Non-Hermitian topology in rock–paper–scissors games

Non-Hermitian topology is a recent hot topic in condensed matters. In this paper, we propose a novel platform drawing interdisciplinary attention: rock–paper–scissors (RPS) cycles described by the evolutionary game theory. Specifically, we demonstrate the emergence of an exceptional point and a skin effect by analyzing topological properties of their payoff matrix. Furthermore, we discover striking dynamical properties in an RPS chain: the directive propagation of the population density in the bulk and the enhancement of the population density only around the right edge. Our results open new avenues of the non-Hermitian topology and the evolutionary game theory.

A study of brain functional network and alertness changes in temporal lobe epilepsy with and without focal to bilateral tonic–clonic seizures

Background Temporal lobe epilepsy (TLE) is commonly refractory. Epilepsy surgery is an effective treatment strategy for refractory epilepsy, but patients with a history of focal to bilateral tonic-clonic seizures (FBTCS) have poor outcomes. Previous network studies on epilepsy have found that TLE and idiopathic generalized epilepsy with generalized tonic-clonic seizures (IGE-GTCS) showed altered global and nodal topological properties. Alertness deficits also were found in TLE. However, FBTCS is a common type of seizure in TLE, and the implications for alertness as well as the topological rearrangements associated with this seizure type are not well understood. Methods We obtained rs-fMRI data and collected the neuropsychological assessment data from 21 TLE patients with FBTCS (TLE- FBTCS), 18 TLE patients without FBTCS (TLE-non- FBTCS) and 22 controls, and constructed their respective functional brain networks. The topological properties were analyzed using the graph theoretical approach and correlations between altered topological properties and alertness were analyzed. Results We found that TLE-FBTCS patients showed more serious impairment in alertness effect, intrinsic alertness and phasic alertness than the patients with TLE-non-FBTCS. They also showed significantly higher small-worldness, normalized clustering coefficient (γ) and a trend of higher global network efficiency (gE) compared to TLE-non-FBTCS patients. The gE showed a significant negative correlation with intrinsic alertness for TLE-non-FBTCS patients. Conclusion Our findings show different impairments in brain network information integration, segregation and alertness between the patients with TLE-FBTCS and TLE-non-FBTCS, demonstrating that impairments of the brain network may underlie the disruptions in alertness functions.

Computing of Existence and Uniqueness Solutions for Differential Equations in Metric Spaces by Using MATLAB

A metric space is a set along with a measurement on the set, A metric actuates topological properties like open and shut sets, which lead to the investigation of more theoretical topological spaces. It also has many applications in functional analysis. The aim of this work is design and develop highly efficient algorithms that provide the existence of unique solutions to the differential equation in metric spaces using MATLAB. The quality algorithm was used and developed to solve the differential equation in metric spaces. For accurate results. The proposed model contributed to providing an integrated computer solution for all stages of the solution starting from the stage of solving differential equations in metric space and the stage of displaying and representing the results graphically in the MATLAB program

Topological properties of Sb(111) surface: A first-principles study

First-principles calculations based on density functional theory were performed to systematically study the electronic properties of the thin film of antimony in (111) orientation. Considering the spinorbit interaction, for stoichiometric surface, the topological states keep robust for six-bilayer case, and can be recovered in the three-bilayer film, which are guaranteed by time-reversal symmetry and inverse symmetry. For reduced surface doped by non-magnetic Bi or magnetic Mn atom, localized three-fold symmetric features can be identified. Moreover, band structures show that the non-trivial topological states stand for non-magnetic substitutional Bi atom, while can be eliminated by adsorbed or substitutional magnetic Mn atom.

On tensor network representations of the (3+1)d toric code

We define two dual tensor network representations of the (3+1)d toric code ground state subspace. These two representations, which are obtained by initially imposing either family of stabilizer constraints, are characterized by different virtual symmetries generated by string-like and membrane-like operators, respectively. We discuss the topological properties of the model from the point of view of these virtual symmetries, emphasizing the differences between both representations. In particular, we argue that, depending on the representation, the phase diagram of boundary entanglement degrees of freedom is naturally associated with that of a (2+1)d Hamiltonian displaying either a global or a gauge Z2-symmetry.

Field-induced tricritical phenomenon and magnetic structures in magnetic Weyl semimetal candidate NdAlGe

Non-centrosymmetric NdAlGe is considered to be a candidate for magnetic Weyl semimetal in which the Weyl nodes can be moved by magnetization. Clarification of the magnetic structures and couplings in this system is thus crucial to understand its magnetic topological properties. In this work, we conduct a systematical study of magnetic properties and critical behaviors of single-crystal NdAlGe. Angle-dependent magnetization exhibits strong magnetic anisotropy along the c-axis and absolute isotropy in the ab-plane. The study of critical behavior with H//c gives critical exponents β = 0.236(2), γ = 0.920(1), and δ = 4.966(1) at critical temperature TC = 5.2(2) K. Under the framework of the universality principle, M(T, H) curves are scaled into universality curves using these critical exponents, demonstrating reliability and self-consistency of the obtained exponents. The critical exponents of NdAlGe are close to the theoretical prediction of a tricritical mean-field model, indicating a field-induced tricritical behavior. Based on the scaling analysis, a H −T phase diagram for NdAlGe with H//c is constructed, revealing a ground state with an up-up- down spin configuration. The phase diagram unveils multiple phases including up-up-down domains, up-up-down ordering state, polarized ferromagnetic (PFM), and paramagnetic (PM) phases, with a tricritical point (TCP) located at the intersection [TT CP = 5.27(1) K, HT CP = 30.1(3) kOe] of up-up-down, PFM, and PM phases. The multiple phases and magnetic structures imply a delicate competition and balance between variable interactions and couplings, laying a solid foundation for unveiling topological properties and critical phenomena in this system.