Preconcentration of the target compound is a critical step that ensures the accuracy of the subsequent chemical analysis. In this work, we present a straightforward yet effective liquid-liquid extraction approach based on surface nanodroplets (i.e., nanoextraction) for offline analysis of highly diluted sample solutions. The extraction and sample collection were streamlined in a 3-m microcapillary tube. The concentration of the target analyte in surface nanodroplets was significantly increased compared to the concentration in the sample solution, reaching several orders of magnitudes. A limit of detection (LOD) was decreased by a factor of $\sim 10^3$ for an organic model compound in Fourier-transform infrared spectroscopy (FTIR) measurements and $\sim 10^5$ for a model fluorescent dye in fluorescence detection. The quantitative analysis of the organic compound was also achieved in a wide concentration region from $10^{-3}$ M to $10^{-4}$ M. The total volume of surface nanodroplets can be manipulated to further enhance extraction efficiency, according to the principle that governs droplet formation by solvent exchange. Additionally, our method exhibited significantly improved sensitivity compared to traditional dispersive liquid-liquid microextraction (DLLME). The LOD of the fluorescent dye and the organic model compound obtained with DLLME was 3 orders of magnitude and 20 times higher than the LOD achieved through nanoextraction approach. The nanoextraction developed in this work can be applied to preconcentrate multi-compounds from river water samples, without clear interference from each other. This can further extend its applicability for the detection and quantification of target analytes in complex aqueous samples by common analytical instruments.

Hongyan Wu Quynh Nhu Le Binglin Zeng Xuehua Zhang

Consider a rational map from a projective space to a product of projective spaces, induced by a collection of linear projections. Motivated by the the theory of limit linear series and Abel-Jacobi maps, we study the basic properties of the closure of the image of the rational map using a combination of techniques of moduli functors and initial degenerations. We first give a formula of multi-degree in terms of the dimensions of intersections of linear subspaces and then prove that it is Cohen-Macaulay. Finally, we compute its Hilbert polynomials.

Binglin Li

Recently many works attempt to develop image compression models based on deep learning architectures, where the uniform scalar quantizer (SQ) is commonly applied to the feature maps between the encoder and decoder. In this paper, we propose to incorporate trellis coded quantizer (TCQ) into a deep learning based image compression framework. A soft-to-hard strategy is applied to allow for back propagation during training. We develop a simple image compression model that consists of three subnetworks (encoder, decoder and entropy estimation), and optimize all of the components in an end-to-end manner. We experiment on two high resolution image datasets and both show that our model can achieve superior performance at low bit rates. We also show the comparisons between TCQ and SQ based on our proposed baseline model and demonstrate the advantage of TCQ.

Binglin Li Mohammad Akbari Jie Liang Yang Wang

Dataset distillation, a pragmatic approach in machine learning, aims to create a smaller synthetic dataset from a larger existing dataset. However, existing distillation methods primarily adopt a model-based paradigm, where the synthetic dataset inherits model-specific biases, limiting its generalizability to alternative models. In response to this constraint, we propose a novel methodology termed "model pool". This approach involves selecting models from a diverse model pool based on a specific probability distribution during the data distillation process. Additionally, we integrate our model pool with the established knowledge distillation approach and apply knowledge distillation to the test process of the distilled dataset. Our experimental results validate the effectiveness of the model pool approach across a range of existing models while testing, demonstrating superior performance compared to existing methodologies.

Binglin Zhou Linhao Zhong Wentao Chen

Inside a product of projective spaces, we try to understand which Chow classes come from irreducible subvarieties. The answer is closely related to the theory of integer polymatroids. The support of a representable class can be (partially) characterized as some integer point inside a particular polymatroid. If the class is multiplicity-free, we obtain a complete characterization in terms of representable polymatroids. We also generalize some of the results to the case of products of Grassmannians.

Federico Castillo Binglin Li Naizhen Zhang

Recently, skeleton-based approaches have achieved rapid progress on the basis of great success in skeleton representation. Plenty of researches focus on solving specific problems according to skeleton features. Some skeleton-based approaches have been mentioned in several overviews on object detection as a non-essential part. Nevertheless, there has not been any thorough analysis of skeleton-based approaches attentively. Instead of describing these techniques in terms of theoretical constructs, we devote to summarizing skeleton-based approaches with regard to application fields and given tasks as comprehensively as possible. This paper is conducive to further understanding of skeleton-based application and dealing with particular issues.

Jie Li Binglin Li Min Gao

Compositional data, such as human gut microbiomes, consist of non-negative variables whose only the relative values to other variables are available. Analyzing compositional data such as human gut microbiomes needs a careful treatment of the geometry of the data. A common geometrical understanding of compositional data is via a regular simplex. Majority of existing approaches rely on a log-ratio or power transformations to overcome the innate simplicial geometry. In this work, based on the key observation that a compositional data are projective in nature, and on the intrinsic connection between projective and spherical geometry, we re-interpret the compositional domain as the quotient topology of a sphere modded out by a group action. This re-interpretation allows us to understand the function space on compositional domains in terms of that on spheres and to use spherical harmonics theory along with reflection group actions for constructing a compositional Reproducing Kernel Hilbert Space (RKHS). This construction of RKHS for compositional data will widely open research avenues for future methodology developments. In particular, well-developed kernel embedding methods can be now introduced to compositional data analysis. The polynomial nature of compositional RKHS has both theoretical and computational benefits. The wide applicability of the proposed theoretical framework is exemplified with nonparametric density estimation and kernel exponential family for compositional data.

Binglin Li Jeongyoun Ahn

Monte Carlo simulations based on a first-principles-derived Hamiltonian are conducted to study the properties of PZT alloys compositionally modulated along the [100] pseudocubic direction near the morphotropic phase boundary (MPB). It is shown that compositional modulation causes the polarization to continuously rotate away from the modulation direction, resulting in the unusual triclinic and C-type monoclinic ground states and huge enhancement of electromechanical responses (the peak of piezoelectric coefficient is as high as 30000 pC/N). The orientation dependence of dipole-dipole interaction in modulated structure is revealed as the microscopic mechanism to be responsible for these anomalies.

Ningdong Huang Zhirong Liu Zhongqing Wu Jian Wu Wenhui Duan Binglin Gu Xiaowen Zhang

A novel stable crystallographic structure is discovered in a variety of ABO3, ABF3 and A2O3 compounds (including materials of geological relevance, prototypes of multiferroics, exhibiting strong spin-orbit effects, etc...), via the use of first principles. This novel structure appears under hydrostatic pressure, and is the first "post-post-perovskite" phase to be found. It provides a successful solution to experimental puzzles in important systems, and is characterized by one-dimensional chains linked by group of two via edge-sharing oxygen/fluorine octahedra. Such unprecedented organization automatically results in anisotropic elastic properties and new magnetic arrangements. Depending on the system of choice, this post-post-perovskite structure also possesses electronic band gaps ranging from zero to ~ 10 eV being direct or indirect in nature, which emphasizes its "universality" and its potential to have striking, e.g., electrical or transport phenomena.

Changsong Xu Bin Xu Yurong Yang Huafeng Dong A. R. Oganov Shanying Wang Wenhui Duan Binglin Gu L. Bellaiche

Inspired by work of Cartwright and Sturmfels, in a previous paper we introduced two classes of multigraded ideals named after them. These ideals are defined in terms of properties of their multigraded generic initial ideals. The goal of this paper is showing that three families of ideals that have recently attracted the attention of researchers are Cartwright-Sturmfels ideals. More specifically, we prove that binomial edge ideals, multigraded homogenizations of linear spaces, and multiview ideals are Cartwright-Sturmfels ideals, hence recovering and extending recent results of Herzog-Hibi-Hreinsdottir-Kahle-Rauh, Ohtani, Ardila-Boocher, Aholt-Sturmfels-Thomas, and Binglin Li. We also propose a conjecture on the rigidity of local cohomology modules of Cartwright-Sturmfels ideals, that was inspired by a theorem of Brion. We provide some evidence for the conjecture by proving it in the monomial case.

Aldo Conca Emanuela De Negri Elisa Gorla