Related papers: Continuous attractor-based clocks are unreliable p…

The Dick effect can be a limitation of the achievable frequency stability of a passive atomic frequency standard when the ancillary frequency source is only periodically sampled. Here we analyze the Dick effect for a pulsed vapor cell clock…

Long term behavior of nonlinear deterministic continuous time signals can be studied in terms of their reconstructed attractors. Reconstructed attractors of a continuous signal are meant to be topologically equivalent representations of the…

We experimentally demonstrated that the stability of an atomic clock improves at fastest rate $\tau^{-1}$ (where $\tau$ is the averaging time) when the phase of a local oscillator is genuinely compared to the continuous phase of many atoms…

Brownian clocks are biomolecular networks that can count time. A paradigmatic example are proteins that go through a cycle thus regulating some oscillatory behaviour in a living system. Typically, such a cycle requires free energy often…

Current state-of-the-art frequency standards are passive optical atomic clocks where the frequency of an optical resonator is stabilized to a narrow atomic transition. Passive clocks have achieved unprecedented stabilities of 6.6 x 10--19…

All clocks, classical or quantum, are open non equilibrium irreversible systems subject to the constraints of thermodynamics. Using examples I show that these constraints necessarily limit the performance of clocks and that good clocks…

The in vivo circadian clock in single cyanobacteria is studied here by time-lapse fluorescence microscopy when the temperature is lowered below 25{\deg}C . We first disentangle the circadian clock behavior from the bacterial cold shock…

Understanding different aspects of time is at the core of many areas in theoretical physics. Minimal models of continuous stochastic and quantum clocks have been proposed to explore fundamental limitations on the performance of timekeeping…

Stochastic systems consisting of a very large number of independent elementary processes of the same kind, especially the radioactive decay, are considered as quantum clocks. By adapting the framework of the previously introduced concept of…

We formulate an attention mechanism for continuous and ordered sequences that explicitly functions as an alignment model, which serves as the core of many sequence-to-sequence tasks. Standard scaled dot-product attention relies on…

We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…

Time crystals are classified as discrete or continuous depending on whether they spontaneously break discrete or continuous time translation symmetry. While discrete time crystals have been extensively studied in periodically driven systems…

The dynamics of an unique type of clock mechanism known as grasshopper escapement is investigated with the aim of evaluating its accuracy in a noisy environment. It is demonstrated that the clock's precision scales linearly with the rate of…

There are many different types of time keeping devices. We use the phrase ticking clock to describe those which -- simply put -- "tick" at approximately regular intervals. Various important results have been derived for ticking clocks, and…

This paper deals with the phase noise affecting communication systems, where local oscillators are employed to obtain reference signals for carrier and timing synchronizations. The most common discrete-time phase noise channel model is…

We study the properties of a noisy time series generated by a continuous-valued feed-forward network in which the next input vector is determined from past output values. Numerical simulations of a perceptron-type network exhibit the…

We consider the problem of estimating unknown parameters in stochastic differential equations driven by colored noise, which we model as a sequence of Gaussian stationary processes with decreasing correlation time. We aim to infer…

We study local and global stability of nonhyperbolic chaotic attractors contaminated by noise. The former is given by the maximum distance of a noisy trajectory from the noisefree attractor, while the latter is provided by the minimal…

We present an enhanced entangled quantum clock protocol that incorporates a quantum phase estimation algorithm to directly estimate proper-time differences as an unknown phase. By employing highly entangled multi-clock states, the…

We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of…