In this paper, we prove that discrete Morse functions on digraphs are flat Witten-Morse functions and Witten complexes of transitive digraphs approach to Morse complexes. We construct a chain complex consisting of the formal linear combinations of pa
ths which are not only critical paths of the transitive closure but also allowed elementary paths of the digraph, and prove that the homology of the new chain complex is isomorphic to the path homology. On the basis of the above results, we give the Morse inequalities on digraphs.
Expensive bounding-box annotations have limited the development of object detection task. Thus, it is necessary to focus on more challenging task of few-shot object detection. It requires the detector to recognize objects of novel classes with only a
few training samples. Nowadays, many existing popular methods based on meta-learning have achieved promising performance, such as Meta R-CNN series. However, only a single category of support data is used as the attention to guide the detecting of query images each time. Their relevance to each other remains unexploited. Moreover, a lot of recent works treat the support data and query images as independent branch without considering the relationship between them. To address this issue, we propose a dynamic relevance learning model, which utilizes the relationship between all support images and Region of Interest (RoI) on the query images to construct a dynamic graph convolutional network (GCN). By adjusting the prediction distribution of the base detector using the output of this GCN, the proposed model can guide the detector to improve the class representation implicitly. Comprehensive experiments have been conducted on Pascal VOC and MS-COCO dataset. The proposed model achieves the best overall performance, which shows its effectiveness of learning more generalized features. Our code is available at https://github.com/liuweijie19980216/DRL-for-FSOD.
The nonlinear Hall effect is mostly studied as a Berry curvature dipole effect in nonmagnetic materials, which depends linearly on the relaxation time. On the other hand, in magnetic materials, an intrinsic nonlinear Hall effect can exist, which does
not depend on the relaxation time. Here we show that the intrinsic nonlinear Hall effect can be observed in an antiferromagnetic metal: tetragonal CuMnAs, and the corresponding conductivity can reach the order of mA/V$^2$ based on density functional theory calculations. The dependence on the chemical potential of such nonlinear Hall conductivity can be qualitatively explained by a tilted massive Dirac model. Moreover, we demonstrate its strong temperature-dependence and briefly discuss its competition with the second order Drude conductivity. Finally, a complete survey of magnetic point groups are presented, providing guidelines for finding candidate materials with the intrinsic nonlinear Hall effect.
We apply the empirical galaxy--halo connection model UniverseMachine to dark matter-only zoom-in simulations of isolated Milky Way (MW)--mass halos along with their parent cosmological simulations. This application extends textsc{UniverseMachine} pre
dictions into the ultra-faint dwarf galaxy regime ($ 10^{2},mathrm{M_{odot}} leqslant M_{ast} leqslant 10^{5},mathrm{M_{odot}}$) and yields a well-resolved stellar mass--halo mass (SMHM) relation over the peak halo mass range $10^8,mathrm{M_{odot}}$ to $10^{15},mathrm{M_{odot}}$. The extensive dynamic range provided by the zoom-in simulations allows us to assess specific aspects of dwarf galaxy evolution predicted by textsc{UniverseMachine}. In particular, although UniverseMachine is not constrained for dwarf galaxies with $M_* lesssim 10^{8},mathrm{M_{odot}}$, our predicted SMHM relation is consistent with that inferred for MW satellite galaxies at $z=0$ using abundance matching. However, UniverseMachine predicts that nearly all galaxies are actively star forming below $M_{ast}sim 10^{7},mathrm{M_{odot}}$ and that these systems typically form more than half of their stars at $zlesssim 4$, which is discrepant with the star formation histories of Local Group dwarf galaxies that favor early quenching. This indicates that the current UniverseMachine model does not fully capture galaxy quenching physics at the low-mass end. We highlight specific improvements necessary to incorporate environmental and reionization-driven quenching for dwarf galaxies, and provide a new tool to connect dark matter accretion to star formation over the full dynamic range that hosts galaxies.
The observation of the electrically tunable and highly confined plasmons in graphene has stimulated the exploration of interesting properties of plasmons in other two dimensional materials. Recently, hyperbolic plasmon resonance modes are observed in
exfoliated WTe2 films, a type-II Weyl semimetal with layered structure, providing a platform for the assembly of plasmons with hyperbolicity and exotic topological properties. However, the plasmon modes were observed in relatively thick and small-area films, which restrict the tunability and application for plasmons. Here, large-area (~ cm) WTe2 films with different thickness are grown by chemical vapor deposition method, in which plasmon resonance modes are observed in films with different thickness down to about 8 nm. Hybridization of plasmon and surface polar phonons of the substrate is revealed by mapping the plasmon dispersion. The plasmon frequency is demonstrated to be tunable by changing the temperature and film thickness. Our results facilitate the development of a tunable and scalable WTe2 plasmonic system for revealing topological properties and towards various applications in sensing, imaging and light modulation.
For three-dimensional metals, Landau levels disperse as a function of the magnetic field and the momentum wavenumber parallel to the field. In this two-dimensional parameter space, it is shown that two conically-dispersing Landau levels can touch at
a diabolical point -- a Landau-Dirac point. The conditions giving rise to Landau-Dirac points are shown to be magnetic breakdown (field-induced quantum tunneling) and certain crystallographic spacetime symmetry. Both conditions are realizable in topological nodal-line metals, as we exemplify with CaP$_3$. A Landau-Dirac point reveals itself in anomalous batman-like peaks in the magnetoresistance, as well as in the onset of optical absorption linearly evolving to zero frequency as a function of the field magnitude/orientation.
The purpose of gesture recognition is to recognize meaningful movements of human bodies, and gesture recognition is an important issue in computer vision. In this paper, we present a multimodal gesture recognition method based on 3D densely convoluti
onal networks (3D-DenseNets) and improved temporal convolutional networks (TCNs). The key idea of our approach is to find a compact and effective representation of spatial and temporal features, which orderly and separately divide task of gesture video analysis into two parts: spatial analysis and temporal analysis. In spatial analysis, we adopt 3D-DenseNets to learn short-term spatio-temporal features effectively. Subsequently, in temporal analysis, we use TCNs to extract temporal features and employ improved Squeeze-and-Excitation Networks (SENets) to strengthen the representational power of temporal features from each TCNs layers. The method has been evaluated on the VIVA and the NVIDIA Gesture Dynamic Hand Gesture Datasets. Our approach obtains very competitive performance on VIVA benchmarks with the classification accuracies of 91.54%, and achieve state-of-the art performance with 86.37% accuracy on NVIDIA benchmark.
The increasing extreme weather events poses unprecedented challenges on power system operation because of their uncertain and sequential impacts on power systems. This paper proposes the concept of an extended steady-state security region (ESSR), and
resilience enhancement for transmission systems based on ESSR in consideration of uncertain varying topology changes caused by the extreme weather events is implemented. ESSR is a ploytope describing a region, in which the operating points are within the operating constraints. In consideration of uncertain varying topology changes with ESSR, the resilience enhancement problem is built as a bilevel programming optimization model, in which the system operators deploy the optimal strategy against the most threatening scenario caused by the extreme weather events. To avoid the curse of dimensionality with regard to system topologies for a large scale system, the Monte Carlo method is used to generate uncertain system topologies, and a recursive McCormick envelope-based approach is proposed to connect generated system topologies to optimization variables. Karush Kuhn Tucker (KKT) conditions are used to transform the suboptimization model in the second level into a group of equivalent constraints in the first level. A simple test system and IEEE 118-bus system are used to validate the proposed.
We study the evolutionary trend of the total density profile of early-type galaxies (ETGs) in IllustrisTNG. To this end, we trace ETGs from $z=0$ to $z=4$ and measure the power-law slope $gamma^{prime}$ of the total density profile for their main pro
genitors. We find that their $gamma^{prime}$ steepen on average during $zsim4-2$, then becoming shallower until $z=1$, after which they remain almost constant, aside from a residual trend of becoming shallower towards $z=0$. We also compare to a statistical sample of ETGs at different redshifts, selected based on their luminosity profiles and stellar masses. Due to different selection effects, the average slopes of the statistical samples follow a modified evolutionary trend. They monotonically decrease since $z=3$, and after $zapprox 1$, they remain nearly invariant with a mild increase towards $z=0$. These evolutionary trends are mass-dependent for both samples, with low-mass galaxies having in general steeper slopes than their more massive counterparts. Galaxies that transitioned to ETGs more recently have steeper mean slopes as they tend to be smaller and more compact at any given redshift. By analyzing the impact of mergers and AGN feedback on the progenitors evolution, we conjecture a multi-phase path leading to isothermality in ETGs: dissipation associated with rapid wet mergers tends to steepen $gamma^{prime}$ from $z=4$ to $z=2$, whereas subsequent AGN feedback (especially in the kinetic mode) makes $gamma^{prime}$ shallower again from $z=2$ to $z=1$. Afterwards, passive evolution from $z=1$ to $z=0$, mainly through gas-poor mergers, mildly decreases $gamma^{prime}$ and maintains the overall mass distribution close to isothermal.
Because failures in distribution systems caused by extreme weather events directly result in consumers outages, this paper proposes a state-based decision-making model with the objective of mitigating loss of load to improve the distribution system r
esilience throughout the unfolding events. The sequentially uncertain system states, e.g., feeder line on/off states, driven by the unfolding events are modeled as Markov states, and the probabilities from one Markov state to another Markov state throughout the unfolding events are determined by the component failure caused by the unfolding events. A recursive optimization model based on Markov decision processes (MDP) is developed to make state-based actions, i.e., system reconfiguration, at each decision time. To overcome the curse of dimensionality caused by enormous states and actions, an approximate dynamic programming (ADP) approach based on post-decision states and iteration is used to solve the proposed MDP-based model. IEEE 33-bus system and IEEE 123-bus system are used to validate the proposed model.
