Finite time singularities of the K\"ahler-Ricci flow

We establish the scalar curvature and distance bounds, extending Perelman's work on the Fano K\"ahler-Ricci flow to general finite time solutions of the K\"ahler-Ricci flow. These bounds are achieved by our Li-Yau type and Harnack estimates for weighted Ricci potential functions of the K\"ahler-Ricci flow. We further prove that the Type I blow-ups of the finite time solution always sub-converge in Gromov-Hausdorff sense to an ancient solution on a family of analytic normal varieties with suitable choices of base points. As a consequence, the Type I diameter bound is proved for almost every fibre of collapsing solutions of the K\"ahler-Ricci flow on a Fano fibre bundle. We also apply our estimates to show that every solution of the K\"ahler-Ricci flow with Calabi symmetry must develop Type I singularities, including both cases of high codimensional contractions and fibre collapsing.Comment: All comments welcome; improved introduction and minor edit

Geometric regularity of blow-up limits of the K\"ahler-Ricci flow

We establish geometric regularity for Type I blow-up limits of the K\"ahler-Ricci flow based at any sequence of Ricci vertices. As a consequence, the limiting flow is continuous in time in both Gromov-Hausdorff and Gromov-$W_1$ distance. In particular, the singular sets of each time slice and its tangent cones are close and of codimension no less than $4$.Comment: All comments welcome. arXiv admin note: text overlap with arXiv:2310.0794

From Petrov-Einstein-Dilaton-Axion to Navier-Stokes equation in anisotropic model

In this paper we generalize the previous works to the case that the near-horizon dynamics of the Einstein-Dilaton-Axion theory can be governed by the incompressible Navier-Stokes equation via imposing the Petrov-like boundary condition on hypersurfaces in the non-relativistic and near-horizon limit. The dynamical shear viscosity $\eta$ of such dual horizon fluid in our scenario, which isotropically saturates the Kovtun-Son-Starinet (KSS) bound, is independent of both the dilaton field and axion field in that limit.Comment: 13 pages,no figures; v2: 15 page, Equation.(33), some discussions and references added, minor corrections , Version accepted for publication in Physics Letters

CANONICAL MEASURES AND KÄHLER-RICCI FLOW

We show that the Kähler-Ricci flow on an algebraic manifold of positive Kodaira dimension and semi-ample canonical line bundle converges to a unique canonical metric on its canonical model. It is also shown that there exists a canonical measure of analytic Zariski decomposition on an algebraic manifold of positive Kodaira dimension. Such a canonical measure is unique and invariant under birational transformations under the assumption o

Dual selections based knowledge transfer learning for cross-subject motor imagery EEG classification

IntroductionMotor imagery electroencephalograph (MI-EEG) has attracted great attention in constructing non-invasive brain-computer interfaces (BCIs) due to its low-cost and convenience. However, only a few MI-EEG classification methods have been recently been applied to BCIs, mainly because they suffered from sample variability across subjects. To address this issue, the cross-subject scenario based on domain adaptation has been widely investigated. However, existing methods often encounter problems such as redundant features and incorrect pseudo-label predictions in the target domain.MethodsTo achieve high performance cross-subject MI-EEG classification, this paper proposes a novel method called Dual Selections based Knowledge Transfer Learning (DS-KTL). DS-KTL selects both discriminative features from the source domain and corrects pseudo-labels from the target domain. The DS-KTL method applies centroid alignment to the samples initially, and then adopts Riemannian tangent space features for feature adaptation. During feature adaptation, dual selections are performed with regularizations, which enhance the classification performance during iterations.Results and discussionEmpirical studies conducted on two benchmark MI-EEG datasets demonstrate the feasibility and effectiveness of the proposed method under multi-source to single-target and single-source to single-target cross-subject strategies. The DS-KTL method achieves significant classification performance improvement with similar efficiency compared to state-of-the-art methods. Ablation studies are also conducted to evaluate the characteristics and parameters of the proposed DS-KTL method

Game Study on Collusion in the First-price Sealed-bid Reverse Auction

Collusion between suppliers in reverse auctions may damage buyers’ benifits and then lower efficiency of resource allocation. Under first-price sealed-bid reverse auction mechanism, suppliers\u27 equilibrium bidding strategy and buyers\u27 revenue loss was analyzed considering collusion. Then some general conclusions were given: suppliers\u27 bidding strategy is relevant to some factors such as valuation costs, the number of suppliers and Cartel; the number of suppliers and Carter can lead to buyers revenue loss. Finally, considering two different kinds of distribution function, the strategies of improving buyer’s revenue were discussed