Nested sampling (NS) is a popular algorithm for Bayesian computation. We investigate statistical errors in NS both analytically and numerically. show two analytic results. First, we that the leading terms Skilling's expression using information theory match Keeton's from an analysis of moments. This approximate agreement was previously only known numerically somewhat mysterious. Second, uncerta...

In bacterial chemotaxis, E. coli cells drift up chemical gradients by a series of runs and tumbles. Runs are periods of directed swimming, and tumbles are abrupt changes in swimming direction. Near the beginning of each run, the rotating helical flagellar filaments that propel the cell form a bundle. Using resistive-force theory, we show that the counterrotation of the cell body necessary for t...

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Runs of the NSTAB equilibrium and stability code show there are many 3D solutions of the advanced tokamak problem subject to axially symmetric boundary conditions. These numerical simulations based on mathematical equations in conservation form predict that the ITER project will encounter pervasive disruptions and ELMs crashes. Test particle runs of the TRAN Monte Carlo code suggest that for qu...

In the literature of game theory, the information sets of extensive form games have different interpretations, which may lead to confusions and paradoxical cases. We argue that the problem lies in the mix-up of two interpretations of the extensive form game structures: game rules or game runs which do not always coincide. In this paper, we try to separate and connect these two views by proposin...

We develop a testing theory for real-time systems. We keep the usual notion of success or failure (based on finite runs) but we also provide a mechanism of determining the success or failure of infinite runs, using a formalism similar to the acceptance in Büchi automata. We present two refinement timed preorders similar to De Nicola and Hennessy’s may and must testing. We then provide alternati...

The mass function of dark halos in a Λ-dominated cold dark matter (ΛCDM) universe is investigated. 529 output files from five runs of N-body simulations are analyzed using the friends-of-friends cluster finding algorithm. All the runs use 5123 particles in the box size of 35 h−1Mpc to 140 h−1Mpc. Mass of particles for 35 h−1 Mpc runs is 2.67 ×107h−1 M⊙. Because of the high mass resolution of ou...

Motivated by a problem in quantum field theory, we study the up and down structure of circular and linear permutations. In particular, we count the length of the (alternating) runs of permutations by representing them as monomials and find that they can always be decomposed into so-called ‘atomic’ permutations introduced in this work. This decomposition allows us to enumerate the (circular) per...