A Faster kk-means++ Algorithm

K-means++ is an important algorithm to choose initial cluster centers for the k-means clustering algorithm. In this work, we present a new algorithm that can solve the $k$-means++ problem with near optimal running time. Given $n$ data points in $\mathbb{R}^d$, the current state-of-the-art algorithm runs in $\widetilde{O}(k )$ iterations, and each iteration takes $\widetilde{O}(nd k)$ time. The overall running time is thus $\widetilde{O}(n d k^2)$. We propose a new algorithm \textsc{FastKmeans++} that only takes in $\widetilde{O}(nd + nk^2)$ time, in total

The Gap Seal's Influences on the Leakage and Clamping of Multi-way Directional Valves

Defects coming from processing and assembly inevitably bring geometric and concentricity error to the fitting gap between valve core and frame. To overcome this problem, grooving was proven to be the most simple and effective method to reduce the hydraulic clamping force, and widely used on cylinder valve cores. Theoretically unbalanced forces kept going smaller with the increase of pressure equalizing grooves. When groove width increased, linearly the gap leakage extended. When the width was relatively small leakage was gradually reduced when depth increased. When the width was 1 mm, 1.5 mm or 2 mm, and the depth to width ratio was less than 1, leakage got worse with the increment of depth

Fast and Efficient Matching Algorithm with Deadline Instances

Online weighted matching problem is a fundamental problem in machine learning due to its numerous applications. Despite many efforts in this area, existing algorithms are either too slow or don't take $\mathrm{deadline}$ (the longest time a node can be matched) into account. In this paper, we introduce a market model with $\mathrm{deadline}$ first. Next, we present our two optimized algorithms (\textsc{FastGreedy} and \textsc{FastPostponedGreedy}) and offer theoretical proof of the time complexity and correctness of our algorithms. In \textsc{FastGreedy} algorithm, we have already known if a node is a buyer or a seller. But in \textsc{FastPostponedGreedy} algorithm, the status of each node is unknown at first. Then, we generalize a sketching matrix to run the original and our algorithms on both real data sets and synthetic data sets. Let $\epsilon \in (0,0.1)$ denote the relative error of the real weight of each edge. The competitive ratio of original \textsc{Greedy} and \textsc{PostponedGreedy} is $\frac{1}{2}$ and $\frac{1}{4}$ respectively. Based on these two original algorithms, we proposed \textsc{FastGreedy} and \textsc{FastPostponedGreedy} algorithms and the competitive ratio of them is $\frac{1 - \epsilon}{2}$ and $\frac{1 - \epsilon}{4}$ respectively. At the same time, our algorithms run faster than the original two algorithms. Given $n$ nodes in $\mathbb{R} ^ d$, we decrease the time complexity from $O(nd)$ to $\widetilde{O}(\epsilon^{-2} \cdot (n + d))$

Hybrid optimization assisted deep convolutional neural network for hardening prediction in steel

Hardness is a property that prevents forced scraping or surface penetration of material surfaces against deformation. Indeed, some methods in the tradition of forecasting the mechanical properties of the steel used to recommend a new hardening forecast using a profound learning model. More particularly, an Optimized Deep Convolutional Neural Network (DCNN) framework is used that makes the prediction more accurate and precise. The input given to the model is the chemical composition of steel along with the distance from the quenched end, which directly predicts the hardening of steel as the model already knows of it. Moreover, to make the prediction more accurate, this paper aims to make a fine-tuning of Convolutional layers in DCNN. This paper suggests a new hybrid algorithm for optimal tuned, which is then hybridized Sea Lion Optimization (SLNO), Dragonfly Algorithm (DA), and Sea Lion insisted on Dragon Fly Modification (SL-DU). This is an optimal tuning. Finally, the performance of the proposed work is compared and validated over other state-of-the-art models for error measures. Finally, the performance of the adopted system was evaluated compared with other traditional systems and the results were achieved. According to the analysis, the MAE of the pattern used for distance 1.5 was 77.16%, 9.84%, 12.71%, and 23.36% better than regression, MVR, ANN, and CNN

Research on PID Controller of Excavator Electro-Hydraulic System Based on Improved Differential Evolution

An electrical hydraulic control system (electro-hydraulic system) is thought to be a key component in excavator operation systems. Control methods with fixed parameters may not yield optimal system performances because a hydraulic system has various nonlinear uncertainties due to the leakage and compressibility of the fluid medium. Hence, a novel PID controller based on improved differential evolution (IDE) is introduced to excavator electro-hydraulic systems for interconnected hydraulic systems. The proposed algorithm not only adjusts the PID parameters of the different working conditions but also adjusts the scaling factor and crossover probability. Then, the proposed PID controller based on IDE and the excavator bucket control system are modeled and simulated on the MATLAB simulation platform. The simulation results demonstrate that the proposed controller has better performance in settling time, rise time, and convergence speed compared to the PID controller based on standard differential evolution and the Ziegler–Nichols (ZN) PID controller with a novel object function. Eventually, the IDE-PID controller is assessed on a 23-ton excavator, and good transient behavior and trajectory accuracy are obtained in comparison to the SDE-PID controller

Effects of U-shaped two-step throttling groove parameters on cavitation erosion characteristics

Throttling usually occurs when a fluid passes through an orifice, sometimes even severe cav- itation erosion may occur. In this study, the equation for the cavitation index of a throttling valve was proposed and the cavitation erosion area in the throttle valve was found to change its position with the orifice opening (X). Cavitation features of singular and two-port se- ries throttling grooves were characterized by defining cavitation indexes σ1and σ2, because the cavitation index-σ can determine the occurrence and intensity of cavitation. Then the indexes σ1 and σ2 included internal geometric parameters and external pressure boundaries were obtained, and cavitation indexes curves σ1-X and σ2-X were also plotted. From the curves of the cavitation index, it was observed that cavitation concentration section also would transfer with opening X changes in the U-shaped groove. The depth of the U-shaped groove had a more evident impact on cavitation, whereas the effect of width on cavitation erosion was not so obvious. The intensity of cavitation erosion when the fluid flowed into the orifice section of the U-shaped groove was always larger than that when the fluid flowed away

Phase Equilibria of the Fe–Cr–Er Ternary System in the Range 973–1273 K

Phase relations of the Fe–Cr–Er system in the temperature range 973–1273 K were experimentally investigated using equilibrated alloys. The isothermal sections consisted of 9 single-phase regions, 16 two-phase regions, and 8 three-phase regions at 973 K and 1073 K. At 1273 K, the σ phase disappeared, and liquid appeared. All single phases had a solid solubility range that showed a downward trend with a decrease in temperature. The homogeneity range of the ErFe12−xCrx ternary compound was determined to be x = 1.8–4.5. The more accurate phase relations obtained in this work can better guide the preparation of Fe–Cr–Er alloys in actual production

PPP1R12A Copy Number Is Associated with Clinical Outcomes of Stage III CRC Receiving Oxaliplatin-Based Chemotherapy

Aim. To investigate the correlation between PPP1R12A gene copy number and clinical outcomes of oxaliplatin-based regimen in stage III colorectal cancer (CRC). Methods. A total of 139 paraffin-embedded tissue samples of stage III CRC patients who received oxaliplatin-based treatment after radical surgery were recruited. Genomic DNA was extracted and purified from paraffin-embedded sections. Quantitative PCR methods were used to detect the relative copy number (RCN) of PPP1R12A. Results. Statistical analysis demonstrated that low PPP1R12A RCN was associated with poor RFS (HR = 2.186, 95% CI: 1.293-3.696; = 0.003) and OS (HR = 2.782, 95% CI: 1.531-5.052; < 0.001). Additionally, when patients were stratified according to subgroups of stage III and tumor location, poor RFS and OS were also observed in the low PPP1R12A RCN group with significance (RFS: IIIB HR = 2.870, < 0.001; colon HR = 1.910, = 0.037; OS: IIIB HR = 3.527, < 0.001; IIIC HR = 2.662, = 0.049; rectum HR = 4.229, = 0.002). Conclusion. Our findings suggest the copy number of PPP1R12A can independently predict recurrence and overall survival of stage III colorectal cancer patients receiving oxaliplatin-based chemotherapy