The Economic Behavior (Function) of Chinese Militia during the Second World War (Anti-Japanese War)

A militia is an organization that operates like an army but whose members are not professional soldiers. The functions of a militia vary in different periods, particularly during a war, when the militia not only plays a special role in national defense but also plays a unique role in economic production, which has a vital impact on a war scenario. This paper is about the militia in the Shandong Province of China during the Second World War. It explores archival materials to examine the unique economic functions of the militia during this period, and it shows how the militia’s economic role affected the Pacific War

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

Operators which are polynomially isometric to a normal operator

Let $\mathcal{H}$ be a complex, separable Hilbert space and $\mathcal{B}(\mathcal{H})$ denote the algebra of all bounded linear operators acting on $\mathcal{H}$. Given a unitarily-invariant norm $\| \cdot \|_u$ on $\mathcal{B}(\mathcal{H})$ and two linear operators $A$ and $B$ in $\mathcal{B}(\mathcal{H})$, we shall say that $A$ and $B$ are \emph{polynomially isometric relative to} $\| \cdot \|_u$ if $\| p(A) \|_u = \| p(B) \|_u$ for all polynomials $p$. In this paper, we examine to what extent an operator $A$ being polynomially isometric to a normal operator $N$ implies that $A$ is itself normal. More explicitly, we first show that if $\| \cdot \|_u$ is any unitarily-invariant norm on $\mathbb{M}_n(\mathbb{C})$, if $A, N \in \mathbb{M}_n(\mathbb{C})$ are polynomially isometric and $N$ is normal, then $A$ is normal. We then extend this result to the infinite-dimensional setting by showing that if $A, N \in \mathcal{B}(\mathcal{H})$ are polynomially isometric relative to the operator norm and $N$ is a normal operator whose spectrum neither disconnects the plane nor has interior, then $A$ is normal, while if the spectrum of $N$ is not of this form, then there always exists a non-normal operator $B$ such that $B$ and $N$ are polynomially isometric. Finally, we show that if $A$ and $N$ are compact operators with $N$ normal, and if $A$ and $N$ are polynomially isometric with respect to the $(c,p)$-norm studied by Chan, Li and Tu, then $A$ is again normal.Comment: submitte

Multi-Agent Combinatorial Path Finding with Heterogeneous Task Duration

Multi-Agent Combinatorial Path Finding (MCPF) seeks collision-free paths for multiple agents from their initial locations to destinations, visiting a set of intermediate target locations in the middle of the paths, while minimizing the sum of arrival times. While a few approaches have been developed to handle MCPF, most of them simply direct the agent to visit the targets without considering the task duration, i.e., the amount of time needed for an agent to execute the task (such as picking an item) at a target location. MCPF is NP-hard to solve to optimality, and the inclusion of task duration further complicates the problem. This paper investigates heterogeneous task duration, where the duration can be different with respect to both the agents and targets. We develop two methods, where the first method post-processes the paths planned by any MCPF planner to include the task duration and has no solution optimality guarantee; and the second method considers task duration during planning and is able to ensure solution optimality. The numerical and simulation results show that our methods can handle up to 20 agents and 50 targets in the presence of task duration, and can execute the paths subject to robot motion disturbance

Normal operators with highly incompatible off-diagonal corners

Let $\mathcal{H}$ be a complex, separable Hilbert space, and $\mathcal{B}(\mathcal{H})$ denote the set of all bounded linear operators on $\mathcal{H}$. Given an orthogonal projection $P \in \mathcal{B}(\mathcal{H})$ and an operator $D \in \mathcal{B}(\mathcal{H})$, we may write $D=\begin{bmatrix} D_1& D_2 D_3 & D_4 \end{bmatrix}$ relative to the decomposition $\mathcal{H} = \mathrm{ran}\, P \oplus \mathrm{ran}\, (I-P)$. In this paper we study the question: for which non-negative integers $j, k$ can we find a normal operator $D$ and an orthogonal projection $P$ such that $\mathrm{rank}\, D_2 = j$ and $\mathrm{rank}\, D_3 = k$? Complete results are obtained in the case where $\mathrm{dim}\, \mathcal{H} < \infty$, and partial results are obtained in the infinite-dimensional setting.Comment: submitte

BEV-IO: Enhancing Bird's-Eye-View 3D Detection with Instance Occupancy

A popular approach for constructing bird's-eye-view (BEV) representation in 3D detection is to lift 2D image features onto the viewing frustum space based on explicitly predicted depth distribution. However, depth distribution can only characterize the 3D geometry of visible object surfaces but fails to capture their internal space and overall geometric structure, leading to sparse and unsatisfactory 3D representations. To mitigate this issue, we present BEV-IO, a new 3D detection paradigm to enhance BEV representation with instance occupancy information. At the core of our method is the newly-designed instance occupancy prediction (IOP) module, which aims to infer point-level occupancy status for each instance in the frustum space. To ensure training efficiency while maintaining representational flexibility, it is trained using the combination of both explicit and implicit supervision. With the predicted occupancy, we further design a geometry-aware feature propagation mechanism (GFP), which performs self-attention based on occupancy distribution along each ray in frustum and is able to enforce instance-level feature consistency. By integrating the IOP module with GFP mechanism, our BEV-IO detector is able to render highly informative 3D scene structures with more comprehensive BEV representations. Experimental results demonstrate that BEV-IO can outperform state-of-the-art methods while only adding a negligible increase in parameters (0.2%) and computational overhead (0.24%in GFLOPs).Comment: v

Quantitative uniqueness estimates for stochastic parabolic equations on the whole Euclidean space

In this paper, a quantitative estimate of unique continuation for the stochastic heat equation with bounded potentials on the whole Euclidean space is established. This paper generalizes the earlier results in [29] and [17] from a bounded domain to an unbounded one. The proof is based on the locally parabolic-type frequency function method. An observability estimate from measurable sets in time for the same equation is also derived.Comment: 26 page

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