SINC: a scale-invariant deep-neural-network classifier for bulk and single-cell RNA-seq data
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Abstract Motivation Scaling by sequencing depth is usually the first step of analysis of bulk or single-cell RNA-seq data, but estimating sequencing depth accurately can be difficult, especially for single-cell data, risking the validity of downstream analysis. It is thus of interest to eliminate the use of sequencing depth and analyze the original count data directly. Results We call an analysis method ‘scale-invariant’ (SI) if it gives the same result under different estimates of sequencing depth and hence can use the original count data without scaling. For the problem of classifying samples into pre-specified classes, such as normal versus cancerous, we develop a deep-neural-network based SI classifier named scale-invariant deep neural-network classifier (SINC). On nine bulk and single-cell datasets, the classification accuracy of SINC is better than or competitive to the best of eight other classifiers. SINC is easier to use and more reliable on data where proper sequencing depth is hard to determine. Availability and implementation This source code of SINC is available at https://www.nd.edu/∼jli9/SINC.zip. Supplementary information Supplementary data are available at Bioinformatics online.Keywords:
Sinc function
The DE-Sinc formulas, resulting from a combination of the Sinc approximation formula with the double exponential (DE) transformation, provide a highly efficient method for function approximation. In many cases they are more efficient than the SE-Sinc formulas, which are the Sinc approximation formulas combined with the single exponential (SE) transformations. Function classes suited to the SE-Sinc formulas have already been investigated in the literature through rigorous mathematical analysis, whereas this is not the case with the DE-Sinc formulas. This paper identifies function classes suited to the DE-Sinc formulas in a way compatible with the existing theoretical results for the SE-Sinc formulas. Furthermore, we identify alternative function classes for the DE-Sinc formulas, as well as for the SE-Sinc formulas, which are more useful in applications in the sense that the conditions imposed on the functions are easier to verify.
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Constant (computer programming)
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The DE-Sinc formulas, resulting from a combination of the Sinc approximation formula with the double exponential (DE) transformation, provide a highly efficient method for function approximation. In many cases they are more efficient than the SE-Sinc formulas, which are the Sinc approximation formulas combined with the single exponential (SE) transformations. Function classes suited to the SE-Sinc formulas have already been investigated in the literature through rigorous mathematical analysis, whereas this is not the case with the DE-Sinc formulas. This paper identifies function classes suited to the DE-Sinc formulas in a way compatible with the existing theoretical results for the SE-Sinc formulas. Furthermore, we identify alternative function classes for the DE-Sinc formulas, as well as for the SE-Sinc formulas, which are more useful in applications in the sense that the conditions imposed on the functions are easier to verify.
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The energy levels of the time-independent Schrödinger equation are computed in three dimensions by applying double exponential Sinc collocation method. Numerical results are provided to demonstrate the high accuracy of the proposed approach for different potential functions. Comparative tests with the single exponential Sinc collocation method are made to confirm the superiority of the double exponential Sinc collocation method.
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Abstract Several bounds of trigonometric-exponential and hyperbolic-exponential type for sinc and hyperbolic sinc functions are presented. In an attempt to generalize the results, some known inequalities are sharpened and extended. Hyperbolic versions are also established, along with extensions.
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Gaussian-Sinc pulse is presented according to the Fourier transformation. Its frequency domain profiles were calculated by means of the analytical solutions of Bloch equations. The effects of parameter in Gaussian-Sinc pulse on the selective, side band and phase were studied. The advantages and defects of Gaussian-Sinc pulse are discussed and some valuable conclusions are gained. The corresponding experimental results coincide well with the above conclusions.
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Collocation (remote sensing)
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Frequency diverse array (FDA) has received much attention due to its capability of forming range–angle-dependent beampatterns. However, the standard FDA can only provide S-shaped beampatterns, leading to weakening the signal-to-interference-plus-noise ratio (SINR). Several window-based FDAs have been proposed to remove the coupling. However, the performance of these FDAs is limited by the use of conventional window functions, hindering further improvements. In this article, the "window-shaped" Sinc function (Sinc-FDA) is innovatively exploited into the frequency offset form to decouple the beampattern rather than using traditional window functions. Moreover, the sidelobe performance of existing window-based FDAs degrades in higher frequency offset bandwidth and wider observation area and is limited by the sidelobes near the main lobe. A weighted function is introduced to further flexibly suppress sidelobes, which forms a new weighted Sinc-FDA (W-Sinc-FDA). Simulation results compared with other optimization algorithm and function-based FDAs further demonstrate the effectiveness of the proposed Sinc-FDA and W-Sinc-FDA.
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In this work, the time-dependent Schrödinger equations were implemented by the RK-Sinc method. It offers a high quality in spatial approximations with the Sinc function and a high-efficiency procedure to close to the time advance with the strong stability and low storage Runge-Kutta method. Both the theoretical analysis and the simulation results demonstrate that the RK-Sinc method performs better than the traditional FDTD method.
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Some properties of the sinc function are investigated.First,some basic properties of the sinc function are recalled.Then,a function which dominated the sinc function is obtained.Based on those,the result sinc ∈Lp(R) for 1p≤+∞ is proved.An upper bound of ‖sinc‖, is obtained,and a lower bound of ‖sinc‖p for positive integer p is given.Finally,the limit of ‖sinc‖ when p→∞ is obtained.
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