Research on the Application of PBL+SPOC Blended Teaching Model in Probability and Statistics Course

To cultivate talents with an exploratory spirit and practical skills in the era of information technology,it is imperative to reform teaching methods and approaches.In the teaching process of the Probability and Statistics course,an application-oriented blended teaching model combining problem-based learning and small private online course was explored.By organizing and implementing online and offline teaching activities based on problem-based learning,a multidimensional process-oriented learning assessment system was established.Practice has shown that this model can effectively enhance classroom teaching effectiveness,benefiting the improvement of students’overall skills and mathematical literacy.

Integration of Ideological and Political Education into the Probability Theory and Mathematical Statistics Course:A Teaching Design Based on Estimation and Hypothesis Testing

With the rapid development of higher education in China,colleges and universities are facing new challenges and impacts in talent training.Probability Theory and Mathematical Statistics is one of the important courses in higher education for science and engineering majors and economics and management majors.Its critical role in cultivating students’thinking skills and improving their problem-solving skills is self-evident.Course ideological and political education construction is an important link in college talent training work.Combining ideological and political education with course teaching can help students establish correct value concepts and play a certain role in improving their comprehensive ability and quality.At present,the construction of ideological and political education in the Probability Theory and Mathematical Statistics course still faces some problems,mainly manifested in the lack of attention paid by teachers to course ideological and political education,insufficient exploitation of ideological and political elements,and the simplification of ideological and political education implementation methods.In order to comprehensively deepen the construction of course ideological and political education in line with the actual needs of Probability Theory and Mathematical Statistics course teaching,we should strengthen the construction of teacher teams,improve teachers’ability to carry out course ideological and political education,integrate educational resources,develop educational resources for ideological and political education,and innovate teaching methods to improve the overall effect of ideological and political education integration.

Fatigue Life Prediction of Horizontal Press Frame Based on Statistical Probability and Its Redesign

Horizontal press as an important part of hydro-forming machine is used to output the horizontal force to keep the high internal pressure during tube hydro-forming. However,the horizontal press frame is usually mounted on the press bed and not pre-stressed. Meanwhile it will be subjected to the reaction force caused by liquid pressure. Stresses are concentrated severely on the assemble region due to deformation,and total fatigue life will decrease. In order to predict the total fatigue life of the frame,the simulations are used firstly to determine to stress concentration region,and then strain gauge measurements are carried out under different loads. Next,the methods of statistical probability are conducted to calculate the fatigue life based on long-term load history. Finally a structure with the considerable longer fatigue life is redesigned.

Research on the Reliability Tolerance Analysis Method of Electromagnetic Relay in Aerospace

Electromagnetic relay in aerospace is one of the main electronic components in aerospace electronic systems for information transfer, control and power distribution, and its reliability will influence the reliability of the whole aerospace electronic systems. Reliability design is the key technique of electromagnetic relay reliability engineering. This paper synthetically analyzes the present reliability design methods, and presents the reliability tolerance analyzing mathematic models of electromagnetic force basing on orthogonal design, mechanical spring force basing on probability statistics theory, and matching characteristics of electromagnetic force and mechanical spring force basing on method of stressstrength interference. Some instructive conclusions are draw by researching on the reliability tolerance of some type electromagnetic relay in aerospace.

The Grade-Tonnage Model for China's Molybdenum Deposits

The authors have studied the statistical characteristics of China＇s molybdenum deposits to establish the grade-tonnage model based on the data updated to the end of 2010. The results showed that each type of China＇s molybdenum deposits complied with Lasky＇s law approximately and the characteristics of grade-tonnage model obey the lognormal distribution. However, there are poor correlations between grade and tonnage respectively. Ultimately, we aimed to fit the grade-tonnage model through the known distribution function, draw the cumulative probability curves, and evaluated undiscovered mineral resources of China＇s molybdenum deposits by means of Monte Carlo simulation integrated in MRAS.

Simulating the particle size distribution of rockfill materials based on its statistical regularity

The particle size distribution of rockfill is studied by using granular mechanics, mesomechanics and probability statistics to reveal the relationship of the distribution of particle size to that of the potential energy intensity before fragmentation, which finds out that the potential energy density has a linear relation to the logarithm of particle size and deduces that the distribution of the logarithm of particle size conforms to normal distribution because the distribution of the potential energy density does so. Based on this finding and by including the energy principle of rock fragmentation, the logarithm distribution model of particle size is formulated, which uncovers the natural characteristics of particle sizes on statistical distribution. Exploring the properties of the average value, the expectation, and the unbiased variance of particle size indicates that the expectation does notequal to the average value, but increases with increasing particle size and its ununiformity, and is always larger than the average value, and the unbiased variance increases as the ununiformity and geometric average value increase. A case study proves that the simulated results by the proposed logarithm distribution model accord with the actual data. It is concluded that the logarithm distribution model and Kuz-Ram model can be used to forecast the particle-size distribution of inartificial rockfill while for blasted rockfill, Kuz-Ram model is an option, and in combined application of the two models, it is necessary to do field tests to adjust some parameters of the model.

Theoretical Study on Stochastic Modeling of Combined Gravity-Magnetic-Electric-Seismic Inversion and Its Application

As gravity field, magnetic field, electric field and seismic wave field are all physical fields, their object function, reverse function and compound function are certainly infinite continuously differentiable functions which can be expanded into Taylor (Fourier) series within domain of definition and be further reduced into solving stochastic distribution function of series and statistic inference of optimal approximation. This is the basis of combined gravity-magnetic-electric-seismic inversion of stochastic modeling. It is an uncertainty modeling technology of combining gravity-magnetic-electric-seismic inversion built on the basis of separation of field and source gravity-magnetic difference-value (D-value) trend surface, taking distribution-independent fault system as its unit, depths of seismic and electric interfaces of interests as its corresponding bivariate compound reverse function of gravity-magnetic anomalies and using high order polynomial (high order trigonometric function) approximating to its series distribution. The difference from current dominant inversion techniques is that, first, it does not respectively create gravity-seismic, magnetic-seismic deterministic inversion model from theoretical model, but combines gravity-magnetic-electric-seismic stochastic inversion model from stochastic model; second, after the concept of equivalent geological body being introduced, using feature of independent variable of gravity-magnetic field functions, taking density and susceptibility related to gravity-magnetic function as default parameters of model, the deterministic model is established owing to better solution to the contradiction of difficulty in identifying strata and less test analytical data for density and susceptibility in newly explored area; third, under assumption of independent parent distribution, a real modeling by strata, the problem of difficult plane closure arising in profile modeling is avoided. This technology has richer and more detailed fault and strata information than sparse pattern seismic data in newly explored area, successfully inverses and plots structural map of Indosinian discontinuity in Hefei basin with combined gravity-magnetic-electric-seismic inversion. With development of high precision gravity-magnetic and overall geophysical technology, it is certain for introducing new methods of stochastic modeling and computational intelligence and promoting the development of combined gravity-magnetic-electric-seismic inversion to open a new substantial path.

ON DESIGN METHOD OF THE PRECISION CAM PROFILE WITH RANDOM PROCESSING ERRORS

Based on probability and statistic, a design method of precision cam profileconcerning the influence of random processing errors is advanced. Combining the design with theprocess, which can be used to predict that cam profiles will be successfully processed or not in thedesign stage, design of the cam can be done by balancing the economization and reliability. Inaddition, an fuzzy deduction method based on Bayers formula is advanced to estimate processingreasonable of the designed precision cam profile, and it take few samples.

Quantifying Likelihood in Digital Forensic Investigations

While the conventional forensic scientists routinely validate and express the results of their investigations quantitatively using statistical measures from probability theory,digital forensics examiners rarely if ever do so.In this paper,we review some of the quantitative tools and techniques which are available for use in digital forensic investigations,including Bayesian networks,complexity theory,information theory and probability theory,and indicate how they may be used to obtain likelihood ratios or odds ratios for the relative plausibility of alternative explanations for the creation of the recovered digital evidence.The potential benefits of such quantitative measures for modern digital forensics are also outlined.

Wave Energy Estimation by Using A Statistical Analysis and Wave Buoy Data near the Southern Caspian Sea

Statistical analysis was done on simultaneous wave and wind using data recorded by discus-shape wave buoy. The area is located in the southern Caspian Sea near the Anzali Port. Recorded wave data were obtained through directional spectrum wave analysis. Recorded wind direction and wind speed were obtained through the related time series as well. For 12-month measurements（May 25 2007-2008）, statistical calculations were done to specify the value of nonlinear auto-correlation of wave and wind using the probability distribution function of wave characteristics and statistical analysis in various time periods. The paper also presents and analyzes the amount of wave energy for the area mentioned on the basis of available database. Analyses showed a suitable comparison between the amounts of wave energy in different seasons. As a result, the best period for the largest amount of wave energy was known. Results showed that in the research period, the mean wave and wind auto correlation were about three hours. Among the probability distribution functions, i.e Weibull, Normal, Lognormal and Rayleigh, ＂Weibull＂ had the best consistency with experimental distribution function shown in different diagrams for each season. Results also showed that the mean wave energy in the research period was about 49.88 k W/m and the maximum density of wave energy was found in February and March, 2010.

Applications of probability and statistics in cancer genomics

Background:The past decade has witnessed a rapid progress in our understanding of the genetics of cancer and its progression.Probabilistic and statistical modeling played a pivotal role in the discovery of general patterns from cancer genomics datasets and continue to be of central importance for personalized medicine.Results:In this review we introduce cancer genomics from a probabilistic and statistical perspective.We start from(1)functional classification of genes into oncogenes and tumor suppressor genes,then(2)demonstrate the importance of comprehensive analysis of different mutation types for individual cancer genomes,followed by(3)tumor purity analysis,which in turn leads to(4)the concept of ploidy and clonality,that is next connected to(5)tumor evolution under treatment pressure,which yields insights into cancer drug resistance.We also discuss future challenges including the non-coding genomic regions,integrative analysis of genomics and epigenomics,as well as early cancer detection.Conclusion:We believe probabilistic and statistical modeling will continue to play important roles for novel discoveries in the field o f cancer genomics and personalized medicine.

Robust and Efficient Reliability Estimation for Exponential Distribution

In modeling reliability data,the exponential distribution is commonly used due to its simplicity.For estimating the parameter of the exponential distribution,classical estimators including maximum likelihood estimator represent the most commonly used method and are well known to be efficient.However,the maximum likelihood estimator is highly sensitive in the presence of contamination or outliers.In this study,a robust and efficient estimator of the exponential distribution parameter was proposed based on the probability integral transform statistic.To examine the robustness of this new estimator,asymptotic variance,breakdown point,and gross error sensitivity were derived.This new estimator offers reasonable protection against outliers besides being simple to compute.Furthermore,a simulation study was conducted to compare the performance of this new estimator with the maximum likelihood estimator,weighted likelihood estimator,and M-scale estimator in the presence of outliers.Finally,a statistical analysis of three reliability data sets was conducted to demonstrate the performance of the proposed estimator.

On the non-Gaussian errors in high-z supernovae type Ia data

The nature of random errors in any data set is Gaussian, which is a well established fact according to the Central Limit Theorem. Supernovae type Ia data have played a crucial role in major discoveries in cosmology. Unlike in laboratory experiments, astronomical measurements cannot be performed in controlled situations. Thus, errors in astronomical data can be more severe in terms of systematics and non-Gaussianity compared to those of laboratory experiments. In this paper, we use the Kolmogorov-Smiruov statistic to test non-Gaussianity in high-z supernovae data. We apply this statistic to four data sets, i.e., Gold data （2004）, Gold data （2007）, the Union2 catalog and the Union2.1 data set for our analysis. Our results show that in all four data sets the errors are consistent with a Gaussian distribution.

Vertical temperature gradients of concrete box girder caused by solar radiation in Sichuan-Tibet railway

Spatial and temporal temperature variations are critical for concrete box girders,and non-uniform temperature distributions induced by solar radiation depend on the structural shapes and shadows cast on them.There have been many studies of temperature distributions and temperature gradients of concrete box girders,but few have considered a high altitude plateau climatic environment.In this study,the nonlinear temperature distributions of concrete box girders in the Sichuan-Tibet railway caused by solar radiation were investigated based on experimental analysis,real-time shadow-selection algorithm,and finite element method.Furthermore,a vertical temperature gradient model of the concrete box girders was obtained.The vertical temperature gradient values first rise,then decrease,and finally rise again from Chengdu to Lhasa,with samples forming a normal distribution.The recommended vertical temperature gradient value was 25℃with a confidence interval of 95%.This provides a reference for the design and maintenance of concrete box girders on the Sichuan-Tibet railway.