What can a mean-field model tell us about the dynamics of the cortex?

In this chapter we examine the dynamical behavior of a spatially homogeneous two-dimensional model of the cortex that incorporates membrane potential, synaptic flux rates and long- and short-range synaptic input, in two spatial dimensions, using parameter sets broadly realistic of humans and rats. When synaptic dynamics are included, the steady states may not be stable. The bifurcation structure for the spatially symmetric case is explored, identifying the positions of saddle–node and sub- and supercritical Hopf instabilities. We go beyond consideration of small-amplitude perturbations to look at nonlinear dynamics. Spatially-symmetric (breathing mode) limit cycles are described, as well as the response to spatially-localized impulses. When close to Hopf and saddle–node bifurcations, such impulses can cause traveling waves with similarities to the slow oscillation of slow-wave sleep. Spiral waves can also be induced. We compare model dynamics with the known behavior of the cortex during natural and anesthetic-induced sleep, commenting on the physiological significance of the limit cycles and impulse responses

Land and Resource Management on Typic Quartzipsamments

Survival and growth of seven species/treatment combinations were tested on Tonkawa fine sand (thermic, coated Typic Quartzipsamment) in Nacogdoches County, Texas. In January 1983, seedlings were hand-planted on an intensively prepared clearcut site on the Tonkawa soil series in northern Nacogdoches County. Tonkawa sands serve as recharge zones for the Carrizo aquifer, a major source of clean groundwater for much of East Texas. Intensive management practices on this sensitive site created severe site conditions, providing incentive for the study. Species/ treatment combinations were: untreated loblolly (Pinus taeda L.) pine (LOB/CON); Terra-SorbTM -treated loblolly (LOB/Tm);olin clay slurry-treated loblolly (LOB/CLA); untreated slash (P. elliottii Engelm.) pine (SLA/CON); Terra-Sorb-treated slash (%A/ TBR); kaolin clay slurry-treated slash (SLA/ CLA); and containerized longleaf pine (P. alustris Mill.) (LL/CONT). Treatments were applied as a bareroot+up prior to planting, to increase soil moisture retention near the roots, and subsequently increase survival. Containerized longleaf yielded the highest survival (greater than 50 percent) throughout the study, followed by LOB/TER (38 percent), while all other treatments were unacceptable (below 30 percent by the end of the sixth year). Management recommendations include reforest the site in longleaf pine or allow the natural scrub vegetation to inhabit the site, while managing for nontimber resources, such as groundwater, wildlife, and recreation

Statistical Theory of Asteroid Escape Rates

Transition states in phase space are identified and shown to regulate the rate of escape of asteroids temporarily captured in circumplanetary orbits. The transition states, similar to those occurring in chemical reaction dynamics, are then used to develop a statistical semianalytical theory for the rate of escape of asteroids temporarily captured by Mars. Theory and numerical simulations are found to agree to better than 1%. These calculations suggest that further development of transition state theory in celestial mechanics, as an alternative to large-scale numerical simulations, will be a fruitful approach to mass transport calculations

Site/stand factors influencing Nantucket pine tip moth in loblolly pine plantations

Tip moth infestation and loblolly pine growth were examined on sandy, loamy and clayey sites in 2-3 year old plantations. Infestations were greatest on loamy sites. Following fertilizer and herbicide applications, tip moth infestations were lowest on fertilized plots following application of phosphorus

Changes in Understory Woody Vegetation in Red-Cockaded Woodpecker (Picoides Borealis) Nesting Clusters

Understory woody vegetation in red-cockaded woodpecker nesting clusters located in Pinus taeda (L.) and P. echinara (Mill.) dominated stands were inventoried from December 1986 through January 1987 and later in January 1995 to determine what effects court-ordered management schemes had on the composition, abundance, and diversity of these stands. There was a significant difference (Pin the composition between the first sampling period and the second with species diversity increasing and a change from a P. (aeda/P. echinara dominated community to a P. weda/Rubus spp. understor

Population Dynamics, Impacts, and Integrated Management of Forest Defoliating Insects

Pine plantations on Typic Quartzipsamments in East Texas are difficult to establish. Forest management options following clearcutting are limited. An 8-year regeneration study of the growth and survival of loblolly, Pinus taeda, L. shortleaf, P. echinata Mill., slash, P. elliotii Engelm and longleaf pines P. palustris Mill. was conducted to determine optimum tree species and treatments for reforestation, and to recommend practical alternative land uses and management strategies for Typic Quartzipsamments. Successful regeneration provides new opportunities for insects and pathogens. Impacts of the Nantucket pine tip moth, R}iyacionia frustrana (Comstock), the Deodar weevil, Pissodes nemorensis, Germar, Annosus root rot, Heterobasidion annosum (Fr: Fr) Bref, fusiform rust, Cronartium quercuum (Berk.) Miyabe ex Shirai f. sp. fusiforme (hedge and N. Hunt) Burdsall and G. Snow and the Texas leaf-cutting ant, Atta texana, (Buckley) will be discussed in the context of droughty site management