Vertex-based Networks to Accelerate Path Planning Algorithms

Path planning plays a crucial role in various autonomy applications, and RRT* is one of the leading solutions in this field. In this paper, we propose the utilization of vertex-based networks to enhance the sampling process of RRT*, leading to more efficient path planning. Our approach focuses on critical vertices along the optimal paths, which provide essential yet sparser abstractions of the paths. We employ focal loss to address the associated data imbalance issue, and explore different masking configurations to determine practical tradeoffs in system performance. Through experiments conducted on randomly generated floor maps, our solutions demonstrate significant speed improvements, achieving over a 400% enhancement compared to the baseline model.Comment: Accepted to IEEE Workshop on Machine Learning for Signal Processing (MLSP'2023

Norm and time optimal control problems of stochastic heat equations

This paper investigates the norm and time optimal control problems for stochastic heat equations. We begin by presenting a characterization of the norm optimal control, followed by a discussion of its properties. We then explore the equivalence between the norm optimal control and time optimal control, and subsequently establish the bang-bang property of the time optimal control. These problems, to the best of our knowledge, are among the first to discuss in the stochastic case

Optimal Actuator Location of the Norm Optimal Controls for Degenerate Parabolic Equations

This paper focuses on investigating the optimal actuator location for achieving minimum norm controls in the context of approximate controllability for degenerate parabolic equations. We propose a formulation of the optimization problem that encompasses both the actuator location and its associated minimum norm control. Specifically, we transform the problem into a two-person zero-sum game problem, resulting in the development of four equivalent formulations. Finally, we establish the crucial result that the solution to the relaxed optimization problem serves as an optimal actuator location for the classical problem

Null controllability of two kinds of coupled parabolic systems with switching control

The focus of this paper is on the null controllability of two kinds of coupled systems including both degenerate and non-degenerate equations with switching control. We first establish the observability inequality for measurable subsets in time for such coupled system, and then by the HUM method to obtain the null controllability. Next, we investigate the null controllability of such coupled system for segmented time intervals. Notably, these results are obtained through spectral inequalities rather than using the method of Carleman estimates. Such coupled systems with switching control, to the best of our knowledge, are among the first to discuss

Observability inequalities for the backward stochastic evolution equations and their applications

The present article delves into the investigation of observability inequalities pertaining to backward stochastic evolution equations. We employ a combination of spectral inequalities, interpolation inequalities, and the telegraph series method as our primary tools to directly establish observability inequalities. Furthermore, we explore three specific equations as application examples: a stochastic degenerate equation, a stochastic fourth order parabolic equation and a stochastic heat equation. It is noteworthy that these equations can be rendered null controllability with only one control in the drift term to each system

Some controllability results of a class of N-dimensional parabolic equations with internal single-point degeneracy

This paper investigates the controllability of a class of $N$-dimensional degenerate parabolic equations with interior single-point degeneracy. We employ the Galerkin method to prove the existence of solutions for the equations. The analysis is then divided into two cases based on whether the degenerate point $x=0$ lies within the control region $\omega_0$ or not. For each case, we establish specific Carleman estimates. As a result, we achieve null controllability in the first case $0\in\omega_0$ and unique continuation and approximate controllability in the second case $0\notin\omega_0$

Stable homotopy, 1-dimensional NCCW complexes, and Property (H)

In this paper, we show that the homomorphisms between two unital one-dimensional NCCW complexes with the same KK-class are stably homotopic, i.e., with adding on a common homomorphism (with finite dimensional image), they are homotopic. As a consequence, any one-dimensional NCCW complex has the Property (H).Comment: Add motivation and backgroun

Once is Enough: A Light-Weight Cross-Attention for Fast Sentence Pair Modeling

Transformer-based models have achieved great success on sentence pair modeling tasks, such as answer selection and natural language inference (NLI). These models generally perform cross-attention over input pairs, leading to prohibitive computational costs. Recent studies propose dual-encoder and late interaction architectures for faster computation. However, the balance between the expressive of cross-attention and computation speedup still needs better coordinated. To this end, this paper introduces a novel paradigm MixEncoder for efficient sentence pair modeling. MixEncoder involves a light-weight cross-attention mechanism. It conducts query encoding only once while modeling the query-candidate interaction in parallel. Extensive experiments conducted on four tasks demonstrate that our MixEncoder can speed up sentence pairing by over 113x while achieving comparable performance as the more expensive cross-attention models.Comment: Accepted to EMNLP 202

Observation-constrained projection of flood risks and socioeconomic exposure in China

As the planet warms, the atmosphere's water vapor holding capacity rises, leading to more intense precipitation extremes. River floods with high peak discharge or long duration can increase the likelihood of infrastructure failure and enhance ecosystem vulnerability. However, changes in the peak and duration of floods and corresponding socioeconomic exposure under climate change are still poorly understood. This study employs a bivariate framework to quantify changes in flood risks and their socioeconomic impacts in China between the past (1985–2014) and future (2071–2100) in 204 catchments. Future daily river streamflow is projected by using a cascade modeling chain based on the outputs of five bias-corrected global climate models (GCMs) under three shared socioeconomic CMIP6 pathways (SSP1-26, SSP3-70, and SSP5-85), a machine learning model and four hydrological models. We also utilize the copula function to build the joint distribution of flood peak and duration, and calculate the joint return periods of the bivariate flood hazard. Finally, the exposure of population and regional gross domestic product to floods are investigated at the national scale. Our results indicate that flood peak and duration are likely to increase in the majority of catchments by 25%–100% by the late 21st century depending on the shared socioeconomic pathway. China is projected to experience a significant increase in bivariate flood risks even under the lowest emission pathway, with 24.0 million dollars/km2 and 608 people/km2 exposed under a moderate emissions scenario (SSP3-70). These findings have direct implications for hazard mitigation and climate adaptation policies in China