure action in the rotation-dominated unstable focal topologies. Unexpectedly, forcing acts to reduce VG magnitudes in regions of strong dissipation. In these regions, forcing balances the non-local pressure effects whereas viscous action offsets the nonlinear inertial effects. In regions of very low dissipation, forcing combines with inertia and pressure effects to offset viscous action. With regard to the probability distribution of the normalised VG invariants, the primary role of forcing is to nullify certain features (dilatational probability currents) of inertia, pressure and viscous action. This results in the emergence of universal statistical features (solenoidal probability currents) that are determined largely by inertia–pressure–viscous interactions. These findings serve to enhance our understanding of small-scale processes in turbulence and guide VG model development.

Experimental and first-principles studies of superconductivity in topological nodal line semimetal SnTaS2

We report a detailed study of superconductivity in polycrystalline SnTaS2 using electrical transport, magnetization and heat capacity measurements. SnTaS2 crystallizes in centrosymmetric hexagonal structure with space group . Electrical resistivity, magnetization and specific heat data suggest SnTaS2 to be a weakly coupled, type-II superconductor with K. First-principles calculations show signature for nodal line topology in the electronic band structure, protected by the spatial-inversion and time-reversal symmetries, that strongly gapped out by the inclusion of spin–orbit coupling. Superconductivity in layered SnTaS2 with nodal line topological state makes it a strong candidate to be considered for a 3D topological superconductor.

Using graph convolutional network to characterize individuals with major depressive disorder across multiple imaging sites.

SummaryBackgroundEstablishing objective and quantitative neuroimaging biomarkers at individual level can assist in early and accurate diagnosis of major depressive disorder (MDD). However, most previous studies using machine learning to identify MDD were based on small sample size and did not account for the brain connectome that is associated with the pathophysiology of MDD. Here, we addressed these limitations by applying graph convolutional network (GCN) in a large multi-site MDD dataset.MethodsResting-state functional MRI scans of 1586 participants (821 MDD vs. 765 controls) across 16 sites of Rest-meta-MDD consortium were collected. GCN model was trained with individual whole-brain functional network to identify MDD patients from controls, characterize the most salient regions contributing to classification, and explore the relationship between topological characteristics of salient regions and clinical measures.FindingsGCN achieved an accuracy of 81·5% (95%CI: 80·5–82·5%, AUC: 0·865), which was higher than other common machine learning classifiers. The most salient regions contributing to classification were primarily identified within the default mode, fronto-parietal, and cingulo-opercular networks. Nodal topologies of the left inferior parietal lobule and left dorsolateral prefrontal cortex were associated with depressive severity and illness duration, respectively.InterpretationThese findings based on a large, multi-site dataset support the feasibility and effectiveness of GCN in characterizing MDD, and also illustrate the potential utility of GCN for enhancing understanding of the neurobiology of MDD by detecting clinically-relevant disruption in functional network topology.FundingThis study was supported by the National Natural Science Foundation of China (Grant Nos. 81621003, 82027808, 81820108018).

Subphases in the superconducting state of CeIrIn5 revealed by low-temperature c -axis heat transport

Low-temperature (down to $\sim$ 50 mK) thermal conductivity measurements with the heat flow direction along the inter-plane tetragonal $c$-axis, $\kappa_c$, were used to study the superconducting state of heavy fermion CeIrIn$_5$. Measurements were performed in the magnetic fields both parallel to the heat flow direction, $H\parallel c$, and transverse to it, $H \parallel a$. Inter-plane heat conductivity in $H \parallel c$ configuration shows negligible initial increase with magnetic field and a rapid rise on approaching $H_{c2}$ from below, similar to the expectations for the superconducting gap without line nodes. This observation is in stark contrast to monotonic increase found in the previous in-plane heat transport measurements. In the configuration with the magnetic field breaking the tetragonal symmetry of the lattice, $H \parallel a$, $\kappa_c$ reveals non-monotonic evolution with temperature and magnetic field suggesting sub-phase boundary in the superconducting state. The characteristic temperature $T_{kink} \sim$ 0.07~K of the sub-boundary is well within the domain of bulk superconductivity $T_c \sim$ 0.4~K and $H_{c2}\sim$ 1.0~T. These results are consistent with a superconducting gap with an equatorial line node and polar point nodes, a gap symmetry of the D$_{4h}$ point group, for which magnetic field along the tetragonal plane breaks the degeneracy of the multi-component order parameter and induces a phase transition with nodal topology change.

Classification of exceptional nodal topologies protected by PT symmetry

Exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, and parity-time ($\mathcal{PT}$) symmetry, reflecting balanced gain and loss in photonic systems, are paramount concepts in non-Hermitian systems. We here complete the topological classification of exceptional nodal degeneracies protected by $\mathcal{PT}$ symmetry in up to three dimensions and provide simple example models whose exceptional nodal topologies include previously overlooked possibilities such as second-order knotted surfaces of arbitrary genus, third-order knots and fourth-order points.

Anisotropic nonlinear optical response of nodal-loop materials

Nodal line semimetals have lately aroused much experimental and theoretical interest, with their gap closing along unconventional trajectories in the 3D Brillouin zone. These trajectories or nodal lines can close into loops and trace out intricate knotted or linked configurations with complicated topologies. In this work, we investigate the semi-classical optical response of two nodal loops in linked, unlinked and touching configurations, focusing particularly on the interplay of response anisotropy and non-linearity. We provide a geometric picture that unifies these aspects and sheds light on the effects of nodal topology and geometry. Based on a model abstracted from generic multi nodal loop scenarios, both with or without linkages, our findings will be applicable for a large class of nodal semimetal materials with multiple nodal lines or loops.

Tidal surface states as fingerprints of non-Hermitian nodal knot metals

Non-Hermitian nodal knot metals (NKMs) contain intricate complex-valued energy bands which give rise to knotted exceptional loops and new topological surface states. We introduce a formalism that connects the algebraic, geometric, and topological aspects of these surface states with their parent knots. We also provide an optimized constructive ansatz for tight-binding models for non-Hermitian NKMs of arbitrary knot complexity and minimal hybridization range. Specifically, various representative non-Hermitian torus knots Hamiltonians are constructed in real-space, and their nodal topologies studied via winding numbers that avoid the explicit construction of generalized Brillouin zones. In particular, we identify the surface state boundaries as “tidal” intersections of the complex band structure in a marine landscape analogy. Beyond topological quantities based on Berry phases, we further find these tidal surface states to be intimately connected to the band vorticity and the layer structure of their dual Seifert surface, and as such provide a fingerprint for non-Hermitian NKMs.

Near wall Prandtl number effects on velocity gradient invariants and flow topologies in turbulent Rayleigh\u2013B\xe9nard convection

The statistical behaviours of the invariants of the velocity gradient tensor and flow topologies for Rayleigh–Bénard convection of Newtonian fluids in cubic enclosures have been analysed using Direct Numerical Simulations (DNS) for a range of different values of Rayleigh (i.e. Ra=10^7-10^9) and Prandtl (i.e. Pr=1 and 320) numbers. The behaviours of second and third invariants of the velocity gradient tensor suggest that the bulk region of the flow at the core of the domain is vorticity-dominated whereas the regions in the vicinity of cold and hot walls, in particular in the boundary layers, are found to be strain rate-dominated and this behaviour has been found to be independent of the choice of Ra and Pr values within the range considered here. Accordingly, it has been found that the focal topologies S1 and S4 remain predominant in the bulk region of the flow and the volume fraction of nodal topologies increases in the vicinity of the active hot and cold walls for all cases considered here. However, remarkable differences in the behaviours of the joint probability density functions (PDFs) between second and third invariants of the velocity gradient tensor (i.e. Q and R) have been found in response to the variations of Pr. The classical teardrop shape of the joint PDF between Q and R has been observed away from active walls for all values of Pr, but this behavior changes close to the heated and cooled walls for high values of Pr (e.g. Pr=320) where the joint PDF exhibits a shape mirrored at the vertical Q-axis. It has been demonstrated that the junctions at the edges of convection cells are responsible for this behaviour for Pr=320, which also increases the probability of finding S3 topologies with large negative magnitudes of Q and R. By contrast, this behaviour is not observed in the Pr=1 case and these differences between flow topology distributions in Rayleigh–Bénard convection in response to Pr suggest that the modelling strategy for turbulent natural convection of gaseous fluids may not be equally well suited for simulations of turbulent natural convection of liquids with high values of Pr.

Classification and Graphical Analysis of Alzheimer's Disease and Its Prodromal Stage Using Multimodal Features From Structural, Diffusion, and Functional Neuroimaging Data and the APOE Genotype.

Graphical, voxel, and region-based analysis has become a popular approach to studying neurodegenerative disorders such as Alzheimer’s disease (AD) and its prodromal stage [mild cognitive impairment (MCI)]. These methods have been used previously for classification or discrimination of AD in subjects in a prodromal stage called stable MCI (MCIs), which does not convert to AD but remains stable over a period of time, and converting MCI (MCIc), which converts to AD, but the results reported across similar studies are often inconsistent. Furthermore, the classification accuracy for MCIs vs. MCIc is limited. In this study, we propose combining different neuroimaging modalities (sMRI, FDG-PET, AV45-PET, DTI, and rs-fMRI) with the apolipoprotein-E genotype to form a multimodal system for the discrimination of AD, and to increase the classification accuracy. Initially, we used two well-known analyses to extract features from each neuroimage for the discrimination of AD: whole-brain parcelation analysis (or region-based analysis), and voxel-wise analysis (or voxel-based morphometry). We also investigated graphical analysis (nodal and group) for all six binary classification groups (AD vs. HC, MCIs vs. MCIc, AD vs. MCIc, AD vs. MCIs, HC vs. MCIc, and HC vs. MCIs). Data for a total of 129 subjects (33 AD, 30 MCIs, 31 MCIc, and 35 HCs) for each imaging modality were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) homepage. These data also include two APOE genotype data points for the subjects. Moreover, we used the 2-mm AICHA atlas with the NiftyReg registration toolbox to extract 384 brain regions from each PET (FDG and AV45) and sMRI image. For the rs-fMRI images, we used the DPARSF toolbox in MATLAB for the automatic extraction of data and the results for REHO, ALFF, and fALFF. We also used the pyClusterROI script for the automatic parcelation of each rs-fMRI image into 200 brain regions. For the DTI images, we used the FSL (Version 6.0) toolbox for the extraction of fractional anisotropy (FA) images to calculate a tract-based spatial statistic. Moreover, we used the PANDA toolbox to obtain 50 white-matter-region-parcellated FA images on the basis of the 2-mm JHU-ICBM-labeled template atlas. To integrate the different modalities and different complementary information into one form, and to optimize the classifier, we used the multiple kernel learning (MKL) framework. The obtained results indicated that our multimodal approach yields a significant improvement in accuracy over any single modality alone. The areas under the curve obtained by the proposed method were 97.78, 96.94, 95.56, 96.25, 96.67, and 96.59% for AD vs. HC, MCIs vs. MCIc, AD vs. MCIc, AD vs. MCIs, HC vs. MCIc, and HC vs. MCIs binary classification, respectively. Our proposed multimodal method improved the classification result for MCIs vs. MCIc groups compared with the unimodal classification results. Our study found that the (left/right) precentral region was present in all six binary classification groups (this region can be considered the most significant region). Furthermore, using nodal network topology, we found that FDG, AV45-PET, and rs-fMRI were the most important neuroimages, and showed many affected regions relative to other modalities. We also compared our results with recently published results.

Enhanced higher harmonic generation from nodal topology

Among topological materials, nodal loop semimetals (NLSMs) are arguably the most topologically sophisticated, with their valence and conduction bands intersecting along arbitrarily intertwined nodes. But unlike the well-known topological band insulators with quantized edge conductivities, nodal loop materials possess topologically nontrivial Fermi surfaces, not bands. Hence an important question arises: Are there also directly measurable or even technologically useful physical properties characterizing nontrivial nodal loop topology? In this work, we provide an affirmative answer by showing, for the first time, that nodal linkages protect the higher harmonic generation (HHG) of electromagnetic signals. Specifically, nodal linkages enforce non-monotonicity in the intra-band semi-classical response of nodal materials, which will be robust against perturbations preserving the nodal topology. These nonlinearities distort incident radiation and produce higher frequency peaks in the teraHertz (THz) regime, as we quantitatively demonstrate for a few known nodal materials. Since THz sources are not yet ubiquitous, our new mechanism for HHG will greatly aid applications like material characterization and non-ionizing imaging of object interiors.

Full-Scale Distribution System Topology Identification Using Markov Random Field

The identification of the distribution system topology is the key concern in distribution system state estimation and the precondition for its energy management. However, lacking sufficient measurement devices, full-scale identification of entire distribution grid can hardly be achievable in practice. The frequent topology changes in distribution systems impose challenges for topology identification. This paper proposes a novel topology identification method by deeply mining the data obtained from gird terminals and smart meters at end-users premises. The proposed method starts with data processing, followed by nodal correlation analysis and topology modeling based on the Markov Random Field (MRF) method, where the pseudo-likelihood method and L2 regularization theory are introduced to improve the computation efficiency while preventing the over-fitting problem. Then the iterative screening method is developed to generate the distribution system topology of medium/low-voltage distribution systems. Finally, the incremental learning and parallel programming models are proposed to implement the algorithms on single/multi-terminal. The effectiveness of the proposed model is validated on IEEE 33-node, IEEE 123-node and actual distribution systems.

Shear viscosity as a probe of nodal topology

Electronic materials can sustain a variety of unusual, but symmetry protected touchings of valence and conduction bands, each of which is identified by a distinct topological invariant. Well-known examples include linearly dispersing pseudo-relativistic fermions in monolayer graphene, Weyl and nodal-loop semimetals, biquadratic (bicubic) band touching in bilayer (trilayer) graphene, as well as mixed dispersions in multi-Weyl systems. Here we show that depending on the underlying band curvature, the shear viscosity in the collisionless regime displays a unique power-law scaling with frequency at low temperatures, bearing the signatures of the band topology, which are distinct from the ones when the system resides at the brink of a topological phase transition into a band insulator. Therefore, besides the density of states (governing specific heat, compressibility) and dynamic conductivity, shear viscosity can be instrumental to pin nodal topology in electronic materials.