A renormalizable supersymmetric SO(10) model

A realistic grand unified model has never been constructed in the literature due to three major difficulties: the seesaw mechanism without spoiling gauge coupling unification, the doublet-triplet splitting and the proton decay suppression. We propose a renormalizable supersymmetric SO(10) model with all these difficulties solved naturally by imposing an extra discrete symmetry.Comment: 12 page

Adaptive Domain Generalization via Online Disagreement Minimization

Deep neural networks suffer from significant performance deterioration when there exists distribution shift between deployment and training. Domain Generalization (DG) aims to safely transfer a model to unseen target domains by only relying on a set of source domains. Although various DG approaches have been proposed, a recent study named DomainBed, reveals that most of them do not beat the simple Empirical Risk Minimization (ERM). To this end, we propose a general framework that is orthogonal to existing DG algorithms and could improve their performance consistently. Unlike previous DG works that stake on a static source model to be hopefully a universal one, our proposed AdaODM adaptively modifies the source model at test time for different target domains. Specifically, we create multiple domain-specific classifiers upon a shared domain-generic feature extractor. The feature extractor and classifiers are trained in an adversarial way, where the feature extractor embeds the input samples into a domain-invariant space, and the multiple classifiers capture the distinct decision boundaries that each of them relates to a specific source domain. During testing, distribution differences between target and source domains could be effectively measured by leveraging prediction disagreement among source classifiers. By fine-tuning source models to minimize the disagreement at test time, target domain features are well aligned to the invariant feature space. We verify AdaODM on two popular DG methods, namely ERM and CORAL, and four DG benchmarks, namely VLCS, PACS, OfficeHome, and TerraIncognita. The results show AdaODM stably improves the generalization capacity on unseen domains and achieves state-of-the-art performance.Comment: 11 pages, 4 figure

Nonlinear Hall Effects in Strained Twisted Bilayer WSe2_2

Recently, it has been pointed out that the twisting of bilayer WSe$_2$ would generate topologically non-trivial flat bands near the Fermi energy. In this work, we show that twisted bilayer WSe$_2$ (tWSe$_2$) with uniaxial strain exhibits a large nonlinear Hall (NLH) response due to the non-trivial Berry curvatures of the flat bands. Moreover, the NLH effect is greatly enhanced near the topological phase transition point which can be tuned by a vertical displacement field. Importantly, the nonlinear Hall signal changes sign across the topological phase transition point and provides a way to identify the topological phase transition and probe the topological properties of the flat bands. The strong enhancement and high tunability of the NLH effect near the topological phase transition point renders tWSe$_2$ and related moire materials new platforms for rectification and second harmonic generations.Comment: 5 pages, 3 figures. Comments are welcom

Inverting the General Order Sweep Map

Inspired by Thomas-Williams work on the modular sweep map, Garsia and Xin gave a simple algorithm for inverting the sweep map on rational $(m,n)$-Dyck paths for a coprime pairs $(m,n)$ of positive integers. We find their idea naturally extends for general Dyck paths. Indeed, we define a class of Order sweep maps on general Dyck paths, using different sweep orders on level $0$. We prove that each such Order sweep map is a bijection. This includes sweep map for general Dyck paths and incomplete general Dyck paths as special cases

A renormalizable supersymmetric SO(10) model with natural doublet-triplet splitting

We propose a renormalizable supersymmetric SO(10) model where the doublet-triplet splitting problem is solved using the Dimopoulos-Wilczek mechanism. An unwanted coupling is forbidden through a filter sector. To suppress proton decay without spoiling gauge coupling unification, there is a problem in the weak doublets which requires further improvements.Comment: 14 Pages, 1 figure

GRB 221009A with an unconventional precursor: a typical two-stage collapsar scenario?

As the brightest Gamma-Ray burst (GRB) ever detected, GRB 221009A may offer a chance that reveals some interesting features which are hidden in those bursts that are not so bright. There seems a very weak emission with a flux of $10^{-8}\sim10^{-7}$ erg cm$^{-2}$ s$^{-1}$ between the first pulse ($T_0\sim T_0+50$~s, $T_0$ is the trigger time) and the main burst (appears from $T_0+180$ s). Thus the gap time between them is not really quiescent, and the first pulse could be taken as an unconventional precursor, which may provide a peculiar case study for the GRB-precursor phenomena. A two-stage collapsar scenario is proposed as the most likely origin for this burst. In this model, the jet for the precursor is produced during the initial core-collapse phase, and should be weak enough not to disrupt the star when it breaks out of the envelope, so that the fallback accretion process and the forming of the disk could continue. We present an approach in which the duration and flux both provide constraints on the luminosity ($L_{\rm j}$) and the Lorentz factor at the breakout time ($\Gamma_{\rm b}$) of this weak jet. The estimated $L_{\rm j}\lesssim 10^{49}$ erg s$^{-1}$ and $\Gamma_{\rm b}$ has an order of ten, which are well consistent with the theoretical prediction. Besides, the weak emission in the gap time could be interpreted as a MHD outflow due to a magnetically driven wind during the period from the proto-neutron star phase to forming the accretion disk in this scenario.Comment: 12 pages, 5 figures, submmited the revised version on June 17t