On the unique representability of spikes over prime fields

For an integer $n>2$, a rank-$n$ matroid is called an $n$-spike if it consists of $n$ three-point lines through a common point such that, for all $k\in\{1, 2, ..., n - 1\}$, the union of every set of $k$ of these lines has rank $k+1$. Spikes are very special and important in matroid theory. In 2003 Wu found the exact numbers of $n$-spikes over fields with 2, 3, 4, 5, 7 elements, and the asymptotic values for larger finite fields. In this paper, we prove that, for each prime number $p$, a $GF(p$) representable $n$-spike $M$ is only representable on fields with characteristic $p$ provided that $n \ge 2p-1$. Moreover, $M$ is uniquely representable over $GF(p)$.Comment: 8 page

Simple, high-performance type II β-BaB2O4 optical parametric oscillator

A visible /near-IR optical parametric oscillator (OPO) based on type II phase matching in β-BaB2O4 (BBO) is described. Pumped at 355 nm, this OPO covers 410-2500 nm completely with a single set of standard Nd:YAG cavity optics. The output efficiency is >25 %, the linewidth of the OPO is narrower than 1 -2 cm^-1 without the use of gratings or etalons, and the signal-beam divergence is <400 µrad. Three type I BBO doubling crystals are used to extend the tuning range from 208 to 415 nm. Doubling efficiencies as high as 40% are easily obtained. The reasons for the high doubling and overall system efficiency are discussed

An intelligent bearing fault diagnosis method based on the AFEEMD and 1D CNNs

To process the non-stationary vibration signals and improve accuracy of bearing fault diagnosis, this paper presents a novel intelligent fault diagnosis method based on the adaptive fast ensemble empirical mode decomposition (AFEEMD) and one-dimensional convolutional neural networks (1D CNNs). First, the AFEEMD algorithm is utilized to decompose the raw signals into intrinsic mode functions (IMFs). Then, the time and frequency statistic features of the first several IMFs are analyzed to form feature vector, which are used as the input of 1D CNNs to identify the bearing fault. The performance of the proposed method is validated using the dataset from the Case Western Reserve University (CWRU). Compared with the traditional back propagation neural network (BPNN), the results show that the proposed AFEEMD-1D CNNs method not only can obtain higher accuracy and achieve more reliable performance, but also can improve the generalization performance. Due to the end-to-end feature learning capacity, it can be extended to other machinery for fault diagnosis

Large deviations of invariant measure for the 3D stochastic hyperdissipative Navier-Stokes equations

In this paper, we consider the large deviations of invariant measure for the 3D stochastic hyperdissipative Navier-Stokes equations driven by additive noise. The unique ergodicity of invariant measure as a preliminary result is proved using a deterministic argument by the exponential moment and exponential stability estimates. Then, the uniform large deviations is established by the uniform contraction principle. Finally, using the unique ergodicity and the uniform large deviations results, we prove the large deviations of invariant measure by verifying the Freidlin-Wentzell large deviations upper and lower bounds

Hierarchical CuO/ZnO Membranes for Environmental Applications under the Irradiation of Visible Light

Solar visible light is a source of clean and cheap energy. Herein, a new kind of hierarchical CuO/ZnO nanomaterial was synthesized using a facile process. Characterized by FESEM, TEM, XRD, XPS, and so forth, this CuO/ZnO naomaterial shows a special hierarchical nanostructure with CuO nanoparticles grown on ZnO nanorods. By assembling the hierarchical CuO/ZnO nanomaterials on a piece of commercial glassfiber membrane, a novel hierarchical CuO/ZnO membrane was fabricated. This CuO/ZnO membrane demonstrated excellent environmental applications, such as improved photodegradation of contaminants and antibacterial activity, under the irradiation of visible light. Compared with pure ZnO nanorod membrane, the improved photodegradation and antibacterial capacities of this hierarchical CuO/ZnO membrane result from the special hierarchical nanostructure of CuO/ZnO nanomaterials, which could enhance light utilization rate, enlarge specific surface area, and retard the recombination of electrons and holes at the interfacial between CuO and ZnO. This hierarchical CuO/ZnO membrane is also easy to be regenerated by completely mineralizing the adsorbed contaminants under the irradiation of visible light. All the above characteristics of this hierarchical CuO/ZnO membrane indicate its great potential in environmental applications with solar visible light

A Conjugated Aptamer-Gold Nanoparticle Fluorescent Probe for Highly Sensitive Detection of rHuEPO-α

We present here a novel conjugated aptamer-gold nanoparticle (Apt-AuNPs) fluorescent probe and its application for specific detection of recombinant human erythropoietin-α (rHuEPO-α). In this nanobiosensor, 12 nm AuNPs function as both a nano-scaffold and a nano-quencher (fluorescent energy acceptor), on the surface of which the complementary sequences are linked (as cODN-AuNPs) and pre-hybridized with carboxymethylfluorescein (FAM)-labeled anti-rHuEPO-α aptamers. Upon target protein binding, the aptamers can be released from the AuNP surface and the fluorescence signal is restored. Key variables such as the length of linker, the hybridization site and length have been designed and optimized. Full performance evaluation including sensitivity, linear range and interference substances are also described. This nanobiosensor provides a promising approach for a simple and direct quantification of rHuEPO-α concentrations as low as 0.92 nM within a few hours

ESPT: A Self-Supervised Episodic Spatial Pretext Task for Improving Few-Shot Learning

Self-supervised learning (SSL) techniques have recently been integrated into the few-shot learning (FSL) framework and have shown promising results in improving the few-shot image classification performance. However, existing SSL approaches used in FSL typically seek the supervision signals from the global embedding of every single image. Therefore, during the episodic training of FSL, these methods cannot capture and fully utilize the local visual information in image samples and the data structure information of the whole episode, which are beneficial to FSL. To this end, we propose to augment the few-shot learning objective with a novel self-supervised Episodic Spatial Pretext Task (ESPT). Specifically, for each few-shot episode, we generate its corresponding transformed episode by applying a random geometric transformation to all the images in it. Based on these, our ESPT objective is defined as maximizing the local spatial relationship consistency between the original episode and the transformed one. With this definition, the ESPT-augmented FSL objective promotes learning more transferable feature representations that capture the local spatial features of different images and their inter-relational structural information in each input episode, thus enabling the model to generalize better to new categories with only a few samples. Extensive experiments indicate that our ESPT method achieves new state-of-the-art performance for few-shot image classification on three mainstay benchmark datasets. The source code will be available at: https://github.com/Whut-YiRong/ESPT.Comment: Accepted by AAAI 202

Enhancing Rock Image Segmentation in Digital Rock Physics: A Fusion of Generative AI and State-of-the-Art Neural Networks

In digital rock physics, analysing microstructures from CT and SEM scans is crucial for estimating properties like porosity and pore connectivity. Traditional segmentation methods like thresholding and CNNs often fall short in accurately detailing rock microstructures and are prone to noise. U-Net improved segmentation accuracy but required many expert-annotated samples, a laborious and error-prone process due to complex pore shapes. Our study employed an advanced generative AI model, the diffusion model, to overcome these limitations. This model generated a vast dataset of CT/SEM and binary segmentation pairs from a small initial dataset. We assessed the efficacy of three neural networks: U-Net, Attention-U-net, and TransUNet, for segmenting these enhanced images. The diffusion model proved to be an effective data augmentation technique, improving the generalization and robustness of deep learning models. TransU-Net, incorporating Transformer structures, demonstrated superior segmentation accuracy and IoU metrics, outperforming both U-Net and Attention-U-net. Our research advances rock image segmentation by combining the diffusion model with cutting-edge neural networks, reducing dependency on extensive expert data and boosting segmentation accuracy and robustness. TransU-Net sets a new standard in digital rock physics, paving the way for future geoscience and engineering breakthroughs

Controllable 3D Face Synthesis with Conditional Generative Occupancy Fields

Capitalizing on the recent advances in image generation models, existing controllable face image synthesis methods are able to generate high-fidelity images with some levels of controllability, e.g., controlling the shapes, expressions, textures, and poses of the generated face images. However, these methods focus on 2D image generative models, which are prone to producing inconsistent face images under large expression and pose changes. In this paper, we propose a new NeRF-based conditional 3D face synthesis framework, which enables 3D controllability over the generated face images by imposing explicit 3D conditions from 3D face priors. At its core is a conditional Generative Occupancy Field (cGOF) that effectively enforces the shape of the generated face to commit to a given 3D Morphable Model (3DMM) mesh. To achieve accurate control over fine-grained 3D face shapes of the synthesized image, we additionally incorporate a 3D landmark loss as well as a volume warping loss into our synthesis algorithm. Experiments validate the effectiveness of the proposed method, which is able to generate high-fidelity face images and shows more precise 3D controllability than state-of-the-art 2D-based controllable face synthesis methods. Find code and demo at https://keqiangsun.github.io/projects/cgof