Gaussian Primes in Narrow Sectors

We generalize a Theorem of Ricci and count Gaussian primes $\mathfrak{p}$ with short interval restrictions on both the norm and the argument of $\mathfrak{p}$. We follow Heath-Brown’s method for counting rational primes in short intervals.

Comparison of Holt and Brown's Double Exponential Smoothing Methods in The Forecast of Moving Price for Mutual Funds

Mutual funds are one of the promising investment media where the risk is directly proportional to the size of investment growth. With proper forecasting of NAV price movements will greatly help investors to make purchases and sales transactions, therefore the authors offer the use of two different forecasting methods namely Brown's method and Holt method in double exponential smoothing to get predictions of NAV price movements. The effectiveness of the use of the method will be measured from the value of Mean Average Percentage Error (MAPE). From the calculation results obtained by the data that the Holt method produces forecasting for 1809,657 with the best α value of 0.6 and MAPE of 0.644373568, while for the Holt method obtained forecasting value of 1810,924 with the α value and the best β value of 0.9 and 0.1 and the smaller MAPE value of 0.61604262 . Looking at the amount of MAPE generated, the Holt method has a smaller forecasting error rate when compared to Brown’s method.

Detecting differential protein abundance by combining peptide level P-values

Application of empirical Brown's method to peptide intensities from comparative LC-MS proteomics experiments accurately detects differentially abundant proteins.

Multiaxial cycle counting method for non-proportional multiaxial variable loading signals based on modified maximal shear stress

One of the most challenging task in field of multiaxial fatigue is fatigue lifetime estimation of components loaded with multiaxial non-proportional variable amplitude loading. While this task consists of multiple smaller problems, one of the most crucial ones is loading cycles identification (and extraction) for future use with multiaxial damage criterions. By now, several cycle counting methods have been proposed for multiaxial loading conditions. The most wildly accepted methods are Bannantine-Socie’s method and Wang-Brown’s method (which has been later modified by Meggiolaro and Castro). The aim of this paper is the comparison of newly developed method with Bannantine-Socie’s method and Wang-Brown’s method. The new cycle counting method is based on cycle identification in relative maximum shear stress histories (calculated from multiaxial loading histories). The extracted data than composes part of each loading channel of multiaxial loading histories corresponding to identified loading cycle. The comparison of chosen methods has been done by using data sets created by authors as well as using real measured data from real operation.

Performance of chosen multiaxial cycle counting method under non-proportional multiaxial variable loading.

One of the most crucial tasks in fatigue life-time estimation of components loaded with multiaxial variable amplitude loading is to correctly identify loading cycles that can be used with multiaxial damage criterions. During past years, several cycle counting methods have been proposed for multiaxial loading conditions. The aim of this text is the comparison of selected multiaxial cycle counting methods, namely Wang-Brown’s method, Modified Wang-Brown’s method, Bannantine-Socie’s method and then a critical analysis of the obtained results. For the comparison of chosen methods, a new data set, consisting of experimentally obtained results from multiaxial non-proportional variable amplitude loading tests carried on by authors, has been used. The tested specimens were made from S355J0 structural steel and the testing procedure has been carried out on the MTS Axial/Torsion servo hydraulic testing machine. Findley and McDiarmid multiaxial criterion with Palgren-Miner summation rule have been used for fatigue life-time estimation of the tested specimens.

Combining Dependent P-values with an Empirical Adaptation of Brown's Method

Combining P-values from multiple statistical tests is a common exercise in bioinformatics. However, this procedure is non-trivial for dependent P-values. Here we discuss an empirical adaptation of Brown's Method (an extension of Fisher's Method) for combining dependent P-values which is appropriate for the correlated data sets found in high-throughput biological experiments. We show that Fisher's Method is biased when used on dependent sets of P-values with both simulated data and gene expression data from The Cancer Genome Atlas (TCGA). When applied on the same data sets, the Empirical Brown's Method provides a better null distribution and a more conservative result. The Empirical Brown's Method is available in Python, R, and MATLAB and can be obtained from https://github.com/IlyaLab/CombiningDependentPvaluesUsingEBM.