Flow cytometry (FC) is an analytical technique which is used in biological research to identify cell types and in the clinical context to diagnose human diseases including hematological malignancies[1]. FC characterizes cell types by measuring the light scatter and fluorescence emission properties of fluorochrome-labeled antibodies from each of the thousands of cells a sample contains[2]. Based on the measured intensity of the fluorescence and the light scatter of these cell events, cells are distinguished from contaminants, and then each cell is classified into a specific cell population. Traditionally, this classification is done by manually identifying and partitioning (i.e. 'gating') these populations based on visual inspection of mostly two-dimensional intensity histograms of two respective fluorescence emission detectors (Figure 1). Figure 1 Schematic manual gating workflow which corrects for measurement variances across samples caused by the batch effect. The first obstacle during gating is the batch effect, i.e. technical variance of event measurements across samples, caused e.g. by the variability of the staining procedure or by the decay of the exciting laser and the fluorescence emissions of fluorophore-bound antibodies.

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the proposed design. In each equation, a deep neural network is used to approximate the unknown function. Three forms of fractional differential equations have been examined to highlight the method's versatility: a fractional ordinary differential equation, a fractional order integrodifferential equation, and a fractional order partial differential equation. The results show that the proposed architecture solves different forms of fractional differential equations with excellent precision.