Related papers: Kepler versus Akaike
Model selection is of fundamental importance to high dimensional modeling featured in many contemporary applications. Classical principles of model selection include the Kullback-Leibler divergence principle and the Bayesian principle,…
This paper reviews the standard algorithm for converting spacecraft state vectors to Keplerian orbital elements with a focus on its computer implementation. It analyzes the shortcomings of the scheme as described in the literature, and…
In many applications, it is important to be able to explain the decisions of machine learning systems. An increasingly popular approach has been to seek to provide \emph{counterfactual instance explanations}. These specify close possible…
Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We…
When knowledge is obtained from a database, it is only possible to deduce confidence intervals for probability values. With confidence intervals replacing point values, the results in the set covering model include interval constraints for…
The obliquity of a terrestrial planet is an important clue about its formation and critical to its climate. Previous studies using simulated photometry of Earth show that continuous observations over most of a planet's orbit can be inverted…
Robust model-fitting to spectroscopic transitions is a requirement across many fields of science. The corrected Akaike and Bayesian information criteria (AICc and BIC) are most frequently used to select the optimal number of fitting…
The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed…
This paper applies Algorithmic Information Theory to simple examples of replication processes to illustrate how replicating structures can generate and maintain order in a non equilibrium system. Variation in replicating structures enhances…
In this paper we represent a different approach to the calculation of the perihelion shift than the one presented in common text books. We do not rely on the Schwarzschild metric and the Hamilton Jacobi technique to obtain our results.…
The theoretical foundation for a number of model selection criteria is established in the context of inhomogeneous point processes and under various asymptotic settings: infill, increasing domain, and combinations of these. For…
The Kepler mission has provided high-accurate photometric data in a long time span for more than two hundred thousands stars, looking for planetary transits. Among the detected candidates, the planetary nature of around 15% has been…
Many widely used models amount to an elaborate means of making up numbers--but once a number has been produced, it tends to be taken seriously and its source (the model) is rarely examined carefully. Many widely used models have little…
Engineering methodologies predominantly revolve around established principles of decomposition and recomposition. These principles involve partitioning inputs and outputs at the component level, ensuring that the properties of individual…
Many topics in planetary studies demand an estimate of the collision probability of two objects moving on nearly Keplerian orbits. In the classic works of \"Opik (1951) and Wetherill (1967), the collision probability was derived by…
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…
The Akaike information criterion (AIC) is commonly used to select a logistic regression model for optimal prediction of a binary response by a specified family of models. It however lacks a convincing method of prescribing a proper family…
We prove the existence of periodic orbits of the two fixed centers problem bifurcating from the Kepler problem. We provide the analytical expressions of these periodic orbits when the mass parameter of the system is sufficiently small.
The motion of astronomical bodies and the centre of mass of the system is not always well perceived by students. One of the struggles is the conceptual change of reference frame, which is the same that held back the acceptance of the…
World models have garnered substantial interest in the AI community. These are internal representations that simulate aspects of the external world, track entities and states, capture causal relationships, and enable prediction of…