A Novel Dynamic Event-triggered Mechanism for Dynamic Average Consensus

This paper studies a challenging issue introduced in a recent survey, namely designing a distributed event-based scheme to solve the dynamic average consensus (DAC) problem. First, a robust adaptive distributed event-based DAC algorithm is designed without imposing specific initialization criteria to perform estimation task under intermittent communication. Second, a novel adaptive distributed dynamic event-triggered mechanism is proposed to determine the triggering time when neighboring agents broadcast information to each other. Compared to the existing event-triggered mechanisms, the novelty of the proposed dynamic event-triggered mechanism lies in that it guarantees the existence of a positive and uniform minimum inter-event interval without sacrificing any accuracy of the estimation, which is much more practical than only ensuring the exclusion of the Zeno behavior or the boundedness of the estimation error. Third, a composite adaptive law is developed to update the adaptive gain employed in the distributed event-based DAC algorithm and dynamic event-triggered mechanism. Using the composite adaptive update law, the distributed event-based solution proposed in our work is implemented without requiring any global information. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.Comment: 9 pages, 8 figure

Superconductivity and vortex structure on Bi2_{2}Te3_{3}/FeTe0.55_{0.55}Se0.45_{0.45} heterostructures with different thickness of Bi2_{2}Te3_{3} films

Using scanning tunnel microscopy (STM), we investigate the superconductivity and vortex properties in topological insulator Bi$_{2}$Te$_{3}$ thin films grown on the iron-based superconductor FeTe$_{0.55}$Se$_{0.45}$. The proximity-induced superconductivity weakens in the Bi$_{2}$Te$_{3}$ film when the thickness of the film increases. Unlike the elongated shape of vortex cores observed in the Bi$_{2}$Te$_{3}$ film with 2-quintuple-layer (QL) thickness, the isolated vortex cores exhibit a star shape with six rays in the 1-QL film, and the rays are along the crystalline axes of the film. This is consistent with the sixfold rotational symmetry of the film lattice, and the proximity-induced superconductivity is still topologically trivial in the 1-QL film. At a high magnetic field, when the direction between the two nearest neighbored vortices deviates from that of any crystalline axes, two cores connect each other by a pair of adjacent rays, forming a new type of electronic structure of vortex cores. On the 3-QL film, the vortex cores elongate along one of the crystalline axes of the Bi$_{2}$Te$_{3}$ film, similar to the results obtained on 2-QL films. The elongated vortex cores indicate a twofold symmetry of the superconducting gap induced by topological superconductivity with odd parity. This observation confirms possible topological superconductivity in heterostructures with a thickness of more than 2 QLs. Our results provide rich information for the vortex cores and vortex-bound states on the heterostructures consisting of the topological insulator and the iron-based superconductor.Comment: 8 pages, 8 figure

A study of energy correction for the electron beam data in the BGO ECAL of the DAMPE

The DArk Matter Particle Explorer (DAMPE) is an orbital experiment aiming at searching for dark matter indirectly by measuring the spectra of photons, electrons and positrons originating from deep space. The BGO electromagnetic calorimeter is one of the key sub-detectors of the DAMPE, which is designed for high energy measurement with a large dynamic range from 5 GeV to 10 TeV. In this paper, some methods for energy correction are discussed and tried, in order to reconstruct the primary energy of the incident electrons. Different methods are chosen for the appropriate energy ranges. The results of Geant4 simulation and beam test data (at CERN) are presented

Endogenous merger waves in vertically related industries

We study merger waves in vertically related industries where firms can engage in both vertical and horizontal mergers. Even though any individual merger would have been profitable, firms may refrain from merging for fear of negative impacts from other mergers. When they do merge, however, they always merge in waves, which is either vertical or horizontal depending on the relative intensity of double markup and horizontal competitions in the two industries. Finally, merger waves may happen with or without any fundamental change in the underlying economic conditions

A Study of Neural Collapse Phenomenon: Grassmannian Frame, Symmetry, Generalization

In this paper, we extends original Neural Collapse Phenomenon by proving Generalized Neural Collapse hypothesis. We obtain Grassmannian Frame structure from the optimization and generalization of classification. This structure maximally separates features of every two classes on a sphere and does not require a larger feature dimension than the number of classes. Out of curiosity about the symmetry of Grassmannian Frame, we conduct experiments to explore if models with different Grassmannian Frames have different performance. As a result, we discover the Symmetric Generalization phenomenon. We provide a theorem to explain Symmetric Generalization of permutation. However, the question of why different directions of features can lead to such different generalization is still open for future investigation.Comment: 25 pages, 2 figure