Related papers: A mathematical model for the atomic clock error in…
We consider the problem of estimating timing of measurements and actuation in distributed sensor and control systems with central processing. The focus is on direct timing estimation for scenarios where clock synchronization is not feasible…
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 consider estimation of the quadratic (co)variation of a semimartingale from discrete observations which are irregularly spaced under high-frequency asymptotics. In the univariate setting, results by Jacod (2008) are generalized to the…
In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism…
We consider a free massive particle inside a box which is dragged by Rindler observers. Admitting that the particle obeys the Klein-Gordon equation, we find the frequencies of the stationary states of this system. Transitions between the…
We investigate the convergence of hitting times for jump-diffusion processes. Specifically, we study a sequence of stochastic differential equations with jumps. Under reasonable assumptions, we establish the convergence of solutions to the…
Stochastic clocks represent a class of time change methods for incorporating trading activity into continuous-time financial models, with the ability to deal with typical asymmetrical and tail risks in financial returns. In this paper we…
Several experiments [1-3] show significant deviations from predictions of the statistical model of nuclear reactions. We summarize unsuccessful recent theoretical efforts to account for such disagreement in terms of a violation of…
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
This paper explores backward error analysis for numerical solutions of ordinary differential equations, particularly focusing on chaotic systems. Three approaches are examined: residual assessment, the method of modified equations, and…
The widespread adoption of machine learning surrogate models has significantly improved the scale and complexity of systems and processes that can be explored accurately and efficiently using atomistic modeling. However, the inherently…
The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are…
We investigate the stability problem for discrete-time stochastic switched linear systems under the specific scenarios where information about the switching patterns and the probability of switches are not available. Our analysis focuses on…
Context: Low-frequency radio observations are heavily impacted by the ionosphere, where dispersive delays can outpace even instrumental clock offsets, posing a serious calibration challenge. Especially below 100 MHz, phase unwrapping…
The environmental perturbation on atoms is the key factor restricting the performance of atomic frequency standards, especially in long term scale. In this letter, we demonstrate a real-time noise distinguish operation of atomic clocks. The…
The current algorithms are based on linear model, for example, Precision Time Protocol (PTP) which requires frequent synchronization in order to handle the effects of clock frequency drift. This paper introduces a nonlinear approach to…
A clock steps a computer through a cycle of phases. For the propagation of logical symbols from one computer to another, each computer must mesh its phases with arrivals of symbols from other computers. Even the best atomic clocks drift…
Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…