Hierarchical spherical model from a geometric point of view

A continuous version of the hierarchical spherical model at dimension d=4 is investigated. Two limit distributions of the block spin variable X(gamma), normalized with exponents gamma = d + 2 and gamma=d at and above the critical temperature, are established. These results are proven by solving certain evolution equations corresponding to the renormalization group (RG) transformation of the O(N) hierarchical spin model of block size L(d) in the limit L down arrow 1 and N ->infinity. Starting far away from the stationary Gaussian fixed point the trajectories of these dynamical system pass through two different regimes with distinguishable crossover behavior. An interpretation of this trajectories is given by the geometric theory of functions which describe precisely the motion of the Lee-Yang zeroes. The large-N limit of RG transformation with L(d) fixed equal to 2, at the criticality, has recently been investigated in both weak and strong (coupling) regimes by Watanabe (J. Stat. Phys. 115:1669-1713, 2004) . Although our analysis deals only with N = infinity case, it complements various aspects of that work.

Potassium Current in Mature Bovine Spermatozoa

Ion channels have been assigned a pivotal importance in various sperm functions and are therefore promising targets for contraceptive development. The lack of data on channel functionality and pharmacology has hampered this goal. This is a consequence of technical problems of applying electrophysiological techniques to spermatozoa due to their small size and form. By using a laminin coating to increase adherence of spermatozoa and nystatin in the patch pipette for pore formation, we have adapted the whole-cell recording technique to study currents in mature uncapacitated bovine spermatozoa. Employing these conditions, in the head region, patched spermatozoa could be transferred into the whole-cell configuration. For the first time we document an outward rectifying current in mature bovine spermatozoa was blocked by tetraethyl ammonium (TEA) chloride. The observation of a shift in the reversal potential as a response to changes in the extracellular concentration of K+ ions allowed us to identify this current as K+ selective. This result shows that K+ channels in the head region of mature uncapacitated bovine spermatozoa can be suitably investigated using the whole-cell recording patch-clamp technique.