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The surface tension coefficient is a key parameter in fluid mechanics. The conventional method to measure it is to determine the critical surface tension that causes the rupture of a liquid film. However, this method has a large error because the surface tension coefficient is very sensitive to environmental factors. In this paper, we propose a new method based on equal thickness interference to study the mathematical model of the stationary liquid surface shape and measure it by the interference technique. This method enables the accurate measurement of the liquid surface tension coefficient. The experimental results demonstrate that this method has the advantages of high accuracy, low cost, and simple instrumentation. The maximum measurement error is less than 3.1\%. Moreover, this method can be applied to measure the liquid-liquid interfacial tension, which has a good application prospect.

We investigate the $W^{1,p}$ estimates of the Neumann problem for the Schr\"odinger equation $-\Delta u+ V u={\rm div}(f)$ in the region above a convex graph. For any $p>2$, we obtain a sufficient condition for the $W^{1,p}$ solvability. As a result, we obtain sharp $W^{1,p}$ estimate $$\|\nabla u\|_{L^p(\Omega)}+\|V^\frac{1}{2}u\|_{L^p(\Omega)}\leq C\|f\|_{L^p(\Omega)}$$ for $1

In this paper we investigate the $L^p$ regularity, $L^p$ Neumann and $W^{1,p}$ problems for generalized Schr\"odinger operator $-\text{div}(A\nabla )+ V $ in the region above a Lipschitz graph under the assumption that $A$ is elliptic, symmetric and $x_d-$independent. Specifically, we prove that the $L^p$ regularity problem is uniquely solvable for $$1

The automatic generation of anchor-style product promotion videos presents promising opportunities in online commerce, advertising, and consumer engagement. However, this remains a challenging task despite significant advancements in pose-guided human video generation. In addressing this challenge, we identify the integration of human-object interactions (HOI) into pose-guided human video generation as a core issue. To this end, we introduce AnchorCrafter, a novel diffusion-based system designed to generate 2D videos featuring a target human and a customized object, achieving high visual fidelity and controllable interactions. Specifically, we propose two key innovations: the HOI-appearance perception, which enhances object appearance recognition from arbitrary multi-view perspectives and disentangles object and human appearance, and the HOI-motion injection, which enables complex human-object interactions by overcoming challenges in object trajectory conditioning and inter-occlusion management. Additionally, we introduce the HOI-region reweighting loss, a training objective that enhances the learning of object details. Extensive experiments demonstrate that our proposed system outperforms existing methods in preserving object appearance and shape awareness, while simultaneously maintaining consistency in human appearance and motion. Project page: https://cangcz.github.io/Anchor-Crafter/

The applications of LLM Agents are becoming increasingly complex and diverse, leading to a high demand for structured outputs that can be parsed into code, structured function calls, and embodied agent commands. These developments bring significant demands for structured generation in LLM inference. Context-free grammar is a flexible approach to enable structured generation via constrained decoding. However, executing context-free grammar requires going through several stack states over all tokens in vocabulary during runtime, bringing non-negligible overhead for structured generation. In this paper, we propose XGrammar, a flexible and efficient structure generation engine for large language models. XGrammar accelerates context-free grammar execution by dividing the vocabulary into context-independent tokens that can be prechecked and context-dependent tokens that need to be interpreted during runtime. We further build transformations to expand the grammar context and reduce the number of context-independent tokens. Additionally, we build an efficient persistent stack to accelerate the context-dependent token checks. Finally, we co-design the grammar engine with LLM inference engine to overlap grammar computation with GPU executions. Evaluation results show that XGrammar can achieve up to 100x speedup over existing solutions. Combined with an LLM inference engine, it can generate near-zero overhead structure generation in end-to-end low-LLM serving.

Open-generation bias benchmarks evaluate social biases in Large Language Models (LLMs) by analyzing their outputs. However, the classifiers used in analysis often have inherent biases, leading to unfair conclusions. This study examines such biases in open-generation benchmarks like BOLD and SAGED. Using the MGSD dataset, we conduct two experiments. The first uses counterfactuals to measure prediction variations across demographic groups by altering stereotype-related prefixes. The second applies explainability tools (SHAP) to validate that the observed biases stem from these counterfactuals. Results reveal unequal treatment of demographic descriptors, calling for more robust bias metric models., Comment: NeurIPS 2024 EvalEval Workshop

Relative state estimation is crucial for vision-based swarms to estimate and compensate for the unavoidable drift of visual odometry. For autonomous drones equipped with the most compact sensor setting -- a stereo camera that provides a limited field of view (FoV), the demand for mutual observation for relative state estimation conflicts with the demand for environment observation. To balance the two demands for FoV limited swarms by acquiring mutual observations with a safety guarantee, this paper proposes an active localization correction system, which plans camera orientations via a yaw planner during the flight. The yaw planner manages the contradiction by calculating suitable timing and yaw angle commands based on the evaluation of localization uncertainty estimated by the Kalman Filter. Simulation validates the scalability of our algorithm. In real-world experiments, we reduce positioning drift by up to 65% and managed to maintain a given formation in both indoor and outdoor GPS-denied flight, from which the accuracy, efficiency, and robustness of the proposed system are verified., Comment: Accepted by IROS 2024, 8 pages, 10 figures

The interactions between a large population of high-frequency traders (HFTs) and a large trader (LT) who executes a certain amount of assets at discrete time points are studied. HFTs are faster in the sense that they trade continuously and predict the transactions of LT. A jump process is applied to model the transition of HFTs' attitudes towards inventories and the equilibrium is solved through the mean field game approach. When the crowd of HFTs is averse to running (ending) inventories, they first take then supply liquidity at each transaction of LT (throughout the whole execution period). Inventory-averse HFTs lower LT's costs if the market temporary impact is relatively large to the permanent one. What's more, the repeated liquidity consuming-supplying behavior of HFTs makes LT's optimal strategy close to uniform trading.

Swarm robots have sparked remarkable developments across a range of fields. While it is necessary for various applications in swarm robots, a fast and robust coordinate initialization in vision-based drone swarms remains elusive. To this end, our paper proposes a complete system to recover a swarm's initial relative pose on platforms with size, weight, and power (SWaP) constraints. To overcome limited coverage of field-of-view (FoV), the drones rotate in place to obtain observations. To tackle the anonymous measurements, we formulate a non-convex rotation estimation problem and transform it into a semi-definite programming (SDP) problem, which can steadily obtain global optimal values. Then we utilize the Hungarian algorithm to recover relative translation and correspondences between observations and drone identities. To safely acquire complete observations, we actively search for positions and generate feasible trajectories to avoid collisions. To validate the practicability of our system, we conduct experiments on a vision-based drone swarm with only stereo cameras and inertial measurement units (IMUs) as sensors. The results demonstrate that the system can robustly get accurate relative poses in real time with limited onboard computation resources. The source code is released.

We investigate a market with a normal-speed informed trader (IT) who may employ mixed strategy and multiple anticipatory high-frequency traders (HFTs) who are under different inventory pressures, in a three-period Kyle's model. The pure- and mixed-strategy equilibria are considered and the results provide recommendations for IT's randomization strategy with different numbers of HFTs. Some surprising results about investors' profits arise: the improvement of anticipatory traders' speed or a more precise prediction may harm themselves but help IT.

Most deep noise suppression (DNS) models are trained with reference-based losses requiring access to clean speech. However, sometimes an additive microphone model is insufficient for real-world applications. Accordingly, ways to use real training data in supervised learning for DNS models promise to reduce a potential training/inference mismatch. Employing real data for DNS training requires either generative approaches or a reference-free loss without access to the corresponding clean speech. In this work, we propose to employ an end-to-end non-intrusive deep neural network (DNN), named PESQ-DNN, to estimate perceptual evaluation of speech quality (PESQ) scores of enhanced real data. It provides a reference-free perceptual loss for employing real data during DNS training, maximizing the PESQ scores. Furthermore, we use an epoch-wise alternating training protocol, updating the DNS model on real data, followed by PESQ-DNN updating on synthetic data. The DNS model trained with the PESQ-DNN employing real data outperforms all reference methods employing only synthetic training data. On synthetic test data, our proposed method excels the Interspeech 2021 DNS Challenge baseline by a significant 0.32 PESQ points. Both on synthetic and real test data, the proposed method beats the baseline by 0.05 DNSMOS points - although PESQ-DNN optimizes for a different perceptual metric.

In an extended Kyle's model, the interactions between a large informed trader and a high-frequency trader (HFT) who can anticipate the former's incoming order are studied. We find that, in equilibrium, HFT may play the role of Small-IT or Round-Tripper: both of them trade in the same direction as IT in advance, but when IT's order arrives, Small-IT continues to take liquidity away, while Round-Tripper supplies liquidity back. So Small-IT always harms IT, while Round-Tripper may benefit her. What's more, with an anticipatory HFT, normal-speed small uninformed traders suffer less and price discovery is accelerated.

Wideband codecs such as AMR-WB or EVS are widely used in (mobile) speech communication. Evaluation of coded speech quality is often performed subjectively by an absolute category rating (ACR) listening test. However, the ACR test is impractical for online monitoring of speech communication networks. Perceptual evaluation of speech quality (PESQ) is one of the widely used metrics instrumentally predicting the results of an ACR test. However, the PESQ algorithm requires an original reference signal, which is usually unavailable in network monitoring, thus limiting its applicability. NISQA is a new non-intrusive neural-network-based speech quality measure, focusing on super-wideband speech signals. In this work, however, we aim at predicting the well-known PESQ metric using a non-intrusive PESQ-DNN model. We illustrate the potential of this model by predicting the PESQ scores of wideband-coded speech obtained from AMR-WB or EVS codecs operating at different bitrates in noisy, tandeming, and error-prone transmission conditions. We compare our methods with the state-of-the-art network topologies of QualityNet, WaweNet, and DNSMOS -- all applied to PESQ prediction -- by measuring the mean absolute error (MAE) and the linear correlation coefficient (LCC). The proposed PESQ-DNN offers the best total MAE and LCC of 0.11 and 0.92, respectively, in conditions without frame loss, and still is best when including frame loss. Note that our model could be similarly used to non-intrusively predict POLQA or other (intrusive) metrics. Upon article acceptance, code will be provided at GitHub.

This paper studies the influences of a high-frequency trader (HFT) on a large trader whose future trading is predicted by the former. We conclude that HFT always front-runs and the large trader is benefited when: (1) there is sufficient high-speed noise trading; (2) HFT's prediction is vague enough. Besides, we find surprisingly that (1) making HFT's prediction less accurate might decrease large trader's profit; (2) when there is little high-speed noise trading, although HFT nearly does nothing, the large trader is still hurt.

Perceptual evaluation of speech quality (PESQ) requires a clean speech reference as input, but predicts the results from (reference-free) absolute category rating (ACR) tests. In this work, we train a fully convolutional recurrent neural network (FCRN) as deep noise suppression (DNS) model, with either a non-intrusive or an intrusive PESQNet, where only the latter has access to a clean speech reference. The PESQNet is used as a mediator providing a perceptual loss during the DNS training to maximize the PESQ score of the enhanced speech signal. For the intrusive PESQNet, we investigate two topologies, called early-fusion (EF) and middle-fusion (MF) PESQNet, and compare to the non-intrusive PESQNet to evaluate and to quantify the benefits of employing a clean speech reference input during DNS training. Detailed analyses show that the DNS trained with the MF-intrusive PESQNet outperforms the Interspeech 2021 DNS Challenge baseline and the same DNS trained with an MSE loss by 0.23 and 0.12 PESQ points, respectively. Furthermore, we can show that only marginal benefits are obtained compared to the DNS trained with the non-intrusive PESQNet. Therefore, as ACR listening tests, the PESQNet does not necessarily require a clean speech reference input, opening the possibility of using real data for DNS training.

In this paper, we investigate the existence of multiple positive solutions to the following multi-critical Schr\"{o}dinger equation \begin{equation} \label{p} \begin{cases} -\Delta u+\lambda V(x)u=\mu |u|^{p-2}u+\sum\limits_{i=1}^{k}(|x|^{-(N-\alpha_i)}* |u|^{2^*_i})|u|^{2^*_i-2}u\quad \text{in}\ \mathbb{R}^N,\\ \qquad\qquad\qquad u\,\in H^1(\mathbb{R}^N), \end{cases} \end{equation} where $\lambda,\mu\in \mathbb{R}^+, \, N\geqslant 4$, and $2^*_i=\frac{N+\alpha_i}{N-2}$ with $N-4<\alpha_i

Floquet multipliers (characteristic multipliers) play significant role in the stability of the periodic equations. Based on the iterative method, we provide a unified algorithm to compute the Floquet multipliers (characteristic multipliers) and determine the stability of the periodic linear differential equations on time scales unifying discrete, continuous, and hybrid dynamics. Our approach is based on calculating the value of A and B (see Theorem 3.1), which are the sum and product of all Floquet multipliers (characteristic multipliers) of the system, respectively. We obtain an explicit expression of A (see Theorem 4.1) by the method of variation and approximation theory and an explicit expression of B by Liouville's formula. Furthermore, a computer program is designed to realize our algorithm. Specifically, you can determine the stability of a second order periodic linear system, whether they are discrete, continuous or hybrid, as long as you enter the program codes associated with the parameters of the equation. In fact, few literatures have dealt with the algorithm to compute the Floquet multipliers, not mention to design the program for its computer realization. Our algorithm gives the explicit expressions of all Floquet multipliers and our computer program is based on the approximations of these explicit expressions. In particular, on an arbitrary discrete periodic time scale, we can do a finite number of calculations to get the explicit value of Floquet multipliers (see Theorem 4.2). Therefore, for any discrete periodic system, we can accurately determine the stability of the system even without computer! Finally, in Section 6, several examples are presented to illustrate the effectiveness of our algorithm.

Speech enhancement employing deep neural networks (DNNs) for denoising are called deep noise suppression (DNS). During training, DNS methods are typically trained with mean squared error (MSE) type loss functions, which do not guarantee good perceptual quality. Perceptual evaluation of speech quality (PESQ) is a widely used metric for evaluating speech quality. However, the original PESQ algorithm is non-differentiable, and therefore cannot directly be used as optimization criterion for gradient-based learning. In this work, we propose an end-to-end non-intrusive PESQNet DNN to estimate the PESQ scores of the enhanced speech signal. Thus, by providing a reference-free perceptual loss, it serves as a mediator towards the DNS training, allowing to maximize the PESQ score of the enhanced speech signal. We illustrate the potential of our proposed PESQNet-mediated training on the basis of an already strong baseline DNS. As further novelty, we propose to train the DNS and the PESQNet alternatingly to keep the PESQNet up-to-date and perform well specifically for the DNS under training. Our proposed method is compared to the same DNS trained with MSE-based loss for joint denoising and dereverberation, and the Interspeech 2021 DNS Challenge baseline. Detailed analysis shows that the PESQNet mediation can further increase the DNS performance by about 0.1 PESQ points on synthetic test data and by 0.03 DNSMOS points on real test data, compared to training with the MSE-based loss. Our proposed method also outperforms the Challenge baseline by 0.2 PESQ points on synthetic test data and 0.1 DNSMOS points on real test data.

Data-driven speech enhancement employing deep neural networks (DNNs) can provide state-of-the-art performance even in the presence of non-stationary noise. During the training process, most of the speech enhancement neural networks are trained in a fully supervised way with losses requiring noisy speech to be synthesized by clean speech and additive noise. However, in a real implementation, only the noisy speech mixture is available, which leads to the question, how such data could be advantageously employed in training. In this work, we propose an end-to-end non-intrusive PESQNet DNN which estimates perceptual evaluation of speech quality (PESQ) scores, allowing a reference-free loss for real data. As a further novelty, we combine the PESQNet loss with denoising and dereverberation loss terms, and train a complex mask-based fully convolutional recurrent neural network (FCRN) in a "weakly" supervised way, each training cycle employing some synthetic data, some real data, and again synthetic data to keep the PESQNet up-to-date. In a subjective listening test, our proposed framework outperforms the Interspeech 2021 Deep Noise Suppression (DNS) Challenge baseline overall by 0.09 MOS points and in particular by 0.45 background noise MOS points.