Related papers: A Stochastic Process Approach of the Drake Equatio…
For more than 60 years, the predominant SETI search paradigm has entailed the observation of stars in an effort to detect alien electromagnetic signals that deliberately target Earth. However, this strategy is fraught with challenges when…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…
We consider particles emanating from a source point inside an interval in one-dimensional space and passing through detectors situated at the endpoints of the interval that register their arrival time. Unambiguous measurements of arrival or…
Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…
The Fermi paradox highlights the dichotomy between the lack of physical contact with other civilizations and the expectation that technological civilizations are assumed likely to evolve in many locations in the Milky Way galaxy, given the…
There have been many studies to examine whether one trait is correlated with another trait across a group of present-day species (for example, do species with larger brains tend to have longer gestation times. Since the introduction of the…
The classical Fokker-Planck equation (FPE) is a key tool in physics for describing systems influenced by drag forces and Gaussian noise, with applications spanning multiple fields. We consider the fractional Fokker-Planck equation (FFPE),…
I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…
The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions.…
The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-partial differential equation. In this paper we propose a…
The Milky Way is a unique laboratory, where stellar properties can be measured and analyzed in detail. In particular, stars in the older populations encode information on the mechanisms that led to the formation of our Galaxy. In this…
Stochastic homogenization is achieved for a class of elliptic and parabolic equations describing the lifetime, in large domains, of stationary diffusion processes in random environment which are small, statistically isotropic perturbations…
The first passage time (FPT) problem is studied for superstatistical models assuming that the mesoscopic system dynamics is described by a Fokker-Planck equation. We show that all moments of the random intensive parameter associated to the…
Mean-field SDEs, also known as McKean-Vlasov equations, are stochastic differential equations where the drift and diffusion depend on the current distribution in addition to the current position. We describe an efficient numerical method…
Sequential filtering and spatial inverse problems assimilate data points distributed either temporally (in the case of filtering) or spatially (in the case of spatial inverse problems). Sometimes it is possible to choose the position of…
Over a period of several decades a concerted effort has been made to determine whether intelligent life exists outside of our solar system, known as the Search for Extraterrestrial Intelligence or SETI. This has been based primarily upon…
The Fermi paradox is the conflict between an expectation of a high {\em ex ante} probability of intelligent life elsewhere in the universe and the apparently lifeless universe we in fact observe. The expectation that the universe should be…
Spacecraft attitude control using only magnetic torques is a periodic time-varying system as the Earth magnetic field in the spacecraft body frame changes periodically while the spacecraft circles around the Earth. The optimal controller…
SETI researchers believe that the basic principles of our science and the science of extraterrestrial beings should be fundamentally the same, and we should be able to communicate with them by referring to those things we share, such as the…
Stochastic partial differential equations (SPDE) on graphs were introduced by Cerrai and Freidlin [Ann. Inst. Henri Poincar\'e Probab. Stat. 53 (2017) 865-899]. This class of stochastic equations in infinite dimensions provides a minimal…