Topological Classification Research Articles

High-order brain network feature extraction and classification method of first-episode schizophrenia: an EEG study

IntroductionA multimodal persistent topological feature extraction and classification method is proposed to enhance the recognition accuracy of first-episode schizophrenia patients. This approach addresses the limitations of traditional higher-order brain network analyses that rely on single persistent features (e.g., persistent images).MethodsThe study utilized resting-state EEG data from 198 subjects recruited at Huilongguan Hospital in Beijing, comprising 102 males and 96 females, with a mean age of 30 years and mean education of 14 years. Persistent topological features were extracted using adaptive thresholding during persistent homology (PH) filtrations. The distribution of these features was visualized through heatmaps and persistence entropies, while the generation process was elucidated using Betti curves and persistence landscapes.ResultsThe classification performance of the multimodal persistent topological features was assessed using various machine learning classifiers. The classifier yielding the highest performance was selected for comparison with traditional brain network features derived from graph theory and single persistent topological features. The results revealed significant topological changes in first-episode schizophrenia patients throughout the persistent homology filtering compared to healthy subjects. The univariate feature selection algorithm achieved a classification accuracy of 94.6% with a combination of attributes meeting the criterion of AC ≥ 0.6.DiscussionThe proposed method demonstrates clinical significance for the early identification and diagnosis of first-episode schizophrenia patients, offering a new research perspective for constructing higher-order functional connectivity networks and extracting topological structure features.

Identification and classification of clusters of dipolar colloids in an external field.

Colloids can acquire a dipolar interaction in the presence of an external AC electric field. At high field strength, the particles form strings in the field direction. However, at weaker field strength, competition with isotropic interactions is expected. One means to investigate this interplay between dipolar and isotropic interactions is to consider clusters of such particles. Therefore, we have identified, using the GMIN basin-hopping tool, a rich library of lowest energy clusters of a dipolar colloidal system, where the dipole orientation is fixed to lie along the z axis and the dipole strength is varied for m-membered clusters of 7 ≤ m ≤ 13. In the regime where the isotropic and dipolar interactions are comparable, we find elongated polytetrahedral, octahedral, and spiral clusters as well as a set of non-rigid clusters, which emerge close to the transition to strings. We further implement a search algorithm that identifies these minimum energy clusters in bulk systems using the topological cluster classification [J. Chem. Phys. 139 234506 (2013)]. We demonstrate this methodology with computer simulations, which show instances of these clusters as a function of dipole strength.

Physical states and transition amplitudes in piecewise flat quantum gravity

In this paper, we show how the path integral for gravity and matter on a piecewise flat spacetime can be used to define the physical quantum gravity states and the related transition amplitudes. The physical states are given by the path integrals for open manifolds from a certain topological class, while the corresponding transition amplitudes are obtained by gluing two such open manifolds into a closed one and calculating the corresponding path integral. We also solve the problem of how to associate a quantum gravity state to an effective action. This is done by using the path integral for a closed manifold from the transition-amplitude topological class so that the state which corresponds to the effective action can be chosen to be the Hartle–Hawking or the Vilenkin wavefunction for the vacuum manifold component of the transition-amplitude manifold.

On maximal nowhere dense sublocales

The aim of this paper is to study some variants of nowhere dense sublocales called maximal nowhere dense and homogeneous maximal nowhere dense sublocales. These concepts were initially introduced by Veksler in classical topology. We give some general properties of these sublocales and further examine their relationship with both inaccessible sublocales and remote sublocales. It turns out that a locale has all of its non-void nowhere dense sublocales maximal nowhere dense precisely when all of its its non-void nowhere dense sublocales are inaccessible. We show that the Booleanization of a locale is inaccessible with respect to every dense and open sublocale. In connection to remote sublocales, we prove that, if the supplement of an open dense sublocale S is homogeneous maximal nowhere dense, then every S#-remote sublocale is *-remote from S. Every open localic map that sends dense elements to dense elements preserves and reflects maximal nowhere dense sublocales. If such a localic map is further injective, then it sends homogeneous maximal nowhere dense sublocales back and forth.

Improved Reduced Switch Converter Topology for Torque Ripple Reduction in Four-Phase Switched Reluctance Motor Under Dynamic Loading

In this paper, simulation, and performance comparison of a switched reluctance motor (SRM) for a classical asymmetric bridge converter and an improved reduced switch converter topology are provided. In an improved converter, switches are shared by adjacent phases, and one diode is connected in series with each phase winding to avoid reversal of current. Double-phase magnetization is adopted for the analysis of both converter topologies. The performance of both converter topologies are demonstrated using a proportional plus integral (PI) based hysteresis current controller and dynamic load on a 7.5 kW, 8/6 pole, 4- phase SRM. Improved reduced switch converter topology uses half the number of switches as compared to the classical asymmetric bridge converter. According to the simulation results, an improved converter offers superior starting and average torque with less speed settling time. An improved converter reduces the most serious problem of torque ripple in SRM by 50% compared to the classical topology. The reduced switches lower the winding losses and improve the efficiency of the drive system.

Impact of Barrow’s entropy on topological classification of higher-dimensional black holes

In this paper, we explore the impact of Barrow’s entropy on the topological classification of d-dimensional black holes (BHs). Specifically, we examine the Gauss–Bonnet (GB) and singly rotating Kerr black holes (KBHs) as well as their AdS counterparts. We notice that Barrow’s entropy significantly influences the topological numbers of these BHs. To understand these effects, we use the thermodynamic domain — the space defined by thermodynamic variables like temperature and pressure — to study topologically inspired defects in the BHs. These defects are points in the thermodynamic domain where singular or discontinuous behavior occurs. By computing the winding numbers of these defects, which are integers that count how many times a loop around the defect encircles the origin, we can understand the local and global topology of the BHs. Our analysis suggest that the topological number [Formula: see text] derived from Barrow’s statistics differs from the one obtained using Gibbs–Boltzmann statistics. Furthermore, we observe that BHs can undergo topological phase transitions that characterize them in different thermodynamic topological classes. Overall, these findings demonstrate the importance of Barrow’s entropy in understanding the topological classification of BHs, and highlight the potential for further research in this area.

Enhancement of clinical signs in C3H/HeJ mice vaccinated with a highly immunogenic Leptospira methyl-accepting chemotaxis protein following challenge.

Leptospirosis is the most widespread zoonosis and a life-threatening disease in humans and animals. Licensed killed whole-cell vaccines are available for animals; however, they do not offer heterologous protection, do not induce long-term protection, or prevent renal colonization. In this study, we characterized an immunogenic Leptospira methyl-accepting chemotaxis protein (MCP) identified through a reverse vaccinology approach, predicted its structure, and tested the protective efficacy of a recombinant MCP fragment in the C3H/HeJ mice model. The predicted structure of the full-length MCP revealed an architecture typical for topology class I MCPs. A single dose of MCP vaccine elicited a significant IgG antibody response in immunized mice compared to controls (P < 0.0001), especially the IgG1 and IgG2a subclasses. The vaccination with MCP, despite eliciting a robust immune response, did not protect mice from disease and renal colonization. However, survival curves significantly differed between groups, and the MCP-vaccinated group developed clinical signs faster than the control group. There were differences in gross and histopathological changes between the MCP-vaccinated and control groups. The factors leading to enhanced disease process in vaccinated animals need further investigation. We speculate that anti-MCP antibodies may block the MCP signaling cascade and may limit chemotaxis, preventing Leptospira from reaching its destination, but facilitating its maintenance and replication in the blood stream. Such a phenomenon may exist in endemic areas where humans are highly exposed to Leptospira antigens, and the presence of antibodies might lead to disease enhancement. The role of this protein in Leptospira pathogenesis should be further evaluated to comprehend the lack of protection and potential exacerbation of the disease process. The absence of immune correlates of protection from Leptospira infection is still a major limitation of this field and efforts to gather this knowledge are needed.

Real Topological Phonons in 3D Carbon Allotropes

AbstractThere has been a significant focus on real topological systems that enjoy space‐time inversion symmetry and lack spin‐orbit coupling. While the theoretical classification of the real topology has been established, more progress has yet to be made in the materials realization of real topological phononic states in 3D. To address this crucial issue, high‐throughput computing is performed to inspect the real topology in the phonon spectrums of the 3D carbon allotropes. Among 1661 carbon allotropes listed in the Samara Carbon Allotrope Database (SACADA), 79 candidates host a phononic real Chern insulating (PRCI) state, 2 candidates host a phononic real nodal line (PRNL) state, 12 candidates host a phononic real Dirac point (PRDP) state, and 10 candidates host a phononic real triple‐point pair (PRTPP) state. The PRCI, PRNL, PRTPP, and PRDP states of 27‐SG. 166‐pcu‐h, 1081‐SG. 194‐42T13‐CA, 52‐SG. 141‐gis, and 132‐SG. 191‐3,4T157 are exhibited as illustrative examples, and the second‐order phononic hinge modes are explored. This study broadens the understanding of 3D topological phonons and expands the material candidates with phononic hinge modes and phononic real topology.

Current Mirror Improved Potentiostat (CMIPot) for a Three Electrode Electrochemical Cell.

This work presents a novel compact CMOS potentiostat-designed circuit for an electrochemical cell. The proposed topology functions as a circuit interface, controlling the polarization of voltage signals at the sensor electrodes and facilitating current measurement during the oxidation-reduction process of an analyzed solution. The potentiostat, designed for CMOS technology, comprises a two-stage amplifier, two current mirror blocks coupled to this amplifier, and a CMOS push-pull output stage. The electrochemical method of cyclic voltammetry is employed, operating within a voltage range of ±0.8 V and scan rates of 10 mV/s, 25 mV/s, 100 mV/s, and 250 mV/s. The circuit is capable of reading currents ranging from 10 µA to 500 µA. Experimental results were obtained using a potassium ferrocyanide K3[Fe(CN)6] redox solution with concentrations of 10, 15, and 20 mmol/L, and their corresponding voltammograms were evaluated. The experimental results from a discrete circuit demonstrate that the proposed potentiostat topology produces outcomes consistent with those of classical topologies presented in the literature and industrial equipment.

Dynamics and control of two-dimensional discrete-time biological model incorporating weak Allee's effect.

Incorporating a weak Allee effect in a two-dimensional biological model in ℜ2, the study delves into the application of bifurcation theory, including center manifold and Ljapunov-Schmidt reduction, normal form theory, and universal unfolding, to analyze nonlinear stability issues across various engineering domains. The focus lies on the qualitative dynamics of a discrete-time system describing the interaction between prey and predator. Unlike its continuous counterpart, the discrete-time model exhibits heightened chaotic behavior. By exploring a biological Mmdel with linear functional prey response, the research elucidates the local asymptotic properties of equilibria. Additionally, employing bifurcation theory and the center manifold theorem, the analysis reveals that, for all α1 (i.e., intrinsic growth rate of prey), ð1˙ (i.e., parameter that scales the terms yn), and m (i.e., Allee effect constant), the model exhibits boundary fixed points A1 and A2, along with the unique positive fixed point A∗, given that the all parameters are positive. Additionally, stability theory is employed to explore the local dynamic characteristics, along with topological classifications, for the fixed points A1, A2, and A∗, considering the impact of the weak Allee effect on prey dynamics. A flip bifurcation is identified for the boundary fixed point A2, and a Neimark-Sacker bifurcation is observed in a small parameter neighborhood around the unique positive fixed point A∗=(mð1˙-1,α1-1-α1mð1˙-1). Furthermore, it implements two chaos control strategies, namely, state feedback and a hybrid approach. The effectiveness of these methods is demonstrated through numerical simulations, providing concrete illustrations of the theoretical findings. The model incorporates essential elements of population dynamics, considering interactions such as predation, competition, and environmental factors, along with a weak Allee effect influencing the prey population.

Cosmic topology. Part IVa. Classification of manifolds using machine learning: a case study with small toroidal universes

Non-trivial spatial topology of the Universe may give rise to potentially measurable signatures in the cosmic microwave background. We explore different machine learning approaches to classify harmonic-space realizations of the microwave background in the test case of Euclidean E 1 topology (the 3-torus) with a cubic fundamental domain of a size scale significantly smaller than the diameter of the last scattering surface. This is the first step toward developing a machine learning approach to classification of cosmic topology and likelihood-free inference of topological parameters. Different machine learning approaches are capable of classifying the harmonic-space realizations with accuracy greater than 99% if the topology scale is half of the diameter of the last-scattering surface and orientation of the topology is known. For distinguishing random rotations of these sky realizations from realizations of the covering space, the extreme gradient boosting classifier algorithm performs best with an accuracy of 88%. Slightly lower accuracies of 83% to 87% are obtained with the random forest classifier along with one- and two-dimensional convolutional neural networks. The techniques presented here can also accurately classify non-rotated cubic E 1 topology realizations with a topology scale slightly larger than the diameter of the last-scattering surface, if enough training data are provided. While information compressing methods like most machine learning approaches cannot exceed the statistical power of a likelihood-based approach that captures all available information, they potentially offer a computationally cheaper alternative. A principle challenge appears to be accounting for arbitrary orientations of a given topology, although this is also a significant hurdle for likelihood-based approaches.

Three-dimensional topological crystalline insulator without spin–orbit coupling in nonsymmorphic photonic metacrystal

Abstract By including certain point group symmetry in the classification of band topology, Fu proposed a class of three-dimensional topological crystalline insulators (TCIs) without spin–orbit coupling in 2011. In Fu’s model, surface states (if present) doubly degenerate at Γ ¯ and M ¯ when time-reversal and C 4 symmetries are preserved. The analogs of Fu’s model with surface states quadratically degenerate at M ¯ are widely studied, while surface states with quadratic degeneracy at Γ ¯ are rarely reported. In this study, we propose a three-dimensional TCI without spin–orbit coupling in a judiciously designed nonsymmorphic photonic metacrystal. The surface states of photonic TCIs exhibit quadratic band degeneracy in the (001) surface Brillouin zone (BZ) center ( Γ ¯ point). The gapless surface states and their quadratic dispersion are protected by C 4 and time-reversal symmetries, which correspond to the nontrivial band topology characterized by Z 2 topological invariant. Moreover, the surface states along lines from Γ ¯ to the (001) surface BZ boundary exhibit zigzag feature, which is interpreted from symmetry perspective by building composite operators constructed by the product of glide symmetries with time-reversal symmetry. The metacrystal array surrounded with air possesses high order hinge states with electric fields highly localized at the hinge that may apply to optical sensors. The gapless surface states and hinge states reside in a clean frequency bandgap. The topological surface states emerge at the boundary of the metacrystal and perfect electric conductor (PEC), which provide a pathway for topologically manipulating light propagation in photonic devices.

Interacting local topological markers: A one-particle density matrix approach for characterizing the topology of interacting and disordered states

While topology is a property of a quantum state itself, most existing methods for characterizing the topology of interacting phases of matter require direct knowledge of the underlying Hamiltonian. We offer an alternative by utilizing the one-particle density matrix formalism to extend the concept of the Chern, chiral, and Chern-Simons markers to include interactions. The one-particle density matrix of a free-fermion state is a projector onto the occupied bands, defining a Brillouin zone bundle of the given topological class. This is no longer the case in the interacting limit, but as long as the one-particle density matrix is gapped, its spectrum can be adiabatically flattened, connecting it to a topologically equivalent projector. The corresponding topological markers thus characterize the topology of the interacting phase. Importantly, the one-particle density matrix is defined in terms of a given state alone, making the local markers numerically favorable, and providing a valuable tool for characterizing topology of interacting systems when only the state itself is available. To demonstrate the practical use of the markers we use the chiral marker to identify the topology of midspectrum eigenstates of the Ising-Majorana chain across the transition between the ergodic and many-body localized phases. We also apply the chiral marker to random states with a known topology, and compare it with the entanglement spectrum degeneracy. Published by the American Physical Society 2024

Thermodynamic topology of quantum corrected AdS-Reissner-Nordstrom black holes in Kiselev spacetime

In this paper, we consider the intricate thermodynamic topology of quantum-corrected Anti-de Sitter-Reissner-Nordstrm (AdS-RN) black holes within the framework of Kiselev spacetime. By employing the generalized off-shell Helmholtz free energy approach, we meticulously compute the thermodynamic topology of these selected black holes. Furthermore, we establish their topological classifications. Our findings reveal that quantum correction terms influence the topological charges of black holes in Kiselev spacetime, leading to novel insights into topological classifications. Our research findings elucidate that, in contrast to the scenario in which ω = 0 and a = 0.7 with total topological charge W = 0 and ω = –4/3 with total topological charge W = –1, in other cases, the total topological charge for the black hole under consideration predominantly stabilizes at +1. This stabilization occurs with the significant influence of the parameters a, c, and ω on the number of topological charges. Specifically, when ω assumes the values of ω = –1/3, ω = –2/3, and ω = –1, the total topological charge will consistently be W = +1.

Topology of SmB6 revisited by means of topological quantum chemistry

The mixed-valence compound SmB6 with partially filled samarium 4f flat bands hybridizing with 5d conduction bands is a paramount example of a correlated topological heavy-fermion system. In this study, we revisit the topology of SmB6 within the formalism of topological quantum chemistry and symmetry-based indicators. Based on this approach, we reach a detailed classification of the material's topology, and we reformulate the origin of topology in terms of band representations. We corroborate these aspects by constructing a minimal TB model that is consistent with all the symmetries of the system and is able to reproduce the topology of the material. We finally unveil the previously overlooked formation of multiple topological gaps, and we discuss its implications for experiments. Published by the American Physical Society 2024

Exploring mesophase formation: Structural characterization approaches in a soft sphere model

This study employs Molecular Dynamics simulations to enhance the structural characterization of sphere mixture systems, focusing on local order parameters to identify order-disorder transitions within lamellar and hexagonal mesophases. The structural characterization included the use of neural networks and the search for clusters with topological order. We have identified the order-disorder transition at a characteristic temperature TOD, effectively captured by the structural parameters analyzed. Below TOD, the system organizes into an ordered mesophase, while above this temperature, it transitions into an isotropic liquid state. Moreover, within the isotropic region, we observe that the liquid begins to form clusters. This clustering phenomenon becomes evident below a specific temperature, denoted as T⁎. At T⁎, there are noticeable changes in the volume versus temperature curves, indicating a process of micellization or clustering in the system. The structural parameters used in our study also register this behavioral change at T⁎, further supporting the occurrence of this phenomenon. Additionally, our analysis of the overlap in detecting ordered particles between the two structural parameters using the Sørensen-Dice similarity coefficient reveals a significant spatial correlation in the isotropic phase, with a correlation higher than what would be expected in a random case. This indicates that both neural networks and topological cluster classification detect statistically similar ordered regions in the isotropic phase, highlighting the clustering. Our findings reveal that the structural parameters effectively capture both the order-disorder transition at TOD and the clustering process at T⁎. These results provide valuable insights into the self-assembly mechanisms and phase behavior in this soft-sphere model, advancing our understanding of self-assembly processes in material science, particularly in exploring phase behavior in mesogenic nanoparticle systems.

Gauge-invariant optical selection rules for excitons

Presently, the optical selection rules for excitons under circularly-polarized light are manifestly gauge-dependent. Recently, Fernando et al. introduced a gauge-invariant, quantized interband index. This index may improve the topological classification of material excited states because it is intrinsically an inter-level quantity. In this work, we expand on this index to introduce its chiral formulation, and use it to make the selection rules gauge-invariant. We anticipate this development to strengthen the theory of quantum materials, especially two-dimensional semiconductor photophysics.

Thermodynamic topology of phantom AdS black holes in massive gravity

In this work, we explore the thermodynamic topology of phantom AdS black holes in the context of massive gravity. To this end, we evaluate these black holes in two distinct ensembles: the canonical and grand canonical ensembles (GCE). We begin by examining the topological charge linked to the critical point and confirming the existence of a conventional critical point (CP1) in the canonical ensemble (CE), this critical point has a topological charge of −1 and acts as a point of phase annihilation, this situation can only be considered within the context of the classical Einstein–Maxwell (CEM) theory (η=1), while no critical point is identified in the GCE. Furthermore, we consider black holes as a topological defect within the thermodynamic space. To gain an understanding of the local and global topological configuration of this defect, we will analyze its winding numbers, and observe that the total topological charge in the CE consistently remains at 1. When the system experiences a pressure below the critical threshold, it gives rise to the occurrence of annihilation and generation points. The value of electric potential determines whether the total topological charge in the GCE is zero or one. As a result, we detect a point of generation point or absence of generation/annihilation point. Based on our analysis, it can be inferred that ensembles significantly impact the topological class of phantom AdS black holes in massive gravity.

Engineering Topological States in 1D Pi-Conjugated Polymers

The emergence of topological states is at the vanguard of modern condensed matter physics. In this talk, I will revise our recent findings regarding the expression of topological SSH edge states on 1D acene and periacene pi-conjugated polymers. Importantly, thanks to the resolution capabilities provided by scanning probe microscopies, complemented by theory, I will provide the relation between the dominant resonant form and the topological quantum class of the distinct materials.

Davies-type phase transitions in 4D Dyonic AdS black holes from topological perspective

In this work, we discussed the Davies-type phase transitions in two distinct categories of dyonic AdS black holes (BHs). The first one is dyonic AdS BHs within four-dimensional spacetime framework. The second one is the dyonic BHs with quasitopological electromagnetism (QE) in Einstein-Gauss-Bonnet gravity (EGBG). First, we analyze the increasing and decreasing behavior of divergency depending upon different parameters which provides useful information about the region that are physical and stable. We also discuss the critical behavior of BHs in three different statistical ensembles: the canonical, mixed and grand canonical. It is noted that BHs can be classified into distinct topological classes based on their topological charge (Q) which assumes discrete values of 0,+1,−1. This topological charge plays a pivotal role in determining the phase structure and stability of the BHs within each ensemble. A topological charge of 0 corresponds to a neutral topological state that could be indicative of a more complex underlying structure, while charges of +1 or −1 indicate the presence of additional structures such as magnetic monopoles or dyons, which significantly influence the thermodynamic properties and phase transitions of the system.