Related papers: Kepler versus Akaike
In machine learning or scientific computing, model performance is measured with an objective function. But why choose one objective over another? Information theory gives one answer: To maximize the information in the model, select the…
It is shown that in the case of a single decision maker who optimizes several possibly conflicting objectives, the amount of information available in preference relations among pairs of possible decisions, when compared with all other…
The orbital motion of a binary system is characterized by various characteristic temporal intervals which, by definition, are different from each other: the draconitic, anomalistic and sidereal periods. They all coincide in the Keplerian…
In the past, measures of ``Earth-likeness'' of exoplanets have been qualitative, considered an abiotic Earth, or required discretionary choices of what parameters make a planet Earth-like. With the advent of high-resolution exoplanet…
In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits…
The Observation--Hypothesis--Prediction--Experimentation loop paradigm for scientific research has been practiced by researchers for years towards scientific discoveries. However, with data explosion in both mega-scale and milli-scale…
In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial…
\Kepler\ planets around a given star have similar sizes to each other and regular orbital spacing, like "peas in a pod." Several studies have tested whether detection bias could produce this apparent pattern by resampling planet radii at…
The interval approach to computation of dynamics of celestial bodies in the planetary problem has been considered. It is based on the refusal from idealization of infinitely high resolving capacity of measuring tools, and forms an…
Simplicity is held by many to be the key to general intelligence. Simpler models tend to "generalise", identifying the cause or generator of data with greater sample efficiency. The implications of the correlation between simplicity and…
A fascinating hypothesis is that human and animal intelligence could be explained by a few principles (rather than an encyclopedic list of heuristics). If that hypothesis was correct, we could more easily both understand our own…
We present a derivation of the structure and dynamics of a ticking clock by showing that for finite systems a single natural principle serves to distinguish what we understand as ticking clocks from time-keeping systems in general. As a…
In the past few years, the number of confirmed planets has grown above 2000. It is clear that they represent a diversity of structures not seen in our own solar system. In addition to very detailed interior modeling, it is valuable to have…
The problem of model selection is considered for the setting of interpolating estimators, where the number of model parameters exceeds the size of the dataset. Classical information criteria typically consider the large-data limit,…
A Kepler solver is an analytical method used to solve a two-body problem. In this paper, we propose a new correction method by slightly modifying the Kepler solver. The only change to the analytical solutions is that the obtainment of the…
In this paper we shall relate computational complexity to the principle of natural selection. We shall do this by giving a philosophical account of complexity versus universality. It seems sustainable to equate universal systems to complex…
The current IAU definition of "planet" is problematic because it is vague and excludes exoplanets. Here, we describe aspects of quantitative planetary taxonomy and examine the results of unsupervised clustering of Solar System bodies to…
In a previous work, we developed the idea to solve Kepler's equation with a CORDIC-like algorithm, which does not require any division, but still multiplications in each iteration. Here we overcome this major shortcoming and solve Kepler's…
We study two notions of expressiveness, which have appeared in abstraction theory for model checking, and find them incomparable in general. In particular, we show that according to the most widely used notion, the class of Kripke Modal…
Scientists have long preferred the simplest possible explanation of their data. More re-cently, a worrying trend to favor complex interpretations has taken hold because they are perceived as more impactful.