The halting problem is undecidable --- but can it be solved for most inputs? This natural question was considered in a number of papers, in different settings. We revisit their results and show that most of them can be easily proven in a natural fram
ework of optimal machines (considered in algorithmic information theory) using the notion of Kolmogorov complexity. We also consider some related questions about this framework and about asymptotic properties of the halting problem. In particular, we show that the fraction of terminating programs cannot have a limit, and all limit points are Martin-Lof random reals. We then consider mass problems of finding an approximate solution of halting problem and probabilistic algorithms for them, proving both positive and negative results. We consider the fraction of terminating programs that require a long time for termination, and describe this fraction using the busy beaver function. We also consider approxima
A precision measurement of the muon anomalous magnetic moment, $a_{mu} = (g-2)/2$, was previously performed at BNL with a result of 2.2 - 2.7 standard deviations above the Standard Model (SM) theoretical calculations. The same experimental apparatus
is being planned to run in the new Muon Campus at Fermilab, where the muon beam is expected to have less pion contamination and the extended dataset may provide a possible $7.5sigma$ deviation from the SM, creating a sensitive and complementary bench mark for proposed SM extensions. We report here on a preliminary study of the target subsystem where the apparatus is optimized for pions that have favorable phase space to create polarized daughter muons around the magic momentum of 3.094 GeV/c, which is needed by the downstream g 2 muon ring.
Novel magnetic helical channel designs for capture and cooling of bright muon beams are being developed using numerical simulations based on new inventions such as helical solenoid (HS) magnets and hydrogen-pressurized RF (HPRF) cavities. We are clos
e to the factor of a million six-dimensional phase space (6D) reduction needed for muon colliders. Recent experimental and simulation results are presented.
Fast muon beam six dimensional (6D) phase space cooling is essential for muon colliders. The Helical Cooling Channel (HCC) uses hydrogen-pressurized RF cavities imbedded in a magnet system with solenoid, helical dipole, and helical quadrupole compone
nts that provide the continuous dispersion needed for emittance exchange and effective 6D beam cooling. A series of HCC segments, each with sequentially smaller aperture, higher magnetic field, and higher RF frequency to match the beam size as it is cooled, has been optimized by numerical simulation to achieve a factor of 105 emittance reduction in a 300 m long channel with only a 40% loss of beam. Conceptual designs of the hardware required for this HCC system and the status of the RF studies and HTS helical solenoid magnet prototypes are described.
We present an inference system for a version of the Pi-calculus in Haskell for the session type proposed by Honda et al. The session type is very useful in checking if the communications are well-behaved. The full session type implementation in Haske
ll was first presented by Pucella and Tov, which is semi-automatic in that the manual operations for the type representation was necessary. We give an automatic type inference for the session type by using a more abstract representation for the session type based on the de Bruijn levels. We show an example of the session type inference for a simple SMTP client.
Type theories with higher-order subtyping or singleton types are examples of systems where computation rules for variables are affected by type information in the context. A complication for these systems is that bounds declared in the context do not
interact well with the logical relation proof of completeness or termination. This paper proposes a natural modification to the type syntax for F-Omega-Sub, adding variables bound to the variable type constructor, thereby separating the computational behavior of the variable from the context. The algorithm for subtyping in F-Omega-Sub can then be given on types without context or kind information. As a consequence, the metatheory follows the general approach for type systems without computational information in the context, including a simple logical relation definition without Kripke-style indexing by context. This new presentation of the system is shown to be equivalent to the traditional presentation without bounds on the variable type constructor.
This paper presents accurate absolute positions from a 24 GHz Very Long Baseline Array (VLBA) search for compact extragalactic sources in an area where the density of known calibrators with precise coordinates is low. The goals were to identify addit
ional sources suitable for use as phase calibrators for galactic sources, determine their precise positions, and produce radio images. In order to achieve these goals, we developed a new software package, PIMA, for determining group delays from wide-band data with much lower detection limit. With the use of PIMA we have detected 327 sources out of 487 targets observed in three 24 hour VLBA experiments. Among the 327 detected objects, 176 are within 10 degrees of the Galactic plane. This VGaPS catalogue of source positions, plots of correlated flux density versus projected baseline length, contour plots, as well as weighted CLEAN images and calibrated visibility data in FITS format, are available on the Web at http://astrogeo.org/vgaps. Approximately one half of objects from the 24 GHz catalogue were observed at dual band 8.6 GHz and 2.3 GHz experiments. Position differences at 24 GHz versus 8.6/2.3 GHz for all but two objects on average are strictly within reported uncertainties. We found that for two objects with complex structure positions at different frequencies correspond to different components of a source.
A controversy has developed regarding the stellar wind mass loss rates in O-stars. The current consensus is that these winds may be clumped which implies that all previously derived mass loss rates using density-squared diagnostics are overestimated
by a factor of ~ 2. However, arguments based on FUSE observations of the P V resonance line doublet suggest that these rates should be smaller by another order of magnitude, provided that P V is the dominant phosphorous ion among these stars. Although a large mass loss rate reduction would have a range of undesirable consequences, it does provide a straightforward explanation of the unexpected symmetric and un-shifted X-ray emission line profiles observed in high energy resolution spectra. But acceptance of such a large reduction then leads to a contradiction with an important observed X-ray property: the correlation between He-like ion source radii and their equivalent X-ray continuum optical depth unity radii. Here we examine the phosphorous ionization balance since the P V fractional abundance, q(P V), is fundamental to understanding the magnitude of this mass loss reduction. We find that strong XUV emission lines in the He II Lyman continuum can significantly reduce q(P V). Furthermore, owing to the unique energy distribution of these XUV lines, there is a negligible impact on the S V fractional abundance (a key component in the FUSE mass loss argument). We conclude that large reductions in O-star mass loss rates are not required, and the X-ray optical depth unity relation remains valid.
In the pyrochlore lattice Heisenberg antiferromagnet, for large spin length $S$, the massive classical ground state degeneracy is partly lifted by the zero-point energy of quantum fluctuations at harmonic order in spin-waves. However, there remains a
n infinite manifold of degenerate collinear ground states, related by a gaugelike symmetry. We have extended the spin-wave calculation to quartic order, assuming a Gaussian variational wavefunction (equivalent to Hartree-Fock approximation). Quartic calculations emph{do} break the harmonic-order degeneracy of periodic ground states. The form of the effective Hamiltonian describing this splitting, which depends on loops, was fitted numerically and also rationalized analytically. We find a family of states that are still almost degenerate, being split by the term from loops of length 26. We also calculated the anharmonic terms for the checkerboard lattice, and discuss why it (as well as the kagome lattice) behave differently than the pyrochlore at anharmonic orders.
This paper presents the sixth part to the Very Long Baseline Array (VLBA) Calibrator Survey. It contains the positions and maps of 264 sources of which 169 were not previously observed with very long baseline interferometry (VLBI). This survey, based
on two 24 hour VLBA observing sessions, was focused on 1) improving positions of 95 sources from previous VLBA Calibrator surveys that were observed either with very large a priori position errors or were observed not long enough to get reliable positions and 2) observing remaining new flat-spectrum sources with predicted correlated flux density in the range 100-200 mJy that were not observed in previous surveys. Source positions were derived from astrometric analysis of group delays determined at the 2.3 and 8.6 GHz frequency bands using the Calc/Solve software package. The VCS6 catalogue of source positions, plots of correlated flux density versus projected baseline length, contour plots and fits files of naturally weighted CLEAN images, as well as calibrated visibility function files are available on the Web at http://vlbi.gsfc.nasa.gov/vcs6
