Diagonal Invariant Ideals of Topologically Graded C~*-algebras

We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.

Topologically protected edge gap solitons of interacting Bosons in one-dimensional superlattices

We comprehensively investigate the nontrivial states of an interacting Bose system in a cosine potential under the open boundary condition. Our results show that there exists a kind of stable localized state： edge gap solitons. We argue that the states originate from the eigenstates of independent edge parabolas. In particular, the edge gap solitons exhibit a nonzero topological-invariant behavior. The topological nature is due to the connection of the present model to the quantized adiabatic particle transport problem. In addition, the composition relations between the gap solitons and the extended states are also discussed.

A Devaney Chaotic System Which Is Neither Distributively nor Topologically Chaotic

Weiss proved that Devaney chaos does not imply topological chaos and Oprocha pointed out that Devaney chaos does not imply distributional chaos. In this paper, by constructing a simple example which is Devaney chaotic but neither distributively nor topologically chaotic, we give a unified proof for the results of Weiss and Oprocha.

Edge Modes and Teleportation in a Topologically Insulating Quantum Wire

We find a simple model of an insulating state of a quantum wire which has a single isolated edge mode. We argue that, when brought to proximity, the edge modes on independent wires naturally form Bell entangled states which could be used for elementary quantum processes such as teleportation. We give an example of an algorithm which teleports the spin state of an electron from one quantum wire to another.

Topologically Stable States of the Anti-Centrifugal Potential

We present a study of the anti-centrifugal potential based on the incorporation of the quantum geometric potential of a surface [1] into the generalised anti-centrifugal potential [2]. As a basic variable we will use the unit normal to the surface. Then the total quantum effective potential appears to be the nonlinear sigma model plus positive terms. A 2d bilayer geometry smoothly connected by a neck is used to show that the anti-centrifugal potential creates topologically stable states.

The precipitation and effect of topologically close-packed phases in Ni-based single crystal superalloys

The precipitation of topologically close-packed(TCP)phases is the result of microstructure instabilities of Ni-based superalloys.This review seeks to comprehensively collate all the available information on TCP phases in SX superalloys based on the latest findings.First,the thermodynamics and kinetics of the TCP phase precipitation are introduced.Meanwhile,the morphology,composition and orientation of TCP phases and their sequential transformation are summarized in detail.Further,the factors affecting the precipitation of these phases are sorted out.Besides,the proposed damage mechanisms of TCP phases are listed.Finally,several control and prediction methods of the TCP phase precipitation are reviewed,so the alloy designer can better balance the relationship between microstructure stabilities and properties of the superalloy.

Chaos in a topologically transitive system

The chaotic phenomena have been studied in a topologically transitive system and it has been shown that the erratic time dependence of orbits in such a topologically transitive system is more complicated than what described by the well-known technology "Li-Yorke chaos". The concept "sensitive dependency on initial conditions" has been generalized, and the chaotic phenomena has been discussed for transitive systems with the generalized sensitive dependency property.

A Characterization of Topologically Transitive Attributes for a Class of Dynamical Systems

In this work, by virtue of the properties of weakly almost periodic points of a dynamical system （X, T） with at least two points, the authors prove that, if the measure center M（T） of T is the whole space, that is, M（T） = X, then the following statements are equivalent： （1） （X, T） is ergodic mixing; （2） （X, T） is topologically double ergodic; （3） （X, T） is weak mixing; （4） （X, T） is extremely scattering; （5） （X, T） is strong scattering; （6） （X × X, T × T） is strong scattering; （7） （X × X, T × T） is extremely scattering; （8） For any subset S of N with upper density 1, there is a c-dense Fα-chaotic set with respect to S. As an application, the authors show that, for the sub-shift aA of finite type determined by a k × k-（0, 1） matrix A, erA is strong mixing if and only if aA is totally transitive.

Experimental preparation of topologically ordered states via adiabatic evolution

Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement. Certain topologically ordered systems are proposed as potential realization of fault-tolerant quantum computation. Topological orders can arise in two-dimensional spin-lattice models. In this paper, we engineer a time-dependent Hamiltonian to prepare a topologically ordered state through adiabatic evolution. The other sectors in the degenerate ground-state space of the model are obtained by applying nontrivial operations corresponding to closed string operators. Each sector is highly entangled, as shown from the completely reconstructed density matrices. This paves the way towards exploring the properties of topological orders and the application of topological orders in topological quantum memory.

A novel flexible nerve guidance conduit promotes nerve regeneration while providing excellent mechanical properties

Autografting is the gold standard for surgical repair of nerve defects>5 mm in length;however,autografting is associated with potential complications at the nerve donor site.As an alternative,nerve guidance conduits may be used.The ideal conduit should be flexible,resistant to kinks and lumen collapse,and provide physical cues to guide nerve regeneration.We designed a novel flexible conduit using electrospinning technology to create fibers on the innermost surface of the nerve guidance conduit and employed melt spinning to align them.Subsequently,we prepared disordered electrospun fibers outside the aligned fibers and helical melt-spun fibers on the outer wall of the electrospun fiber lumen.The presence of aligned fibers on the inner surface can promote the extension of nerve cells along the fibers.The helical melt-spun fibers on the outer surface can enhance resistance to kinking and compression and provide stability.Our novel conduit promoted nerve regeneration and functional recovery in a rat sciatic nerve defect model,suggesting that it has potential for clinical use in human nerve injuries.

Topologically minimal surfaces versus self-amalgamated Heegaard surfaces

Let V ∪SW be a Heegaard splitting of M,such that αM = α-W = F1 ∪ F2 and g(S) = 2g(F1)= 2g(F2). Let V * ∪S*W * be the self-amalgamation of V ∪SW. We show if d(S) 3 then S* is not a topologically minimal surface.

Simplified Deep Reinforcement Learning Based Volt-var Control of Topologically Variable Power System

The high penetration and uncertainty of distributed energies force the upgrade of volt-var control(VVC) to smooth the voltage and var fluctuations faster. Traditional mathematical or heuristic algorithms are increasingly incompetent for this task because of the slow online calculation speed. Deep reinforcement learning(DRL) has recently been recognized as an effective alternative as it transfers the computational pressure to the off-line training and the online calculation timescale reaches milliseconds. However, its slow offline training speed still limits its application to VVC. To overcome this issue, this paper proposes a simplified DRL method that simplifies and improves the training operations in DRL, avoiding invalid explorations and slow reward calculation speed. Given the problem that the DRL network parameters of original topology are not applicable to the other new topologies, side-tuning transfer learning(TL) is introduced to reduce the number of parameters needed to be updated in the TL process. Test results based on IEEE 30-bus and 118-bus systems prove the correctness and rapidity of the proposed method, as well as their strong applicability for large-scale control variables.

ERRATUM A TOPOLOGICALLY MIXING MAP WITH TRIVIAL ROTATION SET

We showed in [G. H], if f is a Cr-topologically mixing map of the circle (r ≥0),then its rotation set will be non-trivial. But this statement is only satisfied for generic(open and dense) subset of all Cr-topologically mixing maps of the circle (r≥0). Here,we present another proof of the above statement. Moreover, we introduce a topologicallymixing map of the circle with trivial rotation set.

Topologically Protected Edge State in Two-Dimensional Su–Schrieffer–Heeger Circuit

Topological circuits,an exciting feld just emerged over the last two years,have become a very accessible platform for realizing and exploring topological physics,with many of their physical phenomena and potential applications as yet to be discovered.In this work,we design and experimentally demonstrate a topologically nontrivial band structure and the associated topologically protected edge states in an RF circuit,which is composed of a collection of grounded capacitors connected by alternating inductors in the x and y directions,in analogy to the Su–Schriefer–Heeger model.We take full control of the topological invariant(i.e.,Zak phase)as well as the gap width of the band structure by simply tuning the circuit parameters.Excellent agreement is found between the experimental and simulation results,both showing obvious nontrivial edge state that is tightly bound to the circuit boundaries with extreme robustness against various types of defects.Te demonstration of topological properties in circuits provides a convenient and fexible platform for studying topological materials and the possibility for developing fexible circuits with highly robust circuit performance.

Manipulating cavity photon dynamics by topologically curved space

Asymmetric microcavities supporting Whispering-gallery modes(WGMs)are of great significance for on-chip optical information processing.We establish asymmetric microcavities on topologically curved surfaces,where the geodesic light trajectories completely reconstruct the cavity mode features.The curvature-mediated photon-lifetime engineering enables the enhancement of the quality factors of periodic island modes by up to 200 times.Strong and weak coupling between modes of very different origins occurs when the space curvature brings them into resonance,leading to fine tailoring of the cavity photon energy and lifetime and the observation of non-Hermitian exceptional point(EP).At large space curvatures,the role of the WGMs is replaced by high-Q periodic modes protected by the high stability of island-like light trajectory.Our work demonstrates interesting physical mechanisms at the crosspoint of optical chaotic dynamics,non-Hermitian physics,and geodesic optical devices,and would initiate the novel area of geodesic microcavity photonics.

Topologically protecting squeezed light on a photonic chip

Squeezed light is a critical resource in quantum sensing and information processing. Due to the inherently weak optical nonlinearity and limited interaction volume, considerable pump power is typically needed to obtain efficient interactions to generate squeezed light in bulk crystals. Integrated photonics offers an elegant way to increase the nonlinearity by confining light strictly inside the waveguide. For the construction of large-scale quantum systems performing many-photon operations, it is essential to integrate various functional modules on a chip. However, fabrication imperfections and transmission cross talk may add unwanted diffraction and coupling to other photonic elements, reducing the quality of squeezing. Here, by introducing the topological phase, we experimentally demonstrate the topologically protected nonlinear process of four-wave mixing, enabling the generation of squeezed light on a silica chip. We measure the cross-correlations at different evolution distances for various topological sites and verify the nonclassical features with high fidelity. The squeezing parameters are measured to certify the protection of cavity-free, strongly squeezed states. The demonstration of topological protection for squeezed light on a chip brings new opportunities for quantum integrated photonics,opening novel approaches for the design of advanced multi-photon circuits.

Configural processing of different topologically structured figures:an ERP Study

According to Chen's theory, topological differences are perceived faster than feature differences in early visual perception. We hypothesized that topological perception is caused by the sensitivity in discriminating figures with and without "holes" . An ERP experiment was conducted utilizing a passive paradigm to investigate the differences in perceiving figures with "hole" and with "no-hole" . The results showed differences in N170 components between figures with "holes" and with "no-holes" . The inversion of the "hole" could influence the latency of N170, but the inversion of the "no-hole" could not, which indicated that global features are processed first in the "hole" perception whilst local features are given priority to the "no-hole" perception. This result was similar to studies concerning face and non-face objects, suggesting a configural processing of the "hole" .

Topologically protected long-range coherent energy transfer

The realization of robust coherent energy transfer with a long range from a donor to an acceptor has many important applications in the field of quantum optics.However,it is hard to be realized using conventional schemes.Here,we demonstrate theoretically that robust energy transfer can be achieved using a photonic crystal platform,which includes the topologically protected edge state and zero-dimensional topological corner cavities.When the donor and the acceptor are put into a pair of separated topological cavities,the energy transfer between them can be fulfilled with the assistance of the topologically protected interface state.Such an energy transfer is robust against various kinds of defects,and can also occur over very long distances,which is very beneficial for biological detections,sensors,quantum information science,and so on.

Topologically Protected Polarization Quantum Entanglement on a Photonic Chip

Quantum entanglement,as the strictly non-classical phenomenon,is the kernel of quantum computing and quantum simulation,and has been widely applied ranging from fundamental tests of quantum physics to quantum information processing.Meanwhile,the topolog-ical phase is found inherently capable of protecting physical fields from unavoidable fabrication-induced disorder,which inspires the po-tential application of topological protection to quantum states.Here,we present the experimental demonstration of topologically protected quantum entangled states on a photonic chip.The process tomogra-phy shows that quantum entanglement can be well preserved by the topological states even when the chip material introduces disorder and relative polarization rotation in phase space.Our work links the fields of materials,topological science and quantum physics,opening the door to wide applications of topological enhancement in quantum regime.

CHAOS, TOPOLOGICAL ENTROPY AND ALL TOPOLOGICALLY TRANSITIVE SUBSYSTEMS FOR SELF-MAPS OF THE INTERVAL

Now, we discuss the relationship between the chaos occurring on the nonwandering set, topological entropy and all topologically transitive subsystems for self-maps of the interval and obtain the