Conjugation of injections by permutations

Let X be a countably infinite set, and let f, g, and h be any three injective self-maps of X, each having at least one infinite cycle. (For instance, this holds if f, g, and h are not bijections.) We show that there are permutations a and b of X such that h=afa^{-1}bgb^{-1} if and only if |X\Xf|+|X\Xg|=|X\Xh|. We also prove a version of this statement that holds for infinite sets X that are not necessarily countable. This generalizes results of Droste and Ore about permutations.Comment: 27 pages, 4 figure

Impact of stout-link smearing in lattice fermion actions

The impact of stout-link smearing in lattice fermion actions is examined through the consideration of the mass and renormalization functions of the overlap quark propagator over a variety of smeared configurations. Up to six sweeps of stout-link smearing are investigated. For heavy quark masses, the quark propagator is strongly affected by the smearing procedure. For moderate masses, the effect appears to be negligible. A small effect is seen for light quark masses, where dynamical mass generation is suppressed through the smearing procedure.Comment: 7 pages, 3 figures, presented at the XXVII International Symposium on Lattice Field Theory - LAT2009, July 26-31 2009, Peking University, Beijing, Chin

Stout-link smearing in lattice fermion actions

The properties of the momentum space quark propagator in Landau gauge are studied for the overlap quark action in quenched lattice QCD. Numerical calculations are performed over four ensembles of gauge configurations, where three are smeared using either 1, 3, or 6 sweeps of stout-link smearing. We calculate the non-perturbative wave function renormalization function $Z(p)$ and the non-perturbative mass function $M(p)$ for a variety of bare quark masses. We find that the wave-function renormalization function is slightly sensitive to the number of stout-link smearing sweeps. For the mass function we find the effect of the stout-link smearing algorithm to be small for moderate to light bare quark masses. For a heavy bare quark mass we find a strong dependence on the number of smearing sweeps.Comment: 8 pages, 4 figure

Reconciling taxonomy and phylogenetic inference: formalism and algorithms for describing discord and inferring taxonomic roots

Although taxonomy is often used informally to evaluate the results of phylogenetic inference and find the root of phylogenetic trees, algorithmic methods to do so are lacking. In this paper we formalize these procedures and develop algorithms to solve the relevant problems. In particular, we introduce a new algorithm that solves a "subcoloring" problem for expressing the difference between the taxonomy and phylogeny at a given rank. This algorithm improves upon the current best algorithm in terms of asymptotic complexity for the parameter regime of interest; we also describe a branch-and-bound algorithm that saves orders of magnitude in computation on real data sets. We also develop a formalism and an algorithm for rooting phylogenetic trees according to a taxonomy. All of these algorithms are implemented in freely-available software.Comment: Version submitted to Algorithms for Molecular Biology. A number of fixes from previous versio

Criticality of natural absorbing states

We study a recently introduced ladder model which undergoes a transition between an active and an infinitely degenerate absorbing phase. In some cases the critical behaviour of the model is the same as that of the branching annihilating random walk with $N\geq 2$ species both with and without hard-core interaction. We show that certain static characteristics of the so-called natural absorbing states develop power law singularities which signal the approach of the critical point. These results are also explained using random walk arguments. In addition to that we show that when dynamics of our model is considered as a minimum finding procedure, it has the best efficiency very close to the critical point.Comment: 6 page

Size-fractionated 234Th in continental shelf waters off New England: Implications for the role of colloids in oceanic trace metal scavenging

Measurements of 234Th (t1/2 = 24.1 days) in dissolved, colloidal, and particulate forms have been made to investigate the role of colloids in reactive metal scavenging in the surface waters of Buzzards Bay, over an annual cycle, and in the shelf and slope waters off New England. At-sea sampling involved prefiltering seawater through 0.2 μm filters followed by cross-flow filtration using a 10,000 nominal molecular weight filter to collect colloidal (10,000 NMW-0.2 μm) and dissolved (\u3c10,000 NMW) phases. Total 234Th activities increase with distance from shore, indicative of enhanced scavenging in the particle-rich nearshore waters. Clearly seen in Buzzards Bay are seasonal changes in total 234Th, with activities ranging from ≈0.7 dpm I−1 in the winter, preceeding a phytoplankton bloom, to ≈0.2 dpm I−1 in the summer. Throughout the annual cycle, 2–16% of total 234Th is colloidal, 22–40% is dissolved, and 45–75% is particulate. In the offshore waters, ≈1% of total 234Th is colloidal, 2–6% is particulate, and 93–98% is dissolved. The 234Th size-distribution exhibits a systematic increase in the association of 234Th with particulate and, to a lesser extent, colloidal matter with increasing suspended particle concentration (Cp). Moreover, a first-order prediction of the fractionation of 234Th between the various size classes is demonstrated using measured solid-solution partition coefficients. Box model calculations indicate a mean residence time of colloidal 234Th with respect to aggregation into particles of 0.3 days in Buzzards Bay, which compares with 2 days for dissolved and 4 days for particulate 234Th. In the offshore surface waters, colloidal and particulate 234Th residence times are ≈0.5 days and 2–3 days respectively, compared with 30–85 days for the dissolved phase. The short and relatively invariant residence time of colloidal 234Th suggests that colloidal aggregation may not be rate-limiting in controlling the scavenging of thorium and, by analogy, other particle-reactive trace metals. An implication of these results is that colloidal 234Th may be tracing a reactive intermediate in the bacterially mediated decomposition of large, rapidly-sinking biogenic aggregates. Using the size-fractionated 234Th data, we demonstrate that Kd values for thorium are invariant with Cp and that scavenging rate constants exhibit a first-order dependence on Cp. Thus, “particle-concentration effects” are negligible for oceanic waters (Cp ≈0.01–1 mg I−1)

Diversity of opinions promotes herding in uncertain crowds

Classic and recent studies demonstrate how we fall for the ‘tyranny of the majority' and conform to the dominant trend when uncertain. However, in many social interactions outside of the laboratory, there is rarely a clearly identified majority and discerning who to follow might be challenging. Here, we asked whether in such conditions herding behaviour depends on a key statistical property of social information: the variance of opinions in a group. We selected a task domain where opinions are widely variable and asked participants (N = 650) to privately estimate the price of eight anonymous paintings. Then, in groups of five, they discussed and agreed on a shared estimate for four paintings. Finally, they provided revised individual estimates for all paintings. As predicted (https://osf.io/s89w4), we observed that group members converged to each other and boosted their confidence following social interaction. We also found evidence supporting the hypothesis that the more diverse groups show greater convergence, suggesting that the variance of opinions promotes herding in uncertain crowds. Overall, these findings empirically examine how, in the absence of a clear majority, the distribution of opinions relates to subjective feelings of confidence and herding behaviour

Unsung Heroes: Military Families After Ten Years of War

This report describes the economic and educational impact of service on families, the strains of the deployment cycle, and gives suggestions on how to support America's veterans, including a recommended reading list and a list of resources for military families