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Interpretation of chest computed tomography (CT) is time-consuming. Previous studies have measured the time-saving effect of using a deep-learning-based aid (DLA) for CT interpretation. We evaluated the joint impact of a multi-pathology DLA on the time and accuracy of radiologists' reading. 40 radiologists were randomly split into three experimental arms: control (10), who interpret studies without assistance; informed group (10), who were briefed about DLA pathologies, but performed readings without it; and the experimental group (20), who interpreted half studies with DLA, and half without. Every arm used the same 200 CT studies retrospectively collected from BIMCV-COVID19 dataset; each radiologist provided readings for 20 CT studies. We compared interpretation time, and accuracy of participants diagnostic report with respect to 12 pathological findings. Mean reading time per study was 15.6 minutes [SD 8.5] in the control arm, 13.2 minutes [SD 8.7] in the informed arm, 14.4 [SD 10.3] in the experimental arm without DLA, and 11.4 minutes [SD 7.8] in the experimental arm with DLA. Mean sensitivity and specificity were 41.5 [SD 30.4], 86.8 [SD 28.3] in the control arm; 53.5 [SD 22.7], 92.3 [SD 9.4] in the informed non-assisted arm; 63.2 [SD 16.4], 92.3 [SD 8.2] in the experimental arm without DLA; and 91.6 [SD 7.2], 89.9 [SD 6.0] in the experimental arm with DLA. DLA speed up interpretation time per study by 2.9 minutes (CI95 [1.7, 4.3], p<0.0005), increased sensitivity by 28.4 (CI95 [23.4, 33.4], p<0.0005), and decreased specificity by 2.4 (CI95 [0.6, 4.3], p=0.13). Of 20 radiologists in the experimental arm, 16 have improved reading time and sensitivity, two improved their time with a marginal drop in sensitivity, and two participants improved sensitivity with increased time. Overall, DLA introduction decreased reading time by 20.6%., Comment: 17 pages, 6 figures, 8 tables

We generalize two results about subgroups of multiplicative group of finite field of prime order. In particular, the lower bound on the cardinality of the set of values of polynomial $P(x,y)$ is obtained under the certain conditions, if variables $x$ and $y$ belong to a subgroup $G$ of the multiplicative group of the filed of residues. Also the paper contains a proof of the result that states that if a subgroup $G$ can be presented as a set of values of the polynomial $P(x,y)$, where $x\in A$, and $y\in B$ then the cardinalities of sets $A$ and $B$ are close (in order) to a square root of the cardinality of subgroup $G$.