Small-Deviation Inequalities for Sums of Random Matrices

Random matrices have played an important role in many fields including machine learning, quantum information theory and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices. Although there are intensive studies on the large-deviation inequalities for random matrices, only a few of works discuss the small-deviation behavior of random matrices. In this paper, we present the small-deviation inequalities for the largest eigenvalues of sums of random matrices. Since the resulting inequalities are independent of the matrix dimension, they are applicable to the high-dimensional and even the infinite-dimensional cases

Matrix Infinitely Divisible Series: Tail Inequalities and Applications in Optimization

In this paper, we study tail inequalities of the largest eigenvalue of a matrix infinitely divisible (i.d.) series, which is a finite sum of fixed matrices weighted by i.d. random variables. We obtain several types of tail inequalities, including Bennett-type and Bernstein-type inequalities. This allows us to further bound the expectation of the spectral norm of a matrix i.d. series. Moreover, by developing a new lower-bound function for $Q(s)=(s+1)\log(s+1)-s$ that appears in the Bennett-type inequality, we derive a tighter tail inequality of the largest eigenvalue of the matrix i.d. series than the Bernstein-type inequality when the matrix dimension is high. The resulting lower-bound function is of independent interest and can improve any Bennett-type concentration inequality that involves the function $Q(s)$. The class of i.d. probability distributions is large and includes Gaussian and Poisson distributions, among many others. Therefore, our results encompass the existing work \cite{tropp2012user} on matrix Gaussian series as a special case. Lastly, we show that the tail inequalities of a matrix i.d. series have applications in several optimization problems including the chance constrained optimization problem and the quadratic optimization problem with orthogonality constraints.Comment: Comments Welcome

Ruthenium Incorporated Cobalt Phosphide Nanocubes Derived From a Prussian Blue Analog for Enhanced Hydrogen Evolution

Electrochemical water splitting in alkaline media plays an important role in mass production of hydrogen. Ruthenium (Ru), as the cheapest member of platinum-group metals, has attracted much attention, and the incorporation of trace amount of Ru with cobalt phosphide could significantly improve the hydrogen evolution reaction (HER) catalytic activity. In this work, ruthenium-incorporated cobalt phosphide nanocubes are synthesized via a reaction between Co–Co Prussian blue analog (Co-PBA) and ruthenium chloride (RuCl3) followed by the phosphidation. The sample with a Ru content of ~2.04 wt.% exhibits the best HER catalytic activity with a low overpotential of 51 and 155 mV, to achieve the current densities of −10 and −100 mA cm−2, respectively, and the Tafel slope of 53.8 mV dec−1, which is comparable to the commercial Pt/C. This study provides a new perspective to the design and construction of high performance electrocatalysts for HER and other catalytic applications in a relatively low price

The feasibility and safety of his-purkinje conduction system pacing in patients with heart failure with severely reduced ejection fraction

ObjectiveThe purpose of this study was to evaluate the feasibility and outcomes of conduction system pacing (CSP) in patients with heart failure (HF) who had a severely reduced left ventricular ejection fraction (LVEF) of less than 30% (HFsrEF).MethodsBetween January 2018 and December 2020, all consecutive HF patients with LVEF < 30% who underwent CSP at our center were evaluated. Clinical outcomes and echocardiographic data [LVEF and left ventricular end-systolic volume (LVESV)], and complications were all recorded. In addition, clinical and echocardiographic (≥5% improvement in LVEF or ≥15% decrease in LVESV) responses were assessed. The patients were classified into a complete left bundle branch block (CLBBB) morphology group and a non-CLBBB morphology group according to the baseline QRS configuration.ResultsSeventy patients (66 ± 8.84 years; 55.7% male) with a mean LVEF of 23.2 ± 3.23%, LVEDd of 67.33 ± 7.47 mm and LVESV of 212.08 ± 39.74 ml were included. QRS configuration at baseline was CLBBB in 67.1% (47/70) of patients and non-CLBBB in 32.9%. At implantation, the CSP threshold was 0.6 ± 0.3 V @ 0.4 ms and remained stable during a mean follow-up of 23.43 ± 11.44 months. CSP resulted in significant LVEF improvement from 23.2 ± 3.23% to 34.93 ± 10.34% (P < 0.001) and significant QRS narrowing from 154.99 ± 34.42 to 130.81 ± 25.18 ms (P < 0.001). Clinical and echocardiographic responses were observed in 91.4% (64/70) and 77.1% (54/70) of patients. Super-response to CSP (≥15% improvement in LVEF or ≥30% decrease in LVESV) was observed in 52.9% (37/70) of patients. One patient died due to acute HF and following severe metabolic disorders. Baseline BNP (odds ratio: 0.969; 95% confidence interval: 0.939–0.989; P = 0.045) was associated with echocardiographic response. The proportions of clinical and echocardiographic responses in the CLBBB group were higher than those in the non-CLBBB group but without significant statistical differences.ConclusionsCSP is feasible and safe in patients with HFsrEF. CSP is associated with a significant improvement in clinical and echocardiographic outcomes, even for patients with non-CLBBB widened QRS

Perovskite-molecule composite thin films for efficient and stable light-emitting diodes

Abstract: Although perovskite light-emitting diodes (PeLEDs) have recently experienced significant progress, there are only scattered reports of PeLEDs with both high efficiency and long operational stability, calling for additional strategies to address this challenge. Here, we develop perovskite-molecule composite thin films for efficient and stable PeLEDs. The perovskite-molecule composite thin films consist of in-situ formed high-quality perovskite nanocrystals embedded in the electron-transport molecular matrix, which controls nucleation process of perovskites, leading to PeLEDs with a peak external quantum efficiency of 17.3% and half-lifetime of approximately 100 h. In addition, we find that the device degradation mechanism at high driving voltages is different from that at low driving voltages. This work provides an effective strategy and deep understanding for achieving efficient and stable PeLEDs from both material and device perspectives

Low-Light Image Enhancement via Retinex-Style Decomposition of Denoised Deep Image Prior

Low-light images are a common phenomenon when taking photos in low-light environments with inappropriate camera equipment, leading to shortcomings such as low contrast, color distortion, uneven brightness, and high loss of detail. These shortcomings are not only subjectively annoying but also affect the performance of many computer vision systems. Enhanced low-light images can be better applied to image recognition, object detection and image segmentation. This paper proposes a novel RetinexDIP method to enhance images. Noise is considered as a factor in image decomposition using deep learning generative strategies. The involvement of noise makes the image more real, weakens the coupling relationship between the three components, avoids overfitting, and improves generalization. Extensive experiments demonstrate that our method outperforms existing methods qualitatively and quantitatively

Small-Deviation Inequalities for Sums of Random Matrices

Random matrices have played an important role in many fields including machine learning, quantum information theory, and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices. Although there are intensive studies on the large-deviation inequalities for random matrices, only a few works discuss the small-deviation behavior of random matrices. In this paper, we present the small-deviation inequalities for the largest eigenvalues of sums of random matrices. Since the resulting inequalities are independent of the matrix dimension, they are applicable to high-dimensional and even the infinite-dimensional cases

Fatigue crack initiation and propagation of 100Cr6 steel under torsional loading in very high cycle regime

International audienceCyclic torsional fatigue properties of a high strength steel 100Cr6 are investigated using an ultrasonic torsional fatigue testing machine, and the results are compared with those obtained with fatigue tests under axial loading. Fatigue crack initiation and growth under torsion loading are observed in the very high cycle regime. Results show that fatigue cracks initiated from specimen surface as well as subsurface inclusions under torsion loading. However, subsurface MnS inclusions play a dominant role in crack initiation under torsion loading in the very high cycle regime. The initiation and early propagation of fatigue cracks are mostly controlled by the direction of the maximum shear stress. For surface crack initiation, cracks initiated in parallel to the longitudinal direction of the specimens. Once the shear crack propagated to a crack length of about 20-30 μm, crack branched to the angle close to the direction perpendicular to the remote maximum principal stresses. As for the subsurface fatigue crack initiation, the cracks parallel to the longitudinal direction of the specimens could not be observed, and crack propagation followed a spiral shape on a plane with an orientation of 45° with respect to the loading direction, which corresponds to the maximum principal stress plane