Improved Algorithms for Clustering with Outliers

Clustering is a fundamental problem in unsupervised learning. In many real-world applications, the to-be-clustered data often contains various types of noises and thus needs to be removed from the learning process. To address this issue, we consider in this paper two variants of such clustering problems, called k-median with m outliers and k-means with m outliers. Existing techniques for both problems either incur relatively large approximation ratios or can only efficiently deal with a small number of outliers. In this paper, we present improved solution to each of them for the case where k is a fixed number and m could be quite large. Particularly, we gave the first PTAS for the k-median problem with outliers in Euclidean space R^d for possibly high m and d. Our algorithm runs in O(nd((1/epsilon)(k+m))^(k/epsilon)^O(1)) time, which considerably improves the previous result (with running time O(nd(m+k)^O(m+k) + (1/epsilon)k log n)^O(1))) given by [Feldman and Schulman, SODA 2012]. For the k-means with outliers problem, we introduce a (6+epsilon)-approximation algorithm for general metric space with running time O(n(beta (1/epsilon)(k+m))^k) for some constant beta>1. Our algorithm first uses the k-means++ technique to sample O((1/epsilon)(k+m)) points from input and then select the k centers from them. Compared to the more involving existing techniques, our algorithms are much simpler, i.e., using only random sampling, and achieving better performance ratios

Evaluation and comparison of the processing methods of airborne gravimetry concerning the errors effects on downward continuation results: Case studies in Louisiana (USA) and the Tibetan Plateau (China)

Gravity data gaps in mountainous areas are nowadays often filled in with the data from airborne gravity surveys. Because of the errors caused by the airborne gravimeter sensors, and because of rough flight conditions, such errors cannot be completely eliminated. The precision of the gravity disturbances generated by the airborne gravimetry is around 3–5 mgal. A major obstacle in using airborne gravimetry are the errors caused by the downward continuation. In order to improve the results the external high-accuracy gravity information e.g., from the surface data can be used for high frequency correction, while satellite information can be applying for low frequency correction. Surface data may be used to reduce the systematic errors, while regularization methods can reduce the random errors in downward continuation. Airborne gravity surveys are sometimes conducted in mountainous areas and the most extreme area of the world for this type of survey is the Tibetan Plateau. Since there are no high-accuracy surface gravity data available for this area, the above error minimization method involving the external gravity data cannot be used. We propose a semi-parametric downward continuation method in combination with regularization to suppress the systematic error effect and the random error effect in the Tibetan Plateau; i.e., without the use of the external high-accuracy gravity data. We use a Louisiana airborne gravity dataset from the USA National Oceanic and Atmospheric Administration (NOAA) to demonstrate that the new method works effectively. Furthermore, and for the Tibetan Plateau we show that the numerical experiment is also successfully conducted using the synthetic Earth Gravitational Model 2008 (EGM08)-derived gravity data contaminated with the synthetic errors. The estimated systematic errors generated by the method are close to the simulated values. In addition, we study the relationship between the downward continuation altitudes and the error effect. The analysis results show that the proposed semi-parametric method combined with regularization is efficient to address such modelling problems

A Unified Framework of FPT Approximation Algorithms for Clustering Problems

In this paper, we present a framework for designing FPT approximation algorithms for many k-clustering problems. Our results are based on a new technique for reducing search spaces. A reduced search space is a small subset of the input data that has the guarantee of containing k clients close to the facilities opened in an optimal solution for any clustering problem we consider. We show, somewhat surprisingly, that greedily sampling O(k) clients yields the desired reduced search space, based on which we obtain FPT(k)-time algorithms with improved approximation guarantees for problems such as capacitated clustering, lower-bounded clustering, clustering with service installation costs, fault tolerant clustering, and priority clustering

A Coumarin–Hemicyanine Deep Red Dye with a Large Stokes Shift for the Fluorescence Detection and Naked-Eye Recognition of Cyanide

In this study, we synthesized a coumarin–hemicyanine-based deep red fluorescent dye that exhibits an intramolecular charge transfer (ICT). The probe had a large Stokes shift of 287 nm and a large molar absorption coefficient (ε = 7.5 × 105 L·mol−1·cm−1) and is best described as a deep red luminescent fluorescent probe with λem = 667 nm. The color of probe W changed significantly when it encountered cyanide ions (CN−). The absorption peak (585 nm) decreased gradually, and the absorption peak (428 nm) increased gradually, so that cyanide (CN−) could be identified by the naked eye. Moreover, an obvious fluorescence change was evident before and after the reaction under irradiation using 365 nm UV light. The maximum emission peak (667 nm) decreased gradually, whilst the emission peak (495 nm) increased gradually, which allowed for the proportional fluorescence detection of cyanide (CN−). Using fluorescence spectrometry, the fluorescent probe W could linearly detect CN− over the concentration range of 1–9 μM (R2 = 9913, RSD = 0.534) with a detection limit of 0.24 μM. Using UV-Vis spectrophotometry, the linear detection range for CN− was found to be 1–27 μM (R2 = 0.99583, RSD = 0.675) with a detection limit of 0.13 μM. The sensing mechanism was confirmed by 1H NMR spectroscopic titrations, 13C NMR spectroscopy, X-ray crystallographic analysis and HRMS. The recognition and detection of CN− by probe W was characterized by a rapid response, high selectivity, and high sensitivity. Therefore, this probe provides a convenient, effective and economical method for synthesizing and detecting cyanide efficiently and sensitively

Faster Ray Tracing through Hierarchy Cut Code

We propose a novel ray reordering technique to accelerate the ray tracing process by encoding and sorting rays prior to traversal. Instead of spatial coordinates, our method encodes rays according to the cuts of the hierarchical acceleration structure, which is called the hierarchy cut code. This approach can better adapt to the acceleration structure and obtain a more reliable encoding result. We also propose a compression scheme to decrease the sorting overhead by a shorter sorting key. In addition, based on the phenomenon of boundary drift, we theoretically explain the reason why existing reordering methods cannot achieve better performance by using longer sorting keys. The experiment demonstrates that our method can accelerate secondary ray tracing by up to 1.81 times, outperforming the existing methods. Such result proves the effectiveness of hierarchy cut code, and indicate that the reordering technique can achieve greater performance improvement, which worth further research

The Correlation Between Body Mass Index and Computed Tomography Angiography on Vascular Positioning in Anterolateral Thigh Flap Transplantation

Objective: This work aimed to investigate the correlation between body mass index (BMI) and computed tomography angiography (CTA) in the vascular positioning of anterolateral thigh perforator flap (ALT) and to discuss the influence of CTA on the vascular positioning of the ALT by taking BMI as a variable. Methods: A total of 117 patients who admitted to our hospital (Wuxi Ninth People’s Hospital) from January 2017 to May 2019, hospitalized due to limb injury and needed ALT transplantation were collected in this work. According to the BMI, the patients were divided into group A (BMI < 18.5) with 18 cases, group B (18.5 ≤ BMI < 24) with 56 cases, and group C (BMI ≥ 24) with 43 cases. CTA was used to locate the perforator vessels in anterolateral thigh (ALT) flap of the three groups. All surgical and CTA data were collected. Results: There was a significant positive correlation between BMI and CTA positioning (P < 0.05). Conclusion: The larger the BMI, the more accurate the CTA positioning. When the BMI was not less than 18.5, CTA positioning should be the most accurate

Activation of AMP-Activated Protein Kinase Is Required for Berberine-Induced Reduction of Atherosclerosis in Mice: The Role of Uncoupling Protein 2

Berberine, a botanical alkaloid purified from Coptidis rhizoma, is reported to activate the AMP-activated protein kinase (AMPK). Whether AMPK is required for the protective effects of berberine in cardiovascular diseases remains unknown. This study was designed to determine whether AMPK is required for berberine-induced reduction of oxidative stress and atherosclerosis in vivo.ApoE (ApoE⁻/⁻) mice and ApoE⁻/⁻/AMPK alpha 2⁻/⁻ mice that were fed Western diets were treated with berberine for 8 weeks. Atherosclerotic aortic lesions, expression of uncoupling protein 2 (UCP2), and markers of oxidative stress were evaluated in isolated aortas.In ApoE⁻/⁻ mice, chronic administration of berberine significantly reduced aortic lesions, markedly reduced oxidative stress and expression of adhesion molecules in aorta, and significantly increased UCP2 levels. In contrast, in ApoE⁻/⁻/AMPK alpha 2⁻/⁻ mice, berberine had little effect on those endpoints. In cultured human umbilical vein endothelial cells (HUVECs), berberine significantly increased UCP2 mRNA and protein expression in an AMPK-dependent manner. Transfection of HUVECs with nuclear respiratory factor 1 (NRF1)-specific siRNA attenuated berberine-induced expression of UCP2, whereas transfection with control siRNA did not. Finally, berberine promoted mitochondrial biogenesis that contributed to up-regulation of UCP2 expression.We conclude that berberine reduces oxidative stress and vascular inflammation, and suppresses atherogenesis via a mechanism that includes stimulation of AMPK-dependent UCP2 expression

Improvement of downward continuation values of airborne gravity data in Taiwan

An airborne gravity survey was carried out to fill gaps in the gravity data for the mountainous areas of Taiwan. However, the downward continuation error of airborne gravity data is a major issue, especially in regions with complex terrain, such as Taiwan. The root mean square (RMS) of the difference between the downward continuation values and land gravity was approximately 20 mGal. To improve the results of downward continuation we investigated the inverse Poisson&#8217;s integral, the semi-parametric method combined with regularization (SPR) and the least-squares collocation (LSC) in this paper. The numerically simulated experiments are conducted in the Tibetan Plateau, which is also a mountainous area. The results show that as a valuable supplement to the inverse Poisson&#8217;s integral, the SPR is a useful approach to estimate systematic errors and to suppress random errors. While the LSC approach generates the best results in the Tibetan Plateau in terms of the RMS of the downward continuation errors. Thus, the LSC approach with a terrain correction (TC) is applied to the downward continuation of real airborne gravity data in Taiwan. The statistical results show that the RMS of the differences between the downward continuation values and land gravity data reduced to 11.7 mGal, which shows that an improvement of 40% is obtained