The stabilization of the Frobenius--Hecke traces on the intersection cohomology of orthogonal Shimura varieties

The orthogonal Shimura varieties are associated to special orthogonal groups over $\mathbb Q$ of signature $(n,2)$ at infinity. We consider the intersection cohomology of their Baily--Borel compactifications, and prove a version of Morel's formula for the Frobenius--Hecke traces on it for almost all primes. Our main result is the stabilization of this formula. As an application, we compute the Hasse--Weil zeta function of the intersection cohomology in some special cases, using the recent work of Arthur and Ta\"ibi on the endoscopic classification of automorphic representations of special orthogonal groups

6G Non-Terrestrial Networks Enabled Low-Altitude Economy: Opportunities and Challenges

The unprecedented development of non-terrestrial networks (NTN) utilizes the low-altitude airspace for commercial and social flying activities. The integration of NTN and terres- trial networks leads to the emergence of low-altitude economy (LAE). A series of LAE application scenarios are enabled by the sensing, communication, and transportation functionalities of the aircrafts. The prerequisite technologies supporting LAE are introduced in this paper, including the network coverage and aircrafts detection. The LAE functionalities assisted by aircrafts with respect to sensing and communication are then summarized, including the terrestrial and non-terrestrial targets sensing, ubiquitous coverage, relaying, and traffic offloading. Finally, several future directions are identified, including aircrafts collaboration, energy efficiency, and artificial intelligence enabled LAE.Comment: This paper has been submitted to IEEE for possible publicatio

Integer and fractional Chern insulators in twisted bilayer MoTe2

Chern insulators, which are the lattice analogs of the quantum Hall states, can potentially manifest high-temperature topological orders at zero magnetic field to enable next-generation topological quantum devices. To date, integer Chern insulators have been experimentally demonstrated in several systems at zero magnetic field, but fractional Chern insulators have been reported only in graphene-based systems under a finite magnetic field. The emergence of semiconductor moir\'e materials, which support tunable topological flat bands, opens a new opportunity to realize fractional Chern insulators. Here, we report the observation of both integer and fractional Chern insulators at zero magnetic field in small-angle twisted bilayer MoTe2 by combining the local electronic compressibility and magneto-optical measurements. At hole filling factor {\nu}=1 and 2/3, the system is incompressible and spontaneously breaks time reversal symmetry. We determine the Chern number to be 1 and 2/3 for the {\nu}=1 and {\nu}=2/3 gaps, respectively, from their dispersion in filling factor with applied magnetic field using the Streda formula. We further demonstrate electric-field-tuned topological phase transitions involving the Chern insulators. Our findings pave the way for demonstration of quantized fractional Hall conductance and anyonic excitation and braiding in semiconductor moir\'e materials

Enhancing Spatio-Temporal Fusion of MODIS and Landsat Data by Incorporating 250 m MODIS Data

Spatio-temporal fusion of MODIS and Landsat data aims to produce new data that have simultaneously the Landsat spatial resolution and MODIS temporal resolution. It is an ill-posed problem involving large uncertainty, especially for reproduction of abrupt changes and heterogeneous landscapes. In this paper, we proposed to incorporate the freely available 250 m MODIS images into spatio-temporal fusion to increase prediction accuracy. The 250 m MODIS bands 1 and 2 are fused with 500 m MODIS bands 3-7 using the advanced area-to-point regression kriging approach. Based on a standard spatio-temporal fusion approach, the interim 250 m fused MODIS data are then downscaled to 30 m with the aid of the available 30 m Landsat data on temporally close days. The 250 m data can provide more information for the abrupt changes and heterogeneous landscapes than the original 500 m MODIS data, thus increasing the accuracy of spatio-temporal fusion predictions. The effectiveness of the proposed scheme was demonstrated using two datasets

Anomalous stopping of laser-accelerated intense proton beam in dense ionized matter

Ultrahigh-intensity lasers (10$^{18}$-10$^{22}$W/cm$^{2}$) have opened up new perspectives in many fields of research and application [1-5]. By irradiating a thin foil, an ultrahigh accelerating field (10$^{12}$ V/m) can be formed and multi-MeV ions with unprecedentedly high intensity (10$^{10}$A/cm$^2$) in short time scale ($\sim$ps) are produced [6-14]. Such beams provide new options in radiography [15], high-yield neutron sources [16], high-energy-density-matter generation [17], and ion fast ignition [18,19]. An accurate understanding of the nonlinear behavior of beam transport in matter is crucial for all these applications. We report here the first experimental evidence of anomalous stopping of a laser-generated high-current proton beam in well-characterized dense ionized matter. The observed stopping power is one order of magnitude higher than single-particle slowing-down theory predictions. We attribute this phenomenon to collective effects where the intense beam drives an decelerating electric field approaching 1GV/m in the dense ionized matter. This finding will have considerable impact on the future path to inertial fusion energy.Comment: 8 pages, 4 figure