A set partition $sigma$ of $[n]={1,dots,n}$ contains another set partition $pi$ if restricting $sigma$ to some $Ssubseteq[n]$ and then standardizing the result gives $pi$. Otherwise we say $sigma$ avoids $pi$. For all sets of patterns consisting of p
artitions of $[3]$, the sizes of the avoidance classes were determined by Sagan and by Goyt. Set partitions are in bijection with restricted growth functions (RGFs) for which Wachs and White defined four fundamental statistics. We consider the distributions of these statistics over various avoidance classes, thus obtaining multivariate analogues of the previously cited cardinality results. This is the first in-depth study of such distributions. We end with a list of open problems.
Goldman, Joichi, and White proved a beautiful theorem showing that the falling factorial generating function for the rook numbers of a Ferrers board factors over the integers. Briggs and Remmel studied an analogue of rook placements where rows are re
placed by sets of $m$ rows called levels. They proved a version of the factorization theorem in that setting, but only for certain Ferrers boards. We generalize this result to any Ferrers board as well as giving a p,q-analogue. We also consider a dual situation involving weighted file placements which permit more than one rook in the same row. In both settings, we discuss properties of the resulting equivalence classes such as the number of elements in a class. In addition, we prove analogues of a theorem of Foata and Schutzenberger giving a distinguished representative in each class as well as make connections with the q,t-Catalan numbers. We end with some open questions raised by this work.
The usage of the high-level scripting language Python has enabled new mechanisms for data interrogation, discovery and visualization of scientific data. We present yt, an open source, community-developed astrophysical analysis and visualization toolk
it for data generated by high-performance computing (HPC) simulations of astrophysical phenomena. Through a separation of responsibilities in the underlying Python code, yt allows data generated by incompatible, and sometimes even directly competing, astrophysical simulation platforms to be analyzed in a consistent manner, focusing on physically relevant quantities rather than quantities native to astrophysical simulation codes. We present on its mechanisms for data access, capabilities for MPI-parallel analysis, and its implementation as an in situ analysis and visualization tool.
The SuperB international team continues to optimize the design of an electron-positron collider, which will allow the enhanced study of the origins of flavor physics. The project combines the best features of a linear collider (high single-collision
luminosity) and a storage-ring collider (high repetition rate), bringing together all accelerator physics aspects to make a very high luminosity of 10$^{36}$ cm$^{-2}$ sec$^{-1}$. This asymmetric-energy collider with a polarized electron beam will produce hundreds of millions of B-mesons at the $Upsilon$(4S) resonance. The present design is based on extremely low emittance beams colliding at a large Piwinski angle to allow very low $beta_y^star$ without the need for ultra short bunches. Use of crab-waist sextupoles will enhance the luminosity, suppressing dangerous resonances and allowing for a higher beam-beam parameter. The project has flexible beam parameters, improved dynamic aperture, and spin-rotators in the Low Energy Ring for longitudinal polarization of the electron beam at the Interaction Point. Optimized for best colliding-beam performance, the facility may also provide high-brightness photon beams for synchrotron radiation applications.
We present multi-configuration Breit-Pauli distorted-wave photoionization (PI) cross sections and radiative recombination (RR) and dielectronic recombination (DR) rate coefficients for the first six krypton ions. These were calculated with the AUTOST
RUCTURE code, using semi-relativistic radial wavefunctions in intermediate coupling. Kr has been detected in several planetary nebulae (PNe) and H II regions, and is a useful tracer of neutron-capture nucleosynthesis. PI, RR, and DR data are required to accurately correct for unobserved Kr ions in ionized nebulae, and hence to determine elemental Kr abundances. PI cross sections have been determined for ground configuration states of Kr^0--Kr^5+ up to 100 Rydbergs. Our Kr^+ PI calculations were significantly improved through comparison with experimental measurements. RR and DR rate coefficients were determined from the direct and resonant PI cross sections at temperatures (10^1--10^7)z^2 K, where z is the charge. We account for Delta n=0 DR core excitations, and find that DR is the dominant recombination mechanism for all but Kr^+ at photoionized plasma temperatures. Internal uncertainties are estimated by comparing results computed with three different configuration-interaction expansions for each ion, and by testing the sensitivity to variations in the orbital radial scaling parameters. The PI cross sections are generally uncertain by 30-50% near the ground state thresholds. Near 10^4 K, the RR rate coefficients are typically uncertain by <10%, while those of DR exhibit uncertainties of factors of 2 to 3, due to the unknown energies of near-threshold autoionizing resonances. With the charge transfer rate coefficients presented in the third paper of this series, these data enable robust Kr abundance determinations in photoionized nebulae for the first time.
We present multi-configuration Breit-Pauli AUTOSTRUCTURE calculations of distorted-wave photoionization (PI) cross sections, and total and partial final-state resolved radiative recombination (RR) and dielectronic recombination (DR) rate coefficients
for the first six ions of the trans-iron element Se. These calculations were motivated by the recent detection of Se emission lines in a large number of planetary nebulae. Se is a potentially useful tracer of neutron-capture nucleosynthesis, but accurate determinations of its abundance in photoionized nebulae have been hindered by the lack of atomic data governing its ionization balance. Our calculations were carried out in intermediate coupling with semi-relativistic radial wavefunctions. PI and recombination data were determined for levels within the ground configuration of each ion, and experimental PI cross-section measurements were used to benchmark our results. For DR, we allowed dn=0 core excitations, which are important at photoionized plasma temperatures. DR is the dominant recombination process for each of these Se ions at temperatures representative of photoionized nebulae (~10^4 K). To estimate the uncertainties of these data, we compared results from three different configuration-interaction expansions for each ion, and tested the sensitivity of the results to the radial scaling factors in the structure calculations. We find that the internal uncertainties are typically 30-50% for the direct PI cross sections and ~10% for the computed RR rate coefficients, while those for low-temperature DR can be considerably larger (from 15-30% up to two orders of magnitude) due to the unknown energies of near-threshold autoionization resonances. The results are suitable for incorporation into photoionization codes used to numerically simulate astrophysical nebulae, and will enable robust determinations of nebular Se abundances.
We present the results of new X-ray observations of XMMU 122939.7+075333, the black hole (BH) in the globular cluster RZ 2109 in the Virgo Cluster galaxy NGC 4472. A combination of non-detections and marginal detections in several recent Swift and Ch
andra observations show that the source has varied by at least a factor of 20 in the past 6 years, and that the variations seem not just to be flickering. This variation could be explained with changes in the absorption column intrinsic to the source no larger than those which were previously seen near the peak of the 1989 outburst of the Galactic BH X-ray binary V404 Cyg. The large amplitude variations are also a natural expectation from a hierarchical triple system with Kozai cycles -- the mechanism recently proposed to produce BH-white dwarf (WD) binaries in globular clusters. On the other hand, variation by such a large factor on timescales of years, rather than centuries, is very difficult to reconcile with the scenario in which the X-ray emission from XMMU 122939.7+075333 is due to fallback of material from a tidally destroyed or detonated WD.
Two-particle femtoscopy reveals the space-time substructure of the freeze-out configuration from heavy ion collisions. Detailed fingerprints of bulk collectivity are evident in space-momentum correlations, which have been systematically measured as a
function of particle type, three-momentum, and collision conditions. A clear scenario, dominated by hydrodynamic-type flow emerges. Reproducing the strength and features of the femtoscopic signals in models involves important physical quantities like the Equation of State, as well as less fundamental technical details. An interesting approximate factorization in the measured systematics suggests that the overall physical freeze-out scale is set by final state chemistry, but the kinematic substructure is largely universal. Referring to previous results from hadron and lepton collisions, we point to the importance of determining whether these universal trends persist from the largest to the smallest systems. We review theoretical expectations for heavy ion femtoscopy at the LHC, and point to directions needing further theory and experimental work at RHIC and the LHC.
Let $B^{alpha_i}$ be an $(N_i,d)$-fractional Brownian motion with Hurst index ${alpha_i}$ ($i=1,2$), and let $B^{alpha_1}$ and $B^{alpha_2}$ be independent. We prove that, if $frac{N_1}{alpha_1}+frac{N_2}{alpha_2}>d$, then the intersection local time
s of $B^{alpha_1}$ and $B^{alpha_2}$ exist, and have a continuous version. We also establish H{o}lder conditions for the intersection local times and determine the Hausdorff and packing dimensions of the sets of intersection times and intersection points. One of the main motivations of this paper is from the results of Nualart and Ortiz-Latorre ({it J. Theor. Probab.} {bf 20} (2007)), where the existence of the intersection local times of two independent $(1,d)$-fractional Brownian motions with the same Hurst index was studied by using a different method. Our results show that anisotropy brings subtle differences into the analytic properties of the intersection local times as well as rich geometric structures into the sets of intersection times and intersection points.
