The RAM equivalent of P vs. RP

One of the fundamental open questions in computational complexity is whether the class of problems solvable by use of stochasticity under the Random Polynomial time (RP) model is larger than the class of those solvable in deterministic polynomial time (P). However, this question is only open for Turing Machines, not for Random Access Machines (RAMs). Simon (1981) was able to show that for a sufficiently equipped Random Access Machine, the ability to switch states nondeterministically does not entail any computational advantage. However, in the same paper, Simon describes a different (and arguably more natural) scenario for stochasticity under the RAM model. According to Simon's proposal, instead of receiving a new random bit at each execution step, the RAM program is able to execute the pseudofunction $\textit{RAND}(y)$, which returns a uniformly distributed random integer in the range $[0,y)$. Whether the ability to allot a random integer in this fashion is more powerful than the ability to allot a random bit remained an open question for the last 30 years. In this paper, we close Simon's open problem, by fully characterising the class of languages recognisable in polynomial time by each of the RAMs regarding which the question was posed. We show that for some of these, stochasticity entails no advantage, but, more interestingly, we show that for others it does.Comment: 23 page

Gas depletion in Local Group dwarfs on ~250 kpc scales: Ram pressure stripping assisted by internal heating at early times

A recent survey of the Galaxy and M31 reveals that more than 90% of dwarf galaxies within 270 kpc of their host galaxy are deficient in HI gas. At such an extreme radius, the coronal halo gas is an order of magnitude too low to remove HI gas through ram-pressure stripping for any reasonable orbit distribution. However, all dwarfs are known to have an ancient stellar population (\geq 10 Gyr) from early epochs of vigorous star formation which, through heating of HI, could allow the hot halo to remove this gas. Our model looks at the evolution of these dwarf galaxies analytically as the host-galaxy dark matter halo and coronal halo gas builds up over cosmic time. The dwarf galaxies - treated as spherically symmetric, smooth distributions of dark matter and gas - experience early star formation, which sufficiently heats the gas allowing it to be removed easily through tidal stripping by the host galaxy, or ram-pressure stripping by a tenuous hot halo (n_H = 3x10^{-4} cm^{-3} at 50 kpc). This model of evolution is able to explain the observed radial distribution of gas-deficient and gas-rich dwarfs around the Galaxy and M31 if the dwarfs fell in at high redshifts (z~3-10).Comment: ApJ accepted. 32 pages, 11 figure

Dynamical segregation of galaxies in groups and clusters

We have performed a systematic analysis of the dynamics of different galaxy populations in galaxy groups from the 2dFGRS. For this purpose we have combined all the groups into a single system, where velocities v and radius r are expressed adimensionally. We have used several methods to compare the distributions of relative velocities of galaxies with respect to the group centre for samples selected according to their spectral type (as defined by Madgwick et al., 2002), bj band luminosity and B-R colour index. We have found strong segregation effects: spectral type I objects show a statistically narrower velocity distribution than that of galaxies with a substantial star formation activity (type II-IV). Similarly, the same behavior is observed for galaxies with colour index B-R>1 compared to galaxies with B-R<1. Bright (Mb-19) galaxies show the same segregation. It is not important once the sample is restricted to a given spectral type. These effects are particularly important in the central region (Rp<Rvirial/2) and do not have a strong dependence on the mass of the parent group. These trends show a strong correlation between the dynamics of galaxies in groups and star formation rate reflected both by spectral type and by colour index.Comment: 7 pages, 8 figures. Accepted for publication in MNRA