Automatic math problem solving has recently attracted increasing attention as a long-standing AI benchmark. In this paper, we focus on solving geometric problems, which requires a comprehensive understanding of textual descriptions, visual diagrams,
and theorem knowledge. However, the existing methods were highly dependent on handcraft rules and were merely evaluated on small-scale datasets. Therefore, we propose a Geometric Question Answering dataset GeoQA, containing 5,010 geometric problems with corresponding annotated programs, which illustrate the solving process of the given problems. Compared with another publicly available dataset GeoS, GeoQA is 25 times larger, in which the program annotations can provide a practical testbed for future research on explicit and explainable numerical reasoning. Moreover, we introduce a Neural Geometric Solver (NGS) to address geometric problems by comprehensively parsing multimodal information and generating interpretable programs. We further add multiple self-supervised auxiliary tasks on NGS to enhance cross-modal semantic representation. Extensive experiments on GeoQA validate the effectiveness of our proposed NGS and auxiliary tasks. However, the results are still significantly lower than human performance, which leaves large room for future research. Our benchmark and code are released at https://github.com/chen-judge/GeoQA .
Crowd counting is a fundamental yet challenging task, which desires rich information to generate pixel-wise crowd density maps. However, most previous methods only used the limited information of RGB images and cannot well discover potential pedestri
ans in unconstrained scenarios. In this work, we find that incorporating optical and thermal information can greatly help to recognize pedestrians. To promote future researches in this field, we introduce a large-scale RGBT Crowd Counting (RGBT-CC) benchmark, which contains 2,030 pairs of RGB-thermal images with 138,389 annotated people. Furthermore, to facilitate the multimodal crowd counting, we propose a cross-modal collaborative representation learning framework, which consists of multiple modality-specific branches, a modality-shared branch, and an Information Aggregation-Distribution Module (IADM) to capture the complementary information of different modalities fully. Specifically, our IADM incorporates two collaborative information transfers to dynamically enhance the modality-shared and modality-specific representations with a dual information propagation mechanism. Extensive experiments conducted on the RGBT-CC benchmark demonstrate the effectiveness of our framework for RGBT crowd counting. Moreover, the proposed approach is universal for multimodal crowd counting and is also capable to achieve superior performance on the ShanghaiTechRGBD dataset. Finally, our source code and benchmark are released at {url{http://lingboliu.com/RGBT_Crowd_Counting.html}}.
We generalize the definition of Proof Labeling Schemes to reactive systems, that is, systems where the configuration is supposed to keep changing forever. As an example, we address the main classical test case of reactive tasks, namely, the task of t
oken passing. Different RPLSs are given for the cases that the network is assumed to be a tree or an anonymous ring, or a general graph, and the sizes of RPLSs labels are analyzed. We also address the question of whether an RPLS exists. First, on the positive side, we show that there exists an RPLS for any distributed task for a family of graphs with unique identities. For the case of anonymous networks (even for the special case of rings), interestingly, it is known that no token passing algorithm is possible even if the number n of nodes is known. Nevertheless, we show that an RPLS is possible. On the negative side, we show that if one drops the assumption that n is known, then the construction becomes impossible.
Canonical Feynman integrals are of great interest in the study of scattering amplitudes at the multi-loop level. We propose to construct $dlog$-form integrals of the hypergeometric type, treat them as a representation of Feynman integrals, and projec
t them into master integrals using intersection theory. This provides a constructive way to build canonical master integrals whose differential equations can be solved easily. We use our method to investigate both the maximally cut integrals and the uncut ones at one and two loops, and demonstrate its applicability in problems with multiple scales.
Tropospheric nitrogen dioxide (NO$_2$) concentrations are strongly affected by anthropogenic activities. Using space-based measurements of tropospheric NO$_2$, here we investigate the responses of tropospheric NO$_2$ to the 2019 novel coronavirus (CO
VID-19) over China, South Korea, and Italy. We find noticeable reductions of tropospheric NO$_2$ columns due to the COVID-19 controls by more than 40% over E. China, South Korea, and N. Italy. The 40% reductions of tropospheric NO$_2$ are coincident with intensive lockdown events as well as up to 20% reductions in anthropogenic nitrogen oxides (NO$_x$) emissions. The perturbations in tropospheric NO$_2$ diminished accompanied with the mitigation of COVID-19 pandemic, and finally disappeared within around 50-70 days after the starts of control measures over all three nations, providing indications for the start, maximum, and mitigation of intensive controls. This work exhibits significant influences of lockdown measures on atmospheric environment, highlighting the importance of satellite observations to monitor anthropogenic activity changes.
Crowd counting is an application-oriented task and its inference efficiency is crucial for real-world applications. However, most previous works relied on heavy backbone networks and required prohibitive run-time consumption, which would seriously re
strict their deployment scopes and cause poor scalability. To liberate these crowd counting models, we propose a novel Structured Knowledge Transfer (SKT) framework, which fully exploits the structured knowledge of a well-trained teacher network to generate a lightweight but still highly effective student network. Specifically, it is integrated with two complementary transfer modules, including an Intra-Layer Pattern Transfer which sequentially distills the knowledge embedded in layer-wise features of the teacher network to guide feature learning of the student network and an Inter-Layer Relation Transfer which densely distills the cross-layer correlation knowledge of the teacher to regularize the students feature evolutio Consequently, our student network can derive the layer-wise and cross-layer knowledge from the teacher network to learn compact yet effective features. Extensive evaluations on three benchmarks well demonstrate the effectiveness of our SKT for extensive crowd counting models. In particular, only using around $6%$ of the parameters and computation cost of original models, our distilled VGG-based models obtain at least 6.5$times$ speed-up on an Nvidia 1080 GPU and even achieve state-of-the-art performance. Our code and models are available at {url{https://github.com/HCPLab-SYSU/SKT}}.
Chinese calligraphy is a unique art form with great artistic value but difficult to master. In this paper, we formulate the calligraphy writing problem as a trajectory optimization problem, and propose an improved virtual brush model for simulating t
he real writing process. Our approach is inspired by pseudospectral optimal control in that we parameterize the actuator trajectory for each stroke as a Chebyshev polynomial. The proposed dynamic virtual brush model plays a key role in formulating the objective function to be optimized. Our approach shows excellent performance in drawing aesthetically pleasing characters, and does so much more efficiently than previous work, opening up the possibility to achieve real-time closed-loop control.
Chinese calligraphy is a unique art form with great artistic value but difficult to master. In this paper, we formulate the calligraphy writing problem as a trajectory optimization problem, and propose an improved virtual brush model for simulating t
he real writing process. Our approach is inspired by pseudospectral optimal control in that we parameterize the actuator trajectory for each stroke as a Chebyshev polynomial. The proposed dynamic virtual brush model plays a key role in formulating the objective function to be optimized. Our approach shows excellent performance in drawing aesthetically pleasing characters, and does so much more efficiently than previous work, opening up the possibility to achieve real-time closed-loop control.
Feeding external data to a blockchain, a.k.a. data feed, is an essential task to enable blockchain interoperability and support emerging cross-domain applications, notably stablecoins. Given the data-intensive feeds in real life (e.g., high-frequency
price updates) and the high cost in using blockchain, namely Gas, it is imperative to reduce the Gas cost of data feeds. Motivated by the constant-changing workloads in finance and other applications, this work focuses on designing a dynamic, workload-aware approach for cost effectiveness in Gas. This design space is understudied in the existing blockchain research which has so far focused on static data placement. This work presents GRuB, a cost-effective data feed that dynamically replicates data between the blockchain and an off-chain cloud storage. GRuBs data replication is workload-adaptive by monitoring the current workload and making online decisions w.r.t. data replication. A series of online algorithms are proposed that achieve the bounded worst-case cost in blockchains Gas. GRuB runs the decision-making components on the untrusted cloud off-chain for lower Gas costs, and employs a security protocol to authenticate the data transferred between the blockchain and cloud. The overall GRuB system can autonomously achieve low Gas costs with changing workloads. We built a GRuB prototype functional with Ethereum and Google LevelDB, and supported real applications in stablecoins. Under real workloads collected from the Ethereum contract-call history and mixed workloads of YCSB, we systematically evaluate GRuBs cost which shows a saving of Gas by 10% ~ 74%, with comparison to the baselines of static data-placement.
With the seamless coverage of wireless cellular networks in modern society, it is interesting to consider the shape of wireless cellular coverage. Is the shape a regular hexagon, an irregular polygon, or another complex geometrical shape? Based on fr
actal theory, the statistical characteristic of the wireless cellular coverage boundary is determined by the measured wireless cellular data collected from Shanghai, China. The measured results indicate that the wireless cellular coverage boundary presents an extremely irregular geometrical shape, which is also called a statistical fractal shape. Moreover, the statistical fractal characteristics of the wireless cellular coverage boundary have been validated by values of the Hurst parameter estimated in angular scales. The statistical fractal characteristics of the wireless cellular coverage boundary can be used to evaluate and design the handoff scheme of mobile user terminals in wireless cellular networks.
