4 papers
An Interval Type-2 Version of Bayes Theorem Derived from Interval Probability Range Estimates Provided by Subject Matter Experts
John T. Rickard, William A. Dembski, James Rickards
Bayesian inference is widely used in many different fields to test hypotheses against observations. In most such applications, an assumption is made of precise input values to prod…
Prime and thickened prime components in Apollonian circle packings
Holley Friedlander, Elena Fuchs, Piper Harris +5
Inspired by a question of Sarnak, we introduce the notion of a prime component in an Apollonian circle packing: a maximal tangency-connected subset having all prime curvatures. We…
Primes represented by shifted quadratic forms: on primitivity and congruence classes
Elena Fuchs, Catherine Hsu, James Rickards +2
We prove lower bounds of the form for the number of primes up to primitively represented by a shifted positive definite integral binary quadratic form, a…
Reciprocity obstructions in semigroup orbits in SL(2, Z)
James Rickards, Katherine E. Stange
We study orbits of semigroups of , and demonstrate reciprocity obstructions: we show that certain such orbits avoid squares, but not as a consequence of ob…