The factorization approximation for the Master Equation

We examine the validity of the application of the Factorization Approximation to derive the Master Equation for a microscopic system coupled to a reservoir. We developed a formal perturbation expansion for the time evolution of the system reduced density matrix. We employed a diagrammatic schemes to produce each term of the perturbation series. The diagrams in the time domain provide a distinct criteria to distinguish the diagrams which survive the Factorization Approximation. The Feynmann-like diagrams in the energy domain, originated from the Resolvent method, are used for execution of diagram summations to estimate their overall contributions. We demonstrated that for a two level atomic system, interacting with a thermal reservoir, the summation over the diagrams which survived the Factorization Approximation, yields the proper time evolution of the system, in agreement with the solution of the Master Equation. The summation of the diagrams which are excluded by applying the Factorization Approximation are characterized by a dimensionless parameter: Γ/ω₀, where ω₀ is the frequency of the transition line, and Γ is the line width. The Factorization Approximation is thus rigorously justified when this expansion parameter is very small.     

The entropies of renewal systems

Renewal systems are symbolic dynamical systems originally introduced by Adler. IfW is a finite set of words over a finite alphabetA, then the renewal system generated byW is the subshiftX _W ⊂A ^Z formed by bi-infinite concatenations of words fromW. Motivated by Adler’s question of whether every irreducible shift of finite type is conjugate to a renewal system, we prove that for every shift of finite type there is a renewal system having the same entropy. We also show that every shift of finite type can be approximated from above by renewal systems, and that by placing finite-type constraints on possible concatenations, we obtain all sofic systems. The authors were supported in part by NFS grants DMS-8706284, DMS-8814159 and DMS-8820716.     

On centroid branches of trees from certain families

We obtain various results involving the centroid branches of randomly chosen trees from simply generated families.     

Prevalence of voice disorders in African American and European American preschoolers

Several studies have reported prevalence rates for voice disorders in school-aged children. Less is known, however, about such prevalence in preschoolers, and whether racial, ethnic, or cultural diversity may influence it. The presence of voice disorders in a total of 2445 African-American and European-American preschool children, 1246 males and 1199 females, from 2 to 6 years of age is reported here. Presence of a voice disorder characterized by hoarseness was identified by a three-prong approach including teacher identification, investigator screening, and parent identification. Speech-language pathologists listened individually to each child's speech as they engaged each child in play-conversation activities. A voice disorder was identified on the basis of the judgment of two speech-language pathologists. Voice disorders characterized by hoarseness were identified in 95 children or 3.9% of the total sample by the investigators. Statistical analysis revealed no significant differences for age, gender, or race.     

Some asymptotic results useful in enumeration problems

Suppose one is given two related generating functionsa(x) = a _n x ⁿ andb(x) = b _n x ⁿ , often it is of interest to determine the limiting behaviour of the quantitiesa _n /b _n We survey some earlier results of this nature and give some new ones     

Neuronal activation by GPI-linked neuroligin-1 displayed in synthetic lipid bilayer membranes

We have characterized, in vitro, interactions between hippocampal neuronal cells and silica microbeads coated with synthetic, fluid, lipid bilayer membranes containing the glycosylphosphatidyl inositol (GPI)-linked extracellular domain of the postsynaptic membrane protein neuroligin-1. These bilayer-neuroligin-1 beads activated neuronal cells to form presynaptic nerve terminals at the point of contact in a manner similar to that observed for live PC12 cells, ectopically expressing the full length neuroligin-1. The synthetic membranes exhibited biological activity at neuroligin-1 densities of approximately 1 to 6 proteins/microm(2). Polyolycarbonate beads with neuroligin-1 covalently attached to the surface failed to activate neurons despite the fact that neuroligin-1 binding activity is preserved. This implies that a lipid membrane environment is likely to be essential for neuroligin-1 activity. This technique allows the study of isolated proteins in an environment that has physical properties resembling those of a cell surface; proteins can diffuse freely within the membrane, retain their in vivo orientations, and are in a nondenatured state. In addition, the synthetic membrane environment affords control over both lipid and protein composition. This technology is easily implemented and can be applied to a wide variety of cellular studies.     

Facile purification of rare cucurbiturils by affinity chromatography

A practical method for the separation and purification of cucurbituril (CB) hexamers was developed on the basis of affinity chromatography using aminopentylaminomethylated polystyrene beads. This recyclable resin, which can be used repeatedly, facilitates the general preparation of cucurbituril derivatives and compensates for the usually moderate yields and mixed products that characterize the acid-catalyzed synthesis of CB derivatives. This technique allows convenient, rapid isolation of rare substituted cucurbiturils, including hexacyclohexanocucurbit[6]uril and dodecamethylcucurbit[6]uril. [reaction: see text]