Critical percolation of free product of groups

In this article we study percolation on the Cayley graph of a free product of groups. The critical probability $p_c$ of a free product $G_1*G_2*...*G_n$ of groups is found as a solution of an equation involving only the expected subcritical cluster size of factor groups $G_1,G_2,...,G_n$. For finite groups these equations are polynomial and can be explicitly written down. The expected subcritical cluster size of the free product is also found in terms of the subcritical cluster sizes of the factors. In particular, we prove that $p_c$ for the Cayley graph of the modular group $\hbox{PSL}_2(\mathbb Z)$ (with the standard generators) is $.5199...$, the unique root of the polynomial $2p^5-6p^4+2p^3+4p^2-1$ in the interval $(0,1)$. In the case when groups $G_i$ can be "well approximated" by a sequence of quotient groups, we show that the critical probabilities of the free product of these approximations converge to the critical probability of $G_1*G_2*...*G_n$ and the speed of convergence is exponential. Thus for residually finite groups, for example, one can restrict oneself to the case when each free factor is finite. We show that the critical point, introduced by Schonmann, $p_{\mathrm{exp}}$ of the free product is just the minimum of $p_{\mathrm{exp}}$ for the factors

The Use of Commercial Bacterial Soil Inoculant Regime in an Urban Prairie Restoration

For successful grassland restoration, commercial soil inoculants are often recommended to increase establishment success. In spring 2009, a 0.94-ha tract was targeted for restoration at Phil Hardberger Park, a 126-ha park in the heart of San Antonio, Texas. Woody species, mainly Texas persimmon (Diospyros texana Scheele), and Ashe juniper (Juniperus asheiiBuchholz), were removed and the area was divided into 10 subplots measuring 911 m2 on average. In September 2009, over 40,000 plugs of seven native grass species were planted. In addition, native prairie seed mixes, including various grass and forb seeds, were sown into the site at a rate of 11.26 kg/ha. Half of the native grass plants were treated with a soil bacteria inoculant plus additional nutrients (IN) (BioGensis IIITM DS Tainio Technology and Technique Inc.), and half were left as controls (C). Soil samples from the plots were taken in February 2010 and 2011 and analyzed for soil nutrients, bacteria, protozoa, and fungi. Vegetation data were collected October 2010 and May and October 2011 to assess differences in percent cover between the treatments. The IN treatment resulted in significantly higher percent cover in the second growing season of three native grasses,Eriochloa sericea (Scheele) Munro ex Vasey, Bouteloua gracilis (Willd. ex Kunth) Lag. ex Griffiths, and B. curtipendula (Michx.) Torr; however, no significant differences were found between the IN and C plots for measures of overall native species abundance, soil resources, or the presence of soil microbes. We concluded that commercial soil inoculants may not have been necessary for the successful establishment of a native grassland community

Microwave properties of DyBa_2Cu_3O_(7-x) monodomains and related compounds in magnetic fields

We present a microwave characterization of a DyBa$_{2}$Cu$_{3}$O$_{7-x}$ single domain, grown by the top-seeded melt-textured technique. We report the (a,b) plane field-induced surface resistance, $\Delta R_s(H)$, at 48.3 GHz, measured by means of a cylindrical metal cavity in the end-wall-replacement configuration. Changes in the cavity quality factor Q against the applied magnetic field yield $\Delta R_s(H)$ at fixed temperatures. The temperature range [70 K ; T_c] was explored. The magnetic field $\mu_0 H <$ 0.8 T was applied along the c axis. The field dependence of $\Delta R_s(H)$ does not exhibit the steep, step-like increase at low fields typical of weak-links. This result indicates the single-domain character of the sample under investigation. $\Delta R_s(H)$ exhibits a nearly square-root dependence on H, as expected for fluxon motion. From the analysis of the data in terms of motion of Abrikosov vortices we estimate the temperature dependences of the London penetration depth $\lambda$ and the vortex viscosity $\eta$, and their zero-temperature values $\lambda(0)=$165 nm and $\eta(0)=$ 3 10$^{-7}$ Nsm$^{-2}$, which are found in excellent agreement with reported data in YBa$_{2}$Cu$_{3}$O$_{7-x}$ single crystals. Comparison of microwave properties with those of related samples indicate the need for reporting data as a function of T/T_c in order to obtain universal laws.Comment: 6 pages, 4 figures, LaTeX, submitted to Journal of Applied Physic

Distribution and Ecotypic Variation of the Invasive Annual Barb Goatgrass (\u3cem\u3eAegiolops triuncialis\u3c/em\u3e) on Serpentine Soil

Successful colonization of newly introduced species is driven by a multitude of factors and is highly dependent on the species. It has long been hypothesized that preadaptation and postestablishment natural selection of introduced species can facilitate their invasion; however, to date, limited research has been dedicated to these theories. In addition, although the correlation between establishment of invasive species and disturbance has been noted and widely studied, the susceptibility of undisturbed habitats to invasion remains unclear. In California, serpentine habitats are severe edaphic environments that have been relatively free of anthropogenic disturbance and nonindigenous species invasions. In this study, we documented the occurrence of the nonindigenous barb goatgrass on serpentine and nonserpentine grasslands in the California Northern Interior Coast Range and the western foothills of the Sierra Nevada Mountains and conducted greenhouse and field experiments to assess the species\u27 degree of adaptation to serpentine soils. Reconnaissance of serpentine intrusions and yearly monitoring suggest that barb goatgrass may grow preferentially on serpentine soil, particularly disturbed serpentine sites. In the greenhouse, for most measures of performance, serpentine populations performed better than nonserpentine populations when grown on serpentine soil. Particularly noteworthy was that serpentine populations had higher root-mass ratios than nonserpentine populations when grown on serpentine soil. In contrast to the greenhouse study, field-grown populations from serpentine and nonserpentine sources performed equally well on nonserpentine; alluvial, disturbed serpentine; and shallow, undisturbed serpentine, although the overall species\u27 performance was diminished on severe serpentine soils. Alarmingly, even in the absence of previous exposure to serpentine, barb goatgrass was capable of establishing and spreading into minimally disturbed sites with strong serpentinitic characteristics

Evaluation of exercises designed to improve children's use of descriptive words in oral language

Thesis (Ed.M.)--Boston Universit

Emergence of long memory in stock volatility from a modified Mike-Farmer model

The Mike-Farmer (MF) model was constructed empirically based on the continuous double auction mechanism in an order-driven market, which can successfully reproduce the cubic law of returns and the diffusive behavior of stock prices at the transaction level. However, the volatility (defined by absolute return) in the MF model does not show sound long memory. We propose a modified version of the MF model by including a new ingredient, that is, long memory in the aggressiveness (quantified by the relative prices) of incoming orders, which is an important stylized fact identified by analyzing the order flows of 23 liquid Chinese stocks. Long memory emerges in the volatility synthesized from the modified MF model with the DFA scaling exponent close to 0.76, and the cubic law of returns and the diffusive behavior of prices are also produced at the same time. We also find that the long memory of order signs has no impact on the long memory property of volatility, and the memory effect of order aggressiveness has little impact on the diffusiveness of stock prices.Comment: 6 pages, 6 figures and 1 tabl

The Origin of Time Asymmetry

It is argued that the observed Thermodynamic Arrow of Time must arise from the boundary conditions of the universe. We analyse the consequences of the no boundary proposal, the only reasonably complete set of boundary conditions that has been put forward. We study perturbations of a Friedmann model containing a massive scalar field but our results should be independent of the details of the matter content. We find that gravitational wave perturbations have an amplitude that remains in the linear regime at all times and is roughly time symmetric about the time of maximum expansion. Thus gravitational wave perturbations do not give rise to an Arrow of Time. However density perturbations behave very differently. They are small at one end of the universe's history, but grow larger and become non linear as the universe gets larger. Contrary to an earlier claim, the density perturbations do not get small again at the other end of the universe's history. They therefore give rise to a Thermodynamic Arrow of Time that points in a constant direction while the universe expands and contracts again. The Arrow of Time does not reverse at the point of maximum expansion. One has to appeal to the Weak Anthropic Principle to explain why we observe the Thermodynamic Arrow to agree with the Cosmological Arrow, the direction of time in which the universe is expanding.Comment: 41 pages, DAMTP R92/2

Adaptive constraints for feature tracking

In this paper extensions to an existing tracking algorithm are described. These extensions implement adaptive tracking constraints in the form of regional upper-bound displacements and an adaptive track smoothness constraint. Together, these constraints make the tracking algorithm more flexible than the original algorithm (which used fixed tracking parameters) and provide greater confidence in the tracking results. The result of applying the new algorithm to high-resolution ECMWF reanalysis data is shown as an example of its effectiveness

Fluid/solid transition in a hard-core system

We prove that a system of particles in the plane, interacting only with a certain hard-core constraint, undergoes a fluid/solid phase transition

Influence of oxygen ordering kinetics on Raman and optical response in YBa_2Cu_3O_{6.4}

Kinetics of the optical and Raman response in YBa_2Cu_3O_{6.4} were studied during room temperature annealing following heat treatment. The superconducting T_c, dc resistivity, and low-energy optical conductivity recover slowly, implying a long relaxation time for the carrier density. Short relaxation times are observed for the B_{1g} Raman scattering -- magnetic, continuum, and phonon -- and the charge transfer band. Monte Carlo simulations suggest that these two relaxation rates are related to two length scales corresponding to local oxygen ordering (fast) and long chain and twin formation (slow).Comment: REVTeX, 3 pages + 4 PostScript (compressed) figure