The Number of Hierarchical Orderings

An ordered set-partition (or preferential arrangement) of n labeled elements represents a single ``hierarchy''; these are enumerated by the ordered Bell numbers. In this note we determine the number of ``hierarchical orderings'' or ``societies'', where the n elements are first partitioned into m <= n subsets and a hierarchy is specified for each subset. We also consider the unlabeled case, where the ordered Bell numbers are replaced by the composition numbers. If there is only a single hierarchy, we show that the average rank of an element is asymptotic to n/(4 log 2) in the labeled case and to n/4 in the unlabeled case.Comment: 7 page

Dissociation and isomerization of vibrationally excited species. II. Unimolecular reaction rate theory and its application

Data on quasi-unimolecular reactions have usually been compared with theoretical equations based on classical treatments, because the expressions are simpler than those obtained on the basis of a quantum model. The quantum reformulation of the RRK theory in Part I is used to compute the pressure dependence of the rate constants and the limiting low-pressure rates for a variety of unimolecular reactions without employing adjustable parameters. An asymptotic expansion of the integral for the limiting low-pressure second-order rate constant provides a very simple expression for this quantity.The errors inherent in corresponding classical calculations are estimated by comparing these results with those obtained from the theory in its classical limit. The error is temperature dependent and at low pressures increases from a factor of about three (under typical experimental conditions) for small reactants such as O3 and N2O to 105 or more for large molecules such as cyclopropane, C2H6, and N2O5. In most cases the rates calculated from the quantum form are in reasonable agreement with those obtained experimentally when all of the reactant oscillators are assumed effective in intramolecular energy transfer

Exact and Approximate Stochastic Simulation of Intracellular Calcium Dynamics

In simulations of chemical systems, the main task is to find an exact or approximate solution of the chemical master equation (CME) that satisfies certain constraints with respect to computation time and accuracy. While Brownian motion simulations of single molecules are often too time consuming to represent the mesoscopic level, the classical Gillespie algorithm is a stochastically exact algorithm that provides satisfying results in the representation of calcium microdomains. Gillespie's algorithm can be approximated via the tau-leap method and the chemical Langevin equation (CLE). Both methods lead to a substantial acceleration in computation time and a relatively small decrease in accuracy. Elimination of the noise terms leads to the classical, deterministic reaction rate equations (RRE). For complex multiscale systems, hybrid simulations are increasingly proposed to combine the advantages of stochastic and deterministic algorithms. An often used exemplary cell type in this context are striated muscle cells (e.g., cardiac and skeletal muscle cells). The properties of these cells are well described and they express many common calcium-dependent signaling pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms

Wallpaper Fermions and the Nonsymmorphic Dirac Insulator

Recent developments in the relationship between bulk topology and surface crystal symmetry have led to the discovery of materials whose gapless surface states are protected by crystal symmetries. In fact, there exists only a very limited set of possible surface crystal symmetries, captured by the 17 "wallpaper groups." We show that a consideration of symmetry-allowed band degeneracies in the wallpaper groups can be used to understand previous topological crystalline insulators, as well as to predict new examples. In particular, the two wallpaper groups with multiple glide lines, $pgg$ and $p4g$, allow for a new topological insulating phase, whose surface spectrum consists of only a single, fourfold-degenerate, true Dirac fermion. Like the surface state of a conventional topological insulator, the surface Dirac fermion in this "nonsymmorphic Dirac insulator" provides a theoretical exception to a fermion doubling theorem. Unlike the surface state of a conventional topological insulator, it can be gapped into topologically distinct surface regions while keeping time-reversal symmetry, allowing for networks of topological surface quantum spin Hall domain walls. We report the theoretical discovery of new topological crystalline phases in the A$_2$B$_3$ family of materials in SG 127, finding that Sr$_2$Pb$_3$ hosts this new topological surface Dirac fermion. Furthermore, (100)-strained Au$_2$Y$_3$ and Hg$_2$Sr$_3$ host related topological surface hourglass fermions. We also report the presence of this new topological hourglass phase in Ba$_5$In$_2$Sb$_6$ in SG 55. For orthorhombic space groups with two glides, we catalog all possible bulk topological phases by a consideration of the allowed non-abelian Wilson loop connectivities, and we develop topological invariants for these systems. Finally, we show how in a particular limit, these crystalline phases reduce to copies of the SSH model.Comment: Final version, 6 pg main text + 29 pg supplement, 6 + 13 figure

Experimental nitrogen addition alters structure and function of a boreal bog: critical load and thresholds revealed

Bogs and fens cover 6% and 21%, respectively, of the 140,329 km2 Oil Sands Administrative Area in northern Alberta. Development of the oil sands has led to increasing atmospheric N deposition, with values as high as 17 kg N.ha-1yr-1; regional background deposition is N.ha-1yr-1. Bogs, being ombrotrophic, may be especially susceptible to increasing N deposition. To examine responses to N deposition, over five years, we experimentally applied N (as NH4NO3) to a bog near Mariana Lake, Alberta, unaffected by oil sands activities, at rates of 0, 5, 10, 15, 20, and 25 kg N.ha-1yr-1, plus controls (no water or N addition). Increasing N addition: (1) stimulated N2 fixation at deposition .ha-1yr-1, and progressively inhibited N2 fixation as N deposition increased above this level; (2) had no effect on Sphagnum fuscum net primary production (NPP) in years 1, 2, and 4, but inhibited S. fuscum NPP in years 3 and 5; (3) stimulated dominant shrub and Picea mariana NPP; (4) led to increased root biomass and production; (5) changed Sphagnum species relative abundance (decrease in S. fuscum, increase in S. magellanicum, no effect on S. angustifolium); (6) led to increasing abundance of Rhododendron groenlandicum and Andromeda polifolia, and to vascular plants in general; (7) led to increasing shrub leaf N concentrations in Andromeda polifolia, Chamaedaphne calyculata, Vaccinium oxycoccos, V. vitis-idaea, and Picea mariana; (8) stimulated cellulose decomposition, with no effect on S. fuscum peat or mixed vascular plant litter decomposition; (9) had no effect on net N mineralization rates or on porewater NH4+-N, NO3--N, or DON concentrations; and (10) had minimal effects on peat microbial community composition. Increasing experimental N addition led to a switch from new N being taken up primarily by Sphagnum to being taken up primarily by shrubs. As shrub growth and cover increase, Sphagnum abundance and NPP decrease. Because inhibition of N2 fixation by increasing N deposition plays a key role in bog structural and functional responses, we recommend a N deposition critical load of 3 kg N.ha-1yr-1 for northern Alberta bogs

Bog plant/lichen tissue nitrogen and sulfur concentrations as indicators of emissions from oil sands development in Alberta, Canada

Increasing gaseous emissions of nitrogen (N) and sulfur (S) associated with oil sands development in northern Alberta (Canada) has led to changing regional wet and dry N and S deposition regimes. We assessed the potential for using bog plant/lichen tissue chemistry (N and S concentrations, C:N and C:S ratios, in 10 plant/lichen species) to monitor changing atmospheric N and S deposition through sampling at five bog sites, 3-6 times per growing season from 2009 to 2016. During this 8-year period, oil sands N emissions steadily increased, while S emissions steadily decreased. We examined the following: (1) whether each species showed changes in tissue chemistry with increasing distance from the Syncrude and Suncor upgrader stacks (the two largest point sources of N and S emissions); (2) whether tissue chemistry changed over the 8 year period in ways that were consistent with increasing N and decreasing S emissions from oil sands facilities; and (3) whether tissue chemistry was correlated with growing season wet deposition of NH4+-N, NO3--N, or SO42--S. Based on these criteria, the best biomonitors of a changing N deposition regime were Evernia mesomorpha, Sphagnum fuscum, and Vaccinium oxycoccos. The best biomonitors of a changing S deposition regime were Evernia mesomorpha, Cladonia mitis, Sphagnum fuscum, Sphagnum capillifolium, Vaccinium oxycoccos, and Picea mariana. Changing N and S deposition regimes in the oil sands region appear to be influencing N and S cycling in what once were pristine ombrotrophic bogs, to the extent that these bogs may effectively monitor future spatial and temporal patterns of deposition

Adaptive partitioning of real-time tasks on multiple processors

This paper presents a new algorithm for scheduling real-time tasks on multiprocessor/multicore systems. This new algorithm is based on combining EDF scheduling with a migration strategy that moves tasks only when needed. It has been evaluated through an extensive set of simulations that showed good performance when compared with global or partitioned EDF: a worst-case utilisation bound similar to partitioned EDF for hard real-time tasks, and a tardiness bound similar to global EDF for soft real-time tasks. Therefore, the proposed scheduler is effective for dealing with both soft and hard real-time workloads