Photoplethysmography (PPG) devices are widely used in clinical practice but the origin of PPG signal is still under debating. The classical theory assumes that the PPG waveform stems from variations of blood volume in pulsating arteries. In this research we analysed high-speed video recordings of capillaries in a fingernail bed. It was found that speed of erythrocytes in capillaries has pronounced modulation in time, which follows variations of instantaneous blood pressure in arteries. However, the mean speed significantly differs even for neighbour capillaries whereas change of the speed occurs in phase for the most of capillaries. Moreover, the light intensity remitted from the papillary dermis is also modulated at the heartbeat frequency displaying significant correlation with waveforms of the RBC speed. Obtained results can hardly be explained by the classical theory of PPG signal formation. Shallow penetrating visible light acquires modulation of erythrocytes density in the capillary bed without interacting with deeper situated pulsating arteries. Therefore, the capillary bed could serve as a distributed sensor for monitor the status of deep vessels. Better understanding of the photoplethysmography basis will result in a wider range of applications of this fast growing technology in both medical and research practice.

The dynamic light scattering methods are widely used in biomedical diagnostics involving evaluation of blood flow. However, there exist some difficulties in quantitative interpretation of backscattered light signals from the viewpoint of diagnostic information. This study considers the application of the high‐speed videocapillaroscopy (VCS) method that provides the direct measurement of the red blood cells (RBCs) velocity into a capillary. The VCS signal presents true oscillation nature of backscattered light caused by moving RBCs. Thus, the VCS signal can be assigned as a reference one with respect to more complicated signals like in laser Doppler flowmetry (LDF). An essential correlation between blood flow velocity oscillations in a separate human capillary and the integral perfusion estimate obtained by the LDF method has been found. The observation of blood flow by the VCS method during upper arm occlusion has shown emergence of the reverse blood flow effect in capillaries that corresponds to the biological zero signal in the LDF. The reverse blood flow effect has to be taken into account in interpretation of LDF signals.

We study the Finite Basis Problem for finite additively idempotent semirings whose multiplicative reducts are inverse semigroups. In particular, we show that each additively idempotent semiring whose multiplicative reduct is a nontrivial rook monoid admits no finite identity basis, and so do almost all additively idempotent semirings whose multiplicative reducts are combinatorial inverse semigroups.

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We report on the noninvasive method for in vivo study of fish's cardiovascular system, that is, the heart and the structure of vessels that carry blood throughout the body. The proposed approach is based on combined photoplethysmographic and videocapillaroscopic microscopic imaging and enables noncontact two‐dimensional mapping of blood volume changes. We demonstrate that the obtained data allows precise measurements of heartbeat, blood flow velocity and other important parameters (see Videos S1 and S2). To validate the developed image processing technique, we have carried out multiple experiments on zebrafish—a well‐proven informative model organism widely used to understand cardiac development. The proposed approach may be effective for the study of cardiovascular system formation and functioning as well as the impact of various influencing factors on them.