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Continuous clocks, i.e. the clocks that measure time in a continuous manner, are regarded as an essential component of sensing technology. Precision and recurrence time are two basic features of continuous clocks. In this paper, in the…

Many biological processes display oscillatory behavior based on an approximately 24 hour internal timing system specific to each individual. One process of particular interest is gene expression, for which several circadian transcriptomic…

There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…

We study the problem of determining self-sustained oscillations in discrete-time linear time-invariant relay feedback systems. Concretely, we are interested in predicting when such a system admits unimodal oscillations, i.e., when the…

Three abilities - the ability to recognize sounds, the ability to visually recognize movement and the ability to keep an upright standing position - can function only with using precise measurements of the short time intervals. Other…

We study oscillation death (OD) in a well-known coupled-oscillator system that has been used to model cardiovascular phenomena. We derive exact analytic conditions that allow the prediction of OD through the two known bifurcation routes, in…

Creating precise timing devices at ultra-short time scales is not just an important technological challenge, but confronts us with foundational questions about timekeeping's ultimate precision limits. Research on clocks has either focused…

The accuracy of the time information generated by clocks can be enhanced by allowing them to communicate with each other. Here we consider a basic scenario where a quantum clock receives a low-accuracy time signal as input and ask whether…

We study the stabilization of networked control systems with asynchronous sensors and controllers. Offsets between the sensor and controller clocks are unknown and modeled as parametric uncertainty. First we consider multi-input linear…

Synchronization is a widespread phenomenon encountered in many natural and engineered systems with nonlinear classical dynamics. How synchronization concepts and mechanisms transfer to the quantum realm and whether features are universal or…

We show that for two identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony is an unstable attractor and arbitrarily weak noise can destroy entrainment and generate intermittent phase slips. Small…

The dynamics of a semiconductor-laser array whose individual elements are coupled in a global way through an external mirror is numerically analysed. A coherent in-phase solution is seen to be preferred by the system at intermediate values…

In this work we demonstrate for an experimental system, that exhibits the Lorenz butterfly attractor behavior, that perfect chaotic phase synchronization cannot be achieved in systems with an unbounded distribution of intrinsic time scales.…

Synchronization among arrays of beating cilia is one of the emergent phenomena in biological processes at meso-scopic scales. Strong inter-ciliary couplings modify the natural beating frequencies, $\omega$, of individual cilia to produce a…

Information processing in the brain requires integration of information over time. Such an integration can be achieved if signals are maintained in the network activity for the required period, as quantified by the intrinsic timescale.…

Recent experiments elucidated the structure and function of the cyanobacterial circadian oscillator, which is driven by sunlight intensity variation and therefore by Earth's rotation. It is known that cyanobacteria appeared about 3.5…

Context. Among options for definition of the lunar reference time, the option taking Lunar Coordinate Time (O1) has its simplicity but cannot be realized by any clock without steering, while another option adopting the lunar geoid…

The phenomenon of superoscillation, where band limited signals can oscillate over some time period with a frequency higher than the band limit, is not only very interesting but it also seems to offer many practical applications. The first…

We study a wide range of neutral atoms and ions suitable for ultra-precise atomic optical clocks with naturally suppressed black body radiation shift of clock transition frequency. Calculations show that scalar polarizabilities of clock…

We study the problem of clock synchronization in a networked system with arbitrary starts for all nodes. We consider a synchronous network of $n$ nodes, where each node has a local clock that is an integer counter. Eventually, clocks must…