A Direct NMR Method To Measure Self-Diffusion Coefficients in Liquids by Monitoring Diffusing Molecules through One-Dimensional Imaging

Diffusion processes can be followed directly by recording one-dimensional images of a selected slice at variable intervals after selective inversion of the magnetization. The resulting diffusion coefficients of H₂O and DMSO are consistent with earlier studies at different temperatures, obtained by monitoring the attenuation of NMR signals as a function of the gradient amplitude in gradient echo sequences.     

Quantum algorithm for neighborhood preserving embedding

Neighborhood preserving embedding (NPE) is an important linear dimensionality reduction technique that aims at preserving the local manifold structure. NPE contains three steps, i.e., finding the nearest neighbors of each data point, constructing the weight matrix, and obtaining the transformation matrix. Liang et al. proposed a variational quantum algorithm (VQA) for NPE [Phys. Rev. A 101 032323 (2020)]. The algorithm consists of three quantum sub-algorithms, corresponding to the three steps of NPE, and was expected to have an exponential speedup on the dimensionality n. However, the algorithm has two disadvantages: (i) It is not known how to efficiently obtain the input of the third sub-algorithm from the output of the second one. (ii) Its complexity cannot be rigorously analyzed because the third sub-algorithm in it is a VQA. In this paper, we propose a complete quantum algorithm for NPE, in which we redesign the three sub-algorithms and give a rigorous complexity analysis. It is shown that our algorithm can achieve a polynomial speedup on the number of data points m and an exponential speedup on the dimensionality n under certain conditions over the classical NPE algorithm, and achieve a significant speedup compared to Liang et al.'s algorithm even without considering the complexity of the VQA.     

Facile Synthesis of Manganese Tellurite Nanoparticles for Magnetic Resonance Imaging-Guided Photothermal Therapy

In this study, manganese tellurite (MnTeO₃) nanoparticles are developed as theranostic agents for magnetic resonance imaging (MRI)-guided photothermal therapy of tumor. MnTeO₃ nanoparticles are synthesized via a simple one-step method. The as-synthesized MnTeO₃ nanoparticles with uniform size show good biocompatibility. In particular, MnTeO₃ nanoparticles exhibit a high photothermal conversion efficiency (η = 26.3%), which is higher than that of gold nanorods. Moreover, MnTeO₃ nanoparticles also have high MRI performance. The longitudinal relaxivity (r₁) value of MnTeO₃ nanoparticles is determined to be 8.08 ± 0.2 mm ⁻¹ s⁻¹, which is higher than that of clinically approved T₁-contrast agents Gd-DTPA (4.49 ± 0.1 mm ⁻¹ s⁻¹). The subsequent MnTeO₃ nanoparticles-mediated photothermal therapy displays a highly efficient ablation of tumor cells both in vitro and in vivo with negligible toxicity. It is demonstrated that MnTeO₃ nanoparticles can serve as promising theranostic agents with great potentials for MRI-guided photothermal therapy.     

全局优化问题的一个新的无参数填充函数

求全局最优化问题的填充函数算法被提出以来，参数的选取和调整一直是制约算法有效性的因素。如何在实际的计算过程中选取合适的参数，直接影响和决定了运算速度和效率。因此，构造不含参数的填充函数就显得极为重要。提出一个新的无参数的填充函数，对其理论性质进行了分析，并给出相应的填充函数算法，数值计算验证了算法的有效性。     

Performance guarantees of forward and reverse greedy algorithms for minimizing nonsupermodular nonsubmodular functions on a matroid

This letter studies the problem of minimizing increasing set functions, equivalently, maximizing decreasing set functions, over the base matroid. This setting has received great interest, since it generalizes several applied problems including actuator and sensor placement problems in control, task allocation problems, video summarization, and many others. We study two greedy heuristics, namely, the forward and reverse greedy. We provide two novel performance guarantees for the approximate solutions obtained by them depending on both submodularity ratio and curvature.     

3.0T MRI检查结合X线钼靶诊断乳腺恶性肿瘤的研究

本研究探讨3.0T磁共振成像(MRI)结合X线钼靶诊断乳腺恶性肿瘤的价值。采用回顾性研究方法,选取乳腺肿块患者110例162个病灶,给予3.0T MRI及X线钼靶检查。经病理确诊为恶性病变101个;恶性病灶形态不规则、边缘毛刺、时间-信号强度曲线(TIC)类型Ⅲ型和早期增强率≥60%比例明显高于良性病灶(P<0.05),而分叶状比例和表观扩散系数(ADC)值明显低于良性病变(P<0.05);恶性病变X线钼靶表现:形态不规则、钙化、结构不对称和大导管征比例明显高于良性病变(P<0.05);MRI联合X线钼靶诊断乳腺恶性病变的灵敏性、准确性和阴性预测值明显高于MRI诊断(P<0.05)。3.0T MRI检查结合X线钼靶诊断乳腺恶性肿瘤有较好的价值。     

NIFTy 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters

NIFTy , “Numerical Information Field Theory,” is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high‐dimensional real‐world problems. This paper introduces NIFTy  3, a major upgrade to the original NIFTy  framework. NIFTy  3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy  3 is able to handle non‐scalar fields, such as vector or tensor fields. The functionality and performance of the software package is demonstrated with example code, which implements a mock inference inspired by a real‐world algorithm from the realm of information field theory. NIFTy  3 is open‐source software available under the GNU General Public License v3 (GPL‐3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/tree/NIFTy_3 .     

求解矩阵方程AXB+CXD=F参数迭代法的最优参数分析

本文针对求矩阵方程AXB+CXD=F唯一解的参数迭代法，分析当矩阵A，B，C，D均是Hermite正（负）定矩阵时，迭代矩阵的特征值表达式，给出了最优参数的确定方法，并提出了相应的加速算法.     

Linearly χ-bounding (P6, C4)-free graphs*

Given two graphs and , a graph is -free if it contains no induced subgraph isomorphic to or . Let and be the path on vertices and the cycle on vertices, respectively. In this paper we show that for any -free graph it holds that , where and are the chromatic number and clique number of , respectively. Our bound is attained by several graphs, for instance, the 5-cycle, the Petersen graph, the Petersen graph with an additional universal vertex, and all -critical -free graphs other than (see Hell and Huang [Discrete Appl. Math. 216 (2017), pp. 211–232]). The new result unifies previously known results on the existence of linear -binding functions for several graph classes. Our proof is based on a novel structure theorem on -free graphs that do not contain clique cutsets. Using this structure theorem we also design a polynomial time -approximation algorithm for coloring -free graphs. Our algorithm computes a coloring with colors for any -free graph in time.     

One‐Step Labeling of Collagen Hydrogels with Polydopamine and Manganese Porphyrin for Non‐Invasive Scaffold Tracking on Magnetic Resonance Imaging

Biomaterial scaffolds are the cornerstone to supporting 3D tissue growth. Optimized scaffold design is critical to successful regeneration, and this optimization requires accurate knowledge of the scaffold's interaction with living tissue in the dynamic in vivo milieu. Unfortunately, non‐invasive methods that can probe scaffolds in the intact living subject are largely underexplored, with imaging‐based assessment relying on either imaging cells seeded on the scaffold or imaging scaffolds that have been chemically altered. In this work, the authors develop a broadly applicable magnetic resonance imaging (MRI) method to image scaffolds directly. A positive‐contrast “bright” manganese porphyrin (MnP) agent for labeling scaffolds is used to achieve high sensitivity and specificity, and polydopamine, a biologically derived universal adhesive, is employed for adhering the MnP. The technique was optimized in vitro on a prototypic collagen gel, and in vivo assessment was performed in rats. The results demonstrate superior in vivo scaffold visualization and the potential for quantitative tracking of degradation over time. Designed with ease of synthesis in mind and general applicability for the continuing expansion of available biomaterials, the proposed method will allow tissue engineers to assess and fine‐tune the in vivo behavior of their scaffolds for optimal regeneration.