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While Boolean logic has been the backbone of digital information processing, there exist classes of computationally hard problems wherein this paradigm is fundamentally inefficient. Vertex coloring of graphs, belonging to the class of combinatorial optimization, represents one such problem. It is well studied for its applications in data sciences, life sciences, social sciences and technology, and hence, motivates alternate, more efficient non-Boolean pathways towards its solution. Here we demonstrate a coupled relaxation oscillator based dynamical system that exploits insulator-metal transition in Vanadium Dioxide (VO

Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming insects, flocking birds, or schooling fish; now the individuals move through space, but without conspicuously altering their internal states. Here we explore systems in which both synchronization and swarming occur together. Specifically, we consider oscillators whose phase dynamics and spatial dynamics are coupled. We call them swarmalators, to highlight their dual character. A case study of a generalized Kuramoto model predicts five collective states as possible long-term modes of organization. These states may be observable in groups of sperm, Japanese tree frogs, colloidal suspensions of magnetic particles, and other biological and physical systems in which self-assembly and synchronization interact., Collective self-organized behavior can be observed in a variety of systems such as colloids and microswimmers. Here O’Keeffe et al. propose a model of oscillators which move in space and tend to synchronize with neighboring oscillators and outline five types of collective self-organized states.

We studied the properties of low-frequency (LF) heart rate variability (HRV) and photoplethysmographic waveform variability (PPGV) and their interaction under conditions where the hemodynamic connection between them is obviously absent, as well as the LF regulation of PPGV in the absence of heart function. The parameters of HRV and finger PPGV were evaluated in 10 patients during cardiac surgery under cardiopulmonary bypass (on-pump cardiac surgery) with or without cardioplegia. The following spectral indices of PPGV and HRV were ertimated: the total spectral power (TP), the high-frequency (HF) and the LF ranges of TP in percents (HF% and LF%), and the LF/HF ratio. We assessed also the index S of synchronization between the LF oscillations in finger photoplethysmogram (PPG) and heart rate (HR) signals. The analysis of directional couplings was carried out using the methods of phase dynamics modeling. It is shown that the mechanisms leading to the occurrence of oscillations in the LF range of PPGV are independent of the mechanisms causing oscillations in the LF range of HRV. At the same time, the both above-mentioned LF oscillations retain their activity under conditions of artificial blood circulation and cardioplegia (the latter case applies only to LF oscillations in PPG). In artificial blood circulation, there was a coupling from the LF oscillations in PPG to those in HR, whereas the coupling in the opposite direction was absent. The coupling from the LF oscillations in PPG to those in HR has probably a neurogenic nature, whereas the opposite coupling has a hemodynamic nature (due to cardiac output).