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Motivation: Accurate estimation of false discovery rate (FDR) of spectral identification is a central problem in mass spectrometry-based proteomics. Over the past two decades, target decoy approaches (TDAs) and decoy-free approaches (DFAs), have been widely used to estimate FDR. TDAs use a database of decoy species to faithfully model score distributions of incorrect peptide-spectrum matches (PSMs). DFAs, on the other hand, fit two-component mixture models to learn the parameters of correct and incorrect PSM score distributions. While conceptually straightforward, both approaches lead to problems in practice, particularly in experiments that push instrumentation to the limit and generate low fragmentation-efficiency and low signal-to-noise-ratio spectra. Results: We introduce a new decoy-free framework for FDR estimation that generalizes present DFAs while exploiting more search data in a manner similar to TDAs. Our approach relies on multi-component mixtures, in which score distributions corresponding to the correct PSMs, best incorrect PSMs, and second-best incorrect PSMs are modeled by the skew normal family. We derive EM algorithms to estimate parameters of these distributions from the scores of best and second-best PSMs associated with each experimental spectrum. We evaluate our models on multiple proteomics datasets and a HeLa cell digest case study consisting of more than a million spectra in total. We provide evidence of improved performance over existing DFAs and improved stability and speed over TDAs without any performance degradation. We propose that the new strategy has the potential to extend beyond peptide identification and reduce the need for TDA on all analytical platforms.

The transient electromagnetic (TEM) method is a time-domain, controlled source, electromagnetic (EM) geophysical technique which is often applied to image the subsurface conductivity distributions of shallow layers due to its effectiveness and adaptability to complex site working conditions. The means for an express analysis of such experimental data in several practical cases have advantages and are suitable for use. We developed our approach for determining the approximate one-dimensional (1D) model of background conductivity based on the formal transformation of the TEM experimental data and the mathematical analysis of continuous functions. Our algorithm, which allows the 1D model&rsquo, s parameters to be obtained in terms of a layer&rsquo, s thickness and resistivity, widely utilizes the numerical differentiation of experimental curves as well as of transformed ones. Since the noise level increases with time in the attenuating TEM signals and differentiation even enhances it, special procedures are required to calculate the derivative values. We applied the piecewise cubic spline approximation to solve this problem. In that case, the derivatives are obtained using polynomial coefficients which are available for each node. The application of the created facilities is demonstrated using real experimental data of the TEM soundings.