Haar integrals over the unitary group contain subleading terms that are needed for unitarity. We study analogous effects in the time evolution operators of JT gravity and Brownian SYK. In JT gravity with bulk matter we find an explanation for the fir
st subleading terms, and in Brownian SYK we find configurations that can explain the full series. An important role is played by slightly off-shell modes that are exponentially amplified by chaos.
We show theoretically that the characteristic modes of dielectric resonator antennas (DRAs) must be capacitive in the low frequency limit, and show that as a consequence of this constraint and the Poincar{e} Separation Theorem, the modes of any DRA c
onsisting of partial elements of an encompassing super-structure cannot resonate at a frequency that is lower than that of the encompassing structure. Thus, design techniques relying on complex sub-structures to miniaturize the antenna, including topology optimization and meandered windings, cannot apply to DRAs. Due to the capacitive nature of the DRA modes, it is also shown that the Q factor of any DRA sub-structure will be bounded from below by that of the super-structure at frequencies below the first self-resonance of the super-structure. We demonstrate these bounding relations with numerical examples.
Path representations are critical in a variety of transportation applications, such as estimating path ranking in path recommendation systems and estimating path travel time in navigation systems. Existing studies often learn task-specific path repre
sentations in a supervised manner, which require a large amount of labeled training data and generalize poorly to other tasks. We propose an unsupervised learning framework Path InfoMax (PIM) to learn generic path representations that work for different downstream tasks. We first propose a curriculum negative sampling method, for each input path, to generate a small amount of negative paths, by following the principles of curriculum learning. Next, emph{PIM} employs mutual information maximization to learn path representations from both a global and a local view. In the global view, PIM distinguishes the representations of the input paths from those of the negative paths. In the local view, emph{PIM} distinguishes the input path representations from the representations of the nodes that appear only in the negative paths. This enables the learned path representations to encode both global and local information at different scales. Extensive experiments on two downstream tasks, ranking score estimation and travel time estimation, using two road network datasets suggest that PIM significantly outperforms other unsupervised methods and is also able to be used as a pre-training method to enhance supervised path representation learning.
In this paper, we study an adaptive planewave method for multiple eigenvalues of second-order elliptic partial equations. Inspired by the technique for the adaptive finite element analysis, we prove that the adaptive planewave method has the linear convergence rate and optimal complexity.
Optical observations of the Oort cloud comet C/2017 K2 (PANSTARRS) show that its activity began at large heliocentric distances (up to 35 au), which cannot be explained by either the sublimation or the crystallization of water ice. Supervolatile subl
imation, most likely of carbon monoxide (CO), has been proposed as a plausible driver of the observed mass loss. Here, we present the detection of the J = 2$-$1 rotational transition in outgassed CO from C/2017 K2 when at heliocentric distance $r_H$ = 6.72 au, using the James Clerk Maxwell Telescope. The CO line is blue-shifted by 0.20$pm$0.03 km s$^{-1}$ with an area and width of 8.3$pm$2.3 mK km s$^{-1}$ and $0.28pm$0.08 km s$^{-1}$, respectively. The CO production rate is $Q_{CO} = (1.6pm0.5) times10^{27}$ s$^{-1}$. These are the first observations of a gaseous species in C/2017 K2 and provide observational confirmation of the role of supervolatile sublimation in this comet.
Recent study predicts that structural disorder, serving as a bridge connecting a crystalline material to an amorphous material, can induce a topological insulator from a trivial phase. However, to experimentally observe such a topological phase trans
ition is very challenging due to the difficulty in controlling structural disorder in a quantum material. Given experimental realization of randomly positioned Rydberg atoms, such a system is naturally suited to studying structural disorder induced topological phase transitions and topological amorphous phases. Motivated by the development, we study topological phases in an experimentally accessible one-dimensional amorphous Rydberg atom chain with random atom configurations. In the single-particle level, we find symmetry-protected topological amorphous insulators and a structural disorder induced topological phase transition, indicating that Rydberg atoms provide an ideal platform to experimentally observe the phenomenon using state-of-the-art technologies. Furthermore, we predict the existence of a gapless symmetry-protected topological phase of interacting bosons in the experimentally accessible system. The resultant many-body topological amorphous phase is characterized by a $mathbb{Z}_2$ invariant and the density distribution.
The interstellar traveler, 2I/Borisov, is the first clearly active extrasolar comet, ever detected in our Solar system. We obtained high-resolution interferometric observations of 2I/Borisov with the Atacama Large Millimeter/submillimeter Array (ALMA
), and multi-color optical observations with the Very Large Telescope (VLT) to gain a comprehensive understanding of the dust properties of this comet. We found that the dust coma of 2I/Borisov consists of compact pebbles of radii exceeding ~1 mm, suggesting that the dust particles have experienced compaction through mutual impacts during the bouncing collision phase in the protoplanetary disk. We derived a dust mass loss rate of >= 200 kg/s and a dust-to-gas ratio >=3. Our long term monitoring of 2I/Borisov with VLT indicates a steady dust mass loss with no significant dust fragmentation and/or sublimation occurring in the coma. We also detected emissions from carbon monoxide gas (CO) with ALMA and derived the gas production rate of Q(CO) (3.3+/-0.8)x10^{26} mole/s. We found that the CO/H$_2$O mixing ratio of 2I/Borisov changed drastically before and after perihelion, indicating the heterogeneity of the cometary nucleus, with components formed at different locations beyond the volatile snow-line with different chemical abundances. Our observations suggest that 2I/Borisovs home system, much like our own system, experienced efficient radial mixing from the innermost parts of its protoplanetary disk to beyond the frost line of CO.
In this paper, we propose an efficient saliency map generation method, called Group score-weighted Class Activation Mapping (Group-CAM), which adopts the split-transform-merge strategy to generate saliency maps. Specifically, for an input image, the
class activations are firstly split into groups. In each group, the sub-activations are summed and de-noised as an initial mask. After that, the initial masks are transformed with meaningful perturbations and then applied to preserve sub-pixels of the input (i.e., masked inputs), which are then fed into the network to calculate the confidence scores. Finally, the initial masks are weighted summed to form the final saliency map, where the weights are confidence scores produced by the masked inputs. Group-CAM is efficient yet effective, which only requires dozens of queries to the network while producing target-related saliency maps. As a result, Group-CAM can be served as an effective data augment trick for fine-tuning the networks. We comprehensively evaluate the performance of Group-CAM on common-used benchmarks, including deletion and insertion tests on ImageNet-1k, and pointing game tests on COCO2017. Extensive experimental results demonstrate that Group-CAM achieves better visual performance than the current state-of-the-art explanation approaches. The code is available at https://github.com/wofmanaf/Group-CAM.
Heat generated as a result of the breakdown of an adiabatic process is one of the central concepts of thermodynamics. In isolated systems, the heat can be defined as an energy increase due to transitions between distinct energy levels. Across a secon
d-order quantum phase transition (QPT), the heat is predicted theoretically to exhibit a power-law scaling, but it is a significant challenge for an experimental observation. In addition, it remains elusive whether a power-law scaling of heat can exist for a first-order QPT. Here we experimentally observe a power-law scaling of heat in a spinor condensate when a system is linearly driven from a polar phase to an antiferromagnetic phase across a first-order QPT. We experimentally evaluate the heat generated during two non-equilibrium processes by probing the atom number on a hyperfine energy level. The experimentally measured scaling exponents agree well with our numerical simulation results. Our work therefore opens a new avenue to experimentally and theoretically exploring the properties of heat in non-equilibrium dynamics.
We consider a setting where multiple entities inter-act with each other over time and the time-varying statuses of the entities are represented as multiple correlated time series. For example, speed sensors are deployed in different locations in a ro
ad network, where the speed of a specific location across time is captured by the corresponding sensor as a time series, resulting in multiple speed time series from different locations, which are often correlated. To enable accurate forecasting on correlated time series, we proposes graph attention recurrent neural networks.First, we build a graph among different entities by taking into account spatial proximity and employ a multi-head attention mechanism to derive adaptive weight matrices for the graph to capture the correlations among vertices (e.g., speeds at different locations) at different timestamps. Second, we employ recurrent neural networks to take into account temporal dependency while taking into account the adaptive weight matrices learned from the first step to consider the correlations among time series.Experiments on a large real-world speed time series data set suggest that the proposed method is effective and outperforms the state-of-the-art in most settings. This manuscript provides a full version of a workshop paper [1].
