Recurrence of Ancestral Lines and Offspring Trees in Time Stationary Branching Populations

For time stationary Galton- Watson-branching populations on a general type space, the structure of the “individually positive recurrent part” of the system is described: its building blocks consist of finitely many “clans” with positive recurrent trunks. Conditions are given when this nubsystem is void, and when it equals the full system. In addition, positive recurrence on the clan level is characterized. Whereas individual positive recurrence turns out to be a symmetric concept with respect to forward and backward time direction (i. e., with respect to anceatral lines and offspring trees), with individual null recurrence this symmetry can fail even in the absence of branching, i.e., for independently migrating particle systems (Example 13.1). For discrete type spaces a classification of types as to the various individual recurrence concepts (positive, null, forward and backward in time) is proposed and illustrated by a couple of results and examples. For finite type spaces conditiom on the branching dynamics and its mean matrix for the existence of nontrivial equilibria are given.     

Synthesis and Cellular Labeling of Caged Phosphatidylinositol Derivatives

Phosphatidylinositol (PI) is the biosynthetic precursor for seven phosphoinositides, important signaling lipids in cells. A membrane-permeant caged PI derivative featuring a photo-removable coumarinyl group masking the negative charge of the phosphate, as well as two enzymatically removable butyrate esters for increased lipophilicity and for preventing phosphate migration, were synthesized. Rapid cell entry and cellular labeling in fixed cells was demonstrated by a photo-cross-linkable diazirine followed by attachment of a fluorophore through click chemistry. Using this technique, we found that the multifunctional caged PI derivative resided predominantly at internal membranes but rapidly changed to the plasma membrane after uncaging. Accordingly, a preliminary proteomic analysis of the lipid–protein conjugates revealed that the two major PI transport proteins PITPα and β were prime targets of the photo-cross-linked PI derivative.     

In vivo mapping of functional domains and axonal connectivity in cat visual cortex using magnetic resonance imaging

Noninvasive cognitive neuroimaging studies based on functional magnetic resonance imaging (fMRI) are of ever-increasing importance for basic and clinical neurosciences. The explanatory power of fMRI could be greatly expanded, however, if the pattern of the neuronal circuitry underlying functional activation could be made visible in an equally noninvasive manner. In this study, blood oxygenation level-dependent (BOLD)-based fMRI and diffusion tensor imaging (DTI) were performed in the same cat visual cortex, and the foci of fMRI activation utilized as seeding points for 3D DTI fiber reconstruction algorithms, thus providing the map of the axonal circuitry underlying visual information processing. The methods developed in this study will lay the foundation for in vivo neuroanatomy and the ability for noninvasive longitudinal studies of brain development.     

On the Law of The Iterated Logarithm for Rapidly Increasing Subsequences

The usual law of the iterated logarithm states that the partial sums S_n of independent and identically distributed random variables can be normalized by the sequence a_n = √nlog log n, such that limsup_n→∞ S_n/a_n = √2 a.s. As has been pointed out by Gut (1986) the law fails if one considers the limsup along subsequences which increase faster than exponentially. In particular, for very rapidly increasing subsequences {n_k≥1} one has limsup_k→∞ S_nk/a_nk = 0 a.s. In these cases the normalizing constants a_nk have to be replaced by √nk log k to obtain a non-trivial limiting behaviour: limsup_k→∞ S_nk/ √nk log k = √2 a.s. We will present an intelligible argument for this structural change and apply it to related results.     

Polymer chain dynamics under nanoscopic confinements

It is shown that the confinement of polymer melts in nanopores leads to chain dynamics dramatically different from bulk behavior. This so-called corset effect occurs both above and below the critical molecular mass and induces the dynamic features predicted for reptation. A spinodal demixing technique was employed for the preparation of linear poly(ethylene oxide) (PEO) confined to nanoscopic strands that are in turn embedded in a quasi-solid and impenetrable methacrylate matrix. Both the molecular weight of the PEO and the mean diameter of the strands were varied to a certain degree. The chain dynamics of the PEO in the molten state was examined with the aid of field-gradient NMR diffusometry (time scale, 10(-2)-10(0) s) and field-cycling NMR relaxometry (time scale, 10(-9)-10(-4) s). The dominating mechanism for translational displacements probed in the nanoscopic strands by either technique is shown to be reptation. On the time scale of spin-lattice relaxation time measurements, the frequency dependence signature of reptation (i.e., T1 approximately nu(3/4)) showed up in all samples. A "tube" diameter of only 0.6 nm was concluded to be effective on this time scale even when the strand diameter was larger than the radius of gyration of the PEO random coils. This corset effect is traced back to the lack of the local fluctuation capacity of the free volume in nanoscopic confinements. The confinement dimension is estimated at which the crossover from confined to bulk chain dynamics is expected.