The growth model of black hole is still a controversial topic. In the stationary metric, all in-falling matter must be accumulated outside the event horizon of the black hole, as clocked by a distant external observer. In the time-dependent metric, a
ll in-falling matter can fall into the event horizon of the final black hole within very short time. We test these two growth models by joining LIGO and Insight-HXMT observations. We find the stationary model is inconsistent with LIGO and Insight-HXMT observations.
Facing the dilemma of growing energy demand and mitigating carbon emissions, this paper proposes an energy sharing mechanism based on virtual federated prosumers (VFPs) with budget allocation for joint electricity and carbon market to incentivize dis
tributed energy resources to participate in the hierarchical market and reduce carbon emissions. At the transmission level, the regional transmission operator coordinates transactions between two markets, the inter-VFP energy sharing market and the wholesale market, intending to minimize the overall cost of VFPs. The energy sharing market clearing problem is formulated as a generalized Nash game, for which we develop a first-order response algorithm to obtain the equilibrium. At the distribution level, the VFPs play the role of selfless auctioneer that leverage discriminatory weights and benchmark prices to allocate the electricity-carbon budget among entities in the VFP to maximize social welfare. The Nash game is exploited to characterize the budget allocation problem, for which a distributed feedback allocation algorithm is proposed. The entire hierarchical electricity and carbon trading is modeled as an equilibrium problem and is solved iteratively. Case studies based on a practical regional grid verify the effectiveness of the proposed algorithm and show that the mechanism is effective in improving energy efficiency and reducing carbon emissions.
We study the equivalence problem of classifying second order ordinary differential equations $y_{xx}=J(x,y,y_{x})$ modulo fibre-preserving point transformations $xlongmapsto varphi(x)$, $ylongmapsto psi(x,y)$ by using Mosers method of normal forms. W
e first compute a basis of the Lie algebra ${frak{g}}_{{{y_{xx}=0}}}$ of fibre-preserving symmetries of $y_{xx}=0$. In the formal theory of Mosers method, this Lie algebra is used to give an explicit description of the set of normal forms $mathcal{N}$, and we show that the set is an ideal in the space of formal power series. We then show the existence of the normal forms by studying flows of suitable vector fields with appropriate corrections by the Cauchy-Kovalevskaya theorem. As an application, we show how normal forms can be used to prove that the identical vanishing of Hsu-Kamran primary invariants directly imply that the second order differential equation is fibre-preserving point equivalent to $y_{xx}=0$.
For a positive integer $N$, let $mathscr{C}_N(mathbb{Q})$ be the rational cuspidal subgroup of $J_0(N)$ and $mathscr{C}(N)$ be the rational cuspidal divisor class group of $X_0(N)$, which are both subgroups of the rational torsion subgroup of $J_0(N)
$. We prove that two groups $mathscr{C}_N(mathbb{Q})$ and $mathscr{C}(N)$ are equal when $N=p^2M$ for any prime $p$ and any squarefree integer $M$. To achieve this we show that all modular units on $X_0(N)$ can be written as products of certain functions $F_{m, h}$, which are constructed from generalized Dedekind eta functions. Also, we determine the necessary and sufficient conditions for such products to be modular units on $X_0(N)$ under a mild assumption.
Tabular data prediction (TDP) is one of the most popular industrial applications, and various methods have been designed to improve the prediction performance. However, existing works mainly focus on feature interactions and ignore sample relations,
e.g., users with the same education level might have a similar ability to repay the debt. In this work, by explicitly and systematically modeling sample relations, we propose a novel framework TabGNN based on recently popular graph neural networks (GNN). Specifically, we firstly construct a multiplex graph to model the multifaceted sample relations, and then design a multiplex graph neural network to learn enhanced representation for each sample. To integrate TabGNN with the tabular solution in our company, we concatenate the learned embeddings and the original ones, which are then fed to prediction models inside the solution. Experiments on eleven TDP datasets from various domains, including classification and regression ones, show that TabGNN can consistently improve the performance compared to the tabular solution AutoFE in 4Paradigm.
Many search systems work with large amounts of natural language data, e.g., search queries, user profiles, and documents. Building a successful search system requires a thorough understanding of textual data semantics, where deep learning based natur
al language processing techniques (deep NLP) can be of great help. In this paper, we introduce a comprehensive study for applying deep NLP techniques to five representative tasks in search systems: query intent prediction (classification), query tagging (sequential tagging), document ranking (ranking), query auto completion (language modeling), and query suggestion (sequence to sequence). We also introduce BERT pre-training as a sixth task that can be applied to many of the other tasks. Through the model design and experiments of the six tasks, readers can find answers to four important questions: (1). When is deep NLP helpful/not helpful in search systems? (2). How to address latency challenges? (3). How to ensure model robustness? This work builds on existing efforts of LinkedIn search, and is tested at scale on LinkedIns commercial search engines. We believe our experiences can provide useful insights for the industry and research communities.
We present an automatic COVID1-19 diagnosis framework from lung CT images. The focus is on signal processing and classification on small datasets with efforts putting into exploring data preparation and augmentation to improve the generalization capa
bility of the 2D CNN classification models. We propose a unique and effective data augmentation method using multiple Hounsfield Unit (HU) normalization windows. In addition, the original slice image is cropped to exclude background, and a filter is applied to filter out closed-lung images. For the classification network, we choose to use 2D Densenet and Xception with the feature pyramid network (FPN). To further improve the classification accuracy, an ensemble of multiple CNN models and HU windows is used. On the training/validation dataset, we achieve a patient classification accuracy of 93.39%.
From electromagnetic wave equations, it is first found that, mathematically, any current density that emits an electromagnetic wave into the far-field region has to be differentiable in time infinitely, and that while the odd-order time derivatives o
f the current density are built in the emitted electric field, the even-order derivatives are built in the emitted magnetic field. With the help of Faradays law and Amperes law, light propagation is then explained as a process involving alternate creation of electric and magnetic fields. From this explanation, the preceding mathematical result is demonstrated to be physically sound. It is also explained why the conventional retarded solutions to the wave equations fail to describe the emitted fields.
Solar activity cycle varies in amplitude. The last Cycle 24 is the weakest in the past century. Suns activity dominates Earths space environment. The frequency and intensity of the Suns activity are accordant with the solar cycle. Hence there are pra
ctical needs to know the amplitude of the upcoming Cycle 25. The dynamo-based solar cycle predictions not only provide predictions, but also offer an effective way to evaluate our understanding of the solar cycle. In this article we apply the method of the first successful dynamo-based prediction developed for Cycle 24 to the prediction of Cycle 25, so that we can verify whether the previous success is repeatable. The prediction shows that Cycle 25 would be about 10% stronger than Cycle 24 with an amplitude of 126 (international sunspot number version 2.0). The result suggests that Cycle 25 will not enter the Maunder-like grand solar minimum as suggested by some publications. Solar behavior in about four to five years will give a verdict whether the prediction method captures the key mechanism for solar cycle variability, which is assumed as the polar field around the cycle minimum in the model.
Low gravity environment can have a profound impact on the behaviors of biological systems, the dynamics and heat transfer of fluids, and the growth and self-organization of materials. Systematic research on the effects of gravity is crucial for advan
cing our knowledge and for the success of space missions. Due to the high cost and the limitations in the payload size and mass in typical spaceflight missions, ground-based low-gravity simulators have become indispensable for preparing spaceflight experiments and for serving as stand-alone research platforms. Among various simulator systems, the magnetic levitation based simulator (MLS) has received long-lasting interests due to its easily adjustable gravity and practically unlimited operation time. However, a recognized issue with MLSs is their highly non-uniform force field. For a solenoid MLS, the functional volume $V_{1%}$, where the net force results in an acceleration less than 1% of the Earths gravity $g$, is typically a few microliters ($mu L$) or less. In this work, we report an innovative MLS design that integrates a superconducting magnet with a gradient-field Maxwell coil. Through an optimization analysis, we show that an unprecedented $V_{1%}$ of over 4,000 $mu L$ can be achieved in a compact coil with a diameter of 8 cm. We also discuss how such an MLS can be made using existing high-$T_c$ superconducting materials. When the current in this MLS is reduced to emulate the gravity on Mars ($g_M=0.38g$), a functional volume where the gravity varies within a few percent of $g_M$ can exceed 20,000 $mu L$. Our design may break new ground for various exciting future low-gravity research.
