Application of Hyperbolic Paraboloid in Architectural Design

Hyperbolic paraboloid is a kind of ruled space surface with beautiful shape. It is often used in architectural design and can achieve a free and flexible appearance effect. Due to the complexity of curved surfaces, many architects do not know how to navigate them. The main purpose of this article is to explore how to use hyperbolic paraboloids in architectural design. Firstly, the formation principle of hyperbolic paraboloid is analyzed from a mathematical perspective. Then, through investigating examples, it expounds its application in architectural design. Hyperbolic paraboloids are mainly used in building roofs, especially in large span buildings. There are three uses of hyperbolic paraboloids in roofs, corresponding to three different architectural shapes.The first is to cut a hyperbolic paraboloid vertically with four planes, and the contour projection is a rectangle or parallelogram. The second is to cut the hyperbolic paraboloid vertically and horizontally with four planes, and the contour projection is a curved quadrilateral. The third is to cut hyperbolic paraboloid with elliptic surface, and the contour projection is an ellipse. Finally, the conclusion is drawn on how to flexibly use hyperbolic paraboloids in architectural design, and what are the advantages and disadvantages of hyperbolic paraboloids, which has important reference value for architects to carry out related designs

Reduced projection method for quasiperiodic Schr\"{o}dinger eigenvalue problems

This paper presents a reduced algorithm to the classical projection method for the solution of $d$-dimensional quasiperiodic problems, particularly Schr\"{o}dinger eigenvalue problems. Using the properties of the Schr\"{o}dinger operator in higher-dimensional space via a projection matrix of size $d\times n$, we rigorously prove that the generalized Fourier coefficients of the eigenfunctions decay exponentially along a fixed direction associated with the projection matrix. An efficient reduction strategy of the basis space is then proposed to reduce the degrees of freedom from $O(N^{n})$ to $O(N^{n-d}D^d)$, where $N$ is the number of Fourier grids in one dimension and the truncation coefficient $D$ is much less than $N$. Correspondingly, the computational complexity of the proposed algorithm for solving the first $k$ eigenpairs using the Krylov subspace method decreases from $O(kN^{2n})$ to $O(kN^{2(n-d)}D^{2d})$. Rigorous error estimates of the proposed reduced projection method are provided, indicating that a small $D$ is sufficient to achieve the same level of accuracy as the classical projection method. We present numerical examples of quasiperiodic Schr\"{o}dinger eigenvalue problems in one and two dimensions to demonstrate the accuracy and efficiency of our proposed method.Comment: 20 pages, 9 figure

CuNeRF: Cube-Based Neural Radiance Field for Zero-Shot Medical Image Arbitrary-Scale Super Resolution

Medical image arbitrary-scale super-resolution (MIASSR) has recently gained widespread attention, aiming to super sample medical volumes at arbitrary scales via a single model. However, existing MIASSR methods face two major limitations: (i) reliance on high-resolution (HR) volumes and (ii) limited generalization ability, which restricts their application in various scenarios. To overcome these limitations, we propose Cube-based Neural Radiance Field (CuNeRF), a zero-shot MIASSR framework that can yield medical images at arbitrary scales and viewpoints in a continuous domain. Unlike existing MIASSR methods that fit the mapping between low-resolution (LR) and HR volumes, CuNeRF focuses on building a coordinate-intensity continuous representation from LR volumes without the need for HR references. This is achieved by the proposed differentiable modules: including cube-based sampling, isotropic volume rendering, and cube-based hierarchical rendering. Through extensive experiments on magnetic resource imaging (MRI) and computed tomography (CT) modalities, we demonstrate that CuNeRF outperforms state-of-the-art MIASSR methods. CuNeRF yields better visual verisimilitude and reduces aliasing artifacts at various upsampling factors. Moreover, our CuNeRF does not need any LR-HR training pairs, which is more flexible and easier to be used than others. Our code will be publicly available soon

Hard Nominal Example-aware Template Mutual Matching for Industrial Anomaly Detection

Anomaly detectors are widely used in industrial production to detect and localize unknown defects in query images. These detectors are trained on nominal images and have shown success in distinguishing anomalies from most normal samples. However, hard-nominal examples are scattered and far apart from most normalities, they are often mistaken for anomalies by existing anomaly detectors. To address this problem, we propose a simple yet efficient method: \textbf{H}ard Nominal \textbf{E}xample-aware \textbf{T}emplate \textbf{M}utual \textbf{M}atching (HETMM). Specifically, \textit{HETMM} aims to construct a robust prototype-based decision boundary, which can precisely distinguish between hard-nominal examples and anomalies, yielding fewer false-positive and missed-detection rates. Moreover, \textit{HETMM} mutually explores the anomalies in two directions between queries and the template set, and thus it is capable to capture the logical anomalies. This is a significant advantage over most anomaly detectors that frequently fail to detect logical anomalies. Additionally, to meet the speed-accuracy demands, we further propose \textbf{P}ixel-level \textbf{T}emplate \textbf{S}election (PTS) to streamline the original template set. \textit{PTS} selects cluster centres and hard-nominal examples to form a tiny set, maintaining the original decision boundaries. Comprehensive experiments on five real-world datasets demonstrate that our methods yield outperformance than existing advances under the real-time inference speed. Furthermore, \textit{HETMM} can be hot-updated by inserting novel samples, which may promptly address some incremental learning issues

Pythagoras Superposition Principle for Localized Eigenstates of 2D Moir\'e Lattices

Moir\'e lattices are aperiodic systems formed by a superposition of two periodic lattices with a relative rotational angle. In optics, the photonic moir\'e lattice has many promising mysteries such as its ability to localize light, thus attracting much attention to exploring features of such a structure. One fundamental research area for photonic moir\'e lattices is the properties of eigenstates, particularly the existence of localized eigenstates and the localization-to-delocalization transition in the energy band structure. Here we propose an accurate algorithm for the eigenproblems of aperiodic systems by combining plane wave discretization and spectral indicator validation under the higher-dimensional projection, allowing us to explore energy bands of fully aperiodic systems. A localization-delocalization transition regarding the intensity of the aperiodic potential is observed and a novel Pythagoras superposition principle for localized eigenstates of 2D moir\'e lattices is revealed by analyzing the relationship between the aperiodic and its corresponding periodic eigenstates. This principle sheds light on exploring the physics of localizations for moir\'e lattice.Comment: 7 pages, 3 figure

Recent Advances in Multi-modal 3D Scene Understanding: A Comprehensive Survey and Evaluation

Multi-modal 3D scene understanding has gained considerable attention due to its wide applications in many areas, such as autonomous driving and human-computer interaction. Compared to conventional single-modal 3D understanding, introducing an additional modality not only elevates the richness and precision of scene interpretation but also ensures a more robust and resilient understanding. This becomes especially crucial in varied and challenging environments where solely relying on 3D data might be inadequate. While there has been a surge in the development of multi-modal 3D methods over past three years, especially those integrating multi-camera images (3D+2D) and textual descriptions (3D+language), a comprehensive and in-depth review is notably absent. In this article, we present a systematic survey of recent progress to bridge this gap. We begin by briefly introducing a background that formally defines various 3D multi-modal tasks and summarizes their inherent challenges. After that, we present a novel taxonomy that delivers a thorough categorization of existing methods according to modalities and tasks, exploring their respective strengths and limitations. Furthermore, comparative results of recent approaches on several benchmark datasets, together with insightful analysis, are offered. Finally, we discuss the unresolved issues and provide several potential avenues for future research

Skeleton-of-Thought: Large Language Models Can Do Parallel Decoding

This work aims at decreasing the end-to-end generation latency of large language models (LLMs). One of the major causes of the high generation latency is the sequential decoding approach adopted by almost all state-of-the-art LLMs. In this work, motivated by the thinking and writing process of humans, we propose "Skeleton-of-Thought" (SoT), which guides LLMs to first generate the skeleton of the answer, and then conducts parallel API calls or batched decoding to complete the contents of each skeleton point in parallel. Not only does SoT provide considerable speed-up (up to 2.39x across 11 different LLMs), but it can also potentially improve the answer quality on several question categories in terms of diversity and relevance. SoT is an initial attempt at data-centric optimization for efficiency, and reveal the potential of pushing LLMs to think more like a human for answer quality.Comment: Technical report, work in progres

Distributed Deep Learning Optimization of Heat Equation Inverse Problem Solvers

The inversion problem of partial differential equation plays a crucial role in cyber-physical systems applications. This paper presents a novel deep learning optimization approach to constructing a solver of heat equation inversion. To improve the computational efficiency in large-scale industrial applications, data and model parallelisms are incorporated on a platform of multiple GPUs. The advanced Ring-AllReduce architecture is harnessed to achieve an acceleration ratio of 3.46. Then a new multi-GPUs distributed optimization method GradReduce is proposed based on Ring-AllReduce architecture. This method optimizes the original data communication mechanism based on mechanical time and frequency by introducing the gradient transmission scheme solved by linear programming. The experimental results show that the proposed method can achieve an acceleration ratio of 3.84 on a heterogeneous system platform with two CPUs and four GPUs