Related papers: A Stochastic Process Approach of the Drake Equatio…
Searches for radio technosignatures place constraints on the prevalence of extraterrestrial transmitters in our Galaxy and beyond. It is important to account for the complete stellar population captured within a radio telescope's field of…
As the only known intelligent civilization, human beings are always curious about the existence of other communicating extraterrestrial intelligent civilizations (CETIs). Based on the latest astrophysical information, we carry out Monte…
Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…
A period of quenching between the formation of the thick and thin disks of the Milky Way has been recently proposed to explain the observed age-[{\alpha}/Fe] distribution of stars in the solar neighbourhood. However, robust constraints on…
The number of people able to end Earth's technical civilization has heretofore been small. Emerging dual-use technologies, such as biotechnology, may give similar power to thousands or millions of individuals. To quantitatively investigate…
For about the last 60 years the search for extraterrestrial intelligence has been monitoring the sky for evidence of remotely detectable technological life beyond Earth, with no positive results to date. While the lack of detection can be…
Differential Riccati equations (DREs) are semilinear matrix- or operator-valued differential equations with quadratic non-linearities. They arise in many different areas, and are particularly important in optimal control of linear quadratic…
Marcus stochastic differential equations (SDEs) often are appropriate models for stochastic dynamical systems driven by non-Gaussian Levy processes and have wide applications in engineering and physical sciences. The probability density of…
Kramers' rate theory forms a cornerstone for thermally activated barrier crossing. However, its reliance on equilibrium quantities excludes analysis of nonequilibrium dynamics at early times. Most works have thus focused on obtaining rates…
A procedure allowing to construct rigorously discrete as well as continuum deterministic evolution equations from stochastic evolution equations is developed using a Dirac's bra and ket notation. This procedure is an extension of an…
The time evolution problem for non-self adjoint second order differential operators is studied by means of the path integral formulation. Explicit computation of the path integral via the use of certain underlying stochastic differential…
The time equation associated to the Dirac Equation (DE) is studied for the radiation-dominated Friedmann-Robertson-Walker (FRW) universe. The results are analysed for small and large values of time. We also incorporate the corrections of…
New theorems for the moments of the first passage time of one dimensional nonlinear stochastic processes with an entrance boundary are formulated. This important class of one dimensional stochastic processes results among others from…
Cellular differentiation and evolution are stochastic processes that can involve multiple types (or states) of particles moving on a complex, high-dimensional state-space or "fitness" landscape. Cells of each specific type can thus be…
This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…
Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…
For stochastic systems with discrete time delay, the Fokker-Planck equation (FPE) of the one-time probability density function (PDF) does not provide a complete, self-contained probabilistic description. It explicitly involves the two-time…
Stochastic differential equations describe well many physical, biological and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and…
The tracer equations are part of the primitive equations used in ocean modeling and describe the transport of tracers, such as temperature, salinity or chemicals, in the ocean. Depending on the number of tracers considered, several…
Context. Astrobiological evolution of the Milky Way (or the shape of its "astrobiological landscape") has emerged as one of the key research topics in recent years. In order to build precise, quantitative models of the Galactic…