Tropical Support Vector Machine and its Applications to Phylogenomics

Most data in genome-wide phylogenetic analysis (phylogenomics) is essentially multidimensional, posing a major challenge to human comprehension and computational analysis. Also, we can not directly apply statistical learning models in data science to a set of phylogenetic trees since the space of phylogenetic trees is not Euclidean. In fact, the space of phylogenetic trees is a tropical Grassmannian in terms of max-plus algebra. Therefore, to classify multi-locus data sets for phylogenetic analysis, we propose tropical support vector machines (SVMs). Like classical SVMs, a tropical SVM is a discriminative classifier defined by the tropical hyperplane which maximizes the minimum tropical distance from data points to itself in order to separate these data points into sectors (half-spaces) in the tropical projective torus. Both hard margin tropical SVMs and soft margin tropical SVMs can be formulated as linear programming problems. We focus on classifying two categories of data, and we study a simpler case by assuming the data points from the same category ideally stay in the same sector of a tropical separating hyperplane. For hard margin tropical SVMs, we prove the necessary and sufficient conditions for two categories of data points to be separated, and we show an explicit formula for the optimal value of the feasible linear programming problem. For soft margin tropical SVMs, we develop novel methods to compute an optimal tropical separating hyperplane. Computational experiments show our methods work well. We end this paper with open problems.Comment: 27 pages, 6 figures, 2 table

Impacts of different urban canopy schemes in WRF/Chem on regional climate and air quality in Yangtze River Delta, China

AbstractYangtze River Delta (YRD) region has experienced a remarkable urbanization during the past 30years, and regional climate change and air pollution are becoming more and more evident due to urbanization. Impacts of urban canopy on regional climate and air quality in dry- and wet-season are investigated in this paper, utilizing the Weather Research and Forecasting/Chemistry (WRF/Chem) model. Four regimes of urban canopy schemes with updated USGS land-use data in actual state of 2004 base on MODIS observations are examined: (1) SLAB scheme that does not consider urban canopy parameters (the control experiment in this paper); (2) a single-layer urban model with a fixed diurnal profile for anthropogenic heat (UCM); (3) multilayer urban canopy model (BEP-Building effect parameterization); (4) multilayer urban models with a building energy model including anthropogenic heat due to air conditioning (BEP+BEM). Results show that, compared with observations, the best 2-m temperature estimates with minimum bias are obtained with SLAB and BEP+BEM schemes, while the best 10-m wind speed predictions are obtained with BEP and BEP+BEM scheme. For PM10 and ozone predictions, BEP+BEM scheme predicted PM10 well during January, while the best estimate of PM10 is obtained with UCM scheme during July, BEP+BEM and SLAB schemes best estimated ozone concentrations for both the two months. Spatial differences of meteorological factors between canopy schemes and control scheme show that compared with SLAB scheme, BEP and BEP+BEM schemes cause an increase of temperature with differences of 0.5°C and 0.3°C, respectively, UCM scheme simulates lower temperature with decrease of 0.7°C during January. In July, all the canopy experiments calculates lower air temperature with reduction of 0.5°C–1.6°C. All the canopy experiments compute lower 10-m wind speed for both January and July. Decreases were 0.7m/s (0.8m/s) with UCM, 1.7m/s (2.6m/s) with BEP, and 1.8m/s (2.3m/s) with BEP+BEM schemes in January (July), respectively. For chemical field distributions, results show that, compared with SLAB scheme, UCM scheme calculates higher PM10 concentration in both January and July, with the differences of 22.3% (or 24.4μg/m3) in January, and 31.4% (or 17.4μg/m3) in July, respectively. As large as 32.7% (or 18.3 μg/m3) of PM10 increase is found over Hangzhou city during July. While 18.6% (or 22.1 μg/m3) and 16.7% (or 24.6 μg/m3) of PM10 decreases are fund in BEP and BEP+BEM schemes during January. Compared with control experiment during January, 6.5% (or 2.6ppb) to 10.4% (4.2ppb) increases of ozone are computed over mage-cities by canopy experiments. All the three canopy schemes predict lower ozone concentrations and as large as 30.2% (or 11.2ppb) decrease is obtained with UCM scheme, and 16.5% (6.2ppb) decrease with BEP scheme during July. The SLAB scheme is suitable for real-time weather forecast while multiple urban canopy scheme is necessary when quantify the urbanization impacts on regional climate

Optimization of irrigation and fertilization of apples under magnetoelectric water irrigation in extremely arid areas

Apple (Malus pumila Mill.) is one of the important economic crops in the arid areas of Xinjiang, China. For a long time, there has been a problem of high consumption but low yield in water and fertilizer management, prevent improvements in apple quality and yield. In this study, 5-year-old ‘Royal Gala’ apple trees in extremely arid areas of Xinjiang were used as experimental materials to carry out field experiments. considering 5 irrigation levels (W1, 30 mm; W2, 425 mm; W3, 550 mm; W4, 675 mm; W5, 800 mm) and 5 fertilization levels (F1, 280 kg·ha-1; F2, 360 kg·ha-1; F3, 440 kg·ha-1; F4, 520 kg·ha-1; F5, 600 kg·ha-1) under magnetoelectric water irrigation conditions. The results demonstrated that magnetoelectric water combined with the application of 675 mm irrigation amount and 520 kg·ha-1 fertilization amount was the most effective combination. These results occurred by increasing net photosynthetic rate of apple leaves, improved the quality of apples, increased apple yield, and promoted the improvement of water and fertilizer use efficiency. Additionally, the quadratic regression model was used to fit the response process of yield, IWUE and PFP to irrigation amount and fertilization amount, and the accuracy was greater than 0.8, indicating good fitting effects. The synergistic effect of water and fertilizer has a positive effect on optimizing apple water and fertilizer management. Principal component analysis showed that the magnetoelectric treatment combined water and fertilizer mainly affected apple yield, water and fertilizer use efficiency and vitamin C content related to quality. This study provides valuable guidance for improving water and fertilizer productivity, crop yield and quality in extreme arid areas of Xinjiang by using Magnetoelectric water irrigation

NCAPG2 could be an immunological and prognostic biomarker: From pan-cancer analysis to pancreatic cancer validation

More recently, NCAPG2 has emerged as an intrinsically essential participant of the condensin II complex involved in the process of chromosome cohesion and stabilization in mitosis, and its position in particular tumours is now being highlighted. Simultaneously, the genetic properties of NCAPG2 hint that it might have enormous potential to interpret the malignant progression of tumors in a broader perspective, that is, in pan-cancer. Yet, at present, this recognition remains merely superficial and there is a lack of more detailed studies to explore the underlying pathogenesis. To meet this need, the current study was undertaken to comprehensively elucidate the potential functions of NCAPG2 in pan-cancer, based on a combination of existing databases like TCGA and GTEx. NCAPG2 was identified to be overexpressed in almost every tumor and to exhibit significant prognostic and diagnostic efficacy. Furthermore, the correlation between NCAPG2 and selected immune features, namely immune cell infiltration, immune checkpoint genes, TMB, MSI, etc. also indicates that NCAPG2 could potentially be applied in guidance of immunotherapy. Subsequently, in pancreatic cancer, this study further clarified the utility of NCAPG2 that downregulation of its expression could result in reduced proliferation, invasion and metastasis of pancreatic cancer cells, among such phenotypical changes, the epithelial-mesenchymal transition disruption could be at least one of the possible mechanisms raising or enhancing tumorigenesis. Taken above, NCAPG2, as a member of pan-oncogenes, would serve as a biomarker and potential therapeutic target for a range of malignancies, sharing new insights into precision medicine

Fault Diagnosis of Motor Bearing by Analyzing a Video Clip

Conventional bearing fault diagnosis methods require specialized instruments to acquire signals that can reflect the health condition of the bearing. For instance, an accelerometer is used to acquire vibration signals, whereas an encoder is used to measure motor shaft speed. This study proposes a new method for simplifying the instruments for motor bearing fault diagnosis. Specifically, a video clip recording of a running bearing system is captured using a cellphone that is equipped with a camera and a microphone. The recorded video is subsequently analyzed to obtain the instantaneous frequency of rotation (IFR). The instantaneous fault characteristic frequency (IFCF) of the defective bearing is obtained by analyzing the sound signal that is recorded by the microphone. The fault characteristic order is calculated by dividing IFCF by IFR to identify the fault type of the bearing. The effectiveness and robustness of the proposed method are verified by a series of experiments. This study provides a simple, flexible, and effective solution for motor bearing fault diagnosis. Given that the signals are gathered using an affordable and accessible cellphone, the proposed method is proven suitable for diagnosing the health conditions of bearing systems that are located in remote areas where specialized instruments are unavailable or limited