A new method is proposed to predict the topological properties of 1D periodic structures in wave physics, including quantum mechanics. From Bloch waves, a unique complex valued function is ...constructed, exhibiting poles and zeros. The sequence of poles and zeros of this function is a topological invariant that can be linked to the Berry–Zak phase. Since the characterization of the topological properties is done in the complex plane, it can easily be extended to the case of non‐Hermitian systems. The sequence of poles and zeros allows to predict topological phase transitions.
Topological properties of photonic crystals or insulators are generally addressed by means of integer numbers obtained, for example, through the Berry connection. A completely different approach is proposed here : a 1D structure can be characterized by means of the poles and zeros of a function. The approach applies to non‐Hermitian as well as disordered structures.
In this paper we introduce congruence spaces, which are topological spaces that are canonically attached to monoid schemes and that reflect closed topological properties. This leads to satisfactory ...topological characterizations of closed morphisms and closed immersions as well as separated and proper morphisms. We study congruence spaces thoroughly and extend standard results from usual scheme theory to monoid schemes: a closed immersion is the same as an affine morphism for which the pullback of sections is surjective; a morphism is separated if and only if the image of the diagonal is a closed subset of the congruence space; a valuative criterion for separated and proper morphisms.
Mild cognitive impairment is considered the prodromal stage of Alzheimer's disease. Accurate diagnosis and the exploration of the pathological mechanism of mild cognitive impairment are extremely ...valuable for targeted Alzheimer's disease prevention and early intervention. In all, 100 mild cognitive impairment patients and 86 normal controls were recruited in this study. We innovatively constructed the individual morphological brain networks and derived multiple brain connectome features based on 3D-T1 structural magnetic resonance imaging with the Jensen-Shannon divergence similarity estimation method. Our results showed that the most distinguishing morphological brain connectome features in mild cognitive impairment patients were consensus connections and nodal graph metrics, mainly located in the frontal, occipital, limbic lobes, and subcortical gray matter nuclei, corresponding to the default mode network. Topological properties analysis revealed that mild cognitive impairment patients exhibited compensatory changes in the frontal lobe, while abnormal cortical-subcortical circuits associated with cognition were present. Moreover, the combination of multidimensional brain connectome features using multiple kernel-support vector machine achieved the best classification performance in distinguishing mild cognitive impairment patients and normal controls, with an accuracy of 84.21%. Therefore, our findings are of significant importance for developing potential brain imaging biomarkers for early detection of Alzheimer's disease and understanding the neuroimaging mechanisms of the disease.
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•A stable three-dimensional carbon network based on Kagome lattice has been proposed.•The nodal lines and nodal surface exist in three-dimensional Kagome graphene carbon ...networks.•Three types nodal ring form by two sets of Kagome bands coexist in the first type of Kagome graphene carbon networks.
Kagome graphene is a single-layer carbon nanosheet possessing Kagome bands. Here, we propose two types of three-dimensional (3D) Kagome graphene networks (KGNs), which are formed by linking one-dimensional (1D) Kagome graphene nanoribbons. The carbon allotropes show good stabilities although they are completely made of triangle rings. Their cohesive energies are smaller than that of T-carbon approximate 0.3 eV/atom. Remarkably, the new structures exhibit interesting topological properties. The first type of KGN (KGN-1) inherits electronic properties of Kagome graphene. It has two sets of orbital-frustration-induced Kagome bands, and crossings between the bands lead to three kinds of nodal rings, i.e., type I, type II and a critical phase between them. These nodal rings can be observed successively by hole doping. The second type of KGN (KGN-2) is a topological metal. There exist a coexisting phase of a nodal surface and two nodal lines in the momentum space, which are originated from the quantum states in the 1D nanoribbons. In addition, two kinds of electron channels are found in KGN-2.
The discovery of intriguing properties related to the Dirac states in graphene has spurred huge interest in exploring its two-dimensional group-IV counterparts, such as silicene, germanene, and ...stanene. However, these materials have to be obtained via synthesizing on substrates with strong interfacial interactions, which usually destroy their intrinsic π(p z )-orbital Dirac states. Here we report a theoretical study on the existence of Dirac states arising from the p x,y orbitals instead of p z orbitals in silicene on 4H-SiC(0001), which survive in spite of the strong interfacial interactions. We also show that the exchange field together with the spin–orbital coupling give rise to a detectable band gap of 1.3 meV. Berry curvature calculations demonstrate the nontrivial topological nature of such Dirac states with a Chern number C = 2, presenting the potential of realizing quantum anomalous Hall effect for silicene on SiC(0001). Finally, we construct a minimal effective model to capture the low-energy physics of this system. This finding is expected to be also applicable to germanene and stanene and imply great application potentials in nanoelectronics.
Detecting disease-related genes is crucial in disease diagnosis and drug design. The accepted view is that neighbors of a disease-causing gene in a molecular network tend to cause the same or similar ...diseases, and network-based methods have been recently developed to identify novel hereditary disease-genes in available biomedical networks. Despite the steady increase in the discovery of disease-associated genes, there is still a large fraction of disease genes that remains under the tip of the iceberg. In this paper we exploit the topological properties of the protein–protein interaction (PPI) network to detect disease-related genes. We compute, analyze, and compare the topological properties of disease genes with non-disease genes in PPI networks. We also design an improved random forest classifier based on these network topological features, and a cross-validation test confirms that our method performs better than previous similar studies.
•Comparatively analyzed the topological properties between disease-related genes and non-disease genes in protein–protein interaction network.•Disease-related genes were found have distinct network topological properties with non-disease genes.•An improved forest-based model was applied as classifier.•The proposed hybrid networked based disease gene detection method was proven to perform better than previous similar studies in accuracy.
•The molecular structure of yttrium complexes was innovatively optimized by DFT theory.•Theoretical calculation and experimental IR and 1H NMR spectra are in good agreement.•AIM analysis proves the ...close shell interactions between Y3+ and ligands.•H(oct-phe) ligand interacts more strongly with Y3+.
This paper reports a theoretical study of yttrium (III) complexes with acylamino carboxylate ligands (N-octanoyl-alaninates, N-octanoyl-phenylalaninate, N-octanoyl-serinates) (Y(oct-ala)3, Y(oct-phe)3, Y(oct-ser)3). The calculations by density functional theory (DFT) suggest that the acylaminocarboxylate ligands act as a chelating bidentate ligand to the yttrium ions, and the coordination number was six. The reasonable agreement between theoretical and experimental IR, 1H NMR and UV-Vis spectra data provides a strong support to the theoretical structure and optical absorption properties of yttrium complexes. Atoms in molecules (AIM) theory was used to calculate the topological properties of bond critical points. The ▽2ρ and ρc values are in the range of 0.2587–0.2991 and 0.0512–0.0519, respectively, illustrating closed-shell interactions between ligands and yttrium ions. The values of bond degree (BD) were calculated to evaluate the strength of interactions. The results suggest that H(oct-phe) ligand interacts more strongly with Y3+.
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We present more applications of the recently introduced ω1-strongly compact cardinals in the context of either consistency or reflection results in General Topology, focusing on issues related to ...normality. In particular, we show that such large cardinal notion provides a new upper bound for the consistency strength of the statement “All normal Moore spaces are metrizable” (NMSC). The proof uses random forcing, as in the original consistency proof of NMSC due to Nykos-Kunen-Solovay (see Fleissner 10). We establish a compactness theorem for normality (i.e., reflection of non-normality) in the realm of first countable spaces, using the least ω1-strongly compact cardinal, as well as two more similar compactness results on related topological properties. We finish the paper by combining the techniques of reflection and forcing to show that our new upper bound for the consistency strength of NMSC can be also obtained via Cohen forcing, using some arguments from Dow-Tall-Weiss 6.
This study aimed to analyze the topological characteristics of brain structural network in pediatric epilepsy patients with vagus nerve stimulation (VNS) by applying graph theoretical approaches.
...Nine patients with generalized seizures and eight normal controls (NC) were enrolled. Based on diffusion tensor imaging, graph theory analysis was used to characterize the topological properties in preoperative patients (EP-pre), postoperative patients (EP-post) and NC. The global properties included clustering coefficient (Cp), shortest path length (Lp), small-worldness (γ, λ, δ), global network efficiency (Eg) and local network efficiency (Eloc). The regional properties included degree centrality (DC), nodal efficiency (NE), nodal local efficiency (NLE) and nodal shortest path length (Np). Two sample t-test and paired sample t-test were utilized to compare properties difference.
All three groups followed small-world characteristics. There was no significant difference in small-worldness, Cp, Lp, Eg or Eloc between EP-pre and EP-post. Compared with EP-pre: DC in EP-post decreased in the right cuneus and right temporal gyri, while increased in the right paracentral lobule; NE in EP-post decreased in the left dorsolateral superior frontal gyrus, right cuneus, right supramarginal gyrus, and right rolandic operculum, while increased in the right paracentral lobule; NLE in EP-post decreased in the left posterior cingulate gyrus and right supramarginal gyrus, while increased in the left parahippocampal gyrus; NP in EP-post decreased in the right paracentral lobule, while increased in the right cuneus.
VNS causes topological characteristics changes in pediatric patients with generalized seizures through regulating regional properties in some brain structures.
Although there have been many network-based attempts to discover disease-associated genes, most of them have not taken edge weight – which quantifies their relative strength – into consideration. We ...use connection weights in a protein–protein interaction (PPI) network to locate disease-related genes. We analyze the topological properties of both weighted and unweighted PPI networks and design an improved random forest classifier to distinguish disease genes from non-disease genes. We use a cross-validation test to confirm that weighted networks are better able to discover disease-associated genes than unweighted networks, which indicates that including link weight in the analysis of network properties provides a better model of complex genotype–phenotype associations.
•Weight of links is taken into consideration in the construction of a PPI network.•Disease genes show distinct topological properties from non-disease genes.•An improved forest-based model was applied as classifier.•Weighted networks perform better than unweighted networks.
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