Given a hyperelliptic curve $C$ of genus $g$ over a number field $K$ and a Weierstrass model $mathscr{C}$ of $C$ over the ring of integers ${mathcal O}_K$ (i.e. the hyperelliptic involution of $C$ extends to $mathscr{C}$ and the quotient is a smooth
model of ${mathbb P}^1_K$ over ${mathcal O}_K$), we give necessary and sometimes sufficient conditions for $mathscr{C}$ to be defined by a global Weierstrass equation. In particular, if $C$ has everywhere good reduction, we prove that it is defined by a global Weierstrass equation with invertible discriminant if the class number $h_K$ is prime to $2(2g+1)$, confirming a conjecture of M. Sadek.
The multivariate time series forecasting has attracted more and more attention because of its vital role in different fields in the real world, such as finance, traffic, and weather. In recent years, many research efforts have been proposed for forec
asting multivariate time series. Although some previous work considers the interdependencies among different variables in the same timestamp, existing work overlooks the inter-connections between different variables at different time stamps. In this paper, we propose a simple yet efficient instance-wise graph-based framework to utilize the inter-dependencies of different variables at different time stamps for multivariate time series forecasting. The key idea of our framework is aggregating information from the historical time series of different variables to the current time series that we need to forecast. We conduct experiments on the Traffic, Electricity, and Exchange-Rate multivariate time series datasets. The results show that our proposed model outperforms the state-of-the-art baseline methods.
We study a quantum phase transition from a massless to massive Dirac fermion phase in a new two-dimensional bipartite lattice model of electrons that is amenable to sign-free quantum Monte Carlo simulations. Importantly, interactions in our model are
not only invariant under $SU(2)$ symmetries of spin and charge like the Hubbard model, but they also preserve an Ising like electron spin-charge flip symmetry. From unbiased fermion bag Monte Carlo simulations with up to 2304 sites, we show that the massive fermion phase spontaneously breaks this Ising symmetry, picking either anti-ferromagnetism or superconductivity and that the transition at which both orders are simultaneously quantum critical, belongs to a new chiral spin-charge symmetric universality class. We explain our observations using effective potential and renormalization group calculations within the framework of a continuum field theory.
Conventional entity typing approaches are based on independent classification paradigms, which make them difficult to recognize inter-dependent, long-tailed and fine-grained entity types. In this paper, we argue that the implicitly entailed extrinsic
and intrinsic dependencies between labels can provide critical knowledge to tackle the above challenges. To this end, we propose emph{Label Reasoning Network(LRN)}, which sequentially reasons fine-grained entity labels by discovering and exploiting label dependencies knowledge entailed in the data. Specifically, LRN utilizes an auto-regressive network to conduct deductive reasoning and a bipartite attribute graph to conduct inductive reasoning between labels, which can effectively model, learn and reason complex label dependencies in a sequence-to-set, end-to-end manner. Experiments show that LRN achieves the state-of-the-art performance on standard ultra fine-grained entity typing benchmarks, and can also resolve the long tail label problem effectively.
Data augmentation has been widely used in image data and linguistic data but remains under-explored on graph-structured data. Existing methods focus on augmenting the graph data from a global perspective and largely fall into two genres: structural m
anipulation and adversarial training with feature noise injection. However, the structural manipulation approach suffers information loss issues while the adversarial training approach may downgrade the feature quality by injecting noise. In this work, we introduce the local augmentation, which enhances node features by its local subgraph structures. Specifically, we model the data argumentation as a feature generation process. Given the central nodes feature, our local augmentation approach learns the conditional distribution of its neighbors features and generates the neighbors optimal feature to boost the performance of downstream tasks. Based on the local augmentation, we further design a novel framework: LA-GNN, which can apply to any GNN models in a plug-and-play manner. Extensive experiments and analyses show that local augmentation consistently yields performance improvement for various GNN architectures across a diverse set of benchmarks. Code is available at https://github.com/Soughing0823/LAGNN.
We study the understanding of embodied reference: One agent uses both language and gesture to refer to an object to another agent in a shared physical environment. Of note, this new visual task requires understanding multimodal cues with perspective-
taking to identify which object is being referred to. To tackle this problem, we introduce YouRefIt, a new crowd-sourced dataset of embodied reference collected in various physical scenes; the dataset contains 4,195 unique reference clips in 432 indoor scenes. To the best of our knowledge, this is the first embodied reference dataset that allows us to study referring expressions in daily physical scenes to understand referential behavior, human communication, and human-robot interaction. We further devise two benchmarks for image-based and video-based embodied reference understanding. Comprehensive baselines and extensive experiments provide the very first result of machine perception on how the referring expressions and gestures affect the embodied reference understanding. Our results provide essential evidence that gestural cues are as critical as language cues in understanding the embodied reference.
We study the optical appearance of a thin accretion disk around a Schwarzschild black hole pierced by a cosmic string with a semi-analytic method of Luminet [11]. Direct and secondary images with different parameters observed by a distant observer is
plotted. The cosmic string parameter s can modify the shape and size of the thin disk image. We calculate and plot the distribution of both redshift and observed flux as seen by distant observers at different inclination angles. Those distributions are dependent on the inclination angel of the observer and cosmic parameter s.
A recent work from Bello shows that training and scaling strategies may be more significant than model architectures for visual recognition. This short note studies effective training and scaling strategies for video recognition models. We propose a
simple scaling strategy for 3D ResNets, in combination with improved training strategies and minor architectural changes. The resulting models, termed 3D ResNet-RS, attain competitive performance of 81.0 on Kinetics-400 and 83.8 on Kinetics-600 without pre-training. When pre-trained on a large Web Video Text dataset, our best model achieves 83.5 and 84.3 on Kinetics-400 and Kinetics-600. The proposed scaling rule is further evaluated in a self-supervised setup using contrastive learning, demonstrating improved performance. Code is available at: https://github.com/tensorflow/models/tree/master/official.
Recent work on Open Domain Question Answering has shown that there is a large discrepancy in model performance between novel test questions and those that largely overlap with training questions. However, it is as of yet unclear which aspects of nove
l questions that make them challenging. Drawing upon studies on systematic generalization, we introduce and annotate questions according to three categories that measure different levels and kinds of generalization: training set overlap, compositional generalization (comp-gen), and novel entity generalization (novel-entity). When evaluating six popular parametric and non-parametric models, we find that for the established Natural Questions and TriviaQA datasets, even the strongest model performance for comp-gen/novel-entity is 13.1/5.4% and 9.6/1.5% lower compared to that for the full test set -- indicating the challenge posed by these types of questions. Furthermore, we show that whilst non-parametric models can handle questions containing novel entities, they struggle with those requiring compositional generalization. Through thorough analysis we find that key question difficulty factors are: cascading errors from the retrieval component, frequency of question pattern, and frequency of the entity.
Dielectrics with low loss at microwave frequencies are imperative for high-coherence solid-state quantum computing platforms. We study the dielectric loss of hexagonal boron nitride (hBN) thin films in the microwave regime by measuring the quality fa
ctor of parallel-plate capacitors (PPCs) made of NbSe2-hBN-NbSe2 heterostructures integrated into superconducting circuits. The extracted microwave loss tangent of hBN is bounded to be at most in the mid-10-6 range in the low temperature, single-photon regime. We integrate hBN PPCs with aluminum Josephson junctions to realize transmon qubits with coherence times reaching 25 $mu$s, consistent with the hBN loss tangent inferred from resonator measurements. The hBN PPC reduces the qubit feature size by approximately two-orders of magnitude compared to conventional all-aluminum coplanar transmons. Our results establish hBN as a promising dielectric for building high-coherence quantum circuits with substantially reduced footprint and, with a high energy participation that helps to reduce unwanted qubit cross-talk.
