Equivariant Moduli Theory on K3K3 Surfaces

We study the orbifold Hirzebruch-Riemann-Roch (HRR) theorem for quotient Deligne-Mumford stacks, explore its relation with representation theory of finite groups, and derive a new orbifold HRR formula via an orbifold Mukai pairing. As a first application, we use this formula to compute the dimensions of $G$-equivariant moduli spaces of stable sheaves on a $K3$ surface $X$ under the action of a finite subgroup $G$ of its symplectic automorphism group. We then apply the orbifold HRR formula to reproduce the number of fixed points on $X$ when $G$ is cyclic without using the Lefschetz fixed point formula. We prove that under some mild conditions, equivariant moduli spaces of stable sheaves on $X$ are irreducible symplectic manifolds deformation equivalent to Hilbert schemes of points on $X$ via a connection between Gieseker and Bridgeland moduli spaces, as well as the derived McKay correspondence. As a corollary, these moduli spaces are also deformation equivalent to equivariant Hilbert schemes of points on $X.$Comment: Made many minor changes, added more materials, and corrected some mistake

Downside Risk and the Momentum Effect

Stocks with greater downside risk, which is measured by higher correlations conditional on downside moves of the market, have higher returns. After controlling for the market beta, the size effect and the book-to-market effect, the average rate of return on stocks with the greatest downside risk exceeds the average rate of return on stocks with the least downside risk by 6.55% per annum. Downside risk is important for explaining the cross-section of expected returns. In particular of the profitability of investing in momentum strategies can be explained as compensation for bearing high exposure to downside risk.

Downside Risk

Economists have long recognized that investors care differently about downside losses versus upside gains. Agents who place greater weight on downside risk demand additional compensation for holding stocks with high sensitivities to downside market movements. We show that the cross-section of stock returns reflects a premium for downside risk. Specifically, stocks that covary strongly with the market when the market declines have high average returns. We estimate that the downside risk premium is approximately 6% per annum. The reward for bearing downside risk is not simply compensation for regular market beta, nor is it explained by coskewness or liquidity risk, or size, book-to-market, and momentum characteristics.

Game among Interdependent Networks: The Impact of Rationality on System Robustness

Many real-world systems are composed of interdependent networks that rely on one another. Such networks are typically designed and operated by different entities, who aim at maximizing their own payoffs. There exists a game among these entities when designing their own networks. In this paper, we study the game investigating how the rational behaviors of entities impact the system robustness. We first introduce a mathematical model to quantify the interacting payoffs among varying entities. Then we study the Nash equilibrium of the game and compare it with the optimal social welfare. We reveal that the cooperation among different entities can be reached to maximize the social welfare in continuous game only when the average degree of each network is constant. Therefore, the huge gap between Nash equilibrium and optimal social welfare generally exists. The rationality of entities makes the system inherently deficient and even renders it extremely vulnerable in some cases. We analyze our model for two concrete systems with continuous strategy space and discrete strategy space, respectively. Furthermore, we uncover some factors (such as weakening coupled strength of interdependent networks, designing suitable topology dependency of the system) that help reduce the gap and the system vulnerability

Semi-Supervised and Long-Tailed Object Detection with CascadeMatch

This paper focuses on long-tailed object detection in the semi-supervised learning setting, which poses realistic challenges, but has rarely been studied in the literature. We propose a novel pseudo-labeling-based detector called CascadeMatch. Our detector features a cascade network architecture, which has multi-stage detection heads with progressive confidence thresholds. To avoid manually tuning the thresholds, we design a new adaptive pseudo-label mining mechanism to automatically identify suitable values from data. To mitigate confirmation bias, where a model is negatively reinforced by incorrect pseudo-labels produced by itself, each detection head is trained by the ensemble pseudo-labels of all detection heads. Experiments on two long-tailed datasets, i.e., LVIS and COCO-LT, demonstrate that CascadeMatch surpasses existing state-of-the-art semi-supervised approaches -- across a wide range of detection architectures -- in handling long-tailed object detection. For instance, CascadeMatch outperforms Unbiased Teacher by 1.9 AP Fix on LVIS when using a ResNet50-based Cascade R-CNN structure, and by 1.7 AP Fix when using Sparse R-CNN with a Transformer encoder. We also show that CascadeMatch can even handle the challenging sparsely annotated object detection problem.Comment: International Journal of Computer Vision (IJCV), 202