Fast Low-Rank Matrix Learning with Nonconvex Regularization

Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better recovery performance. However, the resultant optimization problem is much more challenging. A very recent state-of-the-art is based on the proximal gradient algorithm. However, it requires an expensive full SVD in each proximal step. In this paper, we show that for many commonly-used nonconvex low-rank regularizers, a cutoff can be derived to automatically threshold the singular values obtained from the proximal operator. This allows the use of power method to approximate the SVD efficiently. Besides, the proximal operator can be reduced to that of a much smaller matrix projected onto this leading subspace. Convergence, with a rate of O(1/T) where T is the number of iterations, can be guaranteed. Extensive experiments are performed on matrix completion and robust principal component analysis. The proposed method achieves significant speedup over the state-of-the-art. Moreover, the matrix solution obtained is more accurate and has a lower rank than that of the traditional nuclear norm regularizer.Comment: Long version of conference paper appeared ICDM 201

Learning Graph Neural Networks with Approximate Gradient Descent

The first provably efficient algorithm for learning graph neural networks (GNNs) with one hidden layer for node information convolution is provided in this paper. Two types of GNNs are investigated, depending on whether labels are attached to nodes or graphs. A comprehensive framework for designing and analyzing convergence of GNN training algorithms is developed. The algorithm proposed is applicable to a wide range of activation functions including ReLU, Leaky ReLU, Sigmod, Softplus and Swish. It is shown that the proposed algorithm guarantees a linear convergence rate to the underlying true parameters of GNNs. For both types of GNNs, sample complexity in terms of the number of nodes or the number of graphs is characterized. The impact of feature dimension and GNN structure on the convergence rate is also theoretically characterized. Numerical experiments are further provided to validate our theoretical analysis.Comment: 23 pages, accepted at AAAI 202

Influence of adjacent surface building on seismic response of shallow buried subway station structure

Taking the 6-storey frame structure as an example, using FLAC numerical simulation, the influence of the adjacent multi-storey buildings on the seismic response of the metro station structure (including the internal force and bias state of the station structure) is studied systematically, and the relationship between the influence and surrounding rock level change is analyzed. The research shows that the existence of surface buildings has obvious amplification effect on the internal force of the subway station and above. It mainly shows that the eccentricity of the vault of the subway station is increased, and the eccentricity of the arch waist is reduced. It has a great influence on the internal force and distribution range of the station structure. The worse the surrounding rock, the greater the internal force and influence range of the building to the station structure

Atomistic simulations of thermodynamic properties of liquid gallium from first principles

In the research of condensed matter, atomistic dynamic simulations play a crucial role, particularly in revealing dynamic processes, phase transitions and thermodynamic statistics macroscopic physical properties in systems such as solids and liquids. For a long time, simulating complex and disordered liquids has been a challenge compared to ordered crystalline structures. The primary reasons for this challenge are the lack of precise force field functions and the neglect of nuclear quantum effects. To overcome these two limits in simulation of liquids, we use a deep potential (DP) with quantum thermal bath (QTB) approach. DP is a machine learning model are sampled from density functional theory and able to do large-scale atomic simulations with its precision. QTB is a method which incorporates nuclear quantum effects by quantum fluctuation dissipation. The application of this first principles approach enable us to successfully describe the phase transition processes in solid and liquid Gallium (Ga) as well as the associated dynamic phenomena. More importantly, we obtain the thermodynamic properties of liquid Ga, such as internal energy, specific heat, enthalpy change, entropy and Gibbs free energy, and these results align remarkably well with experiments. Our research has opened up a new paradigm for the study of dynamics and thermodynamics in liquids, amorphous materials, and other disordered systems, providing valuable insights and references for future investigations.Comment: 7 pages, 11 figures for maintext; 6pages, 8 figures for supplementary material

Lumen contour segmentation in ivoct based on n-type cnn

Automatic segmentation of lumen contour plays an important role in medical imaging and diagnosis, which is the first step towards the evaluation of morphology of vessels under analysis and the identification of possible atherosclerotic lesions. Meanwhile, quantitative information can only be obtained with segmentation, contributing to the appearance of novel methods which can be successfully applied to intravascular optical coherence tomography (IVOCT) images. This paper proposed a new end-to-end neural network (N-Net) for the automatic lumen segmentation, using multi-scale features based deep neural network, for IVOCT images. The architecture of the N-Net contains a multi-scale input layer, a N-type convolution network layer and a cross-entropy loss function. The multi-scale input layer in the proposed N-Net is designed to avoid the loss of information caused by pooling in traditional U-Net and also enriches the detailed information in each layer. The N-type convolutional network is proposed as the framework in the whole deep architecture. Finally, the loss function guarantees the degree of fidelity between the output of proposed method and the manually labeled output. In order to enlarge the training set, data augmentation is also introduced. We evaluated our method against loss, accuracy, recall, dice similarity coefficient, jaccard similarity coefficient and specificity. The experimental results presented in this paper demonstrate the superior performance of the proposed N-Net architecture, comparing to some existing networks, for enhancing the precision of automatic lumen segmentation and increasing the detailed information of edges of the vascular lumen

Ex vivo mono-ring technique simplifies culotte stenting for treatment of true bifurcation lesions: Insights from bench testing and clinical application

Background: Despite various culotte-based stenting techniques available clinically, the optimal one remains undetermined. The study aimed to test whether ex vivo mono-ring culotte stenting (MRC) was technically feasible and superior to mini culotte stenting (MCS) in treatment of coronary bifurcation lesions.Methods: Mono-ring culotte stenting was characterized by ex vivo wiring of the most proximal cell of the side branch (SB) stent to ensure a mono-ring result of the culotte stenting. Comparison of MRC vs. MCS in treatment of true bifurcation lesions was performed in vitro (n = 15 for each group) and in clinical case-controlled study with propensity matching at a ratio of 1:2 (n = 21 for MRC group; n = 42 for MCS group).Results: Compared to MCS, MRC had lower incidence of stent under-expansion band (0% vs. 53.3%, p = 0.002) and less residual ostial area stenosis of SB (9.2 ± 9.0% vs. 20.0 ± 14.8%, p = 0.023), as assessed in vitro by micro-computed tomography. In a case-controlled study, no adverse cardiac events were observed in the MRC group. The procedural success was similar between MRC and MCS (100% vs. 95.2%, p = 0.548), but MRC had less residual ostial stenosis of the SB (8.7% ± 11.0% vs. 16.8% ± 11.2%, p = 0.008), lower procedural(33.3 ± 9.5 min vs. 46.7 ± 15.6 min, p = 0.001) and fluoroscopic (19.7 ± 4.9 min vs. 26.2 ± 7.1 min, p < 0.001) time, and less contrast use (114.3 ± 28.9 mL vs. 156.5 ± 56.4 mL, p = 0.002).Conclusions: Mono-ring culotte stenting as compared to MCS is associated with better bifurcation stent morphology,less procedural complexity and residual ostial SB stenosis

Retrograde venous coil embolization prior to transarterial chemoembolization in hepatocellular carcinoma with arterio-hepatic venous shunts

PURPOSEThis study explored the clinical efficacy of transcatheter retrograde shunt occlusion with coils to prevent pulmonary oil or particle embolization prior to transarterial chemoembolization (TACE) in patients with artero-hepatic venous shunts (AHVS) secondary to hepatocellular carcinoma (HCC).METHODSFrom July 2017 to January 2021, 6 patients with advanced, unresectable HCC were found to have an AHVS by hepatic arteriography at the time of attempted TACE. The AHVS was embolized retrogradely with metal coils through a transfemoral or transjugular venous approach. After venous embolization and confirmation of the absence of the AHVS, TACE was performed using an emulsion of iodized oil and doxorubicin or drug-eluting beads. Follow-up computed tomography (CT) was performed within 1 month after the first TACE to evaluate the results and complications.RESULTSHepatic angiography after venous embolization showed that AHVS had utterly disappeared in all patients during the operation. The immediate technical success of the retrograde venous embolization was 100%. The AHVS had disappeared entirely during the follow-up period through triple-phase enhancement CT scanning. According to the modified response evaluation criteria in solid tumors, TACE in all 6 patients had a disease control response rate of 100% (6/6) with complete response in 2 patients and partial response in 4 patients. One patient died during the 6-month follow-up, and the other 5 were still alive. No complications related to pulmonary embolism occurred.CONCLUSIONRetrograde venous coil embolization of AHVS via the draining hepatic vein appears to be a safe, feasible, and effective treatment to allow TACE treatment without pulmonary embolic events. This approach appears to provide better tumor control and effectively decreases the occurrence of pulmonary embolism