Cryo-EM Data Statistics and Theoretical Analysis of KaiC Hexamer

Cryo-electron microscopy(cryo-EM) provides a powerful tool to resolve the structure of biological macromolecules in natural state. One advantage of cryo-EM technology is that different conformation states of a protein complex structure can be simultaneously built, and the distribution of different states can be measured. This provides a tool to push cryo-EM technology beyond just to resolve protein structures, but to obtain the thermodynamic properties of protein machines. Here, we used a deep manifold learning framework to get the conformational landscape of Kai C proteins, and further obtained the thermodynamic properties of this central oscillator component in the circadian clock by means of statistical physics.

Combinatorial analysis on spatial information statistics for the karst water environment in Guiyang,China

The karst groundwater system is extremely vulnerable and easily contaminated by human activities.To understand the spatial distribution of contaminants in the groundwater of karst urban areas and contributors to the contamination,this paper employs the spatial information statistics analysis theory and method to analyze the karst groundwater environment in Guiyang City.Based on the karst ground water quality data detected in 61 detection points of the research area in the last three years,we made Kriging evaluation isoline map with some ions in the karst groundwater,such as SO4 2-,Fe 3+,Mn 2+and F -,analyzed and evaluated the spatial distribution,extension and variation of four types of ions on the basis of this isoline map.The results of the analysis show that the anomaly areas of SO4 2-,Fe 3+,Mn 2+,Fand other ions are mainly located in Baba’ao,Mawangmiao and Sanqiao in northwestern Gui- yang City as well as in its downtown area by reasons of the original non-point source pollution and the contamination caused by human activities(industrial and domestic pollution).

Microarray Analysis Using Rank Order Statistics for ARCH Residual Empirical Process

Statistical two-group comparisons are widely used to identify the significant differentially expressed (DE) signatures against a therapy response for microarray data analysis. We applied a rank order statistics based on an Autoregressive Conditional Heteroskedasticity (ARCH) residual empirical process to DE analysis. This approach was considered for simulation data and publicly available datasets, and was compared with two-group comparison by original data and Auto-regressive (AR) residual. The significant DE genes by the ARCH and AR residuals were reduced by about 20% - 30% to these genes by the original data. Almost 100% of the genes by ARCH are covered by the genes by the original data unlike the genes by AR residuals. GO enrichment and Pathway analyses indicate the consistent biological characteristics between genes by ARCH residuals and original data. ARCH residuals array data might contribute to refining the number of significant DE genes to detect the biological feature as well as ordinal microarray data.

Multi-factor analysis of initial poor graft function after orthotopic liver transplantation

BACKGROUND: In the early period of orthotopic liver transplantation (OLT), initial poor graft function (IPGF) is one of the complications which leads to primary graft non-function (PGNF) in serious cases. This study set out to establish the clinical risk factors resulting in IPGF after OLT. METHODS: Eighty cases of OLT were analyzed. The IPGF group consisted of patients with alanine aminotransferase (ALT) and/or aspartate aminotransferase (AST) above 1500 IU/L within 72 hours after OLT, while those in the non-IPGF group had values below 1500 IU/L. Recipient-associated factors before OLT analyzed were age, sex, primary liver disease and Child-Pugh classification; factors analyzed within the peri-operative period were non-heart beating time (NHBT), cold ischemia time (CIT), rewarming ischemic time (RWIT), liver biopsy at the end of cold ischemia; and factors analyzed within 72 hours after OLT were ALT and/or AST values. A logistic regression model was applied to filter the possible factors resulting in IPGF. RESULTS: Donor NHBT, CIT and RWIT were significantly longer in the IPGF group than in the non-IPGF group; in the logistic regression model, NHBT was the risk factor leading to IPGF (P < 0.05), while CIT and RWIT were possible risk factors. In one case in the IPGF group, PGNF appeared with moderate hepatic steatosis. CONCLUSIONS: Longer NHBT is an important risk factor leading to IPGF, while serious steatosis in the donor liver, CIT and RWIT are potential risk factors.

A Hybrid Neural Network Model for Marine Dissolved Oxygen Concentrations Time-Series Forecasting Based on Multi-Factor Analysis and a Multi-Model Ensemble

Dissolved oxygen(DO)is an important indicator of aquaculture,and its accurate forecasting can effectively improve the quality of aquatic products.In this paper,a new DO hybrid forecasting model is proposed that includes three stages:multi-factor analysis,adaptive decomposition,and an optimizationbased ensemble.First,considering the complex factors affecting DO,the grey relational(GR)degree method is used to screen out the environmental factors most closely related to DO.The consideration of multiple factors makes model fusion more effective.Second,the series of DO,water temperature,salinity,and oxygen saturation are decomposed adaptively into sub-series by means of the empirical wavelet transform(EWT)method.Then,five benchmark models are utilized to forecast the sub-series of EWT decomposition.The ensemble weights of these five sub-forecasting models are calculated by particle swarm optimization and gravitational search algorithm(PSOGSA).Finally,a multi-factor ensemble model for DO is obtained by weighted allocation.The performance of the proposed model is verified by timeseries data collected by the pacific islands ocean observing system(PacIOOS)from the WQB04 station at Hilo.The evaluation indicators involved in the experiment include the Nash–Sutcliffe efficiency(NSE),Kling–Gupta efficiency(KGE),mean absolute percent error(MAPE),standard deviation of error(SDE),and coefficient of determination(R^(2)).Example analysis demonstrates that:①The proposed model can obtain excellent DO forecasting results;②the proposed model is superior to other comparison models;and③the forecasting model can be used to analyze the trend of DO and enable managers to make better management decisions.

Application of an Error Statistics Estimation Method to the PSAS Forecast Error Covariance Model

In atmospheric data assimilation systems, the forecast error covariance model is an important component. However, the paralneters required by a forecast error covariance model are difficult to obtain due to the absence of the truth. This study applies an error statistics estimation method to the Pfiysical-space Statistical Analysis System （PSAS） height-wind forecast error covariance model. This method consists of two components： the first component computes the error statistics by using the National Meteorological Center （NMC） method, which is a lagged-forecast difference approach, within the framework of the PSAS height-wind forecast error covariance model; the second obtains a calibration formula to rescale the error standard deviations provided by the NMC method. The calibration is against the error statistics estimated by using a maximum-likelihood estimation （MLE） with rawindsonde height observed-minus-forecast residuals. A complete set of formulas for estimating the error statistics and for the calibration is applied to a one-month-long dataset generated by a general circulation model of the Global Model and Assimilation Office （GMAO）, NASA. There is a clear constant relationship between the error statistics estimates of the NMC-method and MLE. The final product provides a full set of 6-hour error statistics required by the PSAS height-wind forecast error covariance model over the globe. The features of these error statistics are examined and discussed.

The k Nearest Neighbors Estimator of the M-Regression in Functional Statistics

It is well known that the nonparametric estimation of the regression function is highly sensitive to the presence of even a small proportion of outliers in the data.To solve the problem of typical observations when the covariates of the nonparametric component are functional,the robust estimates for the regression parameter and regression operator are introduced.The main propose of the paper is to consider data-driven methods of selecting the number of neighbors in order to make the proposed processes fully automatic.We use thek Nearest Neighbors procedure(kNN)to construct the kernel estimator of the proposed robust model.Under some regularity conditions,we state consistency results for kNN functional estimators,which are uniform in the number of neighbors(UINN).Furthermore,a simulation study and an empirical application to a real data analysis of octane gasoline predictions are carried out to illustrate the higher predictive performances and the usefulness of the kNN approach.

Inferential Statistics and Machine Learning Models for Short-TermWind Power Forecasting

The inherent randomness,intermittence and volatility of wind power generation compromise the quality of the wind power system,resulting in uncertainty in the system’s optimal scheduling.As a result,it’s critical to improve power quality and assure real-time power grid scheduling and grid-connected wind farm operation.Inferred statistics are utilized in this research to infer general features based on the selected information,confirming that there are differences between two forecasting categories:Forecast Category 1(0-11 h ahead)and Forecast Category 2(12-23 h ahead).In z-tests,the null hypothesis provides the corresponding quantitative findings.To verify the final performance of the prediction findings,five benchmark methodologies are used:Persistence model,LMNN(Multilayer Perceptron with LMlearningmethods),NARX(Nonlinear autoregressive exogenous neural networkmodel),LMRNN(RNNs with LM training methods)and LSTM(Long short-term memory neural network).Experiments using a real dataset show that the LSTM network has the highest forecasting accuracy when compared to other benchmark approaches including persistence model,LMNN,NARX network,and LMRNN,and the 23-steps forecasting accuracy has improved by 19.61%.

The use of hydrogeochemical analyses and multivariate statistics for the characterization of thermal springs in the Constantine area, Northeastern Algeria

This paper deals with the results of a hydrogeochemistry study on the thermal waters of the Constantine area, Northeastern Algeria, using geochemical and statistical tools. The samples were collected in December2016 from twelve hot springs and were analyzed for physicochemical parameters(electric conductivity, p H,total dissolved solids, temperature, Ca, Mg, Na, K, HCO_3,Cl, SO_4, and SiO_2). The waters of the thermal springs have temperatures varying from 28 to 51 °C and electric conductivity values ranging from 853 to 5630 l S/cm. Q-mode Cluster analysis resulted in the determination of two major water types: a Ca–HCO_3–SO_4 type with a moderate salinity and a Na–K–Cl type with high salinity. The plot of the major ions versus the saturation indices suggested that the hydrogeochemistry of thermal groundwater is mainly controlled by dissolution/precipitation of carbonate minerals, dissolution of evaporite minerals(halite and gypsum), and ion exchange of Ca(and/or Mg) by Na. The Gibbs diagram shows that evaporation is another factor playing a minor role. Principal Component Analysis produced three significant factors which have 88.2% of totalvariance that illustrate the main processes controlling the chemistry of groundwaters, which are respectively: the dissolution of evaporite minerals(halite and gypsum), ion exchange, and dissolution/precipitation of carbonate minerals. The subsurface reservoir temperatures were calculated using different cation and silica geothermometers and gave temperatures ranging between 17 and 279 °C. The Na–K and Na–K-Ca geothermometers provided high temperatures(up to 279 °C), whereas, estimated geotemperatures from K/Mg geothermometers were the lowest(17–53 °C). Silica geothermometers gave the most reasonable temperature estimate of the subsurface waters overlap between 20 and 58 °C, which indicate possible mixing with cooler Mg groundwaters indicated by the Na–K–Mg plot in the immature water field and in silica and chloride mixing models. The results of stable isotope analyses(δ^(18) O and δ~2 H) suggest that the origin of thermal water recharge is precipitation, which recharged from a higher altitude(600–1200 m) and infiltrated through deep faults and fractures in carbonate formations. They circulate at an estimated depth that does not exceed 2 km and are heated by a high conductive heat flow before rising to the surface through faults that acted as hydrothermal conduits.During their ascent to the surface, they are subjected to various physical and chemical changes such as cooling by conduction and change in their chemical constituents due to the mixing with cold groundwaters.

A Measurement Theoretical Foundation of Statistics

It is a matter of course that Kolmogorov’s probability theory is a very useful mathematical tool for the analysis of statistics. However, this fact never means that statistics is based on Kolmogorov’s probability theory, since it is not guaranteed that mathematics and our world are connected. In order that mathematics asserts some statements concerning our world, a certain theory (so called “world view”) mediates between mathematics and our world. Recently we propose measurement theory (i.e., the theory of the quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics. In this paper, we assert that statistics is based on measurement theory. And, for example, we show, from the pure theoretical point of view (i.e., from the measurement theoretical point of view), that regression analysis can not be justified without Bayes’ theorem. This may imply that even the conventional classification of (Fisher’s) statistics and Bayesian statistics should be reconsidered.

Quantification constraints on time gap for comagmatic gold deposits:Evidence from chronological statistics

The time gap between diagenesis and mineralization (TGDM) for comagmatic gold deposits (CGD) plays an important role in confirming the genetic relationship between gold deposits and their related intrusions. With the help of preciously published isotopic ages of some typical gold deposits and their related rocks in China,the authors have discussed and quantified the distribution characteristics and scope of the TGDM. Statistical analyses and Kolmogorov tests showed that mineralizing events are either contemporaneous with or slightly postdate their cognate magma. The TGDM conforms with normal distributions at a 0.05 confidence level and clusters between 0 and 16.0 Ma with a mean of 7.0 Ma. Thus,if the TGDM of CGD is less than 16.0 Ma,it is reasonable to consider,with the aid of other evidence,the possibility of its comagmatic genetic affiliation. The authors also emphasized that to get a precise time gap it is necessary to strengthen the diagenesis-mineralization geological background of the deposits studied,and to pay attention to the study of time gap in combination with trace elements and isotope tracing.

Evaluation of Groundwater Quality in the Deep Maastrichtian Aquifer of Senegal Using Multivariate Statistics and Water Quality Index-Based GIS

A regional groundwater quality evaluation was conducted in the deep Maastrichtian aquifer of Senegal through multivariate statistical analysis and a GIS-based water quality index using physicochemical data from 232 boreholes distributed over the whole country. The aim was to 1) identify the water types and likely factors influencing the hydrochemistry, and 2) determine the suitability of groundwater for drinking and irrigation. Results showed that sodium, chloride, and fluoride are highly correlated with electrical conductivity (EC) reflecting the significant contribution of these elements to groundwater mineralization. The principal component analysis evidenced: 1) salinization processes (loaded by Na+, K+, EC, Cl-, F- and HCO3-) controlled by water/rock interaction, seawater intrusion and cation exchange reactions;2) dolomite dissolution loaded by the couple Ca2+ and Mg2+ and 3) localized mixing with upper aquifers and gypsum dissolution respectively loaded by NO3- and SO42-. The hierarchical clustering analysis distinguished four clusters: 1) freshwater (EC = 594 μs/cm) with mixed-HCO3 water type and ionic contents below WHO standard;2) brackish (Na-mixed) water type with moderate mineralization content (1310 μs/cm), 3) brackish (Na-Cl) water type depicted by high EC values (3292 μs/cm) and ionic contents above WHO and 4) saline water with Na-Cl water type and very high mineralization contents (5953 μs/cm). The mapping of the groundwater quality index indicated suitable zones for drinking accounting for 54% of the entire area. The occurrence of a central brackish band and its vicinity, which were characterized by high mineralization, yielded unsuitable groundwater for drinking and agricultural uses. The approach used in this study was valuable for assessing groundwater quality for drinking and irrigation, and it can be used for regional studies in other locations, particularly in shallow and vulnerable aquifers.

MATHEMATICAL STATISTICS OF HEAVY MINERALS AND THEIR REE AND TRACE ELEMENTS IN THE NORTHWESTERN SEA AREA OF ANTARCTIC PENINSULA

Based on the analysis and mathematical statistics of quantitative data on both the heavy minerals and their REE (La, Ce, Nd, Sm, Eu, Tb, Yb, Lu), trace (Zr, Hf, Th, Ta, U, Rb, Sr, Zn, Co, Ni, Cr, As, Sc) and major (Fe) elements in the surface sediments in the northwestern sea area of Antarctic Peninsula, the authors find that the heavy minerals as the carriers of REE and trace elements should not be overlooked.Q-mode factor analysis of the heavy minerals provides a 3-factor model of the heavy mineral assemblages in the study area, which is mainly controlled by the origin of materials and sea currents. The common factor P1, composed mainly of pyroxene and metal minerals, and common factor P2, composed of hornblende, epidote and accessory minerals, represent two heavy mineral assemblages which are different from each other in both lithological characters and origin of materials. And common factor P3 probably results from mixing of two end members of the above-mentioned assemblages. R-mode group analysis of the heavy minerals indicates that there are two heavy mineral groups in the sea area, which are different from each other in both genesis and origin of materials. With the help of R-mode analysis, 22 elements are divided into 3 groups and 9 subgroups. These element assemblages show that they are genetically related and that they are different in geochemical behaviors during diagenesis and mineral-forming process. In addition, the relationship between the heavy mineral assemblages and the element subgroups is also discussed.

RANDOM SYSTEMS OF HARD PARTICLES:MODELS AND STATISTICS

This paper surveys models and statistical properties of random systems of hard particles. Such systems appear frequently in materials science, biology and elsewhere. In mathematical-statistical investigations, simulations of such structures play an important role. In these simulations various methods and models are applied, namely the RSA model, sedimentation and collective rearrangement algorithms, molecular dynamics, and Monte Carlo methods such as the Metropolis-Hastings algorithm. The statistical description of real and simulated particle systems uses ideas of the mathematical theories of random sets and point processes. This leads to characteristics such as volume fraction or porosity, covariance, contact distribution functions, specific connectivity number from the random set approach and intensity, pair correlation function and mark correlation functions from the point process approach. Some of them can be determined stereologically using planar sections, while others can only be obtained using three-dimensional data and 3D image analysis. They are valuable tools for fitting models to empirical data and, consequently, for understanding various materials, biological structures, porous media and other practically important spatial structures.

Looking at Electric Power Consumption from Statistics

On the basis of the historical statistics on power consumption, this paper analyzes the power consumption trends in China by means of analyzing methods based on consumption proportion curve, fixed base curve, month-on-month increase curve and fixed base index curve. Special attentions are paid to the consumption trend in the first half of 2010, and policy strategies are suggested targeting the problems reflected by the consumption trend.

Quantitative analysis and prediction of the sound field convergence zone in mesoscale eddy environment based on data mining methods

The mesoscale eddy(ME)has a significant influence on the convergence effect in deep-sea acoustic propagation.This paper use statistical approaches to express quantitative relationships between the ME conditions and convergence zone(CZ)characteristics.Based on the Gaussian vortex model,we construct various sound propagation scenarios under different eddy conditions,and carry out sound propagation experiments to obtain simulation samples.With a large number of samples,we first adopt the unified regression to set up analytic relationships between eddy conditions and CZ parameters.The sensitivity of eddy indicators to the CZ is quantitatively analyzed.Then,we adopt the machine learning(ML)algorithms to establish prediction models of CZ parameters by exploring the nonlinear relationships between multiple ME indicators and CZ parameters.Through the research,we can express the influence of ME on the CZ quantitatively,and achieve the rapid prediction of CZ parameters in ocean eddies.The prediction accuracy(R)of the CZ distance(mean R:0.9815)is obviously better than that of the CZ width(mean R:0.8728).Among the three ML algorithms,Gradient Boosting Decision Tree has the best prediction ability(root mean square error(RMSE):0.136),followed by Random Forest(RMSE:0.441)and Extreme Learning Machine(RMSE:0.518).

A Bayesian multi-model inference methodology for imprecise momentindependent global sensitivity analysis of rock structures

Traditional global sensitivity analysis(GSA)neglects the epistemic uncertainties associated with the probabilistic characteristics(i.e.type of distribution type and its parameters)of input rock properties emanating due to the small size of datasets while mapping the relative importance of properties to the model response.This paper proposes an augmented Bayesian multi-model inference(BMMI)coupled with GSA methodology(BMMI-GSA)to address this issue by estimating the imprecision in the momentindependent sensitivity indices of rock structures arising from the small size of input data.The methodology employs BMMI to quantify the epistemic uncertainties associated with model type and parameters of input properties.The estimated uncertainties are propagated in estimating imprecision in moment-independent Borgonovo’s indices by employing a reweighting approach on candidate probabilistic models.The proposed methodology is showcased for a rock slope prone to stress-controlled failure in the Himalayan region of India.The proposed methodology was superior to the conventional GSA(neglects all epistemic uncertainties)and Bayesian coupled GSA(B-GSA)(neglects model uncertainty)due to its capability to incorporate the uncertainties in both model type and parameters of properties.Imprecise Borgonovo’s indices estimated via proposed methodology provide the confidence intervals of the sensitivity indices instead of their fixed-point estimates,which makes the user more informed in the data collection efforts.Analyses performed with the varying sample sizes suggested that the uncertainties in sensitivity indices reduce significantly with the increasing sample sizes.The accurate importance ranking of properties was only possible via samples of large sizes.Further,the impact of the prior knowledge in terms of prior ranges and distributions was significant;hence,any related assumption should be made carefully.

Improved statistical fluctuation analysis for two decoy-states phase-matching quantum key distribution

Phase-matching quantum key distribution is a promising scheme for remote quantum key distribution,breaking through the traditional linear key-rate bound.In practical applications,finite data size can cause significant system performance to deteriorate when data size is below 1010.In this work,an improved statistical fluctuation analysis method is applied for the first time to two decoy-states phase-matching quantum key distribution,offering a new insight and potential solutions for improving the key generation rate and the maximum transmission distance while maintaining security.Moreover,we also compare the influence of the proposed improved statistical fluctuation analysis method on system performance with those of the Gaussian approximation and Chernoff-Hoeffding boundary methods on system performance.The simulation results show that the proposed scheme significantly improves the key generation rate and maximum transmission distance in comparison with the Chernoff-Hoeffding approach,and approach the results obtained when the Gaussian approximation is employed.At the same time,the proposed scheme retains the same security level as the Chernoff-Hoeffding method,and is even more secure than the Gaussian approximation.

Statistical analysis on the influence of mechanical parameters in the vibration of pylons

We present a statistical investigation of the degree of influence that assumptions made in relation to the mechanical parameters of a pylon have on its ground-induced vibrations.The study is set up by using as a key kinematic variable the displacement at the top of a reference,a stand-alone pylon with a uniform cross-section and fixity at its base.Next,statistics are produced using a dimensionless displacement ratio defined between the‘parental’and the‘subsidiary’cases,the latter defined for the pylon(a)resting on compliant soil,(b)having an attached top mass,and(c)being non-uniform with height.Furthermore,two materials are examined,namely,steel and reinforced concrete(R/C).More specifically,this displacement ratio is independent of the excitation and plays the role of a transfer function between the base and the top of the pylon.Both horizontal and vertical motions are considered,and the equations of motion are solved in the frequency domain.The ensuing statistical analysis is conducted for the following parameter combinations:(a)pylon founded on soft,intermediate,and stiff soil;(b)low,intermediate,and high-mass ratios of the attached mass to the pylon′s mass;(c)a constant and quadratic degree of pylon tapering with height.Spearman correlation coefficients are calculated for all the above combinations to arrive at statistical results that establish validity bounds and quantify the degree of influence of each assumption on the pylon′s response.