We prove for the first time a conditional H{o}lder stability related to the multi-dimensional Borg--Levinson theorem, which is concerned with determining a potential from spectral data for the biharmonic operator. The proof depends on the theory of s
cattering resonances to obtain the resolvent estimate and a Weyl-type law for the biharmonic operator.
The existing piano fingering labeling statistical models usually consider the constraints among the fingers and the correlation between fingering and notes, and rarely include the relationship among the notes directly. The limited learned finger-tran
sfer rules often cause that some parts of the fingering cannot be playable in fact. And traditional models often adopt the original notes, which cannot help to explore the mapping nature between the pitches and fingering. Inspired from manual-ly annotation which acquire the fingering knowledge directly from pitch-difference, we proposed a pitch-difference sequence and fingering (PdF) matching model. And to get playable fingering, be-sides learned finger-transfer rules, prior finger-transfer knowledge is especially combined into the model. In order to characterize the playable performance of the model, we also presented a new evaluation index named incapable-performing fingering rate (IFR). Comprehensive experimental re-sults show that compared with the existing state-of-the-art third-order hidden Markov labeling model, the general and the highest matching rate of our model increases by 3% and 1.6% respective-ly, and the fingering for all scores can be playable.
Reasoning on knowledge graph (KG) has been studied for explainable recommendation due to its ability of providing explicit explanations. However, current KG-based explainable recommendation methods unfortunately ignore the temporal information (such
as purchase time, recommend time, etc.), which may result in unsuitable explanations. In this work, we propose a novel Time-aware Path reasoning for Recommendation (TPRec for short) method, which leverages the potential of temporal information to offer better recommendation with plausible explanations. First, we present an efficient time-aware interaction relation extraction component to construct collaborative knowledge graph with time-aware interactions (TCKG for short), and then introduce a novel time-aware path reasoning method for recommendation. We conduct extensive experiments on three real-world datasets. The results demonstrate that the proposed TPRec could successfully employ TCKG to achieve substantial gains and improve the quality of explainable recommendation.
We present analysis of multiple Chandra and XMM-Newton spectra, separated by 9-19 years, of four of the youngest central compact objects (CCOs) with ages < 2500 yr: CXOU J232327.9+584842 (Cassiopeia A), CXOU J160103.1-513353 (G330.2+1.0), 1WGA J1713.
4-3949 (G347.3-0.5), and XMMU J172054.5-372652 (G350.1-0.3). By fitting these spectra with thermal models, we attempt to constrain each CCOs long-term cooling rate, composition, and magnetic field. For the CCO in Cassiopeia A, 14 measurements over 19 years indicate a decreasing temperature at a ten-year rate of 2.2+/-0.2 or 2.8+/-0.3 percent (1sigma error) for a constant or changing X-ray absorption, respectively. We obtain cooling rate upper limits of 17 percent for CXOU J160103.1-513353 and 6 percent for XMMU J172054.5-372652. For the oldest CCO, 1WGA J1713.4-3949, its temperature seems to have increased by 4+/-2 percent over a ten year period. Assuming each CCOs preferred distance and an emission area that is a large fraction of the total stellar surface, a non-magnetic carbon atmosphere spectrum is a good fit to spectra of all four CCOs. If distances are larger and emission areas are somewhat smaller, then equally good spectral fits are obtained using a hydrogen atmosphere with B <= 7x10^10 G or B >= 10^12 G for CXOU J160103.1-513353, B <= 10^10 G or B >= 10^12 G for XMMU J172054.5-372652, and non-magnetic hydrogen atmosphere for 1WGA J1713.4-3949. In a unified picture of CCO evolution, our results suggest most CCOs, and hence a sizable fraction of young neutron stars, have a surface magnetic field that is low early in their life but builds up over several thousand years.
In vision-based reinforcement learning (RL) tasks, it is prevalent to assign the auxiliary task with a surrogate self-supervised loss so as to obtain more semantic representations and improve sample efficiency. However, abundant information in self-s
upervised auxiliary tasks has been disregarded, since the representation learning part and the decision-making part are separated. To sufficiently utilize information in the auxiliary task, we present a simple yet effective idea to employ self-supervised loss as an intrinsic reward, called Intrinsically Motivated Self-Supervised learning in Reinforcement learning (IM-SSR). We formally show that the self-supervised loss can be decomposed as exploration for novel states and robustness improvement from nuisance elimination. IM-SSR can be effortlessly plugged into any reinforcement learning with self-supervised auxiliary objectives with nearly no additional cost. Combined with IM-SSR, the previous underlying algorithms achieve salient improvements on both sample efficiency and generalization in various vision-based robotics tasks from the DeepMind Control Suite, especially when the reward signal is sparse.
In this paper, we study the meromorphic continuation of the resolvent for the Schr{o}dinger operator in a three-dimensional planar waveguide. We prove the existence of a resonance-free region and an upper bound for the resolvent. As an application, t
he direct source problem is shown to have a unique solution under some appropriate assumptions. Moreover, an increasing stability is achieved for the inverse source problem of the Schr{o}dinger operator in the waveguide by using limited aperture Dirichlet data only at multiple frequencies. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the source function, where the latter decreases as the upper bound of the frequency increases.
Coulomb interaction, following an inverse-square force-law, quantifies the amount of force between two stationary, electrically charged particles. The long-range nature of Coulomb interactions poses a major challenge to molecular dynamics simulations
which are major tools for problems at the nano-/micro- scale. Various algorithms aim to speed up the pairwise Coulomb interactions to a linear scaling but the poor scalability limits the size of simulated systems. Here, we conduct an efficient molecular dynamics algorithm with the random batch Ewald method on all-atom systems where the complete Fourier components in the Coulomb interaction are replaced by randomly selected mini batches. By simulating the N-body systems up to 100 million particles using 10 thousand CPU cores, we show that this algorithm furnishes O(N) complexity, almost perfect scalability and an order of magnitude faster computational speed when compared to the existing state-of-the-art algorithms. Further examinations of our algorithm on distinct systems, including pure water, micro-phase-separated electrolyte and protein solution demonstrate that the spatiotemporal information on all time and length scales investigated and thermodynamic quantities derived from our algorithm are in perfect agreement with those obtained from the existing algorithms. Therefore, our algorithm provides a breakthrough solution on scalability of computing the Coulomb interaction. It is particularly useful and cost-effective to simulate ultra-large systems, which was either impossible or very costing to conduct using existing algorithms, thus would benefit the broad community of sciences.
We propose a fast method for the calculation of short-range interactions in molecular dynamics simulations. The so-called random-batch list method is a stochastic version of the classical neighbor-list method to avoid the construction of a full Verle
t list, which introduces two-level neighbor lists for each particle such that the neighboring particles are located in core and shell regions, respectively. Direct interactions are performed in the core region. For the shell zone, we employ a random batch of interacting particles to reduce the number of interaction pairs. The error estimate of the algorithm is provided. We investigate the Lennard-Jones fluid by molecular dynamics simulations, and show that this novel method can significantly accelerate the simulations with a factor of several fold without loss of the accuracy. This method is simple to implement, can be well combined with any linked cell methods to further speed up and scale up the simulation systems, and can be straightforwardly extended to other interactions such as Ewald short-range part, and thus it is promising for large-scale molecular dynamics simulations.
Human skeleton, as a compact representation of human action, has received increasing attention in recent years. Many skeleton-based action recognition methods adopt graph convolutional networks (GCN) to extract features on top of human skeletons. Des
pite the positive results shown in previous works, GCN-based methods are subject to limitations in robustness, interoperability, and scalability. In this work, we propose PoseC3D, a new approach to skeleton-based action recognition, which relies on a 3D heatmap stack instead of a graph sequence as the base representation of human skeletons. Compared to GCN-based methods, PoseC3D is more effective in learning spatiotemporal features, more robust against pose estimation noises, and generalizes better in cross-dataset settings. Also, PoseC3D can handle multiple-person scenarios without additional computation cost, and its features can be easily integrated with other modalities at early fusion stages, which provides a great design space to further boost the performance. On four challenging datasets, PoseC3D consistently obtains superior performance, when used alone on skeletons and in combination with the RGB modality.
We investigate potential correlations between radio source counts (after background corrections) of 22 Galactic globular clusters (GCs) from the MAVERIC survey, and stellar encounter rates ($Gamma$) and masses ($M$) of the GCs. Applying a radio lumin
osity limit of $L_mathrm{lim}=5.0times 10^{27}~mathrm{erg~s^{-1}}$, we take a census of radio sources in the core and those within the half-light radius. By following a maximum likelihood method and adopting a simplified linear model, we find an unambiguous dependence of core radio source counts on $Gamma$ and/or $M$ at 90% confidence, but no clear dependence of source counts within the half-light radius on either $Gamma$ or $M$. Five of the identified radio sources in cores above our adopted limit are millisecond pulsars or neutron star X-ray binaries (XRBs), the dependence of which on $Gamma$ is well-known, but another is a published black hole (BH) XRB candidate, and ten others are not identified. Accounting for the verified cluster members increases the significance of correlation with $M$ and/or $Gamma$ (to 99% confidence), for fits to core and half-light region source counts, while excluding a dependence on $Gamma$ alone at 90% (core) and 68% (half-light) confidence. This is consistent with published dynamical simulations of GC BH interactions that argue $Gamma$ will be a poor predictor of the distribution of accreting BHs in GCs. Future multiwavelength follow-up to verify cluster membership will enable stronger constraints on the dependence of radio source classes on cluster properties, promising a new view on the dynamics of BHs in GCs.
